Divide using synthetic division. (x^3-4x+6)/(x+3)​

Answer: linear pair

Step-by-step explanation:

Because ce is shown to be bisected by line n, then the two expressions are added and will equal 180°. This is what is called a linear pair.

Answer:

Step-by-step explanation:

The explicit formula for a GP is expressed as

Tn = ar^{n-1}

a is the first term

n is the number of terms

r is the common ratio

a) If a3 = 36 and r = 6

a3 = ar^3-1

a3 = ar^2 = 36

ar^2 = 36

a(6)^2 = 36

36a = 36

a = 1

Get the nth term

Tn = 1(6)^{n-1}

Tn = 6^{n-1}

b)  If a6 = 64 and r = 2

a6 = ar^6-1

a6 = ar^5 = 64

ar^5 = 64

a(2)^2 = 64

4a = 64

a = 16

Get the nth term

Tn = 16(2)^{n-1}

Tn = 16*(2^n/2)

Tn = 8(2^n)

Answer:

10.65 inches

Step-by-step explanation:

You simply add Saturday's and Sunday's total together

6.14+4.71=10.85

Answer:

y=x+4

Step-by-step explanation:

2y - 2x = 8

2y=2x+8

y=x+4

Answer:

3

Step-by-step explanation:

Answer:

No its about how many you get PER DAY

Step-by-step explanation:

Answer:

Step-by-step explanation:

-5400/-450

12 minutes

Answer:

12 minutes

Step-by-step explanation:

If the rate of the plane is -450 meters per minute, then you have to use the "division" operation in order to know how much time it takes for the plane to reach an altitude of -5,400 meters.

-5,400 meters ÷ -450 meters/minute = 12 minutes

It will take 12 minutes for the plane to reach an altitude of -5,400 meters.

Let's check:

-450 meters x 12 minutes = -5,400 meters

Answer:

6 I think.

Step-by-step explanation:

6 I think. think

Answer:

Step-by-step explanation:

The  statement "The expression contains 2 terms." is false because the expression contains 3 terms:  7f, 15 and -2g

The given statement "expression contains 2 terms" is false, Because it contains three terms of which two are the variable and one is a constant.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that,

The expression is,

7f + 15 - 2g

The given expression contains 2 terms.

A term is a single expression, a single integer (positive or negative), and a  single variable (a letter), or a number of variables that have been multiplied but never added or canceled are all acceptable.

The given statement is false because it reported only two terms but there are more than two terms.

Thus, the given statement "expression contains 2 terms" is false Because it contains three terms of which two are the variable and one is a constant.

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In other words, everything but choice B

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Explanation:

You could use polynomial long division or synthetic division to check each answer. The shorter route of the two options is synthetic division

There's a much faster way that doesn't involve complicated division. Recall that if (x-k) is a factor of p(x), then p(k) = 0. This is a special case of the remainder theorem.

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Here's a fairly short proof:

Consider a polynomial q(x) such that

p(x) = (x-k)q(x)

which shows that (x-k) is a factor of p(x). We don't need to worry about what q(x) actually is since it will go away effectively.

If we plug x = k into the p(x) function, we get

p(x) = (x-k)q(x)

p(k) = (k-k)q(k)

p(k) = 0*q(k)

p(k) = 0

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How is this useful? Well we can note that the factor (x-3) is in the form (x-k) where k = 3.

So the idea is to plug x = 3 into each of the four functions and see which result in 0. If we get 0 as an output, then we have a factor. Otherwise, it's not a factor.

-------------------------------------------------

Plug x = 3 into the first function

A(x) = x^3 - 2x^2 - 4x + 3

A(3) = 3^3 - 2(3)^2 - 4(3) + 3

A(3) = 0

This shows (x-3) is a factor of the function A(x)

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Repeat for the second function

B(x) = x^3 + 3x^2 - 2x - 6

B(3) = 3^3 + 3(3)^2 - 2(3) - 6

B(3) = 42

We don't get an output of 0, so (x-3) cannot be a factor of B(x)

-----------------------------------------------

Now onto the third function

C(x) = x^4 - 2x^3 - 27

C(3) = 3^4 - 2(3)^3 - 27

C(3) = 0

So (x-3) is a factor of C(x)

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Finally the last function

D(x) = x^4 - 20x - 21

D(3) = 3^4 - 20(3) - 21

D(3) = 0

Therefore (x-3) is a factor of D(x) as well.

