Given:
The equation of a line is
[tex]y=-\dfrac{2}{3}x+2[/tex] ...(i)
The perpendicular line passes through the point (-1,4).
To find:
The equation of the perpendicular line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex] ...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
[tex]m=-\dfrac{2}{3}[/tex]
Product of slopes of two perpendicular lines is -1.
Let the slope of perpendicular line is [tex]m_1[/tex].
[tex]m\times m_1=-1[/tex]
[tex]-\dfrac{2}{3}\times m_1=-1[/tex]
[tex]m_1=\dfrac{3}{2}[/tex]
The slope of the perpendicular line is [tex]m_1=\dfrac{3}{2}[/tex] and it passes through the point (-1,4). So, the equation of the line is:
[tex]y-y_1=m_1(x-x_1)[/tex]
[tex]y-4=\dfrac{3}{2}(x-(-1))[/tex]
[tex]y-4=\dfrac{3}{2}(x+1)[/tex]
[tex]y-4=\dfrac{3}{2}x+\dfrac{3}{2}[/tex]
Add 4 on both sides.
[tex]y-4+4=\dfrac{3}{2}x+\dfrac{3}{2}+4[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{3+8}{2}[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex]
Therefore, the equation of required line is [tex]y=\dfrac{3}{2}x+\dfrac{11}{2}[/tex].
Please help! The question and answer choices are attached.
Classify each pair of angles as adjacent, vertical, supplementary, complementary, or neither.
Adjacent
Vertical
Supplementary
Complementary
Neither
PLEASE HELPP MEE
Answer:
Complementary
Step-by-step explanation:
49°+41° = 90°
an airplane travels at 280 miles per hour. how far in miles will the airplane travel in 20 minutes?
Answer:
93.33 miles
Step-by-step explanation:
60 min/ 20 min = 3
280/3 = 93.333333
Answer:
93.3 miles
Step-by-step explanation:
Since there are 60 minutes in an hour and 20/60 = 1/3, you can divide 280 by 3 to get the amount of miles travelled in 20 minutes.
a father is 24years older than his son. if the son is x years old, how old is the father and if the ratio of their ages is 5:2, what is the age of the son?
x+25/x=5/2
5x=2(x+24) 5x=2x+48
5x-2x=48
3x=48 3x/3=48/3
the age of son=16
father=24+x 24+16=40
F=40 s=16
40/16=5:2
The subtotal of a dinner bill is dd dollars. There is an 8% dine-in tax, and the customer would like to leave an 18% gratuity based on the subtotal amount. Write an expression that represents the total amount the customer spends on dinner, including the tax and gratuity.
Answer:
1.26d
Step-by-step explanation:
Given that :
Subtotal = d
Dime - in tax = 8%
Gratuity = 18% of subtotal
Total amount spent on dinner :
Gratuity = 18% of d
Gratuity = 0.18 * d = 0.18d
Dine - in tax : = 8% of dinner bill
Dine - in tax = 0.08d
Total cost of dinner :
Dinner bill + dine - in tax + Gratuity
d + 0.08d + 0.18d
= 1.26d
Total amount spent on dinner = 1.26d
The length of a rectangular driveway is 3 times its width. If the length is 7 % yards, find
the length of the driveway and the area of the driveway.
Answer:
3 x 7 and 1/6 = 21 and 1/126
Step-by-step explanation:
your going to multiply 3x7 then you get 21 then you multiply by 1/6 and there you go.
Given the definitions of f(c) and g(x) below, find the value of g(f(5)).
f(x) = 2x – 10
g(x) = x2 + 6x – 8
Answer:
gf(5) = -8
Step-by-step explanation:
gf(x) = g(x^-1) = x^2 + 6x - 8
f(x) = 2x - 10
gf(x) = 6(2x - 10) - 8
gf(x) = 12x - 60 - 8
gf(x) = 12x - 68
gf(5) = gf(x) = 12x - 68
gf(5) = 12(5) - 68
gf(5) = 60 - 68
gf(5) = -8
A caircular fountian has a circumference of 21 feet. Which expression can be used to find the diameter of the fountian in feet?
Answer: [tex]21 = 2\pi r[/tex]
Step-by-step explanation:
To find the circumference of a circle, you can use [tex]2\pi r[/tex]. You can set this equal to 21 (feet). The equation to solve at this point would be [tex]21=2\pi r[/tex].
PLEASE HELP, URGENT!!!
John bought a crate of floor tiles $100. The crate had 5 boxes of floor tiles. Each box contained 40 floor tiles. Write an
equation to determine the cost per box, b.
ILL MARK BRAINLIEST IF GOTTEN RIGHT IF YOU DONT KNOW DONT ANSWER
Answer:
A) CPCTC
Step-by-step explanation:
This part of the proof occurs right after two triangles are proven congruent. One could now conclude and establish that every part of each congruent triangle is congruent, which is what is most likely happening in this scenario.
what is equvalint to 1/2a-4
5 fewer than a number, k.
Answer:
k-5. The question seems incomplete though.
Answer:
k - 5
Step-by-step explanation:
5 fewer than a number, k can be written as 5 less than k, which is k - 5.
1 gram = ----- centigrams
Answer:
100 centigrams!!
Step-by-step explanation:
PLEASE HELP MEEEEEEEE :)))
Answer:
26
Step-by-step explanation:
Devaughn = 2x
Sydney = x
x + 2x = 78
3x = 78
x = 78 / 3
x = 26
Hope that helps!
