Find the value of each variable

Answer:

8. y=2x+6

9. y=1/2x-5

Step-by-step explanation:

Use point slope form to figure out the y intercept. Because it needs to be parallel, the same slope will be used to solve for point slope form.

Answer:

-4x

Step-by-step explanation:

Answer:

-4x

Step-by-step explanation:

Answer:

Are you making a new post?

Step-by-step explanation:

Answer: Option B, x ≥ 121

Step-by-step explanation:

We start with the inequality:

√x ≥ 11.

First, we can square each side of the inequality, to get:

(√x)^2 ≥ 11^2

And we know that:

√(x^2) = (√x)^2 = x

Then:

x ≥ 11^2

x ≥ 121

So we only need to have x equal or larger than 121.

The correct option is B.

Answer:

2x +3x =7-13=4+8

Step-by-step explanation:

5x= -6= 12

Answer: It number 4

Step-by-step explanation:

Answer:

(4, 10)

Step-by-step explanation:

Hope this helps

The solution to the system of equations is the ordered pair in option B. (4, 10).

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Population growth of two towns over a period of five years is represented by the system of equations :

y = x + 6

y = 2x + 2

Here y represents the population growth and x represents the number of years.

Solution of the system of equations is the point where the graph of both equations intersect.

Intersecting point is (4, 10).

Algebraically, we can solve this as,

We have y =  x + 6 and y = 2x + 2.

x + 6 = 2x + 2

x - 2x = 2 - 6

x = 4

y = x + 6 = 4 + 6 = 10

So (x, y) = (4, 10)

Hence the solution to the system of equations  y =  x + 6 and y = 2x + 2 is the point (4, 10).

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Answer:

5.25x + 55 is greater than or equal to 399

Step-by-step explanation:

55 is a fixed amount of money that Amelia already has so that will be added to the part of the eqaution: 5.25x.

Her total should be greater than or equal to $399

Answer:

25

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

√9x²

√3²x²

√3²√x²

3x

hope it helps

Answer:

The prime factorization of 56 is 2 * 2 * 2 * 7. This can also be written with exponents as 2^3 * 7.

Step-by-step explanation:

Answer:

the amount left is 16.2

Step-by-step explanation:

The computation of the amount of money spend is shown below;

Given that

Total money available $20

This week 10% would be put in piggy bank

and, in next week 10% of the money would be put again in piggy bank

So the money left is

= $20 - $20 × 10% - ($18 × 10%)

= $20 - $2 - $1.8

= $16.2

Hence, the amount left is 16.2

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

===================

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25

Answer:

We conclude that:

Step-by-step explanation:

Given

We know that the diagonals of a parallelogram bisect each other.

so

[tex]RT = TP[/tex]

Given

so substituting RT = x, and TP = 5x-28

[tex]RT = TP[/tex]

[tex]x = 5x-28[/tex]

[tex]5x = x+28[/tex]

[tex]5x-x = 28[/tex]

[tex]4x = 28[/tex]

divide both sides by 4

[tex]4x/4 = 28/4[/tex]

[tex]x = 7[/tex]

Therefore, the value of x:

Similarly,

[tex]QT = TS[/tex]

Given

so substituting QT = 5y, and TS = 2y+12

[tex]QT = TS[/tex]

[tex]5y = 2y+12[/tex]

[tex]5y-2y = 12[/tex]

[tex]3y = 12[/tex]

divide both sides by 3

[tex]3y/3 = 12/3[/tex]

[tex]y = 4[/tex]

Therefore, the value of y:

y = 4

Therefore, we conclude that:

Answer:

angle B, angle A, angle C

Step-by-step explanation:

Answer:

2*2=4

Step-by-step explanation:

Answer:

[tex]\displaystyle y = x^{-\frac{2}{3}}[/tex]

Step-by-step explanation:

Logarithms

Some properties of logarithms will be useful to solve this problem:

1. [tex]\log(pq)=\log p+\log q[/tex]

2. [tex]\displaystyle \log_pq=\frac{1}{\log_qp}[/tex]

3. [tex]\displaystyle \log p^q=q\log p[/tex]

We are given the equation:

[tex]\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }[/tex]

Applying the second property:

[tex]\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}[/tex]

Substituting:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(xy)[/tex]

Applying the first property:

[tex]\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))[/tex]

Operating:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)[/tex]

Rearranging:

[tex]\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)[/tex]

Simplifying:

[tex]\displaystyle -2\log_{2}(x) =3\log_{2}(y)[/tex]

Dividing by 3:

[tex]\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}[/tex]

Applying the third property:

[tex]\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)[/tex]

Applying inverse logs:

[tex]\boxed{y = x^{-\frac{2}{3}}}[/tex]

Answer:

its 5

Step-by-step explanation:

9514 1404 393

Answer:

  0

Step-by-step explanation:

The expression ...

