In a right triangle the measure of one acute angle is 4 times the difference of the measure of the other acute angle and 5. Find the measure of each acute angle

Answers

Answer 1

Answer:

The measures are 22 and 68 degrees

Step-by-step explanation:

for a right triangle, the total angle measure gives 90

Let one of the acute angle be x and the other be y

The measure of one of the acute angle is 4 times the the difference of the measure of the other angle and 5

x = 4(y-5)

Also x + y = 90

Put i into ii

4(y-5) + y = 90

4y-20 + y = 90

5y-20 = 90

5y = 90 + 20

5y = 110

y = 110/5

y = 22

But;

x = 4(y-5)

x = 4(22-5)

x = 4(17)

x = 68

Answer 2

The sum of the acute angles in a right-angled triangle is 90.

The acute angles are 22 and 68 degrees

Let the acute angles be x and y, such that:

[tex]\mathbf{y = 4(x - 5)}[/tex]

So, we have:

[tex]\mathbf{x + y = 90}[/tex]

Substitute 4(x - 5) for y

[tex]\mathbf{x + 4(x - 5) = 90}[/tex]

Open brackets

[tex]\mathbf{x + 4x - 20 = 90}[/tex]

Add x and 4x

[tex]\mathbf{5x - 20 = 90}[/tex]

Add 20 to both sides

[tex]\mathbf{5x = 110}[/tex]

Divide both sides by 5

[tex]\mathbf{x = 22}[/tex]

Recall that:

[tex]\mathbf{y = 4(x - 5)}[/tex]

So, we have:

[tex]\mathbf{y = 4(22 - 5)}[/tex]

[tex]\mathbf{y = 68}[/tex]

Hence, the acute angles are 22 and 68 degrees

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Related Questions

A participant in an experiment who incorrectly believes she is receiving treatment and reports an improvement in their condition is experiencing

blinding.
placebo.
control group.
placebo effect.

Answers

Answer:

placebo.

Step-by-step explanation:

Placebo bc thats when like u think something is like doing something but its not it that makes sence

I need help quick what does this equal 3 4⁄6 × 7⁄3 × 9⁄2=

Answers

Does this answer your question

Step-by-step explanation:

try that hope this helps out

Look at the photo pick A B C D either one explanation not needed thank you! <3 [13]

Answers

Answer: D

Step-by-step explanation: Correct me if I'm wrong.....

The scatterplot and trend line show the number of pass
attempts and passing yards a football team had during
seven seasons.
Because none of the data points lie on the trend line,
you must find two points on the line.
Point 1 can be
Point 2 can be
Using those twe (26, 2855) ope of theline is|
Football Passing Statistics
2875fy
2870
2865
2860
E2855
2850
2845
(233,2850)
(245, 2860)
230 233 238 239 242 245 248 251 254257
Pass Attempts
Done

Answers

Answer:

Step-by-step explanation:

The slope of the trend line in the given scatter plot, using the two chosen points (236, 2855) and (248, 2865) is: 0.83.

What is the Slope of a Trend Line?

The slope of a trend line = change in y/change in x.

Given the scatter plot, we can choose the following points, which we would use in finding the slope of the trend line:

(236, 2855) and (248, 2865).

Slope = (2865 - 2855)/(248 - 236)

Slope = 10/12

Slope = 0.83

Therefore, the slope of the trend line in the given scatter plot, using the two chosen points (236, 2855) and (248, 2865) is: 0.83.

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In 1983, a microwave oven cost $78.75. Today, a microwave oven costs $92.66. If the CPI is 177, what is the relation of the actual price of a microwave oven to the expected price, to the nearest cent?
a. The actual price is $46.73 lower than the expected price.
b. The actual price is $5.59 lower than the expected price.
C. The actual price is $13.91 higher than the expected price.
d. The actual price is $71.35 higher than the expected price.​

Answers

Answer:

its A on e2020

Step-by-step explanation:

The actual price is $46.73 lower than the expected price.

The actual price is $46.73 lower than the expected price.

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Now, The Formula for Consumer Price Index is,

⇒ [tex]CPI = C_{t} / C_{0}[/tex]

Where, CPI = consumer price index in the current period

Ct = expected cost in current period

C₀ =cost in the base period

Now, It is given that;

Price in base period in 1983 is, C₀= $78.75

The actual cost of the microwave oven = $92.66

Consumer Price Index= 177

So, We Can expected price of microwave oven in the current period

Ct = CPI * C₀ /100

    = 177 × 78.75/100

    = $139.39

Thus, Difference between the actual price and expected price is,

= 139.39 - 92.66

= $46.73

Therefore, The actual price is $46.73 lower than the expected price.

