Answer:
x^3-6x^2-4x-8
Step-by-step explanation:
First you would multiply (x-2) by itself (x-2) to get
x^2-2x-2x+4
then you would combine like terms
x^2-4x+4
Then you would multiply that by x-2
(x^2-4x+4)(x-2)
x^3-2x^2-4x^2-8x+4x-8
then you combine like terms
x^3-6x^2-4x-8
A payday loan store charges $40 for a one month loan of $600. What’s the annual interest rate equivalent to?
Answer:
80%
Step-by-step explanation:
rate=100×Interest/ principal × time
Interest= 40
principal= 600
time= 1 month=1/12
100%×$40×12/$600×1=80%
got another math problem.. please help
the correct answer is 59.
Answer:
59
Step-by-step explanation:
[2+ (4-2)+8²]-[2-(-1)][2+2+64]-[2-(-1)]²68-3²68-959Square A"B"C"D" is the final image after the rule was applied to square ABCD. On a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5). What are the coordinates of vertex A of square ABCD? (–1, –6) (–1, –2) (–1, 6) (–2, 1)
Answer:
The answer is (-2 , 1 ) or D on Edge
Step-by-step explanation:
The coordinates of vertex A of square ABCD is (-1, -2).
What are coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane.
Given:
A(-5, -3), B(-3, -1), C(-1, -3) and D(-3, -5)
By using the rule
T(-4, -1)
So, the coordinate of Vertex A will be
A( -5 + 4, -3 + 1)
=A(-1, -2)
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Find the values of x in the figure below. Express your answer in simplest radical form.
Answer:
Step-by-step explanation:I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me...
write (2n^2)^3 without exponents
Answer:
8n x n x n x n x n x n x n
Step-by-step explanation:
(2n^2)^3 = 8n^ 6
Now just write "n" 6 times and there you go
The given expression without exponents can be written as 8×n×n×n×n×n×n.
The given expression is (2n²)³.
We need to write the given expression without exponents.
What is an exponent?The exponent of a number shows how many times the number is multiplied by itself. For example, 2×2×2×2 can be written as 24, as 2 is multiplied by itself 4 times.
Now, the given expression can be simplified as follows:
(2n²)³=2³×(n²)³
=2×2×2×[tex]n^{6}[/tex] (∵[tex](a^{m}) ^{n}=a^{m\times n}[/tex])
=8×n×n×n×n×n×n
Therefore, the given expression without exponents can be written as 8×n×n×n×n×n×n.
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I would like to purchase 20 products at a cost of $65 per product. What would be my total with 3.5 sales tax
Answer:
Answer:
The total is: $ 1345.5
Step-by-step explanation:
It is given that:
I would like to purchase 20 products at a cost 65.00 per product.
This means that the cost of 20 products will be:
Also, there is a sales tax of 3.5%
This means that a person has to pay a extra 3.5% on the total cost of the items he purchased.
i.e. he need to pay 3/5% on $ 1300
This means that the amount of tax he need to pay is: 3.5% of 1300
= 3.5%×1300
= 0.035×1300
= $ 45.5.
Hence, the total cost is: $ 1300+$ 45.5
This means that the total cost is: $ 134.5
What's 2|–9| – |–2|?
Answer:
Step-by-step explanation: AS YOU KHOW THW ABSOLUTE VALUE OF A QUESTION IS NUMBER ITSELF IF THERE IS MINUS SIGH THEN THE SIGH OF A NUMBER WILL BECOME PLUS OR IF THERE IS A PLUS SIGH THEN THERE IT WILL REMAIN AS IT IS. IF THERE IS NO NUMBER WITH THE MINUS SIGH THEN THE MINUS SIGH WILL REAMIN AS IT IS.
+2 +9 - +2
The answer has same sigh, then Plus answer will you get is
+11 - 2 then you will minus the answer will be
+9
HOPE IT HELP YOU
whatt is the equation of the line that passes through the points (-3,-3) and (3,1)
Answer:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
Step-by-step explanation:
We want an equation given by:
[tex] y=mx+b[/tex]
where m i the slope and b the intercept
We have the following two points given:
[tex] (x_1 = -3, y_1 =-3), (x_2=3, y_2 =1)[/tex]
We can find the slope with this formula:
[tex] m=\frac{y_2 -y_1}{x_2 -x_1}[/tex]
And replacing we got:
[tex] m=\frac{1-(-3)}{3-(-3)}= \frac{4}{6}=\frac{2}{3}[/tex]
And we can use one of the points in order to find the intercept like this:
[tex] -3= \frac{2}{3} (-3) +b[/tex]
[tex] b =-3 +2=-1[/tex]
And the equation would be given by:
[tex] y= \frac{2}{3}x -1[/tex]
Car engine needs ______________ to avoid friction.
a) water
b) smooth surface
c) oil
d) air
Answer:
Oil
Step-by-step explanation:
Car engine needs oil to avoid friction.
