Answer:
The answer is below
Step-by-step explanation:
Expansion using pascal triangle:
a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ =
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
Expansion using binomial where [tex]C(n,r)=\frac{n!}{(n-r)!r!}[/tex]
a) (x + 2)⁶ = C(6,0)[x⁶2⁰] + C(6,1)[(x⁵)(2)¹] + C(6,2)[(x⁴)(2²)] + C(6,3)[(x³)(2³)] + C(6,4)[(x²)(2⁴)] + C(6,5)[(x)(2⁵)] + C(6,6)[(2⁶)]
= x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶)
= x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64
b) (x-4)⁴ = C(4,0)[x⁴] + C(4,1)[(x³)(-4)] + C(4,2)[(x²)(-4)²] + C(4,3)[(x)(-4)³] + C(4,4)[(x⁰)(-4)⁴]
= x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4)⁴
=x⁴-16x³+96x²-256x+256
c) (2x + 3)⁵ = C(5,0)[(2x)⁵] + C(5,1)[(2x)⁴(3)] + C(5,2)[(2x)³(3)²] + C(5,3)[(2x)²(3)³] + C(5,4)[(2x)(3)⁴] + C(5,5)[(2x)⁰(3)⁵]
= (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵
= 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243
d) (2x-3y)⁴ = C(4,0){(2x)⁴(-3y)⁰} + C(4,1)[(2x)³(-3y)] + C(4,2)[(2x)²(-3y)²] + C(4,3)[(2x)(-3y)³] + C(4,4)[(2x)⁰(-3y)⁴]
= 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴
= 16x⁴- 96x³ + 216x² - 216x + 81
In the expansion of (3a + 4b)⁸, the only possible variable terms are a⁵b³, b⁸, a⁴b⁴, a⁸, ab⁷ because for each of them, the sum of there powers is eight. If the sum of the powers is not 8 then it is not correct.
For a²b³, the sum of the power is 5, for ab⁸ the sum of power is 9 and for a⁶b⁵ the sum of the power is 11 therefore thy are not correct.
As per the question expand the bimonoidal theorem and the pascal triangle. Showing the (x+2)6 (x-4)4 (2x+3)5 (2x-3y)4.
Expansion using pascal triangle:a) (x + 2)⁶ = x⁶2⁰ + 6(x⁵)(2)¹ + 15(x⁴)(2²) + 20(x³)(2³) + 15(x²)(2⁴) + 6(x)(2⁵) + 1(2⁶) = x⁶ + 12x⁵ + 60x⁴ + 160x³ + 240x² + 192x + 64b) (x-4)⁴ = x⁴ + 4(x³)(-4) + 6(x²)(-4)² + 4(x)(-4)³ + 1(x⁰)(-4) =x⁴-16x³+96x²-256x+256c) (2x + 3)⁵ = (2x)⁵ + 5(2x)⁴(3) + 10(2x)³(3)² + 10(2x)²(3)³ + 5(2x)(3)⁴ + 1(2x)⁰(3)⁵ = 32x⁵ + 240x⁴ + 720x³ + 1080x² + 810x + 243d) (2x-3y)⁴ = 1(2x)⁴(-3y)⁰ + 4(2x)³(-3y) + 6(2x)²(-3y)² + 4(2x)(-3y)³ + 1(2x)⁰(-3y)⁴ = 16x⁴- 96x³ + 216x² - 216x + 81.Learn more about the use the binomial theorem.
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x/t+m=b need to make x the subject
Answer:
x=(t+m)/b is the answer
Step-by-step explanation:
Hope it will help :)
Answer:
x = t(b-m)
Step-by-step explanation:
x/t + m =b
subtract m from each side
x/t +m-m = b-m
x/t =b-m
Multiply each side by t
x/t *t = t(b-m)
x = t(b-m)
Mele earned scores of 75, 70, 92,95, and 97 points (a
total of 429 points) on the first 5 tests in Economics II
Solving which of the following equations for s gives
the score he needs to earn on the 6th test to average
exactly 85 points for all 6 tests?
+5=85
F. 429
G. 429
H. + 429
+5 = 85
= 85
J. S+429
= 85
6
K. S+ 429
85
100
Answer:
The equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is;
S + 429 = 85 × 6
Step-by-step explanation:
The parameters given are;
The scores earned by Mele on the first five test in Economics II are;
75, 70, 92, 95, and 97 points
The total test points = 429 points
Therefore, the score, S, Mele needs to earn on the 6th test for him to get an average of exactly 85 points for the 6 tests is found as follows;
From the definition of average, μ = (Sum of data values)/(Number of data)
Sum of data values = S + 429
The number of data = 5 test + 6th test = 6
μ = 85 = (S + 429)/6
Therefore;
S + 429 = 85 × 6
Therefore, the equation for S which gives the score he needs to earn on the 6th test to average exactly 85 points for all 6 tests is S + 429 = 85 × 6.
Make up an expression of your own that satisfies the following:
Must have at least: 4 terms, 1 constant, 2 variables with coefficients and appropriate
operation signs.
There are infinitely many ways to answer this as there is no one single answer to pick from.
Here is one possible answer: x^3 + 5x^2 + 7x + 12The four terms are x^3, 5x^2, 7x and 12. They are separated by the plus signs.
The constant is 12. It does not have any variable attached to it.
Terms 5x^2 and 7x have coefficients of 5 and 7 respectively.
The leading term x^3 has a coefficient of 1, but 1*x^3 = x^3, meaning it's convention to leave the 1 out. So technically x^3 does not have a coefficient directly written/shown. Instead, its more implied.
Solve the equation for x
Answer:
x = 33
Step 1:
First, let's add the values together from both parentheses.
2x + x = 3x
1 + (-10) = -9
Now we are left with:
3x - 9 = 90.
Step 2:
Add 9 on the left side to cancel out the 9. Add it to the right side.
3x = 99
Finally, divide both sides by 3 to get our answer.
3x / 3 = x
99 / 3 = 33
x = 33
23^3 (-12)^3 +(-11)^3 without actually calculating cubes
Answer:
9108
Step-by-step explanation:
23^3+(-12)^3+(-11)^3 remove parentheses
= 23^3-12^3-11^3 group difference of two cubes
= (23-12)(23^2+23*12+12^2) + 11^3 factor difference of two cubes
= 11 (23^2+23*12+12^2-11^2) factor ou 11
= 11(23(23+12) + (12+11)(12-11)) apply difference of two squares
= 11 (23*35+23*1) factor out 23
= 11(23*(35+1)) simplify
= 11*23*36 convert 11*23 into difference of 2 squares
= (17^2-6^2)*6^2 expand parentheses
= 102^2-36^2 evaluate squares
= 10404 - 1296 subtraction
= 9108
(no calculator required)
A fruit tray was served at a meeting. During the meeting, 4 out of 10 strawberries were eaten. Which model has a shaded region that represents the amount of strawberries eaten during the meeting?
Answer:
4 of the berries will be shaded
Step-by-step explanation:
The model that shows that 4 out of 10 strawberries were eaten is attached.
What is a expression? What is a mathematical equation? What is a fraction?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.A fraction represents a part of a whole or, more generally, any number of equal parts. A fraction is written as - {x/y}, where [x] is numerator and [y] is denominator.We have, 4 out of 10 strawberries were eaten in a fruit tray.
Refer to the image attached. This model shows that the 4 out of 10 strawberries were eaten.
Therefore, the model that shows that 4 out of 10 strawberries were eaten is attached.
To solve more questions on Equations, Equation Modelling and Expressions visit the link below -
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Elena drank 3 liters of water yesterday. Jada drank 3/4 times as much water as much water as Elena. Lin drank twice as much water as Jada. Did jada drink more or less water than Elena?
Answer:
Jada drank less water than Elina.
Step-by-step explanation:
Water drunk by Elina = 3 liters
Jada drank the water [tex]\frac{3}{4}[/tex] times as much as water as Elina.
Therefore, water drunk by Jada = [tex]\frac{3}{4}\times 3[/tex]
= [tex]\frac{9}{4}[/tex]
= 2.25 liters
Lin drank water twice as much as Jada.
