1) Anna and Jason have summer jobs stuffing envelopes for two different companies. Anna earns $20 for every 400 envelopes she finishes. Jason earns $10 for every 250 envelopes he finishes.

A) Create tables, draw graphs, and write equations that show the earnings, y, as functions of the number of envelopes stuffed, x, for both Anna and Jason.

B) Who makes more from stuffing the same number of envelopes? Explain how you know using the information above.

C) Anna has savings of $100 at the beginning of the summer and she saves all of her earnings from her job. Graph her savings as an equationof the number of envelopes she’s stuffed, n. How does this graph compare to her previous earnings graph? What is the meaning of the initial value and slope in each case?

D)You survey 6 other employees and findthe following data on envelopesstuffed (x) and dollars earned(y). Plot a trend lineon the graph. Find the equation of the trend line.

Answer:

[tex]301.29\ \text{mph}[/tex]

[tex]119.5^{\circ}[/tex]

Step-by-step explanation:

[tex]v_p[/tex] = Velocity of plane = 320 mph

[tex]v_w[/tex] = Velocity of wind = 35 mph

[tex]\theta[/tex] = Angle between wind and plane directions = [tex]125^{\circ}[/tex]

From triangle law we have resultant

[tex]v_r=\sqrt{v_p^2+v_w^2+2v_pv_w\cos\theta}\\\Rightarrow v_r=\sqrt{320^2+35^2+2\times 320\times 35\cos125^{\circ}}\\\Rightarrow v_r=301.29\ \text{mph}[/tex]

Direction is given by

[tex]\phi=\tan^{-1}\dfrac{v_p\sin\theta}{v_w+v_p\cos\theta}\\\Rightarrow \phi=\tan^{-1}\dfrac{320\sin125^{\circ}}{35+320\cos125^{\circ}}\\\Rightarrow \phi=-60.46^{\circ}=180-60.46=119.5^{\circ}[/tex]

The magnitude of the plane is [tex]301.29\ \text{mph}[/tex] moving at an angle of [tex]119.5^{\circ}[/tex].

Step-by-step explanation:

x² + 9x < -20

x² + 9x + 20 < 0

(x + 4)(x + 5) < 0

Therefore -5 < x < -4 / (-5,-4)

Answer:

option B

Step-by-step explanation:

[tex](a+b)^4\\\\=(a+b)^2(a+b)^2\\\\=(a^2+2ab+b^2)(a^2+2ab+b^2)\\\\=a^2(a^2+2ab+b^2)\\\\+2ab(a^2+2ab+b^2)\\\\+b^2(a^2+2ab+b^2)\\\\=a^4+2a^3b+a^2b^2\\\\+2a^3b+4a^2b^2+2ab^3\\\\+a^2b^2+2ab^3+b^4\\\\=a^4+4a^3b+6a^2b^2+4ab^3+b^4[/tex]

Answer:

D. (-3;-3)

Step-by-step explanation:

2x-3y<9

A. 2×6-3×(-4)=24 FALSE, because 24>9

B. 2×(-1)-3×(-9)=25 FALSE, because 25>9

C. 2×2-3×(-5)=11 FALSE, because 11>9

D. 2×(-3)-3×(-3)=9 TRUE, because 3<9

Answer:x = -4

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

6*x+6-3*(x-2)-(x+4)=0

Step by step solution :

STEP

1

:

Equation at the end of step 1

((6x + 6) - 3 • (x - 2)) - (x + 4) = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2x + 8 = 2 • (x + 4)

Equation at the end of step

3

:

2 • (x + 4) = 0

STEP

4

:

Equations which are never true:

4.1 Solve : 2 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation:

4.2 Solve : x+4 = 0

Subtract 4 from both sides of the equation :

x = -4

Answer:

-5, -2, 1, 3.

Step-by-step explanation:

This is how you would put them in order from least to greatest.

Answer:

-5,-2,1,3

Step-by-step explanation:

Hope it helps

Answer:

10

Step-by-step explanation:

Using Euler's formula for polyhedra

F + V - E = 2

Here V = 16 and E = 24, thus

F + 16 - 24 = 2, that is

F - 8 = 2 ( add 8 to both sides )

F = 10

Answer:

b

Step-by-step explanation:

on edge 2021

Answer:

[tex]4[/tex]

Step-by-step explanation:

The line passes through points [tex](2,0)\,,\,(0,2)[/tex]

Let [tex](x_1,y_1)=(2,0)\,,\,(x_2,y_2)=(0,2)[/tex]

Equation of a line passing through points [tex](x_1,y_1)\,,\,(x_2,y_2)[/tex] is given by [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

[tex]y-0=\frac{2-0}{0-2}(x-2)\\y=\frac{2}{-2}(x-2)\\y=-1(x-2)\\y=-x+2[/tex]

So,

[tex]f(x)=y=-x+2[/tex]

Put [tex]x=-2[/tex]

[tex]f(-2)=-(-2)+2=2+2=4[/tex]

Answer: Scale Factor = 1/4

Step-by-step explanation:

The base of triangle X has a length of 12, and the base of triangle x' has a length of 3. Therefore, the scale factor is 1/4, because 12 x 1/4 = 3.

