Mathematics College

5. In the right triangle shown below, the length of side AB is x, the length of side BC is x + 2, and the length of the
hypotenuse AC is x + 4. Use this information to find the length of each side. (Use the Pythagorean theorem to get
an equation, and solve for x.)

I need an answer quick!!!
It’s from the problem set to lesson 17 M.1

Answers

Answer 1

Answer:

[tex]AB = 6[/tex]  [tex]BC = 8[/tex]   [tex]AC = 10[/tex]

Step-by-step explanation:

The picture of the triangle is missing.

Given

[tex]AC = x + 4[/tex]

[tex]BC = x + 2[/tex]

[tex]AB = x[/tex]

Required

Find x

When Pythagoras theorem is applied, we have:

[tex](AC)^2 = (BC)^2 + (AB)^2[/tex]

This is so, because AC is the hypotenuse

So, we have:

[tex](x+4)^2 = (x+2)^2 + x^2[/tex]

Open brackets

[tex]x^2 + 4x + 4x + 16 = x^2+2x + 2x + 4 + x^2[/tex]

[tex]x^2 + 8x + 16 = x^2+4x + 4 + x^2[/tex]

Collect Like Terms

[tex]x^2 -x^2 - x^2 + 8x -4x + 16 - 4 = 0[/tex]

[tex]- x^2 + 4x + 12 = 0[/tex]

Expand:

[tex]- x^2 + 6x -2x+ 12 = 0[/tex]

Factorize:

[tex]-x(x -6) -2(x- 6) = 0[/tex]

[tex](-x -2)(x- 6) = 0[/tex]

Split

[tex]-x - 2 = 0[/tex] or [tex]x - 6 = 0[/tex]

[tex]-x = 2[/tex] or [tex]x = 6[/tex]

[tex]x =-2[/tex] or [tex]x = 6[/tex]

Because [tex]BC = x + 2[/tex] and [tex]AB = x[/tex]

[tex]x =-2[/tex] can not be considered.

Hence:

[tex]x = 6[/tex]

Substitute 6 for x in

[tex]AC = x + 4[/tex]

[tex]BC = x + 2[/tex]

[tex]AB = x[/tex]

[tex]AC = 6 + 4[/tex]

[tex]AC = 10[/tex]

[tex]BC = 6 + 2[/tex]

[tex]BC = 8[/tex]

[tex]AB = 6[/tex]

Related Questions

find the sum of the first 31 terms of 4,11,18,...

Answers

Answer:

3379

Step-by-step explanation:

someone pls help me with this problem , in a rush !!

Answers

Answer:

2.DB=7.5+7.5=15cm

3.DV=12.75+12.75=25.5

Step-by-step explanation:

What is Four more than twice a number is -10?

Answers

4+2x=10
2x=10-4
2x=6
X=6/2
X=3

8x-6y=36
solve the linear equation

Answers

Answer:

The below is the answer to the equation. 4.5, 0

Step-by-step explanation:

If P(A) = .80, P(B) = .65, and P(A ∩ B) = .78, then P(B | A) =

Answers

Answer:

P(B | A) = 1.2

Step-by-step explanation:

Given

P(A) = .80P(B) = .65P(A ∩ B) = .78

To determine

P(B | A) = ?

Using the formula

P(B | A) = P(A ∩ B) / P(B)

             =  .78 / .65

             = 1.2

Therefore,

P(B | A) = 1.2

I need help with this word problem please

Answers

Answer:

Step-by-step explanation:

Given function is,

f(x) = [tex]x\sqrt{x}[/tex]

We can rewrite this function as,

f(x) = [tex]x^{\frac{3}{2}}[/tex]

a). Domain of the function is [0, ∞)

Derivative of the function in this domain,

f'(x) = [tex]\frac{3}{2}x^{(\frac{3}{2}-1)}[/tex]

     = [tex]\frac{3}{2}x^{\frac{1}{2}}[/tex]

Since, f'(x) > 0 in the interval [0, ∞)

Function is increasing in the interval [0, ∞)

b). For local maxima and local minima,

  Second derivative of the function,

  f"(x) = [tex]\frac{3}{2}(\frac{1}{2})x^{\frac{1}{2}-1}[/tex]

         = [tex]\frac{3}{4}x^{-\frac{1}{2}}[/tex]  > 0

   So the function should have a local minima.

   But the function is continuous in the interval x ≥ 0,

   There is no local minima (only absolute minima).

c). Since, second derivative is undefined at x = 0,

   There are no inflection points.

d). Since, f"(x) > 0 in the interval [0, ∞)

   Concavity of the curve is UPWARDS.

All of the following would make a formal proof incomplete except what?
A) A lack of justifications
B) Incomplete sentences
C) Errors in logic
D) Incorrect reasons for statements
Urgent I need this for tonight please!!!

Answers

Answer:

b incorrect sentences

Step-by-step explanation:

got it right on my test

f(x) = -x^2
Find f(3)

Answers

Answer:

9

Step-by-step explanation:

f(x) = -x^2

f(3) = -3^2

f(3) = 9

How do you write 0.060 in scientific notation?

