Mathematics High School

The hypotenuse of a triangle measures 12 inches, and the measure of one of the acute angles is two less than three times the measure of the other acute angle. What is the area of the triangle? Round your answer to the nearest square inch. (Note: The area of a triangle is 1/2bh, where the base and the height of the triangle are perpendicular).

Answers

Answer 1

Answer:

26 sq in.

Step-by-step explanation:

Let x = measure of one acute angle

3x - 2 = measure of other acute angle

Since the triangle is a right triangle, the sum of the measures of the acute angles is 90

x + 3x - 2 = 90

4x - 2 = 90

4x = 92

x = 23

90 - 23 = 67

The acute angles are 23° and 67°

Now, let a = length of side opposite the 23° angle

sin 23 = a/12

a = 12 sin 23

Let b = length of the side opposite the 67° angle

sin 67 = b/12

b = 12 sin 67

Area = 1/2ab = 1/2(12 sin 23°)(12 sin 67°)

= 25.90

26 sq in to the nearest inch

Wow! That is quite the problem.

Related Questions

PLEASE HELP I WILL GIVE BRAINLIEST ACTUALLY PLEASE HELP

Answers

Answer:

$60

Step-by-step explanation:

Can some please help me on question 2 I am just confused.

Answers

Answer:

ok so weknow tht 160 pounds cost 9.60 how much do u think will 1.50 cost

Step-by-step explanation:

A new savings account is opened with $400 and gains 3% every year. What is the value of the account at 32 years?

Answers

Answer:

1072

Step-by-step explanation:

Compare the functions shown below: g(x) f(x) = −3x + 2 cosine function with y intercept at 0, negative 3 h(x) = 4 sin(2x + π) + 3 Using complete sentences, explain which function has the greatest y-intercept.

Answers

Answer:

3 h(x) = 4 sin(2x + π) + 3

Step-by-step explanation:

The function h(x) has a greater y-intercept

How to compare the functions?

The functions are given as:

f(x) = -3x + 2 h(x) = 4 sin(2x + π) + 3

Set x to 0,to calculate the y-intercepts

f(0) = -3(0) + 2 = 2

h(0) = 4 sin(2(0) + π) + 3 = 3

From the above computation, we have:

f(0) = 2

h(0)= 3

By comparison, we have:

h(0) > f(0)

This means that the function h(x) has a greater y-intercept

Answers

Answer:

for the 1st year she earned 160 so for 3 years she will earn $480

If z=2
3 (x-12) and x=39, then what is z?

Answers

Answer:

621

Step-by-step explanation:

23(39-12) > 23(27)

23(27)= 621

what is the product
4/6 x 9

13/16

36/54

3

6

Answers

the answer is 6! have a good day

Which one doesn’t belong?
Come up with one reason for at least 3 different boxes

Answers

Answer:

I think box #1 doesnt't belong because it say spend $100 and get $10 off

Step-by-step explanation:

A .Write an equation for the trend line in slope -intercept form .

Answers

Given:

The graph of a trend line.

To find:

The equation of the trend line is slope intercept form.

Solution:

From the given graph it is clear that the equation of the trend line is passes through the points (0,25) and (5,50).

Slope of the line is:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\dfrac{50-25}{5-0}[/tex]

[tex]m=\dfrac{25}{5}[/tex]

[tex]m=5[/tex]

The line passes through the point (0,25). So, the y-intercept of the line is 25.

Slope intercept form of a line is:

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

The slope intercept from of the line is:

[tex]y=(5)x+(25)[/tex]

[tex]y=5x+25[/tex]

Therefore, the equation for the trend line in slope -intercept form is [tex]y=5x+25[/tex].

Anyone help me solve for y.

