Write the equation of a parabola with the focus at (3, 0) and the directrix at x = –3.

x^2 = –3y
y^2 = –3x
x^2 = 12y
y^2 = 12x

The range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

In this question, we have been given a function f(x) = 4x + 5

We need to find the range of given function for input {-2, -1, 0, 1 , 2}

We know that the range of  a function is the set of all output values for given input.

for x = -2,

f(-2) = 4(-2) + 5

f(-2) = -3

for x = -1,

f(-1) = 4(-1) + 5

f(-1) = 1

for x = 0,

f(0) = 4(0) + 5

f(0) = 5

for x = 1,

f(1) = 4(1) + 5

f(1) = 9

for x = 2,

f(2) = 4(2) + 5

f(2) = 13

Therefore, the range of function f(x) = 4x + 5 for given input values is {-3, 1, 5, 9, 13}

The correct answer is an option (C)

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The ordered pairs that are solutions to the linear equation x + 2y = 4 are given as follows:

The linear function in this problem is defined as follows:

x + 2y = 4.

To complete the ordered pairs, we take the given coordinate and then solve for the missing coordinate .

For the first ordered pair, the given coordinate is of x = -3, hence we have to solve for y when x = -3, thus:

-3 + 2y = 4.

2y = 7.

y = 7/2

y = 3.5.

Hence the ordered pair is:

(-3, 3.5).

For the second ordered pair, the given coordinate is of y = -7, hence we have to solve for x when y = -7, thus:

x + 2y = 4.

x - 14 = 4

x = 18.

Hence the ordered pair is:

(18, -7).

The ordered pairs that we have to complete are given as follows:

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The rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

The surface area of a sphere with radius r is given by4π[tex]r^{2}[/tex]

Given;

S = surface area at time t,  and r = radius at time t

radius of a spherical ball is increasing at a rate of 2 cm/min

radius: 6cm

Area of a sphere is A = 4π[tex]r^{2}[/tex]

Step 1: Differentiate area of a spherical ball

A = 4π[tex]r^{2}[/tex]

[tex]\frac{dA}{dt}[/tex] =[tex]\frac{d}{dt}[/tex](4π[tex]r^{2}[/tex])

=4π [tex]\frac{d}{dt}[/tex]([tex]r^{2}[/tex])

=4π2r [tex]\frac{dr}{dt}[/tex]

[tex]\frac{dA}{dt}[/tex] = 8πr

since we have that dr/dt = 2 cm/min. Thus, the radius of the ball is 6cm, we have;

[tex]\frac{dA}{dt}[/tex]= 8π(6)(2) =96π

So, the rate at which the surface area is changing when r = 6cm is 96[tex]cm^{2}[/tex]/min.

Note that measuring area unit is cm2/min

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The correct option regarding the area of the figure is given as follows:

14+16.25π units².

The figure, given with no scale at the end of the answer, is composed by:

The sides of the right-triangle are given as follows:

The area of a right triangle is given by half the multiplication of the sides, hence:

At = 0.5 x 7 x 4 = 14 units.

The radius of the semicircle is half the hypotenuse of the right triangle, hence, applying the Pythagorean Theorem:

h² = 7² + 4²

h = sqrt(7² + 4²)

r = 0.5sqrt(7² + 4²)

r = 4.03 inches.

The area of a semicircle of radius r is:

As = πr².

Hence:

As = π(4.03)² = 16.25 π.

The total area is obtained as the sum of the areas of each separate part, hence:

A = At + As = 14+16.25π units².

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Answer:

Step-by-step explanation:

14+8.125

C

By using percentage, it can be calculated that

1) Percentage increase in area = 25 %

2) Percentage increase in area = 60 %

3) Percentage decrease in area = 25 %

4) Percentage decrease in area = 40 %

What is percentage?

