Consider the function represented by the equation x - y = 3. What is the equation written in function notation, with x

as the independent variable?

obor(x) = y + 3

Of(x) = -y - 3

Of(x) = -x + 3

O f(x) = x - 3

Answer:

B=41

Step-by-step explanation:

Triangle = 180 degrees.

108+31=139

180-139=41\

B = 41 degrees

Using a system of equations, it is found that Debbie worked 45 hours during the week.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Juan and Debbie each earn 9 per hour at their "jobs", and earned a total of 765 for the week, hence:

9x + 9y = 765

Simplifying the expression by 9:

x + y = 85 -> x = 85 - y.

Debbie worked five hours more than juan during the week, hence:

y = x + 5.

Since x = 85 - y, we replace in the expression:

y = 85 - y + 5.

2y = 90.

y = 45.

Debbie worked 45 hours during the week.

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IF the base area of the pyramid will be 400 square feet. Then the volume of the given pyramid will be 3466.67 cubic feet.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The dimension of the pyramid is shown in the diagram.

Then the base area of the pyramid will be

Area = 20 x 20

Area = 400 square feet

Then the volume of the given pyramid will be

V = 1/3 x area x height

V = 1/3 x 400 x 26

V = 3466.67 cubic feet

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The equation of the translated function is:

g(x) = (x + 3)^2 - 2

We can see that the blue graph is a translation of the red one, where the equation for the red graph is:

f(x) = x^2

Remember that the translations are:

Horizontal translation:

For a general function f(x), a horizontal translation of N units is written as:

g(x) = f(x + N).

If N is positive, the shift is to the left.

If N is negative, the shift is to the right.

Vertical translation:

For a general function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

If N is positive, the shift is upwards.

If N is negative, the shift is downwards.

By analyzing the vertices, we can see that the vertex of the blue graph is at (-3, -2) so we have a translation of 3 units to the left and 2 units down, meaning that we have:

g(x) = f(x + 3) - 2 = (x + 3)^2 - 2

So the correct option is A.

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Answer: 1725

Step-by-step explanation: A= A+B/2 h= 50+65/2x30=1725

Using the normal distribution, it is found that 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

In this problem, the mean and the standard deviation are given, respectively, by [tex]\mu = 15.1, \sigma = 2.2[/tex].

The proportion of penguins from the population have a weight between 13.0 kg and 16.5 kg is the p-value of Z when X = 16.5 subtracted by the p-value of Z when X = 13.

X = 16.5:

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

[tex]Z = \frac{16.5 - 15.1}{2.2}[/tex]

Z = 0.64

Z = 0.64 has a p-value of 0.7389.

X = 13:

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

[tex]Z = \frac{13 - 15.1}{2.2}[/tex]

Z = -0.95

Z = -0.95 has a p-value of 0.1711.

0.7389 - 0.1711 = 0.5678.

0.5678 = 56.78% of the penguins from the population have a weight between 13.0 kg and 16.5 kg.

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Answer: The correct answer is D.

Step-by-step explanation: The darker part in the graph is the area that contains the solutions. The only point out of the choices that is in the dark area is D.

C.8 is the answer.

Step-by-step explanation:

Mode: The number that occurs the highest number of times.

Answer:

The Answer is C). 8

Step-by-step explanation:

bcause there are more 8's then all the other number if that makes sense

Hope this helps!!!

Work Shown:

8 x 22

8 x (20 + 2)

8 x 20 + 8 x 2

160 + 16

176

Answer:

a² = 16

Step-by-step explanation:

substitute a = 4 into the expression

a² = 4² = 4 × 4 = 16

Answer:

16

Step-by-step explanation:

Answer:

75.36

hope this helps :)

The volume of the triangular prism is 1756.3 cubic yd option second is correct.

It is defined as a three-dimensional space enclosed by an object or thing.

We know that the volume of a triangular prism is given by:

[tex]\rm V = \dfrac{1}{2}\times b\times l\times h[/tex]

Where b is the base length, l is the base width, and h is the height of the prism.

[tex]\rm h=\sqrt{13^2-(\dfrac{13}{2}) ^2[/tex]

h = 11.2583 yd

b = 13 yd

l = 24 yd

[tex]\rm V = \dfrac{1}{2}\times 13\times 24\times 11.2583[/tex]

V = 1756.29 ≈ 1756.3 cubic yd

Thus, the volume of the triangular prism is 1756.3 cubic yd option second is correct.

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Answer:

175

Step-by-step explanation:

its easy just multiply 7 and 25

Answer:

33π m²

Step-by-step explanation:

Solving

Answer:

x=4

Step-by-step explanation:

We know that in a parallelogram opposite sides are equal

Hence on equating we get,

[tex]6x - 20 = 4[/tex]

[tex]6x = 4 + 20[/tex]

[tex]6x = 24[/tex]

[tex]x = 4[/tex]

Answer:

A. 1,998,723

Step-by-step explanation:

1.182(1.34)^49

Answer: 7

Step-by-step explanation:

[tex]Mean = \frac{Sum of terms}{Number of terms}[/tex]

          = [tex]\frac{7+6+6+7+6+9+7+8}{8}[/tex]

          = [tex]\frac{56}{8}[/tex]

          = 7

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The correct answer is option A

[tex]~~~~~~6(2+x) = -18\\\\\implies 2+x = -\dfrac{18}6\\\\\implies 2+x = -3\\\\\implies x = -3-2\\\\\implies x =-5[/tex]

Given equation:

Step-by step solution;

Simplifying the distributive property;

⇒ -18 = (6 × 2) + (6 × x)  

Further simplifying the distributive property;

⇒ -18 = (12) + (6x)

Subtracting 12 to both sides of the equation;

⇒ -18 - 12 = (12) + (6x) - 12

Simplifying both sides of the equation;

⇒ -30 = (6x)

Dividing 6 to both sides of the equation;

⇒ -30/6 = (6x)/6

⇒ -5 = x

Therefore, the value of "x" is -5.

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Answer:

its just like doing normal area just work it out then add the different sdhapes areas together

Answer:

-3 -2 -1 = -6 0 times 1 times 2 times 3 = 0 -12 -7 -4 = -23

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

1+3-1= 3

Step-by-step explanation:

Hope you'll understand

Answer:

the answer is the numbers in the expressions inside the bracket should be added not subtracted

Step-by-step explanation:

hope it helps

Answer:

x=3

Step-by-step explanation:

(x+10)+(2x-10)=90

3x (10-10)=90

3x=90

90/3

x=30

(30+10) and (30-10)

=40 and 20

Answer:

7/3

Step-by-step explanation:

12x - 15 = 6 - 3x

=> 12x + 3x =  6 + 15

=> 15x = 21

=> x = 21/15

=> x = 7/3

[tex]\\ \rm\Rrightarrow \left(x+\dfrac{1}{x}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{x^2+1}{x}\right)^2\dots(1)[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{1}{\sqrt{2}+\sqrt{5}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{2+2\sqrt{10}+5}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{1}{2\sqrt{10}+7}[/tex]

Now put in eq(1)

[tex]\\ \rm\Rrightarrow \left(\dfrac{\dfrac{1}{2\sqrt{10}+7}+1}{\dfrac{1}{2\sqrt{10}+7}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{1+2\sqrt{10}+7}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{2\sqrt{10}+8}{2\sqrt{10}+7}\times (2\sqrt{10}+7)\right)^2[/tex]

[tex]\\ \rm\Rrightarrow \left(\dfrac{(2\sqrt{10}+8)\cancel{(2\sqrt{10}+7)}}{\cancel{2\sqrt{10}+7}}\right)^2[/tex]

[tex]\\ \rm\Rrightarrow (2\sqrt{10}+8)^2[/tex]

[tex]\\ \rm\Rrightarrow 40+32\sqrt{10}+64[/tex]

[tex]\\ \rm\Rrightarrow 32\sqrt{10}+94[/tex]

More simplification (If required)

[tex]\\ \rm\Rrightarrow 2^52^{\frac{1}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow 2^{5+\frac{1}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow 2^{\frac{11}{2}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{2^{11}}\sqrt{5}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{2048(5)}+94[/tex]

[tex]\\ \rm\Rrightarrow \sqrt{10240}+94[/tex]

Most accurate

[tex]\\ \rm\Rrightarrow 101.19+94[/tex]

[tex]\\ \rm\Rrightarrow 195.19[/tex]

Answer:

8 hours

Step-by-step explanation:

24 X 8     X 1FOOT DROP =  192 FT ^3

Assuming   .40 ft^3 per MINUTE

192/.4 = 480 minutes   = 8 hours