The equivalent fraction of the distance from City A to City B that Kelly traveled on the third day is D) 1−2/5−2/3(1−2/5).
What is the fraction?The fraction represents a portion or part of a whole.
There are proper, improper, and complex fractions depending on the value of the numerator and the denominator.
The fractional distance traveled on day one = ²/₅
The remaining fractional distance = ³/₅ (1 - ²/₅)
The fractional distance Kelly traveled on day two = ²/₅ (²/₃ of ³/₅)
The fraction of the distance from City A to City B that Kelly traveled on the third day = ¹/₅ (1 - ²/₅ - ²/₅)
Thus, the equivalent fractional distance Kelly traveled on the third day is Option D.
Learn more about equivalent fractions at https://brainly.com/question/17220365
#SPJ1
Laura has done a two-factor factorial completely randomized design. From her experiment, Laura has constructed the following incomplete ANOVA display: Source SS DF MS F A 350.00 2 B 300.00 150 AB 200.00 50 Error 150.00 Total 1000.00 18 a. How many levels of factor B did she use in the experiment? b. How many degrees of freedom are associated with interaction? c. The error mean square is d. The mean square for factor A is e. How many replicates of the experiment were conducted? f. What are your conclusions about interaction and the two main effects? g. An estimate of the standard deviation of the response variable is h. If this experiment had been run in blocks (CRBD) there would have been degrees of freedom for blocks.
a. Two levels of factor B were used in the experiment.
b. The degrees of freedom associated with interaction are 50.
c. The error mean square is 6.00. d. The mean square for factor A is 175.00.e. The experiment was conducted with three replicates.f. The interaction is significant. Factor A is significant. Factor B is not significant.g. An estimate of the standard deviation of the response variable is 2.449. h. If the experiment had been run in blocks (CRBD) there would have been 12 degrees of freedom for blocks.Solution:Factorial design: A factorial design is an experimental design that consists of two or more factors, each with two or more levels, and each subject is assigned to one and only one level of each factor. The objective of a factorial experiment is to analyze the effect of each factor on the response variable and to examine if there is any interaction between factors.a. Two levels of factor B were used in the experiment.b. Interaction degrees of freedom = AB = 50.c.
Mean square for error: MSE = 150/10 = 15.d. Mean square for factor A: MS(A) =[tex]SSA/dfA = 350/2 = 175.e.\\[/tex] Three replicates were conducted (from the error df = 10).f. Interaction is significant. Factor A is significant. Factor B is not significant.g. Estimate of the standard deviation of the response variable: sqrt(15/2) = 2.449.h. If the experiment had been conducted in a CRBD, there would have been 12 degrees of freedom for the block.
for such more questions on standard deviation
https://brainly.com/question/475676
#SPJ11
Write 2/7 + 1/4 as a sum of two equivalent fractions with the same denominator
2/7 + 1/4 = 15/28 ≅ 0.5357143
Add: 2/7 + 1/4 = 2 · 4/7 · 4 + 1 · 7/4 · 7 = 8/28 + 7/28 = 8 + 7/28 = 15/28
It is suitable to adjust both fractions to a common (equal, identical) denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 4) = 28. It is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 7 × 4 = 28. In the following intermediate step, it cannot further simplify the fraction result by canceling.In other words - two sevenths plus one quarter is fifteen twenty-eighths.
The net of a triangular prism is shown. a) Work out the length x. b) Work out the area of the shaded face. 3 cm 7 cm 5 cm 8 9 cm Not drawn accurately
The length of the side on the prism is 5cm. The area of the shaded region is 72 cm².
What is area?Area is the total amount of area occupied by a flat (2-D) surface or an object's shape. The area of a plane figure is the region that its boundary encloses. The quantity of unit squares that span a closed figure's surface is its area. Square units like cm² and m² are used to quantify area. A shape's area is a two-dimensional measurement.
The region inside the perimeter or boundary of a closed shape is referred to as the "area". Such a shape has at least three sides that can be joined together to create a boundary. The "area" formula is used in mathematics to describe this type of space symbolically.
In this figure,
The 5cm flap will be adjacent to the side x. Therefore,
Length of the side x= 5cm
Area of the shaded region= l×b
because the shaded region is a rectangle.
area= 9*x
=9*5= 45 cm²
To know more about area, visit
https://brainly.com/question/27683633
#SPJ1
find the length of the cord pt.3
According to the circle theorem, we can find the length of the cord, x = 4 units.
