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3 years ago

Simplify the rational expression.

Mathematics

1 answer:

o-na [289]3 years ago

7 0

Answer:

$\large\boxed{\dfrac{x^2-4x-32}{x+4}=x-8}$

Step-by-step explanation:

$\dfrac{x^2-4x-32}{x+4}=\dfrac{x^2+4x-8x-32}{x+4}=\dfrac{x(x+4)-8(x+4)}{x+4}\\\\=\dfrac{(x+4)(x-8)}{x+4}\\\\\text{canceled}\ (x+4)\\\\=x-8$

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Jameson is seeking a loan with a simple interest rate of 3% per year. If he wants to borrow $8000, then how much will he be char

Thepotemich [5.8K]

Answer:

$960

Step-by-step explanation:

You are going to want to use the simple interest formula for this. The one below is modified for solving the interest earned.

$I=Prt$

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time

The first step is to change 3% into a decimal:

3% -> $\frac{3}{100}$ -> 0.03

Now, lets plug in the values into the equation:

$I=8,000(0.03)(4)$

$I=960$

Jameson will be charged $960 of interest after 4 years.

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3 years ago

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BabaBlast [244]

A. I believe the hare never catches up to the tortoise
B. The hare waited 50 minutes before walking
C. The tortoise won the race

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3 years ago

Two students in your class, Tucker and Karly, are disputing a function. Tucker says that for the function, between x = –3 and x

Effectus [21]

The difference between Tucker and Karly's take is that Tucker's solution is analytical while Karly's is graphical. But both are correct either way.

For Tucker's solution, let's say at x=-3 the value for y is 4, and at x=3, the value of y is still 4, then the average rate of change or slope is 0. Note that the slope of the curve is Δy/Δx. Since there is no change for Δy, the slope is zero.

For Karly's solution, even if the curve travels high or low but would have the same elevation of x=-3 and x=3, the average rate of change is still zero. It is actually just same with Tucker's but Karly just verbalizes her solution that was observed visually.

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3 years ago

A student theatre charges $9.50 per ticket. The theater has already sold 70 tickets. Write and solve an inequality that represen

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To make the inequality, we will use the ≥ sign to determine how many more tickets we will need. Before we write the inequality, let's see how much money was already made by the present tickets. 70 x 9.50 = $665.
We can write the inequality as $665 + $9.50t ≥ $1000 where t is the number of tickets sold. Now we can solve
$665 + $9.50t ≥ $1000, subtract 665
$9.50t ≥ $335. Now isolate the t by divide 9.50 to both sides
t ≥ 35.26 which we can round up to 36 because you cant sell 35.26 tickets.
So you need at least 36 more tickets to earn at least $1000

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3 years ago

Given: ABCD is a ∥-gram; DE ∩ AB =F Prove: △ADF∼△CDE

Vedmedyk [2.9K]

Answer:

By AA similarity

Step-by-step explanation:

We have been given that ABCD is a parallelogram

So, by the property of parallelogram AB ||CD and FD is cutting the line BC

Hence, FD is transverse line. In transverse line alternate angles are equal.

Therefore, ∠AFD=∠EDC (alternate interior angles)

And ∠FAD=∠ECD (opposite angles in parallelogram)

Therefore, by AA similarity △ADF∼△CDE

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3 years ago