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charle [14.2K]
2 years ago
11

AB is a midsegment of trapezoid DEFG what is x?

Mathematics
1 answer:
Mamont248 [21]2 years ago
5 0

Answer:

D. 2

Step-by-step explanation:

DEFG is a trapezoid and AB is its Midsegment.

Therefore,

AB =\frac{1}{2}(DG + EF)  \\  \\ 12 =  \frac{1}{2} (5x - 4 + 8x + 2) \\  \\ 12  \times 2= (13x - 2) \\  \\ 24 = 13x - 2 \\  \\ 24 + 2 = 13x \\  \\ 26 = 13x \\  \\ x =  \frac{26}{13}  \\  \\ x = 2

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KATRIN_1 [288]
<h2>Answer:</h2>

The solution of the inequality is:

                       x\leq 3

<h2>Step-by-step explanation:</h2>

We are given a inequality in terms of variable x as:

2(4+2x)\geq 5x+5

Now we are asked to find the solution of the inequality i.e. we are asked to find the possible values of x such that the inequality holds true.

We may simplify this inequality as follows:

On using the distributive property of multiplication in the left hand side of the inequality we have:

2\times 4+2\times 2x\geq 5x+5\\\\i.e.\\\\8+4x\geq 5x+5\\\\i.e.\\\\8-5\geq 5x-4x\\\\i.e.\\\\x\leq 3

The solution is:      x\leq 3

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3 years ago
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Which algebraic representation of a transformation on a coordinate grid does NOT preserve congruence?
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3 years ago
A luxury hotel group purchases a deserted island 3. 5 miles offshore and due south of an endangered bird nesting beach. The near
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Answer:

T.C ( 1.1007 ) = T.C_min = $2252  

Step-by-step explanation:

Given:

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- The distance from hotel island = 3.5 miles

- The distance from beach to power source = 10 miles

Find:

Find the least expensive price for which you can bill the job

Solution:

- This problem requires cost optimization. So we need to develop a cost function as follows

Total Cost = C_w*(distance from island to x) + C_g*( distance from x to power)

- Now calculate the relevant distances using Pythagoras theorem:

              Distance from island to x = sqrt ( x^2 + 3.5^2 )

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- Input the distances in the cost function:

              T.C ( x ) = C_w*sqrt ( x^2 + 3.5^2 ) + C_g*(10 - x )

- Input the relevant rates:

              T.C ( x ) = 250*sqrt ( x^2 + 3.5^2 ) + 150*(10 - x )  

- Simplify:

              T.C ( x ) = 250*sqrt ( x^2 + 12.25 ) + 1500 - 150x

- Next, we will optimize the cost to minimum. We need the distance x that would give us the minimum cost. To minimize the function, set its derivative with respect to x equals to zero.

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- Set the derivative to zero and solve for x:

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Squaring both sides:

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Simplify and solve:

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- The cost function is minimized at x = 1.1007 miles. We will input this back into our function and evaluate the minimum cost as follows:

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                 T.C ( 1.1007 ) = T.C_min = $2252  

                                 

- So the minimum cost associated with this plan is $2252.

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