Write the point slope form of the equation of the line through the given point and slope
Answers
Step-by-step explanation:
the point-slope form in general is
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of a point, and m is the slope.
so, we have
y - -1 = 4/3 × (x - 3)
or simplified
y + 1 = 4/3 × (x - 3)
Answer:
[tex]y + 1 =\frac{4}{3} (x-3)[/tex]
Step-by-step explanation:
Pre-SolvingWe are given that a line contains the point (3, -1), and has a slope of [tex]\frac{4}{3}[/tex].
We want to write the equation of this line in point-slope form.
Point-slope form is given as [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1 ,y_1)[/tex] is a point.
SolvingSince we are already given the slope and the point of the line, we can plug these values into the formula to get the equation.
Let's start with the slope; replace m with [tex]\frac{4}{3}[/tex] in the formula.
[tex]y-y_1=\frac{4}{3}(x-x_1)[/tex]
Now, replace 3 as [tex]x_1[/tex] and -1 as [tex]y_1[/tex]. Remember that the formula has subtraction in it.
[tex]y--1=\frac{4}{3} (x-3)[/tex]
This can be simplified to become:
[tex]y + 1 =\frac{4}{3} (x-3)[/tex]
Topic: writing the equation of the line
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Related Questions
someone can help me for all the question ?
Answers
Answer:
1. 5
2. 3 adult tickets; 2 child tickets
3. See below
Step-by-step explanation:
1.
2 adult tickets cost 2 × $12 = $24
Subtract $24 from $64:
$64 - $24 = $40
Divide $40 by $8:
$40 ÷ $8 = 5
Answer: 5 child tickets
2.
x = number of adult tickets
y = number of child tickets
The total number of tickets is 5, so the first equation is:
x + y = 5
The cost of x adult tickets is 12x. The cost of y child tickets is 8y. The total cost is 12x + 8y. We are told the total cost is $52. The second equation is:
12x + 8y = 52
The system of equation is:
x + y = 5
12x + 8y = 52
Let's solve it by substitution.
Solve the first equation for x.
x = 5 - y
Now we substitute x in the second equation by 5 - y.
12(5 - y) + 8y = 52
Distribute:
60 - 12y + 8y = 52
Combine like terms on the left side:
-4y + 60 = 52
Subtract 60 from both sides:
-4y = -8
Divide both sides by 4.
y = 2
Substitute y = 2 in the first original equation and solve for x.
x + y = 5
x + 2 = 5
x = 3
Answer: 3 adult tickets; 2 child tickets
3.
The customer's claim is incorrect. His sum is $71. 71 is an odd number. Since all ticket prices are even numbers, it is impossible to add only even numbers and get an odd sum. A sum of several amounts of 12 and several amounts of 8 can never equal 71.
We can also show his claim is false using a system of equations.
x + y = 7
12x + 8y = 71
Use substitution.
x = 7 - y
12(7 - y) + 8y = 71
84 - 12y + 8y = 71
84 - 4y = 71
-4y = -13
y = 3.25
This means 3.25 child tickets. The problem states that tickets can be purchased only in whole numbers, so 3.25 tickets cannot be purchased, so the customer's claim is false.
Korey and lan are arguing about how to find the perimeter of a rectangle. Korey says you should add the length and the width and then multiply the sum by 2. Ian says you should double both length and width and then add them together who is correct
Answers
Answer:
They are both right
Step-by-step explanation:
This is because you can do it either way.
For example, if you had a rectangle with the side length 10 and a width 5,
-Korey: you could add them to get 15 and them double them to get 30
or
-Ian: double both (5*2=10 and 10*2=20) and then add and 10+20 = 30
So they are the same
what is this equation 6x-4y=18 and -x-6y=7
Answers
Step-by-step explanation:
here you have answer.....
solve the linear system by graphing.
x - 4y = 28
2x + y = 2
Answers
The ordinates of the linear system is mathematically given as
C=(4,-6)
Linear systemQuestion Parameters:
The equations
x - 4y = 28
2x + y = 2
Generally the equation for the linear system is mathematically given as
x - 4y = 28
2x + y = 2
Resolving the equations
x=4 and y=-6
Therefore
co ordinates are
C=(4,-6)
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As the height of the cylinder increases, its volume decreases.