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Tomic and Brooke make a game of shooting free throws. Each basket is worth 2 points. Each miss is worth
they make 16 baskets. What is the correct number of points that Tomic and Brooke scored?
points. Out of 30 free throws,
Select the correct answer.
A 40
B. 50 1 / 2
c. 28
D. 29 1/2

Answers

Answer:

Its technically impossible to tell if you don't tell us how many throws each person did.

Step-by-step explanation:

but i would guess 40

Answer:

Same I would guess A) 40 as well

Step-by-step explanation:

Which of the following angles is one of the two reflexive interior angles in
this polygon?
Pls help me

Answers

Answer:

Its D i got it right

Answer:

the answer is d if u look u will see that h is the

Step-by-step explanation:

The vertices of a polygon are shown below.
P(1, 3). Q2,3), R(-4, 1),S(-4,-3), T(-2, -5), U(1, -5), V(3, -3),w(3, 1)
Which polygon has these vertices?
Hexagon
Plzzz help I will mark brainlest my time is running out!!!!!

Answers

Answer:

The Answer is C

Step-by-step explanation:

This applies to your exam.

Answer:

C

Step-by-step explanation:

This is correct on edge 2020.

Solve 3/5x=15
Please

Answers

Answer:

dude

if 3 = 15

5x = 5.5=25

Step-by-step explanation:

hope it helps

Consider the function () = 2 + 3. Find its average rate of change on the interval −1 ≤ ≤ 3.

Answers

Answer:

See Explanation

Step-by-step explanation:

The function is not properly given. So, to solve this question I'll assume it is:

f(x) = x² + 3

Required

Calculate the average rate of change on −1 ≤ x ≤ 3.

[The average rate of change (R) is calculated using:]

R = (f(b) - f(a))/(b - a)

[Where]

a ≤ x ≤ b = −1 ≤ x ≤ 3.

[This means that]

a = -1

b = 3

[Solving f(b); We have]

f(x) = x² + 3

[Substitute b for x]

f(b) = b² + 3

[Substitute 3 for b]

f(3) = 3² + 3 = 9 + 3 = 12

[Solving f(a); We have]

f(x) = x² + 3

[Substitute a for x]

f(a) = a² + 3

[Substitute -1 for b]

f(-1) = (-1)² + 3 = 1 + 3 = 4

[So, the equation becomes]

R = (f(b) - f(a))/(b - a)

R = (12 - 4)/(3 - (-1)

R = 8/(3+1)

R = 8/4

R = 2

[Hence, the average rate of change is 2]

If the mode of the data is 34.5, find the missing frequency 'f':
Class
0-15
15 - 30
30 – 45
45 - 60
60 – 75
Frequency
2
7
f
3
7​
please answer!

Answers

Given:

Frequency distribution table.

Mode = 34.5

To find:

The value of missing frequency 'f'.

Solution:

Formula for mode is

[tex]Mode=l+\dfrac{f_1-f_0}{2f_1-f_0-f_2}\times h[/tex]

where, l is lower limit of modal class, [tex]f_1[/tex] is frequency of modal class, [tex]f_0[/tex] is frequency of preceding class, [tex]f_2[/tex] is frequency of succeeding class, h is class size.

Mode is 34.5, so the modal class is 30-45. So,

[tex]l=30,f_1=f,f_0=7, f_2=3,h=45-30=15[/tex]

Putting these values in the above formula, we get

[tex]34.5=30+\dfrac{f-7}{2f-7-3}\times 15[/tex]

[tex]34.5-30=\dfrac{f-7}{2f-10}\times 15[/tex]

[tex]4.5=\dfrac{f-7}{2f-10}\times 15[/tex]

Divide both sides by 15.

[tex]\dfrac{4.5}{15}=\dfrac{f-7}{2f-10}[/tex]

[tex]0.3=\dfrac{f-7}{2f-10}[/tex]

[tex]0.3(2f-10)=f-7[/tex]

[tex]0.6f-3=f-7[/tex]

Separating variable terms, we get

[tex]0.6f-f=3-7[/tex]

[tex]-0.4f=-4[/tex]

Divide both sides by -0.4.

[tex]f=\dfrac{-4}{-0.4}[/tex]

[tex]f=10[/tex]

Therefore, the value of f is 10.

