Solve please thanks x+5= the square root of 7x+53

Mathematics

2 answers:

Vesnalui [34]3 years ago

8 0

$x+5= \sqrt{7x+53} \ \ \ and\ \ \ 7x+53 \geq 0\ \ \ \Rightarrow\ \ \ D=\bigg{\langle}- 7\frac{\big{4}}{\big{7}} ,+\infty\bigg{)}\\\\(x+5)^2=( \sqrt{7x+53})^2\\\\x^2+10x+25=7x+53\\x^2+3x-28=0 \\x^2+4x-7x-28=0\\x(x+4)-7(x+4)=0\\(x+4)(x-7)=0\ \ \ \Leftrightarrow\ \ \ x+4=0\ \ \ or\ \ \ x-7=0\\\\x=-4\ \in D\ \ \ and\ \ \ x=7\ \in D\\\\Ans.\ x=-4\ \ or\ \ x=7$

Marina86 [1]3 years ago

6 0

$x+5= \sqrt{7x+53} \\ \\ (x+5)^2= (\sqrt{7x+53} )^2 \\ \\ x^2+10x+25=7x+53 \\ \\ x^2+3x-28=0 \\ \\ (x-4)(x+7)=0 \\ \\ x-4=0 \\ x=4 \\ \\ x+7=0 \\ x=-7 \\ \\ x=-7,4$

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Find the APR, rounded to the nearest tenth of a percent (one decimal place) for the loan. Purchase a living room set for $4,900

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Answer:

14.3%

Step-by-step explanation:

We assume this question is asking for the annual interest rate for an amortized loan that would produce the same total repayment amount as if 8% simple interest were added to the $4900 loan amount. There is no formula for that, but there are a number of apps and spreadsheets that can calculate it. In the attached, we have use a graphing calculator.

The APR is about 14.3%.

_____

The amount to be repaid is calculated using the simple interest formula:

A = P(1 +rt) = $4900(1 +0.08·4) = $6468

Then the required monthly payment (for 48 months) is ...

$6468/48 = $134.75

The payment amount for a 48-payment loan at rate r on a principal of $4900 will be ...

A = 4900(r/12)/(1 -(1 +r/12)^-48)

In the attachment, we show the value of r (in percent) that would make the payment amount A be $134.75. We have done this by casting the problem in the form f(r) = 0 and looking for the x-intercept of f(r).

_____

<em>Additional comment</em>

The second attachment uses a spreadsheet for the same purpose. Here, we have used Go.ogle Sheets with a "Goal Seek" add-on to adjust the value in cell B5 so that the computed payment on the loan (cell B6) is the same as the value we calculated in cell B4.

We found the graphing calculator solution to be much quicker, though in that case we actually had to know the formula to use to calculate the payment. The payment formula is built into the spreadsheet.