Therefore, Lin drank the amount of water = 2 × 2.25
= 4.5 liters
Since Jada drank 2.25 liters of water and Elina drank 3 liters
Therefore, Jada drank less water than Elina.
the points (-2,1), (1,1), (0,-2), and (-3,-2) are vertices of a polygon. what type of polygon is formed by these points? A. rectangle B. square C. pentagon D. parallelogram
Answer:
[tex]\boxed{\sf D. \ Parallelogram}[/tex]
Step-by-step explanation:
When we graph the points, the polygon is a quadrilateral with opposite parallel sides. The type of polygon formed by these points is a parallelogram.
Answer:
Parallelogram
Step-by-step explanation:
We'll graph all of the points from which we'll come to know that it is a parallelogram having opposite sides equal and parallel.
See the attached file for more understanding.
Find the value of a.
3a-9=15
Answer:
a = 8Step-by-step explanation:
3a - 9= 15
To solve the equation send the constants to the right side of the equation
That's
3a = 15 + 9
simplify
3a = 24
Divide both sides by 3
[tex]\frac{3a}{3} = \frac{24}{3}[/tex]
The final answer is
a = 8
Hope this helps you
Answer:
a = 8
Explanation:
Step One - Add nine to both sides of the equation. This is the first step is to isolate the variable, a. This step will remove the negative nine from the equation.
3a - 9 = 15
3a - 9 + 9 = 15 + 9
3a = 24
Step 2 - Divide both sides of the equation by three. This is the last step to isolate the variable, a.
3a = 24
3a/3 = 24/3
a = 8
Since we have fully isolated the variable, a, we have determined its value.
Therefore, in the equation 3a - 9 = 15 the value of the variable is a = 8.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Answer:
2/5
Step-by-step explanation:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now for the difference
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5 , which is the answer :)
The answer is 2/5.
To find the fraction bar in the box.
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
Given that:
First for the sum:
3/5 + 1/5 i + 4/5 - 2/5 i = 7/5 - 1/5 i
Now substract the sum,
9/5 - 1/5 i - (7/5 - 1/5 i)
= 9/5 - 1/5 i - 7/5 + 1/5 i
= 2/5
So, the answer is 2/5.
Learn more about fraction here:
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PLEASE HELP MEEE How can a company use a scatter plot to make future sale decisions
Answer:
by tracking data of how much money was made on one product in a certain amount of time
Step-by-step explanation:
Please answer this question now
Answer:
200 cm³ is the volume of the pyramid
Answer:
200 cubic centimeters
Step-by-step explanation:
l = length = 10 cm
w = width = 10 cm
h = height = 6cm
V = lwh / 3
= 10 * 10 * 6 / 3
= 100 * 6 / 3
= 600 /3
= 200 cubic cm
Hope this helps! Tell me if I am incorrect!
A standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades. Four cards are drawn from the deck at random. What is the approximate probability that exactly three of the cards are diamonds? 1% 4% 11% 44%
Answer:
4%
Step-by-step explanation:
There are ₁₃C₃ ways to choose 3 diamonds from 13.
There are ₃₉C₁ ways to choose 1 non-diamond from 39.
There are ₅₂C₄ ways to choose 4 cards from 52.
Therefore, the probability is:
₁₃C₃ ₃₉C₁ / ₅₂C₄
= 286 × 39 / 270,725
≈ 0.04
The approximate probability that exactly three of the cards are diamonds is 4%.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
We are given that standard deck of 52 playing cards contains 13 cards in each of four suits: hearts, diamonds, clubs, and spades.
Since we can see that there are ₁₃C₃ ways to choose 3 diamonds from 13.
₃₉C₁ ways to choose 1 non-diamond from 39.
₅₂C₄ ways to choose 4 cards from 52.
Therefore, the probability is:
₁₃C₃ ₃₉C₁ / ₅₂C₄
= 286 × 39 / 270,725
≈ 0.04
Therefore, the answer could be 4 percent.
Learn more about probability here;
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On Tuesday, Dec. 3, I began drinking a glass of cola every day except Saturday and Sunday. I drank my 22nd glass of cold on A) Dec. 24 B) Dec. 25 C) Dec. 31 D) Jan. 1
Answer:
The correct option is;
D) Jan. 1
Step-by-step explanation:
The given information are;
The date at which drinking a glass of cola a day of cola began = Dec 3
The days in which to drink cols = Every day of the week except Saturday and Sunday
The number of glasses of drinking cola = 22
In the fires week, number of days in which to drink cola = Tuesday, Wednesday, Thursday, and Friday which is 4 days
On the week commencing Dec 9, 5 glasses drank
On the week commencing Dec 16, 5 glasses drank
On the week commencing Dec 23, 5 glasses drank
On the week commencing Dec 30, 3 glasses drank
Therefore on the week commencing Dec 30, cola was drank on the 30th, 31st and the 22nd glass was drank on Jan. 1
The correct option is Jan. 1.
