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inysia [295]
3 years ago
5

A line is perpendicular to y = - x - 2 and intersects the point (-5, 10)

Mathematics
1 answer:
Lady_Fox [76]3 years ago
6 0

Answer:

y = x + 15

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = - x - 2. Its slope is -1. A line perpendicular to this will have a slope of 1.

Plug this value (1) into your standard point-slope equation of y = mx + b.

y = 1x + b or y = x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-5, 10). Plug in the x and y values into the x and y of the standard equation.

10 = (-5) + b

Simplify.

10 = -5 + b

Now, add 5 to both sides to isolate b.

15 = b

Plug this into your standard equation.

y = x + 15

This equation is perpendicular to your given equation (y = -x - 2) and contains point (-5, 10)

Hope this helps!

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Camacho is buying a monster truck. The price of the truck
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Total cost = a + (13a/100)

<u>Step-by-step explanation:</u>

Let the price of the monster truck be 'a'

He should pay 13% tax

Total cost = price of the truck + tax

Total cost = a + (13a/100)

The equation to represent the total cost is

Total cost= a + (13a/100)

3 0
3 years ago
Pregnant women metabolize some drugs at a slower rate than the rest of the population. The half-life of caffeine is about 4 hour
UkoKoshka [18]

Answer:

Husband:

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Woman:

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

Step-by-step explanation:

The amount of caffeine in the body can be modeled by the following equation:

C(t) = C(0)e^{rt}

In which C(t) is the amount of caffeine t hours after 8 am, C(0) is how much coffee they took and r is the rate the the amount of caffeine decreases in their bodies.

110 mg of caffeine at 8 am,

So C(0) = 110

Husband

Half life of 4 hours. So

C(4) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

55 = 110e^{4r}

e^{4r} = 0.5

Applying ln to both sides

\ln{e^{4r}} = \ln{0.5}

4r = \ln{0.5}

r = \frac{\ln{0.5}}{4}

r = -0.1733

So for the husband

C(t) = 110e^{-0.1733t}

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.1733t}

C(11) = 110e^{-0.1733*11} = 16.35

The husband will have 16.35 mg of caffeine in his body at 7 pm.

Pregnant woman

Half life of 10 hours. So

C(10) = 0.5C(0) = 0.5*110 = 55

C(t) = C(0)e^{rt}

55 = 110e^{10}

e^{10r} = 0.5

Applying ln to both sides

\ln{e^{10r}} = \ln{0.5}

10r = \ln{0.5}

r = \frac{\ln{0.5}}{10}

r = -0.0693

At 7 pm

7 pm is 11 hours after 8 am, so this is C(11)

C(t) = 110e^{-0.0693t}

C(11) = 110e^{-0.0693*11} = 51.33

The pregnant woman will have 51.33 mg of caffeine in her body at 7 pm.

7 0
3 years ago
If Mary is two years old and her sister is half of her age, how old is her sister
Alchen [17]

Answer:

1

Step-by-step explanation:

HOW TF IS THAT A HARD QUESTION


8 0
3 years ago
Read 2 more answers
(-9, -5) and (-1, -9)<br> find the midpoint
irga5000 [103]

Answer:

(-5,-7)

Step-by-step explanation:

6 0
3 years ago
Why will the value of y for the function y equals 5x + 1 always be greater than that of y equals 4x + 1 when X is greater than 1
mezya [45]

"Why?" in math has various meanings.

Let's solve

5x +1 > 4x + 1

That's easily solved,

5x - 4x > 1 - 1

x > 0

Since x>1 is included in x>0, it's in the solution set to the above inequality, so all such x make the inequality true.

6 0
4 years ago
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