Mathematics Middle School

Benjamin solved the equation 3+/2=10 and justified each step as shown. Identify Benjamin’s error and fix his mistake.
3+x/2=10 GIVEN
x/2=7 MULTIPLICATION PROPERTY OF EQUALITY
x=14 SUBTRACTION PROPERTY OF EQUALITY

Answers

Answer 1
How to solve the equation properly:

3 + x / 2 = 10

Multiply 2 on both sides.

3 + x = 20

Subtract 3 from both sides.

x = 17.

What he did wrong:

He subtracted the three on both sides before he multiplied the two. This will make him get the incorrect answer because he did it in the wrong order.

Hope this helps!


Related Questions

Which equation below is a direct variation? A. 0.05x = y B. x + 2 = y C. D. y = 2x + 6

Answers

It’s A because the direct variation formula is y = mx.

Which quadrilaterals always have four right angles?  
Choose all answers that are correct.  

A. square
 
B. rhombus
 
C. trapezoid
 
D. rectangle

Answers

Square and rectangle because the other ones have 4 equal sides too, but they're not RIGHT angles.
Square and rectangle

67a(t+z)=45z+67 solve for z.
I need help. Please?

Answers

67a(t+z)=45z+67
Distribute the 67a to inside the parenthesis.
67at + 67az = 45z + 67
Subtract 67 to the other side.
67at + 67az - 67 = 45z
Divide everything by 45.
1.49at + 1.49az - 1.49 = z

Hope that helped! :)
Hello there, let's get started.

The equation is 67a(t+z)=45z+67.

Let's first distribute "67a" to the "t" and "z" in the parenthesis.
The equation simplifies to: 67at + 67az = 45z + 67. 

Step one is to Add -45z to both sides. 67at+67az+−45z=45z+67+−45z (this crosses 45z out), it is now simplified to 67at+67az−45z=67. 

Step 2 is to now add -67at to both sides. 67at+67az−45z+−67at (this crosses 67at out)=67+−67a. The equation is now simplified to 67az−45z=−67at+67t. 

Step 3: Factor out variable z. z(67a−45)=−67at+67. 

Step 4: Divide both sides by 67a-45. z(67a−45)/67a−45=−67at+67/67a−45.
It's then simplified to: z=−67at+67/67a−45.

The equation: z=−67at+67/67a−45 is the final answer. Sorry if this is confusing.

Consider the graph of the equation y = 5. Which statements are true? Check all that apply. The graph of y = 5 is a vertical line. The graph of y = 5 is a horizontal line. The graph of y = 5 is neither a vertical line nor a horizontal line. The point (5, 3) lies on the line. The point (–4, 5) lies on the line.

Answers

Hello!

y = 5 is a horizontal line whose y-values are all 5. Given this, the true statements are -

- The graph of y = 5 is a horizontal line
- The point (-4, 5) lies on the line

I hope this helps you!

Answer:

B and E

Step-by-step explanation:

Got these right on Ed

Use long division to convert the rational number 5/7 to its equivalent decimal form. In your final answer, include all of your work.

Answers

just show you the first significant figures.


7 /0.71428______
/50
49
........................
10
7
..........
30
28
….........
20
14
………………
60
56
...................
4

If a = 3 and b = 2, what is the value of the expression 11 + a - b ?

Answers

Substitute the values of a and b into the expression:
11 + 3 - 2
Add first because of order of operations (perform addition and subtraction in the order of occurrence from left to right):
14 - 2
Subtract (same justification as above just with subtraction instead):
12
Hope this helps!

mr smith waters one one of his plants every 10 days and another plant every 14 days. If he water both days today when is the next time both plants will be watered on the same day?.

Answers

it will be after 70 days

Answer:

after 70 days.

Step-by-step explanation:

Mr. Smith waters one of his plants every 10 days and another plant ever 14 days.

he waters both plants today we have to find the next time both plants will be watered on the same day.

So we will take LCM of these numbers.

LCM of 10 , 14

= 2 × 5 × 7

= 70

The next time both plants will be watered on the same day after 70 days.

A music download service charges a flat fee each month and $0.99 per download. The total cost for downloading 37 songs this month is $42.72.
How much is the flat fee?
(pls tell me the equation)

Answers

.99x=37.00
42.72-x=answer
there is 37 downloads so .99 times 37 is 36.63 so 36.63 minus 42.72 is 6.09 so the flat fee is $6.09.

Pattern x: Starts at 0. Rule: Add 3.

Pattern y: Starts at 0. Rule: Add 6.

The values of Pattern x and Pattern y are graphed on a coordinate graph. Some of the ordered pairs for this pattern are (0, 0) , (3, 6) , (6, 12) , and (9, 18) .

Which ordered pair also belongs to this pattern?

Answers

I think (0,0) is the only one that starts at 0 for both x and y and stay the same if the add the 3 to x and 6 to y.

you can buy 5 t-shirts at baxter's for the same price that you can buy 4 t-shirts at Bixby's

Answers

Ok
What is the question

Which expression is equivalent to 3 square root 216x27 ?

6x3
6x9
72x3
72x9

Answers

[tex]\sqrt[3]{216\times27}\\\\\text{Use:}\ \sqrt[n]{a\cdot b}=\sqrt[n]a\cdot\sqrt[n]b\\\\\sqrt[3]{216\times27}=\sqrt[3]{216}\cdot\sqrt[3]{27}=6\cdot3=18\\\\.........................................................\\\\\sqrt[3]{216}=6\ \text{because}\ 6^3=216\\\\\sqrt[3]{27}=3\ \text{because}\ 3^3=27[/tex]

The answer to your problem would be answer B. 6x^9. It is the only answer equivalent to the 3 square root 216x27.


Hope this helps. :3

Marty has a fenced yard in the shape of a rectangle. It's area is 635.4 square feet. The width of the yard is 18 feet. What is the length of the fence?

Answers

Area=length*width

635.4=18*L
35.3=L

So the answer is 35.3
Final answer:

The length of the rectangular yard, given an area of 635.4 square feet and a width of 18 feet, can be calculated using the formula for the area of a rectangle. Substituting the given values into the formula, we find that the length is approximately 35.3 feet.

Explanation:

The question is about finding the length of a rectangular yard given its area and width. Recognizing that the formula for the area of a rectangle is Area = Length x Width, we can easily find the length of the yard by rearranging the formula.

To find the length of a rectangle when you know the area and width, use the rearranged area formula: Length = Area ÷ Width.

Given the values from the problem: Area = 635.4 sq ft and Width = 18 ft, we substitute them into the formula: Length = 635.4 ÷ 18. This results in a length of approximately 35.3 feet.

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How much is 24 ounces of spread if it is $6.40 per pound?

Answers

Since a ounce = pound is 16=1 so convert 24 ounces into pounds which is 1.5 pounds so multiply 6×4 by 1×5 and get $9.6 dollars for 24 ounces of the spread.
A pound = 16oz
Half a pound = 8oz

16 + 8 = 24
|| || ||
1lb 1/2lb 1 1/2 lbs


6.40/2 = 3.20
6.40 + 3.20 = 9.60

Your answer is 9.60

Gary read 34 pages of a 340 pages book what percentage did he read

Answers

Gary read 10% of the book. To solve this, I turned the problem to a fraction 34/340 (34 out of 340 pages read) and simplified it to 10/100 so I can convert it to the percent, 10%.

As per linear equation, Gary read 10% of the book.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation."

Gary read 34 pages of a 340 pages book.

Therefore, the percentage of the book he read is

= (34/340) × 100%

= 10%

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What is 231 divided by 42

Answers

5.5 is the answer for the problem
5.5 is the correct answer

find the percent increase for 13 friends to 14 friends round to nearest percent if you can

Answers

From 13 to 14 # is increased by 1

14-14 = 1/13 *100% That equals 7.69%

Your answer is 7.69%

Final answer:

The percent increase from 13 to 14 friends is calculated as [(14 - 13) / 13] × 100, which gives a result of approximately 7.7%. After rounding to the nearest percent, the increase is 8%.

Explanation:

To find the percent increase from 13 friends to 14 friends, we use the formula for percentage change, which is:

Percentage Change = [(New Value - Original Value) / Original Value] × 100

In this case, our original value is 13 (the number of friends at the start) and our new value is 14 (the number of friends after the increase). So, we plug these numbers into our formula:

Percentage Change = [(14 - 13) / 13] × 100 = [1 / 13] × 100

Now, we calculate the fraction and then multiply by 100:

Percentage Change = (0.07692307692) × 100 ≈ 7.7%

When rounded to the nearest percent, the percent increase is approximately 8%.

Kay buys 12 pounds of apples.Each pound costs $20 bills. How much will change should she receive

Answers

You haven't given us enough information.  Does each apple cost $20? If so, how much does she give the apple farmer
20*12=240. You don't give me the change she gave to the cashier.

Eric had 2 liters of water. He gave 0.42 liter to his friend and then drank 0.32 liter. How much water does he have left? Helpppp

Answers

2-0.42-0.32=1.26 L
 ↓     ↓       ↓
 ↓  friend  him
original

Answer:

1.26

Step-by-step explanation:

sence he had 0.42 and 0.32 pluss 2 you would get the answer

How do I do this without a graph to plot points on

Answers

I'm guessing you should write it in the Slope Intercept Formula, which is y = mx + b

For example, #6 would be y = 5x - 1

estimate 102.3 divided by 4.7

Answers

Answer:

20

Explanation:

To estimate, we round.  102.3 rounds to 100 and 4.7 rounds to 5; this means we divide 100/5, which is 20.

Answer:

The estimate result of 102.3 divided by 4.7 is 20.

