Consider the function f(x)=x3+6x2−20x+450.

What is the remainder if f(x) is divided by (x−12)? Report your answer as a number only. Do not include (x−12) in your answer.

Answer:

8 because 32÷8=4,48÷8=6,80÷8=10

Answer:

  the numbers are 7 and 11

Step-by-step explanation:

If you add the smaller to the sum of numbers, you have the sum of the greater and twice the smaller. That is ...

  18 + smaller = 25

  smaller = 25 -18 = 7

  larger = 18 -7 = 11

The two numbers are 7 and 11.

_____

If you like, you can write two equations. Let x and y represent the smaller and larger numbers, respectively.

  x + y = 18

  2x + y = 25

Subtract the first equation from the second:

  (2x +y) -(x +y) = (25) -(18)

  x = 7

  y = 18-x = 18-7 = 11

The numbers are 7 and 11.

The fraction form of the number 10.666666667 is,

⇒ 32/3

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction.

Given that,

A number is,

⇒ 10.6666666667

For the fraction form,

Let us assume that,

⇒ x = 10.666666667 .. (i)

Multiply by 10 on both sides,

⇒ 10x = 106.666666667  .. (ii)

Subtract (ii) from (i);

⇒ 10x - x = 106.666666667 - 10.66666667

⇒ 9x = 96

Divide 9 on  both sides,

⇒ x = 96/9

Or, it can be written as,

⇒ x = 32/3

So, the fraction form is, 32/3

To learn more about the fraction visit:

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Final answer:

To convert the decimal 10.6666666667 to a fraction, we write it as the sum of 10 and the repeating decimal 0.6666666667. The repeating decimal equates to 2/3 after simplification, leading to the mixed number 10 2/3 or the improper fraction 32/3.

Explanation:

To convert the decimal 10.6666666667 to a fraction, we need to express it as the sum of its whole number part and its fractional part. The whole number part is 10, and the fractional part is 0.6666666667.

First, let's focus only on the fractional part. To turn 0.6666666667 into a fraction, notice that it's a repeating decimal. If we denote the repeating part by 'x', the equation will be:

x = 0.6666666667

Multiplying by 10 gives:

10x = 6.6666666667

Subtracting the original equation from this new equation:

9x = 6

Now, we solve for 'x':

x = 6/9

However, this fraction can be simplified to:

x = 2/3

Therefore, the fraction form of 10.6666666667 is 10 2/3, which can also be written as an improper fraction:

The value of x is –3.

Solution:

Given statement:

4 and Start Fraction 3 Over 10 End Fraction minus (2 and two-fifths x + 5 and one-half) = one-half (negative 3 and three-fifths x + 1 and one-fifth)

Let's convert this into algebraic expression.

[tex]$4\frac{3}{10} -\left(2\frac{2}{5}x+5\frac{1}{2}\right)=\frac{1}{2}\left(-3\frac{3}{5}x+1\frac{1}{5}\right)[/tex]

First convert mixed fraction into improper fraction.

[tex]$\frac{43}{10} -\left(\frac{12}{5}x+\frac{11}{2}\right)=\frac{1}{2}\left(-\frac{18}{5}x+\frac{6}{5}\right)[/tex]

[tex]$\frac{43}{10} -\frac{12}{5}x-\frac{11}{2}=-\frac{18}{10}x+\frac{6}{10}[/tex]

Now, take LCM and make the denominators same.

LCM of 2, 5, 10 = 10

[tex]$\frac{43}{10} -\frac{12\times2}{5\times2}x-\frac{11\times5}{2\times5}=-\frac{18}{10}x+\frac{6}{10}[/tex]

[tex]$\frac{43}{10} -\frac{24}{10}x-\frac{55}{10}=-\frac{18}{10}x+\frac{6}{10}[/tex]

Arrange like terms one side of the equation.

[tex]$\frac{18}{10}x -\frac{24}{10}x=\frac{6}{10}-\frac{43}{10}+\frac{55}{10}[/tex]

[tex]$\frac{18x-24x}{10} =\frac{6-43+55}{10}[/tex]

[tex]$\frac{-6x}{10} =\frac{18}{10}[/tex]

[tex]$-6x=\frac{18\times10}{10}[/tex]

[tex]$-6x=18[/tex]

Divide both sides of the expression by –6, we get

⇒ x = –3

Hence the value of x is –3.