Two angles are adjacent and form an angle of 160. Their difference is 34. Find the angles
Answer:
The angles are 63 , 97
Step-by-step explanation:
Let one angle be x
As sum of two angles is 160, the other angle = 160 - x
Their difference = 34
x - [160- x] = 34
Use distributive property to remove the brackets
x - 160 + x = 34
Add like terms
x + x - 160 = 34
2x - 160 = 34
Add 160 to both sides
2x = 34 + 160
2x = 194
Divide both sides by 2
2x/2 = 194/2
x = 97°
One angle = 97°
Other angle = 160 - 97 = 63°
Please help me understand this number sequence
Answer:
Step-by-step explanation:
A=a(r)^t
a=1
time=2.5 hours=25/10 ×60=150 minutes
10t=150
t=150/10=15
[tex]A=1(2)^{15}=32,768[/tex]
Find the coordinates of point G that lies along the directed line segment from F(-1, -1) to H(-8, 20) and partitions the segment in the ratio of 5:2.
Answer:
coordinates of point g is ( -6, 14)
Step-by-step explanation:
The coordinates of the point which divides the point (x1,y1) and (x2,y2) in m:n ratio is given by (nx1+mx2)/(m+n), (ny1+my2)/(m+n).
___________________________________________
given point
F(-1, -1) to H(-8, 20)
ratio : 5:2
the coordinates of point g is
(2*-1+5*-8)/(5+2), (2*-1+5*20)/(5+2)
=> (-2 -40/7 , -2+100/7)
=> (-42/7, 98/7)
=>( -6, 14)
Thus , coordinates of point g is ( -6, 14)
please solve this question.
[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]
[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]
Michael is trying to hang Christmas lights on his house. His house is 17 ft tall and the ladder leaning is 34 degrees above the ground. How long must the ladder be to reach the house? a 24 feet b 17 feet c 34 feet d 30 feet
Answer:
34 feet
Step-by-step explanation:
let length of ladder be x
[tex] \ \sin(34) = \frac{17}{x} [/tex]
[tex]x \sin(34) = 17[/tex]
[tex]x = \frac{17}{ \sin(34) } [/tex]
x = 32.131083564
Find the value of a.
a = 18°
Step-by-step explanation:we have opposite angles =>
=> 6a + 11 = 2a + 83
6a - 2a = 83 - 11
4a = 72
a = 72 : 4
a = 18°
(3)/(22)+(-(1)/(11) find the sum without use of a number line
Answer:
1/22
Step-by-step explanation:
Simplify it.
It becomes 3/22-1/11
Change the denominator to 22 becasue that is the LCM.
It becomes 3/22-2/22 which is 1/22. :)
SOMEBODY PLEASE HELP ME ON THIS ; DUE TODAY, i’ll mark u the brainliest
Answer: Angle Addition Postulate
Step-by-step explanation:
According to the angle addition postulate, the measure of an angle formed by two angles side by side is the sum of the measures of the two angles. It is used to evaluate the measure of an angle formed by two or more angles .In the given picture, we have ∠MRO and ∠MRS on line SRO.
So, ∠SRO = ∠MRO +∠MRS [By angle addition postulate]
So the postulate that justify the statement " ∠SRO = ∠MRO +∠MRS" is Angle Addition Postulate.
