is 12x=7y-10y a linear equation?
Answers
The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function is a function that varies linearly with respect to the changing variable.
Given the line,
12x = 7y - 10y
12x = -3y
-3y = 12x
Divide both sides by -3
y = -4x
The slope of any function is given as dy/dx or first differential
dydx = -4 so the slope is constant thus the line will be a linear equation.
The graph of the line also has been attached for refernce.
Hence "The slope of the given equation 12x = 7y - 10y is -4 (constant) thus it will be a linear equation".
For more about the linear function,
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The equation 12x = 7y - 10y simplifies to 12x = -3y and is a linear equation because it can be rewritten in the form y = mx + b, where m is the slope (-4) and b is the y-intercept (0).
Explanation:The equation 12x = 7y - 10y simplifies to 12x = -3y, which can then be written in the slope-intercept form as y = -4x. This is a linear equation because it can be expressed in the standard form y = mx + b, where m represents the slope and b is the y-intercept. In this equation, m equals -4 and b equals 0, indicating that the line crosses the y-axis at the origin (0,0).
Similar examples of linear equations include 7y = 6x + 8, 4y = 8, and y + 7 = 3x. These equations all have a constant rate of change, which is characteristic of linear relationships, where one variable is a constant multiple of the other plus a constant (y = a + bx). As a real-life example, the equation y = 55x + 75 represents the total labor charges to fix a car, with y being the dependent variable and x the independent variable, showcasing the linear relationship between hours worked and total charges.
Related Questions
Explain how you use the bar model to solve 14-7 equal seven
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A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the seminar on the second day was 15 how many students were in the class on the first day
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The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
Answers
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
[tex]-2x^2+4x=-1[/tex]. Now we factor out the -2:
[tex]-2(x^2-2x)=-1[/tex]. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
[tex]-2(x^2-2x+1)=-1-2[/tex]. Simplifying gives us this:
[tex]-2(x^2-2x+1)=-3[/tex]
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
[tex]-2(x-1)^2+3=y[/tex]
From this form,
[tex]y=-a(x-h)^2+k[/tex]
you can determine the coordinates of the vertex to be (1, 3)
Answer:
(1,3)
Step-by-step explanation:
52.063 divided into 9.2 rounded to the nearest hundredth
Answers
Answer:
The answer is 5.66
Step-by-step explanation:
52.063 divided by 9.2 is 5.65902173913. Then you round of to the nearest hundredth which is two decimal places to the right (so it's 5). Then you round it off one value higher since 9 is above 5. Therefore the final answer is 5.66
What is the area of ABC below? If necessary, round your answer to two decimal places.
Answers
(9.4)^2 + (23.2)^2 = c2
88.36 + 538.24 = c2
626.6 = c2
c= 25.03
Now that we have the base, let us proceed for the Area.
The formula for area would be A = 1/2 (b)(h)
Plug in the values.
A = 1/2(25.03)(7.9)
A= 1/2(197.74)
A= 98.87
Therefore, the area of figure ABC is 98.87.
Hope this answer helps.
The answer I got from apex was- 106.26
Write the distribution of 7×6=
Answers
Denver is called the mile-high city because it is at an altitude of 1 mile. how many feet is the
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what is the value?
5x+3=4x ?? bit confused
Answers
x+3=0
minus 3 from both sides
x=-3
two consecutive odd negative integers have a product of 483, find the integers ...?
Answers
x^2+2x-83=0
From this we can see that a negative X is -23, which when +2 is added results in -21.
You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?
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Henry has 523 baseball cards. He buys 24 each month. What is a explicit rule for the number of baseball cards Henry has in n months?
Answers
Answer:
the answer is a_n= 24n+499 just took the test :)
Step-by-step explanation:
Justine enrolls in a music program. The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. If the average cost per music lesson is $12 and Justine has taken x classes, which equation represents this scenario?
A.12=54/x
B.12=45+9/x
C.12=45+9x/x
D.12=45x+9/x
Answers
If Justine has taken x classes of $9 per lesson, then the total fee for these lessons is $9x.
The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. This means that the total cost of the program in terms of x is
$45 + $9x = $(45 + 9x).