Answers

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

[tex]6 \times 10 {}^{ - 2} [/tex]

Find the solution to each equation mentally or use your calculator. (do the opposite of the number on the left side of the equation)

A: 30+a=40


B: 500+b=200


C: −1+c=−2


D: d+3,​567=0

Answers

A) a=10

B) b= -300

C) c= -1

D) -3567

difference between -20 and -17

Answers

Answer:

-3

Step-by-step explanation:

because it says difference and differences means subtract so -20-(-17)=-3

the difference is -3

Part 1: Determine the domain.
DOMAIN:

Answers

Answer:

The domain is -2 to positive 2.

There are 100 classes at Sun Valley Magnet School. 45% of the classes are Math and Science. How many classrooms are not Math and Science?

Answers

Do 100-45 and you get 55. So it is 55 classrooms that are not Math and Science.

What is the solution to the inequality 5.25- b
6.5?

Answers

-b > 6.5 - 5.25

b < 1.25

Hope this helps!

/////////////////////////////////////////////////////////////////////////////////////////////////////////////

The tape diagram below represents 100%.
100%
?
What percent is represented by the shaded area?
%

Answers

Answer: 50%

Step-by-step explanation:

The shaded portion is half of 100

Answer: 50%

Step-by-step explanation: Since the tape diagram in total represents 100%, and half of the tape diagram is shaded, this means 50% is shaded.

Need help asap please

Answers

It’s the 4 th one I try ink

Answer:

the 4th one hope this helps

Arya saves 30% of his montly paycheck for college. He earned $270 lst month. How much money did Arya save for college?

Answers

Answer:

she saved 900 dollars

Step-by-step explanation:

30/100=270/?

30x9=270

100x9=900

Please help Im confused

Answers

Answer is 40

15/3 = 5
8 x 5 = 40

Answer:

x=40

Step-by-step explanation:

to get from 3 to 15, you multiply by 5

multiply 8 by 5 and you get 40

x is 40

please give me brainliest!!<3

Solve each of the following equations.
(4b + 11)(3b - 7) = 0​

Answers

Answer:

4b = 4(11/4)

3b = 3(7/3)

Which of the following statements are true?
The value of the 5 in 592,841 is 10 times the value of the 5 in 358,764.
The value of the 6 in 861,257 is 10 times the value of the 6 in 651,042.
The value of the 8 in 358,764 is 10 times the value of the 8 in 592,841.
The value of the 5 in 592,841 is in of the value of the 5 in 358,764.
The value of the 6 in 861,257 is in of the value of the 6 in 651,042.
The value of the 8 in 358,764 is id of the value of the 8 in 592,841.

Answers

The value of the 5 in 592,841 is 10 times the value of the 5 in 358,764

Answer:

5/6 is eaqual to 2.5/3

Step-by-step explanation:

what is 1/2 x 60 and what is 3/10 x 1,000​

Answers

1/2 x 60 = 30                                                           3/10 x 1000 = 300

cancel the common factor of 2                          simpplify the expression

Answer:

1/2 x 60= 30 and 3/10 x 1,000= 3,000

Step-by-step explanation:

help me asap now pls

Answers

Answer:

b=60a

Step-by-step explanation:

Angle 1 and Angle 2 are a linear pair. Angle 1=x-15, and angle 2=x+77. Solve for x then find the measure of each angle.

Answers

Answer: x=59, angle 1= 44˚, angle 2= 136˚

Step by step explanation:

Linear pairs add to make 180˚.

So angle 1 + angle 2= 180˚

Therefore x-15+x+77= 180

Add the x’s to get 2x
And then -15+77 to get 62.

So 2x+62=180
Subtract 62 to get 2x=118
Then divide by 2 to get x=59

Then substitute the x value into the angle equations

So angle 1 will be 59-15 which is 44˚
And angle 2 will be 59+77 which is 136˚

What is f(-3) if f(x) = 1/3x

Answers

Answer:

10

Step-by-step explanation:

I did this before and i got it right

what is the equation of a line with a slope of -3 and a y-intercept of 9

Answers

Answer:

The answer to the question provided is y = -3x + 9.

Please help me ASAP........

Answers

Answer:

More on supplies than she earned in sales.

Answer:

She spent 25 dollars from her pocket. No profit

Step-by-step explanation:

someone pls hurry and help !

Answers

Answer: I think false

Someone please help and thank you

Answers

Answer:

7 : 3

Step-by-step explanation:

Divide both numbers by 6

Answer:

Step-by-step explanation:

42:18=42/18=7/3=7:3

I hope it help you

this is so easy

can someone please help meeee

Answers

you need to use pythagorean theorem to find x
97^2 = 9409
65^2 = 4225
4225 + b^2 = 9409
b^2 = 5184
b = 72

then you need to add 65 and 72 to get 137
137 - 95 = 42
42 kilometers closer

The tax on a property with an assessed value of $90,000 is $1,350. Find the tax on a property with an
assessed value of $140,000.
a. $1500.00
b. $150.00
c. $2100.00
d. $210.00
e. $750.00

Answers

Answer:

0.015 or 1.5% tax

Step-by-step explanation:

90000x0.015 = 1350

let’s go to the beach each let’s go get away say say what they gonna say the patron on
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