Write an equation of the line that pass through the given point and is (a) parallel and (b) perpendicular to the given line.
Answers
Answer:
Step-by-step explanation:
Here we need to write the equations that passes through the point (4 , 3) and is parallel to the given line and perpendicular to it. So lets get started,
a)
First we calculate the slope of the given line by using any two points on the given line by the help of the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
we take the points (1 , 6) and (2 , 2) i chose these two you can choose any other two doesn't matter so now we calculate the slope,
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{2-6}{2-1}\\\\m=\frac{-4}{1}\\\\m=-4[/tex]
now since our slope is -4 and the line is parallel to the given line so the line that we need in part a would also have the same slope by the law parallel lines have same slope/gradient.
[tex]m_1=m_2[/tex]
so the slope/gradient of our new line that we need which passes through the point (4,3) is -4
Now using the point slope form formula:
[tex]y-y_1=m(x-x_1)[/tex]
we have our point (4,3) which corresponds to [tex](x_1,y_1)[/tex] and m which corresponds to -4 , so now
[tex]y-y_1=m(x-x_1)\\y-3=-4(x-4)\\y-3=-4x+16\\y=-4x+19[/tex]
sow our new line in part a is
[tex]y=-4x+19[/tex]
b)
In this part we need a line that is perpendicular to the given line which means we use the formula to calculate the slope of the perpendicular line which is:
[tex]m_1m_2=-1[/tex]
where [tex]m_1=-4[/tex] the slope of our given line so the slope of the perpendicular line is,
[tex]m_1m_2=-1\\-4m_2=-1\\\\m_2=\frac{1}{4}[/tex]
so using the point (4,3) and the new slope 1/4 we find the equation of the perpendicular line again by using the point-slope form formula:
[tex]y-y_1=m(x-x_1)\\y-3=\frac{1}{4}(x-4)\\\\4y-12=x-4 \\4y=x+8\\\\y=\frac{x+8}{4}\\\\y=\frac{x}{4}+2[/tex]
I have attached of the graphs as well you can check it out for better understanding.
Related Questions
A tape diagram. There are 35 6th graders with an older sibling out of 100 6th graders. There are question mark 6th graders with an older sibling out of 300 6th graders. StartFraction part Over whole EndFraction = StartFraction 35 times 3 Over 100 times 3 EndFraction = StartFraction question mark Over 300 EndFraction Graph If 35% of the 300 students in 6th grade have an older brother or sister, how many 6th graders have an older sibling? To solve this problem, we can write an equivalent ratio as the percent and then create the percent . 6th graders have an older brother or sister.
Answers
Answer:
35 a
Step-by-step explanation:
ada
Answer:
1. Percent 2. Ratio 3. Ratio 4. 105
Step-by-step explanation:
I just did it
Write "eleven and twenty-one hundredths" as a decimal.
Answers
Answer:
11.21
Step-by-step explanation:trust me bro
Answer:
11.21
Step-by-step explanation:
Can someone help me find x
And why?
PLZZZ I WILL GIVE U 20 POINTS
Answers
Answer: x is on the side we’re the prime example if found if u have a example
Step-by-step explanation:
please answer #3
i have only 5 points left ;(
Answers
Answer:
f(x) = 2,000(0.94)^x; 952 km^2
Step-by-step explanation:
Formula for exponential growth or decay:
f(x) = P(1 + r)^x
where
f(x) = future value in year x
P = present value
r = annual rate of growth (positive) or decrease (negative)
x = time in years
In this problem,
P = 2,000
r = -6% = -0.06; here r is negative since this is a decreasing function
The formula is
f(x) = 2,000(1 - 0.06)^x
f(x) = 2,000(0.94)^x
For year 12, x = 12.
f(x) = 2,000(0.94)^x
f(12) = 2,000(0.94)^12
f(12) = 952
plz help me 25y−4+7−910y =
Answers
Answer:
-885y+3
Step-by-step explanation:
Write the value of the 4. 6.54
Answers
Answer:
Hundredths place
Step-by-step explanation:
6 in 6.54 is ones place
5 in 6.54 is tenths place
4 in 6.54 is hundredths
plz mark me brainliest
Evaluate 36 = (x+9) when x = 3.
O A. 3
O B. 12
O C. 21
O D. 4
Answers
36=(x+9) x=3 ( substitute)
36=(3+9) add
36=(12) multiply
36\12 = 3
00:00
Select all the values of p that are solutions for this inequality
10p - 8 >12
A. -1
B. 0
C. 1
D. 2
E. 3
Answers
Answer:
The answer is D. and E.
Step-by-step explanation:
The answer is D and E because 10 multiplied by 2 is 20 and 20 is bigger then 12 and 10 times 3 is 30 which is also bigger than 12.
P.S Can I have brainliest?
