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3 years ago

DE=4x+10, EF=2x-1, and DF=9x-15, find DF

Mathematics

1 answer:

masya89 [10]3 years ago

3 0

DE and EF are segments of the line DF, so they will add up to DF. This can be represented with this equation:

$(4x + 10) + (2x - 1) = 9x - 15$

Combine like terms:

$4x + 2x = 6x$

$10 + (-1) = 9$

$6x + 9 = 9x - 15$

Add 15 to both sides:

$6x + 24 = 9x$

Subtract 6x from both sides:

$24 = 3x$

Divide both sides by 3 to get x by itself:

$\boxed{x = 8}$

The value of x will be 8.

Plug this value of x into the expression for DF:

$9(8) - 15 = 72 - 15 = \boxed{57}$

DF will equal 57.

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First part: The amount of loan Molly needs is $22,495

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Third part: The total interest Molly will pay using the plan is approximately $1,545.8

Fourth part: The amount the car costs Molly using the plan is approximately $26,540.8

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The question parameters are;

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The total interest, I = Sum of payment - Loan amount

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The total interest Molly will pay using the loan, I ≈ $1,545.8

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The cost of the car, C, using the 1.9% APR financing plan is the sum of the down payment plus sum of the loan repayment

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The cost of the car using the 1.9% APR financing plan, C ≈ $26,540.8

The question parameters obtained from a similar question are;

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Financing = 1.9% APR for 84 months with a cash allowance of $500

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