8. You are skiing down a 1,350 meter ski slope at 60 meters per second. Let t
represent your skiing time in seconds and d(t) represent the distance from the
bottom of the ski slope.

Answer:

A postulate is a statement that is assumed true without proof. A theorem is a true statement that can be proven

Step-by-step explanation:

Answer:

Theorems and postulates are statements of geometrical truth.

Explanation:

We create theorems based on postulates.

Postulates are the mathematical statements we assume to be true without any proof while theorems are mathematical statements we can or must prove as true.

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Hope this helps!

Have a great day and God bless! :)

Answer: $5.49

Step-by-step explanation:

Unit price = 21.96/4 = 5.49

Answer: J(2,2) K(1,-1) thats all I got

Step-by-step explanation:

18 units is the distance between points F and G.

Assume a line with points marked on it.

Center is 0.

Left to the point 0 indicates negative numbers.

Right to the point 0 indicates positive numbers.

Given,

A number line is marked with negative 10 to positive 14.

Point F is placed at negative 6.

Point G is placed at positive 12.

We have to determine the distance between points F and G.

We can consider the number line.

From 0 to negative 10 there were 10 units.

From 0 to positive 14 there were 14 units.

Now points F and G,

From 0 to negative 6 there were 6 units.

From 0 to positive 12 there were 12 units.

We can add this together:

That is,

6 units + 12 units = 18 units.

Therefore, the distance between points F and G is 18 units.

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The total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.

Let the number of labels collected in the first two months be 3 x.

We are given that the number of labels collected in the first two months was three times the number of labels collected in the third month.

So, the number of labels collected in the third month = 3 x / 3 = x

Now, we are also given that:

The total number of labels collected by the students at the school = 2100.

So, we get the equation as:

3 x + x = 2100

4 x = 2100

x = 2100 / 4

x = 525 labels.

Therefore, we get that, the total number of labels collected by the students in the third month is equal to 525 by the equation 3 x + x = 2100.

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Using a proportional relationship, it is found that:

The graph for this relationship is given at the end of the answer.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

For this problem, we have that the variables are:

Hence the proportional relationship between these two variables is given by:

y = 2x.

Then:

The linear graph of the relationship, considering the given points, is given at the end of the answer.

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Using it's concept, the average rate of change is given as follows for the intervals:

a) -6 millions of dollars per year.

b) -18 millions of dollars per year.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

For item a, we have that:

Hence:

r = (366 - 372)/1 = -6 millions of dollars per year.

For item b, we have that:

Hence:

r = (318 - 372)/3 = -18 millions of dollars per year.

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The product of √6 and √12 is option b 6√2.

Given,

Two square roots : √6 and √12

We have to find the product of these square roots:

That is,

√6 × √12

Multiplying square roots:

So here,

Multiply the numbers,

√6 × √12 = 6 × 12 = 72

Now consider the square root of 72

√72 = √36 × √2 = 6√2

That is, the product of the square roots √6 and √12 is 6√2

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Answer:

100 cards?

Step-by-step explanation:

Answer: 27/45

Step-by-step explanation:

[tex]\displaystyle\\\frac{3}{5} =\\\\\frac{3}{5}*1=\\\\ \frac{3}{5}*\frac{9}{9} =\\\\\frac{3*9}{5*9}= \\\\\frac{27}{45}[/tex]

The  the savings, expressed in percent if you order the combo is 18.75%, if the combo is bought at $6.50

What is the amount saved when combo is ordered?

The amount saved when ordering for combo instead of ordering hamburger and French fries is the difference between the total cost cost when for individual orders and the cost of the combo

total cost for individual orders=$5.00+$3.00

total cost for individual orders=$8.00

combo cost=$6.50

savings on combo=total cost for individual orders-combo cost

savings on combo=$8.00-$6.50

savings on combo=$1.50

% savings on combo=$1.50/$8.00

% savings on combo=18.75%

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Answer:

-23

Step-by-step explanation:

Remember Bedmas/Pedmas

P/B = Bractets or parentheses ( )

E = Exponents 3⁵

D = Division ÷

M = Multiply ×

A = Addition

S = Subtract

(4x1)+6-9x3-6

4+6-(9×3)-6

(4+6)-27-6

(10-27)-6

-17-6

-23

Answer:

Vertex: (-1, 4)

Domain: All Real Numbers

Range: y < or equal to 4

Step-by-step explanation:

Vertex: Using my calculator, i determined the vertex. The vertex is the most bottom/top point of the parabola, depending on if it opens down or up.

