Solve all of them step by step (12 points!)
(a) . 2x + 4(x-1) = 2 + 4x
(b) 25 -x = 15 - (3x +10)
(c) 4x = 2x + 2x +5 (x - x)
Answers
Multiply everything in the parenthesis by 4.
2x + 4x - 4 = 2 + 4x
Combine like terms.
6x - 4 = 2 + 4x
Subtract 4x from both sides.
2x - 4 = 2
Add 4 to both sides.
2x = 6
Divide 2 on both sides.
x = 3
b) 25 - x = 15 - (3x + 10)
Multiply everything in the parenthesis by -1.
25 - x = 15 - 3x - 10
Combine like terms.
25 - x = 5 - 3x
Add 3x to both sides.
25 + 2x = 5
Subtract 25 from both sides.
2x = -20
Divide 2 on both sides.
x = -10
c) 4x = 2x + 2x + 5(x - x)
Multiply everything in the parenthesis by 5.
4x = 2x + 2x + 5x - 5x
Combine like terms.
4x = 4x
This means that there is an infinite amount of solutions.
Hope this helps!
Related Questions
what is the definition of perfect cube and can you give an example
Answers
[tex] {a}^{3} = a \times a \times a[/tex]
therefore
[tex]{1}^{3} = 1 \\ {2}^{3} = 8 \\ {3}^{3} = 27 \\ {4}^{3} = 64 \\ {5}^{3 } = 125 \\ . \\ . \\ .\\ .[/tex]
and also you can define it as any natural number who's third root is also a natural number for examble
[tex] \sqrt[3]{1000} = 10[/tex]
so you can say that the tenth perfect cube is 1000
Final answer:
A perfect cube is a number that results from an integer being multiplied by itself two additional times. The number 27 is an example of a perfect cube, which is the result of 3 × 3 × 3. While the concept of a cube is also significant in chemistry, the mathematical perfect cube is different from geometric or chemical descriptions of cubes.
Explanation:
A perfect cube is a number that can be expressed as the product of an integer multiplied by itself three times. It is the cube of an integer. For instance, when you multiply 3 × 3 × 3, you get 27, which is a perfect cube because it is the result of an integer (3) multiplied by itself two more times.
The number 27 is an example of a perfect cube in mathematics.A Rubik's cube, such as the one described with a volume of 185.2 cm³, is a real-world example of a cubic shape, although not related to the mathematical concept of a perfect cube.The properties of geometric shapes, like a cube, are significant in various fields, including chemistry, where the concepts of face-centered cubic unit cell become important in studying crystal structures.
Jessica purchase for the same type of scented candles Each of which are on sale for $2 off added the discount was applied the total cost for each candle is $19 what is the regular price of each candle
Answers
Final answer:
The regular price of each scented candle is $21, calculated by adding the $2 discount to the sale price of $19.
Explanation:
The regular price of each candle can be calculated by adding the discount back to the sale price.
If each candle costs $19 after a $2 discount, we just need to add the $2 discount to the sale price to find the regular price.
To calculate the regular price:
$19 (sale price) + $2 (discount) = $21 (regular price)
So, the regular price of each scented candle is $21 before the discount is applied.
Select all that apply.
Which of the following statements are true of the greatest common factor of two numbers?
A. Each number must share the factor.
B. The number must be large.
C. The greatest common factor could be 1.
D. The number must be the largest factor both numbers share.
and why cant it be the others
PLEASE HELP!!
Answers
Answer : A.Each number must share the factor,C.The greatest common factor could be 1 and D.the number must be the largest factor both numbers share.
I'm not sure... but good luck and have a nice Benevolentpuppy day!
