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2 years ago

What is the slope of the line passing through the points (2, 5) and (0, –4)?

Mathematics

2 answers:

damaskus [11]2 years ago

8 0

I think the gradient would be 1 and the y intercept would be -4

iragen [17]2 years ago

5 0

In order to find the slope of line that passes through 2 points, use the equation slope=rise/run
rise = 5-(-4) =9
run = 2- 0 =2
slope = rise/run = 9/2

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Pamela drove her car 99 kilometers and used 9 liters of fuel. She wants to know how many kilometers (k) she can drive with 12 li

masya89 [10]

Answer:

132 kilometers

Step-by-step explanation:

Given: Pamela drove her car 99 kilometers and used 9 liters of fuel.

To find: Number of kilometers Pamela drove in 12 liters of fuel.

Solution:

It is given that Pamela drove her car 99 kilometers and used 9 liters of fuel. Also the relationship between kilometers and fuel is proportional.

So, let us assume that she can travel x kilometers in 12 liters of fuel.

By proportionality we have,

$99:9 :: x:12$

$\frac{99}{9} =\frac{x}{12}$

$11=\frac{x}{12}$

$x=12\times11$

$x=132$

Hence, she can travel 132 kilometers in 12 liters of petrol.

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3 years ago

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2 years ago

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3 years ago

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egoroff_w [7]

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Step-by-step explanation:

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3 years ago

If a person takes a prescribed dose of 10 milligrams of Valium, the amount of Valium in that person's bloodstream at any time ca

aleksandr82 [10.1K]

Answer:

(a)8.0mg

(b)36.87 hours

(c)-0.168

Step-by-step explanation:

The amount of Valium in that person's bloodstream at any time can be modeled with the exponential decay function $A ( t ) = 10 e^{ -0.0188 t$ (t in hours)

(a)After 12 Hours

$A ( 12) = 10 e^{ -0.0188*12}\\=7.98\\\approx 8.0 mg $(to the nearest tenth of a milligram)$

(b)If A(t)=5mg

Then:

$5= 10 e^{ -0.0188 t}\\$Divide both sides by 10\\0.5=e^{ -0.0188 t}\\$Take the natural logarithm of both sides\\ln (0.5)=-0.0188 t\\t=ln (0.5) \div (-0.0188)\\$t=36.87 hours (to two decimal places.)$

(c)

$A ( t ) = 10 e^{ -0.0188 t}\\A'(t)=10(-0.0188)e^{ -0.0188 t}\\A'(t)=-0.188e^{ -0.0188 t}\\$At 6 hours, the rate at which the amount of Valium is decaying therefore is:\\A'(6)=-0.188e^{ -0.0188*6}\\$=-0.168 ( to three decimal places)$

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2 years ago