Mathematics Middle School

For every real number x, y, and z, the statement (x – y)z = xz – yz is _____ true. An algebraic expression in simplest form _____ has like terms.

Answers

Answer 1
Final answer:

The statement (x – y)z = xz – yz is always true due to the distributive property in mathematics. Moreover, an algebraic expression in the simplest form does have like terms. Like terms are grouped together to simplify the expression.

Explanation:

For every real number x, y, and z, the statement (x – y)z = xz – yz is always true. This is an illustration of the distributive property in mathematics, which states that for all real numbers, the equation a(b + c) = ab + ac holds true. In the given equation, the place of 'a' is taken by 'z', while 'x' and 'y' replace 'b' and 'c' respectively.

On the other hand, an algebraic expression in simplest form does have like terms. Like terms are terms with the same variable part. For instance, in the expression 3x2 + 2x - x2 + 4 +5x - 2, the like terms can be combined to simplify the expression to 2x2 + 7x + 2.

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Related Questions

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.

Use the order of operations to find the value of the expression 5*2+6-5

Answers

You have to use PEMDAS. The first irder of operations to use in this situation is multiply. So 5 x 2 = 10. Now we have to add 10 + 6 = 16. Lastly, you have to subtract 16 - 5 = 11. So your answer would be 11. 


Hope this helps! : - D



Salutations!

BODMAS also called Order of Operations means:

B- Brackets

O - Order

D- Division

M- Multiplication

A- Addition

S- Subtraction.

[tex]5*2+6-5[/tex]

[tex]5*2 =10[/tex]

[tex]10+6=16[/tex]

[tex]16-5=11[/tex]

Hope I helped (:

have a great day!

Find the value of x (5x) (3x+12

Answers

The value that shows the expansion of the given algebraic expression  is 6.

What is the solution to the algebraic expression.

An algebraic expression is a mathematical expression that has the variables, coefficients, and its arithmetic operators

In the complete question attached below, we are to find the value of x.

We can see that the angles are alternate angles.


So, 5x = (3x + 12).Combine like terms, we have:

5x - 3x = 12

2x = 12

x = 12/2

x = 6

Therefore, the value of x is = 6.

Use the scale and map measurements to find the actual distance from New Wilmington to Sharon through Mercer. What is the actual distance if you travel from New Wilmington to Sharon through Volant?
A.) 16.5 mi; 19.5 mi

B.) 33 mi; 39 mi

C.) 66 mi; 78 mi

D.) 49.5 mi; 58.5 mi

Answers

1) New Wilmington-> Mercer: 1.25in
Mercer -> Sharon: 1.5in
-> in total 2.75in
scale 1 in:12 mi

->in total scaled: 2.75*12 mi=24+9mi=33mi

2) New Wilmington-> Volant: 1.25in
Volant -> Sharon: 2in
-> in total 3.25in
scale 1in:12mi

->in total scaled: 3.25*12 mi=36+3mi=39mi

so the answer is B) 33 mi; 39 mi

the other person is incorrect "b.33 Mi; 39Mi" is not even an option on my quiz

the correct answer is 76.5 mi; 67.5 mi



Write 63 as a sum of tens and ones

Answers

you have 60 in your tens place. you have 3 in your ones place. then add both together

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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Kay estimates that Wednesday ride is about 3 miles longer than Tuesday ride . Is her estimate reasonable ?

Answers

Answer:

yes

Step-by-step explanation:

For what value of y does 125=(1/25)^y-1
A -5/2
B -2
C -1
D -1/2

Answers

The value of y that satisfies the equation is -1/2.

The correct option is D.

To solve the equation, using the property of exponents:

125 = (1/25[tex])^{y-1[/tex]

Now, 125 can be written in exponent form as (5³) and (1/25) as (5⁻²):

So, 5³ = (1/5²[tex])^{y-1[/tex]

5³ = (5⁻²[tex])^{y-1[/tex]

5³ =[tex]5^{-2y+2[/tex]

Since the bases are the same, comparing the exponents as:

3 = -2y+ 2

3-2 = -2y

-2y = 1

y= -1/2.

Therefore, the value of y that satisfies the equation is -1/2.

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What is 23/35 simplified?

Answers

There is no least common enominator for this answer due to the fact that these numbers don't share a common factor (23 is odd number with only two factors: 1, 23; while 35 is odd number with 4 factors: 1, 5, 7, 35) other than 1.

*But if you do 1/1, it will be 1; so this won't work properly.

So the answer is 23/35.

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.

Given the binomials (x-1), (x-3), (x+3), (x+5), which one is the factor of f(x) = x^3 + 6x^2 + 12x +35?

Answers

The given polynomial is
f(x) = x³ + 6x² + 12x + 35

According to the Remainder Theorem, if x = a is a zero, then
f(a) = 0, and (x-a) is a factor.

Test (x-1):
f(1) = 1 + 6 +12 + 35 = 54   
Not a factor.

Test (x-3):
f(3) = 3³ +6*3² + 12*3 + 35 = 152
Not a factor.

Test (x+3):
f(-3) = (-3)³ + 6*(-3)² + 12*(-3) + 35 = 26
Not a factor.

Test (x+5):
(-5)³ + 6*(-5)² + 12*(-5) + 35 = 0
It is a factor.