Answer:
A,C,D is the answer
Step-by-step explanation:
Atticus wants to buy of a square yard of wrapping paper. The paper costs $2.40 per square yard. How much will Atticus spend on the wrapping paper?
a.$1.60
b.$4.80
c. $7.20
d. $9.20
Answers
Final answer:
Atticus will spend $1.80 on the wrapping paper when purchasing ¾ of a square yard at a cost of $2.40 per square yard, multiplying 0.75 by 2.40. However, this is not an option provided, indicating a possible typo. The closest choice to the correct answer given the options would be $1.60. (Option a)
Explanation:
The question asks how much Atticus will spend if he wants to buy ¾ of a square yard of wrapping paper, and the cost of one square yard of wrapping paper is $2.40. To find the cost of ¾ of a yard, we multiply ¾ by the cost per square yard. Here is the calculation:
Cost of ¾ yard = ¾ * $2.40
First, we convert ¾ into a decimal to make multiplication easier:
¾ = 0.75
Now, multiply:
0.75 * $2.40 = $1.80
Therefore, Atticus will spend $1.80 on the wrapping paper. However, this amount is not listed in the answer choices provided. If this is simply an error in the choices given, Atticus would spend $1.80, but based on the options presented, the closest correct choice would be (a) $1.60, suggesting there may be a typo in the question.
There is an average of 3.5 x 10^−2 kilograms of dissolved salt in each liter of seawater. The Pacific Ocean contains approximately 6.6 × 10^20 liters of seawater. About how many kilograms of dissolved salt are in the Pacific Ocean? Enter your answer, in scientific notation, in the boxes. __×__10 kg
Answers
___________________________________________
" 2.3 * 10^(19) " kg {dissolved salt in the Pacific Ocean} .
__________________________________________________
Explanation:
_____________________________
3.5 * 10⁻² * 6.6 * 10⁽²⁰⁾ = ? kg dissolved salt in the Pacific Ocean.
______________________________________________________
→ 3.5 * 10⁻² * 6.6 * 10⁽²⁰⁾ = 3.5 * 6.6 * 10⁻² * 10²⁰⁾ ;
___________________________________________
Note the following property of exponents:
___________________________________________
xᵃ * xᵇ = x⁽ᵃ⁺ᵇ⁾ ; so; 10⁻² * 10²⁰ = 10⁽⁻² ⁺ ²⁰⁾ = 10⁽ ¹⁸ ⁾ ;
→ So; we can rewrite our expression as:
___________________________________________
3.5 * 6.6 * 10⁽ ¹⁸ ⁾ ;
→ Note: 3.5 * 6.6 = 23.1 ---> Round to 2 (two) significant figures: 23 ;
Answer: 23 * 10⁽ ¹⁸ ⁾ ; to write in scientific notation; write the "whole number" as: "2.3" (a single digit, whole number integer, followed by a decimal", and adjust the exponent following the "10" accordingly, to make the value equal; and we have:
__________________________________________________
" 2.3 * 10^(19) " kg {dissolved salt in the Pacific Ocean} .
__________________________________________________
To find how many kilograms of dissolved salt are in the Pacific Ocean, multiply the amount of salt per liter by the total volume of water, giving a total of 2.31 x 10^19 kg.
The Pacific Ocean contains approximately 6.6 × 1020 liters of seawater, with an average of 3.5 x 10-2 kilograms of dissolved salt per liter.
To calculate the total amount of salt in the Pacific Ocean, you multiply the amount of salt per liter by the total volume of water.
So, the total amount of salt in the Pacific Ocean is 2.31 x 1019 kg.
what is the cube root of 8/25
Answers
Give me brainliest :D
The graph of the function f(x) = –(x + 1)2 is shown.
Answers
f(x) = -(x^2 + 2x + 1)
f(x) = -x^2 - 2x - 1
Answer:
Use the drop-down menus to complete the statements.
In order for f–1(x) to be a function, the domain of f(x) can be restricted to
✔ x ≥ 1
.
Under this restriction, the domain of f–1(x) would be
✔ x ≥ 2
, having the same minimum value as the
✔ range of f
.
Step-by-step explanation:
Anna made withdrawals from her bank account of $60, $85, and$ 115. Write and solve an addition problem that shows her withdrawals as negative integers.
Answers
The table below shows the salvage value for raw steel.