Which is the independent variable?
height or volume
Answers
Answer:
height is independent
Step-by-step explanation:
as you change the height, the volume changes accordingly.
what are the domain and range of f(x)=2(x-8)-10
Answers
Answer:
Domain: All real numbers
Range: f(x) ≥ - 10
Step-by-step explanation:
I had the same test. Completed it and got it right.
Sorry for the lack of explanation, I can't put it into words at the moment.
What is the equation of the line of best fit that Pat drew?
OA.
y = -51 + 3
OB.
y = -5.7 + 7
O C.
Y =
* + 3
-Br
y = -x + 7
OD.
Answers
Answer:
B) y = -5x + 7
Step-by-step explanation:
Pick 2 points on the line: (10, 5) and (15, 4)
slope = change in y ÷ change in x = (15 - 10) ÷ (4 - 5) = -5
from inspection, the y-intercept is (0, 7)
Therefore, using slope-intercept formula: y = mx + b
(where m is the slope and b is the y-intercept)
y = -5x + 7
HELP I GIVE BRAINYEST The angle measurements in the diagram are represented by the following expressions.
\qquad \blueD{\angle A=8x -10^\circ}∠A=8x−10
∘
start color #11accd, angle, A, equals, 8, x, minus, 10, degrees, end color #11accd \qquad \green{\angle B=3x + 90^\circ}∠B=3x+90
∘
start color #28ae7b, angle, B, equals, 3, x, plus, 90, degrees, end color #28ae7b
Answers
Answer:
B = 150
Step-by-step explanation:
Since angles A and B are opposite interior angles, they are congruent.
8x - 10 = 3x + 90
8x - 3x = 90 + 10
5x = 100
x = 20
Now that we have the value of x, we have to solve for angle B.
B = 3x + 90
B = 3*20 + 90
B = 60 + 90
B = 150
Answer: the right answer on khan academy is 150° (with PROOF)
The population of village was 5000. The male population decreased by 20% and female population increased by 30 % make in change in total population. Find the male and female population of the village in the beginning.
Answers
Answer:
Step-by-step explanation:
Line segment EF is graphed on the coordinate plane below?
What is the length of EF? Record your answer to the nearest tenth of a unit.
Answers
a^2+b^2=c^2
7^2+3^2=c^2
49+9=c^2
58=c^2
sqrt58=sqrtc^2
7.6=c
Please help will give most Brainly
Answers
Write 5y^3 without exponents.
Answers
Answer:
can be written as without exponent.
Given:
To find:
Write the given expression without exponent.
Solution:
Formula to be used:
Step 1:
Write the expanded form of given expression.
Step 2:
simplify
or
125×y×y×y without exponent.
Answer:
5 × y × y × y
Step-by-step explanation:
5y³ ( only y is being cubed with 5 a multiplier ) , so
= 5 × y × y × y
Given the functions f(x) = 6x 11 and g(x) = x2 6, which of the following functions represents f[g(x)] correctly? f[g(x)] = 36x2 132x 127 f[g(x)] = 36x2 132x 121 f[g(x)] = 6x2 47 f[g(x)] = 6x2 36.
Answers
Function defines relationship between variables. The value of the f[g(x)] when the value of f(x)=6x+11 and g(x)=x²+6 is f[g(x)]= 36x²+47.
What is a function?A function assigns the value of each element of one set to the other specific element of another set.
Given to us
f(x) = 6x + 11
g(x) = x² + 6
As we know the two functions, given to us f(x) = 6x + 11, therefore substitute the value of x as g(x) in order to find the value of f[g(x)] ,
[tex]f(x) = 6x + 11\\\\f[g(x)] = 6(x^2 + 6) + 11\\\\f[g(x)] = 6x^2 + 36 + 11\\\\f[g(x)] = 6x^2 + 47[/tex]
Hence, the value of the f[g(x)] when the value of f(x)=6x+11 and
g(x)=x²+6 is f[g(x)]= 36x²+47.
