The equation of a line which is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1) will be [(4y + x) = 2].
As per the question statement, a line is perpendicular to [y = (4x - 11)] and passes through the point (-2, 1).
We are required to determine the equation of the above mentioned line.
Now, we know that, the standard equation of a line goes as [y = (mx + c)] where, "m" is the slope of the line while "c" is the y-intercept.
Comparing [y = (4x - 11)] to the standard form, we can identify that (m = 4), i.e., slope of the given line is 4.
Since the products of the slopes of two perpendicular lines is (-1), and considering the slope of our required line to be "m₁", we can say that,
[tex]4*m_{1}=(-1)\\ or,m_{1}=\frac{-1}{4}[/tex]...[since our required line is perpendicular to [y = (4x - 11)]
and slope of [y = (4x - 11)] is 4]
That is, slope of our required line is [tex](\frac{-1}{4})[/tex].
Another concept we need to know about forming the equation of a line is that, the equation of a line can be written as [tex][(y-y_{1})=m(x-x_{1})][/tex], if the line passes through the point (x₁, y₁).
Here, our concerned line passes through the point (-2, 1) and has a slope of [m = [tex](\frac{-1}{4})[/tex]].
Therefore, equation of our concerned line can be written as
[tex](y-1)=(\frac{-1}{4})[x-(-2)]\\or,(y-1)=(\frac{-1}{4})(x+2)\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{4}*2)\\ or,(y-1)=(\frac{-x}{4})+(\frac{-1*2}{4})\\or,(y-1)=(\frac{-x}{4})+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+1+(\frac{-1}{2})\\or,y=(\frac{-x}{4})+(1-\frac{1}{2})\\or, y=(\frac{-x}{4})+\frac{1}{2}\\or,4y=(-x)+2\\or,4y+x=2[/tex]
Line: In geometry, a line is an one-dimensional figure with infinite length and no width, depth, or curvature.To learn more about Lines, click on the link below.
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c² +16c+n
how to solve for N
Solve the quadratic equation
c² +16c+64 = 0
The solution of this The solution of this quadratic equation are -8 and 0. are -8 and 0.
Step-by-step explanation:
Given that
The quadratic equationc² +16c+64 = 0
To find
The solution of this quadratic equationSo, according to the question
we have,
c² +16c+64 = 0We can solve this quadratic equation by factorising method.
So, we have to convert it on factors,
c² +16c+64 = 0
For getting it's factors, we have to divide 16c part in two parts,
So, we can write 16c = 8c + 8c,
c² +16c+64 = 0
c² +8c+ 8c+ 64 = 0
Now,
c(c +8) + 8(c+ 8) = 0
(c+8)(c+8) = 0
(c+8)² = 0
or,
(c + 8) = √0 (∵ √0 = 0)
c + 8 = 0
Now, we can say that
c = -8 or 0
Answer:
The solution of this quadratic equation are -8 and 0.To learn more about quadratic equation, please click on the link:
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5 2/3 + 29/69 + 6 21/23
Answer:13
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
i hope it's helpful for you
Your teacher has 35 balloons. She buys 4 packs of balloons. Each pack has 10 balloons. How many does she have now?
Answer:
75
Step-by-step explanation:
35+4x where x is 10
35+4*10
35+40
75
Answer:
75
Step-by-step explanation:
4 packs of balloons which each have 10 balloons is 40 total balloons she bought. Add 40 to 35 which is 75.
Drag each number to the correct location on the equations.each number can be used more than once.
(Need help asap)
Answer:
sin = 12/15 cos = 9/15 tan = 12/9
Step-by-step explanation:
Easy way to remember this is
SOH CAH TOA
O is opposite ( 12 in this problem )
H is hypotenuse i.e. opposite of the right angle ( 15 in this problem )
A is adjacent ( 9 in this problem )
420 ÷ d = 30; d= 15
[tex]420 \div d = 30 \: d = 15[/tex]
The required answer for the given equation is d = 1/2, ±√14.
What is division?The division is one of the four basic mathematical operations, the other three being addition, subtraction, and multiplication.
Now the given equation is,
420 ÷ d = 30d = 15
Now if,
30d = 15
Then divide both the side by 30 we get,
30d/30 = 15/30
Solving we get,
d = 1/2
this is the required value of d
Now if,
420 ÷ d = 30d
So simplifying it we get,
420/d = 30d
multiplying both the side by d we get,
d*420/d = 30d*d
Solving we get,
30d^2 = 420
Dividing both the side by 30 we get,
30d^2/30 = 420/30
Solving we get,
d^2 = 14
Taking square root both the side we get,
√d^2 = √14
Solving we get,
d = ±√14
this is the required value of d.
Thus, the required answer for the given equation is d = 1/2, ±√14.
