The function f(x) = 200(0.5)x/50 models the amount in pounds of a particular
radioactive material stored in a concrete vault, where x is the number of years since
the material was put into the vault. Find the amount of radioactive material in the
vault after 140 years. Round to the nearest whole number.

Answers

Answer 1

Answer:

29 years

Step-by-step explanation:

Given the function [tex]f(x)= 200(0.5)^{\frac{x}{50} }[/tex], where x stands for the number of years since the material was put into the vault, we can plug 140 into x to find the amount leftover.Another way of doing this is to change the function to [tex]f(x)=200(0.5^{\frac{1}{50} })^{x}[/tex] which are equivalent functions, and then plug 140 into x. This function is helpful if you also needed to find the rate. I'll use the 1st function because the question doesn't ask for the rate

[tex]f(x)= 200(0.5)^\frac{140}{50}}[/tex]

From here I'll just use a calculator & get 28.7, or 29 years.


Related Questions

Find the missing length of the triangle (Side AC)

Answers

Answer: 17.3 cm

Step-by-step explanation:

[tex]\tan 68^{\circ}=\frac{AC}{7}\\\\AC=7\tan 68^{\circ}\\\\AC \approx 17.3[/tex]

6x^2-19xy-7y^2 HELP ME PLS??

Answers

Answer:

(3x+y) (2x-7y)

Step-by-step explanation:

first write -19xy as a difference and you get 6x^2+2xy-21xy-7y^2

and then take the factor 2x from the expression that is 2x(3x+y) and do the same with the -7 that is = -7(3x+y). So this is you answer= (3x+y)(2x-7)

A grocery store sells a bad of 4 oranges for $1.04. how much would it cost for 11 oranges?

Answers

If a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.

Given that a grocery store sells a bag of 4 oranges for $1.04 means revenue is $1.04 with no profits.

We have to find the cost of 11 oranges. We have assumed that there are no profits as we are require to find cost.  But there is huge difference between cost and profits.

We know that average cost is total cost divided by number of items.

Cost of 4 oranges=$1.04

cost of 1 orange=1.04/4

=$0.26 per orange

Cost of 11 oranges=0.26*11

=$2,86.

Hence if a grocery store sells a bag of 4 oranges for $1.04 then it will cost $2.86 for 11 oranges.

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write the equation of a line this is parallel to y=0.5x-4 and that passes through the point (9,-6).

Answers

Answer:

[tex]y=0.5x-10.5[/tex]

Step-by-step explanation:

Parallel lines have the same slope, so the slope of the line we need to find is 0.5.

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+6=0.5(x-9) \\ \\ y+6=0.5x-4.5 \\ \\ y=0.5x-10.5[/tex]

Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn? limit of (one-fourth) superscript n baseline as n approaches infinity limit of (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (one-fourth) superscript n baseline as n approaches infinity

Answers

The sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)

How to evaluate the sum of the series?

The complete question is added as an attachment

The given series is a geometric series. So, we first calculate the common ratio (r) using:

r = T2/T1

From the series, we have:

T1 = 1/4 and T2 = 1/16

Substitute the known values in the above equation

r = (1/16)/(1/4)

So, the equation becomes

T = 1/16 / 1/4

Rewrite as product

T = 1/16 * 4

Evaluate the product

r = 1/4

The formula to calculate the sum of a geometric series of is:

Sn = a(1 - r^n)/(1 - r)

Where

a = 1/4 -- the first term

r = 1/4 --- the common ratio

Substitute the known values in the above equation

Sn = 1/4 * (1 - (1/4)^n)/(1 - 1/4)

Simplify the denominator

Sn = 1/4 * (1 - (1/4)^n)/(3/4)

Divide 1/4 by 3/4

Sn = 1/3 * (1 - (1/4)^n)

Take the limit to infinity of the series

Sn = lim n⇒∝ 1/3(1 - (1/4)^n)

We can conclude that, the sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)

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Answer:

Step-by-step explanation:

B

A triangle on a coordinate plane has three vertices A(2 , 3), B(5, 4), and C(3, 6). Use this description to do the following transformations (if needed, draw this triangle on a sheet of paper):

a. Dilation 1: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the origin? How did you determine these points?
b. Dilation 2: What would be the new coordinates if this triangle were dilated to a scale factor of 2 with the center of the dilation at the point (6, 8)? How did you determine these points?
c. What series of transformations would carry dilation 1 onto dilation 2? Compare Dilation 1 to Dilation 2. Explain what conclusions you can draw about the scale factor, difference in area, and center of dilation.
d. What is the proportion of the side lengths from Dilation 1 to Dilation 2? What is the proportion of their angle measures? Explain your answer.