2) Graph by making a
table.
y=x-4

Answers

Answer:

Explanation:

y= x-4

is in the slope-intercept form for a linear equation,

y= mx+b

, where

m

is the slope and

b

is the y-intercept. In the given equation,

m= 1

and

b= 4

.

To make a table to graph, give various values to

x

and solve for

y

.

Ordered Pairs

x......y

4...8

2....6

0.......4

2......2

4......0

Plot each ordered pair and draw a straight line through the points.

graph{y=-x-4 [-14.24, 14.23, -7.12, 7.12]}

Mrs. Crimm signed up to bring two dozen cupcakes for the school bake sale. She made one dozen, but her children ate 3 of the cupcakes. Which of the following could be used to determine c, the number of cupcakes Mrs. Crimm needs to bake?

Answers

The number of cookies she needs to bake is 4 bc it’s half of 8

Please help me. Thank you to anyone that helps!

Answers

It would be c or d because the pic shows you how it is slanted

Can someone explain what f(12) means?

Answers

Answer:

A special relationship where each input has a single output. It is often written as "f(x)" where x is the input value. Example: f(x) = x/12 ("f of x equals x divided by 12")

Step-by-step explanation:

open this pic and I'll give brainliest answer ​

Answers

Answer:

wait im confused open the picture or answer it?

Step-by-step explanation:

495 = 165 + 55m
What is m?

Answers

Answer: M = 6 can i have brainliest?

Step-by-step explanation:

Answer:

m=6

Step-by-step explanation:

First isolate the m by subtracting 165 from both sides.

495-165=330

165-165=0

330=55m

Since you know 330 is 55m to find m all you need to do is divide by 55 on both sides.

330/55=6

55m/55=m

6=m

For which x is f(x)=-3?​

Answers

Answer:

This Problem has no answer

Step-by-step explanation:

if you have 1 variable you at least 2 facts that aren't the same to solve for the variable

Answer:

This problem does not have a definite answers

It can have infinite answers

What are the three pairs of parallel segments in ABC?

Answers

Answer:

AB || YZ, BC || XY, AC || XZ

In a school of 450 students, 110 of them are in the choir, 240 of them are in the band and 60 students are in the choir and the band.
please help

Answers

Answer:

whats the question?

Step-by-step explanation:

Answer:

Okay so by the looks of it you need to know how many people aren't in anything.

Step-by-step explanation:

110 + 240 = 350

450 - 350 = 100

100 - 60 = 40

So 40 students are in nothing. But you probably need to know how many students are in band. I would guess around 30 students are in band.

I hope this helped if it didn't I'm sorry.

Find the surface area of this triangular prism.
Please explain as well, I’m struggling with it.

Answers

Answer:

SA= 84 cm^2

Step-by-step explanation:

So first locate all the surfaces

we got 5 sides in total

Now calculate each one

Lets start with the 2 triangles

so formula for area of triangl is 1/2(b*h)

So in this case it’s 6

Now there are 2 identical triangles

So Times the 6 by 2

You’ll get 12

Thats 2 sides

Now for the side with the rectangle of 5cm and 6cm

Area of rectangle is 5*6=30

That would onay be 1 side

Now for the bottom of the prisim which is the side with 4cm and 6cm

Same rectangle so multiply

4*6=24

Thats another side down

The last side is on the left with the back not visible. The two dimensions are 6 and 3

Now multiply 6*3

18

Now add up your total

18+24+12+30=84

So 84 cm^2 OR 84 square centimeters

Answer:

84 [tex]cm^{2}[/tex]

Step-by-step explanation:

To find the surface area of a prism, one will have to find the area of each of the sides of the prism, then add the areas up. First, find the dimensions of each of the sides

Front; 5 x 6

Front triangle; 3 x 4

Back triangle; 3 x 4

Bottom; 4 x 6

Back; 3 x 6

The front is a rectangle, hence one has to [tex]base * height[/tex] to find the area;

5 x 6

= 30

The front triangle is a triangle, hence on has to do [tex]\frac{base * height}{2}[/tex] to find the area;

[tex]\frac{3*4}{2}[/tex]

= 6

The back triangle is a triangle, hence on has to do [tex]\frac{base * height}{2}[/tex] to find the area;

[tex]\frac{3*4}{2}[/tex]

= 6

The back is a rectangle, so one has to do [tex]base * height[/tex] to find the area;

4 * 6

= 24

The bottom is a rectangle,  o one has to do [tex]base * height[/tex] to find the area;

3 * 6

= 18

Noe one has to add up all the areas to find the total surface area;

Front + Front_triangle + Back_triangle + Bottom + Back

30 + 6 + 6 + 24 + 18

= 84

Tim has x beads. Amy has two more beads than Tim. Sarah has five times as many beads as Amy. How many beads does Sarah have?

