Recall that we identified x, x − 1, and x + 2 as three factors of p(x) = x4 − 4x3 − 7x2 + 10x by using the remainder theorem to inspect a set of expressions. We were unable to identify the fourth factor. Now that you’re familiar with synthetic division, write the process you would use to find the fourth factor of p(x).

Answer:   5s -3 = s -3 + 24    5s -3 = s + 21

Step-by-step explanation:

Father   f

Son   s .   present:  f = 5s  use this equation to substitute the equal value

3 years ago .  f-3 = s-3 + 24  

Substitute 5s for f in the second equation

5s -3 = s-3 + 24

works out as  5s -s = - 3  +3 + 24

4s = 24  

4s/4 = 24/4  

s = 6

The son's age is 6, The father is 30

Answer:

(- 1, 3 )

Step-by-step explanation:

Given the 2 equations

2x + y = 1 → (1)

3x - y = - 6 → (2)

Adding the 2 equations term by term eliminates the y- term, that is

5x = - 5 ( divide both sides by 5 )

x = - 1

Substitute x = - 1 into either of the 2 equations and evaluate for y

Substituting into (1)

2(- 1) + y = 1

- 2 + y = 1 ( add 2 to both sides )

y = 3

Solution is (- 1, 3 )

Answer: (-1,-3) or A on the quiz

Got it right

Have a nice day

Answer:

A 5-pound of flour costs $4.80. For this bag of flour, what is the cost of flour per ounce? (1 pound = 16 ounces) a. $0.06.

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

In each pound there are 16 ounces. We can divide $9.60 by 5 to get the cost of one pound of flour, and then divide the result of that by 16 to get the price of flour by the ounce.

$9.60 can be converted to 960 cents to make it easier to divide.

960 ÷ 5 = 192

192 ÷ 16 = 12

Answer:

The table in the top right

Step-by-step explanation:

That table represents the equation y=-2x-1. It is the only table that represents a linear equation.

To be a linear equation it has to consistently add the same amount up and right OR down and right (depending on if it's a positive or negative equation)

I have included a picture of the graph with the equation and all points on it (click/tap on it to see the full picture.)

If this helped please rate, thanks, and mark brainliest :)

The table which represents a linear function is one on the top-right corner.

A linear function is a mathematical relation which is characterized by a constant slope otherwise known as the rate of change of the function.

Upon evaluation of the slope of each table; only the top-right corner table has a constant slope.

Ultimately, a linear function is characterized by a constant slope as observed in the top-right corner table in discuss.

Read more on linear function;

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Answer: CAN YOU PLS MARK AS BRAINLIEST??

a.x=11/4

b.x=6

c.x=21/2

d.x=0

Step-by-step explanation:

-2+3x+x=9-x

-2+3x+x=9

4x=9+2

4x=11

x=11/4

when you move a numerator to the other side it becomes a denominator

x+2=3/4x6

x+2=3/24

x=8-2

x=6

5-2x-12=14

2x=14-5+12

2x=21

x=21/2

1/2x=-3-1/2x+4-1

1/2x+1/2x=-3+4-1

x=0

Answer:

x = -1/2, 3/4

Step-by-step explanation:

Step 1: Isolate everything to 1 side

8x² - 2x - 3 = 0

Step 2: Factor

(4x - 3)(2x + 1) = 0

Step 3: Find roots

4x - 3 = 0

4x = 3

x = 3/4

2x + 1 = 0

2x = -1

x = -1/2

Answer: [tex](x+2)(x+8)[/tex]

Step-by-step explanation:

1) First, we need to see which number multiplies to 16 and adds up to 10.

By looking at the factors of 16, we can see that only 2 and 8 will work.

2) Now, we need to arrange them in the factorized equation, which is always

(x+r)(x+q).

3) This will give us our final equation:

[tex](x+2)(x+8)[/tex]

If you want the roots, just do the negation of r and q and you will get it!

Answer:

[tex]l = 88 cm[/tex]

Step-by-step explanation:

Volume of Cube = [tex]l*l*l[/tex]

Volume of Cube = [tex](Length)^3[/tex]

Where volume = 681472 cubic cm

=> [tex]l^3 = 681472[/tex]

Taking square root on both sides

=> [tex]l = \sqrt{681472}[/tex]

=> [tex]l = 88 cm[/tex]

Answer: 16.991°

Step-by-step explanation:

Used a triangle calculator hope this helped!

Answer:

479,001,600 ways

Step-by-step explanation:

When looking at this problem, there are 13 beads that can be put on first, 12 that can be put on second as the first one was already used, 11 put on third, and so on. This means the amount of necklaces you can make are 13*12*11...*2*1, or 13 factorial (13!). But since you can rotate the necklace this means that there are each combination has 12 others just like it, just rotated(13 in total). This means we must divide 13! by 13, which makes it 12!. 12! is equal to 479,001,600, which is the answer.

