the sum of a number z divided by three and the number

Answer:

[tex]remainder=2802[/tex]

Step-by-step explanation:

Remainder Theorem: When a polynomial [tex]f(x)[/tex] is divided by [tex](x-a)[/tex] the remainder will be [tex]f(a)[/tex]

[tex]Here \ \ f(x)=x^3+6x^2-20x+450[/tex]

[tex]It\ is\ divided\ by\ (x-12)[/tex]

[tex]Then\ remainder =f(12)\\\\remainder=(12)^3+6(12)^2-20\times12+450\\\\remainder=1728+6\times144-240+450\\\\remainder=1728+864-240+450\\\\remainder=3042-240\\\\remainder=2802[/tex]

Final answer:

To find the remainder of the polynomial f(x) = x³ + 6x² - 20x + 450 when divided by (x - 12), we evaluate f(12) using the Remainder Theorem, which yields a remainder of 2802.

Explanation:

To find the remainder when the function f(x) = x³ + 6x² - 20x + 450 is divided by (x - 12), we use the Remainder Theorem. This theorem states that the remainder of a polynomial f(x) divided by (x - a) is f(a). Therefore, to find the remainder of f(x) divided by (x - 12), we evaluate f(12).

Substitute x with 12 into the function:

f(12) = (12)³ + 6(12)² - 20(12) + 450

f(12) = 1728 + 864 - 240 + 450

f(12) = 2802

Thus, the remainder is 2802.

Answer:

Jason is 14 year old.

Step-by-step explanation:

Given: Joe, John and Jason are each a year apart in age.

           Sum of their age is 39.

Lets assume the age of Joe be x

∴ Age of Jahn will be [tex](x+1)[/tex]

And age of Jason will be [tex](x+2)[/tex]

Now, putting up an equation for the sum of their age.

∴ [tex]x+(x+1)+(x+2)= 39[/tex]

Opening the parenthesis.

⇒[tex]x+x+1+x+2= 39[/tex]

⇒[tex]3x+3= 39[/tex]

Subtracting both side by 3

⇒ [tex]3x= 36[/tex]

Dividing both side by 3

⇒[tex]x= \frac{36}{3}[/tex]

∴ [tex]x= 12\ years[/tex]

Hence, Joe is 12 year old.

Next subtituting the value of x to find age of Jason and John.

Jason= [tex](x+2)= 12+2[/tex]

∴Jason= 14 years.

John age= [tex](x+1)= 12+1[/tex]

∴ John Age= 13 years.

Hence, Jason is 14 year of age.

The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]

Step-by-step explanation:

A bag contains:

We need to find the probability of randomly selecting a yellow marble out of the bag

Probability is the ratio of number of favorable outcomes to the total number of possible outcomes P(A) = [tex]\frac{n(A)}{n(outcoms)}[/tex]

∵ A bag contains 7 red marbles, 5 yellow marbles, 6 blue

   marbles, 4 green marbles, and 3 orange marbles

- Add all the color to find the number of total marbles

∴ n(all) = 7 + 5 + 6 + 4 + 3 = 25

∵ There are 5 yellow marbles

∵ P(yellow) = [tex]\frac{n(yellow)}{n(all)}[/tex]

∴ P(yellow) = [tex]\frac{5}{25}[/tex]

- Divide up and down by 5 to simplify the fraction

∴ P(yellow) = [tex]\frac{1}{5}[/tex]

The probability of randomly selecting a yellow marble out of the bag is [tex]\frac{1}{5}[/tex]

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Answer:

1/5

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

You will move the 7 to 18 but bc there is a equal sign you will change the positive sign to negative and just solve -7 plus 18 you will get 11 and that’s b

Answer:

Step-by-step explanation:

18 = 7/b

18b=7

b=7/18

Answer:

Step-by-step explanation:

-3 3/4, -3, 3 1/10, and then 3 1/3 i think this is correct...sorry if it is wrong though.

Answer:

x = 8

y = 10

Step-by-step explanation:

We are given the equations;

-3x + 4Y = 16

3x - y =14

We are required to solve the two equations simultaneously using elimination

In this case, we will eliminate one unknown;

We eliminate x by adding the two equations;

That is;

-3x + 4Y = 16

3x - y =14

.............................