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Please help I will give Brainliest.
Answers
Answer:
$21,600
Step-by-step explanation:
h(x) = 5000 · (1.08)^4
5000 · 4.32
h(x)= 21,600
Answer:
$6802.44
Step-by-step explanation:
We will replace x with 4.
h(4) = 5000 · (1.08)^4
Use a calculator from here if you don't want stress.
1.08 x 1.08 x 1.08 x 1.08 = 1.36048896
1.36048896 x 5000 = 6802.4448
Since we are looking at the cost, we will approximate to the nearest hundredth.
6802.4448 ≈ 6802.44
The cost is $6802.44.
There is a rectangle. The long side is 8.2cm the short side is 3.6cm. Find the area. (Include units)
Answers
Answer:
29.52cm sqauared
Step-by-step explanation:
length x width = area of rectangle
Answer: 29.52cm2
Step-by-step explanation:
8.2 times 3.6=...
What is the product of 8.2 × 109 and 4.5 × 10-5 in scientific notation?
36.9 × 10-45
12.7 × 104
3.69 × 105
3.69 × 1014
Answers
Answer:
(8.2 x 10^9) x (4.5 x 10^-5) = (8.2 x 4.5) x 10 ^(9 - 5) = 36.9 x 10^4 = 3.69 x 10^5
Step-by-step explanation:
3.69 x 10^5
Step-by-step explanation:
The guy above is right if you need more detail it's also C on edge if that helps
What is the name of the platonic solid below
Answers
Answer:
the other person is wrong
Step-by-step explanation:
I looked it up and its HEXAHEDRON
Tetrahedron is a pyramid
I need help. I will give 15 points for the answer.
Answers
Answer:
a) because all the angles of both of the triangle of equal and help by angle angle similarity criteria we can say that ∆ABCis similar to ∆PQRb) since ∆ABC~ ∆PQR[tex] \frac{ab}{ac} = \frac{pq}{pr} [/tex][tex] \frac{6}{ac } = \frac{18}{27} \\ ac = \frac{6 \times 27}{18 } \\ ac = 9cm[/tex]Hope it helps you<3HELP!!!!! convert 4π/7 radians to degrees to the nearest tenth place.
Answers
Answer:
4π/7 radians is 102.86°
Step-by-step explanation:
changing radian to degrees: 1 radian → [tex]\frac{180}{\pi }[/tex]
changing radians to degrees:
[tex]\dfrac{4\pi }{7} *\frac{180}{\pi }[/tex]
[tex]\dfrac{4*180}{7}[/tex]
[tex]\dboxed{102.86}[/tex]
[tex]\\ \rm\longmapsto \dfrac{4\pi}{7}\times \dfrac{180)(\pi}[/tex]
[tex]\\ \rm\longmapsto \dfrac{180(4)}{7}[/tex]
[tex]\\ \rm\longmapsto 720/7[/tex]
[tex]\\ \rm\longmapsto 102.8°[/tex]
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer: A
Step-by-step explanation:
Divide top and bottom by 4
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The simplest form of the fraction is simply finding a common number to divide both the numerator and denominator by.
4/8 , we can divide both sides by 4 since it's possible to do so.
[tex]\frac{4/4}{8/4}[/tex]
[[tex]\frac{1}{2}[/tex]]
A. is the simplest form
in the diagram below, the value of y must be
Answers
Answer:
y = 45°
Step-by-step explanation:
4 sides = 360°
(2y+1)° + y° + 112° + 112° = 360°
2y + y = 360 - 112 - 112 - 1
3y = 135
y = 135÷3
= 45°
There is a $500 prize to share among them. Ms. Cardillo’s class brought in 3,107 pop can tabs. Ms. Camming’s class collectected 1,097 pop can tabs. Mr. Lucas’ class brought in 2,347 pop can tabs. How should they divide the money so that each class gets the same fraction of the prize money as the fraction of pop can tabs that they collected?
