Line a passes through points (2, 1) and (7, 9). Line b is perpendicular to a. What is the slope of line b?
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
please refer to the pic below for the solution! :)
The slope of the perpendicular line will be - 5/8.
What is Equation of line?
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;
Two points on the line are (2, 1) and (7, 9).
Now,
Since, We know that;
The slope of the line passing through the points (x₁ , y₁) and (x₂, y₂) is;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
So, The slope of the line passing through the points (2, 1) and (7, 9) is;
⇒ m = (y₂ - y₁) / (x₂ - x₁)
⇒ m = (9 - 1) / (7 - 2)
⇒ m = 8 / 5
Since, The product of the slope of the perpendicular lines is - 1.
Here, Line b is perpendicular to a.
So, The slope of the line b is,
m₂ = - (1/8/5)
= - 5/8
Thus, The slope of the perpendicular line will be - 5/8.
Learn more about the equation of line visit:
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Related Questions
3-for-1 split. After the split, the price of one share was $39.24. What was the pre-split price per share?
Answers
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Explanation:
Let's say that the company is valued at $300 just as a simple example.
Also, let's say there are 100 shares each worth $3, so we have 100*3 = 300 as the total value of the company.
A 3-for-1 split means that for each share, it will get turned into 3 shares. So you turn in 1 share and in return you get 3 shares back. Or put another way, each share is ripped/cut into 3 equal pieces.
After doing this split, we would have 3*100 = 300 shares and each share would be now worth (1/3)*3 = 1 dollar. Note the new number of shares multiplied with the new value per share is still the same total valuation of $300. Doing a stock split, or a reverse stock split, will not change the value of the company. This is a good thing or else companies would simply do (reverse) splits all the time to increase their value however large they wanted without actually contributing anything to society.
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So quite simply, when we do a 3-for-1 split, we multiply the old price per share by 1/3 to get the new price per share.
Let
x = old price per share
y = new price per share
So x happens before the split and y is after the split.
For a 3-to-1 split, we can form this equation
y = (1/3)x
which solves to
x = 3y
when we multiply both sides by 3
We know that y = 39.24, which means,
x = 3y
x = 3*39.24
x = 117.72
The pre-split price per share was $117.72
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So in short, all we did was multiply the given number (39.24) by 3.
Kelko will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57 and cost an additional $0.08 per mile driven. The second plan has an initial fee of $50 and costs and additional $0.10 per mile driven.
Answers
Questions (contd)
(a) For what amount of driving do the two plans cost the same?
(b) What is the cost when the two plans cost the same?
Answer:
(a) 100 miles
(b) $65
Step-by-step explanation:
Given
Plan 1:
[tex]Initial\ Fee = \$57[/tex]
[tex]Additional = \$0.08[/tex] per mile
Plan 2:
[tex]Initial\ Fee = \$50[/tex]
[tex]Additional = \$0.10[/tex] per mile
Solving (a): Number of miles when both plans are equal
Represent the distance with x and the cost with y
So:
Plan 1:
[tex]y = 57 + 0.08 * x[/tex]
Plan 2:
[tex]y = 50 + 0.10 * x[/tex]
To solve (a), we equate both plans together; i.e.
[tex]y = y[/tex]
[tex]57 + 0.08x = 50 + 0.10x[/tex]
Collect Like Terms
[tex]0.08x - 0.10x= 50 - 57[/tex]
[tex]-0.02x= -2[/tex]
Solve for x
[tex]x = -2/-0.02[/tex]
[tex]x = 100[/tex]
Hence, 100 mile would cost both plans the same
Solving (b): Cost when both plans are the same:
In this case, we simply substitute 100 for x in any of the y equation.
[tex]y = 57 + 0.08 * x[/tex]
[tex]y = 57 + 0.08 * 100[/tex]
[tex]y = 57 + 8[/tex]
[tex]y = 65[/tex]
Hence, the amount is $65
Simplify:
8.7 + 3.2(2p – q) + 2.55 p
Answers
Answer:
8.95p-3.2q+8.7
Step-by-step explanation:
Answer:
8.95, 3.2, 8.7
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!!! Write the equation of the line perpendicular to y=3/4x+9/4 that passes through the point (-5, 2)
Answers
Answer:
y = -4/3x - 6
Step-by-step explanation:
1. Find the slope. Since we know that a line perpendicular to another is it's opposite reciprocal, or the product of the two is equal to -1, we can find the slope. -4/3 times 3/4 is -1, so -4/3 would be the slope of this line.
