What is the justification for each step in the solution of the equation 3(2x + 7) - 4 = 53 - 3x?

Step 1: 3(2x + 7) - 4 = 53 - 3x
Step 2: 6x + 21 - 4 = 53 - 3x
Step 3: 6x + 17 = 53 - 3x
Step 4: 9x + 17 = 53
Step 5: 9x = 36
Step 6: x = 4

Answers

Answer 1

Final answer:

The equation 3(2x + 7) - 4 = 53 - 3x is solved through algebraic processes: distributing, combining like terms, transposing terms, isolating the variable, and dividing to solve for x, resulting in the solution x=4.

Explanation:

The justification for each step in solving the equation 3(2x + 7) - 4 = 53 - 3x involves algebraic manipulation:

Distribute the 3 into the parenthesis: 3(2x) + 3(7) - 4 = 53 - 3x becomes 6x + 21 - 4 = 53 - 3x.Combine like terms on the left side: 6x + 17 = 53 - 3x.Add 3x to both sides to get all x terms on one side: 9x + 17 = 53.Subtract 17 from both sides to isolate the term with x: 9x = 36.Divide both sides by 9 to solve for x: x = 4.

Each step is justified by the rules of algebra which allow us to simplify and rearrange equations to isolate the variable. The final step gives us the solution x = 4.


Related Questions

Solve log 4x + log 13 = 0. Round to the nearest thousandth if necessary. a.0.019 b. 52 c.3.25 d. 0.311 Mathematics

Answers

log4 + logX + log13 = 0
logX = -log13 - log4
logX = -1.716
x= 10^[-1.716]
x= 0.019 A

Jim bought a $576 TV with the cash in his wallet. He now has $137 in his wallet. Write and solve an equation that shows how much he originally had in his wallet.

Answers

576 - 137 = 439. so the TV was 439, The money he originally had was 576, and he now has 137 left. so m - c = t

Final answer:

Jim originally had $713 in his wallet before purchasing the TV. We found this by setting up the equation x - $576 = $137, which represents the situation before and after the purchase, and solving for x.

Explanation:

Jim bought a $576 TV with the cash in his wallet and now has $137 left. To find out how much money Jim originally had, we can write and solve a simple equation. Let's denote the amount of money Jim originally had as x. After buying the TV, he spent $576, so the money left is $137. This gives us the equation x - $576 = $137.

To solve for x, we add $576 to both sides of the equation, which gives us x = $137 + $576. Therefore, x = $713. So, Jim originally had $713 in his wallet before buying the TV.

Li is making beaded necklaces for each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length. Write an equation to find how many beads Li needs for each necklace.
A. Input variable
B. Output variable
C. Equation

Answers

Given that Li is making beaded necklaces for each necklace, she uses 27 spacers, plus 5 beads per inch of necklace length.

The equation to find how many beads Li needs for each necklace can be obtained as follows:

A. The input variable is the number of inches of the necklace length (x).

B. The output variable is the number of beads Li needs for each necklace (y).

C. The required equation is given by

y = 5x
Final answer:

The output variable B (total number of beads needs for each necklace) equals 27 (number of spacers used) plus 5 times the input variable A (length of the necklace in inches). The resulting equation is B = 27 + 5A.

Explanation:

In this question, we're trying to find out the total number of beads Li needs to create each necklace.

Let's define two variables:

A is the input variable, representing the length of the necklace in inches. B is the output variable, which stands for the total number of beads Li needs for each necklace.

Li uses 27 spacers for each necklace regardless of its length and there are 5 beads for every inch of necklace. Given these facts, we can create an equation as follows:

B = 27 + 5A

In this equation, 27 is the number of spacers used, while 5A indicates that 5 beads are strung for each inch of the necklace.

To use this equation, simply replace the variable 'A' with the desired length of the necklace in inches. The result will give the total number of beads Li needs for that particular length of necklace.

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is the line through points P(1,9) and Q(9,6) perpendicular to the line through points R(-6,0) and S(-9,8)? Explain?

Answers

Final answer:

To determine if two lines are perpendicular, we can calculate their slopes. The line through P(1,9) and Q(9,6) has a slope of -3/8, and the line through R(-6,0) and S(-9,8) has a slope of -8/3. The product of these slopes is -1, indicating that the lines are perpendicular.

Explanation:

To determine whether the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8), we can calculate the slope of each line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: slope = (y2 - y1) / (x2 - x1).

For the line through P(1,9) and Q(9,6), the slope is (6 - 9) / (9 - 1) = -3/8.

For the line through R(-6,0) and S(-9,8), the slope is (8 - 0) / (-9 - (-6)) = 8/-3 = -8/3.

