5. What is the equation of a line that is perpendicular to -x + 2y = 4 and passes through the point (-2,1)?
a.
Write the equation -x + 2y = 4 in slope-intercept form
b. Identify the slope of the line represented in part a.
C.
What is the slope of the line perpendicular to the line in steps a and b?
d. Write the equation of the perpendicular line in slope-intercept form.
Answers
Answer:
Please check the explanation.
Step-by-step explanation:
Given the equation
[tex]-x + 2y = 4[/tex]
a) writing the equation in the slope-intercept form
We know that the slope-intercept form of the equation of the line is
[tex]y=mx+b[/tex]
where m is the slope of the line
so writing the equation in the slope-intercept form
[tex]-x + 2y = 4[/tex]
[tex]2y=4+x[/tex]
[tex]y=\frac{1}{2}x+2[/tex]
b) Identify the slope of the line represented in part a
As the equation in slope-intercept form is
[tex]y=\frac{1}{2}x+2[/tex]
Here,
m = slope = 1/2 ∵ [tex]y=mx+b[/tex]
c) What is the slope of the line perpendicular to the line in steps a and b
As we know that the slope of the perpendicular line is basically the negative reciprocal of the slope of the line, so
As the slope = 1/2
So the slope of the perpendicular line will be: -2
d. Write the equation of the perpendicular line in slope-intercept form.
Therefore, the point-slope form of the equation of the perpendicular line that goes through (-2,1) is:
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting the values m = -2 and the point (-2,1)
[tex]\:y-1=-2\left(x-\left(-2\right)\right)[/tex]
[tex]y-1=-2\left(x+2\right)[/tex]
Add 1 to both sides
[tex]y-1+1=-2\left(x+2\right)+1[/tex]
[tex]y=-2x-3[/tex]
Related Questions
f(x) = 3x + 1. Solve for x if f(x) = 19
Answers
3x+1=19
Start by subtracting 1 from each side to start isolating the x.
3x+1=19
-1 -1
————-
3x=18
Next, divide both sides by 3 to completely isolate the x.
3x=18
—- ——
3 3
x=6
Therefore, x for f(x)= 19 is 6
You can check by inserting into the equation 3(6)+1=18+1=19.
Hope this helps!!
Answer:
Step-by-step explanation:
f(x) = 3x + 1
First, we substitute 19 for x :
f(x) = 3(19) + 1
Next we re write the problem and solve for 3 times 19 :
f(x) = 57 + 1
So, the answer should be :
f(x) = 58
what’s the value of x?
Answers
Answer:
X=85
Step-by-step explanation:
the sum of the angels in a triangle adds to 180 so do
180-43-52=85
Step-by-step explanation:
Answer is 85,because x+52+43=180
If the profit of Tk.x in 4 years at the rate of x% is Tk.x, then what is the value of x?
Answers
Answer:
x = 25
Step-by-step explanation:
Given:
Amount invest p = Tk.x
Number of year t = 4
Rate r = x%
Profit = Tk.x
Find:
Value of x
Computation:
Profit = prt / 100
Tk.x = [(Tk.x)(x)(4)] / 100
x = 100 / 4
x = 25
The equation of line L is y=5x+1
The equation of line L is 2y-10x+3=0
Show that these two lines are parallel.
Please help, will award brainliest.
Answers
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
L₁ is y = 5x + 1 ← in slope- intercept form
with slope m = 5
L₂ is 2y - 10x + 3 = 0 ( subtract - 10x + 3 from both sides )
2y = 10x - 3 ( divide all terms by 2 )
y = 5x - [tex]\frac{3}{2}[/tex] ← in slope- intercept form
with slope m = 5
Since L₁ and L₂ have equal slopes then they are parallel lines
Can someone help me solve this equation? x2 + x - 30 = 0
Answers
Answer:
x = 10
Step-by-step explanation:
x x 2 + x - 30 = 0 use the commutative property to reorder the terms
2x + x - 30 = 0 collect like terms
3x - 30 = 0 move constant to the right hand side and change its sign
3x = 30 divide both sides of the equation by 3
x = 10
what is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?
Answers
Answer:
y = 4/3x - 6
Step-by-step explanation:
The slope of the 1st line is -3/4
So for the perpendicular line it has to be the exact opposite.
That looks like this ---> 4/3x
And the y-intercept is -6 because if you make a straight line where the x intercept is it matches.
The equation would look like this
y = 4/3x - 6
Hope this helps! Have a blessed day!
I need help On This !!!!!!!!
