Answers
The location of the image of point S is the midpoint of the line segment RS. A representation of the geometric system and the rigid transformation is shown in the image attached below.
How to find the coordinates of the image of point S by using a transformation rule
Herein we know the center of dilation and the location of point S, which must be dilated by a rigid transformation, that is, a transformation applied on the point such that its Euclidean distance is conserved. The operation is defined by the following equation:
RS' = k · RS
S'(x) - R(x) = k · S(x) - k · R(x)
Where k is the scale factor.
If we know that R(x) = 0, S(x) = 6 and k = 1 / 2, then the location of the point S' is:
S'(x) - 0 = (1 / 2) · 6 - 0
S'(x) = 3
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Related Questions
Solve the following question show your work
Answers
Solution:
iven :
[tex]7\frac{1}{5}\times4\frac{5}{6}[/tex]To solve,
step 1: Convert the mixed fractions into improper fractions.
[tex]\begin{gathered} Given\text{ an improper fraction of the form: a}\frac{b}{c},\text{ to convert to an } \\ improper\text{ fraction, we have} \\ \frac{(c\times a)+b}{c} \\ \end{gathered}[/tex]Thus,
[tex]\begin{gathered} 7\frac{1}{5}=\frac{(7\times5)+1}{5}=\frac{35+1}{5}=\frac{36}{5} \\ 4\frac{5}{6}=\frac{(4\times6)+5}{6}=\frac{24+5}{6}=\frac{29}{6} \end{gathered}[/tex]step 2: Perform the operation of multiplication between both fractions.
Thus,
[tex]\begin{gathered} \frac{36}{5}\times\frac{29}{6}=\frac{36\times29}{5\times6} \\ cancel\text{ out common factor,} \\ =\frac{6\times29}{5} \\ =\frac{174}{5} \end{gathered}[/tex]step 3: Convert the resulting improper fraction into a mixed fraction.
Thus,
[tex]\frac{174}{5}=34+\frac{4}{5}[/tex]Hence, the solution is
[tex]34\frac{4}{5}[/tex]3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual
was 4.1 ft. What is John's percent decrease on his measurement?
measurement
Answers
Jack's percentage decrease on his measurement of painting by 18%.
What is meant by percentage change?
Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.
Given that,
Jack's measurement for his room = 5 ft (taking this as old value)
Actual measurement for Jack's room = 4.1 ft (taking this as new value)
Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%
= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%
= -18%
Here, minus sign represents the decrease in percentage.
Hence, Jack's percentage decrease on his measurement of painting by 18%.
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Correct question will be :
Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?
Graph the linear function p(x) = 4x
Answers
The graph is attached below.
We are given a linear function.The function p(x) equals 4x.We have to graph the function.In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.Let "y" denote p(x).y = 4xNow, we can get several pairs of coordinates that satisfy the above linear function.We plot the points on the graph and join them.We can see that the given function is an equation of a straight line that passes through the origin and has a positive slope of magnitude 4.To learn more about functions, visit :
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The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours
Answers
1.25 is the probability that the aircraft Will last 100 hours.
What is probability?The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given Data
Mean = 80
Standard deviation = 16
P( x < 100)
P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])
P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])
P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])
P(x < 100) = 1.25
1.25 is the probability that the aircraft Will last 100 hours.
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Show how you can make a ten to find the sum of 6+5
Answers
By rewritting the 6 as 5 + 1 we will get:
1 + 5 + 5 = 1 + (5 + 5) = 11
How to make a ten to simplify the sum?
One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).
This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:
6 + 5
We can rewrite this as:
6 + 5 = 1 + 5 + 5
Using the associative property we rewrite:
1 + 5 + 5 = 1 + (5 + 5)
1 + (5 + 5) = 1 + 10 = 11
The sum is equal to 11.
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Assume that when you take a bath, you fill a tub to the haltway point. The tub measures 5 feet by 2 feet by 2.7 feet. When you take a shower, you
use a shower head with
flow rate of 2.03 gallons per minute, and you typically spend 9 minutes in the shower. There are 7.5 gallons in one cubic
foot. Complete parts (a) through (c) below.
a. Do you use more water taking a shower or taking a bath? Select the correct choice below
and fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. Shower; you use
more cubic feet of water than taking a bath.
