The sum of ten and the quotient of a number xxx and 666.

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Solution:

Given roots of the polynomial are:

–3, –2, 1 and 5

If a is the root of the polynomial then the factor is (x –a).

So that, the factors of the given roots are:

(x –(–3)) = x + 3

(x –(–2)) = x + 2

(x – 1) = x – 1

(x – 5) = x –5

Polynomial = Product of the factors

                    = (x + 3)(x + 2)(x – 1)(x – 5)

Multiply first two factors.

                     [tex]=(x^2+2x+3x+6)(x-1)(x-5)[/tex]

                     [tex]=(x^2+5x+6)(x-1)(x-5)[/tex]

Now, multiply the next two factors.

                     [tex]=(x^2+5x+6)(x^2-5x-x+5)[/tex]

                     [tex]=(x^2+5x+6)(x^2-6x+5)[/tex]

Now multiply these two factors.

                    [tex]=x^2(x^2-6x+5)+5x(x^2-6x+5)+6(x^2-6x+5)[/tex]

                     [tex]=x^4-6x^3+5x^2+5x^3-30x^2+25x+6x^2-36x+30[/tex]

                     [tex]=x^4-x^3-19x^2-11x+30[/tex]

The simplest polynomial function with the given roots is

[tex]x^4-x^3-19x^2-11x+30[/tex].

Answer:

64

Step-by-step explanation:

pemdas says parenthesis first

3+5=8

8(8)

8 times 8 equals 64

We can add the numbers inside the parenthenses: 8(3+5)=8(8)

Now just multiply and we get 64.

So 64 is the simplified answer

Hope this helped!

Option A. When m increases , n tends to increase.

Step-by-step explanation:

Positive correlation is a relationship between two variables in which both variables move in the same direction.

Option A. When m increases , n tends to increase.

Answer:

A. When m increase, n tends to increase

Answer:

x=-2/5

y=-1/5

Step-by-step explanation:

[tex]-2x-y=1\\y=3x-1[/tex]

Get the y variables onto 1 side

[tex]y+1=-2x\\y=3x-1[/tex]

Now shift the 1 over

[tex]y=-2x-1\\y=3x-1[/tex]

To solve for x, we can subtract the second equation from the first equation

[tex](y-y)=-2x-3x-1-1 = 0=-5x-2\\5x=-2\\x=-2/5[/tex]

Plug back into the first equation we found and solve for y

[tex]y=-2x-1\\y=-2(-2/5)-1\\y=4/5-1=-1/5[/tex]

Rate of commission as a percent is 12 %

Solution:

Kara weekly paycheck is $6,500 including her salary which is $1,000

Therefore,

Commission amount = Weekly paycheck - salary

Commission amount = 6500 - 1000

Commission amount = 5500

Her sales for the week totaled to $45,000

Therefore rate of commission is given as:

[tex]Commission\ rate = \frac{\text{commission amount}}{\text{sales for week}} \times 100[/tex]

Substituting the values we get,

[tex]Commission\ rate = \frac{5500}{45000} \times 100\\\\Commission\ rate = \frac{550}{45}\\\\Commission\ rate = 12.2 \approx 12[/tex]

Thus rate of commission as a percent is 12 %

Option C:

5, 1, 7

Solution:

Given equation:

y = |3x + 1|

In the chart, x values are given as –2, 0, 2.

To find the value of y for the corresponding x given.

Substitute x  = –2 in the equation of y.

y = |3(–2) + 1|

  = |–6 + 1|

  = |–5|   (Absolute value of a negative number is positive)

y = 5

Substitute x  = 0 in the equation of y.

y = |3(0) + 1|

  = |0 + 1|

  = |1|

y = 1

Substitute x  = 2 in the equation of y.

y = |3(2) + 1|

  = |6 + 1|

  = |7|   (Absolute value of a negative number is positive)

y = 7

Option C is the correct answer.

The values of y are 5, 1, 7.

The answer image of the table is attached below.

Answer:

7,1,7

Step-by-step explanation:

Answer:

4k+3

Step-by-step explanation:

Answer:

a decimal 0.225

Step-by-step explanation:

Answer:

112 will have been paid for their trip

Step-by-step explanation:

You have to divide $3920 by $35 to get your answer

Answer:

Divide 11 by 10 . Place this digit in the quotient on top of the division symbol. Multiply the newest quotient digit (1) by the divisor 10 . Subtract 10 from 11 . :) Hope this helps!

It can be a fraction of 11/10 as a mixed number is 1 1/10.

To convert a fraction into a mixed number, you need to divide the numerator (top number) by the denominator (bottom number).

The whole number part of the result is the whole number of the mixed number, and the remainder becomes the numerator of the fractional part.

As per the question, we have the fraction 11/10.

Dividing 11 by 10 gives:

11 ÷ 10 = 1 remainder 1

So the whole number part is 1, and the fractional part is 1/10. We can express this as a mixed number by writing:

11/10 = 1 1/10

Therefore, 11/10 as a mixed number is 1 1/10.

