Find A n B if A = {4, 7, 10, 13, 17) and B = {3, 5, 7, 9)

Answer:

4(5+4)

Step-by-step explanation:

Answer:

Sample Response: First, I would find that the GCF of 20 and 16 is 4. Then, I would divide both 20 and 16 by 4. Last, I would use the distributive property to write the sum as 4(5 + 4).

Step-by-step explanation:

Answer & Step-by-step explanation:

[tex]1)\\(3x+9)+(2x+4)\qquad\text{combine like terms}\\\\=(3x+2x)+(9+4)\\\\=\boxed{5x+13}\\\\===========================[/tex]

[tex]2)\\(2n+6)+(6n-2)\qquad\text{combine like terms}\\\\=(2n+6n)+(6-2)\\\\=\boxed{8n+4}\\\\===========================[/tex]

[tex]3)\\(-3x+9)+(6x-12)\qquad\text{combine like terms}\\\\=(-3x+6x)+(9-12)\\\\=\boxed{3x-3}\\\\===========================[/tex]

[tex]4)\\\left(\dfrac{1}{4}x+10\right)+\left(\dfrac{1}{2}x-7\right)\qquad\text{combine like terms}\\\\=\left(\dfrac{1}{4}x+\dfrac{1}{2}x\right)+(10-7)\\\\=\left(\dfrac{1}{4}x+\dfrac{1\cdot2}{2\cdot2}x\right)+3\\\\=\left(\dfrac{1}{4}x+\dfrac{2}{4}x\right)+3\\\\=\boxed{\dfrac{3}{4}x+3}\\\\===========================[/tex]

[tex]5)\\(3x+5)-(2x+2)\\\\=3x+5-2x-2\qquad\text{combine like terms}\\\\=(3x+2x)+(5-2)\\\\=\boxed{5x+3}\\\\===========================[/tex]

[tex]6)\\10-8=\boxed{2}\\\\===========================[/tex]

[tex]7)\\7.8x-2.5x=\boxed{6.3x}\\\\===========================[/tex]

[tex]8)\\(5.8x+10)-(3.4x+8)\\\\=5.8x+10-3.4x-8\qquad\text{combine like terms}\\\\=(5.8x-3.4x)+(10-8)\\\\=\boxed{2.4x+2}\\\\===========================[/tex]

[tex]9)\\(8x-2)-(2x+8)\\\\=8x-2-2x-8\qquad\text{combine like terms}\\\\=(8x-2x)+(-2-8)\\\\=\boxed{6x-10}\\\\===========================[/tex]

[tex]10)\\(-4x-3)-(-4x-3)\\\\=-4x-3-(-4x)-(-3)\\\\=-4x-3+4x+3\qquad\text{combine like terms}\\\\=(-4x+4x)+(-3+3)\\\\=0+0\\\\=\boxed{0}\\\\\text{You could do it shorter.}\\\text{The result will be 0 because we subtract}\\\text{ the same expressions from each other.}[/tex]

To add or subtract linear expressions, combine like terms. For example, to add 3x + 9 and 2x + 4, you combine the x terms and the constant terms separately to get 5x + 13. The same method is applied to the rest of the problems, resulting in simplified linear expressions.

Adding and Subtracting Linear Expressions:

To add or subtract linear expressions, you combine like terms, which are terms that have the same variables raised to the same power. Let's go through the problems one by one:

Sum of 3x + 9 and 2x + 4: (3x + 2x) + (9 + 4) = 5x + 13.

Add 2n + 6 and 6n - 2: (2n + 6n) + (6 - 2) = 8n + 4.

Add -3x + 9 and 6x - 12: (-3x + 6x) + (9 - 12) = 3x - 3.

Add 1/4x + 10 and 1/2x - 7: (1/4x + 1/2x) + (10 - 7) = 3/4x + 3.

Find the difference: (3x + 5) - (2x +2) = (3x - 2x) + (5 - 2) = x + 3.

Subtract 8 from 10: 10 - 8 = 2.

