Simplify the expression. 12x^-6 y^10 times 3x^7 y

Your sequence has a common difference of -8, so could be considered an arithmetic sequence with first term 79. A formula for the n-th term might be ...

... a[n] = 79 -8(n -1)

or

... a[n] = 87 -8n

Answer: Please, see the attached file.

Thanks.

Solution:

We can graph using the intercepts:

(1) y-intercept, when x=0

y=4x-3→y=4(0)-3→y=0-3→y=-3

Point=(x,y)=(0,-3)

(2) x-intercept, when y=0

y=4x-3→0=4x-3

Solving for x: Adding 3 both sides of the equation:

0+3=4x-3+3

3=4x

Dividing both sides of the equation by 4:

3/4=4x/4

3/4=x

x=3/4=0.75

Point=(x,y)=(3/4,0)=(0.75,0)

With these pair of points (0, -3) and (0.75,0) we can draw the right line

f(1) = 16

to evaluate f(1) substitute x = 1 into f(x)

f(1) = 3 - 2 - 3 + 18 = 16

When 3x³ - 2x² - 3x + 18 is divided by (x - 1 ) the remainder is 16

D. 5x = 45 because you are trying to find x, the number of tickets that must be sold to earn $45.

Answer:

5x=45

Step-by-step explanation:

Answer:

  about 35

Step-by-step explanation:

This question is asking for an estimate, which means you round the number(s) to something convenient to perform the calculation.

Here, 47% is conveniently rounded to 50% = 50/100 = 1/2. Then 1/2 of 70 is ...

  1/2·70 = 70/2 = 35

A reasonable estimate of 47% of 70 is 35.

___

As you get more sophisticated in your estimating, you can also estimate the error. This estimate is about 3% (of 70) high, so is high by 3/100·70 = 2.1. That means the real answer is 35 - 2.1 = 32.9.

You could also estimate the error as 3% of 100 = 3/100·100 = 3, so you could say the actual value is between 35-3 = 32 and 35. Since 100 is larger than 70, you know that 3% of 100 is larger than 3% of 70, so this is an over-estimate of the error.

There are the following numbers for which that holds:

{-4, -2, -1, 0, 1, 2, 4}

See table below. For larger than 5 it can be proved that the number of digits will never be the same.

x   x^2  x^3

0 0 0

1 1 1

2  4  8

4  16  64

Answer:

the answer if 4 numbers

(sorry i dont have an explenation i litterally guessed it when I entered it in the RSM portal.)

Step-by-step explanation:

a) The sum of your ages is F + (F+B) = 2F+B.

b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.

c) The difference of your ages at any time is B.

Answer:

a) The sum of your ages is F + (F+B) = 2F+B.

b) In 3 years, the sum of your ages will be (F+3)+(F+B+3) = 2F+B+6.

c) The difference of your ages at any time is B.

Curtains:

$24.50 x 3 = $73.50

Bedspread:

$39.95 x 3 = $119.85

Gallon of paint:

$24.96 x 3 = $74.88

Lamp shade:

$9.99 x 3 = $29.97

The cost of all the items:

$73.50 + $119.85 + $74.88 + $29.97 = $298.20

How much money is left:

$325 - $298.20 = $26.80

So the family has $26.80 left.

Hope this Helps!!

Its simply just 8 minus 25 to find x but there is no fraction.

c is right answer because 54.15 is bigger than 54.05

In comparing decimal numbers using inequalities, choice C (54.15 > 54.05) is correct. The other three options incorrectly compare the numbers.

The question is asking us to compare two different decimal numbers using inequalities. Inequalities in mathematics are used to show the order of numbers, illustrating which is greater or less than the other.

Let's look at each option:

Therefore, the choice C correctly compares the two decimal numbers using inequalities.

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800 - 900 = -100. = 100/800=.125 x 100 = 12.5% increase.

Policy value over 20 years = 125000

Per year, 125000/20=$6250

Look up premium table for age 40 and 45, the difference in total premium is C. $12,875.

To find the difference in total premium costs over 20 years for a whole life insurance policy at two age levels, calculate and subtract the total premium at each age.

To find the difference in total premium costs over 20 years for the whole life insurance policy at the two age levels, we need to calculate the total premium at each age and then subtract the two values.

Therefore, the difference in total premium costs over 20 years for this policy at the two age levels is 20 * x - 15 * y.

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C

given x² + 16x = 41

to complete the square on this equation

since the coefficient of the x² term is 1

add (half the coefficient of the x-term )² to both sides

x² + 2(8)x + 64 = 41+ 64

(x + 8 )² = 105 → C

Answer:

Option C is correct

Step-by-step explanation:

Given the equation

[tex]x^2+16x=41[/tex]

we have to find the equation results from completing the square.

For completing the square method, since the coefficient of [tex]x^2[/tex] is 1 therefore we have to divide the coefficient of x by 2 and then squaring of that value adding on both sides of equation, we get

Here coefficient of x is 16 therefore square of half the number adding both sides

[tex]x^2+16x+64=41+64[/tex]

[tex]x^2+8x+8x+64=105[/tex]

[tex]x(x+8)+8(x+8)=105[/tex]

[tex](x+8)(x+8)=105[/tex]

[tex](x+8)^2=105[/tex]

Option C is correct

Answer:

The answer is C

Step-by-step explanation:

Your welcome :)

Graph [tex]f(x) = x^2[/tex]

quadratic function is of the form [tex]f(x) = ax^2 + bx +c[/tex]

In our f(x) there is no x term and constant so we put 0

[tex]f(x) = 1x^2+0x+0[/tex]

The value of a=1 , b=0  and c=0

To find vertex , use formula [tex]x= \frac{-b}{2a}[/tex]

Plug in the values

[tex]x= \frac{-0}{2(1)}[/tex] =0

Now plug in x=0 in f(x) equation

[tex]f(x) = x^2[/tex]

[tex]f(0) = 0^2[/tex]=0

So vertex is (0,0)

Now we pick some number for x below and above 0

Make a table

x            y=x^2

-2           4

0             0

2            4

Now plot all the points (-2,4) (0,0) and (2,4)

The graph is attached below

The point-slope form of the equation of a line with slope m through point (h, k) can be written as

... y = m(x -h) +k

For your problem, where m = -4 and (h, k) = (2, 2), this becomes

... y = -4(x -2) +2

... y = -4x +8 +2 . . . . eliminate parentheses

... 4x +y = 10 . . . . . . .add 4x to put into standard form

We are given

[tex]f(n+1)=-10f(n)[/tex]

we are given

[tex]f(1)=1[/tex]

At n=1:

we can plug n=1 into formula

[tex]f(1+1)=-10f(1)[/tex]

[tex]f(2)=-10f(1)[/tex]

[tex]f(2)=-10*1[/tex]

[tex]f(2)=-10[/tex]

At n=2:

we can plug n=2 into formula

[tex]f(2+1)=-10f(2)[/tex]

[tex]f(3)=-10f(2)[/tex]

[tex]f(3)=-10*-10[/tex]

[tex]f(3)=100[/tex]................Answer

A function assigns the value of each element of one set to the other specific element of another set. The value of f(3) is 100.

A function assigns the value of each element of one set to the other specific element of another set.

As the recursive function is given to us, f(n + 1) = –10f(n), also the value of f(1)=1 , therefore, the value of f(2) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(1 + 1) = -10f(1)\\\\f(2)= -10 \times 1\\\\f(2)=-10[/tex]

Now, the value of f(3) can be written as,

[tex]f(n + 1) = -10f(n)\\\\f(2 + 1) = -10f(2)\\\\f(3)= -10 \times -10\\\\f(3)= 100[/tex]

Hence, the value of f(3) is 100.

Learn more about Function:

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Answer:

  3 8/33

Step-by-step explanation:

You want the mixed-number equivalent of the repeating decimal 3.2424....

A repeating decimal fraction that starts at the decimal point can be converted to a ratio of integers by expressing the repeating digits over the same number of 9s.

Here, the two repeating digits "24" mean the fraction equivalent is ...

  0.2424... = 24/99 = 8/33

The mixed number equivalent of 3.2424... is 3 8/33.

__

Additional comment

If the repeating portion does not start at the decimal point, you can use the following technique to do the conversion.

Effectively, this multiplies and divides the number by ((10^n) -1)/((10^n) -1). In the case here, that would be multiplication by 1 in the form 99/99.

  3.242424... × 99/99 = 321/99 = 3 8/33

The "321" will be manifested on a calculator as 320.99999.... If you multiply by (100 -1) with pencil and paper, you can see that you get ...

  324.2424... - 3.2424... = 321 . . . . . . repeating digits cancel

If the repeat starts somewhere else, you can still use the "fraction with equal number of 9s" technique, but with a multiplier:

  3.6242424... = 3.6 + 0.0242424 ... = 3.6 + (1/10)(24/99)

  = 36/10 + 8/330 = 3 103/165

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3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].

To express the repeating decimal 3.242424... as a mixed number, we can first write it as an infinite geometric series.

Let x = 3.242424.... Then, multiplying x by 100 gives 100x = 324.242424...

Now, subtract x from 100x:

100x - x = 324.242424... - 3.242424...

99x = 321

Now, solve for x:

[tex]\[ x = \frac{321}{99} \][/tex]

Now, express the fraction [tex]\(\frac{321}{99}\)[/tex]as a mixed number.

[tex]\[ \frac{321}{99} = 3 \frac{24}{99} \]\\Now, simplify the fraction:\[ \frac{24}{99} = \frac{8}{33} \][/tex]

So, 3.242424... as a mixed number is [tex]\(3 \frac{8}{33}\)[/tex].

The appropriate choice for the interpretation of a correlation coefficient of 0 is ...

... B. There is not a linear relationship between x and y.

Answer:

B.  

There is not a linear relationship between x and y.

Step-by-step explanation:

PLATO fam

4 years=48 months

A new car costs 25,000, but she will get 13,000 for her used car as long as she takes good car of it. If she takes good care of her used car and gets 13,000 for it, she will only need to save 12,000 total. We can divide 12,000 by 48 to find out how much Courtney should save minimum each month to afford her new car. 12,000/48=250

You can check to see if this is correct by multiplying 48*250=12,000. Paying 250 for each month of the 48 months will equal the $12,000 that Courtney needs.

Courtney needs to save at least $250 per month to afford her new car in 4 years.

I hope this helps :)

Courtney should save at least $250 per month for the next 4 years to be able to pay cash for the new car after considering the amount she'll receive from selling her used car.

Courtney needs to save money to buy a new car in 4 years. The estimated cost of the new car is $25,000, and she expects to get $13,000 for her used car. To find out the least amount she should save each month, we will subtract the expected amount from the sale of her used car from the cost of the new car, and then divide by the number of months in 4 years (48 months).

The calculation is as follows:

Total amount needed = Cost of New Car - Sale of Used Car
= $25,000 - $13,000
= $12,000

Monthly savings required = Total amount needed \/ Number of months
= $12,000 \/ 48
= $250

Therefore, Courtney should save at least $250 per month to pay cash for her new car in 4 years.

The answerer is combining terms in x with constants

that is, 13x + 5 ≠ 18x

13x + 5 + 17x - 4.5 + x

= (13x + 17x + x ) + 5 - 4.5 ← collecting like terms

= 31x + 0.5 ← correct simplification

combining terms in x with constants

13x + 5 ≠ 18x

13x + 5 + 17x - 4.5 + x

= (13x + 17x + x ) + 5 - 4.5 <--- collecting like terms

= 31x + 0.5 <--- correct simplification

Answer:

x+7/8

Step-by-step explanation:

A polynomial has roots at the points where the curve cuts the x axis.

This can also be said as values of x for which the polynomial is 0

Given that when x =a is root means, we have x-a is the factor.

Based on the above, we find when 3/4, -7/8, -3/8 and -1/9 are roots

factors are x-3/4, x+7/8, x+3/8, x+1/9

Hence answer is

B) (x + 3/8)

The other options do not match with the factors only option Bmatches.

Answer: The factor of the polynomial is [tex](x+\frac{3}{8})[/tex]

Step-by-step explanation:

We are given:

4 roots of the polynomial

Root 1: [tex]\frac{3}{4}[/tex]

The factor for this root becomes: [tex](x-\frac{3}{4})[/tex]

Root 2: [tex]\frac{-7}{8}[/tex]

The factor for this root becomes: [tex](x+\frac{7}{8})[/tex]

Root 3: [tex]\frac{-3}{8}[/tex]

The factor for this root becomes: [tex](x+\frac{3}{8})[/tex]

Root 4: [tex]\frac{-1}{9}[/tex]

The factor for this root becomes: [tex](x+\frac{1}{9})[/tex]

Hence, the factor of the polynomial is [tex](x+\frac{3}{8})[/tex]

This can be "unfolded" to ...

... -1 < x+3 < 1

Subtracting 3 gives the solution:

... -4 < x < -2

yes

area = 18 × 22 = 396 ft²

Since 396 > 350

Caroline has more than enough to fill her garden

We are given a pattern:

-9 , -4 , 1 , 6 , ...

We have to describe the pattern and find the next two terms

-9+5= -4

-4+5= 1

1+5= 6

Hence, the numbers are found by adding five to the previous term

The next two numbers are found as:

6+5 =11

11+5 = 16

Hence, next two numbers are:

11 and 16

The range is the output value

f(-2) = 2(-2)+7 =3

f(3)= 2(3)+7 = 13

f(8) = 2(8)+7 = 23

The range is 3,13,23