Sometimes there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100

1) Original area = 12 sq. yard

   New area = 15 sq. yard

   Increase in area = 15 - 12 = 3 sq. yard

   Percentage increase = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 15 sq. yard

   New area = 24 sq. yard

   Increase in area = 24 - 15 = 9 sq. yard

   Percentage increase = [tex]\frac{9}{15}\times 100 \\[/tex]

                                       = 60 %

1) Original area = 12 sq. yard

   New area = 9 sq. yard

   Increase in area = 12 - 9 = 3 sq. yard

  Percentage decrease = [tex]\frac{3}{12}\times 100 \\[/tex]

                                       = 25 %

1) Original area = 10 sq. yard

   New area = 6 sq. yard

   Increase in area = 10 - 6 = 4 sq. yard

   Percentage increase = [tex]\frac{4}{10}\times 100 \\[/tex]

                                       = 40 %

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Using the z-distribution to test the hypothesis, it is found that:

a) The conclusion is that there is not enough evidence to conclude that the percentage has changed from 2016.

b) A Type II error would mean finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

At the null hypothesis, it is tested if the proportion is the same as in 2016, that is:

[tex]H_0: p = 0.581[/tex]

At the alternative hypothesis, it is tested if the proportion is different, hence:

[tex]H_1: p \neq 0.581[/tex]

A Type II error is the non-rejection of a false null hypothesis, that is, finding that there is not enough evidence that the percentage is significantly below 58.1% when in fact it is.

The equation calculating the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the variables are listed as follows:

For this problem, the value for these variables is given as follows:

[tex]\overline{p} = \frac{586}{1048} = 0.559, n = 1048, p = 0.581[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.559 - 0.581}{\sqrt{\frac{0.581(0.419)}{1048}}}[/tex]

z = -1.44.

The critical value for a two-tailed test is with a significance level of 0.05 is:

|z| = 1.96.

The absolute value of the test statistic is of |z| = 1.44 < 1.96, meaning that there is not enough evidence to conclude that the percentage has changed from 2016.

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The length of BC is 50 miles (approx).

What is Trigonometry?

Trigonometry is a field of mathematics that explores the connections between triangle side lengths and angles.

Solution:

In the triangle ABC,

The perpendicular = BC

The Base = AB = 6 miles

by using the trigonometric ratio "tan"

tan (58) = BC / AB

8.33 = BC / 6

49.98 miles = BC

BC = 50 miles (approx)

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The speed of the current is equal to 8 miles per hour.

Mathematically, speed of any physical object can be calculated by using this formula;

Speed = distance/time

Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:

Speed downstream = 14 + c.

Speed upstream = 14 - c.

Additionally, the total time would be given by:

Total time = total distance/speed

Time upstream + time downstream = 6.5 hours

33/(14 - c) + 33/(14 + c) = 7.0

Multiplying both sides of the equation by (14 - c)(14 + c), we have:

33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)

462 + 33c + 462 - 33c = 7.0(196 - c²)

924 = 7.0(196 - c²)

Dividing both sides of the equation by 7.0, we have:

132 = 196 - c²

Speed of the current, c² = 196 - 132

Speed of the current, c² = 64

Speed of the current, c = √64

Speed of the current, c = 8 miles per hour.

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Answer:

6x^2-17x+12

Step-by-step explanation:

Distribute

2x^2-3x+1+x^2-2x+2(-2x+3)^2

Square (2x+3)

(-2x+3)(-2x+3)

FOIL

4x^2-6x-6x+9

Combine like terms

4x^2-12x+9

re-write equation

2x^2-3x+1+x^2-2x+2+4x^2-12x+9

Combine like terms

6x^2-17x+12

The amount of each semiannual interest payment is $7200.

Given that,
A company issues 9%, 4-year bonds with a par value of $160,000 on January 1 at a price of $165,386, when the market rate of interest was 8%. The bonds pay interest semiannually.

Simple interest is defined as the percentage of earnings on the lending for a period of time

Here,
Value of a single bond    =  $160,000
Issue price of bond         =  $165, 386
Rate of interest                =     9%
the market rate of interest =     8%
Interest payment             =      Semi-annually

Semi-annual interest payment      =  Value of the single bond × rate of interest/2
                                                       = $160,000 × 0.09/2
                                                       =  $7200

Thus, the amount of each semiannual interest payment is $7200.

