Answer:
D. [tex]y=-2x+3[/tex]
Step-by-step explanation:
1. Isolate y to convert the original equation to slope-intercept form [tex](y = mx+b)[/tex]:
[tex]4x+2y=8\\ 2y=8-4x\\ y = \frac{8-4x}{2} \\y = -2x+4\\[/tex]
2. To find the equation parallel to a linear equation, use the original slope and plug in the given point to find b.
We know the slope of the original equation is m = -2, found in step (1).
[tex]y = -2x+ b\\(5) = (-2)(-1) + b \\5-2 =b \\3 = b[/tex]
3. Assemble the final equation:
[tex]y = -2x + 3[/tex]
PLEASE This is one of my last questions so please help me its timed
Answer:
=(3,-4)
Step-by-step explanation:
Doug has $100,000 in a savings account that earns 13% interest per year. The interest is
not compounded. How much interest will he earn in 4 years?
PLEASE HELP AGAIN!!!!
Answer:
If Doug has $100,000 in a savings account that earns 13% interest per year and the interest is not compounded, then after four years he will earn $52,000 in interest. This is because 13% of $100,000 is $13,000, and since the interest is not compounded, this amount will remain constant for each year. Therefore, after four years Doug will earn a total of $13,000 + $13,000 + $13,000 + $13,000 = $52,000 in interest.
In general, if a savings account earns x% interest per year and the initial amount in the account is y dollars, then after n years the account will earn n * (x/100) * y dollars in interest. For example, if the interest rate is 13% and the initial amount is $100,000, then after four years the account will earn 4 * (13/100) * $100,000 = $52,000 in interest.
Step-by-step explanation:
Answer: He will earn about $3,756.66
Step-by-step explanation:
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
when me I would say the 1st one but who knows lol
1. Which of the following identifies the a, b, c, and d of the absolute value function g(x) = −|2x| + 5?
The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:
a = -1.b = 2.c = 0.d = 5.How to obtain the parameters of the absolute value function?The standard definition of the absolute value function is given as follows:
f(x) = a|bx + c| + d.
The meaning of each parameter is given as follows:
a is the coefficient of vertical stretch/compression.b is the coefficient of horizontal stretch/compression.c is the coefficient of horizontal shift.d is the coefficient of vertical shift.In this problem, the function is defined as follows:
g(x) = −|2x| + 5.
Compared with the standard absolute value function, the values of these parameters are given as follows:
a = -1, b = 2, c = 0, d = 5.
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WHAT IS 81x1???????????????????????????????????
Answer:
81
Step-by-step explanation:
81 * 1 = 81
If the 81x1 is = 81 * 1 then it should be 81.
If its not I will redo my answer.
Answer:
81 x 1 is 81
81
x 1
81
(Please answer both I will give brainlest)
Find the indicated side x. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume b-10 and c-22. Round your answer to one decimal place.)
X=
(Refer to picture )
7.
Find the indicated angle. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a-10, b-6, and c-12. Round your answer to one decimal place.)
0-
To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:
x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)
x^2 = 100 + 36 - 120
x^2 = 16
x = sqrt(16) = 4
Therefore, the length of the side x is 4.
To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:
10/sin(0) = 12/sin(C)
sin(C) = 0
Therefore, the measure of the angle C is 0 degrees.
this is original answer
To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:
x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)
x^2 = 100 + 36 - 120
x^2 = 16
x = sqrt(16) = 4
Therefore, the length of the side x is 4.
To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:
10/sin(0) = 12/sin(C)
sin(C) = 0
Therefore, the measure of the angle C is 0 degrees.
The cost C, in dollars, for a health club membership depends on the number m of whole months you join. This situation is represented by the function rule c = 49 + 20m
is in continuous or discrete and what would the graph look like
The graph of the function C = 49 + 20m is a discrete function and is represented by vertical lines for whole numbered values of 'm'.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, That no. of months is a whole month and hence it is discrete as it can not take decimal values.
The graph of the equation C = 49 + 20m would have vertical lines at each whole value of 'm'.
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50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
Answer:
A.124
Step-by-step explanation:
Because it's like that
Answer:
A. 124
Step-by-step explanation:
<3
205,201,197,... \text{Find the 48th term.} Find the 48th term.\
Answer:
17
Step-by-step explanation:
You need to use the formula for Arithmetic Sequences.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
You need to plug in the value for [tex]a_{1}[/tex] which is just the first value in your sequence. As well as [tex]n[/tex] which is the term your looking for, in this case it's 48. Lastly [tex]d[/tex] which is the amount that the pattern is increasing or decreasing by. If the sequence is increasing then the [tex]d[/tex] is positive but if the sequence is decreasing then the [tex]d\\[/tex] is negative.
at how many points is sin 0=1/2 on interval [-3 pi, 3 pi]
At two points [tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6 (using trigonometric function)
sinx =[tex]\frac{1}{2}[/tex]
⇒[tex]x_{1}[/tex] = π[tex](2n + \frac{1}{6} )[/tex] or [tex]x_{2}[/tex] = π[tex](2n + \frac{5}{6} )[/tex]
where n is an integer
But hence x belongs to [-3π , 3π]
the acceptable solutions are
[tex]x_{1}[/tex] = π/6 and [tex]x_{2}[/tex] = 5π/6
What are Trigonometric Functions?
