Answers
The values are given below,
Left Hand Limit i.e. [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 ,
Right Hand Limit i.e. [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 ,
Function value at x = 1 [tex]f(1)[/tex] = 1 ,
Left Hand Derivative [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and
Right Hand Derivative [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6.
So, the function f(x) is neither continuous nor differentiable at x = 1.
Given, a piecewise function
3㏑(3 - 2x) + 3 for x < 1
f(x) =
-3x² + 4 for x ≥ 1
Now, for [tex]\lim_{x \to 1^-} f(x)[/tex] we will consider the function 3㏑(3 - 2x) + 3, as we have to find the Left Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] 3㏑(3 - 2x) + 3 = 3㏑(3 - 2(1)) + 3
= 3 ㏑(1) + 3
= 0 + 3
= 3
Now, for [tex]\lim_{x \to 1^+} f(x)[/tex] we will consider the function -3x² + 4, as we have to find the Right Hand Limit of the function, at x = 1.
[tex]\lim_{x \to 1}[/tex] -3x² + 4 = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]f(1)[/tex] we will consider the function -3x² + 4,
[tex]f(1)[/tex] = -3(1)² + 4
= -3 + 4
= 1
Now, for [tex]\lim_{x \to 1^-} f'(x)[/tex] we will consider the derivative of the function
3㏑(3 - 2x) + 3,
[tex]\lim_{x \to 1}[/tex] -6/(3 - 2x) = -6/(3 - 2(1))
= -6
Now, for [tex]\lim_{x \to 1^+} f'(x)[/tex] we will consider the derivative of the function
-3x² + 4,
[tex]\lim_{x \to 1}[/tex] -6x = -6(1)
= -6
So, the function f(x) is neither continuous nor differentiable at x = 1.
Hence, [tex]\lim_{x \to 1^-} f(x)[/tex] = 3 , [tex]\lim_{x \to 1^+} f(x)[/tex] = 1 , [tex]f(1)[/tex] = 1 , [tex]\lim_{x \to 1^-} f'(x)[/tex] = -6 and [tex]\lim_{x \to 1^+} f'(x)[/tex] = -6
The function is neither continuous nor differentiable at x = 1.
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Related Questions
Data is collected about the number of wins and losses by a random sample of teams
with an animal mascot and those with another kind of mascot. The column relative
frequencies are shown in the table. Based on the information in the table, is there an
association between the variables? Explain your reasoning.
wins
losses
animal mascot
74%
26%
other type of mascot
49%
51%
Answers
The relative percentages of the column-wise frequencies are different, indicating that there is indeed an association between the variables.
What does association mean in data?A user-defined collection of related groups and items is referred to as a data association. It may include one or more groupings, as well as some, all, or neither of the items found inside those groups. It is helpful to initially identify various groups and components that you believe to be connected in some way before establishing Rules of Visibility.
Because of the differences in the relative percentages of the column-wise frequencies, there is a link between the variables. The animal mascot in the first column has 74% victories and 26% defeats. These percentages fluctuate greatly from one another. The other type of mascot, which similarly has a significant disparity between them, has 49% victories and 51% losses. The association between the variables is stronger the larger the difference.
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Please Help ASAP!
Which sequences of transformations result in the image being congruent to the pre-image? Select ALL correct answers
Question 1 options:
(x, y) → (-x, -y)
(x, y) → (x - 3, y + 2)
(x, y) → (3x, 3y)
(x, y) → (x, y - 10)
(x, y) → (-x, y)
(x, y) → (y, -x)
(x, y) → (x + 7, y - 2)
(x, y) → (-y, x)
(x, y) → (12x, 12y)
Answers
Answer: ima say something so hopefully this gets more noticed
Step-by-step explanation:
Calculate and give the result as an irreducible fraction
please ;)
=9/7+7/3×-9/4
=[4/5-2]×[3/4-2/3]
Answers
In the fractions given 2/3 + 7/3 * -9/4 and (4/5 - 2) * (3/4 - 2/3) the results of the expressions are -55/12 and -1/10 respectively
FractionsA fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator. The numerator defines the number of equal parts taken, whereas the denominator defines the total number of equal parts in a whole.
