The area of a triangle reduced by the area of the semicircle is ( 48 - 2π ) square meters. The base of the triangle is 12 meters. Find the height of the triangle and radius of the semicircle.

Answers

Answer 1

Answer:

The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters

Step-by-step explanation:

The area of a triangle = [tex]\frac{1}{2}[/tex] × b × h, where

b is the length of the baseh is the length of the height

The area of a semi-circle =  [tex]\frac{1}{2}[/tex] π r², where

r is the length of the radius

∵ The area of the figure = Area Δ - Area semicircle

∵ The area of the figure =  [tex]\frac{1}{2}[/tex] × b × h -  [tex]\frac{1}{2}[/tex] π r²

∵ The base of the triangle is 12 meters

→ Substitute it in the area of the figure above

∴ The area of the figure =  [tex]\frac{1}{2}[/tex] × 12 × h -  [tex]\frac{1}{2}[/tex] π r²

The area of the figure = 6h -  [tex]\frac{1}{2}[/tex] π r²

∵ The area of the figure = 48 - 2 π

→ Equate the two expressions of the area of the figure

6h -  [tex]\frac{1}{2}[/tex] π r² = 48 - 2 π

→ Equate the like terms of the two sides

6h = 48

→ Divide both sides by 6 to find h

h = 8

- [tex]\frac{1}{2}[/tex] π r² = -2 π

→ Divide both sides by -π

∴  [tex]\frac{1}{2}[/tex]  r² = 2

→ Multiply both sides by 2

∴ r² = 4

→ Take √  for both sides

r = 2

The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters


Related Questions

CAN YOU ANSWER THIS PLEASE

Answers

It’s the absolute value of 0 and 5 because it’s the same absolute value the absolute vale is 5 for both 5 and -5 because absolute value of a number is the distance from 0 you can’t have a negative value

Consider the line that passes through each pair of given points, and decide what type of slope the line has.
(2, 4) and (5, 1)
undefined slope
(3,5) and (-1,2)
negative slope
(-7, 8) and (-7,0)
positive slope
(6.-3) and (4, -3)
zero slope

Answers

Answer:

The slope of line through (2, 4) and (5, 1) is Negative

The slope of line through (3,5) and (-1,2) is Positive

The slope of line through (-7, 8) and (-7,0) is Undefined

The slope of line through (6.-3) and (4, -3) is Zero

Step-by-step explanation:

Slope is defined as the steepness of a line.

Slope is denoted by m and the formula for calculating slope is:

[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Here

(x1,y1) and (x2,y2) are coordinates of the points through which the line passes

Now,

For (2, 4) and (5, 1):

[tex]m = \frac{1-4}{5-2} = \frac{-3}{3} =-1[/tex]

NEGATIVE

For (3,5) and (-1,2)

[tex]m = \frac{2-5}{-1-3} = \frac{-3}{-4} = \frac{3}{4}[/tex]

POSITIVE

For (-7, 8) and (-7,0)

[tex]m = \frac{0-8}{-7+7} = \frac{-8}{0}[/tex]

UNDEFINED

For (6.-3) and (4, -3)

[tex]m=\frac{-3+3}{4-6} = \frac{0}{-2} = 0[/tex]

ZERO

Hence,

The slope of line through (2, 4) and (5, 1) is Negative

The slope of line through (3,5) and (-1,2) is Positive

The slope of line through (-7, 8) and (-7,0) is Undefined

The slope of line through (6.-3) and (4, -3) is Zero

Which relation is a function?

Answers

A function maps one input to one output, where x is the input and y is the output.

The input CANNOT BE REPEATED.

Which table shows this fact?

The only table that DOES NOT SHOW a repeated input is choice A.

Answer: choice A

Please help it was due a week ago I numbered them (with poor handwriting) anyways yeah please help

Answers

Answer:

Functions - 2, 3

Not a Function - 1, 4, 5, 6

WHAT % OF 95 DOLLARS = 57 DOLLARS

Answers

Answer: 60%

Step-by-step explanation:

Our answer is 60 because:

57 ÷ 95 = 0.6

We take the 0.6 and multiply.

We get 60% as an answer.

Answer:

60%

Step-by-step explanation:

To find the answer to this equation, you need to use the percent composition formula. It is as follows:

[tex]\frac{part}{whole} * 100 = percent[/tex]

Let's plug in what the question gives us into the equation:

[tex]\frac{57}{90} *100 = 60[/tex]

Therefore, the answer to your question is 60%!

Hope this helps!!

