Which of the following represents the polar equation r = (tan 2θ)(csc θ) as a rectangular equation?
We will have the following:
[tex]r=\tan ^2(\theta)\csc (\theta)\Rightarrow r=(\frac{\sin(\theta)}{\cos(\theta)})^2(\frac{1}{\sin(\theta)})[/tex][tex]\Rightarrow r=\frac{\sin^2(\theta)}{\sin(\theta)\cos^2(\theta)}\Rightarrow r=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]Now, we corroborate with one of the expression, in our case we will analyze y = x^2:
[tex]r\sin (\theta)=(r\cos (\theta))^2\Rightarrow r\sin (\theta)=r^2\cos ^2(\theta)\Rightarrow r=\frac{\sin (\theta)}{\cos ^2(\theta)}[/tex]So, the expression taht represents the value given is:
[tex]y=x^2[/tex]Adam plans to choose a video game from a section of the store where everything is 75% off. He writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
Drag each description to explain each part of both expressions.
Both Adam and Rena re both correct regarding the expression.
What is an expression?An expression simply means an illustration that can be used to represent a scenario or situation.
From the information, Adam writes the expression d−0.75d to find the sale price of the game if the original price is d dollars.
Rena correctly writes another expression, 0.25d, that will also find the sale price of the game if the original price is d dollars.
In this case, they are both correct. This can be illustrated as:
= 1 - 0.75d
= 0.25d
Note that the information was answered based on the information given.
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Find three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two.
The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0.
What is an integer?An integer is a whole number irrespective of the sign that the integer is all whole numbers that are going from 0 to infinite or 0 to minus infinite.
Integer ; ....-2 , -1 , 0 , 1 , 2 , .....
Integers are non-decimal numbers and all integers are rational numbers.
Let's assume that first, even integer is x
Then the second and third will be x + 2,x + 4 respectively.
As per the given,
1 less than 4 times the third → 4(x+4) - 1
It is equal to the 5 more than the sum of x and x + 2
So, x + x + 2 + 5
Therefore, 4(x+4) - 1 = x + x + 2 + 5
4x + 16 - 1 = 2x + 7
4x + 15 = 2x + 7
2x = 7 - 15
x = -4
So integers are -4,-2,0
Hence "The three consecutive even integers such that one less than four times the third is equal to five more than the sum of the first two is -4,-2,0".
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what is the Pythagorean Theorem equation for this right angle 25, 24 and 7?
The equation of the Pythagorean Theorem in the triangle is 25^2 = 24^2 + 7^2
How to determine the Pythagorean Theorem equation?From the question, the side lengths of the triangle are given as
25, 24 and 7
The Pythagorean Theorem states that:
Hypotenuse^2 = Sum of the squares of the other sides
Where
The other sides are the smaller sides
This in other words mean that:
Other sides = 24 and 7
Hypotenuse = 25
Substitute the known values in the above equation
25^2 = 24^2 + 7^2
Hence, the Pythagorean Theorem equation is 25^2 = 24^2 + 7^2
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-0.01a^4*(-10a^5)^3[tex]-0.01a^4*(-10a^5)^3[/tex]
It seems there is some missing info on this question. However, if you are simplifying, then the simplified version of the given expression would be...
[tex]10a^1^9[/tex]
Hope this helps!
HELP ME PLSSS ITS DUE TODAY
Answer:
S': (2, 1)
T': (5, 3)
U': (1, -4)
S'': (1, 3)
T'': (4, 5)
U'': (0, -2)
Step-by-step explanation:
Hi!
For Reflection Across the X-Axis use this :
(x, y) -> (x, - y)
So :
S': (2, 1)
T': (5, 3)
U': (1, -4)
and then the question also asks for a translation so we follow what it gave us:
S'': (1, 3)
T'': (4, 5)
U'': (0, -2)
Please ask me any questions that you still may have!
and Have a great day! :)
Answer:
S' (2, 1) S'' (1, 3)
T' (5, 3) T'' (4, 5)
U' (1, -4) U'' (0, -2)
Step-by-step explanation:
The preimage is S (2,-1), T (5, -3) U(1,4).
Preimage: the original figure prior to a transformation.
The directions say to reflect the preimage over the x-axis.
To do this, follow this transformation rule: (x, y) → (x, -y)
This means keep the x-coordinate as it is, but then change the sign of the y-coordinate.
S (2, -1) → S' (2, 1)
T (5, -3) → T' (5, 3)
U (1, 4) → U' (1, -4)
Next, take the coordinates from the last transformation then translate it using the rule: (x, y) → (x-1, y+2)
This means subtract 1 from the x-coordinate, then add 2 to the y-coordinate.
S' (2, 1) → S'' (1, 3)
T' (5, 3) → T'' (4, 5)
U' (1, -4) → U'' (0, -2)
Notice that each time you do a transformation, you add an apostrophe next to the letter. In math, this symbol is called a 'prime symbol.'
I hope this helped! Let me know if you have any questions.
in serious need of help! i need the answer quick!
The coordinates of G is (d+c, b)
This is because the opposite sides of any parallelogram are equal in length, and so the length of side HG is equal to the length of side EF.
a) The length of side HG is equal to the horizontal distance (x2 - x1): xG - 0
The length of side EF is equal to the horizontal distance (x2 - x1): d - (-c) = d +c
Thus:
xG - 0 = d + c
xG = d + c
Therefore the x-coordinate of G is d + c
b) To find the y-coordinate of G, we also apply the idea that sides GF and HE are equal.
The length of side GF is equal to the vertical distance (y2 - y1): yG - 0
The length of side HE is equal to the vertical distance (y2 - y1): b - 0
Thus:
yG - 0 = b -0
yG = b
Therefore the y-coordinate of G is b
Finally, the coordinates of G is (xG, yG) = (d+c, b)
What was the distance of the first part of yuna's swim? round to the nearest tenth as needed. the distance in the first part of her swim was miles.
Using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.
What are equations?A mathematical statement that has an "equal to" symbol between two expressions with equal values is called an equation. As in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.So, let 'x' be the distance of the 1st part and 'y' be the time in hours of the 1st part.
1st part: 1/4 = x/y (Equation A)2nd part: 0.8 = 1.9 - x/2 - y (Equation B)Plot the equations on the graph as follows:
(Refer to the graph attached below)
Be obtain:
x = 0.7 milesy = 0.5 hoursTherefore, using equations we now know that the distance of the first part of the Yuna's swim is 0.7 miles.
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The complete question is given below:
In training for a triathlon, Yuna swam 1.9 miles in the open ocean, which took her 2 hours. For the first part of her swim, she averaged 1.4 miles per hour. For the second part of her swim, she swam against the current and started to tire, so her average speed decreased to 0.8 mph. What was the distance of the first part of Yuna's swim? Round to the nearest tenth as needed. The distance in the first part of her swim was miles.
Answer:
.7
Step-by-step explanation:
slope for point (7,2) and (1,-1)
Answer: The slope is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
[tex]Slope = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } =\frac{-1-2}{1-7} =\frac{-3}{-6} =\frac{3}{6}=\frac{1}{2}[/tex]
Listen to this on the day she was born, a baby leopard had 9 spots. Each day 4 more spots appeared. After 5 days, how many spots did the baby have?
Answer:29
Step-by-step explanation:
9+4 spots times five days
Plot the ordered pair and state which quadrant or on which axis the point lies
Answer:
Explanation:
Given the ordered pair (-2, 4 1/2), where x = -2 and y = 4 1/2 = 9/2 = 4.5. Plotting this point, we'll have;
Note that quadrants are numbered in an anti-clockwise manner with the top right portion of the graph as Quadrant I. Looking at the plotted point, we can see that it lies in Quadrant II.