Answer: (x+5) is a factor.

Giving who ever answers correctly over 30 points.

1: Solve for x.

x - 3/8 = - 5/8

a: x=1/4
b: x= -1/4
c: x= -1

2: Solve for x.

2x = 15 + x

a: x= -15
b: x= 15
c: x= 15/2

3: Solve for x.

x + 5 = 2x

a: x=3
b: x= -5
c: x= 5

Answers

The first one would be b,

second is b

third is c.

Hope this helps!

Number 1 is b
Number 2 is b
Number 3 is c

What is the smallest power of 10 that would exceed 987,654,321,098,765,432?

Answers

it is 10^18:1000000000000000000

A recipe requires 1/4 lb of onions to make 3 servingsof soup. Mark has 1 1/2 lb of onions. How many servings can mark make?

Answers

16 servings of soup. 1/4 times 4 equals 1 pound and 1/4 times 2 equals 1/2 a pound so it equals 1 1/2.
Hello,

We know that if you have 1/4 Ib of onions, that will make 3 servings. If we make a unit rate table, you'll end up with 18 servings when you have 1 1/2 Ibs of onions.

He would be able to make 18 servings. Hope this helps.

May. 

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

4. Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t)= 10t, where 5

Answers

Given that Grace works from 10 to 20 hours per week while attending college. She earns $9.00 per hour. Her roommate Frances also has a job. Her pay for t hours each week is given by the function f(t)= 10t, where 5 ≤ t ≤ 15.

Part A:

Given that Grace's time is rounded to the nearest quarter of an hour. The domain for Grace is given by {10, 10.25, 10.50, 10.75, - - -, 19.75, 20}.

The range for grace is given by {9(10), 9(10.25), 9(10.50), 9(10.75), - - -, 9(19.75), 9(20)} = {90, 92.25, 94.5, 96.75, - - -, 177.75, 180}

The domain for Frances is given by: 5 ≤ t ≤ 15.

The range for Frances is given by: 10(5) ≤ f(t) ≤ 10(15) = 50 ≤ f(t) ≤ 150.



Part B:

Grace earns $9 per hour and $80 to $180 per week while Frances earns $10 per hour and $50 to $150 per week.


Find the coordinates of the points of intersection of the graphs with coordinate axes:
y=−1.5x+3

x − intercept is ( , )
y − intercept is ( , )

Answers

I only know the y intercept which is 0,3

Answer:

x - intercept is (2,0)

y - intercept is (0,3)

Step-by-step explanation:

y = 0 for x - intercept

0 = - 1.5x + 3

- 3 = - 1.5x

x = 2

x = 0 for y - intercept

y = 0 + 3

y = 3

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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Equation: y= -0.25x+1
After how many minutes is the timer 25% full?

Answers

Answer: 3 minutes

To solve this, I plugged 0.25 into the y value since it represents the amount of sand remaining. I then solved for the x value which gave me a value of 3. (I hope this helps)

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.

204 meters 89 cm = how many cm??

Answers

20,489 because 1 meter is 100 centimeters.

204 meters 89 centimeters is equal to 20,489 centimeters.

To convert 204 meters 89 centimeters to centimeters, we need to consider that 1 meter is equal to 100 centimeters.

204 meters is equal to 204 × 100 = 20,400 centimeters.

Adding the 89 centimeters, the total is 20,400 + 89 = 20,489 centimeters.

Therefore, 204 meters 89 centimeters is equal to 20,489 centimeters.

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What is 45,824 rounded to the nearest thousand

Answers

46,000 is the answer
You have your 1s 10s 100s 1,000s 10,000s. 45,824 you want to round to the nearest thousands so you look at 5,824. if its 5 or more go up if its 4 or round down. 800 is more than 500 so you round up to 6,000. The answer is 46,000.

you can use similar triangles to find the height of a tree. Triangle ABC is similar to triangle DEC. what is the height of the tree?

please explain it too ^_^


Answers

So if triangle ABC is similiar to triangle DEC then we know that when two figures are similar, the ratios of the lengths of their corresponding sides are equal.So we can write:

AC/DC = BC/EC =AB/DE = k

BC= 9ft + 6ft = 15

BC/EC= k
15/6=k

Now that we know the k we can find the height of the tree that's equal to AB:

AB/DE= k
AB/4=15/6
6AB= 15 x 4
AB= 60/6 = 10

The height of the tree is 10ft


The height of the tree is 10 feet.

What is a triangle?

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the ratios of the lengths of the corresponding sides are equal when two figures are similar, if triangle ABC and triangle DEC are similar, then we may write,

AC/DC = BC/EC = AB/DE = k

BC= 9ft + 6ft = 15

BC/EC= k

15/6=k

Now from this value of 'K' we can determine the height of the tree which is,

AB/DE = k

AB/4 = 15/6

6AB = 15 x 4

AB = 60/6 = 10

The height of the tree is 10ft.

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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

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

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

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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Which function describes this graph?

f(x)=4x+2
f(x)=x+2
f(x)=1/4x+2

Answers

f(x) = 1/4x + 2

This means that the y-intercept is 2 and the slope is 1/4.

Hope this helps!
The function that best describes this graph would be f(x)=1/4x+2. The y-int is 2 and it rises once and runs 4 times to the right.

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.

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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