A circle has a sector with area 17/2 pi and central angle of 17/9 pi radians. What is the area of the circle?

Answer:

[tex]4i\sqrt{5}[/tex]

Step-by-step explanation:

[tex]\sqrt{-80}[/tex]

[tex]\sqrt{80*i^2}[/tex]

i^2 is -1

[tex]i\sqrt{80}[/tex]

[tex]i\sqrt{4^2 * 5}[/tex]

[tex]4i\sqrt{5}[/tex]

Answer:  [tex]4i\sqrt{5}[/tex]

Answer:

[tex]4i\sqrt{5}[/tex]

Step-by-step explanation:

The expressions equivalent to (2n+6)(n+3) are Options C and F, E, F.

To determine which expressions are equivalent to (2n+6)(n+3), we can first expand this expression using the distributive property (also known as the FOIL method for binomials). This gives us:

Combining like terms (6n + 6n) gives us the expression [tex]2n^2 + 12n + 18[/tex]. Therefore, option C is equivalent to (2n+6)(n+3).

Looking at option F, [tex]2(n+3)^2[/tex] is indeed the same as (2n+6)(n+3) because if we expand[tex](n+3)^2[/tex], we get [tex]n^2 + 6n + 9[/tex], and multiplying the whole expression by 2 yields [tex]2n^2 + 12n + 18[/tex], which matches our previous result.

Option B, [tex]2n^2+6n+18[/tex], is not equivalent because it lacks the combined coefficient for the n terms that should be 12n rather than 6n. Option A is also correct. Option E, 2(n+3)(n+3), is just a different way of writing option F and is therefore equivalent. Option D, 12n+18, doesn't have the [tex]n^2[/tex] term, so it's not equivalent to the original expression.

Answer:

sqrt of 7 goes between 2 and 3

Square root of 20 goes between four and five

Square root of 90 goes between nine and 10

The 101 goes between 4 &5

The 3 90 goes between 4&5

The 3 20 goes between two and three

And 3 800 goes between 9&10

Answer:

4x^4 + 6x^3 + 9x^2 − 4x + 3

Step-by-step explanation:

Simplify the expression. 4x^4 + 6x^3 + 9x^2 − 4x + 3

Answer:

4x^4 + 6x^3 + 9x^2 - 4x + 3

Step-by-step explanation:

Distribute (x^2 + 2x + 3)(4x^2 - 2x + 1)​

You will get 4x^4 - 2x^3 + x^2 + 8x^3 - 4x^2 + 2x + 12x^2 -6x + 3

Then you need to combine like terms

And you will get the answer:

4x^4 + 6x^3 + 9x^2 - 4x + 3

Answer:

j = 45

Step-by-step explanation:

j/9 = 5

Multiply both sides by 9: j = 45

The required value of j will be 45 when j divided by 9 is 5.

In mathematics, divides left-hand operands into right-hand operands in the division operation.

For example, 62÷31 = 2

To solve for j, we are trying to find the value of j that makes the equation "j / 9 = 5" true.

We can start by setting up the equation:

j / 9 = 5

This equation says that the result of dividing j by 9 is equal to 5.

To solve for j, we can multiply both sides of the equation by 9, the denominator of the fraction on the left-hand side:

j = 9 × 5

= 45

This shows that j = 45 is the solution to the equation. In other words, if we substitute 45 for j in the equation "j / 9 = 5", the equation becomes true:

45 / 9 = 5

Therefore, the value of j that makes the equation "j / 9 = 5" true is 45.

To learn more about the division operation click here :

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Answer:

y = 3

x =7

Step-by-step explanation:

to solve this system of equations using substitution method we say, let

5x + 4y = -22 .................... equation 1

2x – 3y = 5...................... equation 2

from equation 2

2x - 3y = 5

2x = 5 + 3y

divide both sides by 2

we have;

2x/2 = (5+3y)/2

x =(5+3y)/2................................ equation 3

put x = (5+3y)/2 in equation 1

5x + 4y = -22 .................... equation 1

5(5+3y)/2 + 4y = -22

(25 + 15y)/2 + 4y = -22

multiply through by 2

25 + 15y + 8y = -44

25 + 23y = -44

collect the like terms

23y = -44 - 25

23y = -69

divide both sides by 23

23y/23 = -69/23

y = 3

put the value of y= 3 into equation 3

x =(5+3y)/2................................ equation 3

x = (5+3(3)]/2

x = 5+9/2

x =14/2

x =7

Answer:

8 quarters

Step-by-step explanation:

You need to break the $20 into smaller bills. The smaller bills value has to be equal to $20. So far you have three $5 bills and three 1$ bills, so the current value is 3*$5 + 3*$1= $18

The value you need to add more will be $20- $18= $2

You need to add $2 more value to the smaller bills and you want to do it using quarters($0.25). The number of the quarter you need will be: $2/ $0.25= 8 quarters