Answer:

-3

Step-by-step explanation:

Answer:

B. Less than a day

Step-by-step explanation:

From the question, the circuit board manufacturer produces 2000 board per hour.

Let x be the number of hours it will take to produce 16500 boards .

That’s

2000 boards = 1 hour

16500 boards = x hour

Cross multiply

xhour x 2000 = 1 x 16500

x hour = 16500/2000

x hour = 8.25 hours

8.25 hours is less than a day

Answer:

Step-by-step explanation:

The answer is B) B :)

Answer:

The answer is B

Step-by-step explanation:

According to USA Test prep it says so, but i didn't quite get the explanation so bear with me. Thank you :)(:

Answer:

The area of rectangle ABCD is [tex]18\ units^2[/tex]

Step-by-step explanation:

Plot the figure to better understand the problem

we have the vertices

A(-4, -2), B(-2, -2), C(-2, 7), D(-4, 7)

see the  attached figure

The area of the rectangle is equal to

[tex]A=LW[/tex]

where

L is the length

W is the width

In this problem we have

[tex]L=BC=7-(-2)=9\ units[/tex] ---> difference of the y-coordinates

[tex]W=AB=-2-(-4)=2\ units[/tex] ---> difference of the x-coordinates

substitute

[tex]A=(9)(2)=18\ units^2[/tex]

Final answer:

The area of rectangle ABCD is calculated as 18 square units by finding the product of its width (2 units) and height (9 units).

Explanation:

The area of rectangle ABCD with vertices A(-4, -2), B(-2, -2), C(-2, 7), and D(-4, 7) can be calculated by finding the lengths of the sides AB and BC. The length of AB (width) is the difference in the x-coordinates of A and B, which is |-2 - (-4)| = 2.

The length of BC (height) is the difference in the y-coordinates of B and C, which is |7 - (-2)| = 9. Therefore, the area of rectangle ABCD is the product of the width and height, which is 2 * 9 = 18 square units.

Answer:

look at the picture shown

Answer:

  -66, 80

Step-by-step explanation:

Let x represent the first number. Then the second number is 14-x, and the difference is ...

  x - (14-x) = -146

  2x = -132 . . . . . . add 14, collect terms

  x = -66 . . . . . . . . the first number

  14-x = 14-(-66) = 80 . . . . . . the second number

Answer:

-66 & 80

Step-by-step explanation:

Let the two numbers be x and y

x + y = 14 (1)

x - y = -146 (2)

Adding (1) & (2),

2x = -132

x = -66

y = 14 - x = 14 - (-66) = 14 + 66

y = 80

Answer:

likewise your friend is two times older than u and u r two times younger than him then assume the given sum as 120 so your friend"s age will be 2x and ur age will be y so the sum obtained Is 2x+y=120

Answer: Alex had 8 apples to share Amon him and three of his friends. What is 8 / 4 ? It is 2

Step-by-step explanation:

Hi there (◕‿-)

Since both equations are equal to y, they must equal each other. So set them to equal each other.

28 + 0.05x = 25 + 0.07x      (✿ ♥‿♥)

Let's start by subtracting 25 from both sides!

3 + 0.05x = 0.07x (28-25=3, 25-25=0)

Now let's subtract 0.05 from both sides   Ｏ(≧▽≦)Ｏ

3 = 0.02x

We need this x by itself, so let's get rid of it. Do this by divide both sides by 0.02 （ ´_⊃｀）

150 = x

So x = 150. Let's test this. Substitute 150 in for x in both equations! ＼（＾○＾）人（＾○＾）／

28+0.05(150) = 25+0.07(150)

28 + 7.5 = 25 + 10.5 (0.05*150=7.5, 0.07*150 = 10.5)

35.5 = 35.5

It works! (ﾉ◕ヮ◕)ﾉ*:･ﾟ✧

So x = 150

363 gallons of water is in Tank A

Solution:

Water tank A has a capacity of 550 gallons and is 66% full

Let, w = 550

p = 66 % = 0.66

The percent equation is: a = p . w

where,

"a" is the gallons of water in Tank A

p is the percent in fraction or decimal form

w is the capacity of tank A

Therefore,

[tex]a = 0.66 \times 550\\\\a = 363[/tex]