Learn more about the fraction here:

brainly.com/question/10354322

#SPJ5

Answer:

The sum of their ages now is 13

Step-by-step explanation:

Dally's age = x

Dilly's age = x - 7

In 4 years time Dilly will be half Dally’s age, therefore:

Dilly's age plus four equals to half of Dally’s age plus four,

replacing with the values and variables we know:

x - 7 + 4 = (x + 4) /2

x - 3 = (x + 4) /2

2x - 6 = x + 4 (Multiplying by 2 at both sides)

2x - x = 4 + 6 (Like terms)

x = 10 ⇒ x - 7 = 3

The sum of their ages now is 13 (10 + 3)

The sum of their ages now is 13 years

Let the age of Dilly be "x"

Let the age of Dally be "y"

If Dilly is 7 years younger than Dally, then;

x = y - 7 ....... 1

In 4 years time, their age will be:

Dilly = x+ 4

Dally = y + 4

If in 4 years' time she will be half Dally’s age, then;

x+4 = 1/2(y+4) ............... 2

Substitute equation 1 intp 2 to have:

y-7+4 = 1/2(y+4)

y - 3 = 1/2(y+4)

2y - 6 = y + 4

2y - y = 6 + 4

y = 10

Recall that x = y - 7

x = 10 - 7

x = 3

Sum of their ages will be x + y = 10 + 3 = 13 years

Hence the sum of their ages now is 13 years

Learn more here: https://brainly.com/question/13805464

Answer:

-3<x<=4

Step-by-step explanation:

Answer:

0.86(28) = 24.08

Step-by-step explanation:

Turn the percent to decimal and solve

Answer:

28$

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given two relations we can use to find "a" and "b":

  a = 3b

  a² + b² = 30²

Substituting for "a", we have ...

  (3b)² +b² = 900

  10b² = 900

  b² = 90

  b = √90 = 3√10 ≈ 9.5

Then "a" is ...

  a = 3b = 3(3√10) = 9√10 ≈ 28.5

The values of "a" and "b" are about 28.5 and 9.5, respectively.

Answer:

A bag of pop corn costs $8, and each Pretzel costs $4.25.

Step-by-step explanation:

Let [tex]b[/tex] be the price of popcorn, and [tex]p[/tex] the price of Pretzels. If the girl bought 2 bags of popcorn and 5 Pretzels and it cost her $37.25, we have the equation

[tex]2b+5p=37.25[/tex]  (this says that the cost of 2 popcorn bags plus 5 pretzels equals $37.25) .

And, since Zoe bought 8 popcorn bags and 9 Pretzels with a total price of $102.25, we get the equation

[tex]8b+9p=102.25[/tex] (this says that the cost of 8 popcorn bags plus 9 Pretzels equals $102.25).

Thus, we have two equations

1. [tex]2b+5p=37.25[/tex]

2. [tex]8b+9p=102.25[/tex]

and we solve them by first multiplying equation (1) by 4:

[tex]4(2b+5p=37.25 )\rightarrow (8b+20p=149)[/tex],

and then subtracting it from equation (2):

[tex]\:\:\:\:\: 8b+9p=102.25\\-(8b+20p=149)\\\line(1,0){3 cm}\\-11p=-46.75\\\\\boxed{p=\$4.25}[/tex]

Now we put this value of [tex]p[/tex] into equation (1) and get:

[tex]2b+5(4.25)=37.25[/tex]

and we solve for [tex]b[/tex] to get:

[tex]2b=37.25-21.5[/tex]

[tex]\boxed{ b=8}[/tex]

Therefore, a bag of popcorn costs $8, and each Pretzel costs $4.25.

Answer:

8 is your answer

Step-by-step explanation:

Answer:

Option B.

Step-by-step explanation:

Given information: ∠MHL=(3x+20), ∠KHN=(x+25), and ∠JHN=(x+20).

We need to find the measure of ∠JHN.

[tex]\angle MHL=\angle JHK[/tex]                         (Vertical opposite angles)

[tex]\angle MHL=\angle JHN+\angle KHN[/tex]

Substitute the given values.

[tex]3x+20=(x+20)+(x+25)[/tex]

[tex]3x+20=2x+45[/tex]

[tex]3x-2x=45-20[/tex]

[tex]x=25[/tex]

The value of x is 25. So, the measure of ∠JHN is

[tex]\angle JHN=x+20=25+20=45[/tex]

The measure of ∠JHN is 45°.

Therefore, the correct option is B.

Answer:

it's B

Step-by-step explanation:

Answer:

0.00995024875622

Step-by-step explanation:

Answer:

0.0099502487562189054726

Step-by-step explanation:

divide 50 by 5025

Answer:

no

Step-by-step explanation:

6 and 5 are the smaller sides but they only add to 11

the need to get to something higher than 12

no equal or less than

Final answer:

Segments 6, 5, and 12 cannot form a triangle because the length of one segment (12) is equal to the sum of the other two (6 + 5), which violates the Triangle Inequality Theorem.

Explanation:

The question involves determining whether three given segments can form a triangle. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem. Given the segments 6, 5, and 12, we can test this theorem:

Since one of the conditions fails, the segments 6, 5, and 12 cannot form a triangle. Visually, it's also clear that one segment (12) is as long as the sum of the other two (6 + 5), which means they could only form a straight line, not a triangle.