  [tex]f^{-1}(1)[/tex]

can be read as "the value of x that makes f(x) = 1".

We can read that value from the graph. It is the y-intercept of the function f(x):

  (0, 1)

The value of x that makes f(x) = 1 is 0. That is, f(0) = 1.

  [tex]\boxed{f^{-1}(1)=0}[/tex]

Answer:

19.375

Step-by-step explanation:

Answer:

19.375

Step-by-step explanation:

[-15(-1.5)] + [(-2.5) x 1.25]

= [22.5] + [-3.125]

= 19.375

Answer:

56π

Step-by-step explanation:

1. Approach

To find the radius of a circle, use the formula;

[tex]A = r^{2}[/tex]π

To find the area of the shaded region, find the area of the larger circle, and then subtract the area of the smaller circle from it.

It is given that the larger circle has a radius of 9, and the smaller has a radius of 5.

2. Area of the larger circle

[tex]A = r^{2}[/tex]π

Substitute in known value (use 3.14 for π)

[tex]A = (9)^{2} * 3.14[/tex]

A = 254.47

3. Area of the smaller circle

[tex]A = r^{2}[/tex]π

Substitute in known value (use 3.14 for π)

[tex]A = (5)^{2} * 3.14[/tex]

A = 78.54

4. Area of the shaded region

Subtract the area of the smaller circle from the area of the larger circle;

254.47 - 78.54 = 175.93

~ 56π

Answer:

3/10 shade 3 in

Step-by-step explanation:

9514 1404 393

Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  [tex]\text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}[/tex]

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the power rule.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

Answer:

y - 12 = 3(x - 5)

Step-by-step explanation:

Going from (-2, -9) to (5, 12), x (the run) increases by 7 and y (the rise) increases by 21.  Thus, the slope of this line is m = rise / run = 21/7 = 3.

Using the point-slope formula y - k = m(x - h), we get:

y - 12 = 3(x - 5)

Answer:

a. 311 hours

b. i. $3,100 in receipts  

   ii. $2,799 in expenses.

Step-by-step explanation:

a. The company is making $10 per hour and spending $9 an hour. Their profit is therefore:

= 10 - 9

= $1 per hour

Since they spent $311 on the new equipment, the amount of time it would take for them to make this back is:

= 311 / 1

= 311 hours

b. In 311 hours, the total receipts would be:

= 311 * 10

= $3,110

The expenses would be:

= 311 * 9

= $2,799

Answer:

A' = ( 0,4 )

B' = ( -3,6 )

C' = ( -4,3 )

Step-by-step explanation:

Transformation involves changing the coordinates of a shape.

The coordinates of △ABC after the glide transformation are [tex]A' = ( 0,4 )[/tex], [tex]B' = ( -3,6 )[/tex] and  [tex]C' = ( -4,3 )[/tex]

The coordinates of triangle ABC is given as:

[tex]A = (1,3)[/tex]

[tex]B = (4,5)[/tex]

[tex]C = (5,2)[/tex]

The glide reflection is given as: T⟨−1, 1⟩° Ry-axis

So, we start by translating the shape by (x - 1, y + 1).

The coordinate ABC becomes

[tex]A = (1 - 1, 3 + 1) = (0,4)[/tex]

[tex]B = (4 - 1, 5 + 1) = (3,6)[/tex]

[tex]C = (5 - 1, 2 + 1) = (4,3)[/tex]

Next, we reflect the coordinates across the y-axis.

The rule of this reflection is:

[tex](x,y) \to (-x,y)[/tex]

So, we have:

[tex]A' = ( 0,4 )[/tex]

[tex]B' = ( -3,6 )[/tex]

[tex]C' = ( -4,3 )[/tex]

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Answer:

9 years ( approximately)

Step-by-step explanation:

900(1.03)^t = 1200

(1.03)^t= 1.33

( 1.03)^t= ( 1.03)^9

So, t= 9

Answer:

Quotient : 3x² + 5x + 1

Step-by-step explanation: