What is the completely factored form of this polynomial?
7+14x³168x²

7x²(x+4)(x - 6)

7x³(x+4)(x - 6)

7x³(x-4) (x + 6)

7x²(x-4)(x + 6)

Answer:

5.

Step-by-step explanation:

f(x)=x^4+12x^3+30x^2−12x+70

The remainder theorem says that f(a)  is the value of f(x) when f(x) is divided by (x - a).

So when a = -5 f(a) will be 5.

Answer is 5.

Answer:

(2, - 1 )

Step-by-step explanation:

4x - 9y = 17 → (1)

6x - 5y = 17 → (2)

multiplying (1) by 6 and (2) by - 4 and adding will eliminate x

24x - 54y = 102 → (3)

- 24x + 20y = - 68 → (4)

add (3) and (4) term by term to eliminate x

0 - 34y = 34

- 34y = 34 ( divide both sides by - 34 )

y = - 1

substitute y = - 1 into either of the 2 equations and solve for x

substituting into (1)

4x - 9(- 1) = 17

4x + 9 = 17 ( subtract 9 from both sides )

4x = 8 ( divide both sides by 4 )

x = 2

solution is (2, - 1 )

There are 36 dogs in the shelter.

The ratio of dogs to cats in the shelter is given as 9:15.

The total number of dogs and cats is given as 96.

Let the constant of proportionality be x.

The total number of dogs is 9x and the total number of cats is 15x.

This means that:

9x + 15x = 96

24x = 96

x = 4.

The total number of dogs in the shelter = 9 × 4

= 36

Therefore, we have found that there are 36 dogs in the shelter.

Learn more about ratios here: https://brainly.com/question/2914376

#SPJ4

Answer:

406 candles in all.

Step-by-step explanation:

She needs 6 large arrangements with 25 candles in each arrangement.

Multiply 25 and 6 to find how much candles for all large arrangements combined.

25*6=150

She also needs 13 small arrangements with 12 candles in each arrangement.

Multiply 13 and 12 to find how much candles for all the small arrangements combined.

13*12=156

Add the answers together to find how many candles in all.

156+150=406.

She needs 406 candles in all.

Hope this helps!

Answer:

306

Step-by-step explanation:

First we find the number of candles needed for each size of arrangement.

Large Arrangements:

6 large arrangements with 25 candles each:

25 × 6 = 150

Small Arrangements:

13 small arrangements with 12 candles each:

13 × 12 = 156

Now we add the results above to find a grand total:

total = 150 + 156 = 306

Answer:

A. 4(4a + 18)

B. 8(2a + 9)

Step-by-step explanation:

We know that :

16a = 4×4×a

72 = 4×18

Then

16a + 72 = 4×(4a) + 4×(18)

              = 4 × (4a + 18)

On the other hand,

16a = 8×2×a

72 = 8×9

Then

16a + 72 = 8×(2a) + 8×(9)

              = 8 × (2a + 9)

The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.

The z-score for the hypothesis test is calculated by,

z-score = (X - μ)/(σ/√n)

Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.

It is given  that,

Sample size n = 30

Population mean μ = 9.7

Sample mean X = 10.1

Standard deviation σ = 1.8

So, the z-score is

= (10.1 - 9.7)/(1.8/√30)

= 0.4/0.328

= 1.219 ≅ 1.22

Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.

Learn more about hypothesis testing here:

https://brainly.com/question/4232174

#SPJ4

Answer:are u sure its not y=mx+b? And it doesn’t pass thru 1 im pretty sure

Step-by-step explanation:

Answer: Quadrant III

Explanation:

Let's pick example values for m and b

I'll go for m = -2 and b = 5. Anything works as long as m is negative and b is positive.

We go from y = mx+b to y = -2x+5

Plot this graph as shown below. The line passes through quadrants I, II, and IV. Only quadrant III is not touched at all.

The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.

When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."

Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.

The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.

The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.

Learn more about transformations here:

https://brainly.com/question/1548871

#SPJ1

Answer: [tex]x=8, y=2\sqrt 2[/tex]

Step-by-step explanation:

By the Pythagorean theorem, x=8.

So, by the geometric mean theorem,

[tex]y^2 = (6)(2)=8\\\\y=2\sqrt{2}[/tex]

Answer:

g and f are inverse functions because g(f(x)) = f(g(x)) = x

Step-by-step explanation:

Let's start by finding f(g(x)) and g(f(x)). As we discussed in another question, to find a composite function, apply the outer function to whatever the inner function evaluates to. We can start with f(g(x)):

[tex]f(g(x))=f(\frac{x+6}{7})=7(\frac{x+6}{7} )-6=x+6-6=x[/tex]

Now, let's find g(f(x)):

[tex]g(f(x))=g(7x-6)=\frac{(7x-6)+6}{7} =\frac{7x}{7}=x[/tex]

There is a property that says that if f(g(x)) = g(f(x)) = x, the two functions are inverse. This suggests that g and f are inverse functions. We can verify this by taking one function, switching y and x, and then solving for y. If we complete this process and find that we get the OTHER function, it means the two functions are inverse. Let's try that:

[tex]f(x)=y=7x-6[/tex]

Swap x and y:

[tex]x=7y-6[/tex]

Solve for y:

[tex]x+6=7y\\y=\frac{x+6}{7}[/tex]

Notice that we got g, which means f and g are inverse.

The slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.

According to the question,

Line 'a' is perpendicular to the line 'b'. If the slope of the line 'a' is 7.

The condition of slopes if two lines are perpendicular m₁ m₂ = -1

(7)(m₂) = -1

   m₂ = -1/7

Hence, the slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.  

Learn more about perpendicular lines here

https://brainly.com/question/2505127

#SPJ4

The amount for the deposit is $25350, monthly payment is $1436.5 and the total amount that Sipho pays is $178492.

Given price of car $169000, deposit of 15%, monthly installments being 1% of left over price and number of years be 9 years.

We have to find the amount of deposit, monthly installments and the total amount paid by Sipho.

We have been told that deposit is 15% of total amount. So the deposit will be 15%*169000=$25350.

Monthly installment is 1% of the left over amount.

left amount=169000-25350=$143650.

Monthly installment being =143650*1/100

=$1436.5

Total amount paid by Sipho=deposit +installment amount  * numberof installments

Number of installments=12*9

=108

Total amount=25350+1436.5*108

=25350+155142

=$178492

Hence deposit is $25350, monthly payment being $1436.5, total amount be $178492.

Learn more about installments  at https://brainly.com/question/2151013

#SPJ4

Answer:

[tex]100x^2-4\pi x^2[/tex]

Also can be said as:

[tex]4x^2(25-\pi )[/tex]

Step-by-step explanation:

The question is asking you, "how much is left over."

In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).

This means your equation to solve this question is:

[tex]x=B-P[/tex]

The value of B is the area of the backyard.

We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.

The formula is [tex]B=L*W[/tex], where L is the length and W is the width.

Both the length and width are 10x, so we must plug that into this equation.

We end up getting:

[tex]B=10x*10x[/tex]

Which can be simplified to:

[tex]B=100x^2[/tex]

The value of P is the area of the pool.

The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.

The formula is [tex]P=\pi r^2[/tex], where r is the radius.

Plugging in the radius of 2x, we get:

[tex]P=\pi (2x)^2[/tex]

By solving this out, we end up with:

[tex]P=4\pi x^2[/tex]

From the scenario, we have the equation:
[tex]x=B-P[/tex]

And from steps 1 and 2, we have the values:

[tex]B=100x^2[/tex] and [tex]P=4\pi x^2[/tex]

Now we just plug those values in to get:

[tex]x=100x^2-4\pi x^2[/tex]

And finally, the amount of the backyard remaining is:

[tex]100x^2-4\pi x^2[/tex]

This answer may be simplified to:

[tex]4x^2(25-\pi )[/tex]

There is no change in the temperature.

To find how much temperature is changed:

Let, 'F' be the temperature.

Temperature decreased by [tex]33\frac{1}{3}[/tex]%.

F × (1-.33333) = Temperature increases by 50%.

(F × (1-.33333)(1.50)) = F =  No net change, right back to the original temperature F.

Therefore, there is no change in the temperature.

Know more about temperature here:

https://brainly.com/question/24746268

#SPJ4

Area of the entire rectangle is x² + 11x + 30. This can be obtained by adding area of each square.

Method 1

Area of rectangle = length × width  

Area of entire rectangle = x² + 5x + 6x + 30 = x² + 11x + 30

Method 2

Area of entire rectangle = length × width

                                   = (x+6)×(x+5)    

                                  = x² + (6+5)x + (6×5)        [∵(x+a)(x+b) =x² + (a+b)x + ab]

                                    = x² + 11x + 30

Hence area of the entire rectangle is x² + 11x + 30.

Learn more about quadratic equations here:

brainly.com/question/17177510

#SPJ1

The weight of the puppy after the first month as described is; 26.65lbs.

Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;

Weight = 20.5lbs × 130% = 26.65lbs.

Read more on percentages;

https://brainly.com/question/16865197

#SPJ1

Answer:

x=6 because if you multiple 4x6 you get 24

not exactly sure but try

Answer:

it is not possible

Step-by-step explanation:

there are two different variables in one equation, so you cannot solve for one. You would need a system of equations to do that.

you can solve for x in terms of y, which is x = (24+4y)/5 but i dont think thats what the question is asking so the answer is probably just that its not possible

There are 9 positive integers with 1 digit (1 - 9).

There are 90 integers with 2 digits (10 - 99).

There are 900 integers with 3 digits (100 - 999).

There are 9000 integers with 4 digits (1000 - 9999).

And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.

Now,

1000 = 9 + 900 + 91

so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.

Answer:

  b.  n = 7

Step-by-step explanation:

You want to solve the proportion ...

  5/15 = n/21

This is most easily done by multiplying by the inverse of the coefficient of the variable:

  (21/1)(5/15) = (21/1)(n/21)

  7 = n . . . . . . . . . simplify

__

Additional comment

The math is a little easier if you simplify 5/15 to 1/3. Then, n = 21/3 = 7.