Define circle theorem?Geometrical assertions known as "circle theorems" set forward significant conclusions pertaining to circles. These theorems provide significant information regarding several aspects of a circle.
A circle's chord is a line segment that hits the circle twice on its edge, separating it into two equal pieces. The circle is divided into two equal pieces by the longest chord of the circle, which runs through its centre.
Here in the given circle,
As per the intersecting chords theorem,
AB × CB= BE × BD
⇒ 6 × 6 = 9× x
⇒ x = 36/9=4
Therefore, the length of the chord, x = 4 units.
To know more about circle theorem, visit:
https://brainly.com/question/19906313
#SPJ1
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
Answer:
2x=5 > -14
Step-by-step explanation:
6(x - 2) -3 ≥ -4 ( -3 + 9) +10
6x-12-3 > 12-36+10
6x-15 > -36+22
6x-15 > -14
6x=15 > -14
3 3
2x=5 > -14
Jason and Scott plan on biking to the center of town to get ice cream at the convenience store. Since Scott
had to put air in his tires, Jason was able to get 1 mile ahead of Scott before Scott left the house. Both
bikers rode at a speed of 15 miles per hour.
Write an equation in y = mx + b form that represents Jason's trip. Jason =
a.
Write an equation in y = mx + b form that represents Scott's trip.
Will Jason and Scott meet before they both reach the store? Explain.
If you were to graph both lines on the same coordinate plane, predict what your graph would look
like.
Answer:
a. Jason's equation in y = mx + b form is y = 15x + 1.
b. Scott's equation in y = mx + b form is y = 15x.
Since both are moving at the same speed, they will meet at the point where their distances from the starting point are the same. Let d be the distance from Scott's starting point to the store. Then, the distance from Jason's starting point to the store is d + 1. Using the formula distance = rate × time, we can set up an equation:
15t = d
15t - 1 = d + 1
Solving for t in both equations, we get t = d/15 and t = (d+2)/15, respectively. Equating these expressions for t, we get d/15 = (d+2)/15, which simplifies to d = -2. This means that they will not meet before reaching the store, as Jason is already 1 mile ahead of Scott and will stay ahead throughout the trip.
If we were to graph both lines on the same coordinate plane, we would have two parallel lines with a slope of 15, where Jason's line would intersect the y-axis at 1.
10) A rectangle has a width of 2m+3. The length
is twice as long as the width. What is the length
of the rectangle?
Answer:
4m + 6
Step-by-step explanation:
Since the length is twice as long your equation should look like this
2(2m + 3) = L
which would be 4m + 6 as the length of the rectangle
Which pattern shows a quadratic relationship between the step number and the number of dots? Explain or show how you know.
Pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
What is wοrd prοblem?Wοrd prοblems are οften described verbally as instances where a prοblem exists and οne οr mοre questiοns are pοsed, the sοlutiοns tο which can be fοund by applying mathematical οperatiοns tο the numerical infοrmatiοn prοvided in the prοblem statement. Determining whether twο prοvided statements are equal with respect tο a cοllectiοn οf rewritings is knοwn as a wοrd prοblem in cοmputatiοnal mathematics.
Here pattern B shοws a quadratic relatiοnship between the step number and the number οf dοts.
We can write quadradic equation as [tex]y=1+x^2[/tex]
Where y is number οf dοts and x is step number.
Then if x=0 and y=1
If x = 1 and y = 2
If x = 2 and y = 5
If x = 3 and y = 10
Hence Patten B fοllοws the quadratic realatiοnship.
Tο learn more about word problem refer the below link
https://brainly.com/question/21405634
#SPJ1
1) Adam wants to buy a home priced at $215,000. The bank requires him to make a 5% down payment and
he will finance the rest for 30 years at 4.5% interest. He has to also pay the closing costs below. Find the
a) the down payment b) the amount of the mortgage c) the closing costs d) the amount financed with
closing costs e) the monthly payment f) the total amount repaid g) the amount paid to interest.
Application Fee
Borrower's Credit check
Points
Appraisal Fee
Title Search
Title Insurance
Attorney Fee
Documentation stamp
Processing fee
$ 25
65
1.5% of Mortgage
350
215
450
400
0.30% of Mortgage
1.25% of Mortgage
Name the shape that will result from connecting the points (-4, 1) , (-4, -4) , (0, 3) , and (0, 6) .
A: Square
B: Rectangle
C: Trapezoid
D: Parallelogram
The shape that results from connecting the points (-4, 1), (-4, -4), (0, 3), and (0, 6) is a trapezoid.