Domain: All the answers have all real numbers so its obvious.

Range: the parabola opens down at (-1, 4), so all the numbers on the y axis below 4 fit in with the line

Answer:

given

Step-by-step explanation:

When doing a two-column proof, you usually begin with what you are given.

Answer:

14x

Step-by-step explanation:

We just add the bases because they have the same variable terms, (they are like terms)

9 + 5 = 14

14x

Answer:

I. 1) 32124, 32456, 32532, 32934, 32983

 2) 62279, 62312, 62345, 62387, 62398

 3) 89123, 90246, 89345, 89534, 89923

 4) 19087, 19216, 19312, 19432, 19910

 5) 31821, 31839, 31861, 31876, 31890

II. 1) 58240, 58204, 58042, 58024

  2) 10908, 10809, 10098, 10089

  3) 85703, 85370, 85307, 85073

  4) 98705, 98570, 98507, 98057

  5) 41810, 41108, 41081, 41018

Step-by-step explanation:

Step-by-step explanation:

it is always the same. the slope is (y coordinate change / x coordinate change) when going from one point on the line to another.

the direction itself does not matter, but it is important to use the same direction for the x and the y comparison.

I prefer to go from left to right, so let's go from

(-3, 4) to (2, -4).

x changes by +5 (from -3 to 2).

y changes by -8 (from 4 to -4).

the slope is

-8/+5 = -8/5

The polynomial function of least degree with only real coefficients is y = x³ - 8 · x² + 22 · x - 20.

The statement indicates that the polynomial has a leading coefficient of 1 and zeros of 2 and 3 + i. By algebra of quadratic equations, equations with real coefficients with complex roots are α + i β and α - i β. Then, all the roots of the polynomial function of least degree are 2, 3 + i and 3 - i. The complete expression is shown below:

y = 1 · (x - 2) · (x - 3 - i) · (x - 3 + i)

y = (x - 2) · [x² - 3 · x - i · x - 3 · x + i · x + (3 + i) · (3 - i)]

y = (x - 2) · (x² - 6 · x + 9 - i²)

y = (x - 2) · (x² - 6 · x + 10)

y = x³ - 6 · x² + 10 · x - 2 · x² + 12 · x - 20

y = x³ - 8 · x² + 22 · x - 20

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Explanation:

t = number of t-shirts

t = 100 shirts are in the box

Plug this into the equation and simplify to find W

W = 250+132.5t

W = 250+132.5(100)

W = 250+13250

W = 13500

The box weighs 13500 grams

This is equivalent to 13500/1000 = 13.5 kg

Using equations, the solutions for the problems are given as follows:

1. She played 5 games.

2. Gary had 7 rebounds.

3. The width of the rectangle is of 38 inches.

4. Mark had 21 rebounds.

5. Tony spent 45 minutes studying for his Biology test.

6. The length of the rectangle is of 72 inches.

7. He rented the limousine for 6 hours.

8. The two numbers are 11 and 26.

9. Pamela is 8 years old.

10. Debra is 1 year old now.

The situation is modeled by the following linear function:

P(n) = 2.75 + 4.25n.

We have that P(n) = 24, hence we have to solve for n.

24 = 2.75 + 4.25n.

n = (24 - 2.75)/4.25

n = 5.

She played 5 games.

The situation is modeled by the following system of equations:

Hence:

3y + y = 28

4y = 28

y = 7.

Gary had 7 rebounds.

Considering the equations for the perimeter of the triangle, and the situation described, we have that:

Hence:

2(2w - 4 + w) = 220

2(3w - 4) = 220

3w - 4 = 110

3w = 114

w = 114/3

w = 38.

The width of the rectangle is of 38 inches.

Solution x for item 2, hence:

x = 3y = 3 x 7 = 21.

Mark had 21 rebounds.

This situation is modeled by the following equation:

3x + 5 = 140

3x = 135

x = 135/3

x = 45.