Thus 363 gallons of water is in Tank A

Answer:

13.6 years

Step-by-step explanation:

From the question;

We are needed to determine the time it took for the money to reach the given amount;

[tex]A=P(1-\frac{r}{100})^n[/tex]

Where n is the interest periods;

Therefore;

[tex]12800=7500(1-\frac{4}{100})^n[/tex]

Dividing both sides by 7500, we get;

[tex]1.7067=(1-\frac{4}{100})^n[/tex]

[tex]1.7067=(1.04)^n[/tex]

Introducing logarithms on both sides;

[tex]log1.7067=log(1.04)^n\\nlog1.04=log1.7067\\n=\frac{log1.7067}{log1.04} \\n=13.63[/tex]

Thus, n=13.6 years

Thus, it would take 13.6 years for the invested money to accumulate to 12800 dollars

father is 50

Julia's age : a year-old

Wendy is twice the age of Julia

= > Wendy = 2a year-old

Dad's age : b year-old

" The man is now five times as old as Wendy " b / 2a = 5 <=> b = 10a

" In four years he will be six times as old as Julia " :

( B + 4 ) / (a + 4 ) = 6 + 4 = 6. <=> b (a + 4 )

<=> B = 6a +20

I have two equations :

6a + b = 20

b = 10a

= > 10a = 6a + 20 - > a = 5

- > B = 10a = 50

Answer:

50

Step-by-step explanation:

Answer:

seems like you need to learn how to do your own work.  

Step-by-step explanation:

Ask instructor for help or go back to the book

The value of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]

Explanation:

The expression is [tex]12abx^{2} -(9a^{2} -8b^{2} )x-6ab=0[/tex]

Multiplying the term x withing the bracket, we get,

[tex]12abx^{2} -9a^{2} x+8b^{2} x-6ab=0[/tex]

Grouping the terms, we have,

[tex](12abx^{2} -9a^{2} x)+(8b^{2} x-6ab)=0[/tex]

Taking out the common terms in each bracket, we get,

[tex]3ax(4bx -3a)+2b(4bx-3a)=0[/tex]

Simplifying, we get,

[tex](3ax+2b)(4bx -3a)=0[/tex]

Equating each term to zero, we get,

[tex]\begin{aligned}3 a x+2 b &=0 \\3 a x &=-2 b \\x &=-\frac{2 b}{3 a}\end{aligned}[/tex]   and [tex]\begin{aligned}4 b x-3 a &=0 \\4 b x &=3 a \\x &=\frac{3 a}{4 b}\end{aligned}[/tex]

Hence, the values of x is [tex]\frac{3a}{4b}[/tex] and [tex]-\frac{2b}{3a}[/tex]

Answer:

0.25

Step-by-step explanation:

2^-2=0.25

The question is about calculating the center of mass for a triangular sandwich with a semicircular bite and determining the volume and uncertainty for a rectangular box.

The question asked concerns finding the center of mass of a triangular sandwich after taking a semicircular bite out of it, which is a problem related to geometry and mass distribution. When solving such problems, one would typically have to calculate the area of the original triangle and the area of the semicircular bite, then find the centroid of both shapes.

For the rectangular box's volume and uncertainty, this is a measurement and uncertainty calculation question. Here, one must apply the formula for the volume of a rectangle (length  imes width  imes height) and use the rules of propagation of uncertainty to calculate the overall uncertainty of the volume measurement.

Explanation of the number of generations and minutes it would take for gossip to reach everyone in a school.

The total number of students in the school: 2016

Number of students each person tells: 4

Generations needed: Log base 4 of 2016 is approximately 4.033.

Number of minutes: Each generation is 10 minutes, so 4.033 generations would be approximately 40.33 minutes.

Graph: As the number of generations increases, the number of people reached grows exponentially.

Answer:

option c - 12 ab

Step-by-step explanation:

Two numbers are , 24 a³b and 36 a b².

The meaning of G C F between two number is that greatest number which divide both the number.

We will factorize , 24 a³b and 36 a b² and take out the common factors to determine their G CF.

24 a³ b= 2×2×2×3×a×a×a×b  

36 a b²=2×2×3×3×a×b×b

G C F(Greatest common factor)=2×2×3×a×b

please mark me brainliest :)

Answer:

look at the picture shown

Answer:

c

Step-by-step explanation:

Answer:

5.75

Step-by-step explanation:

We can first off make them improper fractions. They're easier to deal with.