Step-by-step explanation:

Given : 102.3 divided by 4.7

We have to estimate 102.3 divided by 4.7

Since, estimation is the roughly calculation and is usually involves rounding to the nearest values so that they are easy to cancel out.

Since, we have to divide,

102.3 divided by 4.7

Rounding 102.7 to nearest tens place , we get, 102. 7 = 100

And Rounding 4.7 to nearest  ones place, we get, 4.7 = 5

Thus, when divide 100 by 5 , we get 20.

Thus,  102.3 divided by 4.7 ≈ 20

Thus, The estimate result of 102.3 divided by 4.7 is 20.

the sum of twice a number and 9 is 43

Answers

2x + 9 = 43 This is the equation.
2x = 34 Subtract 9 from both sides.
x = 17 Divide both sides by 2.

Answer:x=17

Step-by-step explanation:

1.75 rounded to the nearest whole number

Answers

Numbers 0, 1, 2, 3, and 4 are rounded down.
Numbers 5, 6, 7, 8, and 9 are rounded up.

Since we're rounding to the nearest whole number, don't even look at the hundreths place. All you need is the tenths place.

The number in the tenths place is 7, so you round up.

1.75 rounded to the nearest whole number is 2.

Hope this helps!
Your song is "Sincerely Me"

The rounded number is given by A = 2

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Non-zero digits are always significant

Zeros between non-zero digits are always significant

Leading zeros are never significant

Trailing zeros are only significant if the number contains a decimal point

Given data ,

Let the rounded number be represented as A

Let the number be represented as n

Now , the value of n = 1.75

And , when you round to the nearest ones place. The 1 in the ones place rounds up to 2 because the digit to the right in the tenths place is 7.

When the digit to the right is 5 or greater we round away from 0.

So , the rounded number is A = 2

Hence , the rounded number is A = 2

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Are the fractions 1/2 and 3/8 equivalent fractions

Answers

No, 1/2 is equivalent to 4/8

A fraction is a way to describe a part of a whole. The value of the two fractions is not equal.

What is a Fraction?

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

The value of the two fractions can be simplified as,

1/2 = 0.5

3/8 = 0.375

As it can be seen that the value of the two fractions is different, therefore, the value of the two fractions is not equal.

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20 points please answer and write an inequality

A popular cellular phone family plan provides 1,500 minutes. It charges $89.99/month for the first two lines and $9.99/month for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.

Answers

if you're counting the two lines given with the only 89.99 plan its 9 plans if not then its 7 additional plans

Which graph represents the function f(x) = −|x − 2| − 1?

Answers

the 3rd one in the picture

Answer:

option 3

Step-by-step explanation:

[tex]f(x) = -|x -2| - 1[/tex]

The given equation is in the form of [tex]f(x) = a|x -h|+k[/tex]

where (h,k) is the vertex .

[tex]f(x) = -|x -2| - 1[/tex]

h=2 and k=-1 . the value of a=-1

Since the value of 'a' is negative so the graph will be upside down

option 3 is upside down and vertex at (2,-1)

So option 3 graph represents the function

256is what percent of 400=

Answers

So first change this to a fraction.

256/400

And then just divide.

256/400 = 0.64

And then change that to a percent.

64%
The answer is that 256 is 64% of 400.

the attendance at two baseball games on successive nights was 66,000 the attendance on Thursdays game was 6,000 more than 2/3 of the attendance at Friday nights game

Answers

Fridays game = x

 Thursdays game = 2/3x +6000

 x + 2/3x +6000 = 66000

x +2/3x = 5/3x

5/3x + 6000 = 66000

5/3x = 60000

x = 60000 / 5/3 = 36000

 Friday night = 36000

 Thursday night = 30000

what is a solution to (x-2)(x+10)=13?
a: x=3
b: x=8
c: x=10
d: x=11

Answers

(x-2)(x+10)=13

x^2 + 10x - 2x - 20 = 13

x^2 + 8x - 20 - 13 = 0

x ^2 + 8x - 33 = 0

(x + 11) (x - 3) = 0

x + 11 = 0

x = -11

x - 3 = 0

x = 3

The answer is clearly x = 3.

Choice a.
Best answer would be A

Julia left school and travel toward the train station. One hour later Carlos left traveling at 30 mph in an effort to catch up to Julia. After traveling for two hours Carlos finally caught up. Find Julie is average speed

Answers

speed = distance/time

distance = speed * time

Carlos traveled for 2 hours.
Julia traveled for 1 more hour, or 3 hours

Carlos:
time = 2
distance = d
speed = 30 mph

distance = speed * time
d = 30 * 2
d = 60 miles

They both traveled 60 miles.

Julia:
time = 3
distance = 60 miles
speed = s

speed = distance/time = (60 miles)/(3 hours) = 20 mph

Julia's speed is 20 mph.

A pet shop uses 43 pounds of food each day. How many pounds are used in 365 days?

Answers

You know that 43 pounds are used each day, and they say 365 days, so what do you do?





































You multiply
43 lbs. x 365 days=15,695 lbs.
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