Find the missing length of the triangle (Side AC)

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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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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Mercury travels a distance of 153 461 500 kilometers on its orbit.

The statement indicates that Mercury has a circular orbit and indicates the central angle covered by translation. The distance traveled is found by definition of circular arc:

s = (2.65 rad) · (57 910 000 km)

s = 153 461 500 km

Please notice that the radius of translation is the distance from the Sun to Mercury.

Mercury travels a distance of 153 461 500 kilometers on its orbit.

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Answer:

See below

Step-by-step explanation:

y = -6x^2 + 24x-100

solve for 'x'

y + 100 =   -6x^2 + 24x   = -6(x^2-4x)    complete the square for x

(y+100) /(-6 ) =    (x-2)^2 -4                     add 4 to both sides

(y+100)/(-6) +4   = (x-2)^2                       sqrt both sides

sqrt [  ( y+100)/(-6) + 4  ]  + 2 = x           change  x and y

y = ± sqrt [ (x+100)/(-6) + 4 ] + 2            simplify (if needed)

y  = ± sqrt( -x/6 -12.666)  + 2

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)

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

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

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

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.

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.

The area of Entire roof is 12 feet².

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

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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Considering the given linear function, the inequality graphed is:

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

A linear function is modeled by:

y = mx + b

In which:

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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36 students does not watch regularly the programme.

Lets simplify the problem,

Total students = 48

Regular students 1//4*48

=> 12 students

Through Simple Subtraction method,

Irregular students = Total students - regular students

Irregular students = 48-12

=36

Hence 36 students does not watch regularly the programme.

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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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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 five-number summary are as follows:

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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The reason that completes the proof for step 6 is (a) Definition of median

From the graph, point R' to be the midpoint of points M' and O'

Also, points P' and Q' are the midpoints of lines M'N' and N'O', respectively

This means that the three points are the median of the sides of the triangle

The line drawn through the three medians meet at point S

Hence, the reason that completes the proof for step 6 is (a) Definition of median

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Answer: median

Step-by-step explanation:

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

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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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]

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

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)

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

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;

Similarly

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]

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

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

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;

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

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;

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

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Answer:

The angle measures are the same.

Step-by-step explanation:

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

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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Answer:

Graph number 2

Step-by-step explanation:

See attached image.

The simplified expression is the one in option B.

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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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)

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]

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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Answer:

Step-by-step explanation:

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

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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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.

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

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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