Make r the subject of m=√6a+r/5r
Answer:
r=√6a/5m-1
Step-by-step explanation:
m=√6a+r/5r
cross multiply
5mr=√6a+r
5mr-r=√6a
factorise
r(5m-1)=√6a
divide both sides by the coefficient of r
r=√6a/5m-1
hope it helps
please mark brainliest
Answer:
hope it helps u
MATHEMATICS IS OUR OWN LANGUAGE,LETS TALK TOGETHER
On average, people breath 10,000 times per night with a standard deviation of 1400. You study 50 people and record how many breaths they take per night. What is the probability that the average of all participants in the study was fewer than 10,200 breaths each night?I want answer with step by step.
ANSWER
[tex]\begin{equation*} 0.84375 \end{equation*}[/tex]EXPLANATION
We want to find the probability that the average of all participants in the study was fewer than 10,200 breaths each night.
To do this, first, we have to find the z-score corresponding to the sample mean:
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]where x = sample mean
μ = population mean
σ = standard deviation
n = sample size
Therefore, the z-score is:
[tex]\begin{gathered} z=\frac{10200-10000}{\frac{1400}{\sqrt{50}}}=\frac{10200-10000}{\frac{1400}{7.0711}} \\ z=\frac{200}{197.99} \\ z=1.01 \end{gathered}[/tex]Now, using the standard normal table, we can find P(z < 1.01).
Therefore, the probabilityis:
[tex]P(z<1.01)=0.84375[/tex]That is the answer.
please help me please
Answer:
Surface area= 6(5·5)+6(3·3)-2(3·3)
Step-by-step explanation:
first figure out the surface area of both cubes
for the larger cube- 5 multiplied by 5 for the area of one side then multiplied by 6 for all faces
for the smaller cube- 3 multiplied by 3 for the area of one side then multiplied by 6 for all the faces.
the cubes are touching on one face, this is the whole area of one side of the 3 by 3 cube, meaning two of these faces must be subtracted to find the surface area of the whole shape
hope that helps
Which of the following is the correct expansion of the binomial (x + y)6?
A.
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
B. x6 + 155y + 6x4y2 + 20x³y3 + 6x²y + 15xy5+y6
C. x6 + 6x55+ 15x4y4 + 20x³y3 + 15x²y² + 6xy¹+y6
D. x6 + 6x5y + 20x4y² + 15x³y3 + 20x²y4 + 6xy5+y6
Option a is correct using algebric formulas.
What is (x + y)³ and (x + y + z)² formula?(x + y)³ = x³ + y³ +3xy( x + y )
(x + y + z)² = x² + y² + z² + 2( xy + yz + zx )
So breaking it into
(( x + y )³)² = (x³ + y³ +3xy( x + y ))²
(x³ + y³ +3xy( x + y ))² = x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
x^6 + y^6 + 9x²y²(x² + y² + 2xy) + 2( x³y³ + 3xy^4( x + y ) + 3x^4y( x + y) )
So after rearranging the terms
we get (x + y)^6 as
x6 + 6x5y + 15x4y2 + 20x³y3 + 15x²y4 + 6xy5+y6
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Good morning I could really use some help with this problem please!!
Hello!
First, let's write the coordinates of each vertex of this parallelogram:
• A (-4, 2)
,• B (2, 2)
,• C (5, -2)
,• D (-1, -2)
As line AB is parallel to the x-axis, we can find its measurement without formulas. We just need to count the number of squares from one point to the other.
So,
AB = 6 units.We will follow the same reasoning to calculate CD (because it's also parallel to the x-axis).
CD = 6 units.Now we have to use the formula of the distance between two points to calculate the sides BC and DA. The formula is:
[tex]d_{A,B}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]As we know the formula, let's replace it with the coordinates:
BC: 5 units[tex]\begin{gathered} d_{B,C}=\sqrt{\left(x_C-x_B\right)^2+\left(y_C-y_B\right)^2} \\ d_{B,C}=\sqrt{(5-2)^2+(-2-2)^2} \\ d_{B,C}=\sqrt{3^2+(-4)^2} \\ d_{B,C}=\sqrt{9+16} \\ d_{B,C}=\sqrt{25} \\ d_{B,C}=5\text{ units} \end{gathered}[/tex]DA: 5 unitsWe can solve it using the same formula as I used to solve BC, but now I'll show you how to solve it using Pythagoras Theorem (I think it will be easier). Look:
Solving by Pythagoras, we'll obtain:
[tex]\begin{gathered} x^2=4^2+3^2 \\ x^2=16+9 \\ x^2=25 \\ x=\sqrt{25} \\ x=5\text{ units} \end{gathered}[/tex]Remembering: the perimeter is the sum of all the sides of a figure. So, we will have:
[tex]\begin{gathered} P=AB+BC+CD+DA \\ P=6+5+6+5 \\ P=22\text{ units} \end{gathered}[/tex]Part AType an equation to represent the cost of the topsoil.Part BHow does the cost of the topsoil compare to the cost of the mulch?
Step 1
Write the equation of a line in slope point form
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where;
[tex]\begin{gathered} y_2=\text{ 60} \\ x_2=2 \\ y_1=\text{ 30} \\ x_1=\text{ 1} \end{gathered}[/tex]Step 2
Find the equation to represent the cost of the topsoil.
[tex]y-30=\frac{60-30}{2-1}(x-1)[/tex][tex]\begin{gathered} y-30\text{ = }\frac{30}{1}(x-1) \\ y-30=30x-30 \\ y=30x-30+30 \\ y=30x \end{gathered}[/tex]The equation that represents the cost of the topsoil is
y=30x
Step 3
Find how the cost of the topsoil compares to the cost of the mulch.
[tex]\begin{gathered} \text{The equation for the cost of the mulch y, in dollars is} \\ y=25x \\ \text{for x cubic yards of mulch} \\ \text{The equation for the cost of topsoil, y in dollars is} \\ y=30x \\ for\text{ x cubic yards of topsoil} \end{gathered}[/tex][tex]undefined[/tex]
Find measure of angle E
The measure of ∠E will be equal to 38°.
Given,
m∠BFE = 118° and m∠C = 86°
And BF bisects ∠ABD
From the Property of Linear Pair,
∠AFB + ∠BFE = 180°
=> ∠AFB + 118° = 180°
=> ∠AFB = 62°
Now, we can see that ∠AFB and ∠FBD are equal because they are alternate angles.
And ∠FBD and ∠ABF are equal because BF bisects ∠ABD.
So, In ∆ABF,
∠AFB + ∠ABF + ∠BAF = 180° (because of the angle sum property of a triangle)
=>62° + 62° + ∠BAF = 180°
=>∠BAF = 180° - 124°
=> ∠BAF = 56°
Similarly, in ∆ABE,
∠A +∠C +∠E = 180°
=> 56° + 86° + ∠E = 180°
=> ∠E = 38°
Therefore, m∠E = 38°.
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PLEASE HELP ASAP!!
1. Use the space provide to respond to each statement concerning the given graph of a radical function.
a.) State the domain of the function.
b.) State the range of the function.
c.) Identify the end behavior of the function.
d.) Identify the x – intercept. Write as an ordered pair.
e.) Determine the absolute minimum of this function.
Part a
The domain is the set of x-values, which is [tex][1, \infty)[/tex].
Part b
The range is the set of y-values, which is [tex][-3, \infty)[/tex].
Part c
As [tex]x \to \infty[/tex], [tex]y \to \infty[/tex].
Part d
The x-intercept is when y=0, which is [tex](2, 0)[/tex].
Part e
The absolute minimum is the lowest point, which has a y-coordinate of [tex]-3[/tex].
Part a
The domain is the set of x-values, which is .
Part b
The range is the set of y-values, which is .
Part c
As , .
Part d
The x-intercept is when y=0, which is .
Part e
The absolute minimum is the lowest point, which has a y-coordinate of
In ▲ABC, side AC is extended through C to D. If m<dcb=50 which is the longest side of triangle abc?
Answer:
AB
Step-by-step explanation:
the angles DCB and ACB are supplementary angles (together 180°).
simply because the sum of all angles around a single point on one side of a line is suggests 180° (it represents a half-circle).
so, the inner angle ACB is
ACB = 180 - 50 = 130°
because the sum of all angles in a triangle is also always 180°, there are only 50° left for the other 2 angles.
so, the inner angle at C is clearly the largest angle in the triangle ABC.
the larger an angle, the longer the opposing side.
the largest angle has the longest opposing side in the triangle.
the opposing side of the inner angle C is AB. and that is therefore the longest side in the triangle ABC.
A plumber has a 2.5 metre long copper wire. he needs to cut lengths of 60cm, 35cm and 90cm work out how much of the initial 2.5 metre long pipe is left. give your answer in cm
By the concept of measurement of length we get the remaining length of the pipe 65 cm.
The total length of pipe before it was used by the plumber was 2.5 metre = (2.5 x 100)cm = 250cm.
Since,the plumber needs to cut lengths of 60cm, 35cm and 90cm
Thus,total Length of the pipe cut by the plumber = 60cm + 35cm + 90cm = 185cm
After subtracting the length of pipe used by the plumber from the original length of the pipe, we get,
The remaining length of the pipe = 250 - 185 = 65cm
Hence, the remaining length of the pipe is 65 cm.
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Dylan enjoys ramen noodles and music downloads. His monthly budget for these two items is 15 dollars. If the price of a package of ramen noodles is $1.48 and the price of a music download is $1.15, what is Dylan's opportunity cost of a music download? (Round your answer to the nearest tenth. For example: 1.4).
Data:
• Monthly budget: $15
,• Price of a package of ramen: $1.48
,• Price of a music download: $1.15
Procedure:
[tex]\frac{15}{1.48}\approx10.1[/tex]Answer: 10.1
two planes are flying torwards each other. in 45 minutes, the two planes will be 200 miles apart. in 1 hour, plane A will pass plane B. How far apart are the planes now.
800 miles is going to be the distance that separates the two aircraft. The distance between the two airplanes will be 1,300 kilometers at the very least.
What is the distance?It is important to keep in mind that the two aircraft's combined speed will be equal to the sum of their separate speeds when calculating their overall speed. In addition, the pilots of the two aircraft have one hour to find each other.
According to the information that was provided, the distance that separates the aircraft after they have flown for forty-five minutes is two hundred miles. As a result, the following will constitute the remaining distance:
= 1 hour - 45 minutes = 15 minutes.
When this occurs, the distance between the planes will be as follows:
= 200/15 × 60
= 200 × 4
= 800 miles
As a result, there will be a gap of 1300 kilometers between the two aircraft.
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7. The vertices of a triangle are P(-7,-4), Q(-7, -8), and R(3, -3). Name the vertices of the
image reflected across the line y=x.
OP(4, 7), Q8, 7), R'(3,-3)
OP(4,-7), Q8, -7), R'(3, 3)
OP(-4,-7), Q(-8,-7), R'(-3, 3)
OP(-4, 7), Q(-8, 7), R'(-3,-3)
(1 point)
A place where two or more curves, lines, or edges converge is known as a vertex in geometry (plural: vertices or vertexes), and it is frequently identified by letters like,,,. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.
The solutions are:
P' = (-4,-7)
Q ' = (-8,-7) (-8,-7)
R ' = (-3,3) (-3,3)
All you have to do is flip the provided points P, Q, and R's x and y coordinates.