- Kay :)

I'm having trouble understanding this..​

Answers

The fraction you just divide the top from bottom the v thing is 2.236 so just turn all of them into decimals and put it from least to greatest
here is a drawing explanation

$600 a month on groceries, if this is 15% of the monthly budget, what is the monthly budget

Answers

4,000 if you set it up as unit rate with .15 on btm

Answer:

$4,000

Step-by-step explanation:

.15x = $600

.15x = $600.  divide both sides by .15

.15.       .15

x = $4,000

a line has a slope of negative 1 over 2 and a y-intercept of -2 what is the x intercept of the line ​

Answers

Answer:

x=-1

Step-by-step explanation:

plug in zero for y

y= -1/2x -2

0= -1/2x-2

2= -1/2x

-1=x

Solve for the distance between the points (0, -9) and (-4, 3). Simplify your answer.

Answers

Answer:

The distance is [tex]4\sqrt{10[/tex]

Step-by-step explanation:

I used the distance formula

(Giving brainliest!!!)


A dance team is going to spend $1,440 to purchase all sweatshirts or all jackets for the team members. Sweatshirts cost $24 each. Jackets cost $32 each. What is the greatest number of Sweatshirts or Jackets the team can purchase??


The team can purchase_______sweatshirts or________jackets.

Answers

Answer:

60 sweatshirt Or 45 jackets

Step-by-step explanation:

Total amount = $1,440

Sweatshirts = $24

Jackets = $32

What is the greatest number of sweatshirts or jackets the team can purchase?

The greatest number of sweat- shirts the team can purchase = Total amount / cost of sweatshirt

= $1,440 / $24

= 60

The greatest number of jackets the team can purchase =Total amount /cost of jackets

= $1,440 / $32

= 45

Therefore, the greatest number of sweatshirts or jackets the team can purchase is

60 sweatshirt

Or

45 jackets

Answer:

60 Sweatshirts

45 jackets

Step-by-step explanation:

take the amount of money divide by the cost of the jacket or sweatshirt.

How do I factor x2 - 7 = 6x?

Answers

Answer:

x=7,x=-1

Step-by-step explanation:

x^2-6x-7=0

x^2+1x-7x-7=0

x(x+1)-7(x+1)=0

(x-7),(x+1)=0

Help now fast please

Answers

Answer:A. 5m + 40

see in the picture, u can see that the line passes through (0;40) and (10;90)

suppose: the equation of the line is y = am + b (a ≠ 0)

because the line passes through (0;40) => 40 = b

the line passes through (10;90)              => 90 = 10a + b

=> b = 40

    a = 5

=> y = 5m + 40

Step-by-step explanation:

Tim typed a 46-word paragraph in 3/4 of a minute. What is his typing speed per minute?


Iḿ sorry this is prob. so easy I just bad at math. :(

Answers

Answer:

Hmm, I think the answer is 57.5.

Step-by-step explanation:

Since 46 = 3/4, we divide 46 by 4 to get one fourth. That is 11.5 . Then, multiply it by 4 to get by one minute. 11.5 x 4 = 57.5  

The answer is 48/1. You have to change 48 into 48/1. Then just rewrite the equation. You then would want to multiply those and what you would get would be 144/3. To simplify you would have to divide 144 by 3 and what you would get would be 48/1 or just 48. Hope this helps! Please mark this!

92,902 to the nearest ten thousand

Answers

Answer:

90,000 i think sry if im wrong

Step-by-step explanation:

You decide you need to start placing money aside for your new car which you would like to purchase in the next 2 to 3 years. Would this be considered investing?

Answers

Yes! This counts as investing

Can someone please solve this for me?
You have to solve for x and y!

Answers

Answer:

x=−175 and y=−1220

Step-by-step explanation:

Based on the Vertical Angles Theorem, -7x+5=y

Since we know that 2 angles that form a line when combined equal 180 degrees, we know that (4-12x)+y=180

-7x+5=y

(4-12x)+y=180

Now we solve the system:

7x+5=y;−8x+y=180

First, we solve 7x+5=y for y:

7x+5+(−y)=y+(−y)

7x−y+5=0

7x−y+5+ (−5)=0+ (−5)

7x−y=−5

7x−y+(−7x)=−5+(−7x)

−y=−7x−5

-y/-1=(-7x-5)/-1

y=7x+5

Now we will substitute 7x+5 for y in the other equation:

−8x+y=180

−8x+7x+5=180

−x+5=180

−x+5+(−5)=180+(−5)

−x=175

-x/-1 = 175/-1

x=−175

Finally, we'll substitute -175 for x in y=7x+5:

y=7x+5

y=(7)(−175)+5

y=−1220

HTH :)

|y+3|=7

Absolute value! Help!

Answers

Answer:

y=4

Step-by-step explanation:

y+3=7. take 3 off and also off the 7 then you get 4 which is the ansew as 3+4 equals 7 it is simple algebra substitute

-3. -3

7-3=4

ooooooooooooohhhhhhhhh

Answers

Answer:

A

Step-by-step explanation:

2/5 divided by 2/3 ​

Answers

[tex] \frac{2}{5} \div \frac{2}{3} \\ \\ = \frac{2}{5} \times \frac{3}{2} \\ \\ = \frac{6}{10} \\ \\ =0.6[/tex]

..... Hope this will help....

