Find the area of the shaded sector. Leave your answer in terms of pi.
Answer options:
18pi ft2
24pi ft2
32pi ft2
3pi ft2

Answer:

  28

Step-by-step explanation:

It is often convenient to compute the Least Common Multiple (LCM) as the product of the numbers divided by their greatest common factor. In this case, that would be ...

  LCM = (14 × 4)/2 = 28

___

As a check, you can do it by looking at the prime factors of these numbers. The LCM will be the product of the unique factors to their highest powers.

  14 = 2·7

  4 = 2^2

Unique factors are 2 and 7. The highest power of 2 is 2; the highest power of 7 is 1.

  LCM = 2^2·7 = 28

Start by setting up a factor tree for 4 and 14.

4 factors as 2 ·  2 and 14 factors as 7 · 2.

When finding the least common multiple, we're looking for factors that match up and here we have a pair of 2's that matches up.

So our least common multiple is 2 from the 2's that match up × the the 2 that doesn't match up x the 7 from the 7 that doesn't match up.

So we have 2 × 2 × 7 or 4 × 7 which is 28.

On my whiteboard, I have attached my factor tree.

Answer:

Step-by-step explanation:

x^2+2x-9=15

x^2+2x=24

x^2+2x+1=24+1

(because what you do to one side you do to the other) ^

(x+1)^2=25

(x+1)^2 -25=0

(25 is a perfect square)

(x+1-5)(x+1+5)

(x-4)(x+6)

x=4,-6

Answer: x=-6; x=4

Step-by-step explanation:

Answer:

12.5

Step-by-step explanation:

25/200

Answer:

50

Step-by-step explanation:

0.25 x 200 = 50

Answer:

B

Step-by-step explanation:

For each box, there is 1 defective lightbulb. Therefore, a delivery of 4 boxes will have 4 defective lightbulbs. A delivery of 2 boxes has 2 defective lightbulbs. 4 defective lightbulbs subtracted by 2 defective lightbulbs equals 2 more defective lightbulbs in 4 boxes than 2. Therefore, it is B.

Answer:

m= -5/4

Step-by-step explanation:

Slope can be translated to "rise over run". You go down 5 spaces and then move over 4 spaces.

Answer:

A

Step-by-step explanation:

Parallel lines have the same slope. Find the slope by converting the equation x + 5y = 10 into y = mx+b form. It becomes y = -1/5x + 2. The slope is -1/5.

Substitute -1/5 and the point (1,3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y - 3 = -\frac{1}{5}(x - 1)\\y - 3 = -\frac{1}{5}x + \frac{1}{5}\\y = -\frac{1}{5}x + \frac{16}{5}[/tex]

Answer:

It's aaaaaaaaaaaaaaaaaaaaaaa!!!

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Answer:

x       y

15     -1

12     0

9       1

6       2

3       3

0       4

Step-by-step explanation:

This is a function table. For a linear function, find the average rate of change between the listed points called slope. Then use the slope to fill in other inputs and outputs for the function.

[tex]m = \frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{0-12} =\frac{4}{-12} =- \frac{1}{3}[/tex]

This means for every 3 units made in the input, the function moves down 1 output.

x       y

15     -1

12     0

9       1

6       2

3       3

0       4

Answer:

A. t < –15

Step-by-step explanation:

The temperature has to be less than -15

t < -15

The expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).

Therefore, the expressions that illustrate the commutative property are: A, D, E, and F (see attachment below).

Learn more about commutative property on:

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Answer:

[tex]x-1<n<3x+5.[/tex]

Step-by-step explanation:

If a, b and c are the lengths of the triangle's sides, then

[tex]a+b>c,\\ \\a+c>b,\\ \\b+c>a.[/tex]

Since

[tex]a=2x+2,\\ \\b=x+3,\\ \\z=n,[/tex]

then

[tex]2x+2+x+3>n\Rightarrow n<3x+5,\\ \\2x+2+n>x+3\Rightarrow n>1-x,\\ \\x+3+n>2x+2\Rightarrow n>x-1.[/tex]

Thus,

[tex]x-1<n<3x+5.[/tex]

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side. The correct option is A, 3x + 5 > n > x - 1.

Triangle inequality theorem of a triangle says that the sum of any of the two sides of a triangle is always greater than the third side.

Suppose a, b and c are the three sides of a triangle. Thus according to this theorem,

(a+b) > c

(b+c) > a

(c+a) > b

Given the three sides of the triangle 2x + 2 ft, x + 3 ft, and n ft. Now using the triangle inequality theorem we can write,

2x + 2 + x + 3 > n  → 3x + 5 > n

2x + 2 + n > x + 3 → n > -x + 1

x + 3 + n > 2x + 2 → n > x - 1

Since x can not be a negative term therefore, we can write,

3x + 5 > n > x - 1

Hence, the correct option is A, 3x + 5 > n > x - 1.

Learn more about Triangle Inequality Theorem:

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Answer:

y= 3      

  --- X +1

   4

Step-by-step explanation:

-4y=-3x-12+8

-4y=-3x+4

---      ---  -

4        4    4

y= 3      

  --- X +1

   4

To rewrite f(x) = x^2 - 6x - 60 by completing the square, you add and subtract (6/2)^2 within the equation and refactor to get f(x) = (x - 3)^2 - 69, with the vertex at (3, -69).

To rewrite the function f(x) = x^2 - 6x - 60 by completing the square, follow these steps:

The function is now in the completed square form. The vertex of this parabola is at (3, -69).

Answer: Simplifying

4x = 4x

Add '-4x' to each side of the equation.