Answers

Answer:well we need to know how mmch tim has so like

x?+2 is amy

x?+2*5 is sarah

Step-by-step explanation:

Starter
Question 1: Simplify each of the following
(a) y + y + y + y
(b) w+W+W+W + W
(c) a + a + a + a + a + a
(d) 5+$+
(e) nun
Og+ 8 + 8 + g-8
(g) y + y + y + y - y - y
(h) + p-p-p
(1) 3y + 2y
0) 4a + 3a
(k) 9k + 5k
("m+ m
(m) 150 - 200
(n) 6w - 3w
(0) 10y + 3y - 5y
(p) 20 - 140

Answers

Answer:

a)y^3

o)7a^2

I know only that

Simplify
hurrryyyyyy pleaseee

Answers

Answer:

1

Step-by-step explanation:

What is the slope of this line? II y = -3x + 1 ​

Answers

Answer:

-3

Step-by-step explanation:

y = mx + b

m represents the slope, and on this equation, instead of m we have -3. So -3 is the slope

Answer:

Slope m = -3

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

m - slope b - y-intercept

Step-by-step explanation:

Step 1: Define

y = -3x + 1

Step 2: Break Function

Identify Parts

Slope m = -3

y-intercept b = 1

Which is the solution of the quadratic equation (4y - 3)2 = 72?
( O
A y= 3 +677 and y = 3-6v2

D y = 3 +672 and y =
-3-6√
4
O y= 92 and y= -312
4
4
O y = 9/7 and y = 32

Answers

Answer: 2 one number 2

Step-by-step explanation:

It's is number 2

The required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

What is simplification?

Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression.

Here,
Given expression, (4y - 3)² = 72

Simplifying the above expression:
(4y - 3)² = 72

4y - 3 = ±√72
4y - 3 = ±6√2
y = 3 ± 6√2/4

Thus, the required solution of the quadratic equation  (4y - 3)² = 72 is y = 3 ± 6√2/4. Option A is correct.

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Dilate by a scale
factor of 1/2
AL
D

Answers

Answer:

The image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

D' (0, 1) L' (1/2, 5/2) or L'(0.5, 2.5)W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

Step-by-step explanation:

Given the triangle ΔDLW withe the vertices

D(0, 2)L(1, 5)W(5, 4)

As the scale factor 1/2 < 0, thus the image triangle will be smaller than the original triangle.

The rule of dilation is given by

Dilation: (x, y)  →  (1/2x, 1/2y), centered at (0, 0)

D(0, 2)  → D' (1/2x, 1/2y) → D' (1/2(0), 1/2(2)) = D' (0, 1)

L(1, 5)  → L'(1/2x, 1/2y) →  L'(1/2(1), 1/2(5)) = L' (1/2, 5/2)

W(5, 4)  → W'(1/2x, 1/2y) →  W'(1/2(5), 1/2(4)) = W' (5/2, 2)

Therefore, the image triangle ΔD'L'W' after the dilation by a scale factor of 1/2 will have the vertices:

D' (0, 1) L' (1/2, 5/2) or L'(0.5, 2.5)W' (5/2, 2) or W'(2.5, 2)

`The figure of the dilated image is attached below.

The value of (3a – 4b + 2) × (5a + 6) for a = 1 and b = -2 is

Answers

Step-by-step explanation:

We know that

a=1 and b= -2

{3*1-4*(-2)+2} .{5*1+6}

= (13-11)

=2

Answer:

143

Step-by-step explanation:

(3a – 4b + 2) × (5a + 6)

a = 1 ; b = - 2

(3(1) – 4(-2) + 2) × (5(1) + 6)

Inputting the values of a and b

(3 - (-8) + 2) * (5 + 6)

(3 + 8 + 2) * (11)

13 * 11

= 143

Determine what regions make up the given probabilities - shade the Venn Diagram,​

Answers

I hope this helps :)

You are moving to a new apartment and need to hire a moving company. You’ve researched local moving companies and found these price options.

Company Flat Fee Hourly Rate
Company A $50 $25
Company B $40 $30
Company C $60 $20
Company D $150 $5

If you anticipate that it will take about 4 hours to move everything, what is the approximate percentage difference of the best and worst deals according to their unit costs?

A.
16%
B.
18%
C.
19%
D.
21%

Answers

Answer:

answer is C. 19%.

sjjsnsmsmsmamsmsjsk

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