The solutions to (x + 3)^2- 4=0 are x = -1 and x = -5
True or false
Answer:
THE ANSWER WOULD BE TRUE MY FRIEND
Simplify the following expression. (10-4i)(4-5i)+(-15+20i)
Answer:
5-46i
Step-by-step explanation:
1. Multiply (10-4i) and (4-5i), I recomnd using foil:
40-50i-16+20i^2 + (-15+20i)
2. Remove the parenthesis around -15+20i
*we can do this since there is a "+":
40-50i-16+20i^2 + (-15)+20
3. Simplify i^2
* i^2 is -1 by textbook defination:
40-50i-16+20(-1) + (-15)+20
4. Simplify
40-50i-16-20 + (-15)+20
6. Combine like terms:
-5-50i-16i+20i
5-46i
And the problem is done
A vehicle has a will 15 inches in diameter. If the vehicle travels 2 miles, how many revolutions does the wheel make? This is Applications of unit conversions
Find the circumference of the wheel:
Circumference = PI x Diameter = 3.14 x 15 = 47.1 inches.
Every revolution the tire travels 47.1 inches.
1 mile = 5,280 feet, so 2 miles = 5280 x 2 = 10,560 feet.
1 foot = 12 inches.
2 miles = 10,560 feet x 12 = 126,720 inches.
Revolutions = total distance / distance per revolution:
Revolutions = 126,720 / 47.1 = 2,690.45 revolutions ( round answer as needed.)
How to do this question plz answer me step by step plzz
Answer:
Hope it helps U can still ask me if u have confusions
Answer:
60+16√30 cm² ≈ 147.64 cm²
Step-by-step explanation:
You can figure the height of the object from ...
V = Bh
120 cm^3 = (30 cm^2)h
4 cm = h . . . . . divide by 30 cm^2
However, this is insufficient to tell you the surface area.
__
If you assume that the base is square, then its side length is
A = s^2
s = √A = √(30 cm^2) = (√30) cm
The lateral surface area can then be found from the perimeter of the base and the height
LA = Ph = (4√30 cm)(4 cm) = 16√30 cm^2
The total surface area will be the sum of this lateral area and the area of the two bases:
total area = 16√30 cm^2 +2·30 cm^2
total area = (60 +16√30) cm^2 ≈ 147.64 cm^2
__
For any other shape, the total area will be larger. It can be arbitrarily large, unless limits are put on the dimensions of the object.
Consider 6x2 + 6x + 1. Which term immediately tells you that this expression is NOT a perfect square trinomial? Justify your answer.
Answer:
Step-by-step explanation:
The 6x^2 because 6 is not a perfect square.
Answer:
6x^2
Step-by-step explanation:
6 isn't a perfect square
answer it answer it it
Answer:
answer it answer it it
answer it answer it it
Answer:
the answer is answer i hope u have a great day
(if u apricate me giive me a brainly by pressing the crown and giving me a heart) THANKS!!!
Step-by-step explanation:
Nathan, a tutor, buys 5 calculators for $7.50 each at a store, planning to provide one to each of his clients. However, the next day, he discovers that the same calculators has gone on sale for $5.00 and also discovers that he will only have three tutoring clients instead of five. He returns the five calculators and purchases three calculators at the new sale price. He uses the following expression to determine the amount he should receive back from the store. (5 x $7.50) - (3 x $5.00) Which of the following expressions could Nathan have used. 5 ($7.50 - $5.00). $7.50 - $5.00. (5 x $7.50) - $5.00. (5 x $7.50) - $5.00. 3 ($7.50 - $5.00) +2 x $7.50
Answer: 5 (7.50-3 )
Step-by-step explanation:
Given: Previous price of calculator = $7.50
Number of client =5
Total price = (Number of calculators) x (Price for each calculator)
Total price of 5 calculators = (5 x $7.50)
New price of calculator = $5.00
Number of client =3
Total price of 3 calculators = (3 x $5)
Price will receive = (Total price of 5 calculators) -(Total price of 3 calculators )
= (5 x $7.50) - (3 x $5)
= 5 (7.50-3 )
Required expression: 5 (7.50-3 )
Convert to slope-intercept from: y-3=6(x-5)
Answer:
y = 6x -27
Step-by-step explanation:
y-3=6(x-5)
Distribute
y-3 = 6x-30
Add 3 to each side
y-3+3 = 6x-30+3
y = 6x -27
This is in slope intercept form y=mx+b where m is the slope and b is the y intercept
Hey there! I'm happy to help!
Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.
y-3=6(x-5)
We use distributive property to undo parentheses.
y=3=6x-30
We add 3 to both sides.
y=6x-27
Now, this in slope intercept form.
Have a wonderful day! :D
