A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 49 − x2. What is the largest possible area (in squared units) of the rectangle?

Answer:

[tex]x=14[/tex]

Step-by-step explanation:

[tex](5x-14)+(8x+12)=180[/tex]

These two angles on the line is 180°

Solve the equation:

[tex]5x-14+8x+12=180[/tex]

[tex]5x+-14+8x+12=180[/tex]

[tex](5x+8x)+(-14+12)=180[/tex] {combine the like terms}

[tex]13x-2=180[/tex]

[tex]13x=180+2[/tex]

[tex]13x=182[/tex]

[tex]x=182/13[/tex]

[tex]x=14[/tex]

PROOF:

{substitute 14 in the place of x}

[tex](5(14)-14)+(8(14)+12)=180[/tex]

[tex]56+124=180[/tex]

[tex]180=180[/tex]

hope this helps....

Answer:

1. -4

Answer:

Question 1 = 256

Question 2 = ( 7, 8, 12)

Answer:

A rational number is one that may be represented in the manner p/q.

245/1000 = 0.245

Step-by-step explanation:

Answer:

Both triangles are triangle rectangles, but the triangles are not similar.

Step-by-step explanation:

By the Pythagorean's theorem, we know that for a triangle rectangle the sum of the squares of the cathetus is equal to the square of the hypotenuse.

Where the cathetus are always the two sides of smaller length.

We also know that two figures are similar if all the correspondent sides are proportional to each other, this means that the figures have the same shape but different size.

First, for triangle A the measures of the sides are:

48, 55, 73

Here the two catheti are 48 and 55, and the hypotenuse is 73.

Then to answer the first question we need to try to apply the Pythagorean's theorem, we should have:

48^2 + 55^2 = 73^2

solving that we get:

5,329 = 5,329

This is true, thus triangle A is a triangle rectangle.

Now for triangle B the measures are: 36, 77 and 85.

So the catheti are 36 and 77, and the hypotenuse is 85

So to check if triangle B is a triangle rectangle the equation:

36^2 + 77^2 = 85^2

must be true, solving both sides we get:

7,225 = 7,225

This is true, so triangle B is a triangle rectangle.

Finally, to check if the figures are similar we need to compare the correspondent sides of both triangles, such that the quotient of correspondent sides must be always the same.

For the hypotenuses, if we compute:

(hypotenuse B)/(Hypotenuse A) we get:

85/73 = 1.16

Now if we do the same for the two smaller catheti we get:

36/48 = 0.75

The quotients are different, thus the triangles are not similar.

Answer:

(8, 17)

Step-by-step explanation:

y= 3x -7 -----(1)

y= 2x +1 -----(2)

Substitute (1) into (2):

3x -7= 2x +1

Being x terms to one side, constant to the other:

3x -2x= 7 +1

x= 8

Substitute x= 8 into (2):

y= 2(8) +1

y= 16 +1

y= 17

∴ The solution is (8, 17).

Answer:

The possible number that Hall could be thinking of is 144.

Step-by-step explanation:

Difference between 17 and the square root of my mystery number

This is represented by:

[tex]17 - \sqrt{x}[/tex]

is 5

Then:

[tex]17 - \sqrt{x} = 5[/tex]

What are two possible numbers that Hall could be thinking of?

We have to solve the equation, for x. So

[tex]17 - \sqrt{x} = 5[/tex]

[tex]\sqrt{x} = 12[/tex]

[tex](\sqrt{x})^2 = (12)^2[/tex]

[tex]x = 144[/tex]

The possible number that Hall could be thinking of is 144.

Answer:

13.33

Step-by-step explanation:

Because it's only payment one we can easily figure out the interest portion

we first need the effective rate

.08/12= .006666667

We the just mulitply this by loan amount

2000*.006666667= 13.33

Step-by-step explanation:

its your answer

I hope it's help you

Answer:

x=200

Step-by-step explanation:

(1/5)x-(2/3)y=30, y=15

(1/5)x-(2/3)*15=30

(1/5)x=40

x=200

Given:

A line passes through the points (-3,7) and (9,-5).

To find:

The equation of the line in the form of [tex]y=mx+b[/tex].