Answer:
[tex]oil \\ [/tex]
Answer C is correct
Step-by-step explanation:
car engine needs oil to avoid the friction .
hope this helps
brainliest appreciated
good luck! have a nice day!
The probability that a randomly chosen sales prospect will make a purchase is 20%. What is the probability (to three decimal places) that the salesperson will make four or more sales if six sales calls are made on a given day
Answer:
1.7%
Step-by-step explanation:
We have to calculate the probability that the salesperson will make four or more sales if six sales calls are made on a given day, that is:
P (x => 4)
Therefore, we must calculate when x = 4, when x = 5, and when x = 6 and add. p = 0.2, n = 6
P (x = r) = nCr * p ^ r * (1 - p) ^ (n-r)
Also, nCr = n! / (r! * (n-r) !, now replacing:
P (x = 4) = 6! / (4! * (6-4)! * 0.20 ^ 4 * 0.80 ^ (6-4)
P (x = 4) = 15 * 0.001024 = 0.01536
P (x = 5) = 6! / (5! * (6-5)! * 0.20 ^ 5 * 0.80 ^ (6-5)
P (x = 5) = 6 * 0.000256 = 0.001536
P (x = 6) = 6! / (6! * (6-6)! * 0.20 ^ 6 * 0.80 ^ (6-6)
P (x = 6) = 1 * 0.000064 = 0.000064
now,
P (x => 4) = P (x = 4) + P (x = 5) + P (x = 6)
P (x => 4) = 0.01536) + 0.001536 + 0.000064
P (x => 4) = 0.01696 = 0.017
It means that the probability is 1.7%
Determine whether the underlined number is a statistic or a parameter. In a study of all 1963 employees at a college, it is found that "40%" own a computer. Choose the correct statement below.
1. Parameter because the value is a numerical measurement describing a characteristic of a population
2. Statistic because the value is a numerical measurement describing a characteristic of a population
3. Statistic because the value is a numerical measurement describing a characteristic of a sample.
4. Parameter because the value is a numerical measurement describing a characteristic of a sample.
Answer:
1. Parameter because the value is a numerical measurement describing a characteristic of a population
Step-by-step explanation:
A parameter is a fixed measure which describes the whole population while a statistic is a characteristic of a sample (which is a portion of the target population).
In a study of all 1963 employees at a college, it is found that "40%" own a computer.
The study involved the entire population of employees in the college, therefore the result describes the computer owning characteristics of the whole population under study. It is therefore a parameter.
The correct option is 1.
One number is 11 less than the other number. If their sum is increased by 8, the result is 71. Find the numbers.
First number = [tex]x[/tex]
Second number = [tex]x-11[/tex]
[tex]x+x-11+8=71[/tex]
[tex]2x-3=71[/tex]
[tex]2x=71+3[/tex]
[tex]2x=74[/tex]
[tex]x=37[/tex]
First number = [tex]x=37[/tex]
Second number = [tex]x-11=37-11=26[/tex]
Consider the homogeneous second-order linear differential equation y′′+4y′−12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x,y2=e−6x B. y1=e3x,y2=e1x C. y1=e2x,y2=e−2x D. y1=e−12x,y2=xe−12x E. y1=cos(−12x),y2=sin(−12x) F. y1=e−4x,y2=e−12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y(0)=−5,y′(0)=0. y = y1 + y2.
An engineer believes that there is a linear relationship between the thickness of an air filter and the amount of particulate matter that gets through the filter; that is, less pollution should get through thicker filters. The engineer tests many filters of different thickness and fits a linear model. If a linear model is appropriate, what should be apparent in the residual plot
Answer:
There should be no pattern in the residual plot.
Step-by-step explanation
Remember a residual plot is calculating if a linear model is appropriate or not and since the engineer is trying to find a linear relationship with his air filters then he should be looking for no pattern.
Here, we are required to determine what should be apparent in the residual plot.
The residual plot will have a negative slope, i.e the residual plot descends from the top left to the bottom right.
According to the Engineer's believe, the thicker the air filter, the less pollution that gets through it.
By plotting each of the quantities on either of x and y axis on the residual plot, The residual plot therefore, has a negative slope.
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find five rational numbers between ? explain please
Answer:
1.5, 6, 24.7, 384, 404.4, 1,980Step-by-step explanation:
Rational numbers are the result of dividing two integers. Intergers cannot be fractions. So 1.5 is rational but 3/2 is not.
Five rational numbers: 1.5, 6, 24.7, 384, 404.4, 1,980
I'm always happy to help :)
Which table represents a function?
Answer:
The bottom left table
Step-by-step explanation:
the same x value cannot have different y values
A spinner with 6 colors is spun and a number cube is tossed determine the number of outcomes
Answer:
36
Step-by-step explanation:
since there are six outcomes for the spinner and six outcomes for the cube,
6 x 6 = 36
The Gleason family has a monthly budget of $4,500. Mr. Gleason has a full-time job and takes home $900 each week. Mrs. Gleason works part time and brings home $9 each week. For every hour she works. How many hours per month must Mrs. Gleason work to make sure that she and Mr. Gleason have met their monthly budget?
Answer:
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
Step-by-step explanation:
To answer this item, we let x be the number of hours per month that Mrs. Gleason should work. The total budget is equal to sum of the amount acquired by Mr. Gleason and Mrs. Gleason. The equation that would express this is,
4,500 = 900(4) + 9x
The value of x from the equation is 100. Thus, Mrs. Gleason should work for 100 hours per month.
I am sorry if you get this wrong.
Complete the point-slope equation of the line through (− 2 ,6 ) ( 1 , 1 )
Answer:
y=-5/3x+8/3
Step-by-step explanation:
You want to find the equation for a line that passes through the two points:
(-2,6) and (1,1).
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (-2,6), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=-2 and y1=6.
Also, let's call the second point you gave, (1,1), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=1 and y2=1.
Now, just plug the numbers into the formula for m above, like this:
m=
1 - 6
1 - -2
or...
m=
-5
3
or...
m=-5/3
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=-5/3x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(-2,6). When x of the line is -2, y of the line must be 6.
(1,1). When x of the line is 1, y of the line must be 1.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=-5/3x+b. b is what we want, the -5/3 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (-2,6) and (1,1).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(-2,6). y=mx+b or 6=-5/3 × -2+b, or solving for b: b=6-(-5/3)(-2). b=8/3.
(1,1). y=mx+b or 1=-5/3 × 1+b, or solving for b: b=1-(-5/3)(1). b=8/3.
11 — 9y = — 6у +8
solve for y
pleaseee
Answer:
-The value of [tex]y[/tex]:
[tex]y = 1[/tex]
Step-by-step explanation:
-Find the value of [tex]y[/tex]:
[tex]11- 9y = -6y + 8[/tex]
-Add both sides by [tex]6y[/tex] and combine [tex]9y[/tex] and [tex]6y[/tex] together:
[tex]11- 9y + 6y = -6y + 6y+ 8[/tex]
[tex]11 - 3y = 8[/tex]
-Subtract both sides by [tex]11[/tex]:
[tex]11 - 11 - 3y = 8 -11[/tex]
[tex]-3y = -3[/tex]
-Divide both sides by [tex]-3[/tex]:
[tex]\frac{-3y}{-3} = \frac{-3}{-3}[/tex]
[tex]y = 1[/tex]
So the final answer is [tex]y = 1[/tex] .
Calculating conditional probability
G
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride
Groom
29
30
20
1
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride groom)
Complete Question
Calculating conditional probability
The usher at a wedding asked each of the 80 guests whether they were a friend of the bride or of the groom.
Here are the results:
Bride :29
Groom :30
BOTH : 20
Given that a randomly selected guest is a friend of the groom, find the probability they are a friend of the bride.