In the first expression;
2/3 + 7/3 * -9/4
Applying PEDMAS
2/3 + 7/3 * -9/4 = -55/12
In the second expression;
(4/5 - 2) * (3/4 - 2/3) = - 1/10
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(9x-5)°
(6x+20)º
What’s the value of x
Answers
The value of x is=-1
What are angles?When two straight lines or rays intersect at a single endpoint, an angle is created.The vertex of an angle is the location where two points come together.The Latin word "angulus," which means "corner," is where the term "angle" originates.Vertex: The intersection of two lines or sides at an angle is called a vertex. In the diagram, O is the vertex.Arms: The angle's two sides linked at a single end. The arms of an angle are OA and OB.Initial Side: A straight line from which an angle is drawn, sometimes referred to as the reference line. The reference line is OB.The side that the angle measurement is done up to is known as the terminal side. OA is the terminal side in the diagram that is shown below.acc to our question-
(9x-(5)+(6x+20))=0x-5+(6x+20)determining9x+(6x+20)-5We get rid of parentheses9x+6x+20-5We add all the numbers together, and all the variables15x+15Back to the equation:+(15x+15)15x=-15x=-15/15x=-1hence,The value of x is=-1
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Complete the table of values for the equation 9x+2y=18
Answers
Answer:
[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]
Step-by-step explanation:
Given equation:
[tex]9x+2y=18[/tex]
Substitute x = 0 into the given equation and solve for y:
[tex]\begin{aligned}x=0 \implies 9(0)+2y&=18\\2y&=18\\\dfrac{2y}{2}&=\dfrac{18}{2}\\y&=9\end{aligned}[/tex]
Substitute y = 0 into the given equation and solve for x:
[tex]\begin{aligned}y=0 \implies 9x+2(0)&=18\\9x&=18\\\dfrac{9x}{9}&=\dfrac{18}{9}\\x&=2\end{aligned}[/tex]
Substitute x = 4 into the given equation and solve for y:
[tex]\begin{aligned}x=4 \implies 9(4)+2y&=18\\36+2y&=18\\36+2y-36&=18-36\\2y&=-18\\\dfrac{2y}{2}&=\dfrac{-18}{2}\\y&=-9\end{aligned}[/tex]
Therefore:
[tex]\large\begin{array}{c|c|c|}\cline{2-3}&x&y\\\cline{2-3}\phantom{\dfrac12}&0&\boxed{9}\\\cline{2-3}\phantom{\dfrac12}&\boxed{2}&0\\\cline{2-3}\phantom{\dfrac12}&4&\boxed{-9}\\\cline{2-3}\end{array}[/tex]
7×3,012=7×(3,000+12)? Step by step
Answers
Answer:
Yes they are equal
Step-by-step explanation:
First we simplify the left side of the equation
7 x 3,012 = 21084
Next we simplify the right side of the equation. Using PEMDAS we know that we must add whatever is inside the parentheses first.
7 x (3,012)
We then multiply 7 x (3,012) = 21084
21084 = 21084
They are equal.
There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c
where T represents the temperature in degrees Fahrenheit and
c represents the number of times the cricket chirps in one minute. What is the meaning of the c-value when T=65?
A) The change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.
B) The expected temperature in degrees Fahrenheit if the cricket has chirped 0 times per minute.
C)The expected temperature in degrees Fahrenheit if the cricket has chirped 65 times per minute.
D) The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
Answers
The meaning of the c-value when T=65 is: The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
The correct answer is an option (D)
In this question, we have been given a linear relationship.
For a certain type of cricket, this relationship can be expressed using the formula T=34+0.3c,
where T represents the temperature in degrees Fahrenheit and
c represents the number of times the cricket chirps in one minute.
