Given the function h(x) = x^2 + 10x + 32, determine the average rate of change
of the function over the interval 3 < x < 11.

Answer:

Below

Step-by-step explanation:

First I found the area of the triangle on the right

A = bh/2

A = (9)(4.5) / 2

A = 20.25 ft^2

Next, the area of the rectangle in the middle

A = lw

A = (7.5)(9)

A = 67.5 ft^2

And now the area of the right triangle on the left

A = bh/2

A = (5)(9) / 2

A = 22.5 ft^2

Add em all up : 20.25 + 67.5 + 22.5 = 110.25 ft^2

Hope this helps!

Answer:x=1, y=2, z=-1

Step-by-step explanation:

x = 1; y = 2; z = -1

This involves solving simultaneous equations using elimination method.

x + y - 2z = 5  - - - (eq 1)

-x + 2y + z = 2 - - - (eq 2)

2x + 3y – z = 9 - - - (eq 3)

x + y - 2z = 5  - - - (eq 4)

-3x + 6y + 3z = 6 - - - (eq 5)

2x + 3y – z = 9 - - - (eq 6)

Add eq 4, 5 & 6 together to get;

10y = 20

y = 20/10

y = 2

-x - y + 2z = - 5  - - - (eq 7)

-x + 2y + z = 2 - - - (eq 8)

2x + 3y – z = 9 - - - (eq 9)

Add eq 7, 8 and 9 together to get;

4y + 2z = 6

From earlier, we saw that y = 2. Thus;

4(2) + 2z = 6

8 + 2z = 6

2z = 6 - 8

2z = -2

z = - 2/2

z = - 1

Putting -1 for z and 2 for y into;

x + y - 2z = 5  

Gives; x + 2 - 2(-1) = 5

x + 4 = 5

x = 5 - 4

x = 1

Thus; x = 1; y = 2; z = -1

Read more at; brainly.in/question/18335432

Answer:

either it's 1:3 or 1:6

Step-by-step explanation:

3 students went to the zoo, and 15 students went to the aquarium.

15 plus 3 is 18.

3/18 then reduces to 1/6

therefore it is:

1:6

(before, I got my answer deleted so, maybe it is 1:3, but I solved it and got 1:6)

Answer:

0.0125x or x/80

Step-by-step explanation:

Salary: x dollars per year

To find the pay per month, we divide the annual pay by 12.

The monthly pay is x/12

15% of the first month's salary is

15% of x/12 = 0.15 * x/12 = 0.0125x = x/80

Answer: 0.0125x

Answer:

Step-by-step explanation:

Given,

n = 5

and, b = 4

Equation:

n + b × 5

= 5 + 4 × 5

= 5 + 20

= 25 (Ans)

Considering only this customer's premiums, deductible, and claims, the break-even period after which the customer could make a $10,000 claim for property damage without the insurance company suffering a loss is 15 months.

At this break-even period, the company will not make a profit or a loss.

Data and Calculations:

Monthly insurance premium payable = $600 (assumed to be paid monthly)

Deductible on the insurance policy = $1,000

Minimum coverage = 30/50/10

Coverage for injury or death to one person = $30,000

Coverage for injury or death to two or more people = $50,000

Coverage for damage to property = $10,000

Average accidents every year = 2

Total claims cost to the insurance before deductibles = $40,000 ($30,000 + $10,000)

Break-even period = 15 ($10,000 - $1,000)/$600

This break-even period is computed by deducting the deductible from the claim that the customer makes, and then dividing the result by the monthly insurance premium.

Thus, the customer could make a $10,000 claim for property damage without the insurance company suffering a loss after 15 months' break-even period.  

Learn more about break-even here: https://brainly.com/question/22875945

Answer:

x-4

Step-by-step explanation:

If x>4, |x-4|>0 which means |x-4|=x-4

Answer:

Step-by-step explanation:

Relations are only functions if they do not share any x values at all! The 2 graphs there that do not have any of the same x values are graphs A and D. Notice that on graph B, there are several y values that share the x value of 2; on graph C, there are several y values that share the x value of 2.

Answer:

A and D only

Step-by-step explanation:

A function is a relation where each input has its own output ( each x values has its own corresponding y value ) If an input has more than one output than the relation is not a function.

We can tell if a graph shows a function or not by using the vertical line test. If you draw vertical lines on the graph and more than one point is on the vertical line drawn then the graph does not show a function.

