2. The rectangular floor of a garage has an area of 198 square feet. Andy knows that the floor is 7

Mathematics

1 answer:

Charra [1.4K]3 years ago

6 0

Answer:

length = 18 ft

Step-by-step explanation:

Let w = width

L = w+7

Area = l*w

198 = (w+7) (w)

Distribute

198 = w^2 +7w

Subtract 198 from each side

0 = w^2 +7w -198

Factor

What 2 numbers multiply to -198 and add to 7

18* -11 = -198

18+-11 = 7

0=(w+18) (w-11)

Using the zero product property

w+18 =0 w-11=0

w= -18 w=11

We cannot have negative width so w=11

We want the length

l = w+7

l = 11+7 = 18

You might be interested in

What two numbers multiply by 25 but adds up to 6

Natalka [10]

No two intergers can solve this problem. If you're not in Algebra II yet, the answer is probably "none."

Just look at the factor pairs of 25:
1 × 25
-1 × 25
5 × 5
-5 × -5
Clearly none of those can add up to 6.

If you want the more complex answer, I'll show you how here. If you don't understand why it doesn't work, that's okay. I just want you to see that there's not an actual answer to the problem.

a+b = 6
a = 6-b
ab = 25
(6-b)b = 25
6b -b² = 25
-b² + 6b = 25
b² -6b = -25
Factor by splitting the middle.
Half of -6 is -3, (-3)² = 9. Add this to each side.
b² -6b + 9 = -16
Factor the perfect square trinomial.
(b-3)² = -16
Take the square root of each side.
b-3 = 4i
b = 3+4i
a+b = 6
a+3+4i = 6
a= 3-4i
(The "i" stands for an imaginary number, specifically, the square root of -1.)

8 0

3 years ago

Suppose that you have $5,000 to invest. Which investment yields the greater return over a 10 year period: 7.74% compounded daily

marin [14]

Answer:

We should invest in 7.74% compounded daily as it yields a higher return.

The total investment after 10 years is $10,841.22.

Step-by-step explanation:

a.) at 7.74% compounded daily

$final = principal(1 + \frac{i}{m} )^{m \times n} \\ = 5000(1 + \frac{0.0774}{365} )^{365 \times 10} \\ = 10 \: 841.2235$