Answers

The dilation by a scale factor of 2 of the points A(2, 3), B(5, 4), C(3, 6) gives;

a. A'(4, 6), B'(10, 8), C'(6, 12)

b. A'(-2, -2), B'(4, 0), C'(0, 4)

c. The transformation that would carry dilation 1 onto dilation 2 is T(-6, -8)

The area of dilation 1 and 2 are the sameThe center of dilation does not change the area

d. The proportion of the side length of Dilation 1 and Dilation 2 is 1:1

The angle measures are the same

How can the new coordinates be found?

The general formula for finding the coordinates of the image of a point following a dilation is presented as follows;

[tex]D _{(a , \: b)k}(x, \: y) = (a + k \times (x - a) , \: b+ k \times (y - b))[/tex]

Where;

(a, b) = The center of dilation

k = The scale factor of dilation

(x, y) = The coordinate of the pre-image

The given points are;

A(2, 3), B(5, 4), C(3, 6)

a. The scale factor of dilation = 2

The center of dilation = The origin (0, 0)

Therefore;

[tex]D _{(0 , \: 0)2}(2, \: 3) = (0 + 2 \times (2 - 0) , \: 0+ 2 \times (3 - 0)) = (4, \:6)[/tex]

Therefore dilation about the origin, with a scale factor of 2 gives;

A(2, 3) → A'(4, 6)

Similarly

B(5, 4) → B'(10, 8)

C(3, 6) → C'(6, 12)

b. With the center of dilation at (6, 8), we have;

[tex]D _{(6 , \: 8)2}(2, \: 3) = (6 + 2 \times (2 - 6) , \: 8+ 2 \times (3 - 8)) = (-2, \:-2)[/tex]

A(2, 3) → A'(-2, -2)

[tex]D _{(6 , \: 8)2}(5, \: 4) = (6 + 2 \times (5 - 6) , \: 8+ 2 \times (4 - 8)) = (4, \:0)[/tex]

B(5, 4) → B'(4, 0)

[tex]D _{(6 , \: 8)2}(3, \: 6) = \mathbf{(6 + 2 \times (3 - 6) , \: 8+ 2 \times (6 - 8))} = (0, \:4)[/tex]

C(3, 6) → C'(0, 4)

c. The difference between the coordinates of the points on dilation 1 and 2 is a shift left 6 places and a shift downwards 8 places

Using notation, we have;

Dilation 1 T(-6, -8) → Dilation 2

The area of the images of dilation 1 and 2 are equal given that the scale factor is the same.

The location of the center of dilation does not change the area of the image

d. From the above calculation, given that the difference between pre-image point and the center is multiplied by the scale factor followed by the addition of the x and y-values, the lengths of the sides of dilation 1 and 2 are the same, such that we have;

The proportion of the side lengths is 1

Given that the side lengths are the same, by AAA congruency postulate, we have;

The angle measures are the same.

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Answer:

The angle measures are the same.

Step-by-step explanation:

Here are the scores of 14 students on a geography test. 58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87 Notice that the scores are ordered from least to greatest. Give the five-number summary and the interquartile range for the data set.
Five-number summary
Minimum:

Lower quartile:
Median:
Upper quartile:
Maximum:
Interquartile range:

Answers

The five-number summary are as follows:

Minimum = 58Lower quartile(Q₁) = 67Median = 79Upper quartile(Q₃) = 82Maximum = 87Interquartile range = 15

How to solve for five-number summary?

The five-number summary is a set descriptive statistics which consist of the minimum, maximum, median, upper quartile, and lower quartile of a data distribution.

