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3 years ago

Question 10 Express 40 as a product of prime factors

Mathematics

1 answer:

Step2247 [10]3 years ago

5 0

Answer:

2 x 2 x 2 x 5

Step-by-step explanation:

The first few prime numbers: {2, 3, 5, 7, 11, 13, 17, 19}

One way to start is to divide by the first prime until you can't do that any more, then try the next prime and so on until all the numbers in your list are prime.

40 = 2(20) divide 20 by 2 again

40 = 2(2)(10) divide 10 by 2 again

40 = 2(2)(2)(5) stop--all factors are prime.

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Factor completely 36x^2 − 25.

sveticcg [70]

Hello there!

$( (2^2*3^2x^2) - 25) \\ \\ Factoring: \boxed{36x2-25} \\ \\ (PROOF): \\ \\ (A+B) * (A-B) = \\
 A2 - AB + BA - B2 = \\
 A2 - AB + AB - B2 = \\
 A2 - B2 \\ \\$

Your final answer would be (<span> (6x + 5) • (6x - 5)).

Your correct answer would be (option d).

I hope this helps you!</span>

4 0

3 years ago

Read 2 more answers

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Viefleur [7K]

QUESTION 1

Given that:

$f(x)=2x^2+3x-9$ ,

$g(x)=5x+11$ ,

and

$h(x)=-3x^2+1$

Then;

$f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)$

$f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1$

Group similar terms;

$f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1$

Simplify;

$f(x)-g(x)+h(x)=-x^2-2x-19$

QUESTION 2

Given that;

$f(x)=4x-7$ .

$g(x)=(x+1)^2$

and

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

Substitute the functions;

$s(x)=4x-7+(x+1)^2$

Substitute x=3

$s(3)=4(3)-7+(3+1)^2$

$s(3)=12-7+(4)^2$

$s(3)=5+16$

$s(3)=21$

QUESTION 3

Given:

$f(x)=3x+2$

$g(x)=x^2-5x-1$

$f(g(x))=f(x^2-5x-1)$

This implies that;

$f(g(x))=3(x^2-5x-1)+2$

Expand the parenthesis;

$f(g(x))=3x^2-15x-3+2$

$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

Let

$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

$\Rightarrow \sqrt{\frac{y-1}{3}}=x-6$

$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

6 0

3 years ago

It costs 42 dollars for 12 cookies how much is 1 cookie

ArbitrLikvidat [17]

Answer:

$3.50

Step-by-step explanation:

if you divide 42 by 12 you get 3.5

3 0

2 years ago

Jake's water bottle has a capacity of 1.43 L. What is the bottle's capacity in milliliters?

otez555 [7]

Answer:

1430 milliliters

Step-by-step explanation:

so basically all you have to remember is 1 liter is 1000 milliliters so just convert the 1 into 1000 then remember that any decimals in the tenths or hundreds place act like the hundred for the on thousand. So 1000 plus 400 plus 30 equal 1430 milliliters.

5 0

3 years ago

Read 2 more answers

Solve the following exponent:<br><br> 70

Alika [10]

Answer 70 = 7070

Step-by-step explanation: denotes how many times to multiply the base (70)

7 0

2 years ago

Question 10 Express 40 as a product of prime factors​

Question 10 Express 40 as a product of prime factors