     3y = 30

       y = 10

Solving for x

3x - (10) = 14

3x = 14 +10

  3x = 24

   x = 8

Therefore, the solution of the equation is x=8 and y=10

Answer:

(48 m^12)/n^8

Step-by-step explanation:

Simplify the following:

3 ((2 m^3)/(n^2))^4

Multiply each exponent in (2 m^3)/(n^2) by 4:

3×2^4 m^(4×3) n^(-2×4)

4 (-2) = -8:

3×2^4 m^(4×3) n^(-8)

4×3 = 12:

(3×2^4 m^12)/(n^8)

2^4 = (2^2)^2:

(3 (2^2)^2 m^12)/(n^8)

2^2 = 4:

(3×4^2 m^12)/(n^8)

4^2 = 16:

(3×16 m^12)/(n^8)

3×16 = 48:

Answer: (48 m^12)/n^8

Answer:

On the screen shot

Step-by-step explanation:

pretty basic. you can't evaluate it to a single digit if there are 2 variables. lmk which variable you are solving for.

Answer: 6y + 5x = 24

Step-by-step explanation:

The formula for calculating  equation of line with two points is given as :

[tex]\frac{y-y_{1}}{x-x_{1}}[/tex] = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

[tex]x_{1}[/tex] = -12

[tex]x_{2}[/tex] = 6

[tex]y_{1}[/tex] = 14

[tex]y_{2}[/tex] = -1

substituting the values into the formula , we have

[tex]\frac{y-14}{x-(-12)}[/tex] = [tex]\frac{-1-14}{6-(-12)}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-15}{18}[/tex]

[tex]\frac{y-14}{x+12}[/tex] = [tex]\frac{-5}{6}[/tex]

cross multiplying , we have :

6(y - 14 ) = -5 ( x + 12 )

6y - 84 = -5x - 60

6y +5x = -60 + 84

6y + 5x = 24

Answer:

18

you do 2/3=12/n.  and find out n (im to lazy to explain sorry)

Answer:

Step-by-step explanation:

The correct fraction is simply 30/7, where 30 is the distance in miles and 7 is the number of days to complete it.

30/7 = 4.286miles daily but since you've asked to have this as a fraction, 30/7miles is good.

Final answer:

To achieve his goal of running 30 miles in a week, Raul should run 30 miles divided by 7 days, which is approximately 4 2/7 (⅔) miles every day.

Explanation:

If Raul wants to run 30 miles this week and he wants to run the same number of miles each day, we need to divide the total miles by the number of days in a week. There are 7 days in a week, so we will divide 30 miles by 7 days.

Using division: 30 miles ÷ 7 days = ⅔ miles per day. The fraction ⅔ represents the number of miles Raul plans to run each day to meet his goal of running 30 miles in a week.

Answer:

49.6 or 49 3/5

Step-by-step explanation:

62/100*80

Simplify the 62/100 (meaning to make it to its simplest terms as possible).

62/100= 31/50

Now we can solve:

31/50*80= 49.6 or 49 3/5

Answer:

Step-by-step explanation divide 62 by 100 and multiply by 80

= 49.6

Answer:

58/48 to 29/24

Step-by-step explanation:

An easy way that I always remember is that if both the numbers are even, divide by 2. Keep dividing until you get a odd number and then you know that you have your lowest form.

Answer:

The missing figure is attached down

The length of BE is 27 units ⇒ 3rd answer

Step-by-step explanation:

In circle A:

We need to find the length of BE

∵ AB and AD are radii in circle A

∴ AB ≅ AD

In Δs EAB and EAD

∵ ∠BAE ≅ ∠DAE ⇒ given

∵ AB = AD ⇒ proved

∵ EA = EA ⇒ common side in the two triangles

- Two triangles have two corresponding sides equal and the

   including angles between them are equal, then the two

   triangles are congruent by SAS postulate of congruence

∴ Δ EAB ≅ Δ EAD ⇒ SAS postulate of congruence

By using the result of congruence

∴ EB ≅ ED

∵ EB = 3 x - 24

∵ ED = x + 10

- Equate the two expressions to find x

∴ 3 x - 24 = x + 10

- Add 24 to both sides

∴ 3 x = x + 34

- Subtract x from both sides

∴ 2 x = 34

- Divide both sides by 2

∴ x = 17

Substitute the value of x in the expression of the length of BE to find its length

∵ BE = 3 x - 24

∵ x = 17

∴ BE = 3(17) - 24

∴ BE = 51 - 24

∴ BE = 27

The length of BE is 27 units

Answer:

27

Step-by-step explanation:

I TOOK THE QUIZ, AND GOT 100%

To find out how many times 19 goes into 133, you can perform a simple division. 19 goes into 133 seven times with no remainder.