Therefore,

Given:

58, 60, 65, 67, 68, 72, 79, 79, 80, 81, 82, 86, 86, 87

Therefore,

Minimum = 58

Lower quartile(Q₁) = 67

Median = 79 + 79 / 2 = 79

Upper quartile(Q₃) = 82

Maximum = 87

Interquartile range = Q₃ - Q₁ = 82 - 67 = 15

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Suppose you are saving your money to pay for a vacation for your family. so far, you have saved. you plan on saving more each month so you can pay for the vacation at the end of the year. assume that you save more each month than the previous month.

part a: write a formula that would show the amount you will have saved after year.

part b: if the vacation costs a total of , will you be able to pay for it after year?

part c: explain why or why not. show your work to support your answer.

Answers

440 repeat 11 more times.

400+(400*.1)=440 repeat 11 more times. Remember to use a new value each time.

Vacations can get expensive fast. The average cost per person for a week-long vacation is about $1,200 annually. So, if you've got a family of five, you'll need to sock away at least $6,000 for transportation, hotels, meals, and amusement parks.

Financial experts suggest that the average family vacation costs between 5-10% of your total income. If your family makes $40,000 per year then experts say your yearly family vacation budget should average between $2,000-$4000.

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Out of 500 people in a room, 200 of them are wearing red shirts. Of the people wearing red shirts, 15% are wearing red pants. What percentage of the people in the room are wearing both red shirts and red pants?

Answers

Number of people wearing red pants
= 200/100 x 15
= 30

Those who wear both red shirts and red pants is 30.

Therefore the percentage is
= 30/500 x 100%
= 6%

The table below lists the tallest waterfalls in the world, in feet.
Name/Location Height (ft.) Mutarazi - Zimbabwe 24.99 x 102 Gocta Cataracts - Peru 2.532 x 103 Utigord - Norway 2,625 x 100 Angel - Venezuela .3212 x 104 Espelands - Norway 2.307 x 103 Yosemite - California (USA) 2,425 Monge - Norway 25.4 x 102 Tugela - South Africa 3.11 x 103 **Heights are approximations** [Part 1] List the waterfalls from tallest to shortest.. Show all of your work and/or explain your reasoning. [Part 2] What is the difference between the tallest and shortest heights? Show your work.

Answers

The difference between the tallest and shortest heights is 0.787 × 10

Statistics

Mutarazi - Zimbabwe 24.99 x 10²Gocta Cataracts - Peru 2.532 x 10³Utigord - Norway 2,625 x 10^0Angel - Venezuela .3212 x 10⁴Espelands - Norway 2.307 x 10⁴Yosemite - California (USA) 2,425Monge - Norway 25.4 x 10²ugela - South Africa 3.11 x 10³

From tallest to shortest:

Angel - Venezuela 3.212 x 10⁴Espelands - Norway 2.307 x 10⁴ugela - South Africa 3.11 x 10³Utigord - Norway 2,625 x 10^0Monge - Norway 25.4 x 10²Gocta Cataracts - Peru 2.532 x 10³Mutarazi - Zimbabwe 24.99 x 10²Yosemite - California (USA) 2,425

Difference between tallest and shortest heights =

3.212 x 10⁴ - 2,425

= 3.212 x 10⁴ - 2.425 × 10³

= (3.212 - 2.425) × 10^4 - 3

= 0.787 × 10

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which statemennt is false?​

Answers

Answer:

B. Every integer is also an irrational number.

Given: mAngleTRV = 60°
mAngleTRS = (4x)°

Prove: x = 30

3 lines are shown. A line with points T, R, W intersects with a line with points V, R, S at point R. A line extends from point R to point Z between angle V R W. Angle V R T is 60 degrees and angle T, R, S is (4 x) degrees.

What is the missing reason in step 3?

A 2-column table with 6 rows is shown. Column 1 is labeled Statements with entries measure of angle T R V = 60 degrees and measure of angle T R X = (4 x) degrees, angle T R S and angle T R V are a linear pair, measure of angle T R S + measure of angle T R V = 180, 60 + 4 x + 180, 4 x =120, x = 30. Column 2 is labeled Reasons with entries given, definition of a linear pair, question mark, substitution property of equality, subtraction property of equality, division property of equality.

substitution property of equality
angle addition postulate
subtraction property of equality
addition property of equality
Mark this and return

Answers

https://brainly.com/question/68367When two lines intersect at a point, angles are formed. Some of these angles formed are vertically opposite and thus are equal.

