Given:
The given equation is:
[tex]y=-4x+3[/tex]
A line is perpendicular to the given line and passes through the point (4,-1).
To find:
The equation of required line.
Solution:
The slope intercept form of a line is:
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
We have,
[tex]y=-4x+3[/tex]
Here, the slope of the line is -4 and the y-intercept is 3.
Let the slope of required line be m.
We know that the product of slopes of two perpendicular lines is -1. So,
[tex]m\times (-4)=-1[/tex]
[tex]m=\dfrac{-1}{-4}[/tex]
[tex]m=\dfrac{1}{4}[/tex]
The slope of required line is [tex]m=\dfrac{1}{4}[/tex] and it passes through the point (4,-1). So, the equation of the line is:
[tex]y-(-1)=\dfrac{1}{4}(x-4)[/tex]
[tex]y+1=\dfrac{1}{4}(x)-\dfrac{4}{4}[/tex]
[tex]y=\dfrac{1}{4}x-1-1[/tex]
[tex]y=\dfrac{1}{4}x-2[/tex]
Therefore, the equation of the required line is [tex]y=\dfrac{1}{4}x-2[/tex].
Simplify
7p2 x 3p
14p4
Answer:
294(p)^7
Step-by-step explanation:
7(p)^2 x 3p x 14(p)^4
=> 7 x 3 x 14 x (p)^2 x (p) x (p)^4
=> 21 x 14 x (p)^(2+1+4)
=> 294(p)^7
in a group of 120 students,90 students study mathematics and 72 study science. if 10 of the student does not study any subject
1)find the no.of students who study atleast 1 subject
2)number of students studying both subjects
3)how many students will study mathematics only?
4)how many students will study science only?
Answer:
Step-by-step explanation:
Total students = 120
Number of students studying Mathematics P(A) = 90
Number of students studying Science P(B) = 72
Number of students who doesn't study both subjects P(AUB)'= 10
1) Number of students studying atleast on subject = 120 -10 = 110
2) Number of students studying both math and science = (90 +72) -110
= 162 -110 = 52
3) Number of students studying only mathematics = 90 -52 = 38
4) Number of students studying only science = 72 -52 = 20
Find the missing side lengths. Leave your answers as radicals in simplest form. *
That's the isosceles right triangle, one of the two cliche triangles students are expected to learn. The sides of the 45°/45°/90° triangle are in the ratio 1:1:√2.
So v= 3√2 (the two legs are equal) and hypotenuse u = √2 × v = 6.
Answer: C
Dada a função fx=0,15.X+900 , determine a) f(80) b) f(120) c) f(200) d) f(56)
Answer:
See answers below
Step-by-step explanation:
Given the function:
f(x) = 0.15x + 900
a) f(80) = 0.15(80) + 900
f(80) = 12 + 900
f(80) = 912
b) f(120) = 0.15(120) + 900
f(120) = 18 + 900
f(120) = 918
c) f(200) = 0.15(200) + 900
f(200) = 30 + 900
f(200) = 930
d) f(56) = 0.15(56) + 900
f(56) = 8.4 + 900
f(56) = 908.4
What is the length of line
segment AB?
The amounts that two plumbers charge for their services are described.
The first plumber charges a fixed fee of $40 for house calls and $15 per hour of work.
The second plumber charges a fixed fee of $30 for house calls and $19 per hour of work.
For what number of hours work do the first plumber and the second plumber charge the same total amount?
Answer:
See below.
Step-by-step explanation:
40 + 15x = 30 + 19x
15x - 19x = 30 - 40
-4x = -10
x = 2.5
Two and a half hours.
The first plumber and the second plumber charge the same total amount for 2.5 hours of work.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The number of hours worked by both plumbers is "h". Then the total amount charged by the first plumber is:
Total cost for the first plumber = 40 + 15h
And, the total amount charged by the second plumber is:
Total cost for the second plumber = 30 + 19h
To find the number of hours for which both plumbers charge the same total amount, we need to solve the equation:
40 + 15h = 30 + 19h
4h = 10
h = 2.5
Therefore, the first plumber and the second plumber charge the same total amount for 2.5 hours of work.
To learn more on Equation:
https://brainly.com/question/10413253
#SPJ2
Please help me with this question??m
Answer:
75
Step-by-step explanation:
f(1) = 7
f(n) = 3f(n-1) + 3
So what you are trying to do here is find the recursive value (that's what it is called) for f(n). Computers love this sort of thing, but we humans have to do it slowly and carefully.