Answers
Answer:
Step-by-step explanation:
L'= 3, -3 M'= -3, -6 N'= -3, 3
When the equation 16/x = 4 is simplified, the value of x is??
Answers
Answer: x=4
Step-by-step explanation:
multiply each side by the denominator to cancel out the fraction so the new equation is 16=4x then divide by 4 to eliminate the x and 16 divided by 4 is 4 which is the anwser.
Which function is a linear function ?
Answers
Answer:
the answer is E. hope this helps
Step-by-step explanation:
Can someone help. I need it ASAP
Answers
Answer/Step-by-step explanation:
10 is between the perfect squares of 9(3) and 16(4).
This means the square root of 10 is between 3 and 4.
The square root of 10 is about 3.162
So, it is less than 5.
A division of Chapman Corporation manufactures a pager. The weekly fixed cost for the division is $14,000, and the variable cost for producing x pagers/week in dollars is represented by the function V(x). $ V(x) = 0.000001x^3 - 0.01x^2 + 50x $ The company realizes a revenue in dollars from the sale of x pagers/week represented by the function R(x). $ R(x) = -0.02x^2 + 150x \; \quad \; (0 \leq x \leq 7500) $ (a) Find the total cost function C. What is the profit for the company if 2,600 units are produced and sold each week?
Answers
Answer:
P=$-303,424Step-by-step explanation:
given data
fixed cost= $14,000
variable cost function
[tex]V(x) = 0.000001x^3 - 0.01x^2 + 50x[/tex]
revenue function
[tex]R(x) = -0.02x^2 + 150x \; \quad \; (0 \leq x \leq 7500)[/tex]
a. we know that total cost C=fixed cost plus variable cost
C=14000+0.000001x^3 - 0.01x^2 + 50x
[tex]C=14000+0.000001x^3 - 0.01x^2 + 50x[/tex]
profit is given as revenue minus the total cost
P=R(x)-C (x=2600)
[tex]P=-0.02x^2 + 150x -(14000+0.000001x^3 - 0.01x^2 + 50x)[/tex]
substitute x=2600
[tex]P=-0.02(2600)^2 + 150(2600) -(14000+0.000001(2600)^3 - 0.01(2600)^2 + 50(2600))[/tex]
[tex]P=-135200+390000-(1400+17576-67600)[/tex]
[tex]P=-254800-(48624)\\\\P=-254800-48624\\\\P=-303,424[/tex]
suppose that britta decided to take out a private loan for $6,000 for which loan payments start as soon as the loan amount is deposited in her account and continue for 10 years.
Answers
so whats the question to me its feels like your tell us
Joe opened a bank account with $80. He then withdrew $35 and deposited $115. What is his account balance after these transactions?
Answers
Answer:
160 dollars
Step-by-step explanation:
80-35=45
45+115=160 dollars
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The amount after the transaction.
= Amount in account - Amount withdrawn + Amount deposited
The account balance after the transaction is $160.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example:
2 + 3x + 4y = 7 is an expression.
3 + 4 + 4 - 3 is an expression.
3x + 4 = 5 - 3 is an expression.
We have,
Amount at the account when open = $80
Amount withdrawn = $35
Amount deposited = $115
The amount after the transaction.
= Amount in account - Amount withdrawn + Amount deposited
= 80 - 35 + 115
= $160
Thus,
The account balance after the transaction is $160.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ2
Which expression is a perfect cube?
Answers
solve for x I need help on questions 5 & 6
Answers
Answer:
#5 x=8, #6 x=5
Step-by-step explanation:
Theyre vertical so for number 5 you would have the equation
5x+15=55
-15 -15 from both sides
5x=40
divide by 5 from both sides and you get
x=8
Same thing vertical so you would have
16x+7=87
-7 -7 from both sides
16x=80
divide by 16 from both sides
x=5
HURRY PLZ 20 POINTS AND BRAINLIEST TO FIRST CORRECT ANSWER For dinner, Abelita chooses the Italian salad that costs $3.99 before tax, and Franco chooses the fettuccini alfredo that costs $7.17 before tax. If the sales tax is 5 percent, explain how to find the total cost for their dinner.
Answers
Answer: First, add 3.99 + 7.17. Then take the sum of those two numbers and multiply it by .05 to get 0.55. Since we are dealing money, round to the nearest hundredth to get .56. Add the sum of 3.99 and 7.17 (11.16) and .55 to get a total of 11.71. Therefore the total cost of their dinner, including tax, was $11.71.
Step-by-step explanation:
John is planning a trip that he needs to rent a car. The rental car company charges $50 per day plus $0.25 per mile. How many miles will John travel if his bill is $125.
