Write the equation of the line that passes through (5, 6) and (8, 4) in slope-intercept form.

Finding the proportionality constant :

Finding y when x = 17 :

The value of y is 8/17 when x = 17.

The average rate of change of the function is -35/16.

We have to determine the average rate of change of the function f(x) on the interval -8 ≤ x ≤ 8.

so

at x₁ = -8, f(x₁) = f(-8) = 30

at x₂ = 8, f(x₂) = f(8) = -5

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]  

                     = [f(8) - f(-8) ] / [8-(-8)]

                     = [-5 - (30)] / [16]

                     = [-35] / 16

Therefore, the average rate of change of the function is -35/16.

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Answer:

3 pairs

Step-by-step explanation:

10% of 7.50 is 0.75. So one pair will cost $8.25. Now, 25.86/8.25 and you get 3 pairs

Answer:

[tex]\fbox {3 pairs}[/tex]

Step-by-step explanation:

Cost of 3 pairs with tax :

⇒ 7.50 × 3

⇒ 22.50

* Adding tax *

⇒ 22.50 + 22.5 (0.1)

⇒ 22.50 + 2.25

⇒ 24.75

∴ Since 24.75 is less than 25.86, Jean can buy 3 pairs of shoes.

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

Work Shown:

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (2,6,4,8) = \frac{2*6 + 4}{8}\\\\\perp (2,6,4,8) = \frac{12 + 4}{8}\\\\\perp (2,6,4,8) = \frac{16}{8}\\\\\perp (2,6,4,8) = 2\\\\[/tex]

Let m = 2 so we can use this result later.

[tex]\perp (q,r,s,t) = \frac{qr + s}{t}\\\\\perp (4,7,2,6) = \frac{4*7 + 2}{6}\\\\\perp (4,7,2,6) = \frac{28 + 2}{6}\\\\\perp (4,7,2,6) = \frac{30}{6}\\\\\perp (4,7,2,6) = 5\\\\[/tex]

Let n = 5 so we can use this result later.

Add the two results.

m+n = 2 + 5 = 7.0 is the final answer.

Answer:

y = 4x - 12

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

[(27divided by (-3)-9] divided by [15-21}

=[-9-9] divided by 3

= 6divided by 3 = 2

Answer:

you have jbjhgbjhih7g6ginyfygino

follow p

Answer:

x=65

Each NBA team can have a maximum of 15 players, 13 of which can be active each game.

65/5=13 so it's safe to say tgat 5 team can be crated

Step-by-step explanation:

x/5-2=11-->transposing x/5=11+2---->x=13×5--->x=65

verification 65/5-2=11--->13-2=11

Answer:

D

Step-by-step explanation:

The graph in the picture given is obviously a function of f(x) = x^3 which answers whether the graph is a function or not. In addition, the answer the part on why it's a graph, it's because it passes the vertical line test.

Answer:

36

Step-by-step explanation:

when solving for two variables, we need to find one variable in terms of the other.

so, we can turn:

x - y = 5

into

x - y = 5

  + y    + y

x = y + 5

Then, we can substitute "x" in the given equation with "y + 5"

  x² - y² = 30

 (y+5)² - y² = 30

(y + 5)(y + 5)

F: y²    O:  +5y    I:   +5y  L:  25   {foil}

y² + 10y + 25 - y² = 30          {cancel y² - y²}

10y + 25 = 30

      -25      -25

10y  = 5

÷10    ÷10

y = 0.5

x = y + 5

x = 0.5 + 5

x = 5.5

check:

(5.5)² - (0.5)²

30.25  - 0.25 = 30

30 = 30

(TRUE)

now, we must find the value of:

(5.5 + 0.5)²

= (6)²

= 36

So, the value of (x + y)² is found to be 36

hope this helps!!