So let's try f(2)
That means that f(2) = 3*f(n-1) + 3
but if f(2) is used it means that you have to know f(2-1) which is just f(1) and we know that.
so f(2) = 3*f(1)+3
f(2) = 3*7 + 3
f(2) = 21 + 3
f(2) = 24
Now do it again. We now know F(2), so we should be able to find f(3)
f(3) = 3*f(3 - 1) + 3
f(3) = 3*f(2) + 3 We know that f(2) = 24
f(3) = 3* 24 + 3
f(3) = 72 + 3
f(3) = 75
HELP PLEASE I WILL MARK BRAINLIEST
Answer:
i beleive its option number 1
Answer:
first graph
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Then g(x) = | x | - 4 is the graph of f(x) shifted down by 4 units
This is represented by the first graph on the left
Evaluate expression- Which of these answer choices are correct answer to the question
Answer:
i=10^5
eq is 2^n*i
hence 2^3*10^5
8*100000
=800.000 bacteria
pls mark as brainliest
Consider the equation and its solution.
— 15(x-O) = 25
— 15х+ 30 = 25
— 15х = -5
What number should be in the empty box?
-30
-2
Оооо
30
What is the slope of the line passing through the points (-5, -4) and (-1, 6)?
Step-by-step explanation:
using the formula (y2-y1)/(x2-x1)we plug the numbers In the slop formula (6--4)/(-1--5)= 10/4
Answer:
Step-by-step explanation:
(x1,y1)= (-5,-4)
(x2,y2)=(-1,6)
Distance=√(x2-x1)²+(y2-y1)²
=(-1-5)²+(6-4)²
=(-6)²+(10)²
=36+100
=136 answer,,
therefore, the slope of the line is 136unit
If a randomly thrown dart hits the board below, what is the probability it will hit the shaded region?
Please help me please I will really appreciate
Answer:
Step-by-step explanation:
If we draw this triangle with Q as the vertex angle (the one at the top of the triangle) then the 2 sides are congruent and this is an iosceles triangle. Because this is an isosceles triangle, then the 2 base angles, angle R and angle S are congruent. If Q measures 114 degrees, then angles R and S together have to add up to the difference between 180 and 114:
180 - 114 = 66
Divide that in half so R = S = 33 degrees each
Given m || n, find the value of x and y
Step-by-step explanation:
5x-6+7x+18=180
12x=180+6-18
12x=168
168÷12=14
X=14
for y
3y+11=7x+18(7×14+18)
3y+11=116
3y=116-11
3y=105
y= 35
Work out the base of a square with area,
A
= 64cm2.
Answer:
32
Step-by-step explanation:
because 64 divided by 2 is 32
yes need help again im on my math exam review thing i.dk wut it tis also here are some extra points im feelin nice today btw dont jus answer for the points or put a site or ill report.
ᴍɪʟʟʏ~
Answer:
(-5) + 8 + (-5) = -2
Step-by-step explanation:
The first point is 5 points to the left of 0, or -5
Next, it goes right 8 units (+8) and lands on 3
THen it goes back 5 units (-5) and lands on -2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Please Help I've tried like 30 times and I still get it wrong
Answer:
604.4 cm²
Step-by-step explanation:
Surface area of a cone = πr(r + √h² + r²)
π = 3.14
r = diameter/2 = 13.4 cm/2 = 6.7 cm
h = 21 cm
Surface area of a cone = πr(r + √h² + r²)
= 3.14 * 6.7(6.7 + √21² + 6.7²)
= 21.038(6.7 + √441 + 44.89)
= 21.038(6.7 + √485.89)
= 21.038(6.7 + 22.04)
= 21.028(28.74)
= 604.3 cm²
Surface area of a cone = 604.4 cm²
if the sub total is 5.00 and tax is 5% how much is tax
Answer:
$0.25
Step-by-step explanation:
So total of 5.25 after tax Sorry if i am wrong am pretty sure this is correct.
Jacqui likes to travel to the beach on weekends. She starts at her house, drives d miles, and then spends t hours walking the remaining w miles to get to the beach. Jacqui drives three times as long as she walks during the trip. The equation below represents Jacqui's average speed, a, in miles per hour, when traveling to the beach. a=d+w/3t+t What is the meaning of 3t + t3t+t in the equation above? -The total time that Jacqui spends traveling to the beach -The time that Jacqui spends driving to the beach -The total distance that Jacqui travels to the beach -Jacqui's maximum speed during her trip Jacqui's average speed during one trip to the beach was 3636 miles per hour. If Jacqui drove 70 miles and the entire trip to the beach took her 22 hours, how many miles did she walk to get to the beach?
