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Find the co-interior angle measurements for the measured angle.

Thanks! :)

a) The area within the region is [tex]\frac{16}{3}[/tex].

b) The volume of the solid [tex]S[/tex] is [tex]\pi[/tex] cubic units.

c) The volume of the solid of revolution is [tex]\frac{164}{3}\pi[/tex] cubic units.

a) The region is bounded between [tex](0,0)[/tex] and [tex](2, 4)[/tex], the area of the region is defined by the following integral formula:

[tex]A = \int\limits^{b}_{a} {[g(x)-f(x)]} \, dx[/tex]   (1)

Where:

If we know that [tex]f(x) = x^{2}[/tex], [tex]g(x) = 4[/tex], [tex]a = 0[/tex] and [tex]b = 2[/tex], then the area within the region is:

[tex]A = \int\limits^{2}_{0} {4-x^{2}} \, dx[/tex]

[tex]A = \frac{16}{3}[/tex]

The area within the region is [tex]\frac{16}{3}[/tex]. [tex]\blacksquare[/tex]

b) The volume of the solid [tex]S[/tex] is determined by the following integral formula:

[tex]V = \frac{\pi}{8} \int\limits^2_0 {x^{2}} \, dy = \frac{\pi}{8} \int\limits^2_0 {x^{2}\cdot (2\cdot x)} \, dx = \frac{\pi}{4}\int\limits^2_0 {x^{3}} \, dx[/tex]

[tex]V = \pi[/tex]

The volume of the solid [tex]S[/tex] is [tex]\pi[/tex] cubic units. [tex]\blacksquare[/tex]

c) The solid of revolution around an axis parallel to the [tex]x[/tex]-axis is described by the following formula:

[tex]V = \pi \int\limits^b_a {[[f(x)-k]^{2}-[g(x)-k]^{2}]} \, dx[/tex]   (2)

Where [tex]k[/tex] is the y-coordinate of the axis of revolution.

If we know that [tex]f(x) = x^{2}[/tex], [tex]g(x) = 4[/tex], [tex]k = 7[/tex], [tex]a = 0[/tex] and [tex]b = 2[/tex], then the volume of the solid of revolution is:

[tex]V = \pi\int\limits^2_0 {[(x^{2}-7)^{2}-(4-7)^{2}]} \, dx[/tex]

[tex]V = \frac{164}{3}\pi[/tex]

The volume of the solid of revolution is [tex]\frac{164}{3}\pi[/tex] cubic units. [tex]\blacksquare[/tex]

To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504

Answer:

B and D both have a proportional relationship

Step-by-step explanation:

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Your Welcome :)

The equation that could be used to find the length of the tomato patch is 0 = 3x² + 17x -160 option (A) is correct.

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral.

It is defined as the area occupied by the rectangle in two-dimensional planner geometry.

The area of a rectangle can be calculated using the following formula:

Rectangle area = length x width

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex]  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

From the question:

The area of the vegetable garden = 170 square feet

The quadratic equation:

0 = 3x² + 17x -160

D = 2209

D > 0

The positive root of the quadratic equation is:

x = 5 ft (length of the tomato patch)

Thus, the equation that could be used to find the length of the tomato patch is 0 = 3x² + 17x -160 option (A) is correct.

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Answer:

I don't know how sorry ....

The equation from the given equations, representing c, the amount of one check(for the given condition), in dollars is given by: Option C: [tex]358.92 + 3c = 451.89[/tex]

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get.

Thus, if 10 mangoes are there, and 2 people, then 10 ÷ 2 is the number of mangoes each person would get, which is 5.

Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

Thus,  [tex]a \div b[/tex] = a divided in b equal parts.

Also, we can write: [tex]a \div b = a \times \dfrac{1}{b}[/tex]

(it is since a = a times 1 so [tex]a/b = 1 \times (a/b) = (1/b) \times a[/tex])

For the given case, the amount those 3 checks together have is the difference in Jade's account's initial and final balance.

Amount deducted by 3 checks = $451.89 - $358.92

Amount of all 3 checks is $c

Thus, total of their amount = $(c + c + c) = 3c

Thus, we get:

[tex]3c = 451.89 - 358.92\\\\\text{Dividing both the sides by 3}\\\\c = \dfrac{451.89 - 358.92}{3} \text{\: (in dollars)}\\or\\\\358.92 + 3c = 451.89[/tex]

Thus, the equation from the given equations, representing c, the amount of one check(for the given condition), in dollars is given by: Option C: [tex]358.92 + 3c = 451.89[/tex]

Learn more about division here:

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Answer:

Width: 1694 cm or 16.94 m

Length: 1706 cm or 17.06 m

Step-by-step explanation:

1. Write out the known equations:

First, the equation for the perimeter of a rectangle:

[tex]Perimeter = 2(Width) + 2(Length)[/tex]

We also know that the rectangle is 12 cm longer than it is wide. This leads to the second equation:

[tex]Length=Width+12[/tex]

2. Solve the system of equations for width:

Since we know the length in terms of width, and we know the perimeter, we can plug these values into the equation for the perimeter. First, let's rearrange the equation for perimeter to solve for width:

[tex]Perimeter = 2(Width) + 2(Length)\\Perimeter-2(Length)=2(Width)\\2(Width)=Perimeter-2(Length)\\Width=\frac{Perimeter-2(Length)}{2}[/tex]

Now, plug in the known values (since there are 100 cm in one metre, I'm multiplying the perimeter of 68 m by 100 to convert to centimetres--the perimeter of 68 m is equal to 6800 cm):

[tex]Width=\frac{6800-2(Width+12)}{2}[/tex]

Now, solve the equation for width:

[tex]Width=\frac{6800-2(Width+12)}{2}\\2(Width)=6800-2(Width+12)\\2(Width)=6800-2(Width)-24\\2(Width)+2(Width)=6800-24\\4(Width)=6800-24\\4(Width)=6776\\Width=1694cm[/tex]

3. Solve for length using width:

Now that we know the width, we can easily solve for the length using our previously established equation for length, [tex]Length=Width+12[/tex], as shown:

[tex]Length=Width+12\\Length=1694+12\\Length=1706cm[/tex]

4. Convert to metres.

If you want to know the answer in metres, you can convert from centimetres by dividing by 100:

1694/100 = 16.94 m

1706/100 = 17.06 m

(Sorry I'm late)

The capacity of the square base can is 5 x 5 x 14 (bottom face area x height) = 350 (cm3).

The capacity of the circular base can is 3.5 x 3.5 x pi x 12 = 461.814120078.. (round to 462)

So, the circular base can has a greater capacity and by 462-350 = 112 cm3

Answer:

This sounds like you're trying to find the average of a group of numbers. For instance, suppose you want to find the average age of a group of people whose ages are 16, 18, 23, and 28. First, you sum the numbers: 16 + 18 + 23 + 28. You get 85. Then you divide 85 (the sum) by how many numbers you added together (4). So you divide 85 by 4, which gives you 21.25. Hope this helps!

Answer:

g < -7

General Formulas and Concepts:
Algebra I

Equality Properties

Terms/Coefficients

Step-by-step explanation:

*Note:

When dividing or multiplying both sides of the inequality by a negative, flip the inequality sign.

Step 1: Define

Identify.

4 - 5g > 39

Step 2: Solve for g

∴ any number g less than -7 would work as a solution to the inequality.

---

Topic: Algebra I

Unit: Inequalities

Answer:

y = 16

Step-by-step explanation:

y = 11 - x

of x is -5, subtitute it into the equation

y = 11 - (-5)

y = 11 + 5

y = 16

Answer:

16

Step-by-step explanation:

y=11--5

y=11+5

y+16

Answer:

C

Step-by-step explanation:

count on 6 10's from 31 because 6 x 10 is 60 and 31+60 is 91 which is your answer

Since half of the diagonal of the square is 10, that means the whole diagonal is 20.

Area of the square = [tex]\frac{1}{2} *(20)^{2} =200[/tex]

Thus the area is 200. Hope that helps!

Solution:

Given:

To find the diagonal, multiply half the diagonal by 2.

We also know that the sides of the square are equal. Let's use Pythagoras theorem to solve for the side length (c).

Square the side length to obtain the area of the square.

The area of the square is 200 units²

The monthly payment for a $6,000 four-year loan with an APR of

8.50% is $244.04

The formula for calculating compound interest is expressed as:

A = P(1+r)^n

A = 6000(1+0.085)^4
A = 6000(1.95236)
A = 11,714.15

Hence the amount of the loan is 11,714.15

Monthly payment =11,714.15 /48
Monthly payment = 244.04

Hence the monthly payment for a $6,000 four-year loan with an APR of

8.50% is $244.04

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Answer:

y ≤ 1/2x + 5

Step-by-step explanation:

-3x + 6y ≤ 30

add 3x on both sides:

6y ≤ 3x + 30

divide 6 on both sides:

y ≤ 3/6x + 30/6

This is simplified to:

y ≤ 1/2x + 5

Answer:

She would get $80 dollars in 10 weeks

Step-by-step explanation:

[tex]already \: has \: 20 \\ saving \: 6 \: per \: week \\ in \: 10 \: week \\ = 6 \times 10 + 20 \\ = 60 + 20 \\ = 80[/tex]

Answer:

6 dollars a week for every week she saved.

She already has 20 dollars so 10 weeks would be

20 +  10*6 = 10 weeks of saving

20+60=80

$80 would be saved up after 10 weeks.