Therefore, the required proof and answer to the question are stated below:

a) m< TRV = 60° (given)

   m<TRS = 4x° (given)

Thus, it can be concluded from the diagram that:

<TRV ≅ m<BRW  (vertically opposite angle property)

Also,

m<TRS ≅ m<VRW (vertically opposite angle property)

But,

m<VRW = m<VRZ + m<ZRW

Thus,

m<TRV ≅ m<BRW = 60°

m<TRV + m<BRW + m<TRS + m<VRW = [tex]360^{o}[/tex]

60° + 60° + m<TRS + m<VRW = [tex]360^{o}[/tex]

m<TRS + m<VRW =   [tex]360^{o}[/tex] - [tex]120^{o}[/tex]

                             = [tex]240^{o}[/tex]

2m<TRS = [tex]240^{o}[/tex] (since m<TRB = m<VRW )

m<TRS = 120

4x = 120

x = [tex]\frac{120}{4}[/tex]

  = [tex]30^{o}[/tex]

Thus, x = [tex]30^{o}[/tex]

b) The missing reason in step 3 is the angle addition postulate.

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The KM values for the reaction of chymotrypsin with 2 substrates are given below. Which substrate is likely to give a higher value for Vmax

Answers

N-acetyltyrosine ethyl ester may likely have a higher Vmax.

How are the Km and Vmax of an enzyme and substrate related?

Km is inversely proportional enzyme affinity for substrate. The lower the Km, the higher the enzyme affinity for substrate and vice versa.

Vmax is the maximum velocity of the reaction when the enzyme is fully saturated with substrate.

Based on the Km values, chymotrypsin has higher affinity for N-acetyltyrosine ethyl ester, thus, N-acetyltyrosine ethyl ester may likely have a higher Vmax.

In conclusion, the Vmax is the maximum velocity of an enzyme-catalyzed reaction.

Note that the complete question is given below:

The Km for the reaction of chymotrypsin with N-acetylvaline ethyl ester is 8.8 x 10-2 M, and the Km for the reaction of chymotrypsin with N-acetyltyrosine ethyl ester is 6.6 x 10-4 M.

Which of the following substrates is likely to give a higher value for Vmax?

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1. Find the Principal when S.l. = 100 Rate = 5% per annum Time = 2 years.​

Answers

The principal is 1000

SI = PRT/100

Simple interest = 100

Rate = 5%

Time = 2 years.

SI = PRT/100

100 = (P × 5 × 2)/100

10000 = 10P

P = 10000/10

P = 1000

1.rani was selling flowers. each day she made 7 bouquets by arranging 8 roses and 6 marigolds in each bouquet. each bouquet was sold for rs.85. a) find the number of marigolds used in a day. b) find the total number of flowers used by using suitable property of whole numbers. c) if she sold 42 bouquets in a whole week, find the amount she earned. 2. by suitable rearrangement, find the value of a) 819 + 364 + 181 + 436 b) 20 x 348 x 50 3. using suitable property find the value of 492 x 13 + 492 x 37 4. a) name the property 86 + 65 = 65 + 83 b) the multiplicative identity of whole numbers is ______ 5. find the next two numbers in the pattern 1,1,2, 3,5,8, ______, ________

Answers

1.(a) The number of marigolds used in a day is 42.

 (b) The total number of flowers used by using suitable property of whole numbers is 98.

 (c) She earned Rs. 3570

2.(a) The value of [tex]819 + 364 + 181 + 436[/tex] is 1800.

 (b) The value of [tex]20 \times 348 \times 50[/tex] is 348000.

3. The value of [tex]492 \times 13 + 492 \times 37[/tex] is 24600.

4.(a) Name the property 86 + 65 = 65 + 86 is commutative property.

 (b) The multiplicative identity of whole numbers is 1.

5. The next two numbers in the pattern 1,1,2, 3,5,8 are 13 and 21.

1. (a) The number of marigolds used in a day is 42.

Rani made 7 bouquets on each day by arranging 8 roses and 6 marigolds in each bouquet. So number of marigolds used in a day is 7×6 = 42.

