Choose the solution(s) of the following system of equations:
x² + y² = 6
x² - y=6

1. distributive property

2. combine like terms

3. addition property of equality

4. division property of equality

Given that,

Kelsey solved the following equation:

[tex]7x - \frac{1}{2}(8x+2) = 6[/tex]

By distributive property,

a(b + c) = ab + bc

Therefore,

[tex]7x - (\frac{1}{2} \times 8x)+( \frac{-1}{2} \times 2)= 6\\\\7x - 4x - 1 = 6[/tex]

Combine the like terms

7x - 4x - 1 = 6

3x - 1 = 6

Addition property of equality

The property means that when we add the same number to both sides of an equation, the sides remain equal

3x - 1 = 6

Add 1 on both sides

3x - 1 + 1 = 6 + 1

3x = 7

Division property of equality

The Division Property of Equality means that when we divide both sides of an equation by the same non zero number, the sides remain equal

3x = 7

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{7}{3}\\\\x = \frac{7}{3}[/tex]

Thus the correct justifications Kelsey used to solve this equation is:

1. distributive property. 2. combine like terms. 3. addition property of equality. 4. division property of equality

Answer:

I took the test it is  1. Distributive property 2. Combine like terms 3. Addition property of equality 4. Division property of equality

Answer:

True because a right angle can't exist with any parallel lines.

Answer:

true hope this helped.

Step-by-step explanation:

Answer:

37

Step-by-step explanation:

Students who applied or a scholarship=95

Of that:

Men= 41

Minorities= 36

Minorities who are women= 19

Minorities who are men = 36-19=17

Women+ Minorities who are women=Students who applied or a scholarship-(Men+Minorities who are men)

x + 19=95-(41+17)

x+19=95-58

x+19=37

x= 37-19

x=18

Women who are NOT minority=18

Total women=Minorities who are women+Women who are NOT minority

Total women=18+19

Total women=37

By understanding the problem as a basic arithmetic problem, we determine there are 54 women who applied for the scholarship by subtracting the number of men (41) from the total number of students (95).

To resolve the question, 'how many women applied for the scholarship', it's essential to understand the problem as a basic addition and subtraction problem. The numbers provided in the question give us initial points. It's stated that there are 41 men who applied, and if there are 95 students in total, we can calculate the total women by subtracting the number of men from the total. So, 95 total students - 41 men = 54 women. This calculation gives us the number of women that applied for the scholarship.

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The inequality that represent age of marcus is:

[tex]24\geq 6+m\geq 9[/tex]

The possible values for age of Marcus is:

m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

Solution:

Given that,

The sum of ages of Kevin and Marcus was at least 9 years but was at most 24 years

Kevin is 6 years old

Let "m" be the age of Marcus

Thus we frame a inequality as:

[tex]24\geq \text{ sum of ages } \geq 9[/tex]

at least 9 years means that "greater than or equal to 9"

at most 24 years means "less than or equal to" 24

From given,

Sum of ages = kevin age + marcus age

Sum of ages = 6 + m

Thus the inequality is:

[tex]24\geq 6+m\geq 9[/tex]

Solve the inequality

[tex]\mathrm{If}\:a\ge \:u\ge \:b\:\mathrm{then}\:a\ge \:u\quad \mathrm{and}\quad \:u\ge \:b\\\\24\ge \:6+m\quad \mathrm{and}\quad \:6+m\ge \:9\\\\Solve\ them\ separately[/tex]

[tex]24\ge \:6+m\\\\\mathrm{Switch\:sides}\\\\6+m\le \:24\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\le \:24-6\\\\\mathrm{Simplify}\\\\m\le \:18[/tex]

Now solve another inequality

[tex]6+m\ge \:9\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\6+m-6\ge \:9-6\\\\\mathrm{Simplify}\\\\m\ge \:3\\\\\mathrm{Combine\:the\:intervals}\\\\m\le \:18\quad \mathrm{and}\quad \:m\ge \:3\\\\\mathrm{Merge\:Overlapping\:Intervals}\\\\3\le \:m\le \:18[/tex]

[tex]24\ge \:6+m\ge \:9\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:3\le \:m\le \:18\:\\ \:\mathrm{Interval\:Notation:}&\:\left[3,\:18\right]\end{bmatrix}[/tex]

Thus possible values for age of Marcus is:

m = 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

answer: $215.10

the TV's original price is $239, but with 10% off, it is now 90% of the original price. therefore we have to find 90% of 239:

0.90*239=215.10

Answer:

215.10 here ya go

Answer:

61300

Step-by-step explanation:

Slope is the change in Y over the change in. X

Using two of the given points:

Slope = 70-45 / 25-10

Slope= 25/ 15

Slope = 5/3

Answer:

that fraction is an improper fraction I think.

