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3 years ago

The equation of the graphed line is 2x - y = -6.

Mathematics

1 answer:

LuckyWell [14K]3 years ago

6 0

Answer:

-3

Step-by-step explanation:

The given equation is in standard form. We can solve for x in order to find the x intercept.

2x - y = -6

Now, make y equal to 0, because the coordinates of the y intercept have y as 0:

2x - 0 = -6

2x = -6

x = -3

The x intercept is -3. Hope this helps :)

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A certain college graduate borrows 7864 dollars to buy a car. The lender charges interest at an annual rate of 13%. Assuming tha

White raven [17]

Answer:

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = =$1573.17

Step-by-step explanation:

Consider A represent the balance at time t.

A(0)=$ 7864.

r=13 % =0.13

Rate payment = $k

The balance rate increases by interest (product of interest rate and current balance) and payment rate.

$\frac{dB}{dt} = rB-k$

$\Rightarrow \frac{dB}{dt} - rB=-k$ .......(1)

To solve the equation ,we have to find out the integrating factor.

Here p(t)= the coefficient of B =-r

The integrating factor $=e^{\int p(t) dt$

$=e^{\int (-r)dt$

$=e^{-rt}$

Multiplying the integrating factor the both sides of equation (1)

$e^{-rt}\frac{dB}{dt} -e^{-rt}rB=-ke^{-rt}$

$\Rightarrow e^{-rt}dB - e^{-rt}rBdt=-ke^{-rt}dt$

Integrating both sides

$\Rightarrow \int e^{-rt}dB -\int e^{-rt}rBdt=\int-ke^{-rt}dt$

$\Rightarrow e^{-rt}B=\frac{-ke^{-rt}}{-r} +C$ [ where C arbitrary constant]

$\Rightarrow B(t)=\frac{k}{r} +Ce^{rt}$

Initial condition B=7864 when t =0

$\therefore 7864= \frac{k}{r} - Ce^0$

$\Rightarrow C= \frac{k}{r} -7864$

Then the general solution is

$B(t)=\frac{k}{r}-( \frac{k}{r}-7864)e^{rt}$

To determine the payment rate, we have to put the value of B(3), r and t in the general solution.

Here B(3)=0, r=0.13 and t=3

$B(3)=0=\frac{k}{0.13}-( \frac{k}{0.13}-7864)e^{0.13\times 3}$

$\Rightarrow- 0.48\frac{k}{0.13} +11614.98=0$

⇒k≈3145.72

Therefore rate of payment = $ 3145.72

Therefore the rate of interest = ${(3145.72×3)-7864}

=$1573.17

4 0

3 years ago

The heights of a group of boys and girls at a local middle school are shown on the dot plots below.

stira [4]

D, or The girls are generally taller than the boys.

Hope this helps!

8 0

3 years ago

How many zeros are in one million?

Julli [10]

Answer:

six

Step-by-step explanation:

1,000,000

5 0

3 years ago

Read 2 more answers

A collection of nickels and quarters is worth 2.85 . There are 3 more nickels than quarters how many nickels and quarters are th

Zolol [24]

A nickel is equal to 5 cents or 0.05 dollars.

A quarter is equal to 25 cents or 0.25 dollars.

Let number of nickels be = n

Let number of quarters be = q

$0.05n+0.25q=2.85$ ...........(1)

As it is given, there are 3 more nickels than quarters so equation becomes,

$n=q+3$ ................(2)

Plug in the value of 'n' from (2) in (1)

$0.05(q+3)+0.25q=2.85$

= $0.05q+0.15+0.25q=2.85$

$0.30q=2.70$

$q=9$

As $n=q+3$ we get, $n=9+3=12$

Hence, there are 12 nickels and 9 quarters.

3 0

3 years ago

A truck is said to get 18 miles per gallon on a highway, but this value can fluctuate,

Ratling [72]

Answer: 14 miles ≤ D ≤ 22 miles.

Step-by-step explanation:

The mean distance traveled per gallon, is 18 miles.

But this can fluctuate, at most, by 4 miles.

Because we have here the "at most", we know that we should use the ≤, ≥ symbols.

Then, if the mean is 18mi, the range of possible distances traveled per gallon is:

(18 miles - 4 miles) ≤ D ≤ (18 miles + 4 miles)

Where D is the distance.

14 miles ≤ D ≤ 22 miles.

So the truck can get between 14 miles and 22 miles per gallon on the highway.

4 0

3 years ago