Solution:

If a line passes through two points, then the equation of the line is:

[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

A line passes through the points (-3,7) and (9,-5). So, the equation of the given line is:

[tex]y-7=\dfrac{-5-7}{9-(-3)}(x-(-3))[/tex]

[tex]y-7=\dfrac{-5-7}{9+3}(x+3)[/tex]

[tex]y-7=\dfrac{-12}{12}(x+3)[/tex]

[tex]y-7=-1(x+3)[/tex]

On further simplification, we get

[tex]y-7=-x-3[/tex]

[tex]y-7+7=-x-3+7[/tex]

[tex]y=-x+4[/tex]

Therefore, the equation of the required line is [tex]y=-x+4[/tex].

Answer:

Non-linear

Step-by-step explanation:

While the difference in x terms remains constant at 1

The difference between y terms varies.

Answer:

Non-linear.

Step-by-step explanation:

Answer:

First table from left.

Step-by-step explanation:

Equal step of a half.

1,7

2,9

3,13

4,21

Step-by-step explanation:This is the linear function graph i plotted the points

Answer:

a. $0.13 / Ib.

Step-by-step explanation:

Slope of a line:

Suppose we have two data-points in a line. The slope is given by the change in the output divided by the change in the output.

In this question:

Input: weight(in pounds)

Output: Weekly cost to feed.

A hamster weighs half a pound and costs $2 per week to feed, while a Labrador Retriever weighs 62.5 pounds and costs $10 per week to feed.

Inputs: 0.5, 62.5

Outputs: 2, 10

Change in the outputs: 10 - 2 = 8

Change in the inputs: 62.5 - 0.5 = 62

Slope: [tex]m = \frac{8}{62} = 0.13[/tex]

So the correct answer is given by option A.

Answer:

0.13

Step-by-step explanation:

Answer:

With Exponents: 32 × 7 × 401

Without Exponents: 3 × 3 × 7 × 401  

Step-by-step explanation:

Hello,

[tex]25^2*6^3\\\\=(5^2)^2*(2*3)^3\\\\=\boxed{2^3*3^3*5^4}\\[/tex]

Answer:

c on edge2021

Step-by-step explanation:

Step-by-step explanation:

please type the question properly

Answer:

we need to factorise if imaginary number is in the denominator. no action is required if its in the numerator.

you can factorise an imaginary number by multiplying both the numerator and denominator by the conjuncate of the complex number

for instance,

we've given a complex number as follows

[tex] \frac{x}{3x + 4i} [/tex]

factorising

[tex] \frac{x}{3x + 4i} \times \frac{3x - 4i}{3x - 4i} [/tex]

as 3x -4i is the conjugate of 3x + 4i

and 4i is the imaginary number

[tex] \frac{ x(3x - 4i)}{9x {}^{2} - 4 {i}^{2} }[/tex]

and since i² = -1

[tex]\frac{ x(3x - 4i)}{9x {}^{2} + 4}[/tex]

hence factorised

Answer:

I did question no 2 , 4 , 5 , 6

from question attempt any two questions i did 4 and 5.

Step-by-step explanation:

Hope this helps u !!

Mean = 24.47

Variance = 108.31

Standard deviation = 10.41

The probability distribution table has been attached to this response.

(1) To calculate the mean (m)

(a) First multiply each of the values of x by their corresponding probability values.

This is shown in the third column of the table.

(b) The sum of the results in the third column gives the mean of the distribution. i.e

m = ∑xP(x) = 11.52 + 9.36 + 3.15 + 0.44

m = 24.47

(2) To calculate the variance (σ²).

(a) First find the square of the difference between the values of x and the mean (m) calculated in (1b) above. i.e

(x - m)²

The result is shown in the fourth column of the table.

(b) Next, multiply each of the results in the fourth column (x - m)², by their corresponding probability values P(X = x). i.e

(x - m)²(P(X = x))

The result is shown in the fifth column of the table.

(c) Now find the variance (σ²) which is the sum of the results in the fifth column. i.e

σ² = ∑(x - m)²(P(X = x)) = 42.5411 + 0.8427 + 18.8330 + 46.0923

σ² = 108.3091

σ² = 108.31      [to 2 decimal places]

(3) To calculate the standard deviation (σ)

The standard deviation is the square root of the variance of the distribution. Calculate this by finding the square root of the result in (2c) above.