The common principle is (x,y) —-> (y,x)
Thus, when we reflect across the line y = x, something like P = (-7,-4) becomes P'= (-4,-7). The similar approach is taken with the other points.
How do you locate a triangle's vertices?
Finding the triangle's vertices on the line y = x as an image
The steps below are used to locate a triangle's vertices using its midpoints:
Identify the midpoints' x and y values;
Calculate the midpoint using the following equations: A = (x 1+ x 3 - x 2, y 1 + y 3-y 2); B = (x 1+x 2-x 3, y 1+y 2-y3); C = (x 2+x 3-x 1, y 2 + y 3 -y 1);.
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How do I solve y-1=3(x-4)
Step-by-step explanation:
open the bracket
y - 1 = 3x - 12
add 1 to both sides
y = 3x - 11
I think that should be it
Please help ASAP! Select all rational numbers.
The rational numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49
What is a rational number?A rational number can simply be described as a number that is expressed as the ratio of two even or odd integers.
The denominator of the fraction or ratio must be greater than zero.
Rational numbers are represented mathematically as a quotient, say x/y of two integers such that y ≠ 0, that is, the denominator is not equal r equivalent to zero.
It is formed from dividing on integer(whether odd or even) by another integer.
The numbers; √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49 are all rational numbers
Hence, the numbers are √75, 2. √7, √0. 36, √0. 0144, √3/77, -√36/49
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which of the following is not a step in a hypothesis test? a. state the null hypothesis about a population. b. set the alpha level. c. if the sample data is not located in the critical region, we accept the null hypothesis. d. if the sample data is located in the critical region, we reject the null hypothesis.
The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.
How to form the hypotheses?There are two hypotheses. The first one is called the null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test.
The hypothesis which substitutes the null hypothesis is an alternate hypothesis.
We know that the Null hypothesis is the one that researchers try to disprove.
The null hypothesis must be rejected if we choose the 99.7 percent of confidence level.
The following is not a step in a hypothesis test; d. if the sample data is located in the critical region, we reject the null hypothesis.
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A large university accepts 70% of the students who apply. Of the students the university accepts,25% actually enroll. If 20,000 students apply, how many enroll?
The number of students that enrolled = 3,500 students.
What is enrollment?This is defined as the intake of individuals into an organism or students into an institution through adherence to specific orders given by the administrative department of the organisation.
The number of students that apply= 20,000 students
The percentage of students that are accepted= 70% of 20,000
That is, 70/100× 20,000
= 1400000/100
= 14,000 students.
The quantity of students that actually enroll = 25% of 14,000
That is, 25/100× 14000
= 350000/100
= 3,500 students.
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You pick a card at random without putting the 1st card back you pick a second card at random what is the probability of picking an even number and then picking an even number
We will have the following:
First, we can see that the probability of picking an even number at first is:
[tex]P_1=\frac{3}{6}\Rightarrow P_1=\frac{1}{2}[/tex]And then, the probability of picking another even card without replacing the previous one will be:
[tex]P_2=\frac{2}{5}[/tex]Now, the probability of this happening one after the other will be:
[tex]\begin{gathered} P_3=P_1P_2\Rightarrow P_3=\frac{1}{2}\ast\frac{2}{5} \\ \\ \Rightarrow P_3=0.2 \end{gathered}[/tex]So, the probability will be of 20%.
Solve for y
6x+2y=12
Answer:
y = -3x +6
Step-by-step explanation:
You want to solve the equation 6x +2y = 12 for y.
SolutionWe can isolate the y-term by subtracting 6x from both sides.
6x -6x +2y = -6x +12
2y = -6x +12 . . . . . . . . . . simplify
Then we can get y by itself by dividing both sides by 2:
2y/2 = -6x/2 +12/2
y = -3x +6 . . . . . . . . . . . simplify
The expression for y is y = -3x +6.
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