Answer:

84.82 ft³

Step-by-step explanation:

Answer:

84.823

Step-by-step explanation:

The formula of the volume of cone is v= 1/3 (PI* r^2) h

We have that h= 9feet , and r= 3

So, v =1/3 (Pi * 3^2) 9

V=84.82300

Option C: [tex]f(x)=2^x[/tex] is the function rule.

Explanation:

The sequence is [tex]2,4,8,16, \dots \dots[/tex]

Let us find the common difference of this sequence.

Common ratio = [tex]\frac{4}{2} =2[/tex]

Hence, [tex]r=2[/tex]

Thus, the given sequence is a geometric progression.

To determine the function rule, let us substitute the values in the general formula of GP which is given by

[tex]f(x)=ar^{x-1}[/tex] where [tex]a=2, r=2[/tex]

Substituting we get,

[tex]f(x)=2(2)^{x-1}[/tex]

Simplifying, we get,

[tex]f(x)=2\times2^x\times2^{-1[/tex]

Adding the powers, we get,

[tex]f(x)=2^{1+x-1}[/tex]

Simplifying, we get,

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

Hence, the function rule is [tex]f(x)=2^x[/tex]

Thus, Option C is the correct answer.

Answer:

Therefor the probability of having two boys  =  [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

i) In randomly selected family with two children, excluding multiple births

 the children can be in the following combinations:

  a) one girl, one girl    :   GG

  b)  one girl, one boy  :   GB

 c)  one boy, one boy :   BB

The order does not matter for this problem.

Therefor the probability of having two boys  =  [tex]\frac{1}{3}[/tex]

Answer:

1)  (4,6),(-4,6), (4,12),(-4,12)

2) (4,9) or (-4,9)

Step-by-step explanation:

Observe that the two vertices given, (0,6) and (0,12) are on the y-axis.

The distance between this points is |12-6|=6

We know area of a triangle is [tex]A=\frac{1}{2}bh[/tex]

We were given area as 12.

[tex]\frac{1}{2}*b*6=12[/tex]

[tex]3b=12[/tex]

b=4 units

We can find a point 4 units horizontally away from any of the vertex.

So (4,6),(-4,6), (4,12),(-4,12) are feasible vertices.

For the triangle to be isosceles, then the third vertex must be on the horizontal line through the midpoint of (0,6) and (0,12) and must be 4 units away from the line x=0.

Therefore if thr triangle is isosceles, then third vertex must be at (4,9) or (-4,9)

Step-by-step explanation:

"At least x" means "that value x or more"

"At least 2" means "2 or more"

So Billy's plants grow 2 inches or more a month. The smallest increase possible is 2 inches.

We plot a closed circle at 2 on the number line. The closed circle tells us "include this value in the solution set". In contrast, the open circle says "exclude the endpoint from the solution set"

Then we shade to the right indicating all of the possible outcomes (growing 3 inches, growing 4 inches, etc.). 

Answer:

6.3 x 10°

Step-by-step explanation:

6.3 can be written as 6.3 x 1

recall that anything to the power of zero = 1

hence 10° = 1 substitute this back into the expression above to get:

6.3

= 6.3 x 1

= 6.3 x 10°

Answer:

[tex]a_{n} = 0.3(- 0.2)^{n - 1}[/tex]

Step-by-step explanation:

The given sequence is 0.3, - 0.06, 0.012, - 0.0024, 0.00048 ........ so on.

Now, this is a G.P. sequence with common ratio [tex]\frac{- 0.06}{0.3} = - 0.2[/tex].

Now, the explicit formula of the given series will be

[tex]a_{n} = 0.3(- 0.2)^{n - 1}[/tex] , where [tex]a_{n}[/tex] is the nth term of the G.P. sequence.

Now, for n = 1, [tex]a_{1} = 0.3(- 0.2)^{1 - 1} = 0.3[/tex].

For, n = 2, [tex]a_{2} = 0.3(- 0.2)^{2 - 1} = 0.3 \times (- 0.2) = - 0.06[/tex] and so on. (Answer)

Answer:

a n+0.3(-0.2)n-1

Step-by-step explanation:

Answer:

12 centimeters

Step-by-step explanation:

An isosceles triangle has two congruent sides which are legs(2 sides having same length )If x is length of each leg, then we ca write the equation like this

equation: x+x+8=32

combine like terms

2x +8 = 32

minus 8 from each side

2x=32-8

2x=24

divide both sides by 2

2x/2 = 24/2

x=12 centimeters

Answer:

The system of inequalities is given by

i) x + y ≥ 10

ii) 9x + 4y ≤ 100

Step-by-step explanation:

i) let x be the number of grams of fat in the non-carb brownie.

ii) let y be the number of grams of protein in the non-carb brownie.

iii) The brownie must weigh at least 10 grams

iv) therefore we can write x + y ≥ 10

v) The brownie must have no more than 100 calories

vi) therefore we can write 9x + 4y ≤ 100

Answer:

Its 7

Step-by-step explanation:

24÷8= 3

6×3=18

?×3=21

7×3=21

Awnser is 7