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Elden [556K]
3 years ago
13

Find the length of EF

Mathematics
1 answer:
Lisa [10]3 years ago
7 0

Answer:

9

Step-by-step explanation:

1. First, we need to set up an equation to find the value of x and then the length of EF.

2. We know that DG is equal to 33, so we can add all the three sections it's cut into altogether to get 33. Therefore, we get an equation of: 3x - 28 + 3x - 30 + x = 33

3. (Solving for x)

Step 1: Simplify both sides of the equation.

  • 3x - 28 + 3x - 30 + x = 33
  • (3x+3x+x) + (-28-30)=33
  • 7x - 58 = 33

Step 2: Add 58 to both sides.

  • 7x - 58 + 58 = 33 + 58
  • 7x = 91

Step 3: Divide both sides by 7.

  • \frac{7x}{7} = \frac{91}{7}
  • x = 13

4. Now that we know x is equal to 13, we can plug that value in for the expression 3x - 30.

  • 3(13)-30
  • 39 - 30
  • 9

Therefore, the length of EF is 9.

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Tangent Be and secant BC intersect at point B. Find the value of x. If necessary, round to the hundredths place.
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The value of x is 15.56.

Solution:

Tangent and Secant theorem:

If one secant and one tangent are drawn to a circle from one exterior point, then the square of the length of the tangent is equal to the product of the external secant segment and the total length of the secant.

BE = 22 BD = x, CD = x

BC = x + x = 2x

By the tangent and secant theorem,

BE^2=BD \cdot BC

22^2=x \cdot 2x

484= 2x^2

Divide by 2 on both sides of the equation, we get

242=x^2

Take square root on both side of the equation.

x = 15.56

Hence the value of x is 15.56.

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In a school, there is a ratio of 4 boys to 5 girls. If there are a total of 450 students, how many girls are there? *
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Answer: there are 200 girls in the school.

Step-by-step explanation:

In a school, there is a ratio of 4 boys to 5 girls. The total ratio would be the sum of the proportion of boys and the proportion of girls. Therefore,

Total ratio = 4 + 5 = 9

If there are a total of 450 students, it means that the number of girls in the school would be

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The number of girls is

5/9 × 450 = 200

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A building has a ramp to its front doors to accommodate the handicapped. If the distance from the building to the end of the ram
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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