Answers

Answer:

y = - 4

Step-by-step explanation:

Given

y = 2x + ( - 2) , that is

y = 2x - 2 ← substitute x = - 1

y = 2(- 1) - 2 = - 2 - 2 = - 4

This is confirmed by the point (- 1, - 4 ) on the graph

X = -1
So if you Plug that in to your problem it is shown as y=2(-1)+-2.
2•-1 is -2 and when added to -2 you answer is -4.
Y=-4

Tiara attended 12 piano classes in four weeks. If she attended the same number of classes each week, which equation can be used to find the number of classes she attended every week?
A.4 + c = 12
B.4c = 12
C.12c = 4
D.12 - c = 4

Answers

Answer:

Step-by-step explanation:

Because i'm smart and did the math.

I need help I'm struggling :(

Answers

Ohh !! I’ll help you. I think your suppose to find the area of the rectangle prism? I suppose?
To find the rectangular prism, you’ll have to use this formula : LWH
L= length
W=width
H=height
Multiply those together and you will get your answer.

V=LWH
V=6*6*10
V=36*10
V=360 square 2 is your answer! ( remember to put units )

- have a great day :)

He determined that the value of 6 in 76,345 is 100 times the value of 6 in 34,675. Part A: Is Lucas right? Part B: Explain why Lucas is right or wrong.

Answers

Answer:

Lucas is not right.

Step-by-step explanation:

To find: whether the value of 6 in 76,345 is equal to 100 times the value of 6 in 34,675

Solution:

Value of 6 in 76,345 = 6,000

Value of 6 in 34,675 = 600

Now 6000 = 10 × 600

So,

Value of 6 in 76,345 is equal to 10 times the value of 6 in 34,675.

Therefore, Lucas is not right.

Answer:

Part A: Lucas is wrong.

Part B: The value of 6 in 76,345 is 6,000 and the value of 6 in 34,675 is 600.

Part C: The value of 6 in 76,345 is equal to 10 times the value of 6 in 34,675.

10 × 600 = 6,000

Step-by-step explanation:

I put this on each of my answers and I got all three parts correct. Hope this helps you!!!!

Please mark my answer as the Brainiest!!!!!

Thank You!!!!!!!!

What is 2 2/13 divided by 2/3

Answers

Answer:

3.23

Step-by-step explanation:

Answer:

the answer is 3.23 hahahhhhahahhahndjalid;jslakjsakl sorry needed that to submite the answer

PLS HELP I WILL MARK THE BRAINLIEST.

Answers

Answer: HELP ASA! I NEED HELP ON MY TWO LAST QUESTIONS

Step-by-step explanation:

is the value of
is 14?

Answers

Answer: So in the number 14, there is one ten and four ones—10 + 4 = 14. If we change that 1 to a 2, we get 24, or twenty-four. The number 2 in the tens place tells us there are two tens. Each place value is 10 times larger than the place value to the right of it.

Step-by-step explanation:

A bottle of soap costs $3.45 for 64ounces. What is the cost per ounce?

Answers

Five cent per a ounce

Answer:

$0.05

Step-by-step explanation:

All you have to do us divide the cost by the amount of ounces

3.45 ÷ 64 is about 0.05

The full answer is 0.05390625

Since we are talking about money, it should be $0.05

What’s the formula to find the area of a right triangle? (pythagorean theorem)

Answers

Answer:

multiply the hight and length then divide it by 2

Step-by-step explanation:

A zoo starts off with 8 monkeys, and the monkeys population
doubles every year. How many monkeys are in the zoo after 4
years?
monkeys

Answers

Answer:

Step-by-step explanation:

64 because the first year you’ll have 8 monkeys which doubles for the second year where you’ll have 16 monkeys. in the third year they will be 32 and it doubles in the last year making the total 64

write a linear equation using y=mx+b

Answers

Jsjsnsnendndndnndjxjxjcjcjcjjcjxjx

According to the line of best fit, if a batter struck out about 80 times, about how many hours did the batter practice?

