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2 years ago

HELP PLS ACELLUS IM ALMOST DONE W SUMMER SCHOOOL

Mathematics

1 answer:

Alex2 years ago

8 0

Answer:

y = 95

Step-by-step explanation:

x + 120 = 180

25 + x + y = 180

flipping the first equation 180 - 120 = 60 so x is 60.

so plug in 60 into the second equation

25 + 60 + y =180 --> 85 + y =180 flip equation 180 - 85 = 95

so y is 95

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From a piece of tin in the shape of a square 6 inches on a side, the largest possible circle is cut out. What is the ratio of th

wel

Answer:

$\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}$

Step-by-step explanation:

The width of a square is its side length.

The width of a circle is its diameter.

Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.

Formulas

$\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}$

$\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}$

$\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}$

If the diameter is equal to the side length of the square, then:
$\implies \sf r=\dfrac{1}{2}s$

Therefore:

$\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}$

So the ratio of the area of the circle to the original square is:

$\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}$

Given:

side length (s) = 6 in
radius (r) = 6 ÷ 2 = 3 in

$\implies \sf \textsf{Area of square}=6^2=36\:in^2$

$\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)$

Ratio of circle to square:

$\implies \dfrac{28}{36}=\dfrac{7}{9}$

5 0

1 year ago

A limited-edition soccer ball costs $30, and the sales tax is 6%. What is the total cost?

frez [133]

Answer:

$31.80

Step-by-step explanation:

The ball will cost 100% of its price plus 6% of its price for a total of 106%.

To use percentages as a factor and multiply, they must be divide by 100, making the multiplication factor version of 106% 1.06.

Multiply the cost of the ball by your multiplication factor:

30 x 1.06 = 31.8

Money is written to two decimal places, making your answer $31.80

6 0

2 years ago

Read 2 more answers

There are 45 new houses being built in a neighborhood. Last month, 1/3 of them were sold. This month, 1/5 of the remaining house

Makovka662 [10]

45 new houses.....last month 1/3 were sold....
1/3(45) = 45/3 = 15 houses sold last month

this month, 1/5 of the remaining houses were sold...
remaining houses left are (45 - 15) = 30
1/5(30) = 30/5 = 6 houses sold this month

houses left : 45 - 15 - 6 = 45 - 21 = 24 houses remain <==

8 0

3 years ago

Can someone pls help

Katyanochek1 [597]

Answer:

x = 35

Step-by-step explanation:

Sum of angles of triangle = 180°

60 + 60 + 4x - 80 = 180
40 + 4x = 180
4x = 140
x = 140/4
x = 35°

3 0

2 years ago

Read 2 more answers

Which reason justifies step 2 in the proof

faust18 [17]

Answer:

Step-by-step explanation:

Given: ∠N≅∠S, line l bisects TR at Q.

To prove: ΔNQT≅ΔSQR

Proof:

From ΔNQT and ΔSQR

It is given that:

∠N≅∠S (Given)

∠NQT≅∠SQR(Vertical opposite angles)

and TQ≅QR ( Definition of segment bisector)

Thus, by AAS rule,

ΔNQT≅ΔSQR

Hence proved.

Statement Reason

1. ∠N≅∠S given

2. ∠NQT≅∠SQR Vertical angles are congruent

3. line l bisects TR at Q. given

4. TQ≅QR Definition of segment bisector

5. ΔNQT≅ΔSQR AAS theorem

Hence proved.

Thus, option D is correct.

3 0

2 years ago