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Solve for x then give the measure of the bolded angle.
Answer:
73 - Explanation and Check below
Step-by-step explanation:
11x - 4 = 9x + 10
1. Get variable (x) on one side.
11x - 4 = 9x + 10
- 9x - 9x
2x - 4 = 10
2. Solve 2 step equation - add 4 on both sides of equation.
2x - 4 = 10
+ 4 + 4
3. Divide 2 on both sides of equation.
2x = 14
---- ----
2 2
x = 7
Check:
11 (7) - 4 = 9(7) + 10
77 - 4 = 63 + 10
73 = 73 True statement.
Explanation:
If a transversal intersects two parallel lines, the corresponding angles will be always equal.
So in the problem, the two given equations are equal to each other.
The answer for the two angles with equations is 73.
Also, the angles vertical to the two equations are also 73 because vertical angles are congruent (equal).
Hope this helps :)
what is the answer to this-0.8x+40-8x-35
Answer:
-8.8x +5
Step-by-step explanation:
You want to simplify the expression -0.8x+40-8x-35.
Like termsThe expression is simplified by combining like terms. Like terms have the same (set of) variables.
-0.8x +40 -8x -35
= -0.8x -8x +40 -35 . . . . . . group like terms
= (-0.8 -8)x +(40 -35)
= -8.8x +5
Need to find the value of x
Select all the expressions that have 23 as a product.
2125×5063
78×925
130×23
325×712
2027×2730
The expression that have 23 as a product is 130×23
How to select all the expressions that have 23 as a product?For an expression to have 23 as a product, the expression must be a multiple of 23
This is indicated by
x/23 => Integer
So, we have:
2125×5063/23 = 4677..... (false)
78×925/23 = 3136.9....(false)
130×23/23 = 130 --- true
325×712/23 = 10060.... (false)
2027×2730/23 = 240596.. (false)
Hence, the expression that have 23 as a product is 130×23
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can someone help me with this
thanks so much for the help!
For the given graph:
domain is D: [-2, 0)range is R: [0, 2)And yes, it is a function.
How to find the domain and range of the given function?For a given function y = f(x), the domain is the set of the inputs (possible values of x) and the range is the set of outputs (possible values of y).
To identify the domain we need to look at the x-axis (the horizontal one)
We can see in the left side that the first value is -2, whith a closed circle, meaning that the value belongs to the domain.
The right side is x = 0, with a open circle, which means that it does not belong to the domain.
Then the domain is D: [-2, 0)
Similarly, by looking at the y-axis (vertical axis) we can find the range which is:
R: [0, 2)
Finally, how to know if this is a function?
There is something called the "vertical line test". This test says that if you can't draw a vertical line that intersects the graph in two points or more, then it is a function.
And the graph clearly meets that test, so it is a function.
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What is the slope of the line that contains these points?
Answer: Slope=5/3
Step-by-step explanation:
my teacher said
At a basketball game, 54% of people attending were supporting the home team, while 46% were supporting the visiting team. If 1566 people attending the game supported the home team, what was the total number of people attending the game? HELPP FASTT
i know how to do a and c, but how do i do b)?
Explanation:
Start at -1 on the x axis number line. Then move vertically until reaching the function curve. You should arrive at (-1,2). This tells us that g(-1) = 2. In other words, the input x = -1 leads to the output y = 2.
Follow similar steps to find that g(1) = -2
Therefore, g(-1)+g(1) = 2 + (-2) = 0
-48.54 divided by -6
Answer:
-48.54 ÷ -6 = 8.09
so the answer is 8.09
hope this helps
9(3.2)^2+4x-11 how to solve
The solution of the given linear equation is (103.16 + 4x).
What is meant by linear equation?Linear equations are degree 1 equations. It is the straight line equation. The standard linear equation is ax+by+c =0, where a and b are both are not zero. There are only 1 or 2 two variables in a linear equation. In a linear equation, no variable is raised to a power greater than just one or is employed as the denominator of such a fraction. When you find two values that satisfy a linear equation and plot them on a coordinate grid, each of the points fall on the same line.The given equation is;
= 9(3.2)² + 4x - 11
For finding (3.2)² = 3.2×3.2
(3.2)² = 10.24
Put the value in equation;
= 9×10.24 + 4x - 11
Multiply 9×10.24 = 92.16
Put the value;
= 92.16 + 4x + 11
Now, add the constant value
= (92.16 + 11) + 4x
= 103.16 + 4x
As, 4x is a variable part, it will not get added to the constant 103.16.
Thus, the solution of the equation is 103.16 + 4x.