Answer:

6,227,020,800 different necklaces.

Step-by-step explanation:

To start making the necklace, you will have to choose one of the 13 beads. For the next bead, you will have 13 - 1 = 12 beads to choose from. For the next bead, you will have 12 - 1 = 11 beads to choose from, and so on and so forth, until all 13 beads are used.

So, you will have 13! different necklaces, since you would have 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 156 * 110 * 72 * 42 * 120 = 17160 * 362880 = 6227020800.

So, you will have 6,227,020,800 different necklaces.

Hope this helps!

A fraction is a way to describe a part of a whole. The fraction that is closest to 5/8 is 13/20.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Know the fraction that will be close to 5/8 can be found by taking the LCM of denominators. Therefore, the LCM of 8, 3, 20, and 16 is 240.

Thus, the fractions can be rewritten as,

5/8 = (5/8) × (30/30) = 150/240

2/3 = (2/3) × (80/80) = 160/240

13/20 = (13/20) × (12/12) = 156/240

11/16​ = (11/16) × (15/15) = 165/240

Now as it can be seen that 156/240 is closest to 150/240, therefore, the fraction that is closest to 5/8 is 13/20.

Learn more about Fraction:

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Answer:

Hope it helps

sorry fir bad camera view.....

1) -x + 4 = -2x - 6

Add(2x)

x+4=-6

Subtract(4)

x = -10

Check your work

-(-10)+4=-2(-10) - 6

10+4=-2(-10) - 6

14=-2(-10)

14=20 - 6

14=14

Correct :)

2) 4R - 4 = 3R + 10

Add 4

4R=3R+14

Subtract 3R

R = 14

Check your work

4(14)-4=3(14)+10

56-4=3(14)+10

52=3(14)+10

52=42+10

52=52

Correct :)

3) 2Y - 3 = Y - 4

Add 3

2Y = Y - 1

Subtract Y

Y = -1

Check your work

2(-1)-3=-1-4

-2-3=-1-4

-5=-5

Correct :)

Hope it helps <3

Answer:

C

Step-by-step explanation:

Just did the Unit Review

Answer:

P(X/Y) = 0.4545

Step-by-step explanation:

Let's call X that the transferred ball is black, X' that the transferend ball is white and Y the event that the second ball drawn is black.

The probability that the transferred ball was black given that the second ball drawn was black is equal to:

P(X/Y) = P(X∩Y)/P(Y)

Where P(Y) = P(X∩Y) + P(X'∩Y)

Then, the probability P(X∩Y) that the transferred ball is black and the second ball drawn is black is equal to:

P(X∩Y) = (5/12)*(7/11) = 0.2651

Because the urn A has 12 balls and 5 of them are black, then if the transferred ball is black, the urn B will contain 11 balls and 7 of them will be black balls.

At the same way, the probability P(X'∩Y) that the transferred ball is white and the second ball drawn is black is equal to:

P(X'∩Y) = (7/12)*(6/11) = 0.3181

Because the urn A has 12 balls and 7 of them are white, then if the transferred ball is white, the urn B will contain 11 balls and 6 of them will be black balls.

So, P(Y)  and P(X/Y) are equal to:

P(Y) = 0.2651 + 0.3181

P(Y) = 0.5832

P(X/Y) = 0.2651/0.5832

P(X/Y) = 0.4545

Answer:

Step-by-step explanation:

The function is f(x) = -4x²+10x-8

Let Δ be our the dicriminant

The value of the discriminant is -28 and since it is negative this function has no real zeroes

Answer:

-28 for the first box and 0 for the second box.

Step-by-step explanation:

Answer: £ 8

Step-by-step explanation:

Total hours Lena works from Monday to Friday = 34 hours

Hours she works on Saturdays = 4

Overtime rate of Saturday = 1.5 times her normal rate

Let x be the normal rate.

Then , Her total earning = [tex]34 x + 4 \times(1.5x) =34x+6x=40x[/tex]

Since her total earnings for week = £ 320

So,

[tex]320=40x\\\\\Rightarrow\ x=\dfrac{320}{40}\\\\\Rightarrow\ x=8[/tex]

Thus, her normal rate of pay per hour = £ 8

The answer is actually 9 ;)

Answer:

y = 9

Step-by-step explanation:

-2(20) + 4y = -4

-40 + 4y = -4

4y = -4 + 40

4y = -4 + 40

4y = 36

4/4 = y

36/4 = 9

y = 9

Hope this helped! :)

c. because when you di the math it adds up

Answer:

D.

Step-by-step explanation:

x ={-1, 0, 2, 4, 7}

We see every x value only one time, so given pairs (x,y) is a function.

Answer is D.

