Use substitution to prove these algebraic expressions are equivalent 9j + 21 + 3j and 3(3j + j + 7). You may substitute any number for the variables you choose. Show all your work for complete credit.

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Morton will give 3 cookies to each student and 6 cookies to each friend

Solution:

Let "x" be the cookies given to each student

Let "y" be the cookies given to each friend

Each friend will get 3 more cookies than each student

Therefore,

cookies given to each friend = 3 + cookies given to each student

y = x + 3 -------- eqn 1

She has a total of 112 students  and 12 friends and made of total of 408 cookies for everyone

Therefore, we frame a equation as:

112x + 12y = 408 ---------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 1 in eqn 2

112x + 12(x + 3) = 408

112x + 12x + 36 = 408

124x = 372

x = 3

Substitute x = 3 in eqn 1

y = 3 + 3

y = 6

Thus Morton will give 3 cookies to each student and 6 cookies to each friend

Ms. Morton predicts that she will give each friend 4 cookies and each student 7 cookies. So this is incorrect

Answer:

62.5 gallons

Step-by-step explanation:

Divide by 8

Final answer:

To create the equation representing the situation, calculate the total meal cost by multiplying each friend's share by four and then add four times the tip to equal the final bill of $61. The equation is 4 times $12.75 + 4  imes t = $61.

Explanation:

To solve the problem using an equation, we need to consider the cost of each meal and the tip each friend left. Four friends each paid $12.75 for their meal, which gives us the cost of the meals alone: 4 times $12.75 = $51. The tip, t, needs to be added four times (once for each friend) to the total cost of the meals to reach the final bill of $61.

Therefore, the equation to represent the situation would be: 4 times $12.75 + 4 times t = $61.

Once we have the equation, we can solve for the tip, t, to find out how much each friend left for the tip.

Answer:3

Step-by-step explanation:

Based on the shape of the platter and the length of each side, the area of the platter must be 64 inches².

The platter is said to be a square so the area will be that of a square.

Area of a square is:

= Length x Width

A square has the same length and width so the area is:

= 8 x 8

= 64 inches²

In conclusion, the area is 64 inches ².

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Answer:

x=29/8

Step-by-step explanation:

3 5/8=29/8

7 1/4=29/4

---------------

x+29/8=29/4

x=29/4-29/8

x=58/8-29/8

x=29/8

Answer:

50 persons

Step-by-step explanation:

Given:

Aaron’s dad rents out the local skating rink for a party for = $150

Food will cost per person = $3

Question asked :

how many people can Aaron invite = ?

Solution:

Total budget = $300

Rent of skating rink = $150

Remaining money for food = 300 - 150

                                             = $ 150

Each person's food cost = $3

Number of people can Aeron invite = Remaining money divided by each person's food cost

Number of people can Aeron invite = [tex]\frac{150}{3}[/tex]

                                                            = 50 persons

Answer:

C. 15 and 35

Step-by-step explanation:

3 x 15=45-10= 35

15+35=50

So C. is correct

Answer:

C

Step-by-step explanation:

Let the two no.s be x and y

x+y=50 -------(I)

Condition 2:

x=3y-10 -------(2)

Putting eq 2 into 1

3y-10+y=50

4y-10=50

4y=50+10

4y=60

Dividing both sides by 4

y=15

Putting the value of y in 2

x=3(15)-10

x=45-10

x=35

Answer:

D) -30

Step-by-step explanation:

4(-5)+7(3)+3(-5)-2(3)+2(-5)

-20 + 21 - 15 - 6 - 10

1 - 21 - 10

-20 - 10

= -30

Hope this helps

-Amelia

Answer:

x = 41

Step-by-step explanation:

To solve this problem, we want to find the value of 'x' by isolating it (separating 'x' from all other numbers).

First, simplify the expression by using the distributive property, where you multiply the number outside the brackets with each term inside the brackets.

