Answers
Applying the slope formula, we have:
16. Slope = -9/4; Parallel slope = -9/4; Perpendicular slope = 4/9.
17. Slope = -4; Parallel slope = -4; Perpendicular slope = 1/4.
See explanation below for the rest answers.
How to Find the Slope of a Line?Slope of a line = change in y / change in x.
The slope of parallel lines are the same, while the slopes of two lines that are perpendicular to each other are negative reciprocals of each other, i.e. 1/a and -a can be the slopes of two lines that are perpendicular to each other.
In an equation given in slope-intercept form, y = mx + b, the slope is represented as "m".
16. Given, (3, 7) and (7, -2):
Slope (m) = (-2 - 7)/(7 - 3)
Slope = -9/4
Parallel slope = -9/4
Perpendicular slope = 4/9.
17. Given, y = -4x + 2,
Slope = -4
Parallel slope = -4
Perpendicular slope = 1/4.
18. Rewrite 5x - 2y = 8 in slope-intercept form:
-2y = -5x + 8
y = 5/2x - 4
Slope = 5/2
Parallel slope = 5/2
Perpendicular slope = -2/5.
19. Rewrite 4x + 3y = 2 in slope-intercept form:
3y = -4x + 2
y = -4/3x + 2/3
Slope (m) = -4/3
Substitute (a, b) = (2, -5), and m = -4/3 into y - b = m(x - a):
y - (-5)) = -4/3(x - 2)
y + 5 = -4/3(x - 2) [point-slope form]
20. Given, y = -5x + 2
Slope (m) = -5
Substitute (a, b) = (-4, -6), and m = -5 into y - b = m(x - a):
y - (-6) = -5(x - (-4))
y + 6 = -5(x + 4) [point-slope form]
21. Rewrite 9x - 3y = 6 in slope-intercept form:
-3y = -9x + 6
y = 3x - 2
The slope of y = 3x - 2 (9x - 3y = 6) is 3.
The slope of -3x - 5 is -3.
Therefore, the lines are neither parallel nor perpendicular.
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Related Questions
LeeAnn is taking care of her 3 brothers.
She has four pieces of toast and wants
to divide them equally among her
brothers.
How much toast does each get?
Answers
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
What is fraction?A number that is stated mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator. The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line.
Given Data
LeeAnn is taking care of her 3 brothers. She has four pieces of toast and wants to divide them equally among her brothers.
So,
Total pieces of toast = 4
Each gets = 1
Fraction of toast each gets = [tex]\frac{1}{4}[/tex]
Each gets [tex]\frac{1}{4}[/tex] pieces of toast.
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equation. h(x) = x - 11
Answers
Answer:
6
Step-by-step explanation:
Let the required input be y.
[tex]h(y)=y-11=-5 \\ \\ y=6[/tex]
A ball is released from rest and falls 125 meters in 5 seconds. What was the magnitude of its acceleration?
Answers
From the calculations using the data provided, the acceleration of the ball is 10 m/s^2
What is the acceleration?We know that the acceleration is the rate at which there is an increase or a decrease in the velocity of a body. In this case, we are told that A ball is released from rest and falls 125 meters in 5 seconds.
We have the following;
Distance of the object = 125 meters
Time taken = 5 seconds
Given that;
s = ut + 1/2at^2
u = 0 m/s because it was released from rest
s = 1/2at^2
a = 2s/t^2
a = 2(125)/(5)^2
a = 250/25
a = 10 m/s^2
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Store A sells 2 bags of chips for $2.50. Store B sells 3 bags of chips for $3.25. Which store offers the better deal?
Answers
Answer:
Store B
Step-by-step explanation:
Since the lowest common multiple of 2 and 3 is 6, so let's find the cost of 6 bags of chips from each store.
Store A
cost for 6 bags of chips
= 3(2.5)
= $7.50
Store B
cost for 6 bags of chips
= 2(3.25)
= $6.50
Since store B offers a cheaper price for 6 bags of chips, it offers a better deal.
Alternatively, you could work out the cost of each bag of chips for both stores.
pleaseee help, question what is the sum of 4x^2 + 2x - 5 and 7x^2 - 5x + 2
Answers
Answer:
Add the expressions.
11x2−3x−3
Step-by-step explanation:
Simplification of polynomials.
Polynomials are mathematical expressions made up of many terms.To simplify a polynomial the most, you must collect all like terms and rearrange them from highest to lowest power.
4x² + 2x -5 + 7x² - 5x+24x² + 2x -3 + 7x² - 5x+211x² + 2x - 3 - 5x11x² - 3x - 3 ====> Option "A"HELP! PLEASE? The question is in the photo. Work does not need to be shown.
Answers
Answer:
about 22 square units
Step-by-step explanation:
Count the number of squares which is completely inside the border. Then count the number of squares which is half or more than half inside the border as 1 square.
Monica made strawberry lemonade to serve at her birthday party. In a large pitcher, she mixed 8 ounces of strawberry puree and 40 ounces of lemonade. She had some strawberries left over, so she made another smaller batch. She mixed 5 ounces of strawberry puree and 20 ounces of lemonade in a small jug. Which container's strawberry lemonade had a stronger strawberry flavor?
Answers
The container's strawberry lemonade that had a stronger strawberry flavor is the more compact bottle and has a more robust taste.
This is further explained below.
What is the stronger strawberry flavor?Generally, in a bid to understand the context of the scenario we must first write the rato of the flavor's relationship
x=8:40
y=5:20
Therefore
x=8:40
y=10:40
In conclusion, This helps us decipher that Larger container: We add eight ounces of strawberry puree for every forty ounces of lemonade that we make.
We have 10 ounces of strawberry puree for every 40 ounces of lemonade that we have.
Therefore, the more compact bottle has a more robust taste.
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A family is taking a trip to a maill 45 miles away. They have seven gallons of gas in their car's fuel tank and the car gets 22 miles per gallion on this trip. Explain why it is okay to estimate the fuel supply for the trip.
Answers
Trip of 45miles with seven gallons of gas in a car and car gets 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
As given in the question,
Total distance covered in family trip is 45 miles
Total fuel in car is seven gallons
Average of the on trip=22 miles per gallon
Estimate fuel supply for trip =(45 miles )/(22 miles per gallon)
=2.04545gallons
≈2gallons(approximately)
As the fuel used in the trip is 2.04545.. gallons which is nearest to the 2 gallons, it is okay to estimate the fuel supply.
Therefore, trip of 45 miles with 7gallons of gas in a car with average 22 miles per gallon ,estimate fuel supply for trip is 2 gallons.
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is 4.887888 a rational number
Answers
Which of the following functions is graphed below?
Answers
Answer:
It is a quadratic funcion with vertex in (4,0)
Step-by-step explanation:
In 3–5 sentences, explain why the moon appears to be less bright than the sun despite its very close distance to Earth. PLEASE DO NOT COPY OTHER PEOPLE AND RIGHT THISBased on scientific observations and findings, the reasons the moon appears to be less bright than the sun despite its very close distance to earth are the following:
Moon doesn't produce its light but rather takes or reflects the light from the Sun.
Moon only reflects about 12 percent maximum of lights that shines on it from the sun.
Externally, Moon is made of dark-colored soil often referred to as lunar soil. This is unlike the Sun which is made of hydrogen and helium, whose atoms are very light.
Also, Sun is about 400 times bigger than the Moon.
Hence, in this case, it is concluded that there are many reasons the moon appears to be less bright than the sun despite its very close distance to earth. MAKE IT SIMPLE
Answers
Answer:
Since the moon has no atmosphere, all wavelengths of sunlight reach the ground by traveling straight through space. Our sun appears white because it produces all visible wavelengths approximately equally. The sun will appear the same size whether viewed from Earth or the Moon since Earth and the moon are relatively close to the sun. The sun and moon both have an apparent size of one-half of a degree when viewed from Earth.
Step-by-step explanation:
What's 4/9+9/18 please help with this thanks you
Answers
After solving the equation 4/9+9/18, we have to come to find the solution is 1.57.
What is an equation?An equation can be defined in a number of different ways. An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.
In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal." There are one or more variables in even the most fundamental and straightforward algebraic equations.
The value of the variable that makes the equation a true statement is the solution of the equation.
We have been asked to solve the equation 4/9 + 9/8
Lets solve
⇒ 4/9 + 9/8
⇒ (32+81)72 (finding the LCM of denominators and multiplying with
⇒ (32+81)72 numerators)
⇒ 113/72
⇒ [tex]1\frac{41}{72}[/tex]
⇒ 1.57
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B. What is the rate of change of the line that contains the points (2, 4), (6, 6), (12, 9)??
Answers
Answer: 1/2
Step-by-step explanation:
The rate of change is the same as the slope.
Taking the points (2, 4) and (6,6), the slope is [tex]\frac{6-4}{6-2}=\frac{1}{2}[/tex]
A line that includes the points (c, -10) and (-8,-8) has a slope of -1/8 what is the value of c
Answers
Answer:
gradient= y2-y1/x2-x1
-8+10/-8-c=-1/8
2/-8-c=-1/8
-1(-8-c)=8(2)
8+c=16
c=16-8
c=8
Lisa and Joey just became parents to their son, David. They want to start saving for their newborn’s college, so they open a new, empty savings account. They agree that they will put an equal amount of money every month, so that as David gets older and time goes by, the account gets filled with money for David’s future. Describe what is happening to the variables here (hint: time is almost always on the x-axis). Is this a variation equation?
Answers
If Lisa and Joey put the same amount of money every month in the savings account for David's future and the situation is plotted in a graph where time is on the x-axis, then there will be straight line with a constant slope.
As per the question statement, Lisa and Joey just became parents to their son, David and they decided to start a savings account for their newborn's future, where they agreed to put an equal amount of money every month.
We are required to determine the condition of the variables if the above-mentioned situation is plotted into graph and the account gets constantly filled with money as David grows older.
To solve this question, first let us consider the time to be plotted on the X-axis (As mentioned in question statement that "Time" is almost always on the x-axis) and the money collected to be plotted on the Y-axis.
Since, an equal amount of money is put into the account every month, therefore, taking 1 month as unit time to plot our graph, the money will grow diagonally in a straight line with a constant slope. Hence, both the variables (abscissa and ordinates) will increase on a constant ratio along the first quadrant.
Slope of a Line: In mathematics, the slope or gradient of a line is a value that describes both the direction and the steepness of the line and is calculated by the change in y coordinate with respect to the change in x coordinate.To learn more about Slope of a Line, click on the link below.
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A table showing Rate in kilometers per hour, Time in hours, and Distance in kilometers. The first row shows, Trip 1, and has 40, 0.9 minus x, and 40 left-parenthesis 0.9 minus x right-parenthesis.
Talia took the bus from her home to the bank and then walked back to her home along the same route. The bus traveled at an average speed of 40 km/h and she walked at an average speed of 5 km/h. To determine the time, x, that it took Talia to walk home, she used the equation
40(0.9 – x) = 5x.
The time of Trip 2 is
hours.
The distance of Trip 1 is
km.
Answers
Answer:The time of Trip 2 is
⇒ 0.8 hours.
The distance of Trip 1 is
⇒ 4 km.
The time of Trip 2 is 0.8 hours
The distance of trip 1 is 32 km
Given,
The speed of the bus = 40 km/h
Talia's walked at a speed = 5 km/h
To determine the time,x for her walk here used the equation; 40(0.9 – x) = 5x.
We have to find the time from Talia's home to bank in bus and the distance.
Here,
Equation is already given, we can simplify it and get x which is the time.
40(0.9 – x) = 5x.
36 - 40x = 5x
36 = 40x + 5x
36 = 45x
x = 36/45
x = 0.8 hours = 0.8 x 60 = 48 minutes
Now,
Distance from Talia's home to bank;
Speed = distance/time
Distance = speed x time = 40 x 0.8 = 32 km
That is,
The time of Trip 2 is 0.8 hours
The distance of trip 1 is 32 km
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15 points for correct answer! Can someone help me solve:
1<|x|<2
Thank you!
