Find the lengths of all four sides : P (2,2), Q (1,-3),R (-4,2),S (-3,7)

Arizbeth spent $20.08 to put 8 gallons of gas in her car. How much would 13 gallons have cost?

Misha Larkins [42]

Answer:

32.63

Step-by-step explanation:

since arizbeth is spending $20.08 to put 8 gallons in her car the first step is to divide 20.08 by 8.Then since you have per gallon you have to figure out what 13 gallons is so you multiply per gallon by 13

8 0

3 years ago

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 explanation also would be super helpful and very appreciated!

xxTIMURxx [149]

Answer:

26%

Step-by-step explanation:

345. 24 - 274 = 71.24

71.24 / 274 =0.26

0.26 * 100 = 26

8 0

3 years ago

Add the following fractions. See the image below

LenKa [72]

Answer:

$\dfrac{19}{840}$

Step-by-step explanation:

The given fraction is:

$\dfrac{1}{168}+\dfrac{3}{180}$

We need to solve it.

The LCM of 168 and 180 is 2520.

So,

$\dfrac{1}{168}+\dfrac{3}{180}=\dfrac{15+3\cdot14}{2520}\\\\=\dfrac{19}{840}$

So, the required answer is equal to $\dfrac{19}{840}$ .

3 0

2 years ago

Find the area of the triangle with the given base and height. b = 3 m and h = 10 1/2 m

svetoff [14.1K]

Statement:

The base of a triangle is 3m and its height is $10 \frac{1}{2}$ m.

To find out:

The area of the triangle.

Solution:

Given, base = 3m, height = $10 \frac{1}{2}$ m
We know,

$\sf \: area \: \: of \: \: a \: \: triangle = \frac{1}{2} \times base \: \times height$

Therefore, the area of the triangle

$\sf = (\frac{1}{2} \times 3 \times 10 \frac{1}{2} ) {m}^{2} \\ \sf = ( \frac{1}{2} \times 3 \times \frac{21}{2} ) {m}^{2} \\ = \sf \frac{63}{4} {m}^{2} \\ = \sf 15\frac{3}{4} {m}^{2}$

Answer:

The area of the triangle is $\sf \: 15 \frac{3}{4} {m}^{2}$

Hope you could understand.

If you have any query, feel free to ask.

5 0

2 years ago

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