• B. Bath; you use
more cubic feet of water than you do taking a shower.
Answers
The person is therefore using more water for bathing than for showering, according to the conclusion.
Half of the tub's total water is consumed while taking a bath.
Water used divided by volume equals
[tex]\frac{volume}{2}[/tex]
= [tex]\frac{(5)(3)(2.8)}{2}[/tex]
=[tex]\frac{42}{2}[/tex]
=21 cubic feet.
The following will provide the total amount of water utilized while having a shower:
Total water Equals rate ×time
= 1.52 × 12
= 18.24 gallons.
So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount
=[tex]\frac{18.24}{7.5}[/tex]
=2.432 cubic feet.
The person is therefore using more water for bathing than for showering, according to the conclusion.
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The height of a wave in California varies directlywith the seconds that pass by. At 4 seconds,the wave is 6 feet high. Find the constant ofvariation.Weight varies directly with arit
Answers
The constant variation of hight(y) to seconds(x) is 3y/2x.
What is the constant variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation. By dividing the y-coordinate by the x-coordinate, we can find k when given any point because it is constant (the same for every point). For instance, the constant of variation is k = = 3 if y varies directly as x and y = 6 when x = 2.So, let the second be 'x' and the height is 'y'.
At 4 seconds the wavelength is 6 ft high.
Constant variation:
y/x = 6/4 = 3/23y/2xSo,
x = 4, x = 8, x = 12y = 6, y = 12, x = 18Therefore, the constant variation of hight(y) to seconds(x) is 3y/2x.
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A high school band raises $6, 764 to buy instruments
and uniforms for its members. Half the money is spent
on new instruments. They buy 38 new uniforms with
the remaining money.
Answers
Answer:
$89 dollars per uniform
Step-by-step explanation:
Total amount of money raised= $6,764.
Money spent on new instruments= $6,764÷1/2 = $3382
The number of new uniforms bought with the remaining money= 38.
How much was spent on one= $3,382÷38 = $89
simplify (-2)(-3)(6) 20 points plus brainliest if right
Answers
Answer:
36
Step-by-step explanation:
-2(-3)(6)
6(6)
36
Answer:
-8/2 / 6/-3 -8/2 x -3/6 24/12= 2
Step-by-step explanation:
As long as you follow through with a plan to save $2000 a year, at the end of each year, in your account that earns 4% interest how much would you have after 25 years future value?
Answers
We have to use the simple interest formula.
[tex]A=P(1+rt)[/tex]Where P = 2,000, r = 0.04, t = 25. Let's solve for A
[tex]\begin{gathered} A=2,000(1+0.04\cdot25)=2\cdot2,000 \\ A=4,000 \end{gathered}[/tex]Therefore, you will have $4,000 in 25 years.what is an equation
Answers
We have to write the equation of the line that pass through (4,-5) and (2,0).
