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3 years ago

Let f(x) = -6x + 3 and g(x) = 5x + 4. Find fg and state its domain.

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

7 0

Answer:

$f(g(x))=-30x-21$

The domain is all real numbers

Step-by-step explanation:

we have

$f(x)=-6x+3$

$g(x)=5x+4$

we know that

$(fog)(x)=f(g(x))$

In the function f(x) substitute the variable x by the function g(x)

$f(g(x))=-6(5x+4)+3$

$f(g(x))=-30x-24+3$

$f(g(x))=-30x-21$

This is a linear function (equation of a line)

The domain is all real numbers

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Thank you for the answer

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3 years ago

Find all numbers p such that p and p^2 are both prime. prove that you found them all

Anuta_ua [19.1K]

0 and 1 are neither prime nor composite. A prime is any number greater than 1 that has just 1 and itself as factors. Primes can only start at x > 1

When that happens (when you start with numbers greater than one) p^2 is a composite consisting of 2 primes, so any composite will obey the law that he number will have at least 3 factors making it up -- in this case p p^2 and 1.

So the answer to the question by definition is that 0 numbers can have the property of both p and p^2 to be prime.

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3 years ago

Read 2 more answers

Brian invests £1900 into his bank account.

Nat2105 [25]

Answer:

£2585.64

Step-by-step explanation:

FV=PV(1+i)^t

Which means we have

1900(1+.045)^7

1900(1.045)^7

2585.64

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2 years ago

7x-3x-8=24 what is the value of x

Ann [662]

Answer: x=8 and 8=x. *The answer must be have positive sign.*

Step-by-step explanation:

addition property of equality is adding the same number to both sides of an equation does not change the equation.

a+c=b+c

distributive property: a(b+c)=ab+ac

add the numbers.

7x-3x=4x

4x-8=24

add by 8 both sides of an equation.

4x-8+8=24+8

simplify by equation.

24+8=32

4x=32

divide by 4 both sides of an equation.

4x/4=32/4

simplify by equation.

32/4=8

32/8=4

8*4=32

4*8=32

It change negative to positive.

x=8 and 8=x

Hope this helps!

Thanks!

Have a great day!

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3 years ago

Read 2 more answers

The figure below shows a tent with wires attached to help stabilize it. The length of each wire is 8 feet greater than the dista

Anestetic [448]

Answer:

The length of 2 wires are 13 feet and 12 feet [i don't know if the 3rd side is a wire, if so, the length is 5 feet]

Step-by-step explanation:

The image of the tent is attached.

As we can see, it creates a right triangle with "x+8" side being the hypotenuse of the triangle.

The pythagorean theorem tells us:

Hypotenuse^2 = Leg^2 + Leg^2

THe hypotenuse is "x+8", the two legs are "x" and "x+7" respectively. Let's solve for x:

$(x+8)^2=(x+7)^2+x^2$

We expand and solve for x:

$(x+8)^2=(x+7)^2+x^2\\x^2+16x+64=x^2+14x+49+x^2\\x^2+16x+64=2x^2+14x+49\\x^2-2x-15=0\\(x-5)(x+3)=0\\x=5,-3$

Length can't be negative, so x = 5.

Hence, the 3 sides of the triangle are:

x = 5

x + 8 = 13

x + 7 = 12

The length of 2 wires are 13 feet and 12 feet

8 0

2 years ago