Then isolate 'x' by doing reverse operations (on both sides) for every number that is on the same side as 'x'. Reverse operations are opposites (addition and subtraction, multiplication and division) and "cancel out" a number, which "moves" it to the other side.

7(x - 5) = 252        Use the distributive property

7x - 35 = 252        Result of 7 times x and 7 times -5

7x - 35 + 35 = 252 + 35        Add 35 to both sides

7x = 252 + 35        -35+35 on the left side cancelled out. Simplify right side

7x = 287        Continue to isolate 'x'

7x/7 = 287/7        Divide both sides by 7

x = 287/7        Left side cancelled out to be 'x'. Simplify the right side

x = 41        Answer

Check your answer:

Substitute 'x' for 41 in the original equation. Then, make sure that the equation is still balanced. Keep in mind BEDMAS order (brackets, exponents, division, multiplication, addition, subtraction).

7(x - 5) = 252

7(41 - 5) = 252        Simplify inside the brackets first

7(36) = 252        Multiply

252 = 252        Same answer

LS = RS

Since left side (LS) equals (=) right side (RS), the equation is still balanced and we got the correct value for 'x'.

Answer:

see attached picture.

Answer:

17.3

Step-by-step explanation:

241.5 divided by 14 is 17.25 rounded up its 17.3

Incomplete Question the complete Qs is

Which of the following is a correct equation for the line passing through the point (-2,1) and having slope m = 1/2?  

a: y=1/2x+2

b: y=-2x+1/2

c: x-2y=-4

d: y-1=1/2(x+2)

Answer:

The Correct option is c. x-2y=-4

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

Step-by-step explanation:

Given:

[tex]Slope = m =\dfrac{1}{2}[/tex]

point A(x₁, y₁)=(-2,1)  

To Find:  

Equation of Line  =?  

Solution:  

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,  

i.e equation in point - slope form

[tex](y-y_{1})=m(x-x_{1})[/tex]

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2 , 1) we get

[tex](y-1)=\dfrac{1}{2}(x-(-2))\\\\2y-2=x+2\\x-2y=-2-2=-4\\x-2y=-4[/tex] As required

Therefore the correct equation for the line passing through the point (-2,1) and having slope m= 1/2 is

[tex]x-2y=-4[/tex]

Is number2  Extend  I think

Answer:

4 is the square root of 16 :)

Step-by-step explanation:

Answer:

I think the answer you're looking for is four?

Answer:

0.13 tax

Step-by-step explanation:

0.044*3=0.132

The number is 5.

Step-by-step explanation:

Let,

x represent the unknown number.

According to given statement;

add five to twice a number the results is fifteen

2x + 5 = 15

Subtracting 5 from both sides

[tex]2x+5-5=15-5\\2x=10[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{10}{2}\\x=5[/tex]

The number is 5.

Keywords: variable, addition

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Answer:

1 hour and 30 maybe my math might be wrong

Step-by-step explanation:

Answer:

20 %.

Step-by-step explanation:

(40/200) * 100

= (2/ 10) * 100

= 2 * 10

= 20.

Final answer:

To express 40 as a percentage of 200, you set up a proportion and solve for x, finding that 40 is 20% of 200.

Explanation:

To express 40 as a percentage of 200, we can set up a proportion where 40 is to 200 as x is to 100 (since percentages are out of 100). This gives us the proportion 40/200 = x/100. Solving for x, we multiply both sides by 100 to isolate x on one side of the equation. This gives us x = (40 × 100) / 200.

Next, we perform the multiplication and division: x = 4000 / 200. Simplifying that, we get x = 20. Therefore, 40 is 20% of 200.