What is a trapezoid?A trapezoid is a geometric form that has four sides, two of which are parallel and two of which are nonparallel (or skew lines). A trapezoid is also known as a trapezium (UK) or a trapeze (US).
The trapezoid's parallel sides are known as the bases, and the two nonparallel sides are known as the legs or lateral sides. The trapezoid is also sometimes referred to as the irregular quadrilateral.
How to identify a trapezoid?A quadrilateral is a shape that has four sides, four vertices, and four angles. The following are the characteristics of a trapezoid:
It has four sidesIt has two parallel sides and two nonparallel sidesIt has two opposite sides that are parallel to one another and two other sides that are not parallelIt has two acute angles and two obtuse anglesIt has diagonals that intersect at a midpointThe formula for the area of a trapezoid is as follows:
Area of a trapezoid = [ (base 1 + base 2) / 2 ] x height
To know more about the "trapezoid": https://brainly.com/question/1463152
#SPJ11
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Answer:
3 pounds of coffee.
Step-by-step explanation:
Equation
y = -7.37x + 80
substitute 57.89 for y
57.89 = -7.37 + 80 Subtract 80 from both sides
57.89 - 80 = -7.37 + 80 - 80
-22.11 = -7.37x Divide both sides by -7.37
3 = x
3 pound of coffee
Helping in the name of Jesus.
Answer:
rita received a $80 gift card for a coffee store. she used it in buying some coffee that cost $7.37 per pound. after buying the coffee, she had $57.89 left on her card. How many pounds of coffee did she buy?
Step-by-step explanation:
Let's first find out how much money Rita spent on coffee:
$80 (initial balance) - $57.89 (remaining balance) = $22.11 spent on coffee
Now, let x be the number of pounds of coffee that Rita bought. Since the coffee costs $7.37 per pound, we can set up the equation:
$7.37x = $22.11
Solving for x, we can divide both sides by $7.37:
x = 3
Therefore, Rita bought 3 pounds of coffee.
Can someone help me with this math problem pls! #Percents
Answer: $3.64
Step-by-step explanation:
At the store, you buy four toys for $1.5, which means you pay $1.5 * 4, or $6.
Then, you calculate the sales tax, which is 6%, which means you multiply $6 by (100% + 6%), or $6*(1.06) which is $6.36.
Finally, if you hand the cashier $10, and you spent $6.36, your change is $10 - $6.36, which is $3.64.
The perimeter of a rectangular map of the world is 270 cm. It is 90 cm in height. How wide is it?
Answer:
The perimeter of a rectangle is given by:
P = 2(L + W)
where P is the perimeter, L is the length, and W is the width.
In this case, we know that P = 270 cm and L = 90 cm, so we can solve for W as follows:
270 = 2(90 + w)
Divide both sides by 2:
135 = 90 + w
Subtract 90 from both sides:
w = 45
Therefore, the width of the map is 45 cm.
Step-by-step explanation:
By rounding to 1 significant figure , estimate the answer to the questions
216×876
The rounding of the number to 1 significant figure is-
216 × 876 = 180000
What is defined as the significant figure?The term significant figures describes the number of significant single digits (0 to several 9 inclusive) in a scientific notation coefficient.The number of significant figures inside an expression indicates the degree of certainty or precision with where an engineer or scientist states a number.All zeros to the right of the decimals but to the left of a non-zero number in a decimal number between 0 and 1 are not significant.0.00247, for example, only has three significant figures.216 × 876
This number can be written in form of rounding to 1 significant figure as;
200 × 900 = 180000
To know more about the significant figure, here
https://brainly.com/question/293578
A triangle is equal in area to a rectangle which measures 10cm by 9cm. If the base of the triangle is 12cm long, find its altitude
Answer:
h = 15 cm
Step-by-step explanation:
Area of triangle equals the area of rectangle. As the dimensions of the rectangle is given, we can first find the area of the rectangle.
[tex]\boxed{\bf Area \ of \ the \ rectangle = length * width}[/tex]
= 10 * 9
= 90 cm²
Area of triangle = area of rectangle
= 90 cm²
base of the triangle = b = 12 cm
[tex]\boxed{\bf Area \ of \ triangle = \dfrac{1}{2}bh}[/tex] where h is the altitude and b is the base.