Answer: A. When it comes after the decimal point, as in 4.000

Step-by-step explanation: If there are no other numbers after the zeros, there is no reason for them to be place holders. Zeros in decimals act as place holders such as in 4.09 or 4.0009. This actually does change the value of the decimal but 4.000 is just the same as a regular old 4. Hope this helps!

Answer:

9.235

Step-by-step explanation: There you g. Hope it helps!

Answer:

Step-by-step explanation: It B

-3 + 3 = 0

Answer:

2

Step-by-step explanation:

If one bag of stones is sufficient to fill the distance of 4 yards , then to complete 5.5 yards of pond boundary, 2 bags are enough.

Distance is a physical quantity measuring the length over an area covered by an object or place. The change in distance is called displacement. For  a moving object the distance is the product of its speed and time take to cover the distance.

Distance can be measured in meter, kilometer, feet, yard etc. These units can be interchanged in between based on the relationship between them.

It is given that the diameter of the circular fish pond is 5.5 yards. One bag of stones can fills a distance of 4 yards. of the pond. Then two bag of stones is enough  to fill  up the total distance of 5.5 yards.

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Answer:

Step-by-step explanation:

i'm pretty sure that you will have to add it.

so, when we add two fractions such as 3/4 + 3/4, we make sure that the denominators (the bottom numbers) are the same and then we simply add the numerators (the  top numbers).

in this problem, the denominators are the same so we will simply add 3+3 which equals to 6/4. the denominator will remain the same.

               answer:

                      3/4 + 3/4    =   6/4

i hope this is helpful.

The required weight of the candy box is 3 pounds.

Given that,
A balance scale was in perfect balance when Jane placed a box of candy on one pane of the balance and 3/4 of the same-sized candy box together with 3/4 pound weight on the other pane.
To determine how much the full box of candy weighs.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the weight of the candy box be x,
3/4 of the same-sized candy box
weight = 3/4 pound
x = 3/4x + 3/4
x / 4 = 3/4
x = 3

Thus, the required weight of the candy box is 3 pounds.

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Answer:

3/8 and 1/5

Step-by-step explanation:

If the scale factor is 1 then it stays the same. If it's larger than 1 then is gets larger, so the fractions, which are smaller than 1, would make it shorter.

hope this helped :)

Answer:1/5 and 3/8

Step-by-step explanation:

Answer:

Step-by-step explanation:

hello :

a)

let  f(x) = y     so : x = g(y)

in expression = f(x) =3x+12

means : y = 3x +12  calculate : x

3x = y -12

x = (1/3)y - 4

the inverse is : g(x) = (1/3)x - 4

b)f(g(-2) = f(-14/3)

because: g(-2) = (1/3)(-2)-4 = -2/3-4 = -14/3

so : f(g(-2) = f(-14/3)=3(-14/3)+12 = - 2

1. The inverse of the function is g(x) = (1/3)x - 4.

3. The value of f(g(–2)) is -2.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)= 3x+ 12

1. let  f(x) = y then x = g(y)

y = 3x+ 12

y- 12 = 3x

x= y/3 + 4

So, the inverse of the function is g(x) = (1/3)x - 4.

2. For showing the function are inverse we have to that  

(fog)(x) = f(g(x)) =x and (gof)(x) =g(f(x)) = x

Take (fog)(x) = f(g(x))

= f( (1/3)x - 4.)

= 3 ((1/3)x - 4) 12

= x - 12 + 12

= x

Now, (gof)(x)

=g(f(x))

= g(3x+ 12)

= (1/3) ( 3x+ 12) -4

= x + 4 - 4

= x

3. f(g(-2))

So,  g(-2)

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

= -2/3-4

= -14/3

Then, f(g(-2)) = f(-14/3)

=3(-14/3)+12

= - 2

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Step-by-step explanation:

[tex]4 \sqrt{2} = \sqrt{ {4}^{2} \times 2} = \sqrt{16 \times 2} = \sqrt{32} [/tex]

Answer:

  6

Step-by-step explanation:

The numbers in an ordered pair are usually (x, y). That is, the y-value comes second in the pair.

