The missing number in the box is 3, find the value of X and show work please

To find the equation of the parabola, we need to first understand the basic properties of a parabola. A parabola is the set of all points which are equidistant from a point (called focus) and a line (called directrix).

A parabola can either be "upward" or "downward" depending on the position of the focus and directrix. The axis of symmetry is a line that passes through the focus and is perpendicular to the directrix. The vertex is the point where the axis of symmetry intersects the parabola.

If the focus is at point (a,b) and the directrix is y=k, then the equation of the parabola is given by: (y-b)^2=4a(x-a)If the focus is at point (a,b) and the directrix is x=k, then the equation of the parabola is given by: (x-a)^2=4b(y-b)

Here, we have the focus (-10,0) and the directrix x=0. Since the directrix is parallel to the y-axis, the axis of symmetry is the x-axis. The vertex is the midpoint of the line segment joining the focus and the point on the directrix closest to the focus. Since the directrix is x=0, the point on the directrix closest to the focus is (0,b) where b is the distance between the focus and the directrix. Therefore, the vertex is (-5,0).Since the parabola is "upward", we have (y-b)^2=4a(x-a) where a>0. We know that the focus is (-10,0) and the vertex is (-5,0). Therefore, a=5. We also know that the distance between the focus and the vertex is a. Therefore, b=a=5. The equation of the directrix is x=0. Therefore, the equation of the parabola is: (y-5)^2=20(x+5)

Thus, the equation of the parabola that satisfies the given conditions is (y-5)^2=20(x+5).

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Step-by-step explanation:

Reflection about the y-axis followed by a translation left by 2 units

Reflection about the x-axis followed by a translation left by 2 units

Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units

Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units

i hope it can help. thanks

Answer: The answer is C

Step-by-step explanation:

the possible coordinates of point A are (-2, -2) and (-2, 4).

Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

While distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion."

from the question:

Given that point, B has the coordinates (2, 1) and that there are 5 units between A and B, we can apply the distance formula to determine the potential coordinates of point A.

The formula for distance is:

\(d = sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

where d is the distance between the two points, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given values, we get:

5 = sqrt((2 -\((-2))^2\) + \((1 - y)^2)\)

Simplifying, we get:

5 = sqrt(16 + \((1 - y)^2)\)

Squaring both sides, we get:

25 = 16 + \((1 - y)^2\)

Subtracting 16 from both sides, we get:

9 = \((1 - y)^2\)

Taking the square root of both sides, we get:

3 = 1 - y or 3 = -(1 - y)

Solving for y in both cases, we get:

y = -2 or y = 4

Hence, (-2, -2) and are potential values for point A's coordinates (-2, 4).

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identity used is

x³ + y³+ z³– 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx).

then use

(x+y+z)² = x²+y²+z²+2(xy+yz+xz)

225= 83 + 2(xy+yz+xz)

xy+yz+xz = (225-83)/2

xy+yz+xz= 142/2

xy+yz+xz= 71

ok

now use identity

x³ + y³+ z³– 3xyz = (x + y + z) (x² + y² + z² – xy – yz – zx).

now

x³ + y³+ z³– 3xyz = 15 (83 – xy – yz – zx).

= 15[83 - (71)]

= 15×12

=180

Answer:

125

Step-by-step explanation:

Given

f(x) = 5x²

g(x) = 2x + 3

Now

g(-4) = 2 * (- 4) + 3

= - 8 + 3

= - 5

Also

f(g(-4)) = f( -5)

= 5 * ( -5)²

= 5 * 25

= 125

Answer:

C. 1,120 cubic inches

Explanation:

To find the total volume, we will divide the solid as follows:

The edge with a length equal to 10 in was calculated as:

18 in - 8 in = 10 in

Because 18 in is the length of the largest height of the figure and 8 in is the length of the smaller height.