If the average cost per music lesson is $12 (includes a registration fee), then the cost of the program is $12x.
Therefore,
12x = 45 + 9x.
Divide this equation by x:
[tex]12=\dfrac{45+9x}{x}.[/tex]
Answer: correct option is C
The correct option is C) [tex]\[12 = \frac{45 + 9x}{x}\][/tex]. The equation that represents this scenario is [tex]\[12 = \frac{45 + 9x}{x}\][/tex].
To understand why option D is correct, let's break down the costs associated with Justine's music program.
1. The registration fee is a one-time cost of $45. This is a fixed amount and does not depend on the number of classes taken.
2. The cost per lesson is $9, and Justine has taken x classes. Therefore, the total cost for the lessons alone is 9x.
3. The average cost per music lesson, including the registration fee, is $12. This average cost is calculated by taking the total cost (registration fee plus the cost of x lessons) and dividing by the number of classes x.
4. The total cost for x classes, including the registration fee, is the sum of the registration fee and the cost of the lessons, which is [tex]\(45 + 9x\)[/tex].
5. To find the average cost per lesson, we divide the total cost by the number of classes x. This gives us the equation [tex]\(\frac{45 + 9x}{x}\)[/tex].
6. We know that the average cost per lesson is $12, so we set the equation equal to 12: [tex]\(12 = \frac{45 + 9x}{x}\).[/tex]
Therefore, the equation that correctly represents the scenario is: c)
[tex]\[12 = \frac{45 + 9x}{x}\][/tex].
Use the function described below to answer questions 1 - 4.
Yvonne invested $4,000 in a savings account which pays 3.5% interest compounded annually. Use the formula A = P(1 + r)t, where P is the principal, r is the interest rate, and t is the time in years.
1. Approximately, how much money will Yvonne have in 4 years? Round to the nearest cent.
2. Approximately, how much money will Yvonne have in 8 years? Round to the nearest cent.
3. Approximately, how many years will it take for Yvonne to double her money? Write the number of years only.
4 Alex buys a top of the line computer. He did not realize that the computer would lose value so fast. If his computer cost $1800.00 and it depreciates at a rate of 45% each year, in how many years will it be worth less than 1/3 of what he paid for it?
Answers
Heather has $500 in her savings account. she withdraws $20 per week for gas. write an equation heather can use to see how many weeks it will take her to have a balance of $220.
Answers
220 - 500 = -20w
- 280 = -20w
-280/-20 = w
14 = w.....it would take 14 weeks
What is 35/10 convert into a decimal?
Answers
Subtract -34.7 from -7.85
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Lauren bought 6 yellow roses, 10 orange roses, and 12 pink roses to make a bouquet. What is the ratio of the number of yellow roses to the total number of roses in Lauren’s bouquet?
Answers
yellow roses:roses
4x-6=10x-3
?? i am bad at math lol
Answers
4x-6=10x-3
minus 4x both sides
-6=6x-3
add 3 to both sides
-3=6x
divide both sides by 6
-1/2=x
take care.
0.00014s in scientific notation? ...?
Answers
Is the value in scientific notation
Factor completely: 2x3 + 10x2 + 4x + 20
Prime
(2x + 10)(x2 + 2)
2[(x + 5)(x2 + 2)]
(x + 5)(2x2 + 4) ...?
Answers
[tex]2x^3 + 10x^2 + 4x + 20 \\2x^2(x+5)+4(x+5) \\(x+5)(2x^2+4)[/tex]
Answer:
B) 2[(x + 5)(x2 + 2)]
Step-by-step explanation:
Given: 2x^3 + 10x^2 + 4x + 20
Here 2 is a common factor, so we take it out and write the remaining terms in the parenthesis.
2(x^3 + 5x^2 + 2x + 10)
Now let's take (X^3 + 5x^2 +2x + 10), we group and factor them as follows:
(x^3 + 5x^2 + 2x + 10) = x^2(x+5) + 2(x + 5) = (x+5)(x^2 +2)
When we combine them, we get
2x^3 + 10x^2 + 4x + 20 = 2(x+5)(x^2 +2)
Therefore, the answer is B) 2[(x + 5)(x2 + 2)]
Hope this will helpful.