Answer:

[-9,-4]

Step-by-step explanation:

The highest and lowest points this graph gets to on the y axis are -4 and -9 respectively.

This means the range is [-9,-4].

Brackets are used since -9 and -4 are seemingly included.

Answer:

1/3

Step-by-step explanation:

Answer:

it is 1/3

Step-by-step explanation:

it's 1/3 because 1/2 times 2/3 equals 2/6 and you can divide 2 by 2 to get 1 and 6 by 2 to get 3 so the answer is 1/3

Step-by-step explanation:

[tex]v = \pi \times r {}^{2} \times h \div 3 \\ = \pi \times 2 {}^{2} \times 10 \div 3 \\ = 41.8[/tex]

Answer:

Given that V=πr^2h/3

Where V is unknown

π=3

d=4; r=4/2=2

h=10

Substitute the values

V=3×2×2×10 ÷ 3

V= 120÷3

V= 40

Answer:

0.16 tons

Step-by-step explanation:

Answer:

[tex]32 {x}^{5} + 240 {x}^{4} + 720 {x}^{3} + 1080 {x}^{2} + 810x + 243[/tex]

Answer:

y=x+2

Step-by-step explanation:

the standard form is y=mx+b where m is the slope and b is the y intercept

TO FIND THE SLOPE: we take the x and y intercepts as a fraction. in this case the line touches the y axis (vertical) at point/value 2 and the x axis at point 2 as well. This means the slope is 2/2x which can be simplified to 1x or just x.

TO FIND THE Y INTERCEPT: we find where the line touches the y axis at point 2.

the slope is plugged into the m of the equation and the y intercept is plugged into the b of the equation.

Answer:

Step-by-step explanation:

2x + 5y = 1     ⇒    2x = 1 - 5y

y = 2xy + 5

y = (1 - 5y)y + 5

y = y - 5y² + 5

5y² = 5

y² = 1

 y₁ = 1               ∨           y₂ = -1

2x₁ = 1 -5(1)                   2x₂ = 1 - 5(-1)

2x₁ = 1 - 5                      2x₂ = 1 + 5

2x₁ = -4                         2x₂ = 6

 x₁ = -2                           x₂ = 3

Midpoint:

[tex]M=\left(\frac{x_1+x_2}2\ ,\ \frac{y_1+y_2}2\right)=\left(\frac{-2+3}2\ ,\ \frac{1+(-1)}2\right)=\left(\frac12\ ,\ 0\right)[/tex]

The coordinates of the midpoint of the line AB is (0, 1/2).

The equation of the curve is given by y = 2xy + 5.

The equation of the line is given by 2x + 5y = 1.

We have to first find the point of intersection between the curve and the line and then find the coordinates of the midpoint of line AB where A and B is the point of intersection between the curve and the line.

If C(x, y) divides a line AB in m:n then we have,

[tex]x = \frac{mx_2 +nx_1}{m+n},~~~y =\frac{my_2+ny_1}{m+n}[/tex]

And if C(x,y) is the midpoint then m = n.

we have,

[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}[/tex]

Where x and y are the coordinates of the midpoint o the line AB.

Find the point of intersection between the line and the curve.

y = 2xy + 5............(1)

2x + 5y = 1..............(2)

From (2) we have,

2x = 1 - 5yx = (1-5y) / 2..........(3)

Substituting (3) in (1).

[tex]y =2\frac{(1-5y)}{2}y + 5\\\\y =\frac{2y-10y^2}{2} + 5\\\\2y = 2y - 10y^2 + 10\\\\10y^2 = 10\\\\y^2 = 1[/tex]

So we have,

y = 1 and y = -1

Puttin y = 1 in (3) we get,

x = (1 - 5) / 2 = - 4 / 2 = -2

Puttin y = -1 in (3) we get,

x = {1-5(-1)} / 2 = (1+5) / 2 = 6 / 2 = 3

Now we have two points of intersection A( 1, -2 ) and B( -1, 3 ).

