The equation of the straight line is 3y + 2x = 15
The generic form of a straight line, Ax + By = C, is also the typical form for two-variable linear equations.
Standard form is used, for instance, in the linear equation 4x+7y= 1. This method makes it easy to find the two intercepts (x and y) of an equation.
Y = mx + c is the cartesian equation for a straight line, where m denotes the gradient or slope of the line and c denotes the location of its y-axis intersection.
Two geometrical objects are perpendicular if they cross at a right angle.
We are aware that the product of the slopes of two lines when they are perpendicular equals -1.
The given straight line is of the form y =3/2 x - 1 .
Slope of the straight line = 3/2
Slope of the perpendicular(90°) line (m) = -2/3
The equation of a line is formulated by :
y -y₁ = m (x - x₁ )
The straight line passes through (-3 , 7)
∴y - 7 = -(2/3) (x + 3 )
or, -2x - 6 = 3y - 21
or, 3y + 2x = 15
Therefore the equation of the straight line is 3y + 2x = 15 .
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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.
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!
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]
what is7.9 times 0.99
Answer:
7.821 or 7821/1000
Step-by-step explanation:
Answer:
7.821
Step-by-step explanation:
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.
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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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
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:
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
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:
is 4.887888 a rational number
90 is what percent of 81?
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%
equation. h(x) = x - 11
Answer:
6
Step-by-step explanation:
Let the required input be y.
[tex]h(y)=y-11=-5 \\ \\ y=6[/tex]
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.
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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pleaseee help, question what is the sum of 4x^2 + 2x - 5 and 7x^2 - 5x + 2
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"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?
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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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.
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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Multiplying Rational Numbers- 1 3/4 (-2 1/7)
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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Exterior angle, theorem, and triangle sum theorem
Answer:
x = 4Step-by-step explanation:
It is assumed you are looking for the value of x.
According the diagram, we have:
∠JEF is exterior angle to triangle EFG and ∠F and ∠G are remote interior angles.Property of exterior angle - it is same as the sum of remote interior angles.
Set equation:
m∠F + m∠G = m∠JEF16x + 4 + 14x + 6 = 13030x + 10 = 13030x = 120x = 4It is easy to calculate the unknown angle measures if needed:
m∠F = 16*4 + 4 = 68m∠G = 14*4 + 6 = 62The 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
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:
A line that includes the points (c, -10) and (-8,-8) has a slope of -1/8 what is the value of c
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
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
Answer:
Step-by-step-learn is 4
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.
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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B. What is the rate of change of the line that contains the points (2, 4), (6, 6), (12, 9)??
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]
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?
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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What is the least common multiple of 10 and 20?
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.
mp Learning
A fair costs $28 for admission plus $3 for each roller coaster ride.
Given that x represents the number of roller coaster rides, choose the algebraic expression that models this situation.
A
B
D
E
28x + 3
31x
31
28 + 3x
You answer is: 28 + 3[tex]x[/tex]
Since $28 is a one-time fee and does not have to be paid again for each and every ride, it does not need a variable in front of.
But for every ride you want, you pay $3 so you need the variable "[tex]x[/tex]" which represents how many times you ride.
For example, if you ride the roller coaster once, your total amount, in dollars, will be:
T = 28 + 3 * (1)
T = $31
But if you ride the roller coaster 3 times, your cost, in dollars, will be:
T = 28 + 3 * (3)
T = 28 + 9
T = $37
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?
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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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?
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.
I need this answered please
Answer:
x=45
Step-by-step explanation:
20-.24=9.2
can anyone tell my how they came up with the net force? (purple arrow)
Answer:
5 m/s
Step-by-step explanation:
1. 3² + 4² = 25
2. √25 = 5
What's 4/9+9/18 please help with this thanks you
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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The coordinates of point T are (0,5). The midpoint of ST is (5,-8). Find the coordinates of point S.
The other endpoint is
(Type an ordered pair.)
... HELP PLS!!!!
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?
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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