The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg. find the lengths of the three sides of the triangle.

Answers

Answer 1

The sides of the right angle triangle are 20, 48, and 52.

We have given that,

The hypotenuse of a right triangle is 8 feet less than three times the shorter leg and the longer leg is 8 feet more than twice the shorter leg.

Suppose the shortest leg is x, the hypotenuse is then 3x-8, and the longer leg is 2x+8

We use the Pythagorean theorem

What is the Pythagorean theorem?

[tex]hypotenous^2=side^2+side^2[/tex]

Therefore by using Pythagorean theorem

[tex]x^2+(2x+8)^2=(3x-8)^2\\x^2+(4x^2+32x+64)=(9x^2-48x+64)\\4x^2-80x=0[/tex]

x=0 or x=20

So the sides are 20, 48, and 52.

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Related Questions

what is 4,548 in expanded form ?

Answers

4,000+500+40+8
is the correct answer

The average (A) of two number,M and N, is given by the formula A=m+n/2. Find the average of the two numbers 36 and 72.

Answers

Answer: 54

Step-by-step explanation:

Average = Total/ total number

Average= 36 +72/2

             = 108/2

             = 54

54 is the  average of the two numbers 36 and 72.

What is Statistics?

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We need to find the average of the two numbers 36 and 72.

The average (A) of two number, M and N, is given by the formula A=m+n/2

Let m = 36

n=72

Now to find the average of two numbers we have to plug in these values in the formula

A=36+72/2

=108/2

=54

Hence, 54 is the  average of the two numbers 36 and 72.

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You and your friend get the same magazine. You spend $15 for twelve issues. Your friend pays $1.50 per issue but gets the first two issues free. How many issues will your friend get if he also spends $15?

Answers

(1.5 / 15) + 2  = 12 
you add two because he gets two for free 
dived 1.5 by 15 because that will give you how many magazines you can get for $15 

In this ordered pair (4,-5) which number is the ordinate

Answers

The ordinate, or the y-coordinate would be 4 because it comes first in the coordinate pair. In shorter terms, your answer is 4.

Hope this helped! :) Please mark Brainliest and rate!

In the ordered pair (4, -5), the number -5 is the ordinate, which represents the vertical position of a point in a coordinate system.

In the ordered pair (4,-5), the number -5 is the ordinate. In a coordinate system, ordered pairs are used to define locations with two values: the x-coordinate and the y-coordinate. The first number in the pair represents the x-coordinate, which is the horizontal position, and the second number represents the y-coordinate, which is the vertical position, also known as the ordinate.

In this context, the ordinate is the position relative to the horizontal axis in a two-dimensional space. It indicates how far up or down a point lies from the horizontal (x) axis. Hence, in the ordered pair (4, -5), -5 is the ordinate. If a point is above the x-axis, its ordinate is positive; if it's below, as in this case, it's negative.

If a radical is multiplied by a number or variable, you should put the number or variable _____ the radical sign.

Answers

Before---------->Apex

Final answer:

Numbers or variables are placed outside of the radical sign when multiplied by a radical. This representation indicates that the entire radical, not just the number inside, is to be multiplied by that number or variable.

Explanation:

If a radical is multiplied by a number or variable, you should put the number or variable outside the radical sign. In mathematics, multiplication or division by the same number on both sides of an equation does not change the equality. When you multiply a radical by a number or variable, you are essentially multiplying the contents inside the square root by that number or variable, but outside of the radical sign to maintain proper order of operations.

When writing an expression involving radicals mathematically, numbers or variables outside the radical do not directly interact with the values inside until simplification or further operations are performed. For example, if you're multiplying 3 by √2, you would write it as 3√2, not √(3×2). The multiplication of the coefficient (the number in front of the radical) applies to the entire radical, not just the number inside it.

You are going to bake an over-sized sheet cake. The recipe calls for 2 cups of sugar for every 3 cups of flour. How many cups of flour are needed if you use 18 cups of sugar?

Answers

u will set up a ratio
2cups/ 3 cups = 18 cups/ X
X=27 Cups

Answer:27

Step-by-step explanation:

In the diagram shown below, ∠K=18º and ∠H=18º.


Prove KJ=13.75. Justify your steps in a paragraph proof.

Answers

(See the attached graphic)
Since all 3 angles of each triangle are equal, the triangles are similar.

Since the triangles are similar, all 3 sides must be in the same proportion.

8 / 5 = 22 / KJ

(5 * 22) / 8 = KJ

KJ = 13.75

In triangle FGH, ∠G = 112,  ∠ H = 18 (GIVEN) , then ∠ F= 180-(112+18) = 50°
In triangle KIJ, ∠ K=18° (GIVEN), ∠J=112° , then ∠ I = 180-(112+18) = 50°

Since Δ FGH & Δ KJI have all their respective angles EQUAL, then these 

2 triangles are SIMILAR and all their respective sides are proportional.
If so we can write the following proportions:
GF/JI = GH/JK
8/5 = 22/JK. Cross multiplication → 8.JK = (5).(22)  → 8.JK = 110
And JK = 110/8 → JK = 13.75 (JK or KJ are the same)

A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has 15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. Which statement describes when the plans are based on the same number of aerobic exercise sessions?

A. Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.

B. Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.

C. Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.

D. Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.

Answers

"Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week." because. 
Let n be the number of aerobic and strength-training exercises per week.
Let x be the number of strength-training exercises per week on the beginner  

15x + 20n = 90 

Let y be the number of strength-training exercises for  week on the advanced plan.
20y + 30n = 130 

Multiply both sides by 1.5, to get:
22.5x + 30n = 135 
Subtracting equation 2 from 3 we get:
22.5x - 20y = 5 
The answer is B
Hope this helps:)

Sammy has a 10-foot ladder, which he needs to climb to reach the roof of his house. the roof is 12 feet above the ground. the base of the ladder must be at least 1.5 feet from the base of the house. how far is it from the top of the ladder to the edge of the roof? draw a sketch.

Answers

Using the Pythagorean theorum we can solve this v a^2+b^2= c^2. A is the distance from base of house to ladder A= 1.5, c ifls length of ladder, c= 10. (1.5)^2 + ;b^2 = (10)^2. Solve for b. B= 9.88. 12 foot height of house - 9.88 feet to top of angled ladder = 2.11 from top of ladder to edge of roof

Sara has 16 red flowers and 24 yellow flowers. She wants to make a bouquet with the same number of each color flowers in each bouquet. How many red flowers will be in each bouquet.

Answers

Sara can make 8 bouquets, with 3 yellow flowers and 2 red ones in each bouquet. How pretty !

Explain how you can tell without calculating whether the sum of a postitive number and a negative number will be positive, negative or zero.

Answers

if the number is perhaps -24 + 25= it would be a positive and because the lowest number is negative and if perhaps the number are -25 + 24 it would be negative because the highest number is negative

−3/4(x+2)=6 solve for x

Answers

I believe the correct answer is x=-10
-3/4*(x+2) = 6 /multiply both sides by (-4/3)
-4/3*(-3/4)*(x+2) = 6*(-4/3)  /-4/3*(-3/4) = 1
x+2 = -24/3  /-24/3 = -8
x+2 =-8  /subtract 2 from both sides
x = -8-2
x = -10

In a cross-country race with 35 participants , the mean finish time was 21 minutes . Which statement must be true?
A-the most common finish time was 21 minutes
B-at least one participant finished in exactly 21 minutes.
C-over half of the participants finished in less than 21 minutes.
D-if no participants finished in less than 21 minute, than everyone finished in exactly 21 minutes

Answers

The answer is c, all others can be ruled out.

Simplify the fraction

what is 16 over 38

Answers

8/19 is the answer for your question
16/38

both numbers can be divided by 2.

16/2 / 38/2

8/19

the numbers cannot be simplified any further, so 8/19 is your final answer. Hope this helps!


The slope of the line passing through the points (0,0) and (2,3) is

Answers

Slope Formula: (y2-y1)/(x2-x1)
0= x1, 0= y1
2= x2, 3= y2
(3-0)/(2-0)
3/2 is the slope

What is the limit ? And how do I get the answer?

Answers

There is no limit. No solutions. 

On traditional maps, Earth is represented in a flat plane, or by Euclidean geometry. However, a globe is a more accurate model that comes from elliptical geometry. How does a globe represent the fact that there are no parallel lines in elliptical geometry? The equator is not parallel to any other latitudinal lines. The North and South Poles are never connected by a geodesic. The geodesics connecting the North and South Poles never intersect. The geodesics connecting the North and South Poles intersect at both of the Poles.

Answers

Answer:

D. The geodesics connecting the North and South Poles intersect at both of the Poles

Step-by-step explanation:

Answer:

D) The geodesics connecting the North and South Poles intersect at both of the Poles.

Step-by-step explanation:

got it right on edge 2021 :)

a cylinder. With a diameter of 6cm and a height of 10cm. Can you help me work out the volume of this cylinder to 1 decimal place please?

Answers

Greetings!

The formula for the area of a cylinder is:[tex] \pi r^2h[/tex]

Input the information we already know:
[tex] \pi (6/2)^2*10[/tex]

Simplify the expression. Follow PEDMAS.
[tex] =\pi (6/2)^2*10[/tex]
[tex] =\pi (3)^2*10[/tex]
[tex] =\pi (9)*10[/tex]
[tex]=28.2743339*10[/tex]
[tex]=282.743339[/tex]
Round to the tenth decimal place:
[tex]=282.7[/tex]

The area of the cylinder is 282.7 cm³.