We need to interpret the value of c when T = 65.
T = 34 + 0.3c
65 = 34 + 0.3c
c = 103.33
c = 103.33 represents the number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
Therefore, the meaning of the c-value when T=65 is: The number of times the cricket could be expected to chirp in one minute if it's 65 degrees F
The correct answer is an option (D)
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A square on a coordinate plane has one vertex at (0.5,1) and a perimeter of 6 units. If all of the vertices are located in Quadrant I, what are the coordinates of the other 3 vertice s?
Answers
The coordinates of the other 3 vertice s are; Vertex 2 = (0.5, 2.5)
Vertex 3 = (2, 1), Vertex 4 =(2, 2.5 )
What is perimeter?Its the sum of length of the sides used to made the given figure.
Given that the Perimeter, P = 6 units
The Perimeter of a square = 4s ; s = side length
6 = 4s
s = 6/4
s = 1.5 units
If Vertex 1 =(0.5,1) and all vertexes are located in Quadrant I
Vertex 2 = (0.5,1 + 1.5) =(0.5, 2.5)
Vertex 3 = (0.5 + 1.5 ,1) = (2, 1)
Vertex 4 = (2, 1 + 1.5) = (2, 2.5 )
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Nathan has a $75 budget to rent a car for a day. The daily rental charge is $29.50 and then he will also have to pay 0.55 per mile. How many miles can he drive the car without exceeding his budget? (All partial miles are counted as full miles.)
Answers
Answer:
82 miles
Step-by-step explanation:
75-29.50 = 45.50
45.50/0.55 = 82.7272727273
82 x 0.55 = 45.10
45.10+29.50 = 74.60
You are bending a strip of metal into an isosceles triangle for a sculpture. The strip of metal is 20 inches long. The first bend is made 6 inches from one end. Describe two ways you could complete the triangle.
Answers
The two ways of forming isosceles triangle by bending the metal strip using length by length by base are
6 by 6 by 87 by 7 by 6What is an isosceles triangle?A triangle that have the two sides equal is referred to as an isosceles triangle.
Using a strip of 20 inches long to construct an isosceles triangle means that the perimeter of the triangle is 20 inches
the perimeter is equal to base + length + length
bending 6 inches already means one of the dimensions is gotten then fo the other is based on if
the 6 is base the 6 is lengthif the 6 is base then minus the 6 from 20 and divide the rest for the length
20 - 6 = 14
the two lengths is 14 one length is 7. so we have 6 + 7 + 7 = 20
If the 6 is length then get another 6 and the rest is base
20 - 6 = 14
14 - 6 = 8
therefore we have 6 + 6 +8 = 20 inches
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SOLVE AND GRAPH THE INEQUALITY X + 8 > 0
Answers
x>-8
look at the image below for the graph answer.
how do i solve for this
Answers
Answer:
x = -4
Step-by-step explanation:
[tex] \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } = 2[/tex]
[tex] {( \frac{ \sqrt[3]{6x} }{ \sqrt[3]{2x + 5} } )}^{3} = {2}^{3} [/tex]
[tex] \frac{6x}{2x + 5} = 8[/tex]
[tex]6x = 8(2x + 5)[/tex]
[tex]6x = 16x + 40[/tex]
[tex] - 10x = 40[/tex]
[tex]x = - 4[/tex]
[tex] \frac{ \sqrt[3]{6( - 4)} }{ \sqrt[3]{2( - 4) + 5} } = 2[/tex]
[tex] \frac{ \sqrt[3]{ - 24} }{ \sqrt[3]{ - 3} } = 2[/tex]
[tex] \sqrt[3]{ \frac{ - 24}{ - 3} } = 2[/tex]
[tex] \sqrt[3]{8} = 2[/tex]
Part A: What is the equation of the least-squares regression line? (4 points)
Part B: If a basketball player wears a size 11.5 and is 73 inches tall, what their residual? Show all mathematical work. (3 points)
Part C: Interpret the meaning of the residual from part B. (3 points)
Shoe Size (U.S.) Height (inches)
7 64.5
10 70
12.5 72
8.5 71
9 69
10 70
11 75
12.5 69
13 71
10.5 68
Answers
Answer:
12.5 72
Step-by-step explanation:
Because shows that the basketball player wear size 11.5 73 inches tall so basically the answer would be 12.5 72
The equation of the regression line is y = 0.77x + 61.95. The residual is 2.2 inches. The residual means that the gap between the estimated and anticipated values is 2.2 inches.