Finding the coordinates of the midpoint of the line AB.

we have,

[tex]A(1, -2) = A (x_1, y_1)~~and~~B(-1, 3) = B(x_2, y_2)[/tex]

Substituting in the given equation.

[tex]x = \frac{x_2 +x_1}{2},~~~y =\frac{y_2+y_1}{2}\\\\x = \frac{-1 +1}{2},~~~y =\frac{3+(-2)}{2}\\\\x = 0,~~~y=\frac{1}{2}[/tex]

So the coordinates of the midpoint is (x,y) = ( 0, 1/2 ).

Learn more about the midpoint of a given line here:

https://brainly.com/question/24493570

#SPJ2

Answer:

128 and can I get brainliest

Step-by-step explanation:

180-95 = 85

85 plus 43 = 128

180 - 128 = 52

180-52 = 128

Answer:

y=128

Step-by-step explanation:

The exterior pleus interior angle makes a 180 degree

so 180-95=85

now the interior angles of a triangle add up to 180

so the in triangle

get 43+85+?=180

180-85-43=52

nowing this we need to find the exterior angle unlike the first we are given the interior not the exterior but same process goes

180-52=128

y=128

Answer:

The coordinates of Y' will be:  A'(4, -3)

Step-by-step explanation:

Triangle XYZ with vertices

We have to determine the answer for the image Y' of the point Y(-3, 4) with respect to the line mirror y=x.

We know that when P(x, y) is reflected in y = x, we get P'(y, x)

i.e.

The rule of y=x:

As we are given that Y(-3, 4), so the coordinates of Y' will be:

A(-3, 4) → A'(4, -3)

Therefore, the coordinates of Y' will be:  A'(4, -3)

Answer:

Step-by-step explanation:

Equation of the quadratic function given as,

g(x) = [tex]\frac{1}{3}(x-6)^2+1[/tex]

Since, leading coefficient of the function is positive,

Parabola will open upwards.

For x- intercepts,

g(x) = 0

[tex]\frac{1}{3}(x-6)^2+1=0[/tex]

(x - 6)² = -3

(x - 6) = ±√(-3)

x = 6 ± √(-3)

Since, x is an imaginary number, this function has no x-intercepts.

Similarly, for y-intercept,

x = 0

g(0) = [tex]\frac{1}{3}(0-6)^2+1[/tex]

      = 12 + 1

      = 13

y-intercept of the function → y = 13

Vertex of the parabola → (6, 1)

For x = 12,

g(12) = [tex]\frac{1}{3}(12-6)^2+1[/tex]

        = 13

Therefore, one point lying on the graph will be (12, 13).

Now we can graph the quadratic function given in the question.

Answer:

Step-by-step explanation:

Refer to attached table for inputs

Below equation is for total time traveled (middle column of table). Solving for x:

Speed of wind is 6 miles per hour

Answer: 3√2

√3 . √6 = √(3.6) = √(9.2) = √(3².2) = 3√2

Step-by-step explanation:

Answer:

b = 3

Step-by-step explanation:

[tex] \sqrt{6} [/tex]can be written as [tex] \sqrt{3} \times \sqrt{2} [/tex]

So, lets arrange it.

[tex] \sqrt{3} \times \sqrt{6} = \sqrt{3} \times \sqrt{3} \times \sqrt{2} = 3 \sqrt{2} [/tex]

Hence b = 3.

Answer:

28 units

Step-by-step explanation:

Since the perimeter of both triangles is same,

the sum of all sides of first triangle = sum of all sides of second triangle

or, 6x + 3 + 2x + 4x = 5x + 5x + 3x + 2

or, 12x + 4 = 13x + 2

or, 4-2 = 13x - 12x

or, 2 = x

Now,

Putting the value of x in the perimeter of first triangle,

12x + 4= 12* 2+ 4

= 28 units

Answer:

is it 3.00

Step-by-step explanation:

Answer:

0.625.

Step-by-step explanation:

To find the decimal of what Margo spent we have to divide the part ($5.00) by the whole ($8.00). Like this:

(5)/(8) = 0.625

Therefore, the decimal that represents the fraction is 0.625.

I hope this helps!!

- Kay :)

Answer: 24 servings

Step-by-step explanation:

First and foremost, we should note that:

4 cups = 1 quart

Therefore, 3 quarts = 3 × 4 cups = 12 cups

Since she uses 5 cups of milk to make 10 servings, it means that 1 cup of milk is used to make 2 servings. Therefore, 12 cups would be used to make:

= 12 × 2

= 24 servings.