For graph B if you draw a vertical line at x = -2 more than 1 point will be on the line meaning that the graph does not show a function.

For Graph C if you draw a vertical line at x = 2 more than 1 point will be on the line meaning that Graph C also does not show a function.

For Graphs A and D you can draw a vertical line anywhere on the graph and no more than 1 point will be on the line therefore Graphs A and D show functions.

Answer:

1)9 2)18 3)9. 4)4. 5)carpeting

Step-by-step explanation:

1) divide 63 by 7 = 9

2)multiply 54 by 2 = 108 total weight of the boxes then divide 108 by 6 to get 18

3) 75 -30 to get remaining amount which is 45 then divide by 5 to get how much he will pay each month which is 9

4 24- 12= 12 the remaining for the 3 and divide by 3 to get 4

5) multiply 6 * 9 which is $54 which is cheaper than the $81

Answer:

These two triangles are similar triangles. This means that their side lengths are proportional to each other.

Thus, making line segment EC equal to "x", and BC equal to "y" we can write:

8/y = 28/(10+y)

The next step is to get rid of the fractions, which can be done by cross multiplying.

So we have:

8(10+y) = 28(y)

After distribution and some simplification, you should get the value of y.

80+8y = 28y

80 = 20y

80/20 = 20y/20

4 = y

y = 4

Knowing that y = BC, and y = 4, it is clear that BC = 4.

Since BC = 4, one can use the Pythagorean Theorem to solve for segment EC.

Pythagorean Theorem: a^2 + b^2 = c^2, where a and b are the side lengths of a right triangle, and c is the hypotenuse (in other words the longest side)

In our case, a and  b are 8 and 4 (the order doesn't really matter here).

So we have: 8^2 + 4^2 = c^2

64 + 16 = c^2

80 = c^2

c = sqrt 80

c  = 4 sqrt 5

And we arrive at the answer- EC = 4 sqrt 5, making B the correct choice.

Hope this helps!

Answer:

x=4

Step-by-step explanation:

First find the slope

m = ( y2-y1)/(x2-x1)

   = ( -6-5)/(4-4)

  = -11/0

This means the slope is undefined

Then means it is a vertical line

Vertical lines are in the form

x = constant

The constant in this case is the x value of the points

x=4

Answer:

8^18

Step-by-step explanation:

We know that a^b ÷ a^c = a^(b-c)

8^15÷8^−3

8^(15 - -3)

8^(15+3)

8^18

Answer:

4

Step-by-step explanation:

1)

-2x - 5 = x - 17

-2x - 5 + 5 = x - 17 + 5

* cancel out 5 on each side of equal sign.

2)

-2x = x - 12

-2x - x = x - x - 12

* cancel out x on each side of equal sign.

3)

-3x = -12

-3x/ -3 = -12/-3

* cancel out -3x on each side of equal sign.

4) Simplify

x = 4

Hope this helps, good luck! :)

Have a great day!!

Answer:

2 [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

5 ÷ 4 = 1 [tex]\frac{1}{4}[/tex]

1 [tex]\frac{1}{4}[/tex] × 2 = 2 [tex]\frac{2}{4}[/tex] = 2 [tex]\frac{1}{2}[/tex]

5 - 2 [tex]\frac{1}{2}[/tex] = 2 [tex]\frac{1}{2}[/tex]

respuesta: 2 [tex]\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

The supplement of the exterior angle is 180 - 75 = 105

In a cyclic quadrilateral (a four sides figure where all the vertices touch the circumference of a circle), the opposite angles are supplementary. Therefore <a = 180 - 105 = 75

But I think you already knew that.

Answer:

x = -0.5

Step-by-step explanation:

x + 0.25 = -0.25

x = -0.25 - 0.25

x = -0.5

Hi there!  