Answer:
The answer is below
Step-by-step explanation:
1) Average speed is the ratio of the total distance travelled to the total time taken. Hence it is given by:
Average speed = total distance / total time
Total distance = d miles + w miles
Jacqui drives three times as long as she walks during the trip, hence:
time spent driving = 3t
Total time = 3t + t
Average speed = total distance / total time
a = (d + w) / (3t + t)
2) (3t + t) represents the total time that Jacqui spends traveling to the beach.
3) Given that a = 36 miles per hour, total time = 2 hours
a = total distance / total time
36 miles per hour = total distance / 2 hours
total distance = 72 miles
Total distance = distance walk + distance drove
72 = distance walk + 70
Distance walk = 2 miles
Which inequality represents “six times a number is less than negative
6x >-39
4
6 + x>-39
6x < -39
4
6x5-393
4
Answer:
6x < - 39 3/4
Step-by-step explanation:
Pls someone help me with this im struggling!
Answer:
£460.80
Step-by-step explanation:
Do 12% x 4 years= 48%
Then 48% x 960= £460.80
5. The property depicted in the expression 2/( 3) ×(1/3+ 4/5)=(2/3 × 1/3)+(2/3 × 4/5) is *
associative property of addition
associative property of multiplication
distributive property of multiplication
closure property of multiplication
Answer:
distributive property of multiplication over addition
Step-by-step explanation:
a(b + c) = ab + ac
The a to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.
This is the distributive property of multiplication over addition.
2/3 × (1/3 + 4/5) = (2/3 × 1/3) + (2/3 × 4/5)
The 2/3 to the left of the parentheses multiplies both numbers inside the parentheses. The you add the products.
This is the distributive property of multiplication over addition.
State if triangles HAG and CAB are similar and why.
please help. its for an assignment that is due today.
Find the domain of the graphed function. A.x>=0 B. x is all real numbers. C.-9<=x<=5 D.0<=x<=10
The domain of the function represented by the graph is x ≥ 0
How to determine the domain of the graph?The function is represented by the graph of the function
From the given graph, we have the following observations
The graph is a trigonometric graphThe x values of the graph starts from 0 and increases towards the positive axisThis means that the function has a domain of all set of real values greater than or equal to 0
This is represented as
x ≥ 0
So, the domain is x ≥ 0
Read more about domain at
brainly.com/question/2264373
#SPJ1
What is the volume of the prism?
Answer:
[tex]volume \: of \: the \: prism = 4 \frac{1}{2} \times 2 \ \frac{1}{2} \times 6 \\ = \frac{9}{2} \times \frac{5}{2} \times 6 \\ = 67.5 {cm}^{3} [/tex]
What’s the answer. Please help.
Answer:
The answer would be the third one, 3(x -2)=18
A remote-control airplane is descending at a rate of
23.6 meters per second. What will be its change in
height after 3 1/2 seconds? Round your answer to the
nearest meter.
Answer:
83 m
Step-by-step explanation:
23.6 x 3.5 = 82.6 ≈ 83 m
PLEASE HELP!! Look at photo
Answer:
Step-by-step explanation:
The ratio would be 36:4. The bigger number is on either side but when it concludes "for" means it's a ratio.
570
1. Volume of a pyramid: 192 ftº: Volume of a rectangular prism:
2. Volume of a pyramid:
Volume of a rectangular prism: 729m
3. Volume of a cylinder: 285 cm: Volume of a cone:
4. Volume of a sphere:
Volume of a cylinder: 600cm
5. Volume of a cone: 50 m: Volume of a cylinder:
Answer:
576 FT^3
243 m^3
95 cm^3
400 cm^3
150 m^3
Step-by-step explanation:
Volume of a pyramid = 1/3 x ( length base x height)
Volume of a prism= ( length base x height)
1. prism = 192 x 3 = 576 FT^3
2. prism = 729 / 3 = 243 ft^3
volume of a cylinder = nr^2h
Volume of a cone = 1/3(nr^2h)
3. cone = 285/3 = 95
5. cylinder = 50 x 3 = 150
4. sphere = 600 / 1.5 = 400