4x + -4x = 4x + -4x

Combine like terms: 4x + -4x = 0

0 = 4x + -4x

Combine like terms: 4x + -4x = 0

0 = 0

Solving

0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

Answer:

True

Step-by-step explanation:

It was correct on my quiz

Answer:

y+4=-3/2(x-2) is the answer

Step-by-step explanation:

Again over here just use the y=mx+c

m which is the slope is change in y over change in x which in this case is [tex]\frac{-3}{2}[/tex] so which just that we can cross out the first option for the answer secondly to be able to find C just take literally any point from the graphed line, for instance we take (-2,2), just add it in the equation and solve for C

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

y=-3/2-1

Now all you have to see is which of the three equations is equivalent to the one we just found

y+4=-3/2(x-2) is the answer :)

[tex]\huge\boxed{22:7}\ \huge\boxed{29:22}[/tex]

First, we need to find the number of yellow pencils in the basket. We'll represent the number of green pencils with [tex]g[/tex] and the number of yellow pencils with [tex]y[/tex].

[tex]\begin{aligned}7+y&=29&&\smash{\Big|}&&\text{Start with what we already know.}\\y&=22&&\smash{\Big|}&&\text{Subtract 7 from both sides.}\end{aligned}[/tex]

Our first ratio is [tex]y:g[/tex], or [tex]\boxed{22:7}[/tex].

The second ratio is [tex](g+y):y[/tex]:

[tex]\begin{aligned}(g+y)&:y\\(7+22)&:22\\29&:22\end{aligned}[/tex]

Answer:

=2a

Step-by-step explanation:

a-2/5a and a+2/5a cancel each other out and your left with a+a aka 2a

Answer:

c

Step-by-step explanation:

I think its c but I could be wrong

Answer:

8y^3 + 6y^2 - 29y + 15

Step-by-step explanation:

8y^3 + 12y^2 - 20y - 6y^2 - 9y + 15

then

8y^3 + 6y^2 - 29y + 15 is the product

Best regards

Answer:

=8y^3+6y^2−29y+15

Step-by-step explanation:

(4y−3)(2y^2+3y−5)

=(4y+−3)(2y^2+3y+−5)

=(4y)(2y^2)+(4y)(3y)+(4y)(−5)+(−3)(2y^2)+(−3)(3y)+(−3)(−5)

=8y^3+12y^2−20^y−6y^2−9y+15

=8y^3+6y^2−29y+15

Answer:

Step-by-step explanation:

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

From the graph we have the points A(2, 2) and B(-6, 4). Substitute:

[tex]AB=\sqrt{(-6-2)^2+(4-2)^2}=\sqrt{(-8)^2+2^2}=\sqrt{64+4}=\sqrt{68}[/tex]

[tex]AB\approx8.25[/tex]

it went to the right 4 units and up 2 units

Answer:

[tex]\large\boxed{\dfrac{7-x}{x-7}=-1}[/tex]

Step-by-step explanation:

[tex]\dfrac{7-x}{x-7}=\dfrac{-(x-7)}{x-7}\\\\\text{cancel}\ (x-t)\\\\\dfrac{7-x}{x-7}=\dfrac{-1}{1}\\\\\dfrac{7-x}{x-7}=-1[/tex]

Answer:

-1

Step-By Step:

The Answer on Ed

answer: 11

explanation: just plug in -2 for x. the new problem becomes 5(-2)^2 - 9. Negative two squared is 4. 5 times 4 is 20. 20 minus 9 is 11.

Final answer:

When evaluating the expression 5x^2 - 9 for x = -2, we substitute -2 into the expression and find that the value is 11.

Explanation:

To evaluate the expression 5x2 − 9 when x = −2, we first substitute the value of x into the expression and then perform the calculation:

5(−2)2 − 9
→ 5(4) − 9
→ 20 − 9
→ 11

Therefore, when x = −2, the value of the expression 5x2 − 9 is 11.

Answer:

Simplifies to:

748.245949x

Answer:

(2z - 3)(15z - 4)

Step-by-step explanation:

To factor the quadratic

Consider the factors of the product of the coefficient of the z² term and the constant term which sum to give the coefficient of the z- term

product = 30 × 12 = 360 and sum = - 53

The factors are - 45 and - 8

Use these factors to split the z- term

30z² - 45z - 8z + 12 ( factor the first/second and third/fourth terms )

= 15z(2z - 3) - 4(2z - 3) ← factor out (2z - 3)

= (2z - 3)(15z - 4) ← in factored form

Answer:

i did this question b4 but completely forgot the answer ://

Step-by-step explanation:

Answer:

7/12 - 1/12 = 6/12

Step-by-step explanation:

Answer:

The answer should be 6/12 or 1/2

Answer:

x=6.7

Step-by-step explanation:

What you have to do is you have to eliminate y. So you need to make y cancel each other out.

2x+2y=17. I can multiply 2 to the second equation to cancel the y's out.

8x-2y=50.

10x=67.

x=67/10 or 6.7.

The value of x for the system of equations will be x=6.7.

A set of simultaneous equations is a finite set of equations for which common solutions are sought in mathematics. It is also known as a system of equations or an equation system.

Given that the two equations are 2x + 2y = 17 and 4x - y = 25. The value of x will be calculated by eliminating the variable y from the equation.

Multiply the second equation by 2 and subtract from the first equation,

2x+2y=17.

8x-2y=50.

10x=67.

x= 67/10

x = 6.7.

Therefore, the value of x for the system of equations will be x=6.7.

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