Thank you.
The price of a pair of shoes is $63.20. The sales tax rate is 4.5 percent. How much sales tax would you pay if you bought these shoes? A.) $2.84 B.) $3.16 C.) $4.50
Answers
tax=tax rate(change the % to a decimal)xprice of item
which in this case comes out to be $2.84
if (3x^2)+7=0 then (x-1/3)^2
Answers
Add.
(5n^2+4n)+(3n^2+6n)
Answers
5n^2+3n^2+4n+6n=
8n^2+10n
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a_______
.When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, _______vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answers
Answer:The first one is a Reflection
The second one is B
Step-by-step explanation:
A 13 foot ladder is leaning against a wall. If the point where the ladder meets the wall is 12 feet above the ground, how far from the base of the wall is the the ladder?
A) 1 foot
B) 2 feet
C) 5 feet
D) 22 feet
Answers
5 feet.
A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?
Answers
T = 15d +r/4 +2h
or
you can write another way
T = 15d + 0.25r + 2h
Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]
Step-by-step explanation:
Let d = days, r = raffle tickets, and h = hours.
Given: A student earns in a day = $15
Then his earning in d days =$15d
Also, he earns for each riffle = $0.25
Then his earning in for r riffles =$0.25r
And , he earns for each hour he works at the game = $2
Then his earning for h hours = $2h
Then the function he can use to calculate his earnings is given by :_
[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]
Bill makes four payments a year of $128.25 for life insurance; four payments of $161.82 for real estate taxes; twenty-four payments of $37.46 for health insurance; and six payments of $221.65 for auto insurance. What is the total of his annual fixed expenses for these items?
Answers
162.82 × 4 = 651.28
37.46 × 24 = 899.04
221.65 × 6 = 1329.9
So add them all up.
3393.22
To calculate the total annual fixed expenses, we multiply the number of yearly payments by the amount of each payment for the different insurances and taxes, and then add these products together to find that the annual fixed expenses total $3,388.74.
The student has asked to calculate the total of his annual fixed expenses for life insurance, real estate taxes, health insurance, and auto insurance. To determine this, we will multiply the amount of each payment by the number of times the payment is made annually and then sum these amounts to get the total yearly expense:
Life Insurance: 4 payments of $128.25
Real Estate Taxes: 4 payments of $161.82
Health Insurance: 24 payments of $37.46
Auto Insurance: 6 payments of $221.65
Now, we calculate each:
Life Insurance: 4 imes $128.25 = $513.00
Real Estate Taxes: 4 imes $161.82 = $647.28
Health Insurance: 24 imes $37.46 = $898.56
Auto Insurance: 6 imes $221.65 = $1,329.90
Adding these amounts gives us the total annual fixed expenses:
$513.00 (Life Insurance) + $647.28 (Real Estate Taxes) + $898.56 (Health Insurance) + $1,329.90 (Auto Insurance) = $3,388.74 as the annual fixed expenses.
Mark has a baking tray with 24 muffins and the muffin are arranged in 4 equal rows how many are there in each row
Answers
4 equal rows
24 / 4 = 6
The answer is: 6 muffins in each row
Hope the answer helps :)
There are 6 muffins in each row.
Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?
Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.
Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).
Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).
Answers
f(x) = -f(-x) or in other words
-f(x) = f(-x)
9 - 4x^2 = -(9-4(-x)^2) or in other words
-(9-4x^2) = 9 - 4(-x)^2
Answer is third option.
Answer:
Its CCCCCCCCCCCCCCC aka 3 aka third option
on dredful edge im going nuts
Step-by-step explanation:
A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
5 units
10 units
12.5 units
Answers
The diameter of the cylinder with a volume of 175 cubic units and a height of 7 units is 5 units.
To calculate the diameter of a cylinder, we first need to find the radius using the formula for the volume of a cylinder, V = πr²h. Given that the volume is 175 cubic units and the height is 7 units, the radius comes out to be 5 units. Since the diameter is twice the radius, the diameter of the cylinder is 5 units.