Hope this helps.
-Benjamin


Final answer:

The volume of a cylinder with a diameter of 6 cm and a height of 10 cm is 282.8 cm³, calculated using the formula V = πr²h and rounding to one decimal place.

Explanation:

To calculate the volume of a cylinder, we use the formula V = πr²h where V is the volume, r is the radius of the base, and h is the height of the cylinder. In this case, we have a cylinder with a diameter of 6 cm, which means the radius r is half of that, or 3 cm. The height h is 10 cm. So, the volume is calculated by:

V = π × (3 cm)² × 10 cm

Substituting 3.142 for π, we get:

V = 3.142 × 9 cm² × 10 cm

V = 3.142 × 90 cm³

V = 282.78 cm³

Therefore, the volume of the cylinder rounded to one decimal place is 282.8 cm³.

HELPPPPP PLEASEEEEEE

Answers

f(x) = 4^x

so when store sells 64
4^x = 64
4^x = 4^3
    x = 3

answer
B. Month 3
Month 3. When you replace x with 3 to make it 4^3, it means 4*4*4, and u get 64.

Find the measure of each indicated angle

Answers

I think the answer would be 24 but im not 100% sure

Answer:64

Step-by-step explanation:

36+84+x=180

x=180-120

x=60

right angle 90=x+y=60+y

y=90-60=30

y+86+?=180

30+86+?=180

?=180-116

?=64

If function f is defined by f x( ) = 3x2 − 5x + 4, what is f x( − 4) ?

Answers

f(-4) = 3 x 2 - 5(-4) + 4
3x2= 6
-5(-4)= 20
6-20= -14
-14+4= -10
f(-4) = -10

use prime factorization to find gcf of 57 and 27

Answers

gcf (57,27) = 57×27/lcm(57,27)=1539/513 = 3

A store sells a floor lamp for 73.99. The store is having a sale that reduces the lamps price by 35%.How much does the lamp cost during sale?

Answers

73.99 * 0.30 = 22.197 = $22.20

73.99 - 22.20 = 51.79

 Lamp is $51.79

Irst. write an expression for the probability that both socks are bl

Answers

The expression for the probability of both socks, S=bl x2
S=bl x2 is correct answer if you use a calculator you can check my answer for more confirmation

The variance represents how the data is distributed around the mean
b. the variance is always equal to the mean squared (μ2)
c. the variance is negative whenever the mean of x is negative
d. the variance is the value of x that is most likely to occur in the data.

Answers

The variance represents how the data is distributed around the mean.

what are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotensue is 15 units long?

Answers

Refer to the diagram shown below.

Given:
m∠A = 19°
c = 15

By definition,
sin A = a/c
Therefore
a = c*sin A = 15*sin(19°) = 4.8835

cos A = b/c
Therefore
b = c*cos A = 15*cos(19°) =14.1828

Answer:
The lengths are 4.88, 14.18, and 15.00  (nearest hundredth)  

Answer:

For plato users the correct option is D.

Step-by-step explanation:

D. 4.9 units, 14.2 units

If sin theta = 12/13 and theta is an acute angle find cot theta

Answers

3 Rd side would be
13sq=12sq+xsq
Xsq=169-144
X=5
Cot theta = adj side/opp side= 5/12

Answer:

cot θ = [tex]\frac{5}{12}[/tex]

Step-by-step explanation:

If sin θ =  [tex]\frac{12}{13}[/tex] and 'θ' is an acute angle then we have to find the value of cotθ

From the figure attached.

y² + 12² = 13²   [ by Pythagoras Theorem ]

y + 144 = 169

y² = 169 - 144 = 25

y = 5

Now cot θ = [tex]\frac{base}{Height}[/tex]

                 = [tex]\frac{y}{12}[/tex]

                = [tex]\frac{5}{12}[/tex]

Therefore, cot θ =[tex]\frac{5}{12}[/tex] is the answer.

what is the x for 3kx+24=9kx

Answers

x+ 102 hope it helps dude

Find the tax on a dinette set with a cash price of $200 that has been reduced by 20% if the tax rate is 6.5%.

Answers

Hi. First, we need to multiply the $200 x 20% which gives us 40. Next, we subtract the 40 from 200 which gives us $160. Lastly, we multiply the $160 x 6.5% which gives us $10.40.

$200 x 20% = 40
$200 - 40 = 160
$160 x 6.5% = $10.40

Total tax = $10.40

Hope this helps.
Take care,
Diana

A rectangular fountain display has a perimeter of 400 feet and an area of at least 9100 feet. describe the possible widths of the fountain

Answers

Perimeter = 2L + 2W = 400 = 2(L+W) Therefore L + W = 200 Area = L * W = 9100 Where L= Length and W = Width Find Multiples of 9,100 which can sum up to 200. The answer is 130 and 70. Checking. 130 * 70 = 9100 2(130 + 70) = 400 The possible width of the Fountain is 70 feet if the Length is longer or 130 feet if the length is shorter.
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