If the two lines are perpendicular, the product of their slopes should be -1. Let's check: (-3/8) * (-8/3) = 1. Therefore, the line through points P(1,9) and Q(9,6) is perpendicular to the line through points R(-6,0) and S(-9,8).

Need help! Would greatly appreciate help

Answers

i’m pretty sure it is H if not let me know what it is
the answer would be H

What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y=x/3 −1 ?

Answers

The answer is y=12x-2
The anwser is y/x=12

When you do a negative number minus a negative number do you get a positive?

Answers

You get a positive number because you can use the leave, change, change rule for the signs. After the rule it would be a minus + a positive. The answer will vary depend on the size of each number.

What is m∠SVT?



Enter your answer in the box.

Answers

8y - 33 = 5y + 9
8y - 5y = 33 + 9
3y = 42
  y= 14

m∠SVT = 5y + 9
m∠SVT = 5(14) + 9
m∠SVT = 70 + 9
m∠SVT =  79

answer
79

Normally I am not one to make long answers

but if you want an explanation in case you have the same question with different numers, here is an explanation


Plug in the eequation and solve for x

Doing quick math the equation would be 8y-33 = 5y+9

I plugged this into m a t h w a y and got y=14

Then I subsituted y with 14

5 x 14 = 70 70 + 9 =79

Then I did a double check by making sure they were both equal

8 x 14 = 112   112 - 33 = 79

79 = 79

Therefore your answer is 79

Hope this helped, have a great day :)




I NEED QUICK HELP QUICK!!! PLEASE HELP ME SOMEONE!! THANK YOU!!

Which graph does NOT represent a function?

Answers

B or A, either A is not passing the vertical line test or B is just not a real function most likely A, DO. NOT. flame me if I got it wrong

Answer:

ITS B!!!

Step-by-step explanation:

alphametic FOOD+FOOD=SHOP

Answers

what is the question

Maddie throws a baseball from third base to first base. The four 90-foot lines between the bases form a square. Which number is the best estimate of how far Maddie throws the baseball?
What is the height of the ramp, to the nearest foot?
Question 4 options
90 feet
130 feet
150 feet
180 feet

A cyclist pedals up a hill that has a 13° angle. If the cyclist pedals up the hill for 10 kilometers, what is the change in her elevation, x ?

0.22 kilometer


9.7 kilometers


2.2 kilometers


45.0 kilometers

Answers

It seems like there are only two problems here. Problem 1 is the one with Maddie throwing the baseball. Problem 2 deals with the cyclist. For some reason you threw in "What is the height of the ramp, to the nearest foot?" in the middle of the baseball problem. That seems like a typo?

======================================================
Problem 1 (baseball problem with Maddie)

a = 90
b = 90
c = unknown

Pythagorean Theorem
a^2+b^2 = c^2
90^2+90^2 = c^2
8100+8100 = c^2
16200 = c^2
c^2 = 16200
sqrt(c^2) = sqrt(16200)
c = 127.279220613579

If we round to the nearest ten, then we get 130. In other words, 127.279 is closer to 130 than it is to 120.

So it looks like "130 feet" (choice B) is the final answer.
======================================================
Problem 2 (cyclist on a hill problem)

sin(angle) = opposite/hypotenuse
sin(13) = x/10
10*sin(13) = 10*x/10
10*sin(13) = x
x = 10*sin(13)
x = 2.24951054343864
x = 2.2

Answer: 2.2 km

PLEASE HELP PLEASE PLEASE PLEASE!!!!!!!!!!!!!!!!!!!!!!!
Evan earns $12 an hour plus $15 an hour for every hour of overtime. Overtime hours are any hours more than 30 hours for the week. Part A: Create an equation that shows the amount of money earned, M, for working x hours in a week when there is no overtime.
Part B: Create an equation that shows the amount of wages earned, T, for working y hours of overtime. Hint: Remember to include in the equation the amount earned from working 30 hours.
Part C: Evan earned $510 in 1 week. How many hours (regular plus overtime) did he work?

Answers

im trying calm down dont yell at me

a: m=12h 
b: t=12h+15y
c: 510=12h+15y
12*30=360
510=360+15y
15y=15y=10
10+30=40
he worked 40 hours

Let's say we have a circle with a radius of 17 inches. What is the circumference of this circle in inches? Round your answer to the hundredths place.
54.78
86.23
91.1
106.81

Answers

The answer is 108.81 using the formula 2(pi)(r)

Why is looking at cash flow an important step in a good financial plan?