Answer:
26
Step-by-step explanation:
Lets say Devaughn age = d and Sydney age = s
Therefore,
d = 2s
and s + d = 78
Well, we can use substitution for d.
s + (2s) = 78
3s = 78
s = 26
The functions f(x) and g(x) are shown on the graph. f(x) = |x|
what is g(x)
Answer:
D
Step-by-step explanation:
Answer:
i just took it. its actually g(x)=|x+5|
Step-by-step explanation:
Arrange the numbers in ascending order 2121,3625,8750,6540
2121, 3625,6540 and 8750 is the answer.
hope it helps
I'm in a rush but please take your time answering! I'm giving out 100 points and I'll give brainliest right away! Thank you!
Answer:
d
Step-by-step explanation:
(3,-2);slope 1/3 what is the answer?
Answer:
y = [tex]\frac{1}{3}[/tex] x - 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = [tex]\frac{1}{3}[/tex] , then
y = [tex]\frac{1}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, - 2) into the partial equation
- 2 = 1 + c ⇒ c = - 2 - 1 = - 3
y = [tex]\frac{1}{3}[/tex] x - 3 ← equation of line
A family eats at a restaurant. The bill was $54. The family leaves a tip and spends $60 total. How much was the tip as a perentage of the bill? (round to the nearest whole percent)
Answer:
11%
Step-by-step explanation:
60 - 54 = $6 The tip is $6 since they were meant to pay $54 but gave $6 extra.
The bill is $54.
6/54 = 0.1 recurring
0.1 × 100 = 11.1%
11% is the percentage.
I hope that helps!! ^-^
can someone help me?
Answer:
Y=1.5x+1
Step-by-step explanation:
The new law and the rest to the right to be a part of this year and I have to say that I am not a fan of the most important things to do in the future and the other is a great way to get the best out of the way and I have to say that
please help !! What is the area of the trapezoid shown below?
4
5
Answer:
the area of the trapezoid is (8 + 4).3/2 = 18
Answer:
18
Step-by-step explanation:
khan
2. Tiangle ABC has vertices A(3, 3), B(2,-4), and c(0, 0). This triangle is rotated 90
degrees counterelookwise. About vertex C. Draw the rotated shape and write the new
coordinates
10
PLEASE HELP!
Use the Pythagorean Theorem to find the missing length and then round the result to the nearest tenth a=? b = 5, c = 12 what is A
Answer:
Approximately 10.9
Step-by-step explanation:
[tex]a^2+b^2=c^2[/tex]
Plug in b (5) and c (12)
[tex]a^2+5^2=12^2\\a^2+25=144[/tex]
Subtract 25 from both sides
[tex]a^2+25-25=144-25\\a^2=119[/tex]
Take the square root of both sides
[tex]\sqrt{a^2} =\sqrt{119}[/tex]
a = approximately 10.9
I hope this helps!
[tex] \sqrt{2x + 1 } = x - 1[/tex]
Maria averaged 212 miles on the first 3 days of her trip.She averaged only 104 miles on the other six days of her trip what was the overall average number of the miles travel
Answer:
1260
Step-by-step explanation:
212x3=636
104x6=624
636+624=1260
HELP ME NOW PLEASE ASAP HURRY !
Answer:
A
Step-by-step explanation:
A is the answer, as you can see for every rise in 1 unit of x, there is an equivalent rise of 1 unit of y.
A parking space shaped like a parallelogram has a base of 17 feet and a height of 9 feet if a mini car 6 feet long and five feet wide parks in the space, then how many square feet of the parking space is not covered by the car
Answer:
123 cm²
Step-by-step explanation:
First of all, we need to know how exactly to find the area of a parallelogram.
Area of parallelogram= Base*Height
PARALLELOGRAM-
BASE= 17 ft
HEIGHT= 9ft
AREA= 17*9= 153 cm²
The area of parallelogram, will be considered as WHOLE AREA.
Now,
AREA OF MINI CAR-
length= 6 ft
Width= 5 ft
Area= 6*5= 30 ft ²
Square feet uncovere-
153 ft²- 30 ft²= 123 ft²
HOPE IT HELPS!
Helppp no scamming
Triangle ABC has vertices A(0, 4), B(2, 1), and C(4, 3). Find the
coordinates of the vertices of ABC after a reflection over the
x-axis. Then graph the figure and its reflected image.
Answer:
A'= (0,-4)
B'= (2,-1)
C'= (4,-3)
Step-by-step explanation:
After you flip it over the x-axis, it would be
A'= (0,-4)
B'= (2,-1)
C'= (4,-3)
HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP HELP I NEED HELP ASAP
Charlie has dimes and quarters that have a value of $26.50. He has 15 fewer dimes than quarters. Which system of equations can be used to determine the number of dimes, d, and quarters, q?
A. q=d-15, d+q=26.50
B. d=q-15, 0.1d+0.25q=26.50
C. q=d-15, 0,1d+0.25q=26.50
D. d=q-15, d+q=26.50
Can someone help me with this? And no links or random answers please.
Answer:
B, 215483cm^3
Step-by-step explanation:
volume of a cylinder equals its base area by its height;
.
its base area = r^2 x 3.14 = 15^2 x 3.14 = 706.5
.
volume = 706.5 x 305 = 215482.5 cm^3
.
approximately 215483 cm^3