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3 years ago

Select the equation of the line parallel to the equation y = -2x - 7 that passes through the point (3, 1).

Mathematics

1 answer:

motikmotik3 years ago

3 0

Formula of the line

y=mx+b.

For parallel line slope m is the same, so m= -2.

y=-2x+b.

We need to find b,using the point (3,1).

1= - 2*3+b

b=7

y = -2x +7

Answer is A. y = -2x +7.

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

8 0

3 years ago

Amanda is practicing her dives off the diving board. When she dives into the water, the path her body makes and where she resurf

Vilka [71]

Answer:

The number of feet she will travel back is 1 or 7 feet

Step-by-step explanation:

Here, we need to solve the quadratic equation

That will be as follows;

0 = x^2 -8x + 7

x^2-x-7x+ 7 = 0

x(x-1)-7(x-1) = 0

(x-1)(x-7) = 0

x = 1 or 7

The number of feet she will travel before coming back to the surface of the water is 1 or 7 feet

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3 years ago

Determine the slope and the y-Intercept of the line that passes through A(-2,4), B(0,8)

Semenov [28]

Answer and work down below. Let me know if you have questions

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3 years ago

If f(x)=3x-1 and g(x)=x+2, find (f-g)(x)

siniylev [52]

Answer:

(f - g)(x) = 2x - 3

Step-by-step explanation:

(f - g)(x)

= f(x) - g(x)

= 3x - 1 - (x + 2)

= 3x - 1 - x - 2

= 2x - 3

7 0

1 year ago

Use elimination to solve each system of equations<br> 2x-y=-1<br> 3x-2y=1

mixer [17]

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x=-3 \\ \\
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2 \times (-3)-y=-1 \\
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-y=5 \ \ \ |\times (-1) \\
y=-5 \\ \\
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3 years ago

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