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Answer:

r = -8.6

Step-by-step explanation:

ooooo IXL, one of my fav programs from my school days

Anyway

Multiply by -3 to get rid of that awful fraction

[tex]-3*2.2=\frac{r+2}{-3} *-3[/tex]

Solve that:

[tex]-6.6=r+2\\aka: r+2=-6.6[/tex]

Subtract 2 from both sides to isolate the r variable:

[tex]r=-8.6[/tex]

And.... We have our answer!

r = -8.6

Answer:

Step-by-step explanation:

x=5

A total of 12 5/8 pages is not meant for advertisement

From the question, we have the following parameters

First section = 16 pages

Pages for advertisement = 3 and 3/8 pages

Rewrite the above parameters as

First section = 16 pages

Pages for advertisement = 3 3/8 pages

The number of pages that are not for adverts is then calculated as

Pages not for adverts = First section - Pages for advertisement

Substitute the known values in the above equation

So, we have the following equation

Pages not for adverts = 16 - 3 3/8

Evaluate the difference

Pages not for adverts = 12 5/8

Hence, the number of pages that are not for adverts is 12 5/8 pages

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Based on the calculations, this equation 4f + 2(12f − 4) = 3(2f − 4) − f + 3 has one solution, which is equal to -1/23.

In Mathematics, no solution is also referred to as zero solution, and an equation is said to have no solution when the left hand side and right hand side of the equation are not the same or equal.

This ultimately implies that, an equation would have no solution or zero solution when both sides of the equal sign are not the same and the variables cancel out.

From the information provided, we have the following equation:

4f + 2(12f − 4) = 3(2f − 4) − f + 3

Opening the bracket, we have:

4f + 24f - 8 = 6f - 12 - f + 3

28f - 8 = 5f - 9

By collecting like terms, we have the following:

28f - 5f = -9 + 8

23f = -1

Dividing both sides by 23, we have:

f = -1/23

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a. The number of permutations of three letter words that can be formed with repetition is 1000 words

b. The number of permutations of three letter words that can be formed without repetiton is 720 words

Permutations are the number of ways in which x objects can be arranged out of n objects.

The number of permutations is given by ⁿPₓ = n(n - 1)(n -2)...(n - x + 1)

Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" with repetition, we note that there are 10 letters.

Since repetition is allowed, for the first slot, we have 10 letters, for the second position, we have 10 letters and for the third position, we have 10 letters.

So, the total number of permutations is n = 10 × 10 × 10

= 1000 words

So, the number of three letter words that can be formed is 1000 words

Since we require the number of three-letter "words" can be made from 10 letters "FGHIJKLMNO" without repetition, we note that there are 10 letters.

Since repetition is not allowed, for the first slot, we have 10 letters, for the second position, we have 9 letters and for the third position, we have 8 letters.

So, the total number of permutations is ¹⁰P₃ = 10 × 9 × 8

= 720 words

So, the number of three letter words that can be formed is 720 words

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Answer: dont be rude

Step-by-step explanation:

Answer:

Step-by-step explanation:

The rule for dilation of a quadrilaterial is Do.0.08 (z,y) (0.08z, 0.08y). What is the Y coordinate of a new point if the new coordinate is (3-9)? Round to the nearest

hundredth if necessary

The y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

Given:

(-4,5) and slope m = 2

substitute in y=mx+c

5 = 2*(-4) + c

5 = -8 + c

c = 5 + 8

c = 13.

c value in y = 2x + c

y = 2x + 13

To find y-intercept put x = 0.

y = 2(0) + 13

y = 0+13

y = 13

Therefore the y-intercept of the line passes through the point (-4,5) with slope 2 is y = 13.

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Using the percentage concept, it is found that 60.29% of the people surveyed were completely satisfied with the car.

A percentage is the number of desired outcomes, multiplied by 100%, and divided by the number of total outcomes.

In this problem, researching in the internet, it is found that:

A total of 1260 + 650 + 180 = 2090 people were surveyed.

Of those, 1260 were completely satisfied.

Hence:

60.29% of the people surveyed were completely satisfied with the car.

(I suggest using desmos graphing calculator for the future.)

(0,5) and (4,0) or the one in the left upper corner. Hope this helps.

Answer:

The answer is 55, you can figure this out as each number is increasing by 10

a_n=-5+10n

hope it helps

The completed table of the two column method to prove DE = FD is presented as follows;

Statement [tex]{}[/tex]                             Reason

1. CE = CD + DE[tex]{}[/tex]                    Segment addition postulate

2. FG = FD + DG              [tex]{}[/tex]     Segment addition postulate

3. CE = FG              [tex]{}[/tex]               Given

4. CD + DE = FD + DG      [tex]{}[/tex]    Substitution property of equality

5. CD = DG              [tex]{}[/tex]              Given

6. DG + DE = FD + DG    [tex]{}[/tex]      Substitution property of equality

7. DE = FD               [tex]{}[/tex]              Subtraction property of equality

A two column method consists a number of statements alongside the reasons that are known to make the statements true.