Now, the volume of a rectangular prism can be calculated as:

Volume = Length x Width x Height

So, the volume of solid 1 is equal to:

V₁ = 12 in x 4 in x 10 in

V₁ = 480 in³

In the same way, the volume of solid 2 is equal to:

V₂ = 20 in x 4 in x 8 in

V₂ = 640 in³

Therefore, the total volume of the solid is the sum of both parts. Then:

V₁ + V₂ = 480 in³ + 640 in³

V₁ + V₂ = 1120 in³

So, the answer is C. 1,120 cubic inches

The probability that one player gets all aces is 0.0467

From the question, we have the following parameters that can be used in our computation:

Cards, n = 52

Players, r = 4

The 52 cards can be shared to the the 4 players in C(n + r - 1, r - 1) ways

So, we have

C(52 + 4 - 1, 4 - 1) = C(55, 3)

When evaluated, we have

C(52 + 4 - 1, 4 - 1) = 26235

Next:

The remaining 48 cards can be shared to the other 3 players in C(n + r - 1, r - 1) ways

C(48 + 3 - 1, 3 - 1) = C(50, 2)

C(48 + 3 - 1, 3 - 1) = 1225

So, we have

P = 1225/26235

Evaluate

P = 0.0467

Hence, the probability is 0.0467

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This code will print the test statistic for the variance test statistic is 17.99.

The test statistic for the hypothesis test is the ratio of the sample variances, s1^2 / s2^2. In this case, the sample variances are 35^2 / 24^2 = 17.99. The p-value for this test statistic is very small, so we can reject the null hypothesis and conclude that the variance has been reduced.

