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Aleks [24]
4 years ago
10

Niki scored a 78 on her first test and an 85 on her second. Niki forgot what she got on her third test bit she knows that her av

erage is an 85. What did she score on her third test? Write and sole an equation for this problem.
Mathematics
1 answer:
gregori [183]4 years ago
5 0
An average is written by the values / the amount of values.

We know there are 3 values, we know the numbers of 2, this can be modelled by the equation:

(78 + 85 + x)/3 = 85
We solve that ^:
(163+x)/3=85
163+x=255
x=92

The score on her 3rd test is 92

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Find the general solution of (x+3)y’=2y
gregori [183]

Answer:

y=C(x+3)^2

Step-by-step explanation:

We are given:

\displaystyle (x+3)y^\prime=2y

Separation of Variables:

\displaystyle \frac{1}{y}\frac{dy}{dx}=\frac{2}{x+3}

So:

\displaystyle \frac{dy}{y}=\frac{2}{x+3} \, dx

Integrate:

\displaystyle \int\frac{dy}{y}=\int\frac{2}{x+3}\, dx

Integrate:

\displaystyle \ln|y|=2\ln|x+3|+C

Raise both sides to e:

|y|=e^{2\ln|x+3|+C}

Simplify:

|y|=(e^{\ln|x+3|})^2\cdot e^C

So:

|y|=C|x+3|^2

Simplify:

y=\pm C(x+3)^2=C(x+3)^2

5 0
3 years ago
An open rectangular box is 4 feet long and has a surface area of 20 square feet. Find the dimensions of the box for which the vo
sweet-ann [11.9K]
SA=2H(L+W)+LW for open box
20=2H(4+W)+4(W)
distribute
20=8H+2WH+4W
divide both sides by 2
10=4H+WH+2W
solve for 1 variable, pick W
10-4H=WH+2W
10-4H=W(H+2)
(10-4H)/(H+2)=W

V=LWH
subsitute 4 for V, subsitute H for H and (10-4H)/(H+2) for W
V=(4)(H)(10-4H)/(H+2)
V=(40H-16H²)/(H+2)
find max value
take deritivitive of this thing
V'=-16(H²+4H-5)/((H+2)²)
using sign chart
sign changes from positive to negative at H=1

so at H=1
find W

W=(10-4H)/(H+2)
W=2

the dimeionts are

length=4ft
width=2ft
height=1ft
(the volume is 8 cubic feet)
3 0
4 years ago
Occupation
baherus [9]
C is answer no explanation needed
7 0
3 years ago
Write an equation of the line that is perpendicular to y=1/2x-3 and goes through the point (1,3)
Alex_Xolod [135]

Answer:

y = -2x + 5

Step-by-step explanation:

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

Slope of this line m₁ = 1/2

Slope of the line perpendicular to this line = m₂

m₁ *m₂ = -1

m₂ = -1 *2/1 = -2

Slope  = -2; (1,3)

y- y₁ = m(x-x₁)

y - 3 = -2(x - 1)

y - 3 = -2x + 2

y = -2x +2 +3

y = -2x + 5

5 0
3 years ago
Hep me find the measure of angle y
sergiy2304 [10]

Answer:

130

Step-by-step explanation:

first find angle C, which is 180-90-40=50

angle Y=180-50=130

6 0
3 years ago
Read 2 more answers
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