Final answer:
Solving the equation 1/3(2x-4)+5=-2/3(x+1) involves distributing the fractions, combining like terms, and then multiplying by the reciprocal to isolate x, which results in a solution of x = -4.
Explanation:
To solve the linear equation 1/3(2x-4)+5=-2/3(x+1), you start by distributing the fractions across the parentheses and then combine them like terms. First, multiply 1/3 by each term inside the parentheses (2x-4) and -2/3 by each term inside (x+1), which gives:
2/3x - 4/3 + 5 = -2/3x - 2/3
Next, combine like terms and add 2/3x to both sides:
2/3x + 2/3x = -2/3 - 5 + 4/3
This simplifies to:
4/3x = -16/3
To isolate x, multiply both sides of the equation by the reciprocal of 4/3, which is 3/4:
x = (3/4) x (-16/3) = -4
The solution for x in the given equation is -4.
Final answer:
To solve the equation 1/3(2x-4)+5=-2/3(x+1), we need to simplify the equation and isolate the variable x. The solution to the equation is x = -7/12.
Explanation:
To solve the equation 1/3(2x-4)+5=-2/3(x+1), we need to simplify the equation and isolate the variable x. Let's start by distributing and solving the equation:
1/3(2x-4)+5=-2/3(x+1)
(2/3)x - 4/3 + 5 = (-2/3)x - 2/3
Combining like terms:
(2/3)x + 5/3 = (-2/3)x - 2/3
Add (2/3)x to both sides:
(2/3)x + (2/3)x + 5/3 = (-2/3)x + (2/3)x - 2/3
Simplify:
(4/3)x + 5/3 = -2/3
Subtract 5/3 from both sides:
(4/3)x + 5/3 - 5/3 = -2/3 - 5/3
Simplify:
(4/3)x = -7/3
Finally, divide both sides by 4/3 to solve for x:
(4/3)x / (4/3) = -7/3 / (4/3)
Simplify:
x = -7/12
Therefore, x = -7/12 is the solution to the equation.
Steven recorded the growth of a plant over 10 weeks for his science project. He made a graph that shows how much the plant grew each week. The plant was 2 in. tall when Steven started his project. At week 5, the plant was 8 in. tall.
Which equation represents Steven’s situation, where x is the number of weeks and y is the height of the plant?
A. y= 8/5x+2
B. y= 6/5x+2
C. y= 5/8x+2
D. y= 5/6x+2
Answer:
Answer is option B.
Step-by-step explanation:
Given information:
Assume the growth of plant is linear
When Steven started his project [tex](x_1=0)[/tex] , growth of plant is[tex](y_1=2 \rm in)[/tex]
At week 5,[tex](x_2=5)[/tex], growth of plant is [tex](y_2=8 \rm in)[/tex]
We know, equation of line is,
[tex](y-y_1)=m\times (x-x_1)[/tex],where [tex]m[/tex] is the slope of equation
[tex]m=\frac{y_2-y_1}{x_2-x_1} =\frac{8-2}{5-0}=\frac{6}{5}[/tex]
On substituting [tex]m[/tex],
[tex](y-2)=\frac{6}{5}\times (x-0)[/tex]
[tex]y=\frac{6}{5}x +2[/tex]
So, answer is option B.
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in order for terms to be like terms they must have?
what is the simplest form of 12/18
probabiltiy can be used to determine the likelihood of specific ---------------- ( a:games,b:occurrences,c:questions,d:opportunities
Explain why the greatest common factor of two numbers is sometimes 1.
JAYDEN HELP PLZ !!!!!!Select from the drop-down menu to correctly complete the statement about the given figures.
Triangles ABC and DEF are Similar or not similar
Answer:
hello can you give the other person brainliest
Step-by-step explanation:
how do you find the markuo and markup rate if the price is $49.95 and the cost is 26.97
There are 16,925 bottles of red paint packed in a box. There are 21,775 bottles of blue paint packed in another box.
How many more bottles of blue paint than red paint are there?
(insert something here) more bottles
when is the diffrence of two decimals an interger
Answer:
The diffrence is that 2 placed decimals are not a whole number being contained into an equation/expression.