**The code to calculate the above:**

```python

import math

def test_statistic(s1, s2):

 """Returns the test statistic for the variance test."""

 return s1 ** 2 / s2 ** 2

s1 = 35 ** 2

s2 = 24 ** 2

t = test_statistic(s1, s2)

print(f"The test statistic is {t:.2f}")

Therefore,  the variance test statistic is 17.99.

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Answer:

\(y-7=-\dfrac{1}{2}(x+3)\)

Step-by-step explanation:

The point-slope formula is:

\(y-y_1=m(x-x_1)\)

where:

The equation of the original line in point-slope form is:

\(y-25=2(x-10)\)

Therefore, the slope of the line is m = 2.

As the slope of a perpendicular line is the negative reciprocal of the slope of the original line, the slope of the perpendicular line is m = -1/2.

To find the point-slope equation of the line that is perpendicular to the given line and passes through point (-3, 7), substitute m = -1/2 and point (-3, 7) into the point-slope formula:

\(\implies y-7=-\dfrac{1}{2}(x-(-3)\)

\(\implies y-7=-\dfrac{1}{2}(x+3)\)

Therefore, the point-slope equation of the line that is perpendicular to y - 25 = 2(x - 10) and passes through (-3, 7) is:

\(\boxed{y-7=-\dfrac{1}{2}(x+3)}\)

Answer:

\( y -7= \dfrac{-1}{2} (x+3)\)

Step-by-step explanation:

The given equation of the line is ,

\(\implies y - 25 = 2(x-10) \\\)

Simplify the RHS by opening the brackets,

\(\implies y - 25 = 2x - 20\\\)

\(\implies y = 2x + 25 - 20 \\\)

\(\implies y = 2x + 5 \\\)

On comparing it with the the slope intercept form of the line, namely y = mx + c , where m is the slope, we have;

\(\implies m = 2\\\)

Again as we know that the product of slopes of two perpendicular lines is -1 , Hence,

\( \implies m\cdot m_{\perp} = 2 \\ \)

\(\implies m_{\perp} =\dfrac{-1}{2} \\\)

Now the point given to us is (-3,7) , the point slope form of the line is ,

\(\implies y - y_1 = m(x-x_1) \\\)

where ,

On substituting the respective values, we have;

\(\implies y - 7 = \dfrac{-1}{2} \{ x -(-3)\}\\\)

Simplify,

\(\implies \underline{\underline{ y - 7 =\dfrac{-1}{2}(x+3)}}\\\)

This is the required answer in point slope form .

Answer:

there is a button on the side of your keyboard that turns off all caps

ACTUAL ANSWER: 1 dollar a pound

Step-by-step explanation:

The sum of squares for the game, computed by squaring each value and summing them up, is approximately 37.6296.

To compute the sum of squares for the game, we square each value in the set and then add them up. In this case, we have the values {1, 0, 0, 3.64, 2.7, 0.3, 4}. Squaring each value gives us {1, 0, 0, 13.2496, 7.29, 0.09, 16}. Adding up these squared values results in a sum of squares of approximately 37.6296. This value represents the total variability or dispersion of the game outcomes. It can be used to assess the spread or distribution of the values and to compute other statistical measures such as variance and standard deviation.

The sum of squares for the game is a measure of the total variability in the game outcomes. It quantifies the dispersion of the values and can be used in statistical analysis to assess the spread and calculate other descriptive statistics.

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Answer:

$5.22

Step-by-step explanation:

you would subtract so 5.60-.38=$5.22

Answer:

$5.22

Step-by-step explanation:

$5.22-0.38

ĺlllllllllllllllllllllll

Step-by-step explanation:

\( = {( \frac{27}{8} )}^{ \frac{1}{3} } \times ( \frac{243}{32} )^{ \frac{1}{5} } \div {( \frac{2}{3} )}^{2} \)

\( = { ({ (\frac{3}{2} )}^{3}) }^{ \frac{1}{3} } \times {( {( \frac{3}{2}) }^{5} )}^{ \frac{1}{5} } \div {( \frac{2}{3} )}^{2} \)

\( = {( \frac{3}{2} )}^{3 \times \frac{1}{3} } \times {( \frac{3}{2} )}^{5 \times \frac{1}{5} } \times {( \frac{3}{2} )}^{2} \)

\( = \frac{3}{2} \times \frac{3}{2} \times {( \frac{3}{2} )}^{2} \)

\( = {( \frac{3}{2} )}^{1 + 1 + 2} \)

\( = {( \frac{3}{2} )}^{4} \: or \: \frac{81}{16} \)

\(\large\underline{\sf{Solution-}}\)

\(\sf{\longmapsto{\bigg( \dfrac{27}{8} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{243}{32} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

We can write as :

27 = 3 × 3 × 3 = 3³

8 = 2 × 2 × 2 = 2³

243 = 3 × 3 × 3 × 3 × 3 = 3⁵

32 = 2 × 2 × 2 ×2 × 2 = 2⁵

\(\sf{\longmapsto{\bigg( \dfrac{3 \times 3 \times 3}{2 \times 2 \times 2} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{3 \times 3 \times 3 \times 3 \times 3}{2 \times 2 \times 2 \times 2 \times 2} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \dfrac{{(3)}^{3}}{{(2)}^{3}} \bigg)^{\frac{1}{3}} \times \Bigg[\bigg( \dfrac{({3}^{5})}{{(2)}^{5}} \bigg)^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

Now, we can write as :

(3³/2³) = (3/2)³

(3⁵/2⁵) = (3/2)⁵

\(\sf{\longmapsto{\left\{\bigg(\frac{3}{2} \bigg)^{3} \right\}^{\frac{1}{3}} \times \Bigg[\left\{\bigg(\frac{3}{2} \bigg)^{5} \right\}^{\frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

Now using law of exponent :

\({\sf{({a}^{m})^{n} = {a}^{mn}}}\)

\(\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{3 \times \frac{1}{3}} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{5 \times \frac{1}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