Answers

to keep knowing how much money you have i reccomend credit karma to help but money is very important

Answer:

To keep knowing how much money you have i recommend credit karma to help but money is very important


Step-by-step explanation:


ASAP PLEASE ANSWER

Given △ABC≅△JKL, m∠B=55°, and m∠L=25°, what is the measure of ∠J? Enter your answer in the box. °

Answers

It shall be <J = 100!

Answer: [tex]\angle{J}=100^{\circ}[/tex]

Step-by-step explanation:

Given: △ABC≅△JKL,

m∠B=55°, and m∠L=25°

We know that if two triangles are congruent then their corresponding angles are equal.

∴ m∠A=m∠J

m∠B=m∠K=55°

m∠C=m∠L=25°

Now, by angle sum property in triangle JKL we have

[tex]\angle{J}+\angle{K}+\angle{L}=180^{\circ}\\\\\Rightarrow\angle{J}+55^{\circ}+25^{\circ}=180^{\circ}\\\\\Rightarrow\angle{J}=180^{\circ}-55^{\circ}-25^{\circ}\\\\\Rightarrow\angle{J}=100^{\circ}[/tex]

Find two numbers whose difference is 168 and whose product is a minimum

Answers

The two numbers whose difference is 168 and whose product is a minimum will be -50 and 50.

What is the equation?

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, two numbers whose difference is 168 and whose product is a minimum.

Suppose the two numbers are x and Q respectively.

If x - Q = 100, then Q = 100 + x

The function of their product is minimum,

F(x) = xQ

F(x) = x (100 + x)

F(x) = x² + 100x

Find the equation's lowest point on a graph. At x, the lowest point is -50,

f(x) = -2500

If,

Q = 100 + x

Q = 100 + (-50)

Q= 50

The product of the number is,

xQ = 50 × -50

xQ = -2500

Thus, the two numbers whose difference is 168 and whose product is a minimum will be -50 and 50.

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Which transformation is not isometric?

Answers

A is not isometeric, since the squares of the two figures are different sizes

The average value of the function v(x)=6/x2 on the interval [1,c] is equal to 1. find the value of

Answers

∫6/x²=-6/x
F=-6/x
F(c)-F(1)=c
-6/x+6/1=c
c²-6c+6=0
D=36-4*6=12
c₁=(6-√12)/2=1.26795
c₂=(6+√12)/2=4.73205

C can be 1.26795
C can be 4.73205

A student has some​ $1 and​ $5 bills in his wallet. He has a total of 14 bills that are worth ​$38. How many of each type of bill does he​ have?

Answers

There are 7 $1 bills and 8 $5 bills.


They have 6 $5 bills and 8 $1 bills.

mnmn if m=8m=8 and n=3n=3.

Answers

Answer: 8x8x8=512

Step-by-step explanation:

The set of all x values that make up the function is called the

Answers

Domain. I'm pretty sure. please comment if wrong

ms.snork brought two steaks that weighed 2.96 lb and 3.48 lb. If the meat cost $3.60 per pound, what was the total cost of the steaks ?

Answers

total lbs multiplied by cost per pound

1 .determine the total pounds of meat
2. multiply by $3.60

The total cost of the steaks that Ms. Snork brought will be $23.184.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Ms. Snork brought two steaks that weighed 2.96 lb and 3.48 lb. If the meat cost $3.60 per pound. Then the total cost of the steaks will be given as,

⇒ 2.96 x $3.60 + 3.48 x $3.60

⇒ $10.656 + $12.528

⇒ $23.184

The total cost of the steaks that Ms. Snork brought will be $23.184.

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Find points on the line 3x+5y=15 that are equidistant from the coordinate axes.

Answers

Final answer:

Points on the line 3x+5y=15 which are equidistant from the coordinate axes are (15/8, 15/8) and (-15/8, -15/8).

Explanation:

To find points on the line 3x+5y=15 that are equidistant from the coordinate axes, we need a point where the x and y coordinates are equal because the distances to the x-axis and y-axis from any point (x, y) are |x| and |y|, respectively. Since the line is equidistant from both axes, we require |x| = |y|.

Substituting y for x in the equation of the line, we get 3x + 5x = 15, which leads to 8x = 15, and therefore x = 15/8. Since we are looking for points equidistant from the axes, we have to check the signs of x and y to ensure they are at equal distances from both axes. Thus, the possible points are (15/8, 15/8) and (-15/8, -15/8).

Jared needs 2.4 micrograms of vitamin B-12 each day. Today, Jared drank a serving of milk containing 0.44 micrograms of B-12 and ate a lamb chop containing 1.224 micrograms of B-12. Which method can Jared use to find the number of micrograms of vitamin B-12 he still needs?