Answers

Answer:

The batter practice for 4 hours

Step-by-step explanation:

Here, we want to use the line of best fit for an estimation

What we will do here is to identify the point 80 strikecuts on the y-axis

After getting this, we trace this right wards toward the line of best fit

Upon getting this, we trace down to the x-axis to get the number of hours indicative of the strikecuts

By doing this, we can see that the number of hours is simply 4 hours

Emma bought three cans of tennis balls for $4 each. Sales tax for all three cans was $0.95. Wh
expression shows what Emma paid?

Answers

Answer:

4(3)+0.95=X

Step-by-step explanation:

Answer:

A sixth-grade student bought three cans of tennis balls for $4 each.

The sales tax for each can was $0.95.

To Find :

The total amount the student spent.

Solution :

Price of each can including taxes :

p = $( 4 + 0.95 )

p = $4.95

So, price of 3 such cans including tax is :

P = p×3

P = $( 4.95×3 )

P = $14.85

Therefore, total amount spend by the student is $14.85 .

Step-by-step explanation:

Which is equivalent to x2 - 4x = 12 by completing the square

Answers

Answer:

x = 6 , − 2

Step-by-step explanation:

Solve for x

2(x+5)-7=3(x-2)

Answers

x=9

I'm sorry if I'm wrong

Answer:

x=9

Step-by-step explanation:

2(x+5)-7=3(x-2)

distribute the 2 and 3 which gives you

2x+10-7=3x-6

combine like terms

2x+3=3x-6

move the 2x to the other side by subtracting which gives you

3=x-6

add 6 to the other side which gives you

9=x

additive inverse of 8/-13 pls help fast

Answers

Answer:

8/13

hope this answer helps you.....

Please help! Check to see if I have all of them correct! Will mark brainlist

Answers

I am pretty sure they are all right

HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP

Answers

9514 1404 393

Answer:

B. rectangle, not a square

Step-by-step explanation:

When you plot the points, you see the lines between them have a rise/run of 3/2 or -2/3. The product of these numbers is -1, so the sides of the figure are perpendicular (not a rhombus, not a trapezoid). The figure is not square, so is ...

rectangle that is not a square

find the area please

Answers

Answer:

86.54625

Step-by-step explanation:

Formula: a = πr², r = d/2

Given: π = 3.14, d = 10.5

Sub: a = (3.14)r²

Find r.

10.5/2

5.25

Sub: a = (3.14)5.25²

Solve: 86.54625

Someone pls help:( im new tysm if u doo!

Answers

75.5 all you do is add them

59 + 16.5= 75.5! I’m new too let me know if you need anymore help you can always message me! (I’m in seventh grade and I really like to help people!, it’s really entertaining for some reason)

100 POINTS!!! The table shows the values of a function f (x), What is the average rate of change of f (x) over the interval from x = 5 to x = 9? Show your work.

Answers

Answer:

1. (f(x)-f(a))/(x-a) **A(x)=(f(x)-f(a))/(x-a) This average rate of shift attribute is designated by the letter A. *f(x) - f(a) represents the difference in the function f as the input transitions from a to x. x - a represents the change in the input of the function f.

f(5)=-2 f(9)=14 (f(5)-f(9))/(5-9)=(-2-14)/-4=4 (f(5)-f(9))/(5-9)=(-2-14)/-4=4

Over the range of x = 5 to x = 9, the average rate of change is 4.

2. g(x)=2x2+13x+1, f(x)=4x2+6x

(f/g)(x)=(4x2+6x)/(2x2+13x+1) (f/g)(x)=(4x2+6x) (f/g)(x)=(4x2+6x)

f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85,155/116,180/151,238/190,304/233,378/280 f(x): 88/85

3. f(x)=x2-6x+8, g(x)=x-2, g(x)=x-2, f(x)=g (x)

x2-6x+8=x-2, x2-6x-x+8+2=0, x2-7x+10=0, x2-6x-x+8+2=0

x1,2=(7+(72-4*10))/2=(7+3)/2 x1=5, x2=2 x1=5 x2=2

Step-by-step explanation:

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