\( \sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{\frac{3}{3}} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{\frac{5}{5}} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times\Bigg[\bigg(\frac{3}{2} \bigg)^{1} \div \bigg(\dfrac{2}{3} \bigg)^{2}\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3}{2} \bigg)^{2}\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \frac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\frac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3}{2} \times \dfrac{3}{2} \bigg)\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2} \bigg)^{1} \times \bigg(\dfrac{3 \times 3}{2 \times 2}\bigg)\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)^{1} \times \Bigg[\bigg(\dfrac{3}{2} \bigg)^{1} \times \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\\)

\( \sf{\longmapsto{\bigg( \frac{3}{2} \bigg)\times \Bigg[\bigg(\frac{3}{2} \bigg)\times \bigg(\dfrac{9}{4}\bigg)\Bigg]}} \\\)

\(\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{3}{2} \times \dfrac{9}{4} \: \: \Bigg]}}\\\)

\(\sf{\longmapsto{\bigg( \dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{3 \times 9}{2 \times 4} \: \: \Bigg]}} \\\)

\(\sf{\longmapsto{\bigg(\dfrac{3}{2} \bigg)\times \Bigg[ \: \: \dfrac{27}{8} \: \: \Bigg]}} \\\)

\(\sf{\longmapsto{\dfrac{3}{2} \times \dfrac{27}{8}}} \\\)

\(\sf{\longmapsto{\dfrac{3 \times 27}{2 \times 8}}} \\\)

\( \sf{\longmapsto{\dfrac{81}{16}}\: ≈ \:5.0625\:\red{Ans.}} \\\)

Answer:

Choice D

Step-by-step explanation:

Choices A and B does not imply Dilation but Translation. Though Choice C implies Dilation, but it implies that \(\triangle J'K'L'\) is half the size of \(\triangle JKL\) but we can see that \(\triangle J'K'L'\) is larger than \(\triangle JKL\) so Choice D.

Answer:

Step-by-step explanation:

Set this up as a proportion

20/8 = 15/vx           Cross multiply

20*vx = 8 * 15

20 * vx = 120          Divide by 20

vx = 6

Answer:

Irrational number

Step-by-step explanation:

A number which can be written in the form of a fraction \(\frac{p}{q}\), is a rational number.

Examples : \(\frac{1}{2}, \frac{3}{4}, 1.41414141....\)

In 1.41414141..... (41) is the repeating numbers after decimal. Therefore, it's a rational number.

Irrational numbers can't be written in the form of \(\frac{p}{q}\).

Examples : π, √3, 1.41456......

Given number in the question is 6.56556555....

In this number numbers after decimal are not repeating.

Therefore, given number is irrational.

Answer:

-10

Step-by-step explanation:

Answer: 3x

verry eazy just subtract and keep the x

The system is consistent for all values of a and b.

To determine the values of a and b for which the system is consistent, we need to solve the system of equations and check if there is a unique solution, infinitely many solutions, or no solution.

The given system of equations is:

x + 2y = a

3x + 6y = b

We can rewrite the second equation as:

3(x + 2y) = b

Dividing both sides by 3, we get:

x + 2y = b/3

Now we have two equations:

x + 2y = a

x + 2y = b/3

If the slopes (coefficients of x and y) of the two equations are equal, then the system will have infinitely many solutions. If the slopes are not equal, then the system will have no solution.

Comparing the coefficients of x and y in both equations, we have:

1 = 1

2 = 2

The slopes are equal, which means the system will have infinitely many solutions for any values of a and b.

Therefore, the correct answer is not provided in the given options. The system is consistent for all values of a and b.

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Answer:

The amount she saves is 25% of her income

Step-by-step explanation:

She is paid $11 per hour

She works 9 hours per day

and for 24 days per month

So, she works 9(24) hours per month

= 216 hours per month

Now, she is paid $11 hourly, so for 216 hours,

she will have 11(216) = $2376

Total income = $2376 per month

Saving = $594 per month

As a percentage, we divide the savings by the total income,

savings/(total income) = 594/2376 = 1/4 = 0.25

Hence we get 25%

Answer:

\(f'(x)= \frac{13}{(2x+3)^2}\\\)

Step-by-step explanation:

\(f(x)= \frac{3x-2}{2x+3} \\\)

\(f'(x)=\frac{dy}{dx} = \frac{d}{dx}(\frac{3x-2}{2x+3})\\ f'(x)= \frac{(2x+3)\frac{d}{dx}(3x-2)-(3x-2)\frac{d}{dx}(2x+3) }{(2x+3)^{2} } \\f'(x)= \frac{(2x+3)(3)-(3x-2)(2)}{(2x+3)^{2} } \\\)

\(f'(x)= \frac{6x+9-6x+4}{(2x+3)^{2} }\\ f'(x)= \frac{13}{(2x+3)^2}\\\)

Answer:

He must work 34 hours

Step-by-step explanation:

187×20= 3740

3740÷110= 34

If a workman received $110 for working 20 hours. At the same rate of pay, 33.99 hours must be worked to earn $187.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, A workman received $110 for working 20 hours.

We will apply the unitary method in order to solve the given problem.

For $110 he has to work 20 hours.

$110 = 20 hours

For 1 dollar he has to work,

$1 = 20 / 110

$1 =0.1818 hours

The number of hours must he work to earn $187 will be,

$187 = 187 × 0.1818 hours

$187 = 33.99 hours

Thus, if a workman received $110 for working 20 hours. At the same rate of pay, 33.99 hours must be worked to earn $187.

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a)The total energy needed during pregnancy is a quantitative variable because it represents a measurable quantity rather than a non-numerical characteristic.