Answers

Subtract 2.4 – 0.44 = 1.96, then subtract 1.96 – 1.224.

Answer:

the answer is d

Step-by-step explanation:

A private plane leaves the airport and flies 1.3 hours at 110 mph on a bearing if 40 degrees. Then it turns and continues another 1.5 hours at the same speed, but in a bearing if 130 degrees. Through what angle did the plane have to turn to head back to the airport?

Answers

Refer to the diagram shown below.

The first distance traveled is
a = (110 mi/h)*(1.3 h) = 143 mi
The second distance traveled is
b = (110 mi/h)*(1.5 h) = 165 mi

From geometry,
x = 40°
y = 180° - 130° = 50°
x + y = 40° + 50° = 90°
Therefore we have a right triangle.

By definition
tan θ = 165/143 = 1.1538
θ = tan⁻¹ 1.1538 ≈ 49°
Because the sum of angles in a triangle is 180°, therefore
z = 180° - (49° +90°) = 41°

The angle through which the plane has to turn to head back to the airport is
φ = 360° - (y + z)
    = 360° - (50° + 41)°
    = 269°

Answer: 269°

Heading = 269.09 degrees. Plane will turn through an arc of 139.09 degrees. First, lets calculate the length of the 2 legs we know of. Leg1 = 1.3 * 110 = 143 miles. Leg2 = 1.5 * 110 = 165 miles. These distances are short enough that we can ignore the curvature of the earth and stick with euclidean geometry. Let's convert the polar coordinate of (40, 143) to Cartesian. (143sin(40), 143cos(40)) = (91.92, 109.54) So we know the plane flew 109.54 miles to the north, and 91.92 miles east. Lets see about the second leg. (165sin(130), 165cos(130)) = (126.40, -106.06) So the plane then traveled 126.40 miles to the east, and 106.06 miles to the south. Adding those distances together gives (91.92 + 126.40, 109.54 - 106.06) = (218.32, 3.48) So the plane is now 218.32 miles to the east and 3.48 miles to the north of where it originally started. Let's calculate the angle needed to return by first calculating the tangent. 3.48 / 218.32 = 0.01594 atan(0.01594) = 0.91 degrees. Since the plane will have to be going almost due west, that means that the heading will be close to 270 degrees. And since it also needs to go slightly south, we'll subtract the 0.91 degrees from the 270 to get a heading of 269.09 degrees. In order to get to that new heading from it's current heading of 130 degrees, we simply subtract. So 269.09 - 130 = 139.09 degrees

A sample of size n is selected at random from an infinite population. as n increases, the standard error of the sample mean increases.
a. True
b. False

Answers

FALSE!


big time false



hope it helped

When Seb reconciles his accounts, what is the first step he should take?

Answers

Seb must confirm his records are accurate and include all transactions.

Answer:

Seb should check if all is records are accurate and he should include all the transactions.

Step-by-step explanation:

When Seb reconciles his accounts, what is the first step he should take?

We can say that reconciling an account means proving that an account balance is correct.

For this, we need all the correct and accurate transactions and figures.

So, Seb should check if all is records are accurate and he should include all the transactions.

If a certain number is added to both the numerator and denominator of the fraction 7 6 76, the result is 3 2 32 . find the number.

Answers

Assuming that the right statement is that if a certain number is added to both the numerator and the numerator of the fraction 7/6, the result is 3/2, find the number, the solution if found in this way:

Call x the number (certain number)

=> (7+x) / (6 +x ) = 3/2

=> (7 + x)*2 = 3*(6 + x)

=> 14 + 2x = 18 + 3x

=> 14 - 18 = 3x - 2x

=> - 4 = x

verification> ( 7 - 4) / ( 6 - 4) = 3 / 2

Answer: the number is  - 4.


If two angles share a vertex then they are adjacent true or false

Answers

true i think hope this helps

The given statement is true"If two angles share a vertex then they are adjacent".

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called an "Angle."

If two angles in geometry share a side and a vertex, they are said to be adjacent. In other words, consecutive angles do not overlap and are placed side by side.

When an angle's vertex and side are shared by another angle, the two angles are said to be adjacent angles. The vertex of an angle is the point where the rays come to a stop and form the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complementary or supplementary angles.

Thus, the given statement is true"If two angles share a vertex then they are adjacent".

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The school baseball team wants to have each player's name imprinted on the player's jacket. the cost is $75 plus $8.50 for each name. write a function to represent the cost c(n) for n names. what is the cost to have names printed on 25 jackets

Answers

75+8.50(n)=C      75+8.50*25=$287.50
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