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3 years ago

If a(x) = 3x + 1 and b (x) = StartRoot x minus 4 EndRoot, what is the domain of (b circle a) (x)?

Mathematics

1 answer:

Stella [2.4K]3 years ago

8 0

Answer:

The domain is [1,∞)

Step-by-step explanation:

The given functions are:

$a(x)=3x+1$

and

$b(x) = \sqrt{x - 4}$

We want to find the domain of

$(b\circ a)= \sqrt{3x + 1 - 4}$

Simplify to get:

$(b\circ a)= \sqrt{3x -3}$

This function is defined when the expression under the radical is greater or equal to zero.

$3x -3 \geqslant 0 \\ x \geqslant 1$

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If x is 5, then 6x = _____. 30 x 5 x 30

marin [14]

Answer:

6x = 30

Step-by-step explanation:

Let x = 5

6*5 = 30

6x = 30

8 0

2 years ago

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Solve this system of linear equations. Separate the x- and y-values with a comma.

vodomira [7]

Answer:

x = $\frac{5}{2}$ , y = $\frac{5}{4}$

Step-by-step explanation:

1. Isolate for x in one of the equations:

2x = 9x - 14y

2x-9x = 9x-9x -14y

-7x = -14y

-7x/-7 = -14y/-7

x = 2y

2. Substitute 2y in for x in the second equation:

9(2y) = 40 - 14y

3. Simplify:

18y = 40 - 14y

4. Isolate for y:

18y+14y = 40 -14y+14y

32y = 40

32y/32 = 40/32

y = $\frac{5}{4}$

5. Substitute the new y-value into the simplified expression x = 2y:

x = 2(5/4)

x = $\frac{5}{2}$

hope this helps!

7 0

2 years ago

Sally works 40 hours a week and makes $30 an hour, but her kids are in child care each day and the day care center charges her $

Lapatulllka [165]

Answer:

Sally will earn $21.25 per hour after she removes day care charges from her total earnings.

Step-by-step explanation:

Hey there!

Let's start by solving for how much money that Sally earns per week.

To find this value, we will find the product of 40 hours per week and 30 dollars per hour.

$40\times30=1200$

We now know that Sally makes $1,200 a week without deducting the daycare charges per day.

However, we know we need to deduct 70 dollars for each day that Sally works. Since she works for five days a week, we will find the product of 70 dollars per week and five days a week.

$70\times5=350$

Therefore, the day care charges $350 per week.

Finally, we need to subtract the day care charges from the amount of money that Sally earns to find how much she actually makes in a week.

$1200-350=850$

Therefore, for forty hours of work that Sally works each week, she earns $850.

However, we are not done. The question asks us to find how many dollars <u>per hour</u> does she actually make? Therefore, we need to find the quotient of 850 dollars and 40 hours per week.

$\displaystyle \frac{850}{40}=21.25$

Therefore, Sally earns $21.25 each hour after deducting day care costs.

6 0

2 years ago

Pls help I’ll failing ASAP this is due in 10 minutes I need help with 5 and 8

IRINA_888 [86]

Answer:

5) 3/5

8) 2/-4 or -2/4

Step-by-step explanation:

5, based on your work, is 3/5 because we use rise (3) and run (5)

And 8, based on your work, is 2/-4 or -2/4 because you go up 2, and go to the left 4.

5 0

2 years ago

Ms. Vasquez's daughter lives 1,650 miles away. Ms. Vasquez won a gift card for 100 gallons of gas. If her car can travel 35 mile

ivanzaharov [21]

Answer:

yes, since it takes 48 gallons of gas to go one direction to go back it is 96

Step-by-step explanation:

5 0

3 years ago

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