Answer:

(x + y)² = 36

Step-by-step explanation:

x² - y² ← is a difference of squares and factors as

(x - y)(x + y) , then

5(x + y) = x² - y² = 30 ( divide both sides by 5 )

(x + y) = 6 , then

(x + y)² = 6² = 36

Answer:

-7,-6,-5 are the values when x=0,1,2

Step-by-step explanation:

please mark me as brainlest

Answer:

Step-by-step explanation:

y =x - 7

Substitute x = 0 and find the y-value

       y = 0 - 7

      y = -7

(0,-7)

Substitute x = 1,

    y = 1 - 7

    y = - 6

(1,-6)

Substitute x = 2,

        y = 2 - 7

       y = -5

(2,-5)

Answer:

75 Seconds

Step-by-step explanation:

First divide 90,000 by 16 then square root that answer for 75 and when you plug it in you'll end up with -90,000 + 90,000

Answer:

45/32 or 1.40

Step-by-step explanation:

Answer:

3 9/32 or 105/32

Step-by-step explanation:

2 1/2 = 5/2, 1 3/4 = 7/4

5/2 * 7/4 = 35/8

35/8 * 3/4 = 105/32

105/32 = 3 9/32

Brainliest, please :)

The percentage of employees with 8 or more years at the company reported that email is their preferred method of communication  is 20.48%

The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.

See attachment

What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?

A. 44.79% B. 20.48% C. 48.84% D. 67.19%

From the attached image, we have:

Email 8 or more  =  43

The total number of employees in the company is

Total = 210

So, the percentage that prefers email is

Percentage = 43/210 * 100%

Evaluate

Percentage = 20.48%

Hence, the percentage of employees is 20.48%

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Step-by-step explanation:

Step 1: Setting Up the Factors

Our roots are 3, 2, and -4 so

our factors are

[tex](x - 3)(x - 2)(x + 4)[/tex]

Step 2: Initial Test to see if the result equal 30

Let a be a constant, such we have

[tex]a(x - 3)(x - 2)(x + 4) = 30[/tex]

Plug in. 1 for x.

[tex]a(1 - 3)(1 - 2)(1 + 4) = 30[/tex]

[tex]a( - 2)( - 1)(5) = 30[/tex]

[tex]a(10) = 30[/tex]

[tex]a = 3[/tex]

So our equation is

[tex]3(x - 3)(x - 2)(x + 4)[/tex]

Or if you want it simplifed

[tex]3( {x}^{2} - 5x + 6)(x + 4) = 3( {x}^{3} + - {x}^{2} - 14x + 24) = 3 {x}^{3} - 3 {x}^{2} - 42x + 72[/tex]

Answer:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

Step-by-step explanation:

General form of a cubic polynomial function with 3 roots:

[tex]f(x)=a(x-b)(x-c)(x-d)[/tex]

where:

Given roots:

Substitute the given roots into the general form of the function:

[tex]\implies f(x)=a(x-3)(x-2)(x-(-4))[/tex]

[tex]\implies f(x)=a(x-3)(x-2)(x+4)[/tex]

To find the value of a, substitute the given point (1, 30) into the equation:

[tex]\begin{aligned} f(1) & = 30\\\implies a(1-3)(1-2)(1+4) & =30\\a(-2)(-1)(5) & = 30 \\10a & = 30\\\implies a & = 3 \end{aligned}[/tex]

Therefore, the equation of the cubic polynomial function is:

[tex]f(x)=3(x-3)(x-2)(x+4)[/tex]

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Answer: I love the picture example

Step-by-step explanation:

We will first find the heigh of the kite from his hand to a point in the air.

Then, we will add 3 feet to the result.

So, how to find the vertical line of the right triangle?

Well, we have the vertical line = x

We also got the hypothenuse, equal to 100 feet

And also theta, equal to 25 degrees.

We can calculate sine because the sine of 25 degrees = opposite side (the height line) over (divided by) the hypothenuse

sin(25) = x/100 feet

multiply 100 feet on both sides, to cancel to 100 feet on the right side.

100sin(25) = x

100(0.442) = x

x = 42.2  feet

Height = 42.2 + 3 feet (the yoda's hand =) =  45.2 feet (total)

Rounded to the nearest tenth.

I also did the verification, so it is the correct answer.