2. Plug in the point and slope into the slope-point equation. The equation would be y - 2 = -4/3 * (x + 6).
3. Simplify. The simplified equation would be y = -4/3x - 6.
Answer: y = -4/3x - 6
I WILL GIVE BRAINLIEST FOR RIGHT ANSWER
Suppose Triangle MNO has vertices M(-7,3), N(9,8), and 0(2,16). After a dilation centered at the origin, the coordinates of Triangle M'N'O are M'(-10.5, 4.5), N' (13.5, 12), and O' (3,24). Complete the following algebraic description so that it represents the transportation of Triangle MNO, (2, y) + (x, y) The scale factor is
Answers
Answer:
The answer is 1.5
Step-by-step explanation:
Answer:
The scale factor is = 1.5
Step-by-step explanation:
Trust me bro
Express in the form n:1 ratio
16:8
Answers
To get 1 on the right, you divide by 8, so you do the same thing on the left.
16/8:8/8
2:1
Plz help with these 2 questions plz it depends on my grade
for the penny one i need the equation for one of the answers
Answers
Answer:
Yes
Step-by-step explanation:
2 pennies and 3 dimes = 60 cents
I penny = 1 cent
1 dime = 10 cents
How many solutions can be found in this equation 4x - 8 - 4x = 9?
0
1
2
or infinet
Answers
Rewrite this sentence using BOTH a DOP and an IOP.
Voy a dar una naranja a Juan.
Answers
Answer:
Se la voy a dar., Se la voy a dar, se la voy a dar., se la voy a dar, Se la voy a dar a Juan., Se la voy a dar a Juan, se la voy a dar a Juan., se la voy a dar
Step-by-step explanation:
Please help middle school math
Answers
9514 1404 393
Answer:
3 < b-a < 7
Step-by-step explanation:
The maximum difference will occur when the smallest 'a' value is subtracted from the largest 'b' value:
9 -2 = 7
The minimum difference will occur when the largest 'a' value is subtracted from the smallest 'b' value:
7 -4 = 3
So, the possible range of values of b-a is ...
3 < b-a < 7
Identify each following representation as a function or nonfunction and explain your reasoning.
Answers
Answer:
a) and c) - function, b) and d) - nonfunctionStep-by-step explanation:
As per definition, a function is such a relationship that each input has exactly one outputConsidering this we observe that:
a) functionb) not a function as input of -1 has two different outputs o and 1c) functiond) not a function as input of 0 has two different outputs 0 and 0.53. Use trigonometric ratios to solve for the variable. Show your work. Round lengths to the nearest tenth and angles to the nearest whole degree.
Answers
Answer:
x = 3.4
Step-by-step explanation:
recall that for a right angle with an internal angle θ,
cos θ = adjacent length / hypotenuse
in our case,
θ = 55 deg
adjacent length = x units
hypotenuse = 6 units
substitute these into the formula above
cos θ = adjacent length / hypotenuse
cos 55 = x / 6 (multiply both sides by 6)
x = 6 cos 55 (use calculator)
x = 3.4415
x = 3.4 (rounded to nearest tenth)
The car traveled 42.5 miles per gallon of gas. If the gas tank in the car could hold 16.5 gallons, how far can the car travel on one tank of gas? (Don't round answer)
Please, help I am really confused!
Answers
Answer:
2.57575758
Explanation:
42.5 / 16.5
pls help me my class ends soon, i’ll give brainliest
Answers
Answer:
D
Step-by-step explanation:
First of all, she wants to INCREASE her steps per day. A, B, and C all have the same number of steps or fewer steps. I can further prove that the answer is D because if she stars walking 10 extra steps per day, 10 times 100 = 1000 and 5000 + 1000=6000. Please correct me if I am wrong because everybody makes mistakes sometimes. Also, thanks so much for giving me brainiliest!
Edit: If I was helpful to you, please take a shot at my puzzle that's due Monday.
It is worth 100 points and would mean a lot to me if you could try and solve it. Good luck! Here is the link: https://brainly.com/question/19021808
1. Which of the following is the equation of a line that has a slope 5 and passes through the point
(3,- 7)?
Answers
Answer:
Hope this helps!
Step-by-step explanation:
Answer:
Step-by-step explanation:
Given
point (3,-7)
m = 5
Solution
y - y1 = m(x - x1)
y - (-7) = 5(x - 3)
y + 7 = 5x - 15
y = 5x - 15-7
y = 5x-22
Answer
The equation in point-slope form that passes through the point (3,-7)and has a slope of 5 is line Y=5x-22
3. In the figure shown, a circle with center O and radius of length 3 units is
inscribed in a square. What is the area of the shaded region? *
A. 3.86 square units
B. 7.73 square units
C. 28.27 square units
D. 32.86 square units
Answers
Answer:
C
Step-by-step explanation:
To find the area of a circle, take its radius (3) and square it. In this case, 3 times 3 = 9. Then, you multiply the answer by pi, which rounds to 3.14, but is more like 3.14159265......etc, etc. There is a rhyme for that: May I have a large container of coffee beans? Where the length of each word is a number of pi. Anyway, most people would write 9pi, but this is asking for the exact answer, so you can do 3.14 times 9, which equals roughly 28.27. Hope this helped!