From the region (2, ∞) of the inequality the values -1, 0, and 2 are not in the region, but the value 3 is in the region so p = 3 is the solution to the inequality option (E) is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than, known as inequality.
We have inequality:
10p - 8 >12
10p > 12 + 8
10p > 20
p > 2
p ∈ (2, ∞)
Thus, from the region (2, ∞) of the inequality the values -1, 0, and 2 are not in the region, but the value 3 is in the region so p = 3 is the solution to the inequality option (E) is correct.
Learn more about the inequality here:
brainly.com/question/19491153
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find slope of the line that passes through the point (-9,7) and (9,-3)
Answers
Answer:
Step-by-step explanation:
(x₁, y₁) = (-9, 7) & (x₂ , y₂) = (9 , -3)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{-3-7}{9-[-9]}\\\\= \frac{-3-7}{9+9}\\\\=\frac{-10}{18}\\\\= \frac{-5}{9}[/tex]
At the beginning of last year,there were 368 students at the elementary school.By the beginning of this year,72 of those students have moved to other school districts and 64 new students arrived. about how many students started the school year this year
Answers
Answer:
360 students
Step-by-step explanation:
We start off with 368.
Then 72 leave the school, so subtract 72 from our total.
368 - 72 = 296
But, then 64 new students join, so add this to our new total.
296 + 64 = 360.
Ask any questions you have in the comments, and if this helps, maybe consider giving a Brainliest :P
Someone thats extremely 100% good at math and is passing math can you help me with all my math questions. I need to get a better grade in math. ( No Plagiarism and please dont reshare another students answer from brainly either). Will Mark Brainliest. Just click on my name to go to my math questions.
Answers
HELP ME PLZ AND IF YOU HELP ME 10 POINTS
Answers
Answer:
3(c+4)
Step-by-step explanation:
It would usually be 3 x 4, but since there is a variable, it can`t be multiplied (unless you know what the value of the variable is). Thus the expression is 3(c+4).
ask nicely and I'll give you what you want
Answers
Answer:
The expressions that are equivalent to that includes:
[tex]▪ \: 3c + \frac{4}{5} + \frac{1}{2} \\ ▪ \: \frac{4}{5} + \frac{1}{2} + 3c \\ ▪ \: \frac{1}{2} + \frac{4}{5} + 3c[/tex]
Answer:
1, 3, and 5 they all equal to (3c+13/10) which was the answer for the question
Step-by-step explanation:
to find out which is equivalent solve fraction and solve the others to see which one is similiar.
Help it’s due soon all help is appreciated
Answers
5/8 ÷ 3/8 help plz thanks
Answers
Answer:
1.66666666667
Step-by-step explanation:
All ratios equivalent to 24:12
Answers
Answer:
There are so many:
2:1
4:2
6:3
Determine whether or not the relationship between x and y is proportional. Explain how you deter-
mined your answer.
(#1) please help
Answers
Answer:
Al of them are proportional
Step-by-step explanation:
If you see the first one is getting multiplied by 2 same as the second but the third is reversed.
2x,2x,-2x
Eve is organizing a race to raise money for a local children's hospital. She makes $20 for each 5K participant and $45 for each 10K participant. Her goal is to raise $9,500.If x represents the number of participants in the 5K race and y represents the number of participants in the 10K race, the linear equation for the given scenario is
Answers
Answer:
20x + 45y = 9500 is the linear equation for given scenario
Step-by-step explanation:
Given that Eve makes $20 for each 5K participant and $45 for each 10K participant
Cost of each 5k participant = $ 20
Cost of each 10k participant = $ 45
Her goal is to raise $9,500
Let "x" represents the number of participants in the 5K race
Let "y" represents the number of participants in the 10K race
To find: linear equation for given scenario
The standard form for linear equations in two variables is Ax + By = C
Eve makes $20 for each 5K participant and $45 for each 10K participant and goal is to raise $ 9500
From the above statement, we can frame a equation as:
number of participants in the 5K race x Cost of each 5k participant + number of participants in the 10K race x Cost of each 10k participant = $ 9500
20x + 45y = 9500
Therefore, the linear equation for given scenario is found
Answer:
20x + 45y = 9500
yes/no: no
Solution:
Given that Eve makes $20 for each 5K participant and $45 for each 10K participant
Cost of each 5k participant = $ 20
Cost of each 10k participant = $ 45
Her goal is to raise $9,500
Let "x" represents the number of participants in the 5K race
Let "y" represents the number of participants in the 10K race
To find: linear equation for given scenario
The standard form for linear equations in two variables is Ax + By = C
Eve makes $20 for each 5K participant and $45 for each 10K participant and goal is to raise $ 9500
From the above statement, we can frame a equation as:
number of participants in the 5K race x Cost of each 5k participant + number of participants in the 10K race x Cost of each 10k participant = $ 9500
20x + 45y = 9500
If eve raises exactly $9,500, it is NOT possible for there to be 220 participants in the 5K race.