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evaluate -4 - 5+4+(-5)
How do I factor 5X = 3(X+6)
Answer:
Step-by-step explanation: 5x=3(x+6)
5x=3x+18
5x-2x=18
3x=18
x=18/3
x=6
Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $3,500 for their reception. If the reception hall charges a $50 cleanup fee plus $30 per person, find the greatest number of people that they may invite and still stay within their budget
-2(x-5)+10=-3(x+2)+x
Answer:-26
Step-by-step explanation:
-2+10+10=-3(x+2)+x=-26 np
Susan gives five dollars to Joe if Susan started with $18 how much money does she have left
Tyler Tooling Company uses a job order cost system with overhead applied to products on the basis of machine hours. For the upcoming year, the company estimated its total manufacturing overhead cost at $420,000 and total machine hours at 60,000. During the first month of operations, the company worked on three jobs and recorded the following actual direct materials cost, direct labor cost, and machine hours for each job:
Job 101 Job 102 Job 103 Total
Direct materials used $ 19,200 $ 14,400 $ 9,600 $ 43,200
Direct labor $ 28,800 $ 11,200 $ 9,600 $ 49,600
Machine hours 1,000 4,000 2,000 7,000
Job 101 was completed and sold for $60,000.
Job 102 was completed but not sold.
Job 103 is still in process.
Actual overhead costs recorded during the first month of operations totaled $45,000.
Required:
Prepare a journal entry showing the transfer of Job 102 into Finished Goods Inventory upon its completion.
Prepare the journal entries to recognize the sales revenue and cost of goods sold for Job 101.
Prepare the journal entry to transfer the balance of the Manufacturing Overhead account to Cost of Goods Sold
1. The journal entry to show the transfer of Job 102 into Finished Goods Inventory after its completion is as follows:
Journal Entry:Debit Finished Goods $53,600
Credit Work in Process: Job 102 $53,600
2. The journal entries to recognize the sales revenue and cost of goods sold for Job 202 are as follows:
Journal Entries:Debit Cash/Accounts Receivable $60,000
Credit Sales Revenue $60,000
Debit Cost of goods sold $55,000
Credit Finished Goods Inventory $55,000
3. The journal entry to transfer the balance of the Manufacturing Overhead account to the Cost of Goods Sold account is as follows:
Journal Entry:Debit Manufacturing Overhead $4,000
Credit Cost of Goods Sold $4,000
Data and Calculations:Estimated total manufacturing overhead = $420,000
Estimated total machine hours = 60,000 hours
Predetermined overhead rate = $7 ($420,000/60,000)
Job 101 Job 102 Job 103 Total
Direct materials used $ 19,200 $ 14,400 $ 9,600 $ 43,200
Direct labor $ 28,800 $ 11,200 $ 9,600 $ 49,600
Applied overhead $7,000 $28,000 $14,000 $49,000
Total costs $55,000 $53,600 $33,200 $141,800
Machine hours 1,000 hours 4,000 hours 2,000 hours 7,000 hrs
Status of Jobs Sold Finished WIP
Sales revenue (Job 101) = $60,000
Manufacturing Overhead Account:Actual overhead costs for the first month = $45,000
Applied overhead for the first month = $49,000 ($7 x 7,000)
Overapplied overhead = $4,000 ($49,000 - $45,000)
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In the lab, Heather has two solutions that contain alcohol and is mixing them with each other. She uses 4 times as much Solution A as Solution B. Solution A is
15% alcohol and Solution B is 12% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 216 milliliters of pure alcohol?
Answer:
1200 ml
Explanation:
Let x be the quantity ( in ml ) of b solution,
∵ solution a is 100 milliliters less of than solution b.
So, the quantity of solution a = 100 - x,
Now, solution a has 13% alcohol,
∴ Alcohol in solution a = 13% of (100-x) = = 0.13(x-100),
While solution b has 17% alcohol,
∴ Alcohol in solution b = 17% of x = 0.17x,
So, the quantity of alcohol in the mixture of a and b = 0.13(x-100) + 0.17x
= 0.13x - 13 + 0.17x
= 0.30x - 13
According to the question,
Total quantity of alcohol in the mixture = 347 ml,
⇒ 0.30x - 13 = 347
⇒ 0.30x = 347 + 13
⇒ 0.30x = 360
⇒ x = = 1200
Hence, the quantity of solution b is 1200 ml.
The area of a right triangle is 5 in 2. If the length of a leg is x, write the function h(x) that describes the length of the hypotenuse.
