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3 years ago

Explain why a + b = d.

Mathematics

1 answer:

Lilit [14]3 years ago

7 0

Answer:

a + b = d because the inside of a triangle and a line both equal 180 degrees.

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Given sin A = 12/13 and that angle A is in Quadrant 1,

UkoKoshka [18]

We have been given that $\text{sin}(A)=\frac{12}{13}$ and angle A is in quadrant 1. We are asked to find the exact value of $\text{cot}(A)$ in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

$\text{cot}=\frac{\text{Adjacent}}{\text{Opposite}}$

Now we will find adjacent side using Pythagoras theorem as:

$\text{Adjacent}^2=\text{Hypotenuse}^2-\text{Oppoiste}^2$

$\text{Adjacent}^2=13^2-12^2$

$\text{Adjacent}^2=169-144$

$\text{Adjacent}^2=25$

Let us take positive square root on both sides:

$\sqrt{\text{Adjacent}^2}=\sqrt{25}$

$\text{Adjacent}=5$

Therefore, adjacent side of angle A is 5 units.

$\text{cot}(A)=\frac{5}{12}$

Therefore, the exact value of cot A is $\frac{5}{12}$ .

5 0

3 years ago

Mr. McBride ordered 6 cheese pizzas and 7 pepperoni pizzas and paid $153.50 for his son's birthday party. He realized he was goi

Marat540 [252]

Let x = cost of one cheese pizza.

Let y = cost of one pepperoni pizza.

Set up a system of equations.

6x + 7y = 153.50

2x + 2y = 47.00.

Multiply the second equation by -3

6x + 7y = 153.50

-6x - 6y = -141.00.

Add the equations together

y = $12.00.

Plug 12 into one of our original equations.

2x + 2(12) = 47.

Simplify the left side.

2x + 24 = 47.

Subtract 24 from each side.

2x = 23.

Divide each side by 2

x = $11.50

In conclusion, one pepperoni pizza costs $12.00

8 0

3 years ago

X² – x² – 3x + 3<br> all rational zeros to a polynomial

Mrrafil [7]

Answer:

x = 1

Step-by-step explanation:

${x}^{2 } - {x}^{2} - 3x + 3 \\ - 3x + 3 \\ 3x = 3 \\ x = 1$

4 0

3 years ago

Adelaide paid $35 for a manicure and gave the manicurist a 20% tip.

Inessa05 [86]

She paid $42 dollars in total.

3 0

3 years ago

3(t−2)=−1 What value of t t makes the following equation true?

pashok25 [27]

Answer:

t=5/3

Step-by-step explanation:

in order to get our answer, we have to first open it up which comes to 3t-6=-1

next,we have to isolate the variable, so we add (6) to (-1)

then we get 3t=5

so, t=5/3

4 0

3 years ago