Dividing 133 by 19 results in 7, which means 19 goes into 133 seven times exactly. This division is a fundamental arithmetic operation, illustrating how many times one number can be evenly divided into another. It's part of the foundation of mathematics and has practical applications in everyday life, from splitting objects into equal groups to determining quantities in various contexts.

In this case, it's evident that 19 is a factor of 133, and understanding this relationship can help in tasks like distributing items evenly or solving problems involving proportions and ratios. Division is a mathematical concept with broad utility and relevance, making it essential in various mathematical, scientific, and real-world scenarios.

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Answer:

converting to fraction:

0.206 = 0.206/1000 =206//1000

2.06 = 2.06/100 = 206/100

0.026 = 0.026/1000 = 26/1000

0.26 = 0.26/100 = 26/100

answer = 2.06

Step-by-step explanation:

The fraction having the greatest value will be 2.06.

A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.

The greatest value of the fraction will be calculated as below in the calculation:-

0.206 = 0.206/1000 =206//1000

2.06 = 2.06/100 = 206/100

0.026 = 0.026/1000 = 26/1000

0.26 = 0.26/100 = 26/100

Therefore, the fraction having the greatest value will be 2.06.

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Answer:

84m2

Step-by-step explanation:

it is not b because that is only the area of the square inside of the parallelogram i know that for a FACT sorry i answered late.

Answer:

y = -5

x = -2

Step-by-step explanation:

x+7y=-37

2x-5y=21

Multiply first equation by -2

-2 × (x + 7y) = -37 ➡ -2x -14y = 74

now add the equation up

2x-5y -2x -14y = 21 + 74 (-2x will eliminate 2x)

-19y = 95 divide both sides by 19

y = -5 we can find the value for x by using this information

x + 7y = -37 replace y by -5

x + 7×(-5) = -37

x = -2

Answer:

2:1

Step-by-step explanation:

Answer:60:30

Step-by-step explanation:

90-60=30 so 60 blue to 30 red is 60:30

Answer: Fills up something like how inflating a ballon fills it with air

Step-by-step explanation:

Hope it helped

2[tex]\frac{3}{10\\}[/tex]

Answer:

Square root of 8.

Step-by-step explanation:

Given:

Number given : 2 to the power of 3 over 2 equal ...

Using the laws of exponent:

We know that:

⇒ [tex]\sqrt{a} = (a)^1^/^2[/tex]  and

⇒ [tex]\sqrt[3]{a}=(a)^1^/^3[/tex]

So,

According to the question:

2 to the power of 3 over 2  = [tex](2) ^3^/^2[/tex]

Using fractional exponent concept where :  [tex]\sqrt[y]{a^x} = (a)^x^/^y[/tex]

This can be re-written as:

⇒ [tex](2^3)^1^/^2[/tex] and [tex]\sqrt{2^3}[/tex] that is equivalent to [tex]\sqrt{8}[/tex]    as  ...[tex]2^3=2\times 2\times 2=8[/tex]

Square root of 8 is our final answer.

Answer:

9 3/4, 9 3/4, 9.5, 9.125

Step-by-step explanation:

*I converted to decimal form*

9 3/4= 9.75

9.75 is greater than both 9.5 and 9.125, so therefore it is first on the list.

Next, since 9.5 is greater than 9.125, it is arranged next on the list.

9.125 is the only number left, and is clearly the smallest out of all of the numbers shown.

We want to order the given set of numbers from greatest to lest.

The correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

Let's see how to get that.

The given set is:

{9.5, 9 3/4, 9.125, 9 3/4}

Here we can see that we have two times the mixed number (9 3/4).

This can also be written as:

9 + 3/4

And we know that 3/4 = 0.75

Then:

9 + 3/4 = 9.75

Then the mixed number is the largest number.