The second number in your ordered pair is 6. The y-coordinate is 6.

Answer:

a|| b then

<6=<4=<2=146

Answer:

y=3/2x-2

Step-by-step explanation:

m=3/2 A(2,1)=A(x1, y1) ... x1=2,y1 =1

y-y1=m(x-x1)

y-1=3/2(x-2)

y-1=3/2x-3/2*2

y-1=3/2x-3

y=3/2x-3+1

y=3/2x-2

The monthly salary for Job B after x months, which includes a 4% monthly raise, can be represented by the exponential function S(x) = 2000 * (1 + 0.04)^x, where S(x) is the salary and x is the number of months.

To represent the monthly salary for Job B after x months, we need to account for the 4% raise each month. Since the starting salary is $2000, and the raise is 4% (or 0.04 in decimal form) of the previous month's salary, the function to represent the monthly salary can be written using a geometric sequence formula.

Let S(x) be the salary at month x. The function will be an exponential function in the form:

S(x) = 2000 * (1 + 0.04)^x

Here, 2000 is the initial salary, 0.04 represents the 4% raise, and x is the number of months that have passed.

The Answer is D) because it is

Answer:

See explanation

Step-by-step explanation:

Assuming we want to find the slope and equation of the line going through:

(0,1) and (1,2).

Then the slope is given by:

[tex]m = \frac{2 - 1}{1 - 0} [/tex]

This implies that:

[tex]m = 1[/tex]

The equation is given by:

[tex]y = mx + b[/tex]

Where b=1 is the y-intercept since the line passes through (0,1).

Hence the equation is:

[tex]y = x + 1[/tex]

3(p + 2) = 18

3p + 6 = 18

3p = 12

p = 4

Check:

3(p + 2) = 18

3(4 + 2) = 18

3(6) = 18

18 = 18

This proves that p = 4.

⭐ Answered by Hyperrspace (Ace) ⭐

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Answer: p = +4

Step-by-step explanation: To solve this equation for p, our first step is to distribute the 3 through the parentheses on the left side.

3 times p is 3p and 3 times 2 is 6.

So we have 3p + 6 = 18.

Next, we need to isolate the p term by subtracting 6 from both sides of the equation to get 3p = 12.

Finally, we divide both sides of the equation by 3 to get p = +4.

Answer:

The territorial dispute over Taiwan originated in 1949 when the Chinese people fled to Taiwan due to the complete control of Communists in Mainland China.

Explanation:

The event happened after the "Chinese Civil War," a war between the Kuomintang and the Communist Party of China (CPR). This resulted to many Chinese people fleeing from Southern China to Taiwan in order to prevent the advances of the Communist Party. This was also a sign of retreat from the war.

Moving to Taiwan from China took 4 months and this was meant to be a temporary solution rather than being permanent. However, the plan could not be realized thus, resulting to many Chinese people living in Taiwan until today.

So, this led to the controversial issue that Taiwan is, somehow, part of China. In connection with this, territorial disputes arose whether Taiwan should be unified with Mainland China.

Answer:

  Evaluate the expression 1/3(4+18) -2 squared

Step-by-step explanation:

First of all we will add brackets to understand the question as:

= ((1/3) * (4+18) - (2 squared))

= ((1/3) * ( 22) -  2² )

According to Math's rule that Multiplication and division must be completed before addition and subtraction.

=  (( 1/3 * 22) - 4 )

= (( 7.33) - 4 )

= ( 7.33 - 4 )

= 3.33

3.33 is the correct answer.

Answer:

W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)

I hope this helps you. If you can give brainliest that would be greatly appreciated.

Answer:

W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)

Step-by-step explanation:

look at picture

Answer:

Step-by-step explanation:

Add the three digits together:

12+7+16=35

7/35, or 1/5.

Answer:

73-3=70

70-20=50

50-24=26

To solve 73-26, subtract 3 from 73 to get 70. Then, subtract a number from 70 to get 50. The missing number is 20.

To solve the equation 73-26, we can subtract it step by step. The first step is to subtract 3 from 73, which equals 70. The next step is to subtract a number from 70 to get 50. To find that number, we subtract 50 from 70, which is 20. So, the missing number is 20.

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Answer:

y=6x+5

Step-by-step explanation:

y-2=6x+3

y=6x+3+2

y=6x+5