Tony spent 45 minutes studying for his Biology test.

This is the solution for l of item 3, hence:

l = 2w - 4 = 2 x 38 - 4 = 72.

The length of the rectangle is of 72 inches.

The situation is modeled by the following equation:

P(x) = 125 + 50x.

We have that P(x) = 425, hence we solve for x as follows:

425 = 125 + 50x

50x = 300

x = 300/50

x = 6.

He rented the limousine for 6 hours.

The situation is modeled by the following system:

Hence:

15 + y + y = 37

2y = 22

y = 11.

x = 15 + 11 = 26.

The two numbers are 11 and 26.

The situation is modeled by the following system:

Hence:

x + 6 = 2(x - 7 + 6)

x + 6 = 2(x - 1)

x + 6 = 2x - 2

x = 8.

Pamela is 8 years old.

This is the solution for y of the previous item, hence:

y = x - 7 = 8 - 7 = 1.

Debra is 1 year old now.

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[tex](6d+5)-(2-3d)[/tex]

We subtract algebraic expressions exactly as we would integers, or as we would in a 'normal' subtraction sentence. First, we must open up the brackets:

[tex]= 6d+5-2+3d[/tex]

Now, combine like terms:

[tex]= 9d+5-2\\= 9d+3[/tex]

9d+3

Answer:

26

Step-by-step explanation:

[tex]FH=7+19=26[/tex]

Answer:

FH = 26

Step-by-step explanation:

The equation will be,

→ FH = FG + GH

Then the value of FH will be,

→ FH = 19 + 7

→ [ FH = 26 ]

Hence, the value of FH is 26.

Answer:

f(0) = 0

f(-2) = 0

f(5) = 15

f(-10) = 16

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

[tex]f(x)=\begin{cases} \begin{aligned}-2x-4 & \;\;\textsf {if }\;x < 0\\3x & \;\;\textsf {if }\;x\geq 0\\\end{aligned}\end{cases}[/tex]

Therefore, the function has two definitions:

When graphing piecewise functions:

First piece of the function

Substitute zero into the first function:

[tex]\implies f(0)=-2(0)-4=-4[/tex]

Place an open circle at point (0, -4).

To help graph the line, find another point on the line by inputting another value of x that is less than zero into the same function:

[tex]\implies f(-2)=-2(-2)-4=0[/tex]

Place point (-2, 0) and draw a straight line from the open circle at (0, -4) through (-2, 0).  Add an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of the function

Substitute zero into the second function:

[tex]\implies f(0)=3(0)=0[/tex]

Place an closed circle at point (0, 0).

Again, to help graph the line, find another point on the line by inputting another value of x that is more than zero into the same function:

[tex]\implies f(2)=3(2)=6[/tex]

Place point (2, 6) and draw a straight line from the closed circle at (0, 0) through (2, 6).  Add an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

To find the given functions, decide which function to use based on the given value of x, then solve.

f(0) means to find the value of the function when x = 0.

Therefore, input x = 0 into the second function as x ≥ 0.

[tex]\implies f(0)=3(0)=0[/tex]

f(-2) means to find the value of the function when x = -2.

Therefore, input x = -2 into the first function as x < 0.

[tex]\implies f(-2)=-2(-2)-4=0[/tex]

f(5) means to find the value of the function when x = 5.

Therefore, input x = 5 into the second function as x ≥ 0.

[tex]\implies f(5)=3(5)=15[/tex]

f(-10) means to find the value of the function when x = -10.

Therefore, input x = -10 into the first function as x < 0.

[tex]\implies f(-10)=-2(-10)-4=16[/tex]

- - - - - - - - - - - - - - - - - - - - - - - -

Work below!

- - - - - - - - - - - - - - - - - - - - - - - -

Simply multiply the inches by 20 (the scale per inch), and you have your answer!

3.5 x 20 = 70

The height is 70 inches.

- - - - - - - - - - - - - - - - - - - - - - - -

Good luck! :)

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~pinetreee

Answer:

70

Step-by-step explanation:

If you multiply 3.5 times 20 you get 70

Answer:

5

2

8

4

6

1

3

7

Step-by-step explanation:

Number 7:

-8=x-20

-8+20=x

12=x