Subtract 2.5x from 7.8x: 7.8x - 2.5x = 5.3x.

Subtract (3.4x + 8) from (5.8x + 10): (5.8x - 3.4x) + (10 - 8) = 2.4x + 2.

Find the difference: (8x + 5) - (2x + 8) = (8x - 2x) + (5 - 8) = 6x - 3.

Evaluate (-4x -3) - (-4x -3): (-4x + 4x) - (-3 + 3) = 0x + 0 = 0.

These are the simplified forms of the linear expressions after combining like terms.

Answer:

y-intercept is 1

Step-by-step explanation:

We need to find the equation of the line first.

The gradient is found using the formula:

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

[tex]m=\frac{-1-2}{8--4}[/tex]

[tex]m=-\frac{1}{4}[/tex]

So the equation is y = [tex]-\frac{1}{4}[/tex]x + c

To find c we need to substitute the value of x and y into the equation:

-1 = [tex]-\frac{8}{4}[/tex] + c

-1 = -2 + c

1 = c

And c is the y-intercept so it is 1

Answer:

y- intercept = 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (8, - 1) and (x₂, y₂ ) = (- 4, 2)

m = [tex]\frac{2+1}{-4-8}[/tex] = [tex]\frac{3}{-12}[/tex] = - [tex]\frac{1}{4}[/tex], thus

y = - [tex]\frac{1}{4}[/tex] x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (8, - 1), then

- 1 = - 2 + c ⇒ - 1 + 2 = 1 ← y- intercept

Answer:

Y= -3x - 3

Step-by-step explanation:

-3*y= -3y

-3*3= -9

-3y - 9= 9x

-3y= 9x + 9

(9x +9)/-3

y= -3x - 3

Answer:

33,793.2 Kilometers per hour :3

Speed of rocket in kilometer in 13,049.4 miles

Given that;

Speed of rocket = 21,000 miles per hour

Miles in 1 kilometer = 0.6214 miles

Find:

Speed of rocket in kilometer

Computation:

Speed of rocket in kilometer = Speed of rocket × Miles in 1 kilometer

Speed of rocket in kilometer = 21,000 × 0.6214

Speed of rocket in kilometer = 13,049.4 miles

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Answer:

A. 7x + 6y

Step-by-step explanation:

49x² + 84xy + 36y²

Factoring the perfect square:

(7x + 6y)²

7x + 6y is a factor.

Final answer:

The correct binomial factor of the quadratic expression  [tex]49x^2 + 84xy + 36y^2 \ is \ 7x + 6y[/tex], which corresponds to option A.

Explanation:

To determine which binomial is a factor of the quadratic expression  [tex]49x^2 + 84xy + 36y^2,[/tex]we can try to factor the expression by grouping or using the factoring technique of a perfect square trinomial. On inspection, we see that 49, 84, and 36 are all multiples of 7, and also the expression resembles the square of a binomial.

The given expression can be written as:

[tex](7x)^2 + 2(7x)(6y) + (6y)^2[/tex]

This is the expanded form of the square of a binomial:

[tex](7x + 6y)^2 = 49x^2 + 84xy + 36y^2[/tex]

Hence, the factored form of the given expression is  [tex](7x + 6y)^2[/tex], which means that 7x + 6y is indeed a factor. So, the correct answer is option A.

Answer:

 The volume of a baseball is about 13.39 cubic inches.

Step-by-step explanation:

Answer:

[tex]3x+13y=14\\\\6x+11y=-2[/tex]

Step-by-step explanation:

We have to check [tex](-4,2)[/tex] satisfies which system.