Then comes the 9.5, and finally the 9.125

Then the correct order is:

{9 3/4, 9 3/4, 9.5, 9.125}

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Answer: if y is equal to 18 and x is equal to 72

Step-by-step explanation: 18*4=72

Answer:

Explanation:

The ball is dropped from a height of 900 centimeters.

Since the heights form a geometric sequence, you can find a common ratio between consecutive terms. This is:

Hence, the ratio of the geometric sequence is 0.7, and taking bounce 1 as the start of the sequence, the general term of the sequence is:

            [tex]a_n=800(0.7)^{n-1}[/tex]

With that formula you can find any term:

             [tex]n=1,a_1=800(0.7)^{(1-1)}=800(0.7)^0=800\\ \\ n=2,a_{2}=800(0.7)^{(2-1)}=800(0.7)=560\\ \\n=5,a_{5}=800(0.7)^{(5-1)}=800(0.4)^4=192.08[/tex]

Rounding to nearest tenth of centimeter, the ball bounces 192.1 cm high on the 5th bounce.

Answer:

time  |   distance

2       | 50

1.5     | 37.5

t        | 25*t

2       | 50

12      | 300

d/25 | d

Step-by-step explanation:

Answer:

96 blueberries

Step-by-step explanation:

x = number of muffins

Since each blueberry is going to contain 12 blueberries, we can multiply 12 by the number of muffins to get the total number of blueberries.

12x

12(8)

96

Based on the number of people dying from both causes and their relationship with each other, we can calculate that the number of people dead from cancer was 300,000 and those from accidents was 60,000.

Assuming x number of people died from accidents, the number that died from cancer would be 5 times that:

= 5x

The number of people dead from accidents is:

360,000 = 5x + x

6x = 360,000

x = 60,000 people

The number dead from cancer is:

= 5x

= 5 × 60,000

= 300,000 people

In conclusion, 60,000 died from accidents and 300,000 people died from cancer.

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Final answer:

To solve the problem, we created two equations: c = 5a and c + a = 360,000. After substituting and solving these equations, we found that 300,000 people died from cancer and 60,000 from accidents.

Explanation:

The question refers to a situation where the number of people dying from cancer is five times the number who died from accidents, and the total deaths from these two causes amounted to 360,000. To solve this, we can set up a system of equations. Let ‘c’ be the number of cancer deaths and ‘a’ the number of accident deaths. We are given:

Substituting the first equation into the second, we get:

Then we substitute the value of ‘a’ back into the first equation to find ‘c’:

Therefore, 60,000 people died from accidents and 300,000 from cancer.

Answer:

midpoint (5,4)

Step-by-step explanation:

The midpoint(M) of a segment with endpoints (x₁ , y₁) and ( x₂,  y₂) is

where x₁ = 2 and x₂ = 8

y₁ = 0 and y₂ = 8

M = [tex]\frac{x_1 + x_2}{2} ,\frac{y_1 + y_2}{2}[/tex]

M = [tex]\frac{2 + 8}{2} ,\frac{0 + 8}{2}[/tex]

M = 5 , 4

The polar form of z = -7 - 8i is:

z = 3√13 (cos 230.2° + i sin 230.2°)

Converting -7 - 8i to polar form:

The rectangular form of a complex number is given by z = a + bi, where a is the real part and b is the imaginary part. In this case, a = -7 and b = -8.

The polar form of a complex number is given by z = r(cos θ + i sin θ), where:

r is the modulus (or absolute value), which represents the distance of the complex number from the origin in the complex plane.

θ is the argument (or angle), which represents the direction of the complex number relative to the positive real axis.

1. Finding modulus (r):

r = √(a² + b²) = √((-7)² + (-8)²) = √(113) = √(13 * 9) = √13 * 3 (using factorization and perfect squares)

Therefore, r = 3√13.

2. Finding argument (θ):

θ = arctan(b/a) = arctan((-8)/(-7)) ≈ 50.2° (using the arctangent function on a calculator). However, this only gives one possible angle for the complex number.

Note: The arctangent function typically outputs values between -90° and 90°, which corresponds to Quadrant 1 or 4 in the complex plane. Since -7 - 8i lies in Quadrant 3, we need to add 180° to get the correct angle:

θ = 50.2° + 180° = 230.2°

Therefore, the polar form of z = -7 - 8i is:

z = 3√13 (cos 230.2° + i sin 230.2°)