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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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A store is having a sale on jelly beans and trail mix. For 8 pounds of jelly beans and 4 pounds of trail mix, the total cost is
aleksley [76]
Make this on form of a simultaneous equation:

assume jelly beans is J and trail mix is T

8J+4T=21
3J+2T=9
then solve

multiply the first equation by 3 and second equation by 8(SO THE J CAN DISAPPEAR[ELIMINATION METHOD])

24J+12T=63
24J+16T=72

Subtract

-4T=-9
T=0.44

then substitute the T to any one of the equation

3J+2(0.44)=9
3J+0.88=9
3J=8.12
J=2.71


therefore, jelly beans= $2.71 and trail mix=$0.44


7 0
3 years ago
What is the greatest perimeter of a rectangle with an area of 39 square feet
harina [27]
There is no greatest perimeter of a rectangle with an area of 39 square feet.

To see why, consider the length of 3 and width of 13. Area would be 39 and perimeter would be 3 + 3 + 13 + 13 = 32

Now consider length of 3/2 = 1.5 and 13·2 = 26. Then area is same but perimeter is 1.5 + 1.5 + 26 + 26 = 55.

Now we can just repeatedly half the length and double the width.

L = 3.0, W = 13
⇒ A = 39, P = 32.0 

L = 1.5, W = 26   
⇒ A = 39, P = 55.0 

L = 0.75, W = 52   
⇒ A = 39, P = 105.5 

L = 0.375, W = 104  
⇒ A = 39, P = 208.75 

L = 0.1875, W = 208  
⇒ A = 39, P = 416.375 

L = 0.09375, W = 416  
⇒ A = 39, P = 832.1875 

L = 0.046875, W = 832  
⇒ A = 39, P = 1664.09375 

L = 0.0234375, W = 1664 
⇒ A = 39, P = 3328.046875 

L = 0.01171875, W = 3328 
⇒ A = 39, P = 6656.0234375 

L = 0.005859375, W = 6656 
⇒ A = 39, P = 13312.01171875

 Notice how P just kept growing. That's because width grow much faster than length <span>shrinking, </span>so P would grow endlessly.

Hope this helps.
6 0
3 years ago
on the first day of every month Katie gets 450 phones she repairs 10 phones every day how many phones does she have left to repa
MaRussiya [10]

Answer:

340 phones

Step-by-step explanation:

Make an expression

She repairs 10 phones each day, d.

Each day she repairs 10 phones, it is 10 phones off the total number (450) she has to repair, so we can subtract 10d from 450.

450-10d

We want to find how many she has left after 11 days, so we can substitute 11 in for d

450-10(11)

Multiply

450-110

340

She will still have 340 phones left to repair

5 0
3 years ago
What time is 17 hours after 1:00 p.m?
lana66690 [7]

Answer:

6am

Step-by-step explanation:

6 0
4 years ago
Read 2 more answers
Johnny has a locker combination with 1 letter followed by three digits. None of the digits can repeat themselves. How many combi
Vera_Pavlovna [14]
 First, what letter can it be at the beginning?

English Alphabet has 26 letters, so we have 26 possibilities

26*

then it can be any of 10 digits

26*10=260

then any of the remaining 9 digits:

26*10*9

then any of the remaining 8 and 7 digits:

26*10*9*8*7=131040

so the solution is: 131040 possible combinations!
6 0
3 years ago
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