First System:

[tex]3x+13y=14\\\\6x+11y=-2\\\\Substitute\ (-4,2)\ in\ the\ equations\\\\3\times (-4)+13\times (2)=14\\\\-12+26=14\\\\14=14\\\\6\times (-4)+11\times (2)=-2\\\\-24+22=-2\\\\-2=-2\\\\(-4,2) \ satisfies\ this\ system\ of\ equation.\ Hence\ (-4,2)\ is\ the\ solution\ of\ this\ system.[/tex]

Second System:

[tex]4x+5y=12\\\\8x+3y=-4\\\\Substitute\ (-4,2)\\\\4\times (-4)+5\times (2)=-6\\\\-6\not=12\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Third System:

[tex]5x+4y=12\\\\7x+8y=12\\\\Substitute\ (-4,2)\\\\5\times (-4)+4\times (2)=-12\\\\-12\not =12\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Fourth System:

[tex]10x+3y=8\\\\17x+6y=10\\\\Substitute\ (-4,2)\\\\10\times (-4)+3\times (2)=-34\\\\-34\not =8\\\\(-4,2)\ does\ not\ satisfies\ the\ system\ hence\ it\ in\ not\ a\ solution\ of\ this\ system.[/tex]

Answer:

3x+13y=14\\\\6x+11y=-2

Step-by-step explanation:

Question:

What is the measure of angle X?

The image of the measurements is attached below:

Answer:

The measure of angle x is 83°

Explanation:

Since, Vertical angles have equal measure,

Let us consider that the angle opposite to 41° is ∠y and they are equal.

i.e, ∠y = 41°

Since, the angles in a straight line add up to 180°, we have,

∠x + ∠y + 56° = 180°

Substituting the value ∠y = 41°, we have,

∠x + 41° + 56° = 180°

Adding the terms, we get,

∠x + 97° = 180°  

Subtracting both sides by 97°, we get,

∠x = 83°

Thus, the measure of ∠x is 83°

Answer:

83 degrees

Step-by-step explanation:

I took the test

There was a decrease of 20% in membership from October to November.

Step-by-step explanation:

Step 1; To find the percent by which the running clubs membership decreased we must find the difference between the number of members in October and the number of members in November. The number of members in the club in October was 25 whereas it reduced to 20 in the month of November.

Difference in members = Number of members in October -Number of members in November = 25 - 20 = 5

Step 2; To find the percent decrease in number of members in the running club, we divide the difference in number of members by the number of members in November . We multiply this value by 100 to get it in terms of percentage.

Percent decrease in number of members =(Difference in members / number of members in November) *100

                                                                      = (5/25) * 100 = 0.20 * 100 = 20%

So number of members in the club decreased by 20% from October to November.

Answer:

a)  1 quart

b)  2 quarts

c)  33.33 % of the brown paint is made of blue paint

Step-by-step explanation:

6 quarts brown paint =  1/2 of yellow paint and 1/2 violet paint

violet paint = 1/3 red paint 2/3 blue paint

then

6 quarts brown paint =  1/2 of yellow paint and 1/2 (1/3 red paint and 2/3 blue paint)

or

6 quarts brown paint = 1/2 of yellow paint , (1/2*1/3) red paint and (1/2*2/3) blue paint

6 quarts brown paint = 1/2 of yellow paint , 1/6 red paint and 1/3 blue paint

then

a) he uses 1/6 of 6 quarts to make red paint = 1/6*6 = 1 quart

b) he uses 1/3 of 6 quarts to make red paint = 1/3*6 = 2 quarts

c) brown paint is made with 1/3 of blue paint = 33.33 % of the brown paint is made of blue paint

The answer is D. 94.4^2

((Hopefully I helped))

Answer:

2/3

Step-by-step explanation:

-1 - 3 = - 4

-3 - 3 = - 6

-4/-6 = 2/3

[tex]\text{Use the slope formula:}\\\\\frac{y2-y1}{x2-x1}\\\\\text{Plug in your coordinates:}\\\\\frac{-1-3}{-3-3}\\\\\text{Solve:}\\\\\frac{-1-3}{-6}\\\\\frac{-4}{-6}\\\\\boxed{\frac{4}{6}}[/tex]

Answer:

(3,-4)

Step-by-step explanation:

Answer:

3.28

Step-by-step explanation:

You want to find the discount price. Set a relation to where the well i cant really explain it but do 20/100 = x/16.40  because 100% of the price is 16.40 dollars. You want to find 20% of that so you find what you multiply to 100 to get 16.40 which is 6.0975. Then you do the same thing for the 20% to find 20% of the price which is 3.28. sorry im trash at explaining but i hope i helped.

