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svet-max [94.6K]

2 years ago

6

A couple took out a $5,000 loan from the bank. The loan had a simple interest rate of 7.5% per year. By the end of the loan, the

couple had paid $2,250
interest.
What was the length of the couple's loan?

2 answers:

Sholpan [36]2 years ago

8 0

Answer:

6 years

Step-by-step explanation:

t=2250/375

t=6

Hence time of the loan will be 6 years

galben [10]2 years ago

4 0

Answer:

6 years

Step-by-step explanation:

5000 x 0.075 = 375

2250/375 = 6

therfore it is 6 years worth of interest

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What is the image of ( 0 , -6 ) after a reflection over the line y = x?

Alla [95]

Answer:

(-6, 0)

Step-by-step explanation:

(x, y) over y=x = (y, x)

so (0, -6) will be (-6, 0).

3 0

3 years ago

A truck is being filled with cube-shaped packages that have side lengths of 1/4 foot. The part of the truck that is being filled

n200080 [17]

Answer:

24000 pieces.

Step-by-step explanation:

Given:

Side lengths of cube = $\frac{1}{4} \ foot$

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

$Volume\ of\ cube =a^{3}$

$=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot$

Length = 8 foot, Breadth = $6\frac{1}{4} =\frac{25}{4} \ foot$ , Height = $7\frac{1}{2} =\frac{15}{2} \ foot$

$Volume\ of\ rectangular\ prism =length\times breadth\times height$

$=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot$

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = $\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube$

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.

7 0

3 years ago

Complete the following graphic organizer and then to find the missing information

Travka [436]

a) 4

b) 47

c) 225

d) 120/400

4 0

3 years ago

Read 2 more answers

I need to find the derivative. I’m not very good at this so I am answer asap would be sosososo helpful

Bingel [31]

Answer:

See below.

Step-by-step explanation:

First, notice that this is a composition of functions. For instance, let's let $f(x)=\sqrt{x}$ and $g(x)=7x^2+4x+1$ . Then, the given equation is essentially $f(g(x))=\sqrt{7x^2+4x+1}$ . Thus, we can use the chain rule.

Recall the chain rule: $\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x)$ . So, let's find the derivative of each function:

$f(x)=\sqrt{x}=x^\frac{1}{2}$

We can use the Power Rule here:

$f'(x)=(x^\frac{1}{2})'=\frac{1}{2}(x^{-\frac{1}{2} })=\frac{1}{2\sqrt{x}}$

Now:

$g(x)=7x^2+4x+1$

Again, use the Power Rule and Sum Rule

$g'(x)=(7x^2+4x+1)'=(7x^2)'+(4x)'+(1)'=14x+4$

Now, we can put them together:

$y'=f'(g(x))\cdot g'(x)=\frac{1}{2\sqrt{g(x)}} \cdot (14x+4)$

$y'=\frac{14x+4}{2\sqrt{7x^2+4x+1} } =\frac{7x+2}{\sqrt{7x^2+4x+1} }$

5 0

3 years ago

Consider the polynomial P(x)=x⁴+3x³-28x²-36x+144. Write the equation of P in factored form.

garik1379 [7]

Answer:

P(x)=(x-2)(x-4)(x+3)(x+6)

Step-by-step explanation:

Given: P(x)=x⁴+3x³-28x²-36x+144

It is a polynomial with degree 4.

It should maximum four factor.

Hit and trial error method.

Put x = 2 into P(x)

P(2)=2⁴+3×2³-28×2²-36×2+144

P(2) = 0

So, x-2 would be factor of P(x)

Now divide x⁴+3x³-28x²-36x+144 by x-2 to get another factors

$(x^4+3x^3-28x^2-36x+144)\div (x-2) = x^3+5x^2-18x-72$

$P(x)=(x-2)(x^3+5x^2-18x-72)$

Put x = 4

$P(4) = 0$

now divide $x^3+5x^2-18x-72$ by x-4

$(x^3+5x^2-18x-72)\div (x-4) = x^2+9x+18$

$P(x)=(x-2)(x-4)(x^2+9x+18)$

Now factor $x^2+9x+18$

$\Rightarrow x^2+9x+18$

$\Rightarrow (x+6)(x+3)$

Complete factor of P(x)

P(x)=(x-2)(x-4)(x+3)(x+6)

7 0

3 years ago