  (b) The total number of flowers used by using suitable property of whole numbers is 98 flowers used by using distributive property.

What is distributive property of whole numbers?

The distributive property of multiplication states that when multiplying a number by the sum/difference of 2 numbers, the final value is equal to the sum/difference of each addend multiplied by the third number.

Distributive property = a×(b+c) = a×b+a×c

Total number of flowers = 7×(8+6) = 7×14 = 98.

(c) If she sold 42 bouquets in a whole week, find the amount she earned is  rs.3570.

Each bouquet was sold for Rs.85. Then she earned a whole week off = 42×85 = rs.3570.

2. (a)  By suitable rearrangement, the value of 819 + 364 + 181 + 436 is 1800.

Rearrangement of the given numbers = (819+181)+(364+436)

                                                               = 1000+800

                                                               = 1800    

   (b)  By suitable rearrangement, the value of 20 x 348 x 50 is 348000.

Rearrangement of the given numbers = 348×(50×20)

                                                               = 348×1000

                                                               = 348000  

3.  Using suitable property find the value of 492 x 13 + 492 x 37 is 24600 by using distributive property.

By using distributive property = 492 x 13 + 492 x 37

                                                   = 492×(13+37)

                                                  = 492×50

                                                  = 24600

4. (a) Name the property 86 + 65 = 65 + 86 is commutative property.

What is commutative property?

This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer.

By using commutative property,  a+b = b+a

   86 + 65 = 65 + 86

          151 = 151                            

   (b)  The multiplicative identity of whole numbers is 1.

Multiplying a whole number by 1 equals that identical number, the whole number 1 is called the multiplicative identity.

5.  The next two numbers in the pattern 1,1,2, 3,5,8,?,? are 13 and 21.

Just add the no before the given no then you will get the pattern. example first no=1 and no before it is 0

1+0=1

1+1=2

2+1=3

3+2=5

5+3=8

8+5=13

Hence, The next two numbers for the given series are 13 and 21.

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help me w this pls thanks

Answers

Answer:

Perimeter: 4+[tex]\pi \\[/tex] mm

Area: [tex]\pi[/tex] mm^2

Step-by-step explanation:

Perimeter:

90/360 * 4[tex]\pi \\[/tex] +2 + 2 = 4+ [tex]\pi \\[/tex]

Area:

90/360 * 4[tex]\pi[/tex] = [tex]\pi[/tex]

Answer: 7.14 mm and 3.14 mm²

Step-by-step explanation:

The perimeter of a figure is the total length on the outside of the figure. A regular circle has a perimeter of [tex]2\pi r[/tex], where r is the radius and [tex]\pi[/tex] is an irrational constant, approximately 3.14.

Due to the right angle, we know that this is a quarter circle, as it is a quarter of 360°, or a full circle. Hence, the curved portion of the quarter circle is [tex]\frac{1}{4}* 2\pi r[/tex] or [tex]\frac{1}{2} \pi r[/tex]. The radius is 2 mm, so this value is

[tex]\frac{1}{2} \pi*2=\pi[/tex]

However, this isn't the total perimeter, as there are straight edges in the figure too. Both edges are radii of the whole circle, so both would be 2mm. Their total is

[tex]2+2=4[/tex]

By adding [tex]\pi[/tex] to 4 we get [tex]\pi +4[/tex] or 7.14 mm.

The  area is the total space enclosed by a figure. The total area of a whole circle is [tex]\pi r^2[/tex], where r is still the radius. Since this is a quarter circle, it would take up a quarter of the area, or [tex]\frac{1}{4} \pi r^2[/tex]. We can plug in 2 for r and solve to get the area.

[tex]\frac{1}{4}\pi*2^2\\\frac{1}{4}\pi*4\\\pi[/tex]

Hence, the area is [tex]\pi[/tex], or around 3.14 mm².

visualize "4.298" on the number line

Answers

Answer:

Step-by-step explanation:

The visualization of "4.298" on the number line is attached below.

How does the dot plot work?

Suppose we're measuring something whose values are numeric.

For each value of that thing we observe, we plot a dot above that value in the number line.

Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

We know that 4.298 is greater than 4 but less than 5.

The visualization of "4.298" on the number line is attached below.