[tex]\bf \dfrac{1}{2} b* h = 90 \\\\\dfrac{1}{2}*12* h = 90[/tex]
[tex]\bf h = \dfrac{90*2}{12}\\\\\boxed{\bf h = 15 \ cm}[/tex]
Enter the values needed to find the
length BC. (Simplify your answer.)
A (-5x, 4y)
B (-2x, -4y)
BC=√([?])² + (3y)²
C (7x, -1y)
Distance Formula
d = √√(x₂ − ×₁)² + (y₂ − y₁)²
The missing value to find the length of BC is 9x.
What is distance formula?The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.
The distance formula is given as:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the values of the coordinates of B and C we have:
distance = √((7x - (-2x))² + (-1y - (-4y))²)
distance = √((9x)² + (3y)²)
distance = √(81x² + 9y²)
distance = 3√(9x² + y²)
Hence, the missing value to find the length of BC is 9x.
Learn more about distance formula here:
https://brainly.com/question/28956738
#SPJ1
30 points to help me!
Answer:
Step-by-step explanation:
5+3x/4 = 7/12
[(5*4)+3x]/4 = 7/12
(20+3x)/4 = 7/12
20+3x = 7/12*4
20+3x = 7/3
3x = 7/3 - 20
3x = [7-(20*3)]/3
3x = (7-60)/3
3x = -53/3
x = -53/3/3/1 ( reciprocal )
x = -53/3*1/3
x= -53/9
a general principle in the field of tests and measurements is that longer tests tend to be more reliable than shorter ones. in your opinion, is that principle illustrated by the reliability coefficients shown in the table?
This principle is validated by the data shown in the table.
Tests and measurements is an essential aspect of the education process as it enables educators to gauge the level of knowledge and skills their students have acquired. The principle that longer tests tend to be more reliable than shorter ones has some merit because it allows educators to assess a broader range of skills and knowledge, which increases the validity of their assessments.In my opinion, the principle that longer tests tend to be more reliable than shorter ones is illustrated in the reliability coefficients shown in the table. This is because the data shows that the reliability coefficients for longer tests are consistently higher than those for shorter tests. Additionally, the results for the 10-item test indicate a higher reliability coefficient compared to the 5-item test, which supports the notion that longer tests are more reliable than shorter ones.The table displays that the longer tests have higher reliability coefficients compared to the shorter tests. For example, in the 5-item test, the reliability coefficient is .45, while the 10-item test's reliability coefficient is .73. This shows that the 10-item test is more reliable than the 5-item test, as the higher reliability coefficient indicates that the assessment is consistent in measuring the skill or knowledge it is intended to measure. As a result, this principle is validated by the data shown in the table.
Learn more about principle
brainly.com/question/30388578
#SPJ11
What property of real numbers does each statement demonstrate? (3 + 4) + 1 = 3 + (4 + 1)
Answer: Associative property
Step-by-step explanation:
The definition of the associative property is the answer is the same no matter how the terms are grouped. Hope this helped!
What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
The surface area of the rectangular prism is 170 square yards.
What is the surface area formula?Surface area is the total area of a three-dimensional shape's surface. Add the areas of all six faces to find the surface area of a cuboid with six rectangular faces. Alternatively, label the cuboid's length (l), width (w), and height (h) and use the formula: surface area (SA)=2lw+2lh+2hw.
To calculate the surface area of the rectangular prism, add the areas of each of its faces.
The front and back faces are 5 yards by 6 yards in size, so each has an area of:
5 yards x 6 yards equals 30 square yards
The top and bottom faces are 5 yards by 5 yards, so each has an area of:
5 yards x 5 yards equals 25 square yards
The two side faces have dimensions of 6 yards by 5 yards, for a total area of:
30 square yards = 6 yards x 5 yards
As a result, the surface area of the rectangular prism is as follows:
Front face area plus back face area plus top face area plus bottom face area plus left side face area plus right side face area
= 30+30+25+25+30+30
= 170 square yards
As a result, the rectangular prism has a surface area of 170 square yards.
To know more about surface area visit:
hhttps://brainly.com/question/29298005
#SPJ1
Which of the following is equivalent to the inequality 2x + 13 < 5x - 20?
F. x >-11
G. x<?
H. x>;
J. x < 11
K. x > 11
Answer:
k
Step-by-step explanation:
2x+13<5x−20
Subtract 5x from both sides.
Combine 2x and −5x to get −3x.
Subtract 13 from both sides.
Subtract 13 from −20 to get −33.