Answer:

[tex]a_n=(-2)^{n-1}[/tex]

Step-by-step explanation:

So a geometric sequence can be explicitly defined as: [tex]a_n = a_1(r)^{n-1}[/tex]. IN this case we're given r, but we don't know what a_1 is. We can find this by lugging in 4 as n, and -8 as a_n, since they're given values

Plug known values in:

[tex]-8 = a_1(-2)^{4-1}[/tex]

Subtract the values in the exponent

[tex]-8 = a_1(-2)^3[/tex]

Simplify the exponent

[tex]-8 = a_1 (-8)[/tex]

Divide both sides by -8

[tex]1=a_1[/tex]

So the nth term can be defined as: [tex]a_n = 1(-2)^{n-1}[/tex], and since the 1 is redundant, the equation can simply be defined as: [tex]a_n=(-2)^{n-1}[/tex]

Answer:

t=-6

Step-by-step explanation:

If a car manufacturer purchases new labour saving technology for its assembly line then we would not expect the production to be declined,wastage of time and money.

Given that a car manufacturer purchases a new labour saving technology.

We have to write the expectation that the car manufacturer would not make after buying such a technology.

We know that improvement of technology means abolition old technology and adoption of new and improved technology.

The advantages of new technology is:

1) It provides a competitive advantage over the competitor,

2) It increases the production,

3) It saves cost of the company,

4) It saves time also.

If a car manufacturer purchases new labour saving technology for its assembly line then he would not expect the production to be declined, wastage of time and money.

Learn more about technology at https://brainly.com/question/25110079

#SPJ4

Answer:

Step by Step Solution

More Icon

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

c-((4+w)/(w+3))=0

STEP

1

:

4 + w

Simplify —————

w + 3

Equation at the end of step

1

:

(w + 4)

c - ——————— = 0

w + 3

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Subtracting a fraction from a whole

Rewrite the whole as a fraction using (w+3) as the denominator :

c c • (w + 3)

c = — = ———————————

1 (w + 3)

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

c • (w+3) - ((w+4)) cw + 3c - w - 4

——————————————————— = ———————————————

1 • (w+3) 1 • (w + 3)

Equation at the end of step

2

:

cw + 3c - w - 4

——————————————— = 0

w + 3

STEP

3

:

When a fraction equals zero :

3.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

cw+3c-w-4

————————— • w+3 = 0 • w+3

(w+3)

Now, on the left hand side, the w+3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

cw+3c-w-4 = 0

Solving a Single Variable Equation:

3.2 Solve cw+3cw-4 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

We shall not handle this type of equations at this time.

Answer:

w = (4 - 3C)/(C - 1).

Step-by-step explanation:

C=(4+w)/(w+3)

Multiply both sides of the formula by  w+3:-

C(w + 3) = 4 + w

Cw + 3C = 4 + w

Cw - w = 4 - 3C

w(C - 1) = 4 - 3C

w = (4 - 3C)/(C - 1).

Using a proportional relationship, the scaled distances, in sheets of toilet paper, are given as follows:

The real distances are missing, and they are given in the table at the end of the answer.

A proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, in the case of a direct relationship, as follows:

y = kx

In the case of an inverse relationship, we have that:

y = k/x.

k is the constant of proportionality for both cases.

For this problem, the constant for the Scaled Distances as a function of the Real Distances is given as follows:

k = 5/149.6 = 7.6/227.9 = 0.03334795963.

Hence, the relationship for the Scaled Distances is given by:

S = 0.03334795963R

In which R is the real distance.

Then the scaled distances for the planets are given as follows:

More can be learned about proportional relationships at https://brainly.com/question/10424180

#SPJ1

Answer:

edmentum/plato hope this can help someone :)

Step-by-step explanation:

Answer:

y=

[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]

Step-by-step explanation:

calculate the product, use (a+b)^2=a^2+2ab+b^2

Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.

Reason Behind a Biased Estimator

The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a  biased estimator.

Brief Description of Sample Mean Absolute Deviation

The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.

Learn more about biased estimator here:

https://brainly.com/question/26415101

#SPJ4

ItItItIt takes Laura  15 minutes (0.25 hours) to cycle to the post office.

a. It takes Laura  15 minutes (0.25 hours) to cycle to the post office.

b. Speed:

Speed=Distance/Time

Speed=4/0.25

Speed=16 km/hr

c.  It takes Laura  20 minutes to cycle to the post office.

d. Time

Time=20 minutes (1/3 hour)

Speed:

Speed=Distance/Time

Speed=4÷1/3

Speed=12 km/hr

Therefore It takes Laura  15 minutes (0.25 hours) to cycle to the post office.

Learn more about speed here:https://brainly.com/question/13943409

#SPJ1

Answer:

Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)

considering theres no like first hour pay or something then it would be

Equation: m = 8h

Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.

Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost

Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.

Equation:  c = 2h

Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)

Equation: t = 2m