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2 years ago

Drag each expression to show whether it is equivalent to (5⋅9x)+(5⋅1), 45x+15, or 15(3x−1).

Mathematics

1 answer:

JulijaS [17]2 years ago

3 0

Part A: Option e: $5(9 x+1)$

Option f: $45 x+5$

Part B: Option c: $15(3 x+1)$

Option d: $(5 \cdot 9 x)+(5 \cdot 3)$

Part C: Option a: $(5 \cdot 9 x)-(5 \cdot 3)$

Option b: $45 x-15$

Explanation:

Part A: The equation is $(5 \cdot 9 x)+(5 \cdot 1)$

Simplifying, we have,

$45x+5$

Taking the term 5 common out, we have,

$5(9 x+1)$

Thus, the above two expressions are equivalent to the equation $(5 \cdot 9 x)+(5 \cdot 1)$ .

Hence, Option e and Option f are the correct answers.

Part B: The equation is $45 x+15$

Taking the term 15 common out, we have,

$15(3 x+1)$

Also, the equation can be rewritten as,

$(5 \cdot 9 x)+(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $45 x+15$

Hence, Option c and Option d are the correct answers.

Part C: The equation is $15(3 x-1)$

Multiplying, we have,

$45 x-15$

The above expression can be rewritten as,

$(5 \cdot 9 x)-(5 \cdot 3)$

Thus, the above two expressions are equivalent to the equation $15(3 x-1)$

Hence, Option a and Option b are the correct answers.

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2 years ago

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 20.0% but with equal end-of-month pay

Mariulka [41]

Answer:

100% of the 2nd monthly payment go toward the repayment of principal.

Step-by-step explanation:

The loan taken is the Principal which is mentioned as $72,500 with interest at a nominal rate of 20%. Firstly, it is important to understand that nominal rate means non-compounding rate. Simply put will be a "one-time charged" rate on the loan. Since this is given as 20% of the Principal. It is calculated thus: $\frac{20}{100}$ × $\frac{72,500}{1}$ = $14,500. So the interest on the loan is $14,500. Added to the Principal the total amount to be paid back by the company becomes: $72,500 + $14,500 = $87,000. To pay back this amount at equal end-of-month installments in 1 year (12 months), we divide the total amount by 12. i.e $\frac{87000}{12}$ = $7250. This means, the monthly payment will be $7,250. Since the monthly payment pays only 10% of the initial principal $72,500. By the second month only 20% of the Principal would have been paid. So all of the monthly payment will go towards repaying the principal