Easy as that =]]

Height of the kite from 3ft above the ground

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sin25=\dfrac{P}{100}[/tex]

[tex]\\ \rm\Rrightarrow P=100sin25[/tex]

[tex]\\ \rm\Rrightarrow P=42.26\approx 42ft[/tex]

Height from the ground

The value of x in the triangle to the nearest tenth is calculated as; 1.1

We have different trigonometric ratios such as;

sin θ = opp/hyp

cos θ = adj/hyp

tan θ = opp/adja

Thus, from the given triangle we can use the formula for cos θ to get the value of x. Thus;

cos 41° = 0.8/x

x = 0.8/cos 41

x = 1.06

To the nearest tenth, we have x = 1.1

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Answer: -1(x+2)^2+10

Step-by-step explanation:

1. The coefficient of -x^2 is just the number in front, which in this case would be a = -1 So now the function is -1(x^2+4x)+6 since negative one has been factored out of the first two terms.

2. Half of the coefficient of x would be 2 since x has a coefficient of 4, and half pf 4 is 2. Squared, it is 4. That will be added inside the bracket. Subtracted on the outside is the same equation but multiplied by a, which we found out was -1 in the beginning. So, the function becomes -1(x^2+4x+4)+6-(-4).

3. Factor the inside equation to find that it’ll become (x+2)^2, and simplify the outside to get 10. The function will now be;

f(x)=-1(x+2)^2+10

Hope that made sense and make sure to check just in case I did the math wrong :]

a)QM and PM

b)QMN and NMQ

c)M

Answer:

x = 2, y = 1 or (2, 1)

Step-by-step explanation:

Solving by elimination method :

The solution is : x = 2, y = 1 or (2, 1)

An expression is defined as a set of numbers, variables, and mathematical operations. The total number of students is 54.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Let the number of columns in the rollercoaster be represented by x.

If students sit 4 per row on a rollercoaster, 6 students are left without a seat. Therefore, the number of students can be written as,

Total number of students = 4x + 6

If they sit 6 per row, there are 3 rows left empty. Therefore, the total number of students can be written as,

Total number of students = 6(x-3)

The total number of students can be written as,

4x + 6 = 6(x - 3)

4x + 6 = 6x - 18

2x = 24

x = 12

Now, the total number of students in the class are,

4x + 6 = 4(12) + 6 = 54

Hence, the total number of students are 54.

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Answer:

[tex]\fbox {x = 2}[/tex]

Step-by-step explanation:

Given :

14x - 12 = 16

Add 12 to each side :

14x - 12 + 12 = 16 + 12

14x = 28

Divide each side by 14 :

14x/14 = 28/14

x = 2

We need radius

Now

LSA

Answer:

813.4 cm² (nearest tenth)

Step-by-step explanation:

Volume of a cylinder

[tex]\sf V=\pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Given:

Use the Volume of a Cylinder formula and the given values to find the radius of the cylinder:

[tex]\implies \sf 1715=\pi r^2 (18)[/tex]

[tex]\implies \sf r^2=\dfrac{1715}{18 \pi}[/tex]

[tex]\implies \sf r=\sqrt{\dfrac{1715}{18 \pi}[/tex]

Surface Area of a Cylinder

[tex]\sf SA=2 \pi r^2 + 2 \pi r h \quad\textsf{(where r is the radius and h is the height)}[/tex]

Substitute the given value of h and the found value of r into the formula and solve for SA:

[tex]\implies \sf SA=2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)^2 + 2 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)(18)[/tex]

[tex]\implies \sf SA=2 \pi \left(\dfrac{1715}{18 \pi} \right) + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]

[tex]\implies \sf SA=\dfrac{1715}{9} + 36 \pi \left(\sqrt{\dfrac{1715}{18 \pi}\right)[/tex]

[tex]\implies \sf SA=813.3908956...[/tex]

Therefore, the surface area of the cylinder is 813.4 cm² (nearest tenth)

Answer:

D

Step-by-step explanation:

- 0.06 + 7.6p < - 127.74 ( add 0.06 to both sides )

7.6p < - 127.68 ( divide both sides by 7.6 )

p < - 16.8