Tons of Steel Salvage Value
0 $0.00
2 $420.00
4 $840.00
6 $1,260.00
8 $1,680.00
10 $2,100.00
Based on the information in the table, what is the price per ton for raw steel? A. $220 B. $200 C. $210 D. $252
Answers
Answer:
$190
Step-by-step explanation:
The salvage value can be modeled by the function y = kx, where x is the number of tons of steel, y is the salvage value, and k is the price per ton.
Pick a point from the table, (2, 380), and evaluate the function y = kx at this point.
Therefore, the price per ton for raw steel is $190.
Final answer:
Based on the provided table, the price per ton for raw steel is calculated by dividing the salvage value by the tons of steel. The consistent result across the table is $210 per ton, making the correct answer C. $210.
Explanation:
To determine the price per ton for raw steel based on the table provided, we need to analyze the consistent increase in salvage value with respect to the tons of steel. Looking at the table:
For 2 tons of steel, the salvage value is $420.
For 4 tons of steel, the salvage value is $840.
For 6 tons of steel, the salvage value is $1,260.
For 8 tons of steel, the salvage value is $1,680.
For 10 tons of steel, the salvage value is $2,100.
To find the price per ton, we can divide the salvage value by the number of tons of steel. For example:
$$420 \div 2\text{ tons} = $210 \text{ per ton}$$
The price per ton remains consistent for every salvage value given, confirming that the price per ton of raw steel is $210.
Therefore, the correct answer is C. $210.
What is the LCM of two numbers that have no common factors greater than 1?
Answers
Two less than the product of a number and -5 is -42
Answers
-5x-2=-42
-5x=-40
x=8
The value of that number such that two less than the product of a number and -5 is -42 will be 8.
What is multiplication?Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.
If and only if the number being multiplied is more than one, multiplication produces a resultant number that is significantly larger than the original number.
Let's say that number is x
Given condition
Product of x and -5 = -5x
Two is less than = -5x -2
Equal to -42
So,
-5x - 2 = - 42
x = 8
Hence the correct answer is 8.
For more information about multiplication
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Convert the fraction to a decimal. Round to the nearest hundredths. 24/76
Answers
/4
6/19
=0.315789474
Divide the numerator by the denominator.
24/76
I'll approximate the decimal to 0.315 and round it to the nearest hundredths.
= 0.32
what number is 5% of 60?
Answers
Answer: 3
Step-by-step explanation: To find 5% of 60, first rewrite 5% as a decimal by moving the decimal point two places to the left to get .05.
Next the word "of" tells us we need to multiply so we multiply .05 by 60.
(.05) (60) = 3.00
Therefore, 5% of 60 is 3.
Image provided.
8x-2y=12 solve for y and slope
Answers
The required solution is y = 4x - 6 and slope is 4.
What is the equation of line?The general equation of straight line is
y = mx + c
where, m is the slope
and c is the intercept where the line cuts the y-axis.
Now the given equation is,
8x - 2y = 12
Dividing whole equation by 2 we get
4x - y = 6
Substacting 4x to the both side,
4x - y -4x = 6 -4x
Solving,
- y = 6 -4x
Multiplying whole equation by -1 we get,
y = 4x - 6
Comparing the above equation with the general equation of line
y = mx + c
Hence we get,
m= 4 which the slope,
and c = -6
Hence,the required solution is y = 4x - 6 and slope is 4.
More about line :
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Write the subtraction fact 10-3 two ways
Answers
The Subtraction [tex]10-3[/tex] is equal to [tex]\boxed7[/tex].
Further Explanation:
Given:
The expression is [tex]10-3[/tex].
Calculation:
Suppose John has [tex]10[/tex] chocolates in his pocket. He eats [tex]3[/tex] chocolates and then he wants to know how many chocolates he has.
The number of chocolates left can be obtained as,
[tex]10 - 3 = 7[/tex]
John left with [tex]7[/tex] chocolates.
The second way to subtract two numbers is number line.
A straight line that has all real numbers is known as number line.
Steps involve in subtraction of two numbers are as follows.
Step 1
Jump forward the number of times the first number is.
Step 2
Jump backward the number of times the second number is.
Here, we have to subtract 3 from 10.
Steps are as follows,
1. Jump 10 times forward on the number line.
2. Jump 3 times backward on the number line.
The final position is the answer that is 7.
