14. A car worth $27,500 in 2012 is worth $16,720

Mallory is 2 years older than three times her brother Jake’s age. Let j represent Jake’s age. During the Strategize step of the

DedPeter [7]

Let j = Jake's age.
Because Mallory is 2 years older than three times Jake, Mallory's age is
3j + 2.

Answer: Mallory's age is 3j + 2

6 0

4 years ago

Calculus help ASAP!!!

anastassius [24]

Let $c\in(0,\infty)$ . Then the definite integral can be split up at $t=c$ so that

$\displaystyle F(x)=\int_{t=2x}^{t=5x}\frac{\mathrm dt}t$
$\displaystyle=\int_{t=2x}^{t=c}\frac{\mathrm dt}t+\int_{t=c}^{t=5x}\frac{\mathrm dt}t$
$\displaystyle=-\int_{t=c}^{t=2x}\frac{\mathrm dt}t+\int_{t=c}^{t=5x}\frac{\mathrm dt}t$

Now take the derivative. By the fundamental theorem of calculus, you have

$\displaystyle\frac{\mathrm dF}{\mathrm dx}=\frac{\mathrm d}{\mathrm dx}\left[\int_{t=c}^{t=5x}\frac{\mathrm dt}t-\int_{t=c}^{t=2x}\frac{\mathrm dt}t\right]$
$=\displaystyle\frac1{5x}\dfrac{\mathrm d}{\mathrm dx}[5x]-\frac1{2x}\dfrac{\mathrm d}{\mathrm dx}[2x]$
$=\dfrac5{5x}-\dfrac2{2x}$
$=\dfrac1x-\dfrac1x$
$=0$

Then integrating with respect to $x$ , we recover $F(x)$ and find that

$\displaystyle\int\dfrac{\mathrm dF}{\mathrm dx}\,\mathrm dx=\int0\,\mathrm dx$
$F(x)=C$

where $C$ is an arbitrary constant.

7 0

3 years ago

Estimate the product and choose a method

Ainat [17]

What is the product??

3 0

3 years ago

Allison practices her violin for at least 12 hours per week. She [practices for three fourths of an hour each session. If Alliso

Nikolay [14]

Well let’s see...

If she practices 3/4 of an hour a week we need to find out how much time is 3/4 of an hour. To do this we divide 60/4 and get 15. We check by multiplying 15 x 4 and get 60 so we know we are correct.

Now we know that 1/4 of an hour is 15 minutes, but we need to know how long she practices per session. Because 15 is 1/4 we multiply 15 x 3 to make it 3/4.

15 x 3 is 45. We check by dividing 45 by 3 and we do get 15 so we are correct.

If 3/4 of an hour is 45 minutes and she practices for 3/4 of an hour then we know that for every session she practices for 45 minutes.

The question states that she practices for 3 hours every week, since we know that we need to multiply 45 (because she practices 45 minutes every session) by a number that will get us 3 hours.

45 x 4 is 180 minutes (or three hours) we divided 180 by 4 and got 45 thus we are correct.

Which in turn means she has done 4 sessions this week. Since now we know that 4 sessions is 3 hours (making the ratio 4:3) we can multiply to find how many sessions she has left to do this week.

So if we have 4:3 then we can make it 8:6 (which means we know have 8 sessions and 6 hours) now we can make it 12:9 (12 sessions and 9 hours) and add it once more to get 16:12 (or 16 sessions and 12 hours).

Now we know that it takes 16 sessions for her to reach twelve hours, and since she and already done 4 sessions and 3 hours, it means that she has 12 sessions left to do until she is able to get her 12 hour a week goal.

—
Hope this helped, have a great day! :D

4 0

3 years ago

Read 2 more answers

Which of the following is the equation for a line parallel to y=2x−5 and having a y-intercept of −3? Select one: a. y=−3x−5 b.y=

Firdavs [7]

When we write a line equation in the form

$y=mx+q$

m is the slope of the line, and q is the y-intercept.

Since we want the y-intercept to be -3, our line will look like

$y=mx-3$

In order to fix the slope, remember that two parallel lines have the same slope. So, the slope of the given line y=2x-5 is 2, and since we want a line parallel to this line, our slope will be 2 as well.

Plugging the values, we can finish the equation:

$y=2x-3$

6 0

4 years ago