1 2/4 = 6/4.

3 5/6 = 23/6

6/4 * 23/6.

Multiply numerators: 23 * 6 = 138.

Multiply denominators: 4 * 6 = 24.

138/24.

Simplify: 23/4

The true statement about triangle is: b. QR = 5.9 cm.

To understand what it means for two triangles to be congruent. When two triangles are congruent (△PQR ≌ △WVX), all corresponding sides and angles are equal.

Given:

For the triangles to be congruent, the corresponding sides and angles must be equal. Let's match the corresponding parts:

Given this correspondence:

QR must be equal to WX, so QR = 5.9 inches (Option b).

m∠R must be equal to m∠W, so m∠R = 28° (Option c).

m∠Q must be equal to m∠X, so m∠Q = 47° (Option d).

However, m∠R and m∠Q cannot both be correct choices simultaneously; only one can be correct because they refer to the same angle in each corresponding pair QR = 5.9 inches is the correct choice considering the triangle sides.

Complete question

In triangle VWX, VW=4.5 inches, WX=5.9 incheß, m∠ W=28° , and m∠ X=47°. If △ PQR≌ △ WVX , which statement is true?

a. QR=4.5cm

b. QR=5.9cm

c. m∠ R=28°

d. m∠ R=47°

Answer:

15

Step-by-step explanation:

2+1=3

6 divided by 3= 2

20-3-2=15

Answer:

Completely factor both the numerators and denominators of all fractions.

Step-by-step explanation:

Answer:

1.Therefore the solution of given system is (3,4)

2.Therefore the solution of given system is (-1,2)

Step-by-step explanation:

1.

Given the system

2x +3y =18...........(1)

-2x+5y =14...........(2)

Adding the equation (1) and (2)

2x+3y-2x+5y= 18+14

⇔8y = 32

⇔[tex]y = \frac{32}{8}[/tex]

⇔y = 4

Putting the value of y in equation (1)

2x + 3. 4=18

⇔2x+12 =18

⇔2x = 18-12

⇔2x = 6

⇔x =3

Therefore the solution of given system is (3,4)

2.

Given the system

3x +4y = 5..........(a)

2x +7y =12...........(b)

Equation (a) ×2 - equation (b)×3

2(3x+4y)- 3(2x+7y) = 2.5 -12.3

⇔6x + 8y -6x -21y = 10-36

⇔ -13y = -26

⇔[tex]y=\frac{-26}{-13}[/tex]

⇔y = 2

Putting the value of y in equation (a)

3x +4.2 =5

⇔3x = 5 -8

⇔3x = -3

⇔x = -1

Therefore the solution of given system is (-1,2)

Answer:

$256

Step-by-step explanation:

Alright so,

There are 7 days in a week and you're only working 4 of those days. In one week you would make $32 since 4*8=32. (4 being the days you work and 8 being the amount you get a day)

There are about 4 weeks in one month and 4*2=8, therefore there are 8 weeks in 2 months.

Remember, in one week you make $32. What you can do now is multiply, it's easy work and you'll get it fast:)

32x8=$265

Hope it helps!

Answer:

256

Step-by-step explanation:

The least possible number of coins Pirate Jack has, is 81 coins.

Step-by-step explanation:

Given,

When the coins are divided into 7 equal piles, 4 coins are left.

When the coins are divided into 11 equal piles, 4 coins are left.

We will take LCM of both 7 and 11.

7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, ....

11 = 11, 22, 33, 44, 55, 66, 77, 88, ...

The least common multiple of 7 and 11 is 77.

As 4 coins are left, therefore, we will add those coins.

Total possible coins = 77+4 = 81

The least possible number of coins Pirate Jack has, is 81 coins.

Keywords: LCM, addition

Learn more about addition at:

#LearnwithBrainly

Answer:

The rug's area is equal to 49π m².

General Formulas and Concepts:
Geometry

Area of a Circle Formula: A = πr²

Step-by-step explanation:

Step 1: Define

Identify given.

r = 7 m

Step 2: Find Area

∴ the family room circular rug with a circle radius of 7 meters has an area of 49π m². And we have solved our problem!

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Topic: Geometry