Without solving, describe a way to determine if 2, -1,3 and -2 are the roots (ie. factors) of the polynomial equation x^4 - 2x^3 - 7x^2 -8x +12. State the theorem you used.

Answer:

$52.50.

Step-by-step explanation:

Since Val's air conditioner uses 3,500 watts when running, and that Val uses it for 5 hours during summer days, spending 10 cents per kilowatt hour, determining how much money Val will spend during a 30-day summer must be done the following calculation:

3,500 watts = 3.5 kilowatts

3.5 kilowatts per hour = 35 cents

35 cents x 5 hours = 175 cents per day

175 cents per day x 30 days = 5250 cents per month

5250/100 = X

52.5 = X

Thus, during 30 days of summer, Val will spend $ 52.50 on electricity from the use of his air conditionier.

Answer:

  f(x) = x² -2x -35

Step-by-step explanation:

You want a quadratic function that has zeros 7 and -5.

Each zero (p) gives rise to a factor (x-p). The zeros 7 and -5 mean the quadratic has factors (x-7) and (x-(-5)).

  f(x) = (x -7)(x +5)

  f(x) = x² -2x -35

__

Additional comment

You may notice that the coefficient of the linear term is the opposite of the sum of the zeros. The constant term is the product of the zeros. Knowing this, we can write the quadratic without any concern for the factors.

  sum: 7-5 = 2

  product: (7)(-5) = -35

  quadratic: f(x) = x² -2x -35

If the average of 12, 7, 9, a, and b is 12, then

what is the average of a + b?

we know that

the average is equal to

(12+7+9+a+b)/5=12

simplify

(28+a+b)/5=12

Multiply both sides by 5

28+a+b=60

isolate (a+b)

a+b=60-28

Answer:

The answer is 0.

Step-by-step explanation:

Answer:

5, -11. -3, 8. 10, 17. -15, 13.

Step-by-step explanation:

All you have to do is switch x and y

Answer:

Cost of each item bought by Spongebob \(=x=\$3.75\)

Cost of items bought by Spongebob = \(3x=3(3.75)=\$11.25\)

Cost of each item bought by Patrick \(=x-1.50=3.75-1.50=\$2.25\)

Cost of items bought by Patrick = \(5(x-1.50)=5(3.75-1.50)=\$11.25\)

Step-by-step explanation:

Let \(x\) denotes cost of each item bought by Spongebob.

Number of items bought by Spongebob = 3

So,

Cost of items bought by Spongebob = \(3x\)

Cost of each item bought by Patrick = \(x-1.50\)

Number of items bought by Patrick = 5

Cost of items bought by Patrick = \(5(x-1.50)\)

Both Spongebob and Patrick paid the same amount of money.

So,

\(3x=5(x-1.50)\\3x=5x-7.5\\5x-3x=7.5\\2x=7.5\\x=\frac{7.5}{2} \\x=3.75\)

So,

Cost of each item bought by Spongebob \(=x=\$3.75\)

Cost of items bought by Spongebob = \(3x=3(3.75)=\$11.25\)

Cost of each item bought by Patrick \(=x-1.50=3.75-1.50=\$2.25\)

Cost of items bought by Patrick = \(5(x-1.50)=5(3.75-1.50)=\$11.25\)

The coordinates "(-7, 3), (-1, 3), (-1,-5), and (-7,-5)" of the vertices of the image of Building D is not a translation.

In Mathematics, a transformation can be defined as the movement of a point from its original (initial) position to a final (new) location. This ultimately implies that, when an object is transformed, all of its points would be transformed as well.

Generally, there are different types of transformation and these include the following:

A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

By critically observing the graph for the transformation of this buildings, we can logically deduce that the coordinates "(-7, 3), (-1, 3), (-1,-5), and (-7,-5)" of the vertices of the image of Building D is not a translation.

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Susannah's data are illustration of measure of central tendencies

(a) The mean

To calculate the mean, she needs to divide the total number of turkey sandwiches sold, by the number of days.