Kindly refer to the image attached to the question.
Learn more:
1. Learn more about multiplication of two numbers https://brainly.com/question/573729
2. Learn more about subtraction of two numbers https://brainly.com/question/5723059
3. Learn more about division https://brainly.com/question/545132
Answer details:
Grade: junior School
Subject: Mathematics
Chapter: Subtraction
Keywords: subtraction, two ways of subtraction, fact of subtraction, expression, number line, jump, ten, three, seven, real numbers.
in part a and in part b, use each of the digits 2, 3, and 4 exactly once.
B: Write a mixed number that has a repeating decimal, and write the decimal.
I already have the answer to A. Plz help me. thx ;)
Answers
4 2/3 = 4.66 with a line over the 66 because it is repeating
Step-by-step explanation:
you need yo add and multiply the munbers
what is the multiplicative rate of change for the following coordinates (-1, .8) (0,2) (1,5) (2,12.5)
Answers
x y
-1 0.8
0 2
1 5
2 12.5
We work the multiplicative rate of change by finding out the increase ratio
12.5 ÷ 5 = 2.5
5 ÷ 2 = 2.5
2 ÷ 0.8 = 2.5
The ratio results in the same ratio every time, which is 2.5
The multiplicative rate of change = 2.5
A = 9 over 2 (b + 35)
Answers
You have -30 point in a video game. You earn 57 point. What is your final score?
Answers
You have 27 points.
Mr. Collins is constructing a fence around his property. He already has 25 sections up and plans to add 8 sections each Saturday until he is finished. Find the total number of fence sections standing after 15 Saturdays.
Answers
So, we know the Mr. Collins already has 25 sections. So let's write an equation.
25 + 8s
(s = Saturday)
Now our value for s in this equation is 15. So put in the value..
25 + 8 · 15
25 + 120
145
The answer is 145
Hope this helps! :)
The total number of fence sections standing after 15 Saturdays will be 145.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
Mr. Collins has 25 sections up.
And, He plans to add 8 sections each Saturday until he is finished.
Now,
By the given condition we formulate;
The total number of fence sections standing after 15 Saturdays is calculated as;
= 25 + 8 x 15
= 25 + 120
= 145
Thus, The total number of fence sections standing after 15 Saturdays will be 145.
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What is the length of line segment AB?
Answers
Answer:
10 units
Step-by-step explanation:
Alex has 175 baseball cards.Rodney has 3 times as many baseball cards as Alex.How many fewer cards does Alex have than Rodney?
Answers
3 x 175 = 525
alex has 175 and rodney has 525
525 - 175 = 350
alex has 350 less baseball cards than rodney
hope this helped
A photograph is 5 1/3 inches wide. It is being enlarged to 3 times its original size. What is the width of the enlarged photograph?
Answers
Courtney takes 2.4 x 10 to the 4th power steps during her long distance run each step covers an average of 810 mm what's the distance and then it is that going to cover during her run and scientific notation then convert the distance to the appropriate unit kilometers write answer in standard form
Answers
6.8+4.3+5.6 estimate a range for each sum
Answers
math question down below
Answers
what answer i need fast
Answers
2/3 cup pineapple for every 1/3 cup OJ
there are three 1/3 cups in 1 cup
so multiply 2/3 by 3
2/3 * 3 = 6/3 = 2
2 cups of pineapple juice is needed
Could someone pls help
Answers
14.) No, there are no integers between 0 and 1 since integers are whole numbers without any decimals, and the only numbers between 0 and 1 are decimals.
WhAt is the answer to -12 - 3=-51
Answers
Simplify both sides of the equation.
[tex]-12 - 3=-51[/tex]
[tex]-15 \neq -51[/tex]
Both sides of the equation are not equal.
Hope this helps.
-Benjamin
A plumber charges $30 per hour and $42 for each hour of overtime. For a job, the plumber works 3 regular hours, h overtime hours,and charges $195 for new parts. The total amount of the bill for the job is $390. Write and solve an equation to find the number of overtime hours the plumber worked.