P (bride | groom)
Answer:
The probability is [tex]P(B|G) = \frac{2}{3}[/tex]
Step-by-step explanation:
The sample size is [tex]n = 80[/tex]
The friend of the groom are [tex]G = 30[/tex]
The friend of the groom are [tex]B = 29[/tex]
The friend of both bride and groom are [tex]Z = 20[/tex]
The probability that a guest is a friend of the bride is mathematically represented as
[tex]P(B) = \frac{29}{80}[/tex]
The probability that a guest is a friend of the groom is mathematically represented as
[tex]P(G) = \frac{30}{80}[/tex]
The probability that a guest is both a friend of the bride and a friend of the groom is mathematically represented as
[tex]P(B \ n \ G) = \frac{20}{80}[/tex]
Now
[tex]P(B|G)[/tex] is mathematically represented as
[tex]P(B|G) = \frac{P(B \ n \ G)}{P(G)}[/tex]
Substituting values
[tex]P(B|G) = \frac{\frac{20}{80} }{\frac{30}{80} }[/tex]
[tex]P(B|G) = \frac{2}{3}[/tex]
Answer:
the answer is 3/5
Step-by-step explanation:
on Khan
As part of an insurance company’s training program, participants learn how to conduct an analysis of clients’ insurability. The goal is to have participants achieve a time in the range of 30 to 47 minutes. Test results for three participants were: Armand, a mean of 37.0 minutes and a standard deviation of 3.0 minutes; Jerry, a mean of 38.0 minutes and a standard deviation of 2.0 minutes; and Melissa, a mean of 38.5 minutes and a standard deviation of 2.9 minutes.
a.Which of the participants would you judge to be capable? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Participants :
Armand: Cpk _____ Cp Capable ? No/Yes
Jerry: Cpk _____ Capable ? Yes/No
Melissa Cp ________ No/Yes
b.Can the value of the Cpk exceed the value of Cp for a given participant?
yes or no
Answer:
1) cpk < 1.33, therefore it is not capable
b) cpk = 1.33, therefore it is capable
c) cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Step-by-step explanation:
Upper limit (USL) = 47 minutes and Lower limit (LSL) = 30 minutes
1)
a) mean (μ) = 37 minutes, standard deviation (σ) = 3 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-37}{3*3},\frac{37-30}{3*3} )=min(1.11,0.78)=0.78[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*3}=0.94[/tex]
cpk < 1.33, therefore it is not capable
b) mean (μ) = 38 minutes, standard deviation (σ) = 2 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38}{3*2},\frac{38-30}{3*2} )=min(1.5,1.33)=1.33[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2}=1.42[/tex]
cpk = 1.33, therefore it is capable
c) a) mean (μ) = 38.5 minutes, standard deviation (σ) = 2.9 minutes
[tex]cpk=min(\frac{USL-\mu}{3\sigma}, \frac{\mu - LSL}{3\sigma})=min(\frac{47-38.5}{3*2.9},\frac{38.5-30}{3*2.9} )=min(0.98,0.98)=0.98[/tex]
[tex]cp=(\frac{USL-LSL}{6\sigma})=\frac{47-30}{6*2.9}=0.98[/tex]
cpk < 1.33, therefore it is not capable
2) Cpk can never be greater than the Cp, but can be equal to it
Please answer this correctly
Answer:
Band: 30%
Chorus: 18%
Painting: 21%
Robotics: 14%
Coding: 17%
Please answer this correctly
Answer:
Step-by-step explanation:
George Fox university = 10,000,000 + 10,000,000
= full bag + full bag
( click 2 full bag}
Rockhurst university = 10,000,000 +10,000,000 +10,000,000 + 5,000,000
= full bag + full bag + full bag + half bag
(click 3 full bag and 1 half bag}
Lebanon Valley college = 10,000,000 +10,000,000 +10,000,000 +10,000,000+5,000,000
( click 4 full bag and 1 half bag)
Grand view college = 10,000,000
(click 1 full bag}
Directions and Analysis
Task 1: Completing the Square
Look at the quadratic equation below.
2x^2-12x-16=0
This is not an equation that could be easily solved by factoring. Instead, you are going to use the method of completing the square to solve this equation. Follow each step in this task to complete the square and solve the equation.
a. To complete the square, the coefficient of the x2 term must be 1. Divide both sides of the equation by a value and rewrite the equation to meet this criteria.
Type your response here:
b. Rewrite the resulting equation so the constant term is on the right side of the equation and the variable terms are on the left.
Type your response here:
c. Identify the coefficient of the x term in the previous equation. Then divide it by half and square the result. What is the result?
Type your response here:
d. Add the value you identified in part c to both sides of the equation from part b and simplify the right side. Remember that when solving equations, whatever is done to one side of the equation must also be done to the other side the equation: that is why you must add the value to both sides.
