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qaws [65]
3 years ago
12

EF is the median of trapezoid ABD. What is x?

Mathematics
2 answers:
RUDIKE [14]3 years ago
8 0

Answer:

  • x = 6

Step-by-step explanation:

<u>The median is the average of the bases:</u>

  • 15 = 1/2(x + 1 + 3x + 5)
  • 30 = 4x + 6
  • 4x = 30 - 6
  • 4x = 24
  • x = 6
tatiyna3 years ago
3 0

Answer:

The value of x is<u> 6</u><u> </u>.

Step-by-step explanation:

<u>Solution</u> :

Here's the required formula of median of trapezoid :

{\implies{\pmb{\sf{Median=\dfrac{Base_1 + Base_2}{2}}}}}

Where :

  • ➝ Median \rm\overline{EF} = 15
  • ➝ Base₁ (AB) = x + 1
  • ➝ Base₂ (CD) = 3x + 5

Substituting all the given values in the formula to find the value of x :

\begin{gathered}\qquad{\longrightarrow{\sf{Median =\dfrac{Base_1 + Base_2}{2}}}}\\\\\qquad{\longrightarrow{\sf{\overline{EF} =\dfrac{Base_1 + Base_2}{2}}}}\\\\\qquad{\longrightarrow{\sf{15 =\dfrac{(x +1) + (3x + 5)}{2}}}}\\\\\qquad{\longrightarrow{\sf{15 =\dfrac{(x +3x) + (1 + 5)}{2}}}}\\\\\quad{\longrightarrow{\sf{15 =\dfrac{(4x) + (6)}{2}}}}\\\\ \quad{\longrightarrow{\sf{15 \times 2 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{30 = 4x + 6}}}\\\\\quad{\longrightarrow{\sf{4x = 30 - 6}}}\\\\\quad{\longrightarrow{\sf{4x =24}}}\\\\\quad{\longrightarrow{\sf{x = \dfrac{24}{4}}}}\\\\\quad{\longrightarrow{\sf{x =6}}}\\\\\quad{\star{\underline{\boxed{\sf{\purple{x =6}}}}}}\end{gathered}

Hence, the value of x is 6.

\rule{300}{2.5}

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Fynjy0 [20]

Answer:

The player throws 127.3 ft from second base to home plate.

Step-by-step explanation:

Given:

Distance from home to first base = 90 ft

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We need to find the distance from second base to home.

Solution:

Now we can assume the complete scenario to be formed as a right angled triangle with two sides given and to find the third side.

Now by using Pythagoras theorem which states that;

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Rounding to nearest tent we get;

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