What is the slope??? PLEASE HELP!!!
Answers
Answer:
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.
Which sets of values belongs to the domain and range of a relation
Answers
full answer:
As we know that
The domain of a relation is defined as the set of all possible independent values the relation can really take - basically the group of all possible inputs.
The range of a relation is defined as the set of all possible dependent values the relation can generate from the domain values - basically the group of all possible outputs.
As
The domain is the set of independent values, meaning the set of x-coordinates of the ordered pairs as x is an independent variable.
The range is set of dependent values, meaning the set of y-coordinates of the ordered pairs as y is an independent variable.
So, in the set of ordered pairs of a relation
Please help me ASAP
:D
Answers
Answer: I think it 616lbs not 100% sure
Step-by-step explanation:
10^2 = 100 + 64 sweet potatoes = 164
10^1 = 10+80 tangerines= 90
10^3= 300 + 62 spaghetti squash = 362
How much will you get paid if you work 28.5 hours for $7.75 per hour?
Answers
Answer:
$220.875
Step-by-step explanation:
For 1 hour you get $7.75
To find how much money you make in 28.5 hours... you multiply the number of hours with the number of dollars.
28.5 * 7.75
$220.875
first to answer correctly gets brainleist! I need ya to find the slope for me!
Answers
Answer:
m=-1
Step-by-step explanation:
The line is going down as x increases, so the slope is negative. Next, we can find the value for m by taking the equation:
m=(y2-y1)/(x2-x1)
m=(3-(-1))/(0-4)
m=4/-4
m=-1
Adelaide has a credit card with a company that charges $3.00 for every day a payment is late. If she paid $492.93 for a bill that is 3 days late, how much was the bill without the late fee?
Answers
I NEED HELP can someone find the slope from these equations
Answers
y=mx+b with m being slope.
Answers 2, -1/2, and 2/3
Answer:
[tex] \underline{\boxed{if \: y = 2x + \frac{2}{3} \to \: the \: slope\to \boxed{m = 2} }}\\ \underline{\boxed{if \: y = - \frac{1}{2} x - 3 \to \: the \: slope\to \boxed{m = - \frac{1}{2} } }}\\ \underline{\boxed{ if \: y = \frac{2}{3} x\to \: the \: slope\to \boxed{m = \frac{2}{3} }}}\\ [/tex]
find the total cost of a video game that costs 29.99 with 8% tax
Answers
Answer:
32.39
Step-by-step explanation:
29.99 is 100%
? is 8%
?= 29.99*8/100 about 2.40
so the final cost is the price + tax = 29.99 +2.40= 32.39
Student answers 90% of the questions on the math exam correctly if she answers 27 questions correctly how many questions are on exam
Answers
Answer:
30 questions
Step-by-step explanation:
if you cross multiply and divide like this,
[tex]\frac{27}{x}= \frac{90}{100}[/tex]
27 x 100 = 2700
2700 / 90 = 30
you'll get ; 30 !
Answer:
There are 30 total questions on the exam
Explanation:
90% = 0.9
0.9 x TOTAL = 27
27/ 0.9 = TOTAL
30 = TOTAL
Please help!!! 40 points and will give brainliest!!
Answers
Answer:
the answer would be
Step-by-step explanation:
i hope this helped
If you add all four together, you get a %400 increase
What would happen to the product in the following problem:
25×11/11
A.The product will increase
B.The product will decrease
C.the product will stay the same
Answers
Can someone help me plz
Answers
Answer:
6^(7/3)
Step-by-step explanation:
Given 6^2 * cubed_root(6).
The cube root is also equal to 6^1/3
[Multiply the terms, add the powers]
6^2 * 6^(1/3) = 6^(2 + 1/3) = 6^(7/3)
Which correctly explains how to estimate 55 percent of 64?
Round 55 percent to 40 percent and 64 to 60. Think of 40 percent as . So, of 60 is 15.
Round 55 percent to 60 percent and 64 to 70. Think of 60 percent as . So, of 70 is 23.3.
Round 55 percent to 50 percent and 64 to 70. Think of 50 percent as . So, of 60 is 12.
Round 55 percent to 50 percent and 64 to 60. Think of 50 percent as . So, of 60 is 30.
Answers
Step-by-step explanation:
Round 55 percent to 50 percent and 64 to 60. Think of 50 percent as 1/2. So 1/2 of 60 is 30
Answer:D
Step-by-step explanation:
Determine if the two triangles are congruent.
Answers
Answer:
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.
Step-by-step explanation:
If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.