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If a and b are rational numbers and a+b√3=1/2-√3,find a:b=?​

Answers

The value of the ratio a:b is 2:1

What is a surd?

Surds are values of a square roots that cannot be simplified as whole numbers or integers. They are usually called irrational numbers.

Example of some surds are the square root of prime numbers.

Analysis:

a + b[tex]\sqrt{3}[/tex] = [tex]\frac{1}{2 - \sqrt{3} }[/tex]

Rationalizing the right hand side by the conjugate surd which is 2 + [tex]\sqrt{3}[/tex]

[tex]\frac{1}{2 - \sqrt{3} }[/tex]  x [tex]\frac{2 + \sqrt{3} }{2 +\sqrt{3} }[/tex] = [tex]\frac{2 + \sqrt{3} }{4 -2\sqrt{3} +2\sqrt{3} -3}[/tex] = [tex]\frac{2 + \sqrt{3} }{1}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Equating,

a + b[tex]\sqrt{3}[/tex] = 2 + [tex]\sqrt{3}[/tex]

Comparing the variables,

a = 2,   b[tex]\sqrt{3}[/tex] = [tex]\sqrt{3}[/tex], b = 1

The ratio, a: b = 2:1

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Which bag has more fruit? Use the ratios to justify your answer.

Answers

The bag that has more fruits is the second bag, because the ratio is greater.

Which bag has more fruits?

Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).

Number of fruits in the first bag : (3/8) x 60 = 22.50

Number of fruits in the second bag :(7/17) x 60 = 24.71

Here is the complete question:

Tamika has two bags of trail mix. Each has a combination of 60 pieces of fruit and nuts. Ratio of fruit to nuts in the first bag:3 5 Ratio of fruit to nuts in the second bag:7 10 Which bag has more fruit? Use the ratios to justify your answer. The first bag, because the ratio is greater. The first bag, because the ratio is smaller. The second bag, because the ratio is greater. The second bag, because the ratio is smaller.

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5/8 of the students in siena's class have brown eyes. 2/3 of the students with brown eyes are girl. what fraction of the students in siena's class are girls with brown eyes? *

Answers

The fraction of the students in Siena's class are girls with brown eyes is 5/12.

Let the fraction of students in Siena's class with brown eyes be a=5/8.

And the fraction of students in Siena's class with brown eyes are girls be b=2/3.

Then, the fraction of students in Siena's class are girls with brown eyes be z=a×b

Therefore, by substituting the fraction values, we get

z=(5/8)×(2/3)

z=5/12.

Hence, 5/8 of the students in Siena's class have brown eyes. 2/3 of the students with brown eyes are girl. Then, the fraction of students in Siena's class are girls with brown eyes is 5/12.

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id love some help!!!

Answers

Answer : 12.56 inches²
Explanation :
Diameter is twice the radius.
Radius = 4 ÷ 2 = 2 inches
Area = 3.14r² = 3.14 × 2² = 12.56 inches²

Answer:

Circle:

circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

[tex] \sf{formula \: to \: find \: the \: area \: is}[/tex]

[tex] \large{ \boxed{ \tt{A = {\pi \times r}^{2} }}}[/tex]

[tex] \sf{formula \: to \: find \: perimeter \: of \: circle \: is}[/tex]

[tex] \large {\boxed{ \tt{p = 2 \times \pi \times r}}}[/tex]

Continue to Question.

If the radius is 2 inches and

Use 3,14 for π So:

[tex] \tt{ {A = \pi \times {r}^{2} }}[/tex]

[tex] \tt{A = (3.14 \times 2 \times 2)} [/tex]

[tex] \red{ \boxed{ \bold{A = 12.56 {inches}^{2} }}}[/tex]

So, The Area of circle is 12.56inches²

If 4 is the solution set of the equation x² -4 = 0 and B is
the solution set of the equation x²-3x+2=0, how many
elements are in the union of the two sets?
A. 1
C. 3
B. 2
D. 4

Answers

Answer:

3 elements

Step-by-step explanation:

Let A = solution set of x²-4

B = solution set of x²-3x+2

First, find the solution of each sets:

[tex]\displaystyle{x^2-4=0}\\\\\displaystyle{(x+2)(x-2)=0}\\\\\displaystyle{x=2,-2}[/tex]