Answers
Answer:
[tex]-2<x<-1, 1<x<2[/tex]
Step-by-step explanation:
[tex]|x|>1 \implies x<-1[/tex] or [tex]x>1[/tex]
[tex]|x|<2 \implies -2<x<2[/tex]
Taking the union of the intervals, [tex]-2<x<-1, 1<x<2[/tex]
The angle of elevation of the top of the building at a distance of 50 Marin it’s foot on a horizontal plane is found to be 60.Find the height of the building
Answers
Answer:
If the proton proton chain produces gamma ray photons, why are the majority of photons we observe from the sun at visible wavelengths?
Step-by-step explanation:
write the equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6
Answers
The equation of the line that passes through the point (-9, 2) and is perpendicular to the line 10x - 5y = 6 is y = - 1 / 2 x - 5 /2
How to find equation of a line?The equation of a line can be represented in slope intercept form.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, the equation of the line is perpendicular to 10x - 5y = 6.
5y = 10x - 6
y = 2x - 6 / 5
Perpendicular lines follows the rule below:
m₁m₂ = -1
Therefore,
2m₂ = -1
m₂ = -1 / 2
The slope of the line is - 1 / 2. Now, let's find the equation of the line as it passes through (-9, 2)
y = - 1 / 2 x + b
2 = - 1 / 2 (-9) + b
2 = 9 / 2 + b
b = 2 - 9 / 2
b = 4 - 9 / 2
b = - 5 / 2
Therefore, the equation of the line is as follows:
y = - 1 / 2 x - 5 /2
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Which equation represents the written description?
Seven times the difference between 35.8 and a number is equal to 53.4
7(35.8) − m = 53.4
7(35.8 − m) = 53.4
7(m − 35.8) = 53.4
7m − 35.8 = 53.4
Answers
Answer:
the answer to the question is 7(35.8-m)53.4)
Answer:
the answer to the question is 7(35.8-m)53.4)
Step-by-step explanation:
A cube is being compacted. Given that the volume decreases at a rate of 2 cubic meters per minute, find the rate of change of an edge of the cube when the volume is exactly 27 cubic meters.
Answers
The rate of change of an edge of the cube is 0.074 m/min.
What is the rate of change of volume of cube?The rate at which the volume of the cube changes is calculated as follows;
dv/dt = 2 m³/min
where;
v is the volume of the cubeThe length of edge of the cube will be denoted with a, and it is related to the volume of cube in the following equation.
v = a³
a = v^¹/₃
where;
a is the length of the edgeThe change in the edge with volume;
da/dv = 1/3 (1/v)^2/3
The change in edge of the cube with time is given as;
da/dt = da/dv . dv/dt
da/dt = 1/3 (1/v)^2/3 x 2 m³/min
da/dt = 1/3 (1/27)^2/3 /m² x 2 m³/min
da/dt = 1/27 x 2 m/min
da/dt = 2/27 m/min
da/dt = 0.074 m/min
Thus, the rate at which the edge of the cube changes with time is smaller compared to the volume.
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The surface area of a cylinder = 2ny? + 2rh. Use 3.14 for n. What is the
surface area of this cylinder? You may use the calculator tool in the menu.
Answers
The surface area of this cylinder is 6.28y? + 2rh square units.
What does a cylinder's smooth surface look like?
A cylinder has a curving surface that unfolds into a rectangle and two flat surfaces that are both circular.
Given:
The surface area of a cylinder = 2ny? + 2rh.
n = 3.14
therefore putting the value of n
we get,
=2 . 3.14 . y? + 2rh
=6.28y? + 2rh
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90 is what percent of 81?
Answers
Step-by-step explanation:
did you change the reference number ?
I think the original question was "90 is how many % of 80 ?"
now it is 81.
in % calculations the most important things to identify :
what are 100% (or any other reference % level).
then what is 1%.
and then multiply this 1% by the desired number of % or divide the target number by this 1% to find out how many % the target number is.
in our case here
100% = 81
1% = 100%/100 = 81/100 = 0.81
how many % are 90 ?
well, as many as how often 1% fits into these 90 :
90/0.81 = 111.111111111... %
when the reference was 80, then we had
90/0.8 = 112.5%
Determine how many outfit outcomes are possible with the choices of 3 pairs of pants, 4 shirts, and 3 pairs of shoes.
