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Naddik [55]
3 years ago
12

9. Consider the diagram below. First, solve for x, then y.

Mathematics
2 answers:
xz_007 [3.2K]3 years ago
7 0

Answer:

y = 32; x = 59

Step-by-step explanation:

On the top triangle x+y+89=180 because a triangle's angles add up to 180 degrees, while a quadrilateral's angles add up to 360 degrees.

Angle 89 and the angle below it are supplementary, meaning together they equal 180 degrees.

180 - 89 = 91

So the angle below 89 is 81 degrees.

Now we can subtract the other three angles in the quadrilateral to find the fourth:

360 - (78 + 43 + 91) = 148

So the angle below y is 148 degrees.

Angle y and the angle below it are supplementary, meaning together they equal 180 degrees.

y = 180 - 148

y = 32

All of the angles in a triangle equal 180 degrees:

x = 180 - (32 + 89)

x = 59

aniked [119]3 years ago
6 0

Answer:

x = 59

y = 32

Step-by-step explanation:

x + 78 + 43 = 180

x = 59

y + 59 + 89 = 180

y = 32

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If a=10, What is a/ 2 plus 9​
makkiz [27]

Answer:

a=14

Step-by-step explanation:

if a=10, 10/2 = 5 plus 9 = 14

5 0
2 years ago
Find the derivative of f(x) = 6x + 7 at x = 9
Ket [755]

Answer:

f'(9) = 6

Step-by-step explanation:

f(x) = 6x+7

The derivative is

f'(x) = 6

Evaluated at  x=9

f'(9) = 6

3 0
3 years ago
Read 2 more answers
Martha has $10,000 saved and wants to attend a college with a current tuition of $10,000 a year. She will graduate from high sch
galben [10]

Answer:

$1,592.74

Martha will need to pay $1,592.74 more

Step-by-step explanation:

Using the compound interest/inflation formula;

A = P(1+r)^(t)

Where;

A = final value

P = initial value = $10,000

r = inflation rate = 3% = 0.03

t = time = 5 years

Substituting the values;

A = $10,000(1+0.03)^(5)

A = $11592.740743

A = $11,592.74

How much more will Martha need to save;

C = final value - initial value = A - P

C = $11,592.74 - $10,000

C = $1,592.74

Martha will need to pay $1,592.74 more

8 0
3 years ago
Given sin(u)= -7/25 and cos(v) = -4/5, what is the exact value of cos(u-v) if both angles are in quadrant 3
solmaris [256]

Given:

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

To find:

The exact value of cos(u-v) if both angles are in quadrant 3.

Solution:

In 3rd quadrant, cos and sin both trigonometric ratios are negative.

We have,

\sin (u)=-\dfrac{7}{25}

\cos (v)=-\dfrac{4}{5}

Now,

\cos (u)=-\sqrt{1-\sin^2 (u)}

\cos (u)=-\sqrt{1-(-\dfrac{7}{25})^2}

\cos (u)=-\sqrt{1-\dfrac{49}{625}}

\cos (u)=-\sqrt{\dfrac{625-49}{625}}

On further simplification, we get

\cos (u)=-\sqrt{\dfrac{576}{625}}

\cos (u)=-\dfrac{24}{25}

Similarly,

\sin (v)=-\sqrt{1-\cos^2 (v)}

\sin (v)=-\sqrt{1-(-\dfrac{4}{5})^2}

\sin (v)=-\sqrt{1-\dfrac{16}{25}}

\sin (v)=-\sqrt{\dfrac{25-16}{25}}

\sin (v)=-\sqrt{\dfrac{9}{25}}

\sin (v)=-\dfrac{3}{5}

Now,

\cos (u-v)=\cos u\cos v+\sin u\sin v

\cos (u-v)=\left(-\dfrac{24}{25}\right)\left(-\dfrac{4}{5}\right)+\left(-\dfrac{7}{25}\right)\left(-\dfrac{3}{25}\right)

\cos (u-v)=\dfrac{96}{625}+\dfrac{21}{625}

\cos (u-v)=\dfrac{1 17}{625}

Therefore, the value of cos (u-v) is 0.1872.

6 0
3 years ago
HELLPPP????? PLEASEEEESSSS
Verdich [7]

Answer:

\boxed{43.48 \, \%}

Step-by-step explanation:

The formula for calculating percentage is

\text{Percentage} = \dfrac{\text{Part }}{\text{Whole}} \times 100 \, \%

The "part" is the number of single-shot espressos

The "whole" is the total number of espressos.

\begin{array}{rcl}\text{Total espressos} & = & 46\\\text{-Single-shot espressos} & = & 26\\\text{Double-shot espressos} & = & 20\\\end{array}

\text{ \% Double-shot}=\dfrac{20}{46} \times 100 \, \% =\mathbf{43.48 \, \%}\\\\\boxed{\mathbf{43.48 \, \%}} \text{ of the espressos were double-shot}

8 0
3 years ago
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