Let's start by calculating the total value of the five-dollar bills and one-dollar bills:
You have 3 five-dollar bills, and each is worth $5, so:
3 five-dollar bills × $5 per bill = $15
You also have 3 one-dollar bills, and each is worth $1, so:
3 one-dollar bills × $1 per bill = $3
Now, let's add the value of the five-dollar bills and one-dollar bills together:
$15 (from five-dollar bills) + $3 (from one-dollar bills) = $18
You started with a twenty-dollar bill, which is worth $20, so we subtract the total value of the bills you have from $20 to find out how much is left to reach $20:
$20 (initial amount) − $18 (value of bills) = $2
You need to make up this remaining $2 with quarters. Since each quarter is worth $0.25 (25 cents), we divide the remaining amount by the value of each quarter to find out how many quarters you need:
$2 ÷ $0.25 per quarter = 8 quarters
Therefore, you need 8 quarters to complete the conversion to $20.

To solve for x in the equation 4/7 = x-1/12, combine the fractions, cross multiply, and solve to find x=3 and x=-7.

Solve for x: 4/7 = x-1/12

To solve for x, first combine the fractions on the right side: 4/7 = (12x - 1)/12. Then, cross multiply to get 12*4 = 7*(12x - 1). Solve for x to find x=3 and x=-7.

By substituting these values back into the original equation, which is x is equal to (12x-1)/12, you can verify these solutions.

In an 812-hour day, a cereal company that packages 305.50 lbs of cereal an hour would package approximately 76,331 boxes of cereal, given each box contains 3.25 lbs of cereal. The provided options in the question do not match this result.

The subject of this question is Mathematics, specifically division used in a real-world context regarding a cereal company's packaging process. To find the number of cereal boxes produced in an 812-hour day, we need to divide the total weight of cereal packed in a day by the weight of cereal in each box.

Firstly, we find out the total amount of cereal produced by multiplying the hourly rate by the number of hours. This will give us: 305.50 lbs/hour x 812 hours = 248,071 lbs.

Next, we divide the total amount of cereal by the weight of cereal in each box to find the number of boxes. Therefore, 248,071 lbs ÷ 3.25 lbs/box = 76,331 boxes.

None of the options (A) 752 boxes, (B) 757 boxes, (C) 799 boxes, (D) 858 boxes match our result. There might be an error in the question or the choices provided.

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Answer:

x = 12

Step-by-step explanation:

⅔x = 8

x = 8 × 3/2

x = 12

Answer:

12

Step-by-step explanation:

8 divided by 2/3 = 12.01 so 12.

Answer:

6 .74 seconds

Step-by-step explanation:

The height of the ball is given by the equation:

[tex]R(x) = - 16( {x}^{2} - 5x - 6)[/tex]

When the ball hit the ground, then;

[tex]R(x) = 0 \\ - 16( {x}^{2} - 5x - 6) = 0 \\ {x}^{2} - 5x - 6 = 0 \\ x = -0.74 \: Or \: 6.74[/tex]

We discard x=-0.74 since time is not negative.

Therefore the ball hit the ground after 6.74 seconds.

The denominator is equal to the numerator.

Step-by-step explanation:

Answer:

Expected loss = $342 million.

Step-by-step explanation:

The formula to compute the expected loss is:

[tex]E(Loss)=\sum Loss\ amount\times P (Loss)[/tex]

Given:

P (Loss)      Amount of loss

0.30            $320 million

0.30            $820 million

0.40            $0

Compute the expected loss as follows:

[tex]E(Loss)=\sum Loss\ amount\times P (Loss)\\=(0.30\times320)+(0.30\times820)+(0.4\times0)|_{in\ millions}\\=96 +246+0\\=\$342\ million[/tex]

Thus, the expected loss is $342 million.

Answer:

24 Home games

Step-by-step explanation:

let [tex]x[/tex] denote the number of home games played, and [tex]y[/tex] denote the number of home games played. We are given the total number of games played as 49

and total wins as 26.

The problem can be expressed in equation form as:[tex]\frac{2}{3}x+\frac{2}{5}y=26[/tex]...[tex]eqtn1[/tex]

Total games is expressed as [tex]x+y=49[/tex]...[tex]eqtn2[/tex]

Rewrite equation 1 to remove fractions:

[tex]\frac{2}{3}x+\frac{2}{5}y=26\\=>5x+3y=195\\[/tex]

Solve for x to obtain total home games played.