The three even integers are 66, 68 and 70

Solution:

Let the three consecutive even integers be x, x + 2, x + 4

Let the first integer be x

Let the second integer be x + 2

Let the third integer be x + 4

Given that, sum of the first and third of three consecutive integers is 136

Sum of first and third integer = 136

x + x + 4 = 136

2x + 4 = 136

2x = 136 - 4

2x = 132

x = 66

Thus the consecutive integers are:

first even integer = x = 66

second even integer = x + 2 = 66 + 2 = 68

third even integer = x + 4 = 66 + 4 = 70

Thus the three even integers are 66, 68 and 70

The number of questions in the test is 30

Step-by-step explanation:

Let's call the total number of questions in the test N.

We know that Laura answered 27 questions, and these 27 questions represent the 90% of the test.

Therefore, we can say that 27 is the 90% of N.

Re-writing the percentage as a fraction,

[tex]90\% = 0.90[/tex]

This means that:

[tex]0.90 N = 27[/tex]

And now we can solve for N to find the number of questions in the test:

[tex]N=\frac{27}{0.90}=30[/tex]

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The value of z in the equation [tex]1\frac{4}{11}[/tex] of z is 45 is 33.

Solution:

Given: [tex]1\frac{4}{11}[/tex] of z = 45

To find: The value of z

On solving the given equation,

[tex]1\frac{4}{11}\times z=45[/tex]

[tex]\Rightarrow\frac{1\times11+4}{11}\times z=45[/tex]

[tex]\Rightarrow\frac{15}{11}z=45[/tex]

On grouping the like terms in one side we get,

[tex]\Rightarrow z=45\times\frac{11}{15}[/tex]

On solving the values we get,

[tex]\Rightarrow z=3\times11\rightarrow33[/tex]

The required value of z is 33.

Steps to convert a mixed fraction into an improper fraction:

Step 1: Multiply the whole number part by the fraction's denominator.

Step 2: Add that to the numerator.

Step 3: Then write the result on top of the denominator.

Answer:

x=24

Step-by-step explanation:

Here, you need to make proportion and find x.

12:16=18:x

We multiply 12 by x and 16 by 18:

12x=288

Divide by 12 both sides :

x=24

Answer:

11 and 23

Step-by-step explanation:

Answer:

1. Using the Pythagorean theorem.

2. Using the ratio 1 : 1 : √2.

Step-by-step explanation:

There are two options to find the value of x:

1. Using the Pythagorean theorem:

Hypotenuse = 5√2 inches and legs are equal in a 90 - 45 - 45 triangle like this.

Hypotenuse² = Leg² + Leg²

(5√2)² = 2Leg²

50 = 2Leg²

50/2 = Leg²

Leg² = 25

√Leg² = √25

Leg = 5 inches ⇒ x = 5

2. Using the ratio 1 : 1 : √2, this way:

1 : 1 : √2

x : x : 5√2

x = 5√2/√2

x = 5 and let's recall that in a 90 - 45 - 45 triangle legs are equal, therefore. ratio is:

5 : 5 : 5√2

x-5=1

+5   +5

x=6

x-5=-1

 +5  +5

x=4

Answer: x= 6, 4

Answer:

4 im not 100% but i think so

Step-by-step explanation:

Answer:

Step-by-step explanation:

4(x + 8) + 5(y + 3) =

4x + 32 + 5y + 15 =

4x + 5y + 47

total of 3 terms : 4x, 5y, and 47

For this case we must simplify the following expression:

[tex]x ^ 2-3xy-5xy-7y ^ 2 + 4x ^ 2 + 8y ^ 2[/tex]

We must add similar terms taking into account that:

[tex](x ^ 2 + 4x ^ 2) + (- 3xy-5xy) + (- 7y ^ 2 + 8y ^ 2) =\\5x ^ 2-8xy + y ^ 2[/tex]

Thus, the simplified expression is:

[tex]5x ^ 2-8xy + y ^ 2[/tex]

Answer:

[tex]5x ^ 2-8xy + y ^ 2[/tex]

Answer:

Step-by-step explanation:

-x (4x^2 - 6x + 1).....distribute the -x through the parenthesis

- 4x^3 + 6x^2 - x <===

Answer:

b

Step-by-step explanation: