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Masteriza [31]
4 years ago
11

Find the value of x.

Mathematics
1 answer:
Gala2k [10]4 years ago
5 0

Answer:

\large\boxed{2\sqrt7}

Step-by-step explanation:

Look at the picture.

ΔADC and ΔACB are similar. Therefore the corresponding sides are in proportion:

\dfrac{AC}{AD}=\dfrac{AB}{AC}

We have

AC=x,\ AD=2,\ AB=2+12=14

Substitute:

\dfrac{x}{2}=\dfrac{14}{x}           <em>cross multiply</em>

x^2=(2)(14)\\\\x^2=28\to x=\sqrt{28}\\\\x=\sqrt{4\cdot7}\\\\x=\sqrt4\cdot\sqrt7\\\\x=2\sqrt7

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Answer:

89

Step-by-step explanation:

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3 years ago
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Fredo deposits $75 each year in an account earning 3% interest compounded annually. If he deposits an additional $75 per year an
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2.25 will be added into the account of the total of the money
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4 years ago
A train travels from station A to station B. If the train leaves station A and makes 75 km/hr, it arrives at station B 48 minute
SSSSS [86.1K]

Answer:

  • A) 290 km
  • B) 4 hours
  • C) 72.5 km/h

Step-by-step explanation:

Let distance be d and time t

<u>At 75 km/h speed the distance is</u>

  • d = 75(t - 48 min) = 75(t - 48/60 hours)

<u>At 50 km/h speed the distance</u> is

  • d = 50t + 40

<u>Since the distance is same, we get the equation:</u>

  • 75(t - 48/60) = 50t + 40
  • 75t - 75*4/5 = 50t + 40
  • 75t - 60 = 50t + 40
  • 75t - 50t = 40 + 60
  • 25t = 100
  • t = 4 hours

<u>A) The distance between A and B</u>

  • d = 50*5 + 40 = 290 km

<u>B) Time is </u>

  • 4 hours as found above

<u>C) The speed = d/t</u>

  • Speed = 290/4 = 72.5 km/h

6 0
3 years ago
Find the value of each variable for y and z
Sveta_85 [38]

Answer:

y = 102° , z = 75°

Step-by-step explanation:

Assuming this is geometry, you must find the value of 'z' first.

Using the [Supplementary Angles Theorem] for 'z' :

105° + z = 180°

Solve for z.

z = 75°

You may also hear that those two angles are a 'Linear Pair'

Then using the formula for: [Sum of Internal Angles]

Which is: sum = (n-2) * 180°      where 'n' is the number of sides

The total sum of internal angles of a quadrilateral is 360°

Now knowing 3 of the 4 interior angles, you can just do arithmetic:

99° + 84° + 75° + y = 360°

Simplify:

258° + y = 360°

Therefore:

y = 102°

3 0
3 years ago
In the standard (x,y) coordinate plane, what is the slope of the line joining the points (5,4) and (2,-7)?
WINSTONCH [101]

Answer:

slope = \frac{11}{3}

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (2, - 7)

m = \frac{-7-4}{2-5} = \frac{-11}{-3} = \frac{11}{3}

7 0
3 years ago
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