Answers
Hi! Hopefully this helps. The math is there.
find X
15x and 8x-2
i will give brainliest
Answers
Answer:
x = 4
Step-by-step explanation:
15x + 8x -2 = 90
23x - 2 = 90
23x = 90+2
23x = 92
92/23 = 4
check answer:
4 x 15 = 60
4 x 8 = 32
32-2=30
60+30=90
Answer:x=4
Step-by-step explanation: we know,
90 + 8x-2+15x=180
90+23x-2=180
88+23x=180
23x=180-88
x=92/23
x=4
help ill give the 5 star
Answers
Answer:
D of course:
Step-by-step explanation:
Think about it,
50.54 is 50 estimated to the roundest digit, and 20.10 is 20 estimated. So we'll just do 50-20 which is 30
I hope this answers your concern :) Mark me brainliest if you want to (:
Answer:
-30
Step-by-step explanation:
50.54 - 20.10 = 30.44
If we multiply three consecutive integers and then add the middle number to the result, the answer is always the middle number cubed.
5 × 6 × 7 + 6 = 216 = 63
10 × 11 × 12 + 11 = 1331 = 113
15 × 16 × 17 + 16 = 4096 = 163
Use what you have learned in this lesson to write a third-degree polynomial expression in factored form and standard form that represents this pattern. Show that the factored form is equivalent to the expression written in standard form. Substitute three different values for the variable to prove this pattern works for other numbers.
Answers
Step-by-step explanation:
Let use have a interger,n
Thus three consectice intergers can be represented by
[tex]n[/tex]
[tex]n + 1[/tex]
[tex]n + 2[/tex]
Multiply, and we get
[tex]n(n + 1)(n + 2)[/tex]
[tex]n( {n}^{2} + 3n + 2)[/tex]
[tex]n {}^{3} + 3 {n}^{2} + 2n[/tex]
Then add the middle number, n+1.
[tex] {n}^{3} + 3n {}^{2} + 3n + 1[/tex]
We must prove that the middle number cubed = the equation.
Using the binomial theroem,
[tex](n + 1) {}^{3} = {n}^{3} + 3( {n}^{2} 1 {}^{1} ) + 3n( {1}^{2} ) + 1 {}^{3} [/tex]
[tex](n + 1 ){}^{3} = {n}^{3} + 3 {n}^{2} + 3n + 1[/tex]
So this is indeed true.
You can do the subsitue variables for n to prove it.
Factorise x2 + 5x - 84
Answers
(x - 7)(x + 12)
Answer:
[tex] {x}^{2} + 5x - 84 \\ {x}^{2} + 12x - 7x - 84 \\ x(x + 12) - 7(x + 12) \\ (x - 7)(x + 12)[/tex]
Hay algo que, aunque te pertenezca, la gente siempre lo utiliza más que tú. ¿Qué es?
Answers
Answer:
Respuesta: tu nombre (Answer: your name)
Step-by-step explanation:
What is the equation of a line with slope -3 through the point (3, 5)?
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
in a all-area track meet 271 sprinters enter a 200-meter dash competition. the track has 7 lanes so only 7 sprinters can compete at a time. at the end of each race, the six non-winners are eliminated, and the winner will compete again in later race. How many races are needed to determine the champion sprinter?
Answers
The number of races needed to determine the champion sprinter = 39 races.
Calculation of number of racesThe number of sprinters = 271
The number of sprinters per race= 7
The area to be covered for each race = 200m
For every race covered, a champion is selected and the rest is eliminated.
Therefore, to determine the remaining champion from 271 sprinters,
271/ 7 = 38.7
Which is approximately 39 races.
Learn more about meter here:
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Can someone help me with this please
Answers
Answer:
medium: 16large: 18Step-by-step explanation:
Using the variable definitions shown, the two given relations are ...
11 +x +y = 45 . . . . . . 45 total orders
x = y -2 . . . . . . . . . . 2 fewer medium orders than large
__
Using the second equation, we can substitute for x in the first equation to solve this system:
11 +(y -2) +y = 45
2y = 36 . . . . . . . . . . collect terms and subtract 9 from both sides
y = 18 . . . . . . . . . . . divide both sides by 2
x = 18 -2 = 16 . . . . use the second equation to find the value of x
16 people ordered medium, and 18 people ordered large coffees.