We can calculate the slope as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{0-(-5)}{2-4}=\frac{5}{-2}=-2.5[/tex]We can then write the slope-point form of the equation as:
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-0=-2.5(x-2) \\ y=-2.5x+5 \end{gathered}[/tex]Answer: y=-2.5x+5
Ventana High School has found that some offerings on the lunch menu aremuch more popular than others. The following table displays students'favorite lunch choices:1875923PizzaTacosSubSandwichesChineseComboPlate98What is the estimated population proportion of students who prefer tacos?A. 0.12B. 0.32C. 0.16D. 0.06
Answers
Answer:
C. 0.16
Explanation:
In the table there are 59 students that prefer tacos and there are 367 students in total because
187 + 59 + 23 + 98 = 367
Then, the estimated population proportion of students that prefer tacos is calculated as
P = 59/367 = 0.16
Therefore, the answer is
C. 0.16
(x^3y^5)^3 × -x^6y^5
Answers
To simplify the expression you can first use this property of exponents
[tex](a\cdot b)^m=a^mb^m[/tex]Then you have
[tex]\begin{gathered} (x^3y^5)^3=(x^3)^3(y^5)^3 \\ (x^3y^5)^3=x^{3\cdot3}y^{5\cdot3} \\ (x^3y^5)^3=x^9y^{15} \end{gathered}[/tex]Now apply this property of exponents
[tex]a^b\cdot a^c=a^{b+c}[/tex]Therefore, you have
[tex]\begin{gathered} (x^3y^5)^3\cdot-x^6y^5=x^9y^{15}\cdot-x^6y^5 \\ (x^3y^5)^3\cdot-x^6y^5=x^9\cdot-x^6\cdot y^{15}\cdot y^5 \\ (x^3y^5)^3\cdot-x^6y^5=-x^{9+6}\cdot y^{15+5} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}\cdot y^{20} \\ (x^3y^5)^3\cdot-x^6y^5=-x^{15}y^{20} \end{gathered}[/tex]What is the equation of the line that passes through (-3,-1) and has a slope of 2/5? Put your answer in slope intercept form 1. Y=2/5x+1/52. Y=2/5x-1/53. Y= -2/5x-1/5
Answers
We are asked to determine the equation of a line that passes through the point (-3, -1) and has a slope 2/5. To do that we will use the point-slope form of a line equation:
[tex]y-y_0=m(x-x_0)[/tex]Where:
[tex]\begin{gathered} (x_0,y_0)=\text{ point on the line} \\ m=\text{ slope} \end{gathered}[/tex]Now, we plug in the values:
[tex]y-(-1)=\frac{2}{5}(x-(-3))[/tex]Simplifying we get:
[tex]y+1=\frac{2}{5}(x+3)[/tex]Now, we apply the distributive law:
[tex]y+1=\frac{2}{5}x+\frac{6}{5}[/tex]Now, we subtract 1 from both sides:
[tex]\begin{gathered} y=\frac{2}{5}x+\frac{6}{5}-1 \\ \\ y=\frac{2}{5}x+\frac{1}{5} \end{gathered}[/tex]and thus we get the equation of the line.
a₁ = 4; a = (a)²-3 (n ≥2) list the first five terms
Answers
The first five terms of the given sequence are 4, 1, 6, 13, 22
We can solve this problem by following a few steps.
The formula to find the next four terms is, a = (n)²- 3, (n ≥2) as per the question.
Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )
So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1 [As n = 2 for the second term ]
Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6 [ As n = 3 for the third term ] ,
for the 4th term A₄ = 4² - 3 = 16 - 3 = 13 [ As n = 4 for the second term ] ,
for the 5th term A₂ = 5² - 3 = 25 - 3 = 22 [As n = 5 for the second term ]
Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22
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The correct question is :
a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones. Explain why you regroup before the next step
Answers
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.
How to illustrate the information?Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.
The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.
In this case, it should be noted that the value of 5,917 × 29 is 171593.
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n
Find the value of x that makes m ||
(180 − x)°
m
An
to
W
Answers
Answer:
The value of x will be 90°
Find the value of x
Answers
.............................
You purchase 5 tickets to a football game from TicketMaster. In addition to the cost per ticket, the agency charges a convenience charge of $2.50 per ticket. You also choose to pay for rush delivery, which costs $15. The total cost of your order is $352.50. What is the price per ticket before the convenience charge?
Answers
The price per ticket, excluding the convenience charge, is $65.
How to solve for the privce per ticketthe rush delivery is given as $15.
The total cost of the tickets is said to be put at $352.50
Then the value that we would have for the the 5 tickets wpould be 352.50 - 15 = $337.50.
There is the convenience charge of $2.50 per ticket. This charge is excluded from the convenience charge that is to be paid.
Hence you would have to make the payment of
337.50 - 5*2.50
= 325.
Next we are to solve for the price of the ticket whioch is independent of the convenience charge
= 325 / 5
= $65
Hence the price per ticket is given as 65 dollars
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a 20$ bill, two $10 three $5 and four $1 are placed in a bag, if a bill is chosen at random what is the expected value for the amount choses
Answers
The expected value for the amount chosen from the bag is $5.90
How to get the expected value?