The total is:

\(\mathbf{Total = 73 +88+85+88+99+134+129}\)

\(\mathbf{Total = 696}\)

The number of days is:

\(\mathbf{Day = 7}\)

So, the mean is:

\(\mathbf{Mean =\frac{Total}{Days}}\)

\(\mathbf{Mean =\frac{696}{7}}\)

\(\mathbf{Mean =99.4}\)

Hence, the mean number of turkey sandwiches sold is 99.4

(b) The median

To calculate the median, she needs to arrange the data in ascending or descending order, then select the middle item.

In ascending order, we have: 73, 85, 88, 88, 99, 129, 134

The middle item is 88

So:

\(\mathbf{Median = 88}\)

Hence, the median number of turkey sandwiches sold is 88

(c) The mode

This is the data that occurs most.

From the dataset, 88 appears twice (more than others).

So:

\(\mathbf{Mode = 88}\)

Hence, the mode number of turkey sandwiches sold is 88

(d) The range

This is the difference between the highest and least data

From the dataset,

The highest is 134, and the least is 73

So:

\(\mathbf{Range =134 - 73}\)

\(\mathbf{Range =61}\)

Hence, the range of turkey sandwiches sold is 61

The measure that would be most helpful is the median, because it is not affected by outliers.

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Answer:

total cost =$ 16 +$ 4.56=$ 20.56

change received = $25 - $ 20.56 = $4.44 .

Step-by-step explanation:

therefore your answer is 4,44 hope this helps

Answer: Show the table

Step-by-step explanation:

SHow the table

Step-by-step explanation:

3x-2x=5+10 [taking variables on one side and constant on other]

x=15

soln:

3x-5= 2x+10

3x -5+5=2x+10+5 [ adding 5 on both side]

3x=2x+15

3x-2x=2x+15-2x [subtracting 2x on both side]

x=15

Ans=15

Answer:

\(x = 15\)

Step-by-step explanation:

\(3x - 5 = 10 + 2x\)

\(3x - 2x = 10 + 5\)

\(1x = 15\)

\(x = 15\)

Answer:

D. 286.5 in.^2

Step-by-step explanation:

3 X 7.5+ 3 X 11.5 + 3 X 7.5+ 11.5 X 3 + 7.5 X 11.5 + 7.5 X 11.5=

22.5 + 34.5 + 22.5 + 34.5 + 86.25 + 86.25=

total surface area= 286.5 in.^2

Answer: formula

AB= (-1- -3)+((3-1)

(-1+3 )^2+(3-1)^2

2^2+2^2

Sq rt of 8 is 2.83

length of AB is 2

BC= (-3- -1)^2 + (5-3)^2

-3+1 =-2^2+2^2=4+4=8

Sq rt of 8 is 2.828= 2.83

Step-by-step explanation:

Considering the depreciation rate of 11%, the value of car is $11800 in 4.1 years.

Depreciation is the reduction in the value of an asset over time due to wear and tear, age, or obsolescence.

The most basic and widely used method of calculating depreciation is Annual depreciation = (Cost of asset - Salvage value) / Useful life

To find the time it will take for the value of the car to depreciate to $11,800, we can set up the following equation:

24900 - 11800 = 11000

24900 * .11 = 2679

11000 / 2679 = 4.09 years

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See attachment for the graph of  4 > |x + 1| + 2

The absolute value inequality is given as:

4 > |x + 1| + 2

Subtract 2 from both sides of the absolute value inequality.

So, we have

2 > |x + 1|

Rewrite as

|x + 1| < 2

So, we plot the graph of  |x + 1| < 2 to represent 4 > |x + 1| + 2

See attachment for the graph

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Answer:

200 lbs.

Step-by-step explanation:

Divide mass value by 16 to convert oz to lbs.

3,200/16=200

Answer:

y= -x²-4x+2

Step-by-step explanation:

write in vertex form

a(x-h)²+k

in our case h = -2 and k= 6

y=a(x+2)²+6

now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a

-3= a(1+2)²+6

-9=9a

a= -1

thus the formula is -(x+2)²+6

generally, teachers want things in standard form, so expand the exponent and simplify.

-(x²+4x+4)+6

y= -x²-4x+2

Answer:

\(y = -x^2 - 4x + 2\)

Step-by-step explanation:

The equation of a parabola in vertex form is:

\(y = a(x - h)^2 + k\)

where (h, k) is the vertex of the parabola.