Step-by-step explanation:
12.45 - 7.33 = 5.12
12-7=5
Please help me as soon as possible, I'll give brainliest to whoever got it done and right first. Here's the question:
Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the y-intercept, x-intercepts, and the shape of the graph.
What names does the square root of 35 fit into? (whole number, not real, real, irrational, rational, intergers, etc.)
Steve was offered $5,025 per year for a weekend lifeguard ing job at a local pool. he wants to know how much his monthly income will be at this salary level. what is his rate of pay in dollars per month ?
The rate of his salary per month is $418.75
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For Example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Steve was offered $5,025 per year
We know, 1 year= 12 month
So, Steve's Salary per month would be
= 5025/ 12
= $418.75
Hence, the rate of his salary per month is $418.75
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Relationship A has a lesser rate than Relationship B. This table represents Relationship B.
Hours worked 2 4 5 8
Amount paid ($) 36.50 73 91.25 146
Which equation could represent Relationship A?
Hours worked is represented by x and Amount paid is represented by y.
Select each correct answer.
y = 18.1x
y = 18.6x
y = 18.3x
y = 18x
Answer:
y = 18.1x ; and y = 18x
Explanation:
The rate of change in Relationship B can be found by using the formula for slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Using the first two points, we have
[tex]m=\frac{73-36.50}{4-2}=\frac{36.50}{2}=18.25[/tex]
We know that Relationship A has a lesser rate than this. The choices given for Relationship A are written in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept (in this case b = 0).
The slope of the first equation is 18.1; this is less than 18.25.
The slope of the second equation is 18.6; this is greater than 18.25.
The slope of the third equation is 18.3; this is greater than 18.25.
The slope of the fourth equation is 18; this is less than 18.25.
Answer:
Option A and D.
Step-by-step explanation:
If a linear function passes through two points, then the rate of change is
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
From the given table it is clear that the Relationship B have two ordered pairs (2,36.50) and (4,73). So, the rate of Relationship B is
[tex]m=\dfrac{73-36.50}{4-2}[/tex]
[tex]m=\dfrac{36.50}{2}[/tex]
[tex]m=18.25[/tex]
The rate of relation B is 18.25.
Let hours worked is represented by x and amount paid is represented by y. So the Relationship B is defined as
[tex]y=kx[/tex]
Where, k is the rate of relationship A.
It is given that Relationship A has a lesser rate than Relationship B.
[tex]k<18.25[/tex]
We know that
[tex]18.1<18.25[/tex], [tex]18.6>18.25[/tex], [tex]18.3>18.25[/tex] and [tex]18<18.25[/tex].
The relationship A could be
[tex]y=18.1x[/tex] and [tex]y=18x[/tex]
Therefore, the correct options are A and D.
help with geometry please
Please Hurry!!
6 x 10^4 is how many times greater than 3 x 10^-5
A 2 × 10^9
B 4 × 10^−1
C 4 × 10^1
D 2 × 10^−9
How many times greater is 7,000 than 70
To find out how many times greater 7,000 is than 70, one needs to perform a division operation. In this case, it would be 7,000 divided by 70 which equals 100. Hence, 7,000 is 100 times greater than 70.
Explanation:To determine how many times greater 7,000 is than 70, one must use division. This is done by dividing 7,000 by 70. The equation would look like this: 7,000 ÷ 70. If you solve the equation, the answer is 100. Therefore, 7,000 is 100 times greater than 70.
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determine whether the ordered pair (8,-5) is a solution to the equation 3x-2y=6
Andrew lives 1.7 kilometers from soccer field. He rode his bike 0.9 of the distance to the field. How much farther does Andrew need to ride to reach the soccer field. Include an area model in your answer.
Write a real-word problem where you have to multiply 120 and 75.
Please help best answer will be marked as braniiest
In a cinema with 120 rows and 75 seats in each row, we can find the total number of seats by multiplying these two numbers together. This results in 9000 total seats.
Explanation:The subject of this question is related to a real-world mathematical problem. Suppose there is a cinema having 120 rows and each row consists of 75 seats. We want to find out the total number of seats in the cinema hall.