Divide both sides by −3. Since −3 is negative, the inequality direction is changed.
x>11
About 24% of flights departing from New York's John F. Kennedy International Airport were delayed in 2009. Assuming that the chance of a flight being delayed has stayed constant at 24%, we are interested in finding the probability of 10 out of the next 100 departing flights being delayed. Noting that if one flight is delayed, the next flight is more likely to be delayed, which of the following statements is correct? . (A) We can use the geometric distribution with n = 100, k = 10, and p = 0.24 to calculate this probability. (B) We can use the binomial distribution with n = 10, k = 100, and p = 0.24 to calculate this probability. (C) We cannot calculate this probability using the binomial distribution since whether or not one flight is delayed is not independent of another. (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability
The statement that is correct is (D) We can use the binomial distribution with n = 100, k = 10, and p = 0.24 to calculate this probability.
The binomial distribution can be used to calculate the probability of a certain number of successes in a given number of trials, where each trial has a fixed probability of success.
The probability of a flight being delayed is 0.24, and the probability of a flight not being delayed is 0.76. Therefore, the probability of exactly 10 flights out of 100 being delayed can be calculated using the binomial distribution with n = 100, k = 10, and p = 0.24.
Learn more about binomial distribution here: https://brainly.com/question/30049535
#SPJ11
What is the solution to 3(2k + 3)= 6-(3k -5)
Answer:
[tex]\frac{11}{8}[/tex]
Step-by-step explanation:
3(2k+3)=6-(3k-5)
6k +9=6-3k+5
6k+3k=6+5
8k=11
k=[tex]\frac{11}{8}[/tex]
Answer: I think it is k=2/9
Step-by-step explanation:
Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesperson can use the equation b=0. 29h+1. 35
where b
is the size of the BMX bike frame in inches and h
is the height of the rider in inches
The slope in the equation b = 0.29h + 1.35 is the measure of the rate at which the bike frame size changes with the height of the rider.
The slope in the equation b = 0.29h + 1.35 refers to the coefficient of the variable h, which represents the height of the rider. The slope is the measure of the rate at which the bike frame size changes with the height of the rider.
In this equation, the slope is 0.29, which means that for every inch increase in the rider's height, the bike frame size increases by 0.29 inches. The slope is a crucial component of the equation as it determines the proportionality of the two variables.
Moreover, the slope is essential in analyzing the relationship between the rider's height and the bike frame size.
It plays a vital role in determining the appropriate size of the BMX bike frame and analyzing the relationship between the two variables.
To know more about equation here
https://brainly.com/question/10413253
#SPJ4
Complete Question:
Purchasing the correctly sized BMX bike is based on the height of the rider. In order to fit a customer, the salesman can use the equation b 0.29h +1.35 where b is the size of the BMX bike frame in inches and h is the height of the rider in inches.
Which sentence explains the slope in the equation?
In a distribution of 387 values with a mean of 72, at least 344 fall within the interval 64-80. Approximately what percentage of values should fall in the interval 56-88? Use Chebyshev’s theorem. Round your k and s values to one decimal place and final answer to two decimal places.
The required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
Chebyshev’s Theorem:Chebyshev's Theorem states that, for any given data set, the proportion (or percentage) of data points that lie within k standard deviations of the mean must be at least (1 - 1/k2), where k is a positive constant greater than 1.Calculation:Given,Mean (μ) = 72N (Total number of values) = 387Interval (x) = 64-80 and 56-88Minimum values (n) = 344Minimum percentage (p) = (344 / 387) x 100 = 88.85%From the given data we have,1. Calculate the variance of the distribution,Variance = σ2 = [(n × s2 ) / (n-1)]σ2 = [(344 × 42) / 386]σ2 = 18.732. Calculate the standard deviation of the distribution,σ = √(18.73)σ = 4.33. Calculate k = (|x - μ|) / σ for the given interval 56-88,Here, x1 = 56, x2 = 88, k1 = |56-72| / 4.33 = 3.7, k2 = |88-72| / 4.33 = 3.7Thus, k = 3.74. Calculate the minimum percentage of values within the interval 56-88 using Chebyshev's Theorem,p = [1 - (1/k2)] x 100p = [1 - (1/3.7)2] x 100p = 74.37% (approximately)Therefore, the required percentage of values that should fall in the interval 56-88 is approximately 74.37%.
Learn more about Percentage
brainly.com/question/2155156
#SPJ11
Given that the number 33,554,432 is equal to 2^25 , explain how you know that 33,554,432 is not a square number
First of all, perfect squares do not end in 2.
