Add the following numbers and use the checking method (add down and then add up) to make sure your answer is correct. (Copy carefully on scratch paper to work the problem.)

471
+
582

Answer:

-10 + 9x - 8

Step-by-step explanation:

4x2 + 7x - 5 subtracted from

9x2 -2x + 3

8 + 7x - 5

18 - 2x + 3

(8-18) (+7x - -2x) (-5 - +3)

-10 ( +7x +2x) (-5-3)

-10 + 9x -8

The result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3 is found by adding the additive inverse of each term in the polynomial being subtracted. Result is: 5x2 - 9x + 8.

Subtraction of Polynomials:

To find the result when 4x2 + 7x − 5 is subtracted from 9x2 − 2x + 3, first remember that subtraction of polynomials is equivalent to adding the additive inverse of each term in the polynomial being subtracted.

So, 4x2 + 7x − 5 becomes -4x2 - 7x + 5. We then add this to 9x2 − 2x + 3 term by term.

The final result is: (9x2 + -4x2) + (-2x - 7x) + (3 + 5) = 5x2 - 9x + 8

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The cube has the dimensions of:

[tex]1.26m \ by \ 1.26m \ by \ 1.26m[/tex]

A cube is a prism whose sides all have the same length. So the dimension of this cube will be given by one of its sides. For any object that is submerged in water, the volume of the displacement liquid equals the volume of the object.

[tex]For \ any \ cube \ the \ volume \ in \ terms \ of \ one \ side \ (s) \ is: \\ \\ V=s^3[/tex]

Suppose the volume of the tank when full is [tex]16m^3[/tex], so if it is 5/8 filled with water, then:

[tex]V_{5/8}=\frac{5}{8}(16) \\ \\ V_{5/8}=10m^3[/tex]

When the metal cube is placed in the tank, it is 3/4 full:

[tex]V_{3/4}=\frac{3}{4}(16) \\ \\ V_{3/4}=12m^3[/tex]

So the difference between these two volumes is the displacement volumen that equals the volume of the cube:

[tex]V=V_{3/4}-V_{5/8} \\ \\ V=12-10 \\ \\ V=2m^3[/tex]

So, the side of the cube is:

[tex]s=\sqrt[3]{2} \\ \\ \boxed{s\approx 1.26m}[/tex]

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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:

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

Answer:

look at the picture shown

Answer:

c

Step-by-step explanation:

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 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:

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

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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:

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)

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

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!

---

Topic: Geometry

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:

15

Step-by-step explanation:

2+1=3

6 divided by 3= 2

20-3-2=15

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:

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:

Answer:

[tex]13 \frac{1}{8} + 21 \frac{3}{4} = 13 \frac{1}{8} + 21 \frac{6}{8} = 34 \frac{7}{8} [/tex]

[tex]35 \frac{1}{2} - 34 \frac{7}{8} = 35 \frac{4}{8} - 34 \frac{7}{8} = 34 \frac{12}{8} - 34 \frac{7}{8} = \frac{5}{8} [/tex]

The correct answer is C.

Answer:

he had 343 pieces of candy after 22 days

Step-by-step explanation:

You can find this by first divide 10/ 115 this is equal to 15.5 to find how many candies he eats per day. Then you multiply 15.5 by 22(days) to find this answer .

Andre eats 9 pieces of candy per day. After 18 days, he had 43 pieces. By calculating his daily consumption, we can deduce that after 22 days, Andre will have 7 pieces of candy left.

The question asks us to determine how many pieces of candy Andre will have after 22 days, given the information on how many he had after 10 and 18 days.

First, let's find out how much candy Andre eats each day. After 10 days, he had 115 pieces, and after 18 days, he had 43 pieces.

Therefore, Andre will have 7 pieces of candy left after 22 days.

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

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: Reid scored 1 and Maria scored 5.

Step-by-step explanation:

5 x 2 = 10

10-4= 6

5 + 1 = 6

Final answer:

The expression 64-16 simplifies to 48, and does not need the distributive property for simplification as it is a straightforward subtraction.

Explanation:

The question is asking to use the distributive property to simplify the expression 64-16. While this expression doesn't necessarily require the distributive property as it's a simple subtraction, sometimes in mathematics we leverage distributive properties or other algebraic rules to simplify or reorganize expressions. However, if we have a closer look at the provided reference information, none of it relates directly to the expression 64-16, which simplifies to 48. Therefore, there's no need to apply the distributive property here; the expression is already in its simplest form.

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:0

Step-by-step explanation:

Because any multiples by 0 is 0

Answer:

0

Step-by-step explanation:

Since 5 x n = 0, n has to be 0 since you can’t multiply anything but 0 to get the result of 0. Hope this helped!

Answer:

Completely factor both the numerators and denominators of all fractions.

Step-by-step explanation:

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

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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:

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

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