»»————-　★　————-««

I believe your answer is:  

Option A

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Option A:}}\\\\3^{-5}\\\\\rightarrow \frac{1}{3^5}\\\\\rightarrow \frac{1}{243}\\\\\ \text{This is \textbf{NOT} an integer.}}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Option B:}}\\\\-3^5\\\\\rightarrow -3 * -3 * -3 * -3 * -3 \\\\\rightarrow \boxed{-243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]

⸻⸻⸻⸻

[tex]\boxed{\text{Option C:}}\\\\\frac{1}{3}^{-5} \\\\\rightarrow \frac{1}{(\frac{1}{3})^5}\\\\\rightarrow \frac{1}{\frac{1}{243} }\\\\\rightarrow \boxed{243}\\\\\\\text{This \textbf{IS} an integer.}[/tex]

⸻⸻⸻⸻

[tex]\text{Option \textbf{A} does not simplify into an integer.}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

x + 20 = 72

x + 20 - 20 = 72 - 20

x = 52

Answer:

x=52

Step-by-step explanation:

The exterior angle of the triangle is equal to the sum of the opposite interior angles

72 = 20+x

72-20 = 20+x-20

52 =x

Answer:

x = 0

Step-by-step explanation:

Since the points are collinear , then

AB + BC = AC , that is

11 + 2x + 10 = x + 21

2x + 21 = x + 21 ( subtract x from both sides )

x + 21 = 21 ( subtract 21 from both sides )

x = 0

Answer:

0.000000047

Step-by-step explanation:

I have to give 2 Ans form my question so sorry

Answer:

Step-by-step explanation:

whole number with the occasional jump into rational numbers when a down like 2nd and 5 1/2 to go.

Answer:

2x+1

Step-by-step explanation:

f(x) = x + 1

g(x) = 2x

f(g(x)) = Replace x in the function f(x) with the function g(x)

f(g(x)) = g(x) +1

         = 2x+1

Answer:

f(g(x)) = 2x + 1

Step-by-step explanation:

Substitute x = g(x) into f(x) , that is

f(g(x))

= f(2x)

= 2x + 1

Answer:

99

Step-by-step explanation:

If you like my answer than please mark me brainliest

Answer: 99

Step-by-step explanation:

please click thanks and mark brainliest if you like :)

Answer:

height, x is 235 ft

Step-by-step explanation:

From trigonometric ratios:

[tex] \cos( \theta) = \frac{adjacent}{hypotenuse} [/tex]

but:

[tex] \theta = 90 \degree - 36 \degree \\ \theta = 54 \degree[/tex]

adjacent is x

hypotenuse is 400 ft

[tex] \ \cos ( 54 \degree) = \frac{x}{400} \\ \\ x = 400 \ \cos (54 \degree) \\ x = 235 \: \: feet[/tex]

Answer:

[tex]235\ ft[/tex]

Step-by-step explanation:

In this problem, one is given two parallel lines and a few transversals that form a triangle between these parallel lines. The parallel lines, one from the parasailer, and one from the boat have an angle of depression between them. This means the angle of elevation from the boat to the parasailer is also (36) degrees. This is due to the alternate interior angles theorem, which states that when two parallel lines are intersected by a transversal, then the alternate interior angles are congruent.

The triangle formed in this situation is a right triangle, this is indicated by the box around one of the angles. Now that one has found another angle measure in this triangle, one can use right angle trigonometry. Right angle trigonometry is a series of ratios that describe the relationship between the sides and angles of a right triangle. These ratios are as follows:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]

Please note that the names (opposite) and (adjacent) are subjective, and change relative to the angle one is looking at, however (hypotenuse) refers to the side opposite the right angle. This side doesn't change its name. In this situation, it would be most logical to use the ratio of sine, (sin), as one has the measure of the hypotenuse, and one is trying to find the measure of the side opposite the angle. Substitute the given information into the ratio of (sin) and solve to find the unknown:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]sin(36)=\frac{x}{400}[/tex]

Inverse operations,

[tex]sin(36)=\frac{x}{400}[/tex]

[tex]400(sin(36))=x[/tex]

[tex]235.114=x[/tex]

Answer:

27 cubic meters

Step-by-step explanation:

For square, length and width is same.

3x3 = 9 square meters

3x3x3 = 27 cubic meters

Volume of a cube = length · width · height, or:

Volume of a cube = length³

We know that a cube is made up of 6 squares, so if the area of one of the squares is 9, we can take the square root to find the sides:

√9 = ±3

(and in this case, you can't have negative measurements, so it's positive.)

Now, all we have to do is cube the side length, so:

3³ = 27.

If you have any questions, feel free to ask! :)

Answer:

15/40

Step-by-step explanation:

[tex]0.375 = \frac{375}{1000} \\ \\ = \frac{15}{40} [/tex]

Answer:

25

Step-by-step explanation:

product of 18 and -3=18*-3= -54

positive difference=52-29=23

(18x-3)+56+(52-29)

= -54 + 56 + 23

=25