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3 years ago

What are the steps towards solving-5 - 15n = 10

Mathematics

2 answers:

Kryger [21]3 years ago

8 0

Answer:

n=-1

Step-by-step explanation:

First you add 5 to both sides an you would get -15n=15

Next divide by -15 on both sides and get n=-1

sdas [7]3 years ago

7 0

Answer: n= -1

Step-by-step explanation:

move constant to right- (-15n=10+5)

divide both sides by -15

you solution would be n= -1

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What number should be added to both sides of the equation to complete the square? x2 + 3x = 6

sladkih [1.3K]

The answer is B because you are suppose to square and divide once you subtract 6 on both sides.

3 0

3 years ago

Read 2 more answers

Solve the following initial-value problem, showing all work, including a clear general solution as well as the particular soluti

Vikki [24]

Answer:

General Solution is $y=x^{3}+cx^{2}$ and the particular solution is $y=x^{3}-\frac{1}{2}x^{2}$

Step-by-step explanation:

$x\frac{\mathrm{dy} }{\mathrm{d} x}=x^{3}+3y\\\\Rearranging \\\\x\frac{\mathrm{dy} }{\mathrm{d} x}-3y=x^{3}\\\\\frac{\mathrm{d} y}{\mathrm{d} x}-\frac{3y}{x}=x^{2}$

This is a linear diffrential equation of type

$\frac{\mathrm{d} y}{\mathrm{d} x}+p(x)y=q(x)$ ..................(i)

here $p(x)=\frac{-2}{x}$

$q(x)=x^{2}$

The solution of equation i is given by

$y\times e^{\int p(x)dx}=\int e^{\int p(x)dx}\times q(x)dx$

we have $e^{\int p(x)dx}=e^{\int \frac{-2}{x}dx}\\\\e^{\int \frac{-2}{x}dx}=e^{-2ln(x)}\\\\=e^{ln(x^{-2})}\\\\=\frac{1}{x^{2} } \\\\\because e^{ln(f(x))}=f(x)]\\\\Thus\\\\e^{\int p(x)dx}=\frac{1}{x^{2}}$

Thus the solution becomes

$\tfrac{y}{x^{2}}=\int \frac{1}{x^{2}}\times x^{2}dx\\\\\tfrac{y}{x^{2}}=\int 1dx\\\\\tfrac{y}{x^{2}}=x+c$ $y=x^{3}+cx^{2$

This is the general solution now to find the particular solution we put value of x=2 for which y=6

we have $6=8+4c$

Thus solving for c we get c = -1/2

Thus particular solution becomes

$y=x^{3}-\frac{1}{2}x^{2}$

5 0

3 years ago

Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree which was in the middle of the p

padilas [110]

Answer: $10.2\ yards$

Step-by-step explanation:

<h3> "Sara plotted the locations of the trees in a park on a coordinate grid. She plotted an oak tree, which was in the middle of the park, at the origin. She plotted a maple tree, which was 10 yards away from the oak tree, at the point (10,0) . Then she plotted a pine tree at the point (-2.4, 5) and an apple tree at the point (7.8, 5) What is the distance, in yards, between the pine tree and the apple tree in the</h3><h3>park?"</h3>

For this exercise you need to use the following formula, which can be used for calculate the distance between two points:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

In this case, you need to find distance, in yards, between the pine tree and the apple tree in the park.

You know that pine tree is located at the point (-2.4, 5) and the apple tree is located at the point (7.8, 5).

So, you can say that:

$x_2=-2.4\\x_1=7.8\\\\y_2=5\\y_1=5$

Knowing these values, you can substitute them into the formula and then evaluate, in order to find the distance, in yards, between the pine tree and the apple tree in the park.

This is:

$d=\sqrt{(-2.4-7.8)^2+(5-5)^2}=10.2\ yards$