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3 years ago

The graphs below have the same shape. What is the equation of the blue graph?

Mathematics

1 answer:

Tems11 [23]3 years ago

3 0

Answer:

Option (A)

Step-by-step explanation:

Parent function (in red) graph is represented by,

f(x) = x²

If this function is translated by 'a' units to the right, rule to be followed,

f(x) → f(x - a)

If the parent function is shifted by 4 units to the right (blue graph), the new function will be,

g(x) = f(x - 4)

g(x) = (x - 4)²

Therefore, Option (A) will be the correct option.

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Gracie drove 280 miles in 2.5 hours. How long will it take her to drive 710 miles at that same speed?

Ivanshal [37]

Answer:

Step-by-step explanation:

710 miles × (2.5 hours)/(280 miles) ≅ 6.3 hours

7 0

3 years ago

1. If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

creativ13 [48]

Answer:

${x}^{2} + 6x + 5$

Step-by-step explanation:

Required polynomial

${x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ \\ = {x}^{2} - ( - 6)x + 5 \\ \\ = {x}^{2} + 6x + 5$

6 0

3 years ago

please answer the question on the screenshot below, also please explain to me how you got your answer.

frutty [35]

QUESTION 1

The given functions are;

$f(x)=5x^2-2x$ and $g(x)=5x^2+x-4$

$(f+g)(x)=f(x)+g(x)$

$(f+g)(x)=5x^2-2x+3x^2+x-4$

We regroup like terms to obtain;

$(f+g)(x)=5x^2+3x^2-2x+x-4$

This simplifies to;

$(f+g)(x)=8x^2-x-4$

The correct answer is A.

QUESTION 2

The given functions are;

$f(x)=3x^2+5$ and $g(x)=x-2$ .

$(fg)(x)=(f(x))(g(x))$

This implies that;

$(fg)(x)=(3x^2+5)(x-2)$

$\Rightarrow (fg)(x)=3x^3-6x^2+5x-10$

The correct answer is B.

QUESTION 3

The given functions are

$f(x)=3x^2+10x-8$ and $g(x)=3x^2-2x$ .

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$

$(\frac{f}{g})(x)=\frac{3x^2+10x-8}{3x^2-2x},x\ne0,\frac{2}{3}$

We factor to obtain;

$(\frac{f}{g})(x)=\frac{(x+4)(3x-2)}{x(3x-2)},x\ne0,\frac{2}{3}$

We cancel the common factors to obtain;

$(\frac{f}{g})(x)=\frac{x+4}{x},x\ne0,\frac{2}{3}$

The correct answer is A.

5 0

3 years ago

Hi I need help with the question in the image. Step by step, thank you!

VashaNatasha [74]

The exponential function is $f(x) = 18(12)^{-x-4} + 2$

<h3>How to determine the equation?</h3>

An exponential function is represented as:

y = b^x

Where b represents the base.

The base is given as:

b = 12

So, we have:

y = (12)^x

It is vertically compressed by a factor of 1/8.

So, we have:

y = 18(12)^x

When reflected across the y-axis, we have:

$y = 18(12)^{-x}$

The horizontal asymptote is y = 2.

So, we have:

$y = 18(12)^{-x} + 2$

It passes through the point (-3, 4).

So, we shift the function to the right by 4 units

$y = 18(12)^{-x-4} + 2$

Express as a function

$f(x) = 18(12)^{-x-4} + 2$

Hence, the exponential function is $f(x) = 18(12)^{-x-4} + 2$

Read more about exponential functions at:

brainly.com/question/14355665

#SPJ1

6 0

2 years ago

Which problem can be solved by expression 3/8 divided 1/4?

NeTakaya

Answer:

3/8÷1/4=1 1/2

Step-by-step explanation:

I am not sure what you are asking here, So I am gonna explain how you divide this.

So using the KCF method (Keep Change Flip) You would KEEP the first fraction (3/8) and CHANGE the operation (from divide to multiply) then FLIP your second fraction (1/4 to 4/1)

After doing this, it should look like:

3 4

8 1

Now that we got that, you multiply from left to right. 3×4 is 12. 8×1=8.

That should leave you with 12/8. But this is an improper fraction. So you would divide top by bottom to get a mixed fraction.

It should look like this

01. 1 1/2

8 12

Step by step explanation:

8 only goes into 12 one time. So you would subtract 12 by 8, and get 4. From that you would get 1 4/8 but 1 4/8 can be simplified to 1 1/2.

So it is 1 1/2

4 0

3 years ago