Expression, 6 dollars a week which would be if weeks was represented by “w”. Since she already has 20 dollars, thats a base.

20 + 6w

Answer:

D. 20' x 40'

Step-by-step explanation:

Answer:

(-4/8) - (-9/7) = 11/

14

≅ 0.7857143

Spelled result in words is eleven fourteenths.

Step-by-step explanation:

Please tell me if correct

Answer:

3 is the GCF for 15 and 18

Step-by-step explanation:

Q) GCF for 15 and 18?

Possible factors are,

→ 15 = 3 × 5

→ 18 = 2 × 3 × 3

Common factor is,

→ 3 (in 15 and 18)

Hence, 3 is the GCF for 15 and 18.

Answer:
Slope is 3/2
y-intercept is (0,-45)

Answer:

67 1/2 cm

Step-by-step explanation:

v=lxwxh

v=4 1/2x 6x 2 1/2

v=67 1/2 cm^3

Volume of rectangular prism is given by:

‎ㅤ‎ㅤ‎ㅤ➙ V = l × b × h

Here, we have :

Therefore, volume:

[tex] \implies\quad \tt {V =l\times b\times h }[/tex]

[tex] \implies\quad \tt { V =6\times 2\dfrac{1}{2}\times 4\dfrac{1}{2}}[/tex]

[tex] \implies\quad \small{\tt { V = 6\times \dfrac{(2\times 2)+1}{2}\times \dfrac{(4\times 2)+1}{2}}}[/tex]

[tex] \implies\quad \tt {V = 6\times \dfrac{4+1}{2}\times \dfrac{8+1}{2} }[/tex]

[tex] \implies\quad \tt {V =6\times \dfrac{5}{2}\times\dfrac{9}{2} }[/tex]

[tex] \implies\quad \tt {V =\dfrac{6\times 5\times 9}{2\times 2} }[/tex]

[tex] \implies\quad \tt { V =\cancel{\dfrac{270}{4}}}[/tex]

[tex] \implies\quad \tt { V = \dfrac{135}{2}}[/tex]

[tex] \implies\quad \underline{\underline{\pmb{\tt { V = 67\dfrac{1}{2}\:cm^2}}}}[/tex]

Answer:

0.5km/h

Step-by-step explanation:

Assume lake has no current.

.

V=distance / time

V=39km / 3h

V=13km/h

In water Assume boat used same power travelling

V=35km / 2h

V= 12.5km/h

Current is the difference 0.5km/h

Answer: B

Step-by-step explanation: I graphed all the points and all the points on graph b were correct and on the line. i don't know how to put a pic of the graph on here so just trust me or go to desmos and graph the points on there.

Answer:

7.752

Step-by-step explanation:

Well since the both have the same amount of didgets you can just line up like if it were adding thousands.

                  5. 1 2 8

                  2. 6 2 4

                 _________

So were going to add 8 + 4=12

Then so since it was 12 were just going to put 2 and then add a 1 to out result for 2 + 2

2 + 2=4+ the 1 we have to add since our last question was 10 and above so our answer is 5

Next add 6 + 1=7

Now our last step is to add 5 + 2 which=7

So you answer should look like this.

_________

7. 7 5 2

hope this helps have a great day:)

Answer:

729 cm

Step-by-step explanation:

9 x 9 x 9 = 729 cm

Have a great day!

PLEASE MARK BRAINLIEST!

Answer:

486cm^2

Step-by-step explanation:

A is equal to the edge of the cube.

A=6a^2

=6·9^2

= 486

Because we are finding the surface area it would be the unit squared, because surface area is 2 dimensional. If we were finding the volume it would be cubed.

so the answer is 486 cm^2

Step-by-step explanation:

supplementary angles means sum of them is 180°

8x+4+6x+64 = 180

14x+68 = 180

x = 8

angles are 68 and 112

Step-by-step explanation:

How to solve for x?

Eliminate -(9/2) to find out the value of x.

Add 9/2 to both sides of the equation:

[tex]x = - 7.5[/tex]

Answer

[tex]x=[/tex] [tex]-7.5[/tex]

Step-by-step explanation:

[tex]x -\frac{9}{2} = -12[/tex]

[tex]x -\frac{9}{2} + \frac{9}{2} = -12 + \frac{9}{2}[/tex]  (add [tex]\frac{9}{2}[/tex] to both sides)

[tex]x = -\frac{15}{2}[/tex]

[tex]-\frac{15}{2} =[/tex] [tex]-7.5[/tex]

[tex]x=[/tex] [tex]-7.5[/tex]

Step-by-step explanation:

10 minutes = x

60 minutes (1) hour = x/10 * 60

In 60 minute or 1 hour she runs 60x/10 = 6x metre