The remainder theorem will be used to identify the polynomial that has a remainder of zero when divided by (x - 3)

The polynomials that have 0 as a factor are;

Reason:

According to the remainder theorem, we have;

The remainder following the division of a polynomial, by (x - a) is P(a)

Therefore, (x - 3) is a factor of the polynomial P(x) where P(3) = 0

For option (A), we have; A(x) = x³ - 2·x² - 4·x + 3

The remainder when (x³ - 2·x² - 4·x + 3) is divided by (x - 3) is therefore;

A(3) = 3³ - 2 × 2² - 4 × 2 + 3 = 14

Therefore, (x - 3) is not a factor of A(x) = x³ - 2·x² - 4·x + 3

For option (B), we have;

B(x) = x³ + 3·x² - 2·x - 6

The remainder when B(x) is divided by (x - 3) is therefore;

B(3) = 3³ + 3×3² - 2×3 - 6 42

Therefore, (x - 3) is not a factor of B(x) = x³ + 3·x² - 2·x - 6

For option (C), we have;

C(x) = x⁴ - 2·x³ - 27

The remainder when C(x) is divided by (x - 3) is therefore;

C(3) = 3⁴ - 2×3³ - 27 = 0

Therefore;

For option (D), we have;

D(x) = x⁴ - 20·x - 21

The remainder when D(x) is divided by (x - 3) is given as follows;

D(3) = 3⁴ - 20×3 - 21 = 0

Therefore;

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Answer:

c

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

You add 21 twice because 3 is half of 6

Answer:

A - 42

Step-by-step explanation:

21 x 2 = 42

3 x 2 = 6

Answer: $6828

Step-by-step explanation:

James annual income = $85350

Income tax = 8%

The amount of income tax in dollars and cents that James has to pay will be calculated by multiplying the income tax by his annual income. This will be:

= 8% × $85350

= 8/100 × $85350

= 0.08 × $85350

= $6828

Answer:

1/3 or 0.3

Step-by-step explanation:

5/8 x 4/5 x 2/3 =

1/3 or 0.3

Answer:

1/3 in^3

Step-by-step explanation:

In order to find the volume, you must multiply the length, by the width, by the height. This would mean you need to do 2/3x5/8x4/5=40/120

40/120 simplified will give you 1/3

Answer:

it's a

Step-by-step explanation:

its a on edge

Answer: A

Step-by-step explanation:

Answer:

49

Step-by-step

step 1 subtract 10 -3

step 2 multiply 7 x 7

that's your answer

Answer:

49

Step-by-step explanation:

Step 1:

a = 3; b = 2; c = 10         Given

Step 2:

[tex](c-a)^{b}[/tex]         Equation

Step 3:

[tex]( 10 - 3)^{2}[/tex]        Input values

Step 4:

( 7 ) ²           Parentheses

Answer:

49

Hope This Helps :)

Answer:

[tex]y = 75 + 10x[/tex]

Step-by-step explanation:

Given

New Video Games

[tex]Cost = \$25[/tex]

[tex]Number = 3[/tex]

Used Video Games

[tex]Cost = \$10[/tex]

[tex]Number = x[/tex]

Required

Determine the amount spent (y)

First, we need to determine the total spent on new games

1 new game = $25

3 new games will be: 3 * $25

Next, we determine the total spent on old games

1 used game = $10

x used games will be: x * $10

So, total amount y, is:

[tex]y = 3 * 25 + x * 10[/tex]

[tex]y = 75 + 10x[/tex]

Given:

A student says that the graph of the equation [tex]y = 3(x + 8)[/tex] is the same as the graph of [tex]y = 3x[/tex], only translated upwards by 8 units.

To find:

Whether the student is correct or not.

