1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rjkz [21]
3 years ago
6

What is the value of x in the diagram?

Mathematics
1 answer:
makvit [3.9K]3 years ago
6 0

Answer:

x=5

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2

x^2+ ( 2x+2)^2 = (2x+3)^2

FOIL the squared terms

x^2 +(4x^2 + 4x+4x+4) = 4x^2 + 6x+6x +9

Combine like terms

5x^2+8x +4 = 4x^2 +12x +9

Subtract  4x^2 +12x +9 from each side

5x^2+8x +4  -4x^2 -12x -9= 4x^2 +12x +9-4x^2 -12x -9

x^2 -4x -5 =0

Factor

(x-5) (x+1) = 0

Using the zero product property

x=5   x=-1

But x cannot be negative or we would have negative length

x=5

You might be interested in
The graph shows the relationship between the distance a truck can travel and the amount of gasoline used. (5,35) What is the uni
juin [17]
The unit rate is the slope

y=mx+b

m=slope

b=y intercept

equation is y=7x

slope=7

y intercept=0

slope=unit rate because if you use 5 gasoline then you go 5 times 7 miles or 35 miles

The unit rate is 7

Hope I helped :)
8 0
3 years ago
Read 2 more answers
huong and kathyrn each day impeoved their yards by planting rose bushes and ornamental grass. they bought their supplies from th
marta [7]

Answer:

One rose bush = $3

One bunch of ornamental grass = $4

Step-by-step explanation:

We can set up a system of equations to solve for this. Let cost of 1 rose bush be r and cost of 1 ornamental grass be g. Thus we can form 2 equations:

14r+7g=70\\5r+14g=71

We can multiply the first equation by -2 so that we can eliminate g. Thus, we have:

(*-2)14r+7g=70\\5r+14g=71\\-------\\-28r-14g=-140\\5r+14g=71\\--------\\-23r=-69\\r=\frac{-69}{-23}=3

Thus, 1 rose bush is $3. Now plugging in r = 3 into the first original equation, we can solve for g:

14r+7g=70\\14(3)+7g=70\\42+7g=70\\7g=70-42\\7g=28\\g=\frac{28}{7}=4

Thus, 1 bunch of ornamental grass is $4.

5 0
3 years ago
What is 90,000,000,000 in word format
My name is Ann [436]
The answer I believe would be ninety millionth
4 0
3 years ago
Read 2 more answers
Krista has a garden that is 5 yards by
kobusy [5.1K]
Answer: 30 square yards: C
5 0
3 years ago
Geometry
Kobotan [32]

Answer: UV = 52

Concept:

Additive property of length, or the segment addition postulate, states that given 2 points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC.

Solve:

<u>Given information</u>

TU = 4x

UV = 2x + 14

TV = 7x - 5

<u>Given expression deducted from the additive property of length</u>

TV = TU + UV

<u>Substitute values into the expression</u>

7x - 5 = 4x + 2x + 14

<u>Combine like terms</u>

7x - 5 = 6x + 14

<u />

<u>Subtract 6x on both sides</u>

7x - 5 - 6x = 6x + 14 - 6x

x - 5 = 14

<u>Add 5 on both sides</u>

x - 5 + 5 = 14 + 5

x = 19

<u>Find UV by substituting the value of x</u>

UV = 2x + 14 = 2 (19) + 14 = \boxed{52}

Hope this helps!! :)

Please let me know if you have any questions

5 0
3 years ago
Other questions:
  • 5 is subtracted from three-fifths of x...please someone translate this expression for me.​
    14·1 answer
  • 1. Jack is 30 years old and Alice is 35 years old. What percent of Alice's age is Jack, rounded to the nearest tenth of a percen
    5·1 answer
  • What are the coordinates of the point?
    7·1 answer
  • Help plz anyone who’s good with slope?
    9·2 answers
  • Find the distance between A(-1, -1) and B(4, -5). Round your answer to the nearest tenth.
    5·1 answer
  • Find the volume: 8 cm 20 cm 12 cm <br>Answers: 960 cm 1920 cm 3 960 cm 2 240 cm​
    6·2 answers
  • 1) What is the first x in x + 3x = 16?
    15·1 answer
  • What is the equation of the line that passes through the point (-1, -7) and has a<br> slope of 2?
    11·2 answers
  • Please help me find the total surface area
    10·1 answer
  • 1/5n+3/5n=7/9<br><br> Can you help?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!