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3 years ago

Solve for n. -6n = -5 - 5n n=

Mathematics

1 answer:

goblinko [34]3 years ago

4 0

1. Simplify both sides

−6n=−5−5n

−6n=−5+−5n

−6n=−5n−5

2. Add 5n to both sides

−6n+5n=−5n−5+5n

−n=−5

3. Divide both sides by -1.

−n /−1 = −5 /−1

n=5

So the variable n, is equal to 5

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20 out of 25 students were 15 y/o, what percentage of the students is 15 ?

zalisa [80]

Answer:

80% are 15 years old

Step-by-step explanation:

To find the percent , we need to know how many out of 100

20/25

Multiply the top and bottom by 4

20*4

-----------

25*4

80/100

This is 80%

80% are 15 years old

4 0

3 years ago

Read 2 more answers

Rewrite the equation C = 2nr to show the expression that can be used to find the value of r.

STatiana [176]

The process is:

C = 2nr

2nr = c

r (2n) = c

$r = \frac{c}{2n}$

That's the answer☝️☝️☝️☝️

or maybe this one

r = 2n + c

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3 years ago

Read 2 more answers

Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

$y - k = a {(x - h)}^{2}$

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

$y = {x}^{2} - 4x$

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

7 0

3 years ago

What is the slope of the line that passes through the points (-6,1) and (4,-4)

mr Goodwill [35]

Answer:

-1/2

Step-by-step explanation:

change in y/ change in x = -4-1/4-(-6) =-5/10 = -1/2

4 0

3 years ago

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1)

viktelen [127]

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}$

The first line segment can be parameterized by $\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle$ with $0\le t\le1$ . Denote this first segment by $C_1$ . Then

$\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt$
$=108$

The second line segment ( $C_2$ ) can be described by $\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle$ , again with $0\le t\le1$ . Then

$\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt$
$=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt$
$=-\dfrac{229}3$

Finally,

$\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3$

5 0

4 years ago