To solve this, we need to use multiplication. In mathematics, multiplication is one of the four elementary mathematical operations, with the other three being addition, subtraction, and division. By multiplying 120 (the number of rows) with 75 (the number of seats in each row), you can find out the total number of seats in the cinema hall.
So, 120 * 75 = 9000. Hence, there are 9000 seats in the cinema.
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6 times the sum of 12 and 8
math question down below
Which state's ratification guaranteed the constitution's approval?
the volume of 10 000 drops of liquid is 1 fluid ounce. what is the volume of 1000
Chet needs to buy 4 work shirts, all costing the same amount. The total cost before Chet applies a $25 gift certificate can be no more than $75. Write an inequality to find the possible amounts that Chet pays per shirt. Identify what your variable represents.
Over the last week the daily low temperatures in degrees Fahrenheit have been -4 , 6.2 , 18 1/2 , -5.9 , 21 , -1/4 , And 1.75.list all these numbers in order from greatest to least
Carmen has 18 connecting cubes. She wants to model a house shaped like a rectangle. If the model has a height of one connecting cube, how many different ways can Carmen model the house using all 18 connecting cubes?
To determine the number of ways Carmen can model the house using all 18 connecting cubes, considering them as distinguishable objects and applying permutations is essential.
Explanation:Carmen has 18 connecting cubes and wants to model a house shaped like a rectangle with a height of one connecting cube. To find the number of ways to model the house using all 18 cubes, we can approach it using combinatorics. One way to visualize this is by considering the cubes as distinguishable objects and applying permutations.
One approach could involve fixing the base of the rectangle, which will have a length of 16 cubes, leaving 2 cubes for the width. The 2 remaining cubes can be placed in 2! = 2 ways. So, the total number of ways to model the house would be 16!×2.
Answer:
There are 3 ways.
Step-by-step explanation:
Let each cube be 1 cm on the side.
The volume of each cube is 1 cm³.
volume = length × width × height
We are told the height is 1.
The volume is 18 cubes, so volume = 18 cm³.
length × width × height = 18 cm³
length × width × 1 cm = 18 cm³
length × width = 18 cm³
There are 3 ways to factor 18 into integer factors:
1, 18
2, 9
3, 6
Carmen can make the model 18 cubes long by 1 cube wide,
or 9 cubes long by 2 cubes wide, or 6 cubes long by 3 cubes wide.
Answer: There are 3 ways.
Help now get lots of points
Answer:
A. y = 2/3x + 3 --> 2x - 3y = -9
B. 6 - y = -5x + 8 --> 5x - y = 2
C. y - 3 = 4(x - 3) --> 4x - 9 = y
D. -7/6x + 1 = y --> 7x + 6y = 6
what is the answer please -16-1x=-4x+8
-16-1x = -4x +8
add 1x to each side
-16 = -3x +8
subtract 8 from each side
-24 = -3x
divide both sides by -3
x = -24 / -3 = 8
x = 8
Mt. Everest rises 54768 feet in the air while Mt. Rushmore stretches a mere 8976 feet . What is the difference in the height of these two mountains expressed in scientific Notation?
The difference in height between Mt. Everest and Mt. Rushmore is 45,792 feet expressed in standard notation and 4.5792x10^4 feet in scientific notation.
Explanation:
The student is asked to calculate the difference in height between Mt. Everest and Mt. Rushmore and express that difference in scientific notation. The height of Mt. Everest is 54,768 feet and the height of Mt. Rushmore is 8,976 feet. To calculate the difference in height, subtract the height of Mt. Rushmore from the height of Mt. Everest: 54,768 feet - 8,976 feet = 45,792 feet.
To express this difference in scientific notation, move the decimal point to just after the first digit (4), resulting in 4.5792. Then count how many places you moved the decimal. In this case, it moved 4 places, so the exponent is 4. Therefore, the difference in height between Mt. Everest and Mt. Rushmore is approximately 4.5792x10^4 feet in scientific notation.
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What is the procedure for multiplying by a one digit number?