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The area of the right triangle is 5 in², the length of the leg is x, hence:
Area = (1/2) * base * height
5 = (1/2) * x * height
height = 10/x
hypotenuse = √[(leg)² + (height)²]
h(x) = √[x² + (10/x)²]
The length of the hypotenuse is given by the function h(x) = √[x² + (10/x)²]
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(4x y)(5x^2yz) please I need it
Answer:
(4xy)(5x^2yz) = 20x^3y^2z
Step-by-step explanation:
You need to expand the brackets by multiplying compatible terms together.The numerical ones together and algebraic ones of the same variable together as well.You may follow the following steps to understand the way it is done.[tex]\begin{aligned}\\\small (4xy)(5x^2yz) &\equiv \small (4\times5)\times (x \times x^2) \times (y\times y) \times (z)\\\\&\equiv 20 \times x^3 \times y^2 \times z\\\\&\equiv 20x^3 y^2 z\end{aligned}[/tex]
Zodwa, the operations manager of a large production plant would like to estimate the mean
amount of time a worker takes to assemble a new electronic component. Assume that the standard
deviation of this assembly time is 3.6 minutes.
3.1.1. After observing 120 workers assembling similar devices, Zodwa noticed that their
average time was 16.2 minutes. Construct a 92% confidence interval for the mean
assembly time. (9)
The confidence interval for the mean assembly time is [15.625, 16.775].
The mean (x) time of the workers to assemble similar devices is 16.2 minutes.The standard deviation (σ) of this assembly time is 3.6 minutes.The sample size (n) for observation is 120 workers.It is given that the confidence level is 92%.At α = 0.08, the critical value (z) is 1.751.The confidence interval for the mean assembly time is [x ± z(σ/√n)].The confidence interval for the mean assembly time is [16.2 ± 1.751(3.6/√120)].The confidence interval for the mean assembly time is [16.2 ± 1.751(3.6/10.954)].The confidence interval for the mean assembly time is [16.2 ± 1.751(0.329)].The confidence interval for the mean assembly time is [16.2 ± 0.575].The confidence interval for the mean assembly time is [15.625, 16.775].To learn more about standard deviation, visit :
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Write and post THREE word problems that are JWU college-related and that translate to one-variable linear equations.
The three questions mentioned above which translated to one variable linear equation.
Problem first,
The rank of a student is 5 more than the other, Sum of their rank is 7
The solution, rank of student be x
rank of another student = x + 5
According to the question,
x + x + 5 = 7
2x = 2
x = 1
Problem second.
A student has 2 pens less than their friend, the sum of their pens is 6
Solution-
let the student has x pens
His friends have = x + 2 pens
Now. total = x + x + 2
6 = 2x + 2
x = 2
Problem third,
Ashwin is 2 times older than his friend and his friend's age is 24 what is the age of Ashwin,
Solution,
Let the age of Ashwin be x
according to question
x = 24 + 2
x = 26
Thus, the three questions mentioned above which translated to one variable linear equation.
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What is the equation of the line that
contains (2, 3) and has an undefined slope?
Answer:
George C. x=2 is the equation of the line through (2,3) with undefined slope.
Step-by-step explanation:
Answer:
x = 2
Step-by-step explanation:
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (2, 3 ) with x- coordinate 2 , then
x = 2 ← is the equation of the line
Question 7
1 pt:
By January 2014, the US population had grown to 317.3 million
and the US Federal Debt was a reported $17.3 trillion. Calculate
the beginning-2014 Federal Debt per capita.
Express your answer rounded correctly to the nearest dollar.
Remember, do not include units with your answer!
In January 2014, the debt per capita was: = $54,522.53.
What is debt per capita?Net debt per capita is simply the total debt of a country or even other jurisdiction divided by the residents residing there. Net debt per capita can provide insight into how leveraged a government is.
How much debt is considered normal?The average American has $92,727 in consumer debt, according to 2020 Experian research. Consumer debt encompasses a wide range of personal credit accounts, including credit cards, auto loans, mortgage, and personal loans, including school loans.
According to the given data:Population = 317.3 million.
US Federal Debt was a reported = $17.3 trillion.
Federal Debt per capita. = ?
We know that:
by adding short-term and long-term debt, deducting cash and some other liquid assets, then dividing by population.
The debt per capita in Jan 2014 was:
=1.73 x 1013 / 3.173 x 108
= $54,522.53.
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-3 x 58 how do I do it.
Answer:
-174
Step-by-step explanation:
58x2=116<----First two 58's
116+58=174<----last 58
We need to add the negative symbol since it should be negative, so the final answer is -174.
En una proporcion se sabe a=60 b=25 c-d=14 encuentre c y d
The numbers that represents c and d and aligns with the information will be 24 - 10 = 14.
How to illustrate the information?It should be noted that from the proportion, a = 60 and b = 25.
It was also stated that c - d = 14.
It should be noted that 60 and 25 have a common factor of 5. Therefore, the number that's equivalent to them will be:
(60 ÷ 2.5) = 24
25 ÷ 2.5 = 10
Therefore 24 - 10 = 14
The values are 24 and 10.
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