In this case, the vertex is (-2, 6), so h = -2 and k = 6.

We also know that the parabola passes through the point (1, -3).

Plugging these values into the equation, we get:

\(-3 = a(1 - (-2))^2 + 6\)

\(-3 = a(3)^2 + 6\)

-9 = 9a

a = -1

Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:

\(y = -1(x + 2)^2 + 6\)

This equation can also be written as:

\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)

Answer:

Step-by-step explanation:

An engagement ring is likely very precise. The ring sizes used by some jewelers differs from the next size by 0.8 mm. As a % that's .8 / 16.5  * 100 = 4.80 %

The 0.8 is the number of mm needed to go from a size 6 to a size 7 ring size. So if you are ever going to buy a ring, be sure and let a jeweler measure the finger that it will go on.

The 16.5 mm is the diameter of the ring in mm. for a size 6 ring. If you have different information, you should go with what you have,

Size 14 dress

I can't answer this: it depends on where you live -- Europe or the US.

Also the type of dress matters: is it a skirt or a skirt and blouse combination. The % of the sides is much larger than 4% for the ring but it is still a definite description.  

Small Medium or Large

Depends entirely on where the garment is made, and where it is being sold.

Wish tells you to add a size if you live in North America. This too is not very distinct.

Answer:

x = 0

Step-by-step explanation:

x (40 °) ((3 x + 10) °)

40 x (3 x + 10) °^2

Expanded form:

120 x^2 °^2 + 400 x °^2

Roots:

x = -10/3

x = 0

Alternative forms:

40/3 (3 x + 5)^2 °^2 - (1000 °^2)/3

x (120 x °^2 + 400 °^2)

1/810 π^2 x (3 x + 10)

Geometric figure:

Parabola

HOPE I HELPED!

Answer:

4? I could be wrong. Sorry.

Step-by-step explanation:

The equation to represent the situation are as follows:

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

The miles of travel the total cost will be the same is 100 miles.

Your family needs to rent a car for a week while on vacation. Company A charges $3.25 per mile plus a flat fee of $125 per week. Company B charges $3 per mile plus a flat fee of $150 per week.

Therefore, the equation to express the situation is as follows;

Company A;

y = 3.25x + 125

Company B;

y = 3x + 150

where

The number of miles the travel will cost the same can be calculated as follows:

3.25x + 125 = 3x + 150

3.25x - 3x = 150 - 125

0.25x = 25

x = 25 / 0.25

x = 100

Therefore, the number of miles is 100 miles.

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The only true statement about the domain of the given function is:

B. f(x) is negative for all x < -5

The domain of a function is defined as the set of values that we can possibly plug into our function. This set is the x values in a function such as f(x).

Now, we are given the function as:

f(x) = \(\frac{2}{x^{2} } + 3x - 10\)

When x < -5, we have:

f(-4) = \(\frac{2}{(-4)^{2} } + 3(-4) - 10\)

f(-4) = -21.875

This suggests that for all values below x = -5 will result in negative values

When x > 2

f(3) = \(\frac{2}{3^{2} } + 3(3) - 10\)

f(3) = -0.78

Thus, it will get positive for higher values but it can also be negative as seen here.

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Answer:

d = 5 is a solution to the equation 13 - d = 8

Step-by-step explanation:

We have to solve 13 - d = 8

Now,

13 - d = 8,

We add d on both sides,

13 - d + d = 8 + d

13 = 8 + d

we subtract 8 from both sides,

13 - 8 = 8 - 8 + d

5 = d

d = 5

Hence the answer is 5

Answer:

105.

Step-by-step explanation:

21+21+21+21+21=105.

Answer:

12x/2 or 52/2

Step-by-step explanation:

Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.

Answer:

11c

Step-by-step explanation:

They are like terms meaning they all have the same variable you can just add them.

4c+c+6c

11c

Answer:

11c

Explanation:

We are given the expression:

4c+c+6c

We can simplify by combining like terms.  All three terms have a “c” so they can all be combined.

Factor out a “c” and add the coefficients.

4c+1c+6c

(4+1+6)c

(11)c

11c

4c+c+6c simplified is 11c