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harkovskaia [24]

3 years ago

15

What is the quotient?

1 answer:

pshichka [43]3 years ago

7 0

$\text{First factor}\ t^2+7t+12=t^2+4t+3t+12=t(t+4)+3(t+4)\\\\=t^2+7t+12=(t+4)(t+3)\\\\\dfrac{t+3}{t+4}\div(t^2+7t+12)=\dfrac{t+3}{t+4}\div[(t+4)(t+3)]\\\\=\dfrac{t+3}{t+4}\cdot\dfrac{1}{(t+4)(t+3)}\\\\\text{canceled}\ t+3\\\\=\dfrac{1}{t+4}\cdot\dfrac{1}{t+4}=\boxed{\dfrac{1}{(t+4)^2}}$

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Find the slope of a line if the points (2,-1) and (5,3) are on the line

Romashka [77]

Answer:

$\huge{ \boxed{ \sf{ \frac{4}{3} }}}$

Step-by-step explanation:

$\star{ \sf{ \: Let \: the \: points \: be \: A \: and \: B}}$

$\star{ \sf{ \: Let \: a(2,-1) \: be \: (x1 \:, y1) \: and \: b (5,3) \: be \: (x2 \:, y2)}}$

$\underline{ \sf{Finding \: the \: slope \: of \: the \: line}}$

$\boxed{ \sf{Slope = \frac{y2 - y1}{x2 - x1} }}$

$\mapsto{ \sf{Slope = \frac{3 - ( - 1)}{5 - 2} }}$

$\mapsto{ \sf{Slope = \frac{3 + 1}{5 - 2}}}$

$\mapsto{ \sf{Slope = \frac{4}{3} }}$

Hope I helped!

Best regards! :D

~ $\text{TheAnimeGirl}$

4 0

3 years ago

#18-4: Douglas invests $550 in high-yield savings account. The account pays 2.1% simple interest annually. If he doesn't add or

kap26 [50]

Answer:

No

Step-by-step explanation:

You want to calculate the interest on $550 at 2.1% interest per year after 4 years.

The formula we'll use for this is the simple interest formula, or:

I = P x r x t

P is the principal amount, $550.00.

r is the interest rate, 2.1% per year, or in decimal form, 2.1/100=0.021.

t is the time involved, 4 years.

So, t is 4 year time periods.

To find the simple interest, we multiply 550 × 0.021 × 4 to get that:

The interest is: $46.20

3 0

3 years ago

The perimeter of a rectangle is at most 80 inches. The length of the rectangle is 25 inches. The inequality 80-2w>50 can be u

andre [41]

W is less than or equal to 15

5 0

3 years ago

Solve |1-4x| > 7<br> (x-1.5 (xlx < -1.5 UX>1.5)<br> (xx<-1.5 UX > 2)

Setler [38]

If $1-4x\ge0$ , then by definition of absolute value

$|1-4x| = 1-4x > 7 \implies 4x < -6 \implies x < -\dfrac32$

On the other hand, if $1-4x$ , then

$|1-4x| = -(1-4x) = -1 + 4x > 7 \implies 4x > 8 \implies x > 2$

So, the overall solution to the inequality is interval union

$\left(x < -\dfrac32\right) \cup (x > 2)$

3 0

2 years ago

Humaid can shovel the driveway in 3 hours, and Humaid can shovel the driveway in 2 hours. How long will it take them working tog

PIT_PIT [208]

Answer:

2hours and 30 mins

Step-by-step explanation

8 0

3 years ago