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4 years ago

In the expression shown p represents a rational number. 4p. what value of p makes the expression equal a number less than 4?

1 answer:

8 0

C: 7/8
Explanation: Since we want a number that makes 4p less than 4, we need to find a number for p that is less than 1. By looking at each fraction, only 7/8 will render it less than 4

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Factor by grouping (sometimes called the ac-method).

lesya692 [45]

Answer:

Step-by-step explanation:

The arc method is basically finding what the a and c coefficients multiply to, and then finding the factors of that that add up to b.

Since we have the quadratic in the ax^2+bx+c form we don't have to adjust anything. Now, a = 8, b = 2 and c = -3. a*c = -24 so now we want to find all the factors of that.

-1 and 24

1 and -24

-2 and 12

2 and -12

-3 and 8

3 and -8

-4 and 6

4 and -6

And after that they repeat. It is important to note that you can use negative on either side, or if a*c was a positive number you could multiply two negatives like 24 can be and 12 as well as -1 and -12.

Now we want to look at all the factor pairs and find one that add together to equal 2 because b = 2. -4 + 6 does it, so there's our choice. Now we can rewrite the original quadratic as 8x^2-4x+6x-3. You can check that this is equivalent by combining like terms It's the same as rewriting it as 8x^2+2x-2-1 because -2 and -1 will combine to get -3. Anyway, now we can factor.

8x^2-4x+6x-3 You can imagine there being two sets of parenthesis.

( 8x^2-4x)+(+6x-3) Now from here we can factor something out of each parenthesis. e can factor out 4x fromt he first and 3 from the second.

4x(2x-1)+3(2x-3) Now, it may not be obvious but you can factor 2x-3 from each term. If that's not clear pretend 2x-3 = u

4xu + 3u Now hopefully it is clear you can factor out this u

u(4x+3) Then we know u = 2x-3 so

(2x-3)(4x+3) And it's factored.

I do want to mention you could have done this with 8x^2+6x-4x-3 with the +6 and -4 switched. I won't go through it here but it may help to do it yourself if you still don't quite understand. Let me know if there is something I can further explain though.

3 0

3 years ago

Find the following <br> (u•w)(2)=<br> (w•u)(2)=

Stells [14]

Step-by-step explanation:

substitute 2 into x

1. (u ○ w)(2)

u(w(x))

= 4(-5x+1)+2

= 4(-5.2+1)+2

= 4(-9)+2

=-34

2. (w ○ u)(2)

w(u(x))

= -5(4x+2)+1

= -5(4.2+2)+1

= -5(10)+1

= -49

8 0

3 years ago

For the equations given below, which statement is true?

seraphim [82]

Answer:

D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first

equation by any value

Step-by-step explanation:

-21=14 Equ(1)

6.1=-42 Equ(2)

Multiplying the first equation by -3 will give

-63= -42

Which is not equivalent to the second equation

Multiplying the first equation by 3, we have

-63=42

Not equivalent to the second equation

Multiplying both sides of the first equation by -4, we have

84=56

Not equivalent to the second equation

D. The equations do not have the same solution because the second eqlition can never be obtained when multiplying the first

equation by any value

3 0

4 years ago

A student flips a fair coin 6 times. Answer the following questions: 1. Suppose that after flipping the coin all six times the e

VashaNatasha [74]

Answer:

1. 7 outcomes.

2. 64 outcomes.

3. D and H

Step-by-step explanation:

1. The experimenter will record the total number of heads after flipping the coin 6 times, therefore, the possible outcomes are: the experimenter got 0 heads, the experimenter got 1 head,..., the experimenter got 6 heads. Therefore there are 7 possible outcomes: (0, 1, 2, 3, 4, 5, 6).

2. If the experimenter records the result after each flip (H or T), for the first flip she has 2 results (heads or tails), for the second one she has 2 results, same for the third, fourth, fifth and sixth flip.

Therefore the possible outcomes are: $(2)(2)(2)(2)(2)(2)=2^{6}=64$ .

3. Now the experimenter will end up the experiment earlier if she gets two tails or two heads in a row.

A.TTHTT is not possible because in this case she would've ended up the experiment after the second flip since she got two tails.

B.TTH is not possible either for the same reason.

C. HT is not possible because she still needs to get another T or two H in a row.

D. This is a possible outcome because in this one she flipped the coin 6 times and she didn't get two heads or two tails in a row so she didn't finish it earlier.

E. Is not possible because she should've stopped after the second flip.

F. Is not possible because it has 7 letters, therefore, 7 flips.

G. Is not possible because she should've stopped once she got heads in the fourth and fifth flip.

H. Is possible because she got heads in the second and third flip.

6 0

3 years ago

Using exponents don't understand what's 9 cubed and 20 squared how do I do it in expanded form whett

Naily [24]

Expanded form is when you just write it out.

so 9 cubed becomes:

9×9×9

and 20 squared becomes:

20×20

the exponent tells you how many times to multiply that number by itself. so, whenever it asks for expanded form, you just write the number how ever many times the exponent tells you to and multiply them all.

4 0

3 years ago