The segment addition postulate state that a point B is located on a segment AC if and only if AB + BC = AC, therefore;

The substitution property of equality states that if a = b, and a + c = d, then b + c = d

Which gives;

Similarly; CD = DG, then DG + DE = FD + DG

The subtraction (and addition) property of equality states that a quantity of known value can be subtracted (or added) to both sides of an equation and both sides of the equation remains equal.

Mathematically, if x = y, then x - z = y - z, therefore;

Then;

∴ DE = FD

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The distribution that is needed for the problem that we have here is the t distribution.

With its bell-shaped structure and heavier tails, the t-distribution, commonly referred to as the Student's t-distribution, is a kind of probability distribution that resembles the normal distribution.

When there are insufficient samples or unknown variances, it is used to estimate population parameters. T-distributions have broader tails than normal distributions because they are more likely to contain extreme values.

We have tn-1

where n = 70

so that we would have

t70 - 1

= t69

Therefore we would have to use the t distribution here.

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The Greatest Common Factor is [tex]b^{2}[/tex] Option B

The GCF (Greatest Common Factor) of two or more numbers is the greatest number among all the common factors of the given numbers

Find the common factors of each term in order to find the greatest common factor (GCF).

The Prime Factors of:

[tex]b^{5}[/tex] = [tex]b^{5}[/tex]

2[tex]b^{4}[/tex] = 2[tex]b^{4}[/tex]

[tex]3b^{3}[/tex] = [tex]3b^{3}[/tex]

[tex]b^{2}[/tex] = [tex]b^{2}[/tex]

From the common factors, the greatest common factors is [tex]b^{2}[/tex]

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Answer:

Assessment Practice 5. A science teacher has $225 to spend on lab equipment. He buys 4 posters with a guide to classifying rocks, for $19 each. Student rock collections cost $9 each. How many rock collections can he buy? Explain how you solve

Let

x -----> number of rock collections that he can buy

so

the algebraic expression that represents this situation is

Solve the inequality for x

subtract 76 both sides

Divide both sides by 9

therefore

The maximum number of rock collections that he can buy is 16

Step-by-step explanation:

The equation is 9x+76=225 and the number of rock collections he can buy is 17.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, a science teacher has $225 to spend on lab equipment.

Let the number of rocks collected be x.

He buys 4 posters with a guide to classifying rocks, for $19 each.

That is 19×4=76

Student rock collections cost $9 each.

Now, 9×x=9x

So, the equation is 9x+76=225

Subtract 76 on both the sides of equation, we get

9x=149

Divide 9 on both the sides of equation, we get

x=16.5

x≈17

Therefore, the number of rock collections he can buy is 17.

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Josephine have £3882.9 amount after 2 years and £3994.9 amount after 3 years.

Using the formula of compound interest we can find the amount after t years compounded annually at the r per cent rate.

The formula of compound interest is as follows,

[tex]A=p(1+\frac{r}{100} )^t[/tex]

Where P is the principal value, A is the amount, r is the rate and t is the time.

Here we have a principal value of £3,500 and a rate is 4.5%.

Now, finding the amount after 2 years by putting the values in the formula of compound interest,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^2\\\\A=3500(1+0.045 )^2\\A=3500(1.045)^2\\A=3500\times1.092025\\A=3882.0875[/tex]

So, After 2 years Josephine will have £3882.9.

Now, finding the amount after 3 years,

[tex]A=p(1+\frac{r}{100} )^t\\\\A=3500(1+\frac{4.5}{100} )^3\\\\A=3500(1+0.045 )^3\\A=3500(1.045)^3\\A=3500\times1.141166125\\A=3994.0814375[/tex]

So, After 3 years Josephine will have £3994.9.

Therefore, After 2 years Josephine will have £3882.9 and after 3 years Josephine will have £3994.9 when 4.5% interest is compounded annually.

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The percentage of people over speeding on this road on purpose is 9%

Percent of people speeding on this road noticed the sign = Percentage of people who notice the speed limit at the beginning of the road - Percentage of people who notice the sign and follow the speed limit

= 84% - 75%

= 9%

In conclusion, the percentage of people who intentionally speed on purpose is 9%

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