The exponent has to be an even number when 2 is the base. For example 2^8 = 64. 8 is an even number. So 64 is a square number.
a box contains 75 red marbles, 37 white marbles, and 19 blue marbles if a marble is randomly selected from the box, what's the probability that it is not blue
The probability that it the marble taken out of the box is not blue is [tex]\frac{112}{131}[/tex].
What is the probability?Probability is a branch of math that studies the chance or likelihood of an event occurring.
There are [tex]75[/tex] red marbles, [tx]37[/tex] white marbles, and [tex]19[/tex] blue marbles.
If a marble is randomly selected from the box, we have to find the probability that it is not blue.
Then the total number of marbles = [tex]75 + 37 + 19 = 131.[/tex]
The probability that a marble is not blue:-
[tex]P[/tex](Not blue) = [tex]P[/tex](Red or White)
[tex]P[/tex](Red or White) = [tex]\frac{(75 + 37)}{131}[/tex]
[tex]P[/tex](Red or White) = [tex]\frac{112}{ 131}[/tex]
[tex]P[/tex](Not blue) = [tex]1 - P[/tex](Blue)
[tex]P[/tex](Not blue) = [tex]1 - \frac{19}{131}[/tex]
[tex]P[/tex](Not blue) = [tex]\frac{112}{ 131}[/tex]
Therefore, the probability that a marble selected from the box is not blue is [tex]\frac{112}{131}[/tex].
Learn more about Probability here:
https://brainly.com/question/30034780
#SPJ11
thanks if you answer
Answer:
[tex]{ \sf{ = 41 \times 100 + 41 \times { \boxed{2}}}} \\ \\ = { \sf{ \boxed{4100} + { \boxed{82}}}} \\ \\ = { \sf{ \boxed{4182}}}[/tex]
Answer:
A- 2
B- 4,100
C- 82
D- 4,182
Need help with math
The new coordinates of the two points after rotating the parallel lines 180 degrees clockwise are (2, -7) and (-8, 5).
What are parallel lines?
In geometry, parallel lines can be defined as two lines in the same plane that are at equal distance from each other and never meet.
If the set of parallel lines contains the points (-2, 7) and (8, -5), then the two lines are parallel to each other and have the same slope. We can find the slope of the line that passes through these two points using the slope formula:
slope = (y2 - y1) / (x2 - x1)
slope = (-5 - 7) / (8 - (-2))
slope = -12 / 10
slope = -6 / 5
So, the equations of the two parallel lines are:
y - 7 = (-6 / 5)(x + 2) --- equation 1
y + 5 = (-6 / 5)(x - 8) --- equation 2
To rotate the lines 180 degrees clockwise, we need to negate both the x and y coordinates of the points on the lines. That is, we need to replace each point (x, y) with the point (-x, -y).
So, after the rotation, the new coordinates of the two points will be:
(-(-2), -7) = (2, -7) --- for point (-2, 7)
(-(8), -(-5)) = (-8, 5) --- for point (8, -5)
Learn more about parallel lines on:
https://brainly.com/question/30097515
#SPJ1
Write the equation of a line perpendicular to `y=3` that goes through the point (-5, 3).
Answer:
The equation of a line perpendicular to y=3 that goes through the point (-5, 3) is: x = -5.
Step-by-step explanation:
To find the equation of a line perpendicular to y=3 that goes through the point (-5, 3), we need to remember that the slope of a line perpendicular to another line is the negative reciprocal of the slope of the original line.
The equation y=3 is a horizontal line that goes through the point (0,3), and its slope is zero. The negative reciprocal of zero is undefined, which means that the line perpendicular to y=3 is a vertical line.
To find the equation of this vertical line that goes through the point (-5, 3), we can start with the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line. Since the line we want is vertical, its slope is undefined, so we can't use the point-slope form directly. However, we can still write the equation of the line using the point (x1, y1) that it passes through. In this case, (x1, y1) = (-5, 3).
The equation of the vertical line passing through the point (-5, 3) is:
x = -5
This equation tells us that the line is vertical (since it doesn't have any y term) and that it goes through the point (-5, 3) (since it has x=-5).
So, the equation of a line perpendicular to y=3 that goes through the point (-5, 3) is x = -5.
Answer:
x= -5
Step-by-step explanation:
The perpendicular line is anything with x= __.
x= -5 however, will go through the point (-5, 3) and that is our answer.