Answer:

3.28

Step-by-step explanation:

im pretty darn sure this is right lol

Answer:

if $1 coin is for 4 presidents ,then

the number of years it will take to release the the 36 first presidents is given by[tex]\frac{36}{4}=9 years[/tex]

Step-by-step explanation:

step 1: you lay down preliminaries

step 2: you divide 36 presidents by 4 presidents per year, the result is the number of years it will take to publish the first 36 presidents.

Answer: 32767 pennies

Answer:

(b)  (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) =  {x | x = 0}

Step-by-step explanation:

Here, the given expression is : {x | x = 0}

So, the ONLY element in the given set = {0}

Now, take each option and solve the given expression:

(a)  x + 1 < -1

Adding -1 BOTH sides, we get:

x + 1 -1 < -1  -1

or, x < - 2 ⇒ x = { -∞ , .... , -4,-3}

Also,   x + 1 < 1

Adding -1 BOTH sides, we get:

x + 1 -1 < 1  -1

or, x <0 ⇒ x = { -∞ , .... , -4,-3,-2,-1}

So, (x + 1 < -1) ∩ (x + 1 < 1) =  { -∞ , .... , -4,-3}∩ { -∞ , .... , -4,-3,-2,-1}  

=  { -∞ , .... , -4,-3}

⇒ (x + 1 < -1) ∩ (x + 1 < 1) ≠ {0}

Similarly, solving

(b) (x + 1 ≤ 1) ∩ (x + 1 ≥ 1)

(x + 1 ≤ 1) =  x≤ 0 =   { -∞ , .... , -4,-3,-2,-1, 0}

(x + 1 ≥ 1) =  x ≥ 0 =  {0,1,2,3,... ∞}

⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = {0}

(b)(x + 1 < 1) ∩ (x + 1 > 1)

(x + 1 < 1) =  x <  0 =   { -∞ , .... , -4,-3,-2,-1}

(x + 1 > 1) =  x  > 0 =  { 1,2,3,... ∞}

⇒ (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) = Ф

Hence,  (x + 1 ≤ 1) ∩ (x + 1 ≥ 1) =  {x | x = 0}

(x + 1 ≤ 1) ∩ (x + 1 ≥ 1) =  {x | x = 0}

Answer:

13 pins

Step-by-step explanation:

2x=Florida

x=Virginia

39=2x+x

39=3x

÷3 ÷3

13=x

26 pins are from city V.

Let,

x = number of pins from city F.

y = number of pins from city V.

According to the question:

[tex]x+y=39\\y = 2x[/tex]

Solving them, [tex]x = 13, y=26[/tex]

So 26 pins are from city V.

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Answer:

its increasing by 2,u can think of it as taking away the 2 in the ones place and skip counting by 2 like your in the ones place

Answer:

A line plot graph will show the repetition or frequency of information or value in a number line.

This line plot graph can be used to compare numbers over a certain limit. It is a simple and quick way to order data.

Steps to draw plot graph:-

Ascending order: [tex]1\frac{1}{2}, 2\frac{1}{2} ,2\frac{3}{4} ,3,3\frac{1}{2}, 3\frac{3}{4}.\\[/tex]

refer the diagram below for the answer.

Answer:29876

Step-by-step explanation:

Entire population is 100%

Male is 100%-45%

55%x54320=29876

Answer:

29,876 males

Step-by-step explanation:

If 45% of 54320 population is female. The population of male is calculated below.

The total population is 100% and female is 45%. Thus: 100% - 45% = 55%.

Percentage of male population is 55%. Hence, 55% of 54320 is calculated thus:

[tex] \frac{55}{100} \times 54320[/tex]

[tex] = 0.55 \times 54320[/tex]

[tex] = 29876[/tex]

Therefore, population of male if total population is 54320 is 29,876.