σ = √σ²

σ = [tex]\sqrt{108.31}[/tex]

σ = 10.4072

σ = 10.41        [to 2 decimal places]

Answer:

X=2.

Step-by-step explanation:

3 times 2 is equal to 6, and 4 times 2 is equal to 8, 6+8=14.

Step-by-step explanation:

everything can be found in the picture

Answer:

4547.14

Step-by-step explanation:

m increased by %8 so it'll be

[tex]6.588 \times {10}^{ - 5} [/tex]

and t will be

[tex]1.785 \times {10}^{ - 6} [/tex]

so G =

[tex] \sqrt{ \frac{(6.588 \times {10}^{ - 5}) }{ {(1.785 \times {10}^{ - 6}) }^{2} } } [/tex]

G= 4547

Step-by-step explanation:

area of square = 1

area of a circle in square = [tex]\pi r^2 = \pi *(1/2)^2 = \frac{\pi }{4}[/tex]

bu estimate  [tex]p^ = X/n = 760/1000 = 0.76

Therefore,

[tex]\frac{\pi }{4} \approx 0.76[/tex]

[tex]\pi \approx 0.76*4 =3.04[/tex]

b) if n tend to infinity

[tex]\pi will approach 3.14[/tex]

Answer:

uvfhmfa

Step-by-step explanation:

Answer:

The z-score for a home priced at $200,000 in Florida is of -2.5.

The z-score for a home priced at $200,000 in Ohio is of 2.5.

The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean price for a 2,000sq foot home in FL is $240,000 with a Standard Deviation of $16,000. Home of $200,000.

This means that [tex]\mu = 240, \sigma = 16, X = 200[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{200 - 240}{16}[/tex]

[tex]Z = -2.5[/tex]

The z-score for a home priced at $200,000 in Florida is of -2.5.

The mean price of the same sized home in OH is $170,000 with a standard deviation of $12,000. Home of $200,000.

This means that [tex]\mu = 170, \sigma = 12, X = 200[/tex]. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{200 - 170}{12}[/tex]

[tex]Z = 2.5[/tex]

The z-score for a home priced at $200,000 in Ohio is of 2.5.

Which state would a home priced at $200,000 be closer to the mean price, compared to the distribution of prices in the state?

The closeness to the mean is measured by the absolute z-score(disconsidering the signal, the lower the score, the closer to the mean). However, in this case, both z-scores have the same absolute value, so in both Florida and Ohio a home priced at $200,000 is equally close to the mean.

Answer:

7

Step-by-step explanation:

This is correct answer bro...

Answer:

7

Step-by-step explanation:

So first off, two numbers that are to the same root can be combined.

In this case we can combine these two values, since they are to the 5th root and are both 7:

[tex]\sqrt[5]{7*7^4}[/tex]

=

[tex]\sqrt[5]{49^4}[/tex]

This can be broken down into 7^2

This gets us [tex]\sqrt[5]{7^5}[/tex]

Remember that we add exponents, together, so in this case it adds up to 5.

You might be wondering...well if its 7^2 and 7^4, wouldnt it be 7^6?

Well, remember this. One of the 7s in 7^2 is from the 7^4, so tecnically it is 7^3 + 7^2, which is 7^5

Anyway, now we have:

[tex]\sqrt[5]{7^5}[/tex]

When you root a exponent, it works like subtraction.

In this case we have a exponent of 5, and a root of 5.

This is 5-5 = 0

So it will just be 7. Because the square and root cancel each other out, leaving us with 7.

Hope this helps!

Also, I  just watched you waste someone elses answer so you could ask your own question. Instead of wasting other peopes answers, message me on one of my questions or answers, I will help you for free. :D

Answer:

If a point is reflected over the x-axis, the x- coordinate of the image remains the same as the pre-image and the y- coordinate is the opposite of the pre-image. ... If a point is reflected over both axes, both coordinates of the image are opposite of the pre-image.

Answer:

Percent who walk 45%

Percent in car 22.5%

Step-by-step explanation:

The total number of students is

36+26+18 = 80

Percent who walk is 36/80 = .45 =45%

Percent in car is 18/80 =.225= 22.5%