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3 years ago

8

Crystal's soccer team won 14 of the 20 games they played last season. What percent of games played did they win?

1 answer:

love history [14]3 years ago

3 0

Answer:

70%

Step-by-step explanation:

hooe this helps plz follow ❤❤

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If <img src="https://tex.z-dn.net/?f=tan%20%28x%29%20%3D%20%5Cfrac%7B5%7D%7B12%7D" id="TexFormula1" title="tan (x) = \frac{5}{12

Alekssandra [29.7K]

Explanation:

First, we need to find the values of the sine and cosine of x knowing the value of tan x and x being in the 3rd quadrant. Since tan x = 5/12, using Pythagorean theorem, we know that

$\sin x = -\frac{5}{13}\;\;\text{and}\;\;\cos x = -\frac{12}{13}$

Note that both sine and cosine are negative because x is in the 3rd quadrant.

Recall the addition identities listed below:

$\sin(\alpha + \beta) = \sin\alpha\sin\beta + \cos\alpha\cos\beta$

$\Rightarrow \sin(180+x) = \sin180\sin x + \cos180\cos x$

$\;\;\;\;\;\;= -\sin x = \dfrac{5}{13}$

$\cos(\alpha - \beta) = \cos\alpha \cos\beta + \sin\alpha \sin\beta$

$\Rightarrow \cos(180 - x) = \cos180\cos x + \sin180\sin x$

$\;\;\;\;\;\;=-\cos x = \dfrac{12}{13}$

$\tan(\alpha - \beta) = \dfrac{\tan\alpha - \tan\beta}{1 + \tan\alpha\tan\beta}$

$\Rightarrow \tan(360 - x) = \dfrac{\tan 360 - \tan x}{1 + \tan 360 \tan x}$

$\;\;\;\;\;\;= -\tan x = -\dfrac{5}{12}$

Therefore, the expression reduces to

$\sin(180+x) + \tan(360-x) + \frac{1}{\cos(180-x)}$

$\;\;\;\;\;= \left(\dfrac{5}{13}\right) + \left(\dfrac{5}{12}\right) + \dfrac{1}{\left(\frac{12}{13}\right)}$

$\;\;\;\;\;= \dfrac{49}{26}$

5 0

2 years ago

Paraphin [41]

The area of a shape is the amount of space a shape can occupy, while the perimeter is the sum of its lengths.

<em>The perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>
<em>The area of the sanctuary is 27 square units</em>

We have:

$A = (5,7)\\B=(8, 7)\\C=(8, 1)\\D=( 1, 1)\\E=( 1, 4)\\F= ( 5,4)$

<u>Perimeter</u>

See attachment for the layout of the sanctuary

$BC = \sqrt{(8 - 8)^2 + (7 - 1)^2} = 6$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

From the attachment, the sides are

<em>AB, BF, FC, CD, DE and EA</em>

Start by calculating the length of each side using the following distance formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_2)^2}$

So, we have:

$AB = \sqrt{(5 - 8)^2 + (7 - 7)^2} = 3$

$BF = \sqrt{(8 - 5)^2 + (7 -1)^2} = \sqrt{45} = 3\sqrt 5$

$FC = \sqrt{(8 - 5)^2 + (1 -4)^2} = \sqrt{18} = 3\sqrt 2$

$CD = \sqrt{(8 - 1)^2 + (1 - 1)^2} = 7$

$DE = \sqrt{(1 - 1)^2 + (1 - 4)^2} = 3$

$EA = \sqrt{(1 - 5)^2 + (4 -7)^2} = 5$

So, the perimeter (P) is:

$P = AB + BF + FC + CD + DE + EA$

$P = 3 + 3\sqrt 5 + 3\sqrt 2 + 7 + 3 + 5$

$P = 18 + 3\sqrt 5 + 3\sqrt 2$

<em>Hence, the perimeter is </em> $18 + 3\sqrt 5 + 3\sqrt 2$ <em>units</em>

<u />

<u>Area</u>

To calculate the area, we need to divide the sanctuary into three.

<em>Triangle ABF</em>
<em>Triangle EFA</em>
<em>Trapezium CDEF</em>

The area of ABF is:

$Area = \frac 12 \times AB \times FA$

Where:

$AB = 3$

$FA = \sqrt{(5 - 5)^2 + (4 - 7)^2} = 3$

$Area = \frac 12 \times 3 \times 3$

$Area = \frac 92$

The area of EFA is:

$Area = \frac 12 \times EF \times FA$

Where:

$FA = 3$

$EF = \sqrt{(1 - 5)^2 + (4 - 4)^2} = 4$

So:

$Area = \frac 12 \times 4 \times 3$

$Area = 6$

The area of CDEF is:

$Area = \frac 12(CD + EF) \times DE$

Where

$CD = 7$

$EF = 4$

$DE = 3$

So, we have:

$Area = \frac 12 (7 + 4) \times 3$

$Area = \frac 12 \times 11 \times 3$

$Area = \frac {33}2$

So, the area of the sanctuary is:

$Area = \frac 92 + 6 + \frac {33}2$

$Area = \frac {9 +12 + 33}2$

$Area = \frac {54}2$

$Area = 27$

<em>Hence, the area of the sanctuary is 27 square units</em>

Read more about areas and perimeters at:

brainly.com/question/11957651

8 0

3 years ago

3x1 1 5-6 multiply the numbers and simplify the answer

weeeeeb [17]

Answer:

339

Step-by-step explanation:

3*115-6

=345-6

=339

4 0

3 years ago

Margaret bought 1,575 grams of rice. how many kg of rice is that?

bearhunter [10]

1 kg = 1000 grams

? kg = 1575 grams

1.575 kg = 1575 grams

1,575 grams is 1.575 kilograms.

6 0

3 years ago

Which expression is equivalent to x1/2y5/2 in simplified form?

Archy [21]

I hope this helps you

3 0

3 years ago