We have
one $20 bill.two $10 bills.three $5 billsfour $1 bills.So in total, we have 1 + 2 + 3 +4 = 10 bills.
The expected value will be then given by the sum of the products between the value of each bill and the number of bills of that type, divided by the total number of bills.
EV = (1*$20 + 2*$10 + 3*$5 + 4*$1)/10 = $5.9
The expected value is $5.9
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Determine the number of large cups that would contain the same amount as 10 1/2 small cups if a large cup holds 1 3/4 times the quantity of liquid that's in a small cup.
Answers
The number of large cups that would contain the same amount as 10 1/2 small cups is 6.
How to illustrate the information?From the information, it was stated that we should find the number of large cups that would contain the same amount as 10 1/2 small cups if a large cup holds 1 3/4 times the quantity of liquid that's in a small cup.
This simply means that we have to divide the values that are given. This will be illustrated as:
= 10 1/2 ÷ 1 3/4
= 10.5 / 1.75
= 6
There'll be 6 large cups.
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1/16x+1/320y-29=0 rewrite the equation as a function of x
Answers
The equation as a function of x is y = 9280 -20x
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.
The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]
Now rearranging the function we write
[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]
y = 9280 -20x
The equation as a function of x is y = 9280 -20x
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Answer to exercise 1 please
Answers
Using an exponential function and a differential equation, the constant k for the situation is given by:
k = 0.03.
What is an exponential function?An increasing exponential function is modeled according to the following rule:
[tex]A(t) = A(0)e^{kt}[/tex]
In which:
A(0) is the initial amount of the function.k is the exponential growth rate of the function, as a decimal.This exponential function is the solution to the following differential equation:
A'(t) = kA(t)
One example of application of these functions is for continuous compounding, in which the value of an investment of P(0) after t years is given by:
[tex]P(t) = P(0)e^{kt}[/tex]
For the continuous compounding situation in this problem, the interest rate is of 3%, hence k = 0.03, which is the desired parameter.
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Pls help i need this ASAP!
Answers
The solution for the given inequalities are as follows
(17)k≥1 ,(18)c > 14 ,(20)y ≥ 2 ,(21)z < 9 ,(23)x < 1 ,(24)v ≤ -1 .
In the question ,
it is given that
(17) the inequality
3(k-5)+9k≥-3
3k-15+9k ≥ -3
12k -15 ≥ -3
12k ≥ 15-3
12k ≥ 12
k≥1
(18) the inequality
-(7c-18)-2c > 0
-7c+126-2c>0
-9c+126>0
-9c > -126
c > 126/9
c > 14
(20)given the inequality
-4 ≤ 4(6y-12)-2y
-4 ≤ 24y - 48 -2y
-4 ≤ 22y - 48
48-4 ≤ 22y
44/22 ≤ y
y ≥ 2
(21) given the inequality
30 > -(5z+15)+10z
30 > -5z -15 +10z
30 > 5z-15
45 > 5z
45/5 > z
z < 9
(23) given the inequality
4x+3 < 3x+6
4x-3x < 6-3
3x < 3
x < 1
(24) given the inequality
4v+8 ≥ 6v+10
-10+8 ≥ 6v-4v
-2 ≥ 2v
-2/2 ≥ v
-1 ≥ v
v ≤ -1
Therefore , the solution for the given inequalities are (17)k≥1 ,(18)c > 14 ,(20)y ≥ 2 ,(21)z < 9 ,(23)x < 1 ,(24)v ≤ -1 .
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Please help, Pre-Algebra super easy math question
Answers
Answer:
-16
Step-by-step explanation:
b) -x²; x = -4
-(-4)²
-(16)
-16
I hope this helps!
Answer: -16
Step-by-step explanation:
Each of the four shapes represents a positive whole number. The sum of the shapes in
each row and column is displayed at the end of each row and column. Using this
information, determine the numerical value of each shape.