What is the regression line?A regression line shows a linear connection between the y-dependent axis's variables and the x-independent axis's variables. The connection is determined by examining the data pattern created by the variables.
From the table, the points are given as follows:
(7, 64.5), (10, 70), (12.5, 72), (8.5, 71), (9, 69), (10, 70), (11, 75), (12.5, 69), (13, 71), (10.5, 68).
Inserting these points into the linear regression calculator, the equation is given as follows:
y = 0.77x + 61.95 ...(i)
For a shoe size of 11.5 inches, the predicted height is given as below:
y = 0.77(11.5) + 61.95 = 70.8 inches.
The residual is the gap between the estimated and anticipated values, hence:
Residual = 73 inches - 70.8 inches = 2.2 inches.
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In a class of 29 students 9 play an instrument and 23 play a sport there are 5 students who play an instrument and also play a sport. What is the probability that a student plays an instrument given that they play a sport?
Answers
The probability for the given case is 5/23.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lie in the close interval of 0 and 1 [0,1].
Given that,
Total number of students is 29.
The students who play instrument are 23.
Those who play a sport are 9.
And, those who play both are 5.
Given problem is the case of conditional probability which can be solved by Bayes's theorem as,
P(A|B) = P(A ∩ B) / P(B)
Suppose, A be the event the students play instrument.
B be the event the students play a sport.
And, A ∩ B is the event they play th both.
Then A|B implies the event when a student play instrument given he plays sport.
Apply the rule of probability in the equation for Bayes's theorem to get,
P(A|B) = (5/29) / (23/29)
= 5/23
Hence, the probability that a student plays an instrument given that they play a sport is 5/23.
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ABCD is a rhombus. Solve y.
12yº.
A
y=
B
4x + 15
F
D
C
(4y − 1)º
7x+2
Answers
Here in the rhombus ABCD the value of y is 7.5.
What is rhombus?A rhombus is a unique kind of quadrilateral with four equal sides and perpendicular diagonals that cut the angles and one another in half.
So here 4x+15 = 7x+2 and
12y = 90.
To find the remaining values by first solving for each variable, then substituting as necessary.
4x+15=7x+2
15=3x+2
13=3x
13/3 = x
BC is 4x+15
= 4(13/3)+15
= 52/3 + 45/3
= 97/3
CD is 7x+2
= 7(13/3)+2
= 91/3 + 6/3 = 97/3
Then, find 12y=90 and y=7.5.
AFB is a 90° angle (12(7.5)).
BCF is a 4y-1 = 4(7.5)-1 = 29 angle.
Because the diagonal cuts the angle in half, angle BCD is equal to 58. Angle ABC thus becomes 180-58 = 122.
Therefore the value of y is 7.5 .
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HELP ME IT SAyS RECTANGLE AT THE CUT OFF BIT
Answers
The area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].
What is the area of the rectangle?
If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be computed as
Area = l * b
Given data:
The width of the rectangle is 3x/5 cm.
And its length is four times its width so length = 4 * 3x/5
= 12x/5 cm.
Then the area will be
Area = length * breadth
= 12x/5 * 3x/5
= 36x²/25
[tex]=(\frac{6x}{5})^2[/tex]
Hence, the area of the rectangle can be expressed as [tex](\frac{6x}{5})^2[/tex].