Set B:

[tex]\displaystyle{x^2-3x+2=0}\\\\\displaystyle{(x-2)(x-1)=0}\\\\\displaystyle{x=1,2}[/tex]

Now we can write new set as:

A = {2, -2}

B = {1, 2}

The union of A and B means combine both sets together:

A ∪ B = {2, -2, 1, 2}

However, in a set, we do not write duplicate elements, so the union set will be:

A ∪ B = {2, -2, 1}

Hence, there are 3 elements in A ∪ B.

given that 4x-y=5 4y-z=7 and 4z-x=18 what is the value of x+y+z

Answers

Using simultaneous equations,
x=2, y=3, z=5.

Therefore x+y+z
=2+3+5
=10

Answer:

x + y +z= 10

Step-by-step explanation:

4x - y = 5  ---------(I)

 4y - z = 7 ---------(II)

4z - x = 18 ---------(III)

Add all the three equations,

  4x - y + 4y - z + 4z - x = 5 + 7 + 18

  4x - x  -y + 4y -z + 4z  = 30

              3x + 3y + 3z = 30

Divide the entire equation by 3

               [tex]\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}[/tex]

                 x + y + z = 10

Select the correct answer. A linear function on a coordinate plane. A line passing through (1, 4), (minus 2, minus 2), intersects the y- axis at 2 units and intersects the x-axis at (minus 1, 0) to form shaded portions on the left side of the line. Which of the following inequalities is graphed on the coordinate plane? A. y ≤ 2 ⁢ x + 2 B. y ≥ 2 ⁢ x + 2 C. y < 2 ⁢ x + 2 D.

Answers

Considering the given linear function, the inequality graphed is:

B. [tex]y \geq 2x + 2[/tex].

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line intersects the y-axis at 2 units, hence the y-intercept is b = 2. The function also passes through (1,4), hence the slope is:

m = (4 - 2)/(2 - 1) = 2.

Thus the equation of the line is:

y = 2x + 2.

The left-side of the line is the values above the line, hence the inequality is:

B. [tex]y \geq 2x + 2[/tex].

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Simplify the expression using trigonometric identities:

Answers

The simplified expression is the one in option B.

How to simplify the expression?

Remember that:

[tex]sec(x) = 1/cos(x)\\\\cos(x) = cos(-x)[/tex]

With these two, we can rewrite the numerator as:

[tex]sec(x)*sin(-x) + tan(-x)\\\\\frac{1}{cos(x)}*sin(-x) + tan(x)\\\\\frac{1}{cos(-x)}*sin(-x) + tan(-x)\\\\2*tan(-x)[/tex]

Replacing that in the given expression, we have:

[tex]\frac{2*tan(-x)}{1 + sec(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}[/tex]

Now, if we multiply and divide by cos(-x), we get:

[tex]\frac{2*tan(-x)}{1 + 1/cos(-x)} = \frac{2*tan(-x)}{1 + 1/cos(-x)}*\frac{cos(-x)}{cos(-x)} \\\\= \frac{2*sin(-x)}{1 + cos(-x)}[/tex]

Now remember that:

[tex]cos(x) = cos(-x)\\sin(-x) = -sin(x)[/tex]

With these two properties:

[tex]\frac{2*sin(-x)}{1 + cos(-x)} = \frac{-2*sin(x)}{1 + cos(x)}[/tex]

Then the correct option is B.

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Which function is negative for the interval [-1, 1]?
ty
3
2
-3-2-11
-3
ty
O
Intro
123
x
3
2
1
-3-2-1₁
-3
O
x
23
2,
-3-2-1
2 of 11
O
x
123
321
-3-2-11
-2
MAR
-3
ty
x
23
Done
O

Answers

Answer:

Graph number 2

Step-by-step explanation:

See attached image.

Becca's car engine has a capacity of 3.6 quarts and
contains 1.2 quarts of engine oil. One bottle of engine oil is
0.5 quart. Approximately how many bottles of engine oil
does Becca need to completely fill her car engine?

Answers

Becca needs approximately 5 bottles of engine oil to completely fill her car engine.

How to determine the number of bottles of engine oil?