Solution:

Initial equation is

[tex]y=3x[/tex]

[tex]f(x)=3x[/tex]

Equation of after transformation is

[tex]y=3(x+8)[/tex]

[tex]g(x)=3(x+8)[/tex]

Now,

[tex]g(x)=f(x+8)[/tex]      ...(i)

The translation is defined as

[tex]g(x)=f(x+a)+b[/tex]        ...(ii)

Where, a is horizontal shift and b is vertical shift.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

From (i) and (ii), we get

[tex]a=8\text{ and }b=0[/tex]

Therefore, the graph of [tex]y=3x[/tex] translated left by 8 units. Hence, the student is wrong.

Answer:

The total budget is $1260

Step-by-step explanation:

Given

[tex]Props = \$693[/tex]

[tex]Costumes = 45\%[/tex]

Required

Determine the total budget

Since all budgets was spent on Props and Costumes only.

We have that.

[tex]\%Props + \%Costumes = 100\%[/tex]

[tex]\%Props + 45\%= 100\%[/tex]

[tex]\%Props= 100\% -45\%[/tex]

[tex]\%Props= 55\%[/tex]

In other words, 55% was spent on Props

Let the total budget be x, we have:

[tex]55\% * x = \$693[/tex]

Make x the subject

[tex]x = \$693/55\%[/tex]

[tex]x = \$1260[/tex]

Hence, the total budget is $1260

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[tex]b. {b}^{m} = {b}^{1 + m} [/tex]

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Answer:

270

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

21/3=42/x

x=42*3/21

x=6

Answer:

You would need 13.5 2/3 cups.

Step-by-step explanation:

[tex]\frac{2}{3}[/tex]×[tex]\frac{13.5}{1}[/tex]=[tex]\frac{27}{3}[/tex]

27÷3=9

Answer:

I suppose that each number is repeated 3 times, the actual question is:

Courtney walked from her house to the beach at a constant speed of 4 kilometers per hour, and then walked from the beach to the park at a constant speed of 5 kilometers per hour. The entire walk took 2 hours and the total distance Courtney walked was 8 kilometers.

Now, remember the relation:

Distance = Speed*Time

Let's define:

D1 = distance between Courtney's house and the beach.

D2 = distance between the beach and the park.

T1 = time that it took the first walk.

T2 = time that it took the second walk.

We know that the total distance Courtney walked is 8km, then:

D1 + D2 = 8km.

And we also know that the entire walk took 2 hours, then:

T1 + T2 = 2h.

We also have the equations:

D1 = 4km/h*T1

D2 = 5km/h*T2.

Then we have a system of equations:

D1 + D2 = 8km

T1 + T2 = 2h

D1 = 4km/h*T1

D2 = 5km/h*T2.

To solve this, first let's replace equations 3 and 4 in the first equation:

4km/h*T1 + 5km/h*T2 = 8km

Now we have only two equations left:

4km/h*T1 + 5km/h*T2 = 8km

T1 + T2 = 2h

Now we can isolate one of the variables in the second equation and then replace it in the first equation, i will isolate T1:

T1 = 2h - T2.

Replacing this in the first equation gives:

4km/h*(2h - T2) + 5km/h*T2 = 8km

Now let's solve this for T2.

8km - 4km/h*T2 + 5km/h*T2 =  8km

8km + 1km/h*T2 = 8km

1km/h*T2 = 0

from this, we have T2 = 0

This would mean that T1 = 2h.

Then:

D1 = 4km/h*2h = 8km.

T2 = 0

D2 = 5km/h*0 = 0.

This happens because the numbers in the problem were not well thought.

You can see that when she spends the 2 hours walking at the smaller speed, she already reaches the total distance, then if she walked any amount of time at the larger speed, the total distance would be more than 8km.

Answer:

14

Step-by-step explanation:

14

Answer: 105 degrees

Step-by-step explanation:

Both angles equal 180 so if we subtract 75 from 180 we get 105.

Answer:

105º

Step-by-step explanation:

<ONC and <BNJ are a linear pair, the angles are supplementary (eqauls 180º).