Answers
Answer:
300 mile
Step-by-step explanation:
($125–$50)÷$0.25
=$75÷$0.25
=300 miles
Tommy Thomas’s tankard holds 480ml when it is one quarter empty. How much does it hold when it is one quarter full?
Answers
Answer:
Tommy Thomas's tankard holds 160ml when it is one-quarter full.
Step-by-step explanation:
When Tommy's tankard holds 480ml when it's one-quarter empty. There are three other quarters in the tankard. So, you would divide 480 by 3 to see how much is in each of the other 3 quarters. The answer comes down to 160ml per quarter, which equals one-quarter full.
Can somebody plz answer this question quick and correctly!
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :D
Answers
Answer:
42%
Step-by-step explanation:
100% - 58% = 42%
What is the domain and range please?
Answers
Answer:
Both infinate.
Step-by-step explanation:
what does 28-8 represent?
Answers
Step-by-step explanation:
subtraction if that wut u askim
What is the value of ?
Answers
Answer:
65
Step-by-step explanation:
Find one root of the following equation x2 + 8x - 9 = 0
Answers
Answer: was just for a challenge
Step-by-step explanation:
no
Step-by-step explanation:
[tex]x {}^{2} + 8x - 9 = 0 \\ {x}^{2} - x + 9x - 9 = 0 \\ x(x - 1) + 9(x - 1) = 0 \\ (x + 9)(x - 1) = 0 \\ x = 1 \: and \: \: \: \: - 9[/tex]
6
Samir goes to a farmers market to buy some fruit.
He fills a large bag with 29kg of apples.
He realises that he cannot carry this weight, so puts some of the apples into a smaller bag.
The weight of the apples in the large bag is 15kg larger than the smaller bag.
(a) What is the weight of the smaller bag?
Answers
Answer:
Weight of Smaller Bag = 7kg
Weight of Larger Bag = 22kg
Step-by-step explanation:
x = weight of smaller bag
x + (x + 15) = 29
2x + 15 =29
2x = 14
x = 7
The speed of an object can be found by taking the distance it travels and dividing it by the time it takes to travel that distance. An object travels 100 feet in 2.5 seconds. Let the speed, , be measured in feet per second.
Write an equation to represent the relationship between the three quantities (speed, distance, and time).
Answers
speed = [tex]\frac{distance}{time}[/tex]
speed = [tex]\frac{100}{2.5}[/tex]
speed = 40 feet per second
The wait times for two different rides are shown in the table. If there is a minute wait time how many people are in line for the Carousel?
Carousel - 6 minutes for 48 people in line
Swings - 12 minutes for 75 people in line
Answers
Answer:
Step-by-step explanation:
5
in3runvn
HELP HAVING A BAD DAY
Anna is x years old and her sister, Jane, is y years younger.
How old was Anna when her sister was born?
Answers
========================================================
Explanation:
Let's use numbers in place of the variables
Let's say Anna is 25 years old and her sister Jane is 5 years younger.
This means Anna was 25-5 = 20 years old when Jane was born.
-------------------------
As another example:
Anna = 37 years old
Jane = 10 years younger
Anna was 37-10 = 27 when her sister was born
--------------------------
The examples show that all we do is subtract the x and y values to figure out how old Anna was when her sister was born.
For the first example, we basically did x-y = 25-5 = 20
The second example was x-y = 37-10 = 27
A variable is placeholder for a number. Think of it as a box where a single number will go inside.
Answer:
0+y
Step-by-step explanation:
When Jane was born, Anna was y years old because Jane was 0 years old. That is why the Answer if y or 0+y. But I think the 0+y is more accurate.
C:
D:
E:
F:
G:
H:
3 a) If the first coordinate in an ordered pair is 0, where does the point lie?
3 b) If the second coordinate in an ordered pair is 0, where does the point lie?
8. How far does Cal live from Mel?
9. How far does Mia live from Amy?
10. How far apart do Amy and Cal live?
14. Whose house is a reflection of Amy’s house across the y-axis? Explain.
Answers
Answer:
its in progress so tell ur teacher.
Step-by-step explanation:
The members of a crew team can weigh no more than 165 pounds each. Write an inequality for the acceptable weights. Graph the solutions.
Answers
Answer: it would be 100 plus 65 = 165 hope this helped
Step-by-step explanation:
2. At a restaurant, Mike and his three friends decided to divide the bill evenly. If each person paid $13.25
then what was the total bill?
Variable:
Equation:
Answer:
Answers
Step-by-step explanation:
39.75 is your answer for this question
Variable = 13.25
Equation = 13.25+13.25+13.25
Answer = 39.75