Since Becca's car engine has a capacity of 3.6 quarts and contains 1.2 quarts of engine oil, the remaining space left in her car engine is given by:

Space = 3.6 - 1.2

Space = 2.4 quarts.

By applying direct proportion, we have:

1 bottle = 0.5 quart.

x bottles = 2.4 quarts.

Cross-multiplying, we have:

0.5x = 2.4

x = 2.4/0.5

x = 4.8 5 bottles.

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(pls help me with this)

4. The points C and D are (4, 5) and (p, q) respectively,

a) Write down, in terms of p and q, the coordinates of the midpoint of CD.

b) Given that the midpoint of CD is (7, 1), find the coordinates of D.​

Answers

A. The coordinates of the midpoint of CD in terms of p and q is [(4 + p) / 2 , (5 + q) / 2]

B. The coordinates of D, Given that the midpoint of CD is (7, 1) is (10 , -3)

A. How to determine the mid pointCoordinate of C = (4, 5)Coordinate of D = (p, q)Mid point =?

Mid point = (X , Y)

X = (x₁ + x₂) / 2

X = (4 + p) / 2

Y = (y₁ + y₂) / 2

Y = (5 + q) / 2

Thus,

Mid point = (X , Y)

Mid point = [(4 + p) / 2 , (5 + q) / 2]

B. How to determine the coordinates of DMid point = (7, 1)Coordinates of D =?

Mid point = (7, 1) = (X , Y)

X = (4 + p) / 2

7 = (4 + p) / 2

Cross multiply

7 × 2 = 4 + p

14 = 4 + p

Collect like terms

p = 14 - 4

p = 10

Y = (5 + q) / 2

1 = (5 + q) / 2

Cross multiply

1 × 2 = 5 + q

2 = 5 + q

Collect like terms

q = 2 - 5

q = -3

Coordinates of D = (p, q)

Coordinates of D = (10 , -3)

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How much does a $5.40 lunch cost if it is discounted by 10%

Answers

Answer:

$4.86

Step-by-step explanation:

Original price: $5.40

Discount: 10%

Discount amount:

10% of $5.40 = 0.1 × $5.40 = $0.54

Discounted price:

$5.40 - $0.54 = $4.86

Answer:

$4.86

Step-by-step explanation:

There are two approaches to this problem.

1:

You can multiply the original value by 10% and subtract it from the original value. In this case, $5.40-(5.40×10%). This becomes $5.40-$0.54. This is $4.86.

2:

You can simply multiply the original value by 90%. In this case, $5.40×90%. This also becomes $4.86.

Your dad says you can have a new puppy if you build the dog house. Before building, you need to determine the dimensions. Choose the dimensions of the base, the length, and the width of the dog house. Choose dimensions that you think are reasonable for whatever type of puppy you would get. Once you plan the base and walls, you need to decide on the height of the roof (represented by the dotted line in the image below). The roof is a triangle with two sides that are the same length.
Find the height of the roof using the dimensions you chose. You are hoping to put shingles on the roof and need to know what the square footage of the roof will be. Use the dimensions to calculate the area of the roof.

Hint: Remember to find the area of the entire roof.

Answers

Answer is 12 sq feet
Step by step
Roof is 36” x 24” which is 3’ x 2’
So 3 x 2 = 6 multiplied by 2 sides of roof
Total is 12 sq feet
————-
I made the roof peak with a 3” overhang over the entrance
I made the roof overhang the sides with 4”
—————-
So to find the hypotenuse (diagonal of the roof) I used the Pythagorean theorem.
a^2 + b^2 = c ^2
15^2 + 13^2 = c^2
394 = c^2
Take square root of both sides
C= 19.8 rounded to 20
I then added 4” overhang to each side for total diagonal of 24”

The area of Entire roof is 12 feet².

What is Pythagorean theorem?

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)

Given:

As, the roof peak with a 3 and the roof overhang the sides is 4.

Now, Using Pythagorean theorem.

a² + b² = c ²

15² + 13² = c²

c² = 225+ 169

c = 19.8 (or 20)

So, the length of diagonal is 24.

Roof Dimension 36 x 24 or (

Area of Roof = 3 x 2

                      = 6 unit²

and, area of the entire roof = 2 x6 = 12 ft²

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