Exact Form:3/5 Decimal Form:0.6

(03.02 MC)

Which of the following is a factor of 12x2 − 4x − 1? (6 points)

Group of answer choices

A. 6x − 1

B. 2x + 1

C. 2x − 1

D. None of the above

Answers

Answer:

C

Step-by-step explanation:

what is the slope of a line perpendicular to a line whose equation is -2y=3x+7

Answers

Answer:

(2/3)

Step-by-step explanation:

-2y = 3x + 7

y = 3/-2 + 7/-2

y = (-3/2) + (-7/2)

find the reciprocal of the slope (-3/2) which gets you the perpendicular slope of (2/3)

Multiply the binomials.
1) (x + 5)(x-2)

Answers

Answer:

the answer is x²+3x-10

Step-by-step explanation:

(x + 5)(x-2)

x²-2x+5x-10

x²+3x-10

Answer:

x^2+3x-10

Step-by-step explanation:

(x + 5)(x-2)

x^2-2x+5x-10

x^2+3x-10

a bank teller. helps two customers omar makes a $15 withdrawal so he balance changes by -$15. jakes makes a $10 deposit so his balance changesby $10

Answers

Answer:

D. Omar's transaction involves more money, because |-15| is greater than |10|.

Step-by-step explanation:

The absolute value of a number is simply the magnitude or numerical value of a number while ignoring any sign attached to it. For example, given that x is a real number, absolute value of x, |x| = x. The absolute value of x does not take account of any sign attached to it.

Thus:

The absolute value of Omar's transaction is given as |-15| = 15.

While that of Jake is |10| = 10.

15 is greater than 10.

Therefore, we can conclude that:

"Omar's transaction involves more money, because |-15| is greater than |10|."

Answer:

The answer is D

Step-by-step explanation:

Which student best fills the role of group notetaker? Yuna, who is positive and considers other viewpoints Hiroto, who is focused and sticks to a schedule Rin, who is a good speaker and mediator Sora, who is a good listener and writer

Answers

Answer:

Sora

Step-by-step explanation:

she listens well, and will be able to catch and take note of everything along with the fact that her writing is eligible and easy to interpret.

Answer:

sora

Step-by-step explanation:

A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.
One of the friends used the equation One-fourth (t + 34) = StartFraction 40 over 4 EndFraction to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?
Each friend paid $8.50 for the food and $1.50 for the tip.
Each friend paid $10.00 for the food and $6.00 for the tip.
Each friend paid $8.50 for the food and $6.00 for the tip.
Each friend paid $10.00 for the food and $1.50 for the tip.

Answers

Answer:

TOP ONE IS RIGHT

Step-by-step explanation:

Answer:

A. Each friend paid $8.50 for the food and $1.50 for the tip.

Step-by-step explanation:

Quiz on Edge 2021

ΔωΔ Happy Halloween

Jennifer is planning a vacation. The hotel costs $60 per night and her flights cost $150. She has a budget of no more than $500 for hotel and flights. Up to how many nights can she afford n the hotel? Write an inequality and solve.

Answers

Answer:

5 Nights

Step-by-step explanation:

5 nights



Explanations!!!

Need help ASAP. Please

Answers

Answer:

The answer is 100% without a doubt B

Step-by-step explanation:

Over three days I earn 2568. On the first day I made twice as much as the second day. On the third day I made three times as much as the second day. How much did I earn on the first day.

Answers

Answer:

I earned $856 on the first day

Step-by-step explanation:

Let's call

x = earning on the second day

2x = earnings on the first day

3x = earnings on the third day

The total earnings are $2568, thus

x + 2x + 3x = 2568

Simplifying:

6x = 2568

Dividing by 6:

x = 2568/6

x = 428

I earned $428 on the second day.

2x = 2*$428 = $856

I earned $856 on the first day

simplify 3x cubed y4 * 2x6y

Answers

Answer:

(3•2x8y5)

Step-by-step explanation:

find the mean for the scores : 3810;5300;8540;4300,5340

Answers

Answer: 5458

Step-by-step explanation: So the mean is the same thing as the average. To find the mean you add up all of the numbers, and then divide by 5 because there are five numbers. So the sum would be 27,290. Then that divided by 5 would be 5458.

The mean of the scores 3810, 5300, 8540, 4300 and 5340 is, 5466.

What is mean?

Mean is an average of values of a set. Arithmetic mean, geometric mean and harmonic mean are the type of mean.

The given scores are

3810, 5300, 8540, 4300, 5340

Total number of terms is 5.

To find the mean, use formula,  

Mean = sum of terms/number of terms.

Mean = (3810+5300+8540+4300+5340)/5

          = 27330/5

          = 5466

Mean of the given score is, 5466.

To learn more about Mean on:

https://brainly.com/question/27824219

#SPJ2

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