Need help with number 16

If P = 4x^4 - 3x^3 + x² - 5x + 11 and Q = -3x^4 + 6x^3 - 8x² + 4x - 3, what is P - 2Q?

vazorg [7]

Answer:

10x^4-15x^3+17x^2-13x+17

Step-by-step explanation:

P-2Q

Replace P and Q with the given values,

4x^4-3x^3+x^2-5x+11-(2(-3x^4+6x^3-8x^2+4x-3)

4x^4-3x^3+x^2-5x+11-(-6x^4+12x^3-16x^2+8x-6)

4x^4-3x^3+x^2-5x+11+6x^4-12x^3+16x^2-8x+6

10x^4-15x^3+17x^2-13x+17

7 0

2 years ago

X + 4(x-1) = 9-2(x+3)

Genrish500 [490]

Collect like terms
x + 4x - 4 = 9 - 2 x - 6
move the terms
5x - 4 = 3 - 2x
collect like terms calculate
5x + 2x = 3 + 4
7x = 7
answer is x = 1

3 0

2 years ago

Of the students attending a school party, 60% of the students are girls, and 40% of the students like to dance. After these stud

elena-s [515]

Answer:

252 students at the party like to dance

Step-by-step explanation:

Given:

60% of the students are girls

40% of the students like to dance

20 more boy students

Percentage of the girls in the party = 58%

To Find:

How many students now at the party like to dance=?

Solution:

Let the number of girls be g.

Let the number of total people originally be t.

We know that

$\frac{g}{t}=\frac{60}{100}$

$\frac{g}{t}=\frac{3}{5}$ ----------------------------------(1)

We also know that

$\frac{g}{t+20}=\frac{58}{100}$

$\frac{g}{t+20}=\frac{29}{50}$ -----------------------------(2)

We now have a system of equation from (1) and (2)

3t=5g

$g = \frac{3t}{5}$ ------------------------(3)

50g=29t+580------------------------(4)

Substituting 3 in 4, we get

$50(\frac{3t}{5})=29t+580$

$(\frac{150t}{5})=29t+580$

$30t =29t+580$

$30t -29t = 580$

t =589

So originally there was 580 students

In this 580 students 40% liked to dance

Then the number of students liked to dance =

=> $40\% \text{of} 580$

=> $\frac{40}{100} \times 580$

=> $0.4 \times 580$

=> 232

We also know that with these people, 20 boys joined, all of whom like to dance.

Now the number of students like to dance = 232+20 = 252 students

7 0

2 years ago

yuko is volunteering at the food bank. He is creating thanksgiving food baskets to give to local families. He has 192 cornbread

Deffense [45]

Answer:

32 baskets
2 boxes of stuffing mix, 3 cans of vegetables, 6 cornbread muffins

Step-by-step explanation:

The greatest common factor (GCF) will be the greatest number of baskets yuko can create. We can examine the factoring of these numbers to see what it might be.

64 = 2^6

96 = 2^5 × 3

192 = 2^6 × 3

The unique factors are 2 and 3, and the lowest powers of each are 5 and 0, respectively. Then the GCF is ...

2^5 × 3^0 = 32 × 1 = 32

After the factor of 32 is removed from each of these numbers, we have ...

64 = 32·2 boxes of stuffing mix

96 = 32·3 cans of vegetables

192 = 32·6 cornbread muffins

These other factors are the numbers of the corresponding item that will be in each of the 32 baskets:

2 boxes of stuffing mix
3 cans of vegetables
6 cornbread muffins

6 0

3 years ago

Which of the following shows that polynomials are closed under subtraction when polynomial x + 5 is subtracted from 3x2 + 2x − 6

Art [367]

For this case we have the following polynomials:
$P = 3x ^ 2 + 2x - 6

Q = x + 5$
By subtracting both polynomials we have:
$P - Q = (3x ^ 2 + 2x - 6) - (x + 5)
$
What we must do is subtract terms of the same degree.
We have then:
$P - Q = 3x ^ 2 + (2x - x) + (-6 - 5)

P - Q = 3x ^ 2 + x - 11$
Answer:
$3x ^ 2 + x - 11$ will be a polynomial

3 0

3 years ago