A student's parents offer him one of two options to receive scholarship money for college.
Option A: Deposit $17,000.00 into his savings account and then add an additional $1,250.00 each day for 30 days
or
Option B: Deposit $0.50 into his savings account and then triple that amount each day for only 10 days
When rounded to the nearest cent, how much money is deposited into his savings account on the last day (day 30) for Option A, and how much is deposited into his savings account on the last day (day 10) for Option B? If the student keeps only what is deposited on the last day, which option should he choose?
Option A Versus Option B
Option A Option B
Day Amount Deposited Day Amount Deposited
0 $17,000.00 0 $0.50
1 $18,250.00 1 $1.50
2 $19,500.00 2 $4.50
A = $142,845.76, B = $29,524.50; B, because he receives $113,321.26 more
A = $54,500.00, B = $10.50; A, because he receives $54,489.50 more
A = $37,500.00, B = $59,049.00; B, because he receives $21,549.00 more
A = $54,500.00, B = $29,524.50; A, because he receives $24,975.50 more
Answers
Answer:
option a
Step-by-step explanation:
it is because $17,000.00 will make you have more money and have better things to do in the nearest future
The amount received by student in option A and B are A = $54,500.00, B = $29,524.50, Option A is better because student receives $24,975.50 more.
What is Simplification?Simplification in mathematical terms is a process to convert a long mathematical expression in simple and easy form.
(A)
Given that,
Amount deposit by student in starting = $17,000
Also, student add $1250 each day for 30 days,
Amount added in 30 days = 1250 x 30 = $37500
Total amount in account = 17000 + 37500 = 54500
The final amount in account is $54500.
(B)
Amount deposited into saving account = $0.50
Also, student triple that amount for 10 days,
Amount in account in 10 days = 0.50 x 3¹⁰ = 29524.5
Option A is a better deal because the student receives $24,975.50 more.
To know more about Simplification on :
https://brainly.com/question/2804192
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Factor completely
w^2 + 12w -f^2+ 36
Answers
(w+6-f)x (w+6+f)
What is the y-intercept of y = 3 – 4x? Choose 1 answer: (-4,0) (3.0) (0.-4) (0.3)
Answers
Answer:
it is (3.0)
Step-by-step explanation:
because the 3 is the second number without an variable
Find the slop line that passes through each pair of points (-6,1),(4,8)
Answers
Answer:
0.7
Step-by-step explanation:
given cot A= 40/9 and that angle A is in quadrant 1 find the exact value of sec A in the simplest radical form using a rational denominator
Answers
Answer:
41/40Step-by-step explanation:
Given cotA = 40/9
1/tanA = 40/9
tanA = 9/40
According to SOH, CAH, TOA
tan A = 9/40 = opposite/adjacent
Get the hypotenuse
hyp² = opp²+adj²
hyp² = 9²+40²
hyp² = 81+1600
hyp² = 1681
hyp = √1681
hyp = 41
Het sec A
sec A = 1/cosA
Since cos A = adjacent/hypotenuse
cos A = 40/41
secA = 1/(40/41)
SecA = 41/40
Hence the exact value of secA is 41/40
Randy Houck deposited his paycheck for $385.15, a refund check from a mail
order purchase for $125.95, and $37.20 in cash.
Answers
Answer:
The correct option is c. $548.30.
Step-by-step explanation:
Note: This question is not complete. The complete question is therefore provided before answering the question. Please, see the attached pdf file for the complete question.
Also Note: This template does not allow the explanation to be added and saved here as it keeps on indicating that it contains some swearwords. The explanation is now given in the attached pdf file. Please, see the attached pdf file for the answer and explanation.
There are 5,375 pencils in 25 cases. Find the unit rate. pls
Answers
Answer:
5,375/25= 215 pencils per case
Step-by-step explanation:
Answer: 215 Pencils are in each case
Step-by-step explanation:
5,375/25 equals the unit rate
NEED HELP ASAP!!!!! WILL GIVE BRAINLIEST!!!!!!!
Which number line shows the solutions to n > -2?
Answers
Pleaseeeee helpppppp meee
Answers
Answer:
C, F
Step-by-step explanation:
Dont have time rn
Find the following area of this trapezoid.
Answers
Answer:
its c 98
Step-by-step explanation:
multiply hight by width so 14x7 and thats 98 but idrk
The slope of a line is 1/2 and it passes through the point (4,−7)
. Which of the following is the equation of the line?
Select one:
A) y=1/2x+9
B) y=1/2x+4
C) y=1/2x−7
D) y=1/2x−9
Answers
Answer:
Step-by-step explanation:
its the last one heres a graph of it
i hope it helps :)
garett uses 5 apples to bake an apple pie on sunday he bkes 2 pies how many apples does garett need on sunday write an equation
Answers
Answer:
2+x=5
Step-by-step explanation:
i think dont bash me