The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides.
There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant.
Function of Sine
The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function. According to the diagram above, sin is worth:
Sin a =Opp/Hypo = CB/CA
Function of Cosine
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length. The cos function will be derived as follows from the diagram up top.
Cos a = Adjacent/Hypotenuse = AB/CA
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Answer!!!!!!!!!!!!!!!
Using the AAS rule.
ST ≅ UT (given)
∠SRT≅∠UVT (given)
∠RTS ≅ ∠UVT (opposite angles)
∠RST ≅ ∠VUT (AAS rule)
Proved.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
AAS rule:
When two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
From the figure we have,
ST ≅ UT (given)
∠SRT≅∠UVT (given)
∠RTS ≅ ∠UVT (opposite angles)
∠RST ≅ ∠VUT (AAS rule)
Thus,
∠RST is congurent to ∠VUT using the AAS rule.
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14. Higher Order Thinking Mr. Conners put a
fence around the outside of his rectangular
yard shown at the right. Each section of fence
was 8 feet long, How many sections did he use?
102 ft
330 ft
330 ft
Answer:
Mr. Conners will use 144 fence posts.
Step-by-step explanation:
Given question is incomplete; please find the question attached herewith.
As we can see from the attachment, Mr Corner's yard is in the rectangular shape.
Total distance around the yard = Perimeter of a rectangle = 2(Length + width)
Length of the yard = 330 ft
And width of the yard = 102 ft
So perimeter of the yard = 2(330 + 102 = 864 f
Mr. Conners wants to put a fence post at every 6 feet.
So number of posts used =
=
= 144
NO LINKS!! Please help me with the Domain and Range and Functions Part 1bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 21Domain is:
x ∈ [- 4, 2], both ends included as part of the graph or closed circle..Range is:
y ∈ (-6, 6], the lowest point is excluded as open circle, the highest value is included as closed circle..This is not a function as it fails the vertical line test.
Question 22Domain is:
x ∈ [- 6, 2], both ends included as part of the graph.Range is:
y ∈ [-7, 7], both ends included as part of the graph.This is not a function as it fails the vertical line test.
Question 23Domain is:
x ∈ [ -2, 0], both ends included as closed circle or part of the graph.Range is:
y ∈ (-7, 5], the -7 is excluded as open circle, the 5 is included as closed circle.This is not a function as it fails the vertical line test.
Question 24Domain is:
x ∈ [- 6, 6), One end is included and the other end is excluded.Range is:
y ∈ [-7, 1], both ends included as closed circle or part of the graph.This is a function as it passes the vertical line test.
XYZ has coordinates X(-7, 8), Y(2, 5), Z(0,7). What are the coordinates of the image r(90,0) XYZ
The new coordinates are X'(8, 7), Y'(5, -2), Z'(7, 0).
How to determine the image of the rotation?The coordinates of the triangle are given as
X(-7, 8), Y(2, 5), Z(0,7).
The rotation is given as r(90,0) XYZ
This means that
We have (x, y) ⇒ (y, -x)
Substitute X(-7, 8), Y(2, 5), Z(0,7) in (x, y) ⇒ (y, -x)
So, we have
X'(8, 7), Y'(5, -2), Z'(7, 0).
Hence, the coordinates of the image are X'(8, 7), Y'(5, -2), Z'(7, 0).
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Solve the system of linear equations by elimination.
1.5x - 9y = -21
-1.5x - 3y = 9
The solution is:
Answer:
Ordered pair: (- 8, 1)
x = - 8,y = 1
Step-by-step explanation:
[tex]1.5x-9y=-21\\-1.5x-3y=9[/tex]
Add together.
- 12y = - 12
y = 1
1.5x - 9(1) = - 21
1.5x - 9 = - 21
1.5x = - 12
x = - 8
Question 19
Find m ∠ K.
m∠ K=63°
m∠ K=79°
m ∠K=39°
m∠ K=55°
Angle K has a value of 63 degrees.
Given,
The triangle KLM
Angle L = 4x + 7
Angle K = 6x - 9
Angle M = 118° (Exterior)
We have to find the value of angle K.
