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3 years ago

Let f(x) = 5x – 3 and g(x) = 2x². Perform the function operation and then find the domain of the result.

Mathematics

1 answer:

MAXImum [283]3 years ago

7 0

Answer:

(f+g)x= 2x²+5x-3

The domain x∈ Real number.

Step-by-step explanation:

Given that f(x) = 5x - 3 and g(x) = 2x²

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

So, by using the given function

(f+g)x= (5x-3) + (2x²)= 2x²+5x-3

As the result, 2x²+5x-3, is a polynomial, so domain of the result is all the real numbers.

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Factor completely h^3+2h^2-9h-18

guapka [62]

Step 1: Group this into two groups:

$h^3 + 2h^2-9h-18=(h^3 + 2h^2)+(-9h-18)$

When you do that, be sure to group the "–" into the group with the 9 and make sure there's "+" between the groups.

Step 2: Factor out the GCF from both individual groups:

$(h^3 + 2h^2)+(-9h-18) = h^2 (h+2) -9(h+2)$

Step 3: Notice both groups have that (h+2)? That's a new GCF between the two groups, so factor that out:

$h^2 (h+2) -9(h+2) = (h+2)(h^2-9)$

Step 4: That $(h^2-9)$ piece can be factored further, since it's a difference of squares:

$(h+2)(h^2-9) = (h+2)(h+3)(h-3)$

Now it's factored.

8 0

2 years ago

A researcher at a large company has collected data on both the beginning salary and the current salary of 48 randomly selected e

Nadya [2.5K]

Answer:

a. 0.83

b. 44107.3

c. 2252.7

Step-by-step explanation:

The correlation coefficient is calculated as

byx=rSy/Sx

rSy=byx*Sx

⇒r=byx*Sx/Sy

Sy=standard deviation of y=standard deviation of current salary=15300

Sx=standard deviation of x=standard deviation of beginning salary=5970

byx=2.12

r=2.12*5970/15300

r=12656.4/15300

r=0.83

There is a strong positive correlation between current and beginning salary.

Beginning salary=$22000

y^ =−2532.7 + 2.12x.

Current salary=-2532.7+2.12*beginning salary

Current salary=-2532.7+2.12*22000

Current salary=-2532.7+46640

Current salary=$44107.3

The predicted current salary of Mr. Joseph Keller is $44107.3.

Residual=y-y^=Observed-Predicted

Observed Current Salary of Kathy Jones=40000

Beginning salary of Kathy Jones=19000

y^ =−2532.7 + 2.12x.

Predicted Current salary=-2532.7+2.12*beginning salary

Predicted Current salary=-2532.7+2.12*19000

Predicted Current salary=-2532.7+40280

Predicted Current salary=$37747.3

Residual=Observed Current Salary-Predicted Current salary

Residual=40000-27747.3

Residual=$2252.7

The residual for Ms. Jones is $2252.7.

8 0

3 years ago

How to solve 3a+9 and a²-9 i have to find h.c.f

Lesechka [4]

Answer:

First equation = 3a + 9

= 3( a+3 )

Second equation = a²- 9

= a² - 3 ^ 2

= (a+3) (a-3)

Hence,

HCF = ( a+ 3)

Hope this helped

All the best !!

4 0

3 years ago

PLEASE HELP WILL MARK BRAINLIEST!!!

Gala2k [10]

The Unit Rate is the start of the slope/the y-intercept of the slope.To find that we need to make the slope first.

(shown in the first picture)

We can see that the slope is a linear function/a straight line, and if we just follow the line down the slope we can see that it has a y-intercept/unit rate of 2/3 of 1 whole.

(the second picture)

6 0

3 years ago

What is the range of the given set of ordered pairs?<br> (9,-2) (4,3) ( 8, 10) (-4, 8)

otez555 [7]

Answer:

(-2,3,10,8)

Step-by-step explanation:

(x,y)=(domain,range)

x components are domain and y components are range in the given set of ordered pairs

8 0

3 years ago