Answer:

Step-by-step explanation:

Recall that when we are factoring a polynomial, we are implicitly finding its roots. By finding a root, we are looking for a value of x (say c) such that p(c) =0. When this happens, our polynomial has the the polynomial (x-c) as a factor.

We are given the values of p at some values of x. We notice that p(5) = 0 and p(-12) =0. So, this means that our polynomial has as a factor the polynomials (x-5) and (x+12).

Answer:

Factor: x-5 & x+12

Not a Factor: x-1, x+4, x-7, x+10

Step-by-step explanation:

The remainder theorem states that for a polynomial p(x) and a number a, the remainder on division of p(x) by x − a is p(a). So, p(a) = 0 if and only if x − a is a factor of p(x).

Since, p(5) = 0 and p(-12) = 0, the expressions (x − 5) and (x + 12) are factors of the polynomial p(x).

Answer:

D

Step-by-step explanation:

convert miles to feet :

1 mile     5280 foot

2820*5280=14889600 ft

14889600/2=7444800 close to 7500000

D

Step-by-step explanation:

Type A cost 4.05 dollars per pound

Type B cost 5.55 dollars per pound

now...since type A is four times larger than Type B for that month,.the ratio will be 4:1 respectively

total cost was 735 dollars out of which Type A has

4/5 × 735 = 588 dollars while Type B has 1/5 × 735 = 147 dollars

so therefore ....number of pounds of A = 588/4.05=145.18pounds

and number of Pounds of B = 147/5.55= 26.48pounds

Answer:

D. 36 miles

hope this helps :)

Answer:

$296,954.42

Step-by-step explanation:

If any amount P is invested at rate of r% per year for n years then value of money p after n years is given by

FV = p(1 + r/100)^n

where FV is the future value of money after n years.

given

p= $19300

r = 9%

n = 5 years

Thus, FV = 193000(1 + 9/100)^5

FV =  193000((100 + 9)/100)^5

FV =  193000(109/100)^5

FV =  $296,954.42

Thus, value after 5 years for the investment is $296,954.42 to the nearest cent

Answer:

  7200 cm^2

Step-by-step explanation:

The kitchen dimension on the drawing of 14 cm corresponds to an actual kitchen dimension of 40·14 = 560 cm.

The kitchen dimension on the drawing of 22 cm corresponds to an actual kitchen dimension of 40·22 = 880 cm.

The actual kitchen area is ...

  Area = length · width = (880 cm)(560 cm) = 492,800 cm^2.

__

The difference between this area and the bedroom area is ...

  500,000 cm^2 -492,800 cm^2 = 7200 cm^2

The kitchen is 7200 cm^2 smaller than the bedroom.

Answer:

6n^4-10n^2+10n

Step-by-step explanation:

4 n^4+2n^4-3n^2-7n^2+9n+n

6n^4-10n^2+10n

Answer:

[tex]\boxed{6n^4- 10n^2 + 10n}[/tex]

Step-by-step explanation:

[tex](4n^4 - 3n^2 + n)+ (2n^4 -7n^2 + 9n)[/tex]

[tex]\sf Remove \ brackets.[/tex]

[tex]4n^4 - 3n^2 + n+2n^4 -7n^2 + 9n[/tex]

[tex]\sf Group \ like \ terms.[/tex]

[tex]4n^4 + 2n^4- 3n^2 -7n^2 + 9n+n[/tex]

[tex]\sf Combine \ like \ terms.[/tex]

[tex]6n^4- 10n^2 + 10n[/tex]

Answer:

A) 6/7

Step-by-step explanation:

Remember that two negatives will cancel to make a positive. Also, 6 ÷ 7 is 6/7

Answer:

52

Step-by-step explanation:

Number of Students in Key Stage 3 =380

Number of Students in Key Stage 4 =240

Number of Students in Key Stage 5 =110

Total = 380+240+110=730

Since a sample of 100 students stratified by key stage is needed.

The number of students that would be taken from Key Stage 3

[tex]=\dfrac{380}{730}\times 100\\\\=52.1\\\approx 52 $ (to the nearest whole number)[/tex]

Answer:

-2

Step-by-step explanation:

We can find the slope by using the slope formula

m = (y2-y1)/(x2-x1)

    = (-5 - -7)/ ( -2 - -1)

    = ( -5+7) / ( -2 +1)

    = 2/-1

   = -2

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▹ Answer

Slope = [tex]\frac{2}{-1}[/tex] → -2

▹ Step-by-Step Explanation

(-1, -7) (-2, -5)

[tex]\frac{y2 - y1}{x2 - x1}[/tex]

-5 - (-7) = -5 + 7 → 2

-2 - (-1) = -2 + 1 → -1

Slope = [tex]\frac{rise}{run}[/tex] → [tex]\frac{2}{-1}[/tex] → -2

Hope this helps!

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