Answers
The numerical value of each of the four given shapes filled in the rows and columns are;
pentagon shape = 8star shapes = 6spiral shapes = 3rectangle shape = 5How to find numerical value of each shape.let
pentagon shape = AStar shape = BSpiral shape = Crectangle shape = DRow 1: There are 2 stars, one pentagon and one spiral shape.
A + 2B + C = 23 .....(equation 1)
Row 2: There are 2 spiral shapes and 2 rectangle shape.
2C + 2D = 16 ......( equation 2)
Row 3: There are 1 star, one pentagon and 2 rectangle shape.
A + B + 2D = 24 ....(equation 3)
Row 4: There are 3 spiral shapes and one star shape.
B + 3C = 15 ....(equation 4)
Column 1:
2C + A + D = 19 ....(equation 5)
Column 2:
2B + C + D = 20 .....(equation 6)
From equation 4;
B = 15 - 3C
From equation 2:
D = 8 - C
Substitute B = 15 - 3C into equation 1;A + 2B + C = 23
A + 2(15 - 3C) + C = 23
A + 30 - 6C + C = 23
A = 5C - 7
Substituting D = 8 - C and A = 5C - 7 into equation 5;2C + A + D = 19
2C + (5C - 7) + 8 - C = 19
6C + 1 = 19
6C = 18
C = 3
Substitute 3 for C inA = 5C - 7
A = 5(3) - 7
A = 8
Substitute 3 for C inB = 15 - 3C
B = 15 - 3(3)
B = 6
Substitute 3 for C inD = 8 - C
D = 8 - 3
D = 5
Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.
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solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]
Answers
EXPLANATION
Given the expression:
[tex]b=\sqrt[3]{x+a-z}[/tex]Applying the cubic power to both sides:
[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]Simplifying the cubic root with the cubic power:
[tex]b^3=x+a-z[/tex]Subtracting -a to both sides:
[tex]b^3-a=x+a-a-z_{}[/tex]Adding z to both sides:
[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]Simplifying terms:
[tex]b^3-a+z=x[/tex]Switching sides:
[tex]x=b^3-a+z[/tex]The vertices of triangle FGH are F(-5,1,) G(-2,4), and H(-1,2) the vertices of triangle F’G’H are F’(-5,-1) G(-2,-4) H (-1-2)Identify the transformation of triangle FGH to triangle F’G’H A. A translation across the x-axis B. A reflection across the x-axis C. A dilation D. A rotation
Answers
The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
What do we mean by reflection across the x-axis?The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A graph will appear to be inverted or on the other side of an axis, such as the x-axis, when it is reflected along that axis.If you look closer, you'll notice that it's symmetrical, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.As a result, if you reflect a point (x, y) along the x-axis, its x abscissa will remain the same but its y ordinates will negate. So (x,y) becomes (x, -y)
So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.
And as we know that in reflection across x-axis the x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse.Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
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Simplify
Y exponent -5/ y exponent -4
Answers
Answer:
"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.
A possible alternative direction might have been to rewrite without the negative exponent.
Answer:
[tex]\frac{1}{y}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{y^{-5} }{y^{-4} }[/tex]
= [tex]y^{(-5-(-4))}[/tex]
= [tex]y^{(-5+4)}[/tex]
= [tex]y^{-1}[/tex]
= [tex]\frac{1}{y}[/tex]
How would I solve this?
Write an equation of the line containing the given point and parallel to the given line.
(8, -3); 2x - 56 = 3
Type an equation using slope-intercept form or using the given point in point-slope form.
Answers
An equation of the line containing the given point and parallel to the given line is y = 2x - 19.
The condition for two parallel lines.
In Mathematics, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Mathematically, the point-slope form of a line is given by this equation:
y - y₁ = m(x - x₁)
Where:
x and y are the points.m represents the slope.Given the following equation:
2x - 56 = 3 ⇒ m₁ = 2
Therefore, m₁ = m₂ = 2.
At point (8, -3), we have:
y - y₁ = m(x - x₁)
y - (-3) = 2(x - 8)
y + 3 = 2(x - 8)
y + 3 = 2x - 16
y = 2x - 16 - 3
y = 2x - 19
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