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Find the limit, if it exists, analytically using special trig limits
Answers
[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos^2(7x)}{8x^2(~~1-sin^2(7x)~~)}~\hfill \boxed{u=7x\implies \cfrac{u}{7}=x\implies \cfrac{u^2}{49}=x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{1-cos^2(u)}{8\left(\frac{u^2}{49} \right)(~~1-sin^2(u)~~)}\implies \cfrac{1-cos^2(u)}{ ~~ \frac{8u^2(~~1-sin^2(u)~~)}{49} ~~ }\implies \cfrac{[1-cos^2(u)]49}{8u^2(~~1-sin^2(u)~~)} \\\\\\ \cfrac{[1-cos(u)][1-cos(u)]49}{8u^2(~~1-sin^2(u)~~)}\implies \cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\displaystyle \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]}\implies \lim_{x\to 0}~\cfrac{1-cos(u)}{u}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(u)]}{8u[1-sin^2(u)]} \\\\\\ \displaystyle \lim_{x\to 0}~\cfrac{1-cos(7x)}{7x}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]} \\\\\\ \displaystyle \text{\LARGE 0}\cdot \lim_{x\to 0}~\cfrac{49[1-cos(7x)]}{8(7x)[1-sin^2(7x)]}\implies \text{\LARGE 0}[/tex]
Given the point (-4, 2) and the y intercept (0, -5) write the equation of the line in slope-
intercept form.
Answers
The equation of the line in slope - intercept form is [tex]y=\frac{-7}{4}x-5[/tex]
Explain what the slope-intercept form is?
Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This expression is sometimes referred to as y = mx + b form
Given: x = -4 , y = 2 and b = -5
y = mx + b
2 = m (-4) + (-5)
m = [tex]\frac{-7}{4}[/tex]
By putting the value of m we get equation of line
[tex]y=\frac{-7}{4}x-5[/tex]
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In right triangle ABC, altitude CD with length h is drawn to its hypotenuse. We also know AD = 12 and DB = 3. The scale factor of triangle ADC (pre-image) to triangle CDB (image) is . Express answer in the form of a simplified fraction.
Answers
The Scale factor of ΔADC to ΔCDB is 2 .
In the question ,
a right triangle ABC is given (the figure is shown below )
h is the length of the altitude , AD = 12 , DB = 3 ,
to find the scale factor , we first need to find the value of h ,
since triangles ADC is similar to triangle CDB ,
we have , CD / AD = DB / CD
on cross multiplication , we get
CD² = AD × DB
CD² = 12 × 3 = 36
CD = 6
For the scale factor we divide the length of the original triangle ADC with the length of the image triangle CDB .
we get
Scale factor = AD / CD
= 12/6
= 2
Therefore , The Scale factor of triangle ADC to triangle CDB is 2 .
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3/8 to the 2nd power
Answers
Answer:
9/64
Step-by-step explanation:
it is just 3/8 x 3/8
The diameter of the steering wheel of the actual car is 15 inches. What is the diameter of a toy car's steering wheel if the toy is a 1:40 scale model of the real car?
Answers
Answer:
Step-by-step explanation 43 453 645
What is the opposite of l3l
Answers
The opposite of |3| = - |3|
What is Modulus Function?
Regardless of the sign, a modulus function returns the magnitude of a number. The absolute value function is another name for it.
It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.
The value of the modulus function is always non-negative. If f(x) is a modulus function , then we have:
If x is positive, then f(x) = x If x = 0, then f(x) = 0 If x < 0, then f(x) = -xGiven data ,
Let the number be x
x = |3|
Now , the opposite of the number x = -x
So ,
The opposite of |x| = -|x|
And ,
The opposite of |3| = - |3|
Hence , The opposite of |3| = - |3|
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I-ready 3/8+n=7/8 n=
Answers
The required value of n is [tex]\frac{1}{2}[/tex] .
What is an algebraic equation?