Answers
Number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.
As given in the question,
Number of choices given
Possibilities with the choices
Number of pairs of pants 'n' = 3 pairs
Number of shirts 'p' = 4 shirts
Number of pairs of shoes 'r' = 3 pairs of shoes
Using Fundamental counting of Principle
Total number of outfit outcomes with the given choices
= n × p × r
= 3 × 4 × 3
= 36 outfits.
Therefore, number of outfit outcomes are possible with the choices of 3 pairs of pants , 4 shirts and 3 pairs of shoes are equal to 36 outfits.
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A city is paving a bike path. The same length of path is paved each day. After 4 days, 15 miles of path remain to be paved. After 6 more days, 12 miles of path remain to be paved. Find the average rate of change.
Answers
15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days. The average rate of the change is 24.
Given that,
The paving of a bike route by a city. Every day, the same amount of the path is paved. 15 km of walkway still need to be paved after 4 days. There are still 12 miles of trail to be paved after another 6 days.
We have to find the average change rate.
1st we find the slope with the points (4,15) and (6,12).
Slope =[tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
Slope=[tex]\frac{12-15}{6-2}[/tex]
Slope=-3/4
Now,
y=mx+b
15=-3/4(4)+b
b=15+3
b=18
We got the equation of line as y=-3/4x+18
Now take y=0
0=-3/4x+18
-3/4x=-18
x=(18×4)/3
x=72/3
x=24
Therefore, the average rate of the change is 24.
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4. Brianna deposited $2,000 into a savings account that earns
5% simple interest. How much interest did he earn after three
years?
To on
Answers
Answer:
Step-by-step-learn is 4
Multiplying Rational Numbers- 1 3/4 (-2 1/7)
Answers
The rational numbers - 1 3/4 (-2 1/7) are multiplied to give 105/28
What is a fraction?A fraction can be defined as the part of a whole element.
There are several types of fractions, which includes;
Mixed fractionsSimple fractionsImproper fractionsProper fractionsComplex fractionsWhat are rational numbers?Rational numbers are defined as types of real numbers that are in form of fractions.
For instance: a/b where a is not equal to zero.
Given the rational numbers;
- 1 3/4 (-2 1/7)
To determine the product, take the following steps
Turn into improper fractions
-7/4 × -15/ 7
Now, multiply the numerators and denominators
105/28
Hence, the value is 105/28
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can anyone tell my how they came up with the net force? (purple arrow)
Answers
Answer:
5 m/s
Step-by-step explanation:
1. 3² + 4² = 25
2. √25 = 5
Last year, Ken bought a mountain bike for $400. It is now worth $320. What percent
did the value of Ken's bike depreciate over the past year, to the nearest whole
percent?
Answers
The percent by which the value of Ken's bike depreciated over the past year is 20%.
What is the percentage deprecation?
Depreciation is the decline in the value of an asset with the passage of time. Depreciation is as a result of wear and tear of an asset. The price of an item would decline when it depreciates.
Percentage is the fraction of an amount that is expressed as a number out of hundred. Percentage is used to measure the frequency of data. The sign that represents percentage is %. To convert a number to percentage, multiply the number by 100.
Percent depreciation = (value of the mountain bike today / value of the mountain bike last year) - 1
($320 / $400) - 1 = -0.20
0.20 x 100 = 20%
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What is the least common multiple of 10 and 20?
Answers
Answer:
20
Step-by-step explanation
We need to find the multiples of 10 and 20 (multiples of 10 = 10, 20, 30, 40; multiples of 20 = 20, 40, 60, 80) and choose the smallest multiple that is exactly divisible by 10 and 20, i.e., 20.
Answer:
20
Step-by-step explanation:
First, find the factors of both 10 and 20
Factors of 10: 1, 2, 5, 10
Factors of 20: 1, 2, 4, 5, 10, 20
Notice any common factors?: 1, 2, 5, 10
Now multiply the greatest common factor, 10, with another even number to hopefully get 20: 10*2=20.
Hence, the least common multiple is 20.