Making [tex]x[/tex] the subject in eqtn 2:

[tex]x=49-y[/tex]

Substitute for [tex]x[/tex] in eqtn1:

=>

[tex]5(49-y)+3y=195\\-5y+3y=195-245\\-2y=-50\\y=25[/tex]

To obtain [tex]x[/tex], replace y value in eqtn2:

[tex]x+y=49\\y=25\\Therefore\\x=49-25\\x=24[/tex]

Home games played is 24

Step-by-step explanation:

1st term = -n²+6

= -(1)²+6

= -1+6

=5

2nd term = -(2)²+6

= -4+6 = 2

3rd term= -(3)²+6

=-9+6 = -3

4th term= -(4)²+6

= -16+6 = -10

5th term = -(5)²+6 = -25+6 = -19

6th term = -(6)²+6 = -36+6 = -30

5,2, -3,-10,-19, -30

optionB

Answer:

David receives £90

Step-by-step explanation:

Let David's share be D

Let Mark's share be M

Let Henry's share be H

From the question, we obtained the following data:

David gets twice as much as Mark i.e

D = 2M

M = D/2

Mark gets three times as much as Henry i.e

M = 3H

H = M/3

H = (D/2) /3

H = D/6

The sum of their shares is £150 i.e

D + M + H = 150

D + D/2 + D/6 = 150

Multiply through by 6 to clear the fraction

6D + 3D + D = 900

10D = 900

Divide both side by the coefficient of D i.e 10

D = 900/10

D = 90

Therefore, David receives £90

Answer: D

Step-by-step explanation:

Paul's Current score is 42, x = paul's awaiting score

Paul's score has to be greater than 174

Current score plus awaiting score must be greater than 174

Answer:

d. 42 + p > 174

Step-by-step explanation:

Since Paul needs to score more than 174, the sign needs to be > and not ≥ because he does not want to equalize the score of 174.

Since he currently has a score of 42, he needs to add another score. Assuming the next score he needs is p,

42 + p is the equation.

Answer:

Step-by-step explanation:

C=2πr

18=2×3.14×r

18=6.28r

r=2.88

Arc of a circle

A=®/360°πr

6=®/360°×3.14×r

®=239°

6

Answer:

120

Step-by-step explanation:

it is 3+2 = 5 plus a = 5a

Answer:

165 calories

Step-by-step explanation:

110 cal/28.4 g in Cereal X

How m any cals in 42.6 g of Cereal X

110/x=28.4/42.6

28.4x=4686

x=165

Therefore, 165 calories

The number of calories in 42.6 grams of cereal X will be 165 calories.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

There are 110 calories per 28.4 grams of cereal X. Then the number of calories in each gram is calculated as,

Rate = 110 / 28.4

Rate = 275 / 71  calories per gram

Then the number of calories in 42.6 grams of the cereal X will be given as,

⇒ (275 / 71) x 42.6

⇒ 275 x 0.60

⇒ 165

The number of calories in 42.6 grams of cereal X will be 165 calories.

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Answer:

Step-by-step explanation:

A

Answer:

Answer A

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

Final answer:

After John ate 1/3 of the pizza and Liz ate 1/4, we convert these fractions to have a common denominator of 12, resulting in 4/12 + 3/12 = 7/12 eaten. Subtracting this from the whole gives us 5/12 of the pizza remaining.

Explanation:

John and Liz are sharing a large pizza. To determine how much of the pizza is left after John has eaten 1/3 and Liz has eaten 1/4, we need to add those fractions together and subtract the sum from the whole pizza, which is 1 (representing the entire pizza).

First, we find a common denominator, which in this case is 12, so we convert 1/3 to 4/12 and 1/4 to 3/12. Adding these fractions, we get 4/12 + 3/12 = 7/12.

Now we subtract the portion eaten from the whole pizza: 1 - 7/12 = 5/12 of the pizza is left.

Answer:

x = (y - 7)/2

Step-by-step explanation:

from the question given  y=2x+7 , so we are to find the value of x now we first make x the subject of the formulae from  y=2x+7

 y=2x+7............. equation 1

y- 7 = 2x

divide both sides by 2

(y-7)/2= 2x/2

x = (y - 7)/2

to check if your answer is correct

put the value of x in to equation 1

y=2x+7............. equation 1

y = 2[ (y-7)/2] + 7

y = y - 7 + 7

y = y.......... proved

If it decreases by 80٪, then only 20٪ remains.

15×20٪=15×20/100=15×0.2=3

Answer: 3

Answer:

3 arches

Step-by-step explanation:

Given

15 arches decreased by 80%.

First get 80% of 15 arches

That’s 80%/100% x 15

0.8 x 15

12 arches

Now subtract 12 arches from 15 arches to get the decrease

Decrease = (15 - 12) arches

= 3 arches

Therefore, 80% decrease of 15 inches is equal to 3 arches

Answer:

9.36

Step-by-step explanation:

did the test

Answer:

9.36 just did it! :)

Step-by-step explanation:

YESSSSSSSSSSSSSSS

Answer:

a + 2b

Step-by-step explanation:

Perform the indicated multiplication.

This results in 2a + 4b - a - 2b, whiin in turn reduces to

a + 2b

Answer: 600 members of the club

Step-by-step explanation:

A sample is a subset of the population that represents the entire population.

Here , we are given that ,

The club surveys  50 of its 600 members.

Clearly , Population = 600 members of the club

Sample = 50 members

Hence, the population of this study is "600 members of the club " .

Answer:

24/35

Step-by-step explanation 3/5 times 8/7 equals 24/35