Here,
Angle M (Interior) = 180 - 118 = 62° (linear pair of angles)
Now,
Angle L + Angle K + Angle M = 180° (Sum of interior angles of a triangle)
Then,
4x + 7 + 6x - 9 + 62 = 180
10x - 2 + 62 = 180
10x + 60 = 180
10x = 180 - 60
x = 120/10
x = 12
Now,
Angle K = 6x - 9 = 6 × 12 - 9 = 72 - 9 = 63
That is,
The value of Angle K is 63 degrees.
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Minimize subject to: z = 5x + 3y
8x + 5y = 40
4x+10y = 40
x ≥ 0
y ≥ 0.
There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.
How to find the calculation?z = 5x + 3 y
Discover the function's first derivative.
By applying the Sum Rule, the derivative of 5 x + 3 y with respect to x is d d x [ 5 x ] + d /d x [ 3 y ].
d/d x [ 5 x] + d /d x [ 3 y]
Analyze d /d x [ 5 x ].
Tap to take other actions...
5 + d /d x [ 3 y]
Because 5 is independent of x, its derivative is 5 d d x [ x ] since 5 is constant with respect to x.
5 d/ d x [ x ] + d /d x [ 3 y]
The Power Rule, which asserts that d d x [ x n ] is n x n 1 where n = 1. 5 1 + d d x [ 3 y ] is a method of differentiation, says that you should differentiate.
Subtract 1 from 5 and multiply the result by 5 + d /d x [ 3 y ]
The Constant Rule can be used to differentiate.
Because 3 y is constant in relation to x, its derivative in relation to x is 0 (5 + 0).
Subtract 5 from 0 to get 5.
Since 5 is constant in relation to x, its derivative in relation to x is 0 (f " (x ) = 0).
By setting the derivative to 0, you can solve the problem and discover the function's local maximum and lowest values.
5 = 0
There are no local extrema since there isn't any x value that causes the first derivative to be equal to 0.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
The system of equation is 45x+75y=1455.
The number of small boxes is 14 and large boxes is 11.
In the given question,
The paper will be shipped in small boxes and large boxes.
Each small box of paper weights 45 pounds.
Each large box of paper weights 75 pounds.
There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds.
We have to write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped.
We also have to define the variables that we use to write the system.
Let x be the number of small boxes.
Let y be the number of large boxes.
There were 3 more small boxes shipped than large boxes.
So x = y+3
Weight of x number of small boxes = 45x
Weight of y number of small boxes = 75y
Total weight of boxes = 1455
So; 45x+75y=1455
Now putting the value of x to this system of equation
45(y+3)+75y=1455
45y+135+75y=1455
120y+135=1455
Subtract 135 on both side, we get
120y=1320
Divide by 120 on both side, we get;
y=11
Now putting the value of y in x=y+3
x = 14
Hence, the number of small boxes is 14 and large boxes is 11.
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Makayla is a botanist studying production of coconuts by two different groups of her coconut palms. She notices that Group 1 trees produce 25 percent more coconuts than Group 2. based on Makayla's observation, if Group 1 produced 150 coconuts, how many coconuts did group 2 produce?
If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.
What is proportion?Proportion refers to the two ratios equated to each other.
Proportion shows how much quantity or value is contained in another.
We depict proportions using fractional values, such as fractions, decimals, and percentages.
The number of coconuts produced by Group 1 trees = 150
The percentage by which Group 1 trees produce more than Group 2 = 25%
Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)
Let Group 2's production = 100% = 150/125 x 100
= 120 coconuts
Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.
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Standing 8 feet from a puddle of water on the ground Gretchen whose eye height is 5 feet 2 inches can see reflection of the top of a flagpole the puddle is 20 feet from the flagpole how tall is the flagpole
The height of the flagpole in this problem is calculated as follows:
12.9 feet.
How to obtain the height of the flagpole?The height of the flagpole in this problem is obtained using similar triangles, as shown by the image given at the end of the answer.
Similar triangles are used because the equivalent sides have proportional side lengths.
From the image given at the end of the answer, the equivalent sides of each triangle are given as follows:
8 ft and 20 ft.5 and 2/12 ft and x ft. (2/12 is because one feet = 12 inches, x feet is the height of the pole).Then the proportional equation is given as follows:
8/20 = 5.1667/x
Applying cross multiplication, the height of the flagpole is calculated as follows:
8x = 20 x 5.1667
x = 20 x 5.1667/8
x = 12.9 feet.
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What is the slope of the line represented by the given table?
X -14 0 7 14 21
y -6 2 6 10 14
Gerard and Harold have downloaded songs in the ratio 3:7. Harold
and James have downloaded songs in the ratio 14: 15. What is the ratio
of the number of songs that Gerald, Harold, and James downloaded?
The solution is 42 : 98 : 105
The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105
What is Proportion?
The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.
Given data ,
Let the ratio of number of songs downloaded by Gerald and Harold be =
3 : 7
Let the ratio of number of songs downloaded by Harold and James be =
14 : 15
So , the number of songs downloaded by Gerald = 3x
The number of songs downloaded by Harold = 7x
And ,
The number of songs downloaded by Harold = 14y
The number of songs downloaded by James = 15y
So , substituting the values in the equation , we get
7x = 14y
x = 2y
And ,
The number of songs downloaded by Gerald = 3 x 14 z
The number of songs downloaded by Gerald = 42z
The number of songs downloaded by Harold = 7 x 14z
The number of songs downloaded by Harold = 98z
The number of songs downloaded by James = 7 x 15z
The number of songs downloaded by James = 105z
So , the ratio of the number of songs Gerald , Harold and James downloaded = 42z : 98z : 105z
On simplifying the proportion , we get
The ratio will be = 42 : 98 : 105
Hence , The ratio of the number of songs Gerald , Harold and James downloaded is in the ratio 42 : 98 : 105
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Use polynomial identities to multiply (4 + 2x3 )(4 − 2x3 ).
The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶
How to determine the product of the polynomialsFrom the question, we have the following parameters that can be used in our computation:
Polynomial products: (4 + 2x3 )(4 − 2x3 )
Rewrite the above product properly
So, we have the following representation
Polynomial products = (4 + 2x³)(4 − 2x³)
Using the difference of two squares identity
We have the following representation
Polynomial products = (4)² - (2x³)²
Evaluate the exponents
Polynomial products = 16 - 4x⁶
Hence, the product is 16 - 4x⁶
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they figure that the waterfall is at point (3'6). The overlook is at point (0.1). the campsite is at point (3-5). The lake is at point (-4,1). And the parking lot is at point (0.5). Which of these pairs of locations are closest to one another
Answer:
Step-by-step explanation:
I'm sorry, but I'm not sure what you're asking. It's not clear to me what you mean by "point (3'6)" or "(3-5)." Could you please provide more information or clarify your question
Is this correct? (The question with the star on it)
The value of x is x < 2
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
-x-7> -9
Add 7 on both the sides
-x -7 + 7 > -9 +7
-x > -2
divide by -1 and change inequality sign
x < 2
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Answer!!!!!!!!!!!!!!
By ASA, the two triangles are congruent. They share 2 angles and the line in between them.
PLEASE ANSWER THIS IT IS DUE IN 15 MINUTES!!!!
The combined area of the shaded triangles in figure one is 2ab. We have four congruent right triangles given, with legs a and b. The formula to calculate the area of a right triangle is (leg * leg) / 2. So the area of one of the triangles is ab/2. We have four of these triangles, so ab/2 * 4 = 2ab.
The area of the unshaded square in figure one can be represented as c^2. Since the side of the square is given as c, its area must be c^2 (calculate the area of a square by multiplying its side length by itself).
The combined area of the unshaded squares in figure 2 can be represented by a^2 + b^2. Again, we find the areas of each square by multiplying the side lengths togther: (a * a) + (b * b) = a^2 + b^2.
Finally the areas of the squares in figure one and figure two show that a^2 + b^2 = c^2. This is because the shaded triangles in figure one take up the same area as that of figure two. And since the total figure areas are the same, the unshaded parts of each figure must be equal to each other. Therefore, we have a^2 + b^2 = c^2. This is also known as the Pythagorean Theorem.
Graph the line with slope -1 passing through the point (4, -5).
Answer:
y=x-1
Is the line equation.
Step-by-step explanation:
As we know that general equation of line is given by
y=mx + c
M is the slope and C is is Y intercept
Know m = 1 and point (x,y) as (5,4)
So plug in the values and solve for c
4=1*(5)+c
c=-1
So, equation of the line is
y=x-1
You are ordering shirts for the math club at your school. Short-sleeved shirts cost $8 each. Long-sleeved shirts cost $16 each. You have a budget of $300 for the shirts. The equation $8x+16y=160$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. a. Graph the equation. Interpret the intercepts
On the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).
What is a graph equation?To calculate the slope m and the y-intercept, write the equation y = MX + b.
The slope and y-intercept can then be used to graph the equation (0, b).
The three primary forms of linear equations are point-slope, standard, and slope-intercept.
So, the equation is as follows:
8x+16y=160
Now,
The short sleeves are symbolized by an x.
y is a symbol for the long sleeves.
The equation must now be plotted as follows:
(Please see the graph below.)
As a result, the y and x-axis points (0, 10) and (20, 0) intersected by the equation.
Therefore, on the graph, the graph equation has been drawn, crossing the y and x-axis points (0, 10) and (20, 0).
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Is Ax + By = C slope, slope-intercept, point-slope, or standard form?
Answer:
Ax + By = C is standard form.
Step-by-step explanation:
It is standard form because slope intercept is y = mx + b and point slope is y-y₁=m(x-x₁)
Hope this helps
Answer:
Standard form.
Step-by-step explanation:
y=mx + b is the slope-intercept form.