Check,

Female population percentage + male population percentage:

45% + 55% = 100%

24,444 + 29,876 = 54,320

Answer:

x + 2y + 2

Step-by-step explanation:

1. Simplify 3 − 2 to 1

1 · x + 2y + 2

2. Simplify 1 · x to x

x + 2y + 2

The equation of the line is [tex]y=-\frac{3}{4}x+\frac{1}{4}[/tex]

Step-by-step explanation:

The equation of a line can be written using the following form

[tex]y-y_0 = m(x-x_0)[/tex]

where

m is the slope of the line

[tex](x_0,y_0)[/tex] are the coordinates of a point lying on the line

For the line in this problem, we know that:

[tex]m=-\frac{3}{4}[/tex] is the slope

[tex](x_0,y_0)=(-5,4)[/tex] are the coordinates of the point

Therefore, substituting into the equation,

[tex]y-4=-\frac{3}{4}(x-(-5))[/tex]

And re-arranging the equation we get:

[tex]y-4=-\frac{3}{4}(x+5)\\y-4=-\frac{3}{4}x-\frac{15}{4}\\y=-\frac{3}{4}x+(4-\frac{15}{4})\\y=-\frac{3}{4}x+\frac{1}{4}[/tex]

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Answer:

A. $3770

Step-by-step explanation:

The correct answer must be $3770 (not $3270), checking accounts and savings accounts are liquid assets. However, cars are not liquid assets because liquid assets are things that can be quickly turned into cash without losing much if any of their inherent value. In this case, the retirement account is not a liquid asset as it is designed to hold your money until retirement age, and given that Cesar is 35 years old so he has not reached retirement age.

Answer:

the answer is a 3770.

Step-by-step explanation:

Step-by-step explanation:

Given,

The length of a cell phone(l) = 82 mm  and

The width of a cell phone(b) = 36 mm

Find, the ratio of the width to the​ length of a cell phone = ?

∴ The ratio of the width to the​ length of a cell phone

= 36 mm : 82 mm

= 36 : 82

Divided by 2, we get

= [tex]\dfrac{36}{2}[/tex] : [tex]\dfrac{82}{2}[/tex]

= 18 : 41

Thus, the ratio of the width to the​ length of a cell phone is 18 : 41.

Step-by-step explanation:

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

7/8 x 8/3 = ?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

7 x 8

8x3

56/24

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 56 and 24 using

GCF(56,24) = 8

56/8 = 7

24/8 = 3

The fraction 7/3 is the same as 7 divided by 3

Convert to a mixed number using long division for 7 ÷ 3 = 2R1, so

Therefore:

7/3 = 2 1/3

2 1/3

The required quotient is 7/3 when 7/8 is divided by 3/8.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

The division operation is given in the question following as:

⇒ 7/8 ÷ 3/8

We have to determine the quotient when 7/8 is divided by 3/8

As per the given question, we have

⇒ 7/8 ÷ 3/8

⇒ (7/8) / (3/8)

Reciprocal the terms in the numerator, and we get

⇒ (7/8) × (8/3)

Apply the multiplication operation,

⇒ 56/24

Reduce the above fraction to the simplest form

⇒ 7/3

Therefore, the required quotient is 7/3 when 7/8 is divided by 3/8.

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Answer:

The diameter of the arena is 18.3 meters.

Step-by-step explanation:

        As,  14 laps = [tex]\frac{1}{2}[/tex] mile

        so, 1 lap = [tex]\frac{1}{28}[/tex] mile                               ( ∵14 × 2 = 28)

For the horse completing one lap it completes the perimeter of the circle.

            perimeter (P) =  [tex]\frac{1}{28}[/tex] mile

let diameter of that circle be represented as d,

                                  P=  [tex]\pi[/tex] × d

                            or,  [tex]\frac{1}{28}[/tex]  = [tex]\pi[/tex] × d

                            or, d= [tex]\frac{1}{28\pi }[/tex]

                              ∴ d= 18.3 meters.

The diameter of the arena is 18.3 meters.