b) The probability that a randomly selected pregnant woman has an energy need of more than 2625 is approximately 0.3085, or 30.85%.

c) The sample mean daily energy requirement for a random sample of 20 pregnant women, will be approximately normally distributed.

d) the probability corresponding to a z-score of 2.23 is approximately 0.9864.

(a) The total energy needed during pregnancy is a quantitative variable because it represents a measurable quantity (i.e., the amount of energy needed) rather than a non-numerical characteristic.

(b) To calculate the probability that a randomly selected pregnant woman has an energy need of more than 2625, we need to determine the z-score and consult the standard normal distribution table. With the following formula, we determine the z-score:

z = (x - μ) / σ

z = (2625 - 2600) / 50

z = 25 / 50

z = 0.5

Looking up the z-score of 0.5 in the standard normal distribution table, we find that the corresponding probability is approximately 0.6915. However, since we are interested in the probability of a value greater than 2625, we need to subtract this probability from 1:

Probability = 1 - 0.6915

Probability = 0.3085

Interpretation: Approximately 0.3085, or 30.85%, of randomly selected pregnant women have energy needs greater than 2625. This means that there is about a 30.85% chance of selecting a pregnant woman with an energy need greater than 2625.

(c) The sample mean daily energy demand for a randomly selected sample of 20 pregnant women, X, will have a roughly normal distribution. The population mean (2600) will be used as the sampling distribution's mean, and the standard deviation will be calculated as the population standard deviation divided by the sample size's square root. (50 / √20 ≈ 11.18).

(d) We follow the same procedure as in (a) to determine the likelihood that a randomly selected sample of 20 pregnant women has a mean energy need greater than 2625. Now we determine the z-score:

z = (2625 - 2600) / (50 / √20)

z = 25 / (50 / √20)

z = 25 / (50 / 4.47)

z = 2.23

Consulting the standard normal distribution table, we find that the probability corresponding to a z-score of 2.23 is approximately 0.9864.

Interpretation: About 0.9864, or 98.64%, of 20 pregnant women in a random sample would have a mean energy requirement greater than 2625. This means that if we repeatedly take random samples of 20 pregnant women and calculate their mean energy needs, about 98.64% of the time, the sample mean will be greater than 2625.

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Answer:

No, it is 11 \(\frac{1}{3}\) or 11 1/3

Step-by-step explanation:

Answer:

-1/4 because it is a negative line and this a negative slope.

Step-by-step explanation: mr clean

To calculate the volume of a rectangular box, you multiply the lengths of its sides.

In this case, the given box has sides measuring 7 inches, 9 inches, and 13 inches. Therefore, the volume can be calculated as:

Volume = Length × Width × Height

Volume = 7 inches × 9 inches × 13 inches

Volume = 819 cubic inches

So, the volume of the given box is 819 cubic inches. The formula for volume takes into account the three dimensions of the box (length, width, and height), and multiplying them together gives us the total amount of space contained within the box.

In this case, the box has a volume of 819 cubic inches, representing the amount of three-dimensional space it occupies.

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For given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

In this question, we have been given six number cards.

-4 -2 -1 5 6 8

We need to arrange the cards into three pairs with the same total in brackets.

Arranging cards with numbers  -4, -2, -1, 5, 6, 8 making pair with the same total.

i.e.  8 - 4 = 4

so the first pair is (8, -4)

6 - 2 = 4

so the second pair is (6,-2)

5 - 1 = 4

and the last pair is (5,-1)

Therefore, for given six number cards, three pairs with the same total:

(8, -4), (6, -2) and (5, -1)

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The probability of all three events occurring are; 1st even number is 1/2

2nd prime number is 2/3. and 3rd multiple of 5 is 1/3.

We have,,

Probability refers to a possibility that deals with the occurrence of random events.

The probability of all the events occurring need to be 1.

The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.

Given that fair dice is rolled 3 times in a row.

The outcomes are;

1. P( even number) = total even number / total number of outcomes

                              = 3/ 6 = 1/2

2. prime number

P( prime number) = total prime number / total number of outcomes

                              = 4/ 6 = 2/3

2. multiple of 5

P( multiple of 5) = total number that are multiple of 5/ total number of outcomes

                              = 2/ 6 = 1/3

Hence, The probability of all three events occurring are; 1st even number is 1/2 2nd prime number is 2/3. and 3rd multiple of 5 is 1/3.

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Answer: 1 2 and 4 hope this helps

Step-by-step explanation:

Answer:

yes, the correct answers are:

A) 1 = 2(x2 + 2x)

B) 1 = 2x2 + 4x

D) 3 = 2(x + 1)2

Step-by-step explanation:

got it correct in edg 2020 hope this is of help :)

Answer:A

Step-by-step explanation:

.