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3 years ago

3. What is the graph that represents y = x-3

Mathematics

2 answers:

Oduvanchick [21]3 years ago

7 0

Answer:

Option C

Step-by-step explanation:

By looking at the equation y = x - 3 we can see that the slope is positive (so the line will have an upward trend) and that the y intercept is - 3 (which mean the line will go through the y axis in that point. So now we have two following statement....

line has an upward trend
line has the y intercept of (0,-3)

The only line following this statements is line C.

Scrat [10]3 years ago

5 0

Answer:

Option C

Step-by-step explanation:

-3 is the y intercept so the graph should intersect at -3 on the y axis.

x is positive so the graph should point up.

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The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th

vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by $P(t)=1.394(1.006)^t$

To find the derivative you need to:

$\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t$

To find the population growing at the start of 2014 we say t = 0

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year$

To find the population growing at the start of 2015 we say t = 1

$P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year$

To convert billion to million you multiple by 1000

$P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year$

6 0

3 years ago

In the coordinate plane, three vertices of rectangle abcd are a(0, 0, b(0, a, and d(b, 0. what are the coordinates of point c?

serious [3.7K]

So the point would be c)0,0

3 0

4 years ago

Inverse for f(x)=1/2x+3

Semenov [28]

Answer: $f^{-1}(x)=2x-6$

Step-by-step explanation:

To find the inverse, we want to switch the y with x and x with y. Once we do that, we solve for y.

$y=\frac{1}{2}x+3$ [switch x and y]

$x=\frac{1}{2}y+3$ [subtract both sides by 3]

$x-3=\frac{1}{2} y$ [multiply both sides by 2]

$y=2x-6$

Now, we know that $f^{-1}(x)=2x-6$ .

3 0

3 years ago

Read 2 more answers

Wouldn’t it be the 3rd answer 1/3 + 1/4 because you have to convert the dominators into 12 then you will get 4/12 and 3/12 then

marusya05 [52]

Answer:

Yes, correct

Step-by-step explanation:

Hope that helppppps

7 0

3 years ago

Which equation represents the transformed function below?

Marta_Voda [28]

If we know the concepts of transformations and horizontal translation and that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

<h3>How to determine the transformed function in terms of its parent function</h3>

The transformation of functions are operations which modify the relationship between input and outputs in a function. The parent function represents a canonical square root function and the transformed function is the consequence of applying a horizontal translation.

This kind of transformation is defined by the following expression:

g(x) = f(x - k) (1)

Where k represents a rightward translation for k > 0.

If we know that f(x) = √x and k = - 2, then the transformed function is g(x) = √(x + 2).

To learn more on transformations: brainly.com/question/11709244

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5 0

2 years ago