Type your response here:
e. Notice that the left side of the equation now represents a perfect square quadratic expression. Use this fact to rewrite the left side of the previous equation as the square of a linear term and create a new equation.
Type your response here:
f. You have now completed the square. Starting with the result from part e, solve the equation for x. Show your work.
Type your response here:
g. Now that you know how to complete the square to solve a quadratic equation, solve the equation 3x^2 – 3x − 6 = 0. Show your work.
Type your response here:
Answer:
a. [tex]x^2-6x-8=0[/tex]
b. [tex]x^2-6x=8[/tex]
c.
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d. [tex]x^2-6x+9=17[/tex]
e. [tex](x-3)^2=17[/tex]
f, g. [tex]x=3\pm \sqrt{17}[/tex]
Step-by-step explanation:
Given: [tex]2x^2-12x-16=0[/tex]
To solve: the given equation
Solution:
a.
[tex]2x^2-12x-16=0[/tex]
Coefficient of [tex]x^2=2[/tex]
Divide both sides by 2
[tex]x^2-6x-8=0[/tex]
b.
[tex]x^2-6x=8[/tex]
c.
Coefficient of x = -6
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d.
Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]
[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]
e.
[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]
f.
[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]
g.
[tex]x=3\pm \sqrt{17}[/tex]
The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: "Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving." Possible responses were strongly agree, some what agree, some what disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, said that they some what agree, said they some what disagree, and said they strongly disagree with this statement.
Required:
a. Do the responses for this statement provide categorical or quantitative data?
b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?
c. What percentage of respondents strongly agree with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?
Step-by-step explanation:
a. It would provide a quantitative data
b. Yes, it would make more sense to use percentages rather than averages as this is estimating a proportion.
c. 44% of the respondents strongly agree
d. the results do not indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving as the only respondents will be those that agree with the researchers claim and the study will be biased against those who do not agree.
g Brian Vanecek, VP of Operations at Portland Trust Bank, is evaluating the service level provided to walk-in customers. Accordingly, his staff recorded the waiting times for 64 randomly selected walk-in customers, and determined that their mean waiting time was 15 minutes and that the standard deviation was 4 minutes. The 88% confidence interval for the population mean of waiting times is __________.
Answer:
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 64 - 1 = 63
88% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 63 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.88}{2} = 0.94[/tex]. So we have T = 1.9153
The margin of error is:
M = T*s = 1.9153*4 = 7.66.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 15 - 7.66 = 7.34 minutes
The upper end of the interval is the sample mean added to M. So it is 15 + 7.66 = 22.66 minutes.
The 88% confidence interval for the population mean of waiting times is between 7.34 minutes and 22.66 minutes.
What letter completes the puzzle? The answer is probably easy for you guys but I don't understand how the letters go along with the puzzle. Thank you!
Answer:
the answer is E the number at the top tells you which position it falls under in the alphabet
I want the answer of this question
[tex]the \: answer \: is \: 10 \\ please \: see \: the \: attached \: picture \: for \\ full \: solution \\ hope \: it \: helps[/tex]
Answer:
10 is the answer for this question.
Write the equation of the line. Slope = -4, passing through (- 1, 5)
Answer:
y=-4x+1
Step-by-step explanation:
You want to find the equation for a line that passes through the point (-1,5) and has a slope of -4.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was -4. So you can right away fill in the equation for a line somewhat to read:
y=-4x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(-1,5). When x of the line is -1, y of the line must be 5.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: . b is what we want, the -4 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the the point (-1,5).
So, why not plug in for x the number -1 and for y the number 5? This will allow us to solve for b for the particular line that passes through the point you gave!.
(-1,5). y=mx+b or 5=-4 × -1+b, or solving for b: b=5-(-4)(-1). b=1.
The equation of line passes through the point (-1, 5) will be;
⇒ y = - 4x - 2
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (-1, 5).
And, The slope of line is,
⇒ m = - 4
Now,
Since, The equation of line passes through the point (- 1, 5).
And, Slope of the line is,
m = - 4
Thus, The equation of line with slope - 4 is,
⇒ y - 5 = - 4 (x - (-1))
⇒ y - 2 = - 4 (x + 1)
⇒ y - 2 = - 4x - 4
⇒ y = - 4x - 4 + 2
⇒ y = - 4x - 2
Learn more about the equation of line visit:
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