The term "algebraic equation" refers to a formulation of the equality of two expressions using the algebraic operations of addition, subtraction, multiplication, division, raising to a power, and extraction of a root on a set of variables.
Given, [tex]\frac{3}{8} +n=\frac{7}{8}[/tex]
or, [tex]n=\frac{7}{8}- \frac{3}{8}[/tex]
or, [tex]n=\frac{7-3}{8}[/tex]
or, [tex]n=\frac{4}{8} = \frac{1}{2}[/tex]
Hence, the value of n is [tex]\frac{1}{2}[/tex] .
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here is a bag with only milk and dark chocolates. The probability of randomly choosing a dark chocolate is 7/12 . There are 56 dark chocolates in the bag and each is equally likely to be chosen. Work out how many milk chocolates there must be.
Answers
Answer:
Step-by-step explanation:
We are told that P(dark) = 5/12 and Nd = 25. Plugging these numbers in we get:
5/12 = 25 / (25 + Nw)
Solving this equation for Nw yields Nw = 35.
Therefore, there must be 35 milk chocolates in the bag.
Question 8 of 8
Which of the following is equal to the expression?
45 x 12+ 45 x 32
45 × 12 + 32
45+ (12 + 32)
45 x (12 x 32)
45 x (12 + 32)
Answers
Step-by-step explanation:
the expression is
45 × 12 + 45 × 32
this is the same as
45 × (12 + 32)
you can extract a common factor from a sum and make it the central factor for the sum.
it is the opposite operation of simplifying this central multiplication, where you have to multiply every part of the left factor with every part of the right factor and sin things up according to the resulting signs.
so, the 4th answer is correct.
Identify each of the following as rational or
irrational.
√23
104.42
√64
49.396
10.97846727460
Answers
2.rational
3.rational
4.rational
5.irrational
Write an inequality that compares the given numbers -4;-1
Answers
The inequality that compares the given numbers -4;-1 is -4 < -1.
What is an inequality?Inequalities are created through the connection of two expressions.
It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, it should be noted -4 is less than -1. Therefore, the inequality will be -4 < -1.
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The tech group built a go cart with 10in diameter
wheels. This cart must travel 20 FEET to complete the
race. How many rotations will be required to travel this
distance?
Answers
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64.
What is a circle?A circle is a geometrical figure which becomes by plotting a point around a fixed point by keeping a constant distance.
The longest line which can be drawn inside the circle will be the diameter.
The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation.
Distance traveled in one rotation = Perimeter of the wheel.
⇒ 2π(5) = 31.42 inches
The number of rotations = (20×12)/31.42 = 7.63
Hence "The number of rotations will be the ratio of the total distance traveled to the distance traveled in one rotation thus the total rotation to cover 20 feet will be 7.64".
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Line h passes through (2,6) and is parallel to a line that passes through (−3,4) and (1,1).
Answers
The equation of line h that passes through (2,6) and is parallel to a line passing through (-3, 4) and (1, 1) is 4y + 3x = 30
What is slope?Slope is the ratio of the change in the y-coordinates to the change in the x-coordintes of any two given points.
It is a measure of the steepness of a line.
Slope may be positive or negative
slope of the line joining the the points (-3,4) and (1,1)
slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
[tex]x_{1}[/tex] = -3, [tex]x_{2}[/tex] = 1, [tex]y_{1}[/tex] = 4, [tex]y_{2}[/tex] = 1
slope = 1-4 / 1 - -3
slope = -3/4
since the two lines are parallel their slopes are equal.
equation of first line
y = mx + c
where y = 6, x = 2, m = -3/4
6 = -3/4(2) + c
6 = -3/2 + c
c = 6 + 3/2
c = 15/2
Equation, y = -3/4x + 15/2
multiply through by 4
2y = -3x +30
2y + 3x = 30
In conclusion the equation of the line passing through the given point is 2y + 3x = 30
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Rewrite 6/11 each as a multiplecation equation
Answers
Answer:
11 x 6
Step-by-step explanation:
