MATHEMATICS HIGH SCHOOL

Sketch and solve the following triangles.1. The legs of a right triangle measure 5cm and 12cm. What is the measure of its hypotenuse?

2. In ∆ABC and C is a right angle, if c = 12 and b = 10, find cos A.

3. In ∆ABC and C is a right angle, the opposite of ∠A = 12. if the hypotenuse = 13, find tan θ.

4. If sin A = $(15)/(17)$ What is tan A?

5. If cot θ = $(7)/(24)$ What is sec θ?

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Answers

Answer 1

Answer:

Answer:

Use Pythagorean:

c² = a² + b²

Apply to given and find c:

c² = 5² + 12²
c² = 169
c = √169
c = 13 cm

cos = adjacent / hypotenuse
cos A = b/c
cos A = 10/12 = 5/6

Assumed θ is ∠A, this is not too clear

We have:

a = 12
c = 13

We know that:

tan A = a/b

Find b:

b = √c² - a² = √13²-12² = √25 = 5

tan A = 12/5

Given

sin A = 15/17

We know that:

sin A = a/c, so a = 15 and c = 17
tan A = a/b

Find b:

b = √c² - a²= √17²-15²= √64 = 8

tan A = a/b = 15/8

Given

cot θ = 7/24

We know:

cot = adjacent / opposite
sec = 1/cos = hypotenuse / adjacent

From the cot we have:

adjacent = 7, opposite = 24

Hypotenuse is:

√24² + 7² = √625 = 25

So,

sec θ = 25/7

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u were paid 9 dollars an hour

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Answer:

x - 1 and x + 2

Step-by-step explanation:

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A polynomial function has roots –5 and 1. Which of the following could represent this function?

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Answer: f(x)=(x+5)(x-1)

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Two consecutive odd integers have a sum of 32. Find the integers.

Answers

The two consecutive odd integers are 15 and 17.

What is a number system?

A numeral system is a way of writing numbers; it's a way of mathematically notating a set of numbers by using a consistent set of digits or other symbols. In various numeral systems, the same set of symbols may represent various numbers.

Given that two consecutive odd integers have a sum of 32.

Let

x = first consecutive odd

x + 2 = second consecutive odd

Based on the problem, we equate

x + (x + 2) = 32

Solving for x,

2x + 2 = 32

2x = 32 - 2

2x = 30

x = 30/2

x = 15

and x + 2 = 15 + 2 = 17

Therefore, the two consecutive odd integers are 15 and 17.

To know more about a number system follow

brainly.com/question/13162939

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Let
x = first consecutive odd
x + 2 = second consecutive odd

Based on the problem, we equate
x + (x + 2) = 32
Solving for x,
2x + 2 = 32
2x = 32 - 2
2x = 30
x = 30/2
x = 15
and x + 2 = 15 + 2 = 17

Therefore, the integers are 15 and 17.

Does anyone seriously know how to do these

Answers

Thats simple!
h(x)= $(x^(2)+3x )/(4x+27)$
find h(-8)
All we need to do is PLUG IN THE -8
h(-8)= $((-8)^(2)+3(-8) )/(4(-8)+27)$
= $(64-24)/(-32+27)$ (negative²=positive, negative×positive=negative)
= $(40)/(-5)$
h(-8)=-8

A college student realized that he was spending too much money on fast food. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towards fast food. How much can he spend in December, taking into consideration that in the other 4 months he spent $100, $25, $80, and $30, respectively? Round your answer to two decimal places, if necessary.

Answers

Answer:

The college student can spend $15.00 in December.

Step-by-step explanation:

This can be calculated as follows:

Let y represents the amount to spend in December.

The can now us the formula for calculating a mean is as follows:

Mean = Sum of montlhy spending / Number of months ...... (1)

From the question, we have:

Mean = $50

Sum of monthly spending = $100 + $25 + $80 + $30 + y = $235 + y

Number of months = 5

Substituting the values into equation (1) and solve for y, we have:

$50 = ($235 + y) / 5

$50 * 5 = $235 + y

$250 = $235 + y

$250 - $235 = y

$15.00 = y

Therefore, the college student can spend $15.00 in December.

Final answer:

To achieve a mean expenditure of $50 per month on fast food across 5 months, the student can only spend $15 in December, considering that he has already spent a total of $235 in the other 4 months. This keeps his total spending at $250, giving an average of $50 per month.

Explanation:

The student wants to spend a mean of $50 per month on fast food for 5 months. In 4 of those months, he has already spent $100, $25, $80, and $30, respectively. That totals to $235 in spent funds already. Since the goal is a $50 monthly average, we multiply $50 by 5 months to get a total desired spending of $250. To find out how much he can spend in December, we subtract the total already spent from the total desired spending. As such, he can spend $250 - $235, which equals to $15 in December.

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