The system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 has the following solution: (x, y) = (1 / 24, 7 / 8)
How to solve a system of linear equations
In this question we find the case of a system of two linear equations with two variables, this case may have an unique solution. This system can be solved by algebraic properties.
First, write the system of linear equations:
4 · y - 12 · x = 3
y + 3 · x = 1
Second, clear y in the second equation:
y = 1 - 3 · x
Third, substitute in the first equation:
4 · (1 - 3 · x) - 12 · x = 3
Fourth, expand the expression and clear variable x:
4 - 12 · x - 12 · x = 3
4 - 24 · x = 3
24 · x = 4 - 3
24 · x = 1
x = 1 / 24
Fifth, determine the value of variable y:
y = 1 - 3 · (1 / 24)
y = 1 - 1 / 8
y = 7 / 8
The solution to the system of linear equations 4 · y - 12 · x = 3 and y + 3 · x = 1 is (x, y) = (1 / 24, 7 / 8).
RemarkThe statement reports several typing mistakes. The system of linear equations is shown below:
4 · y - 12 · x = 3
y + 3 · x = 1
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Find the equation of this line.
y =
x +[]
Simplify the fractional part.
Answer:
y = 1/3x +2
Step-by-step explanation:
when x =o, y=2
when x= -6, y=0
so slope is always the difference between the Ys divided by diff b/w the Xs
so the slope is (2-0)/(0-(-6)) = 1/3
the intercept by definition is when x=0, so it's 2
so Y = 1/3 X +2
X+6y=-2 show ur work
The equation when making x the subject is X = -2 - 6y
How to make x the subjectTo do this, we would have to take the values that are in the left hand side to the right hand side. When we do this, the signs on the left hand side would have to change
X+6y=-2
we have to take +6y to the right hand side.
When the positive sign crosses the equal sign it becomes negative
X = -2 - 6y
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X+6y=-2 show ur work make x the subject
Rosa gasto 11.52 en 8 collares de dulces para cada una de sus dos amigas cuánto costó cada collar
Answer:
1.44
Step-by-step explanation:
11.52/8=1.44
Luke says 1/5 +2/5 =3/10 Describe the error .
True or false? A hair clip is 1 4/7 inches long. A paper clip is 5/6 inches long. The two items are about the same length.
A bakery used 30% more sugar this month than last month.If the bakery used 560 kilograms of sugar lost month,how much did it use this month?
728 kilograms of sugar is used in this month.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a bakery used 30% more sugar this month than last month.
Let us convert 30% to decimal.
Divide 30 by 100
30/100=0.3
the bakery used 560 kilograms of sugar last month we have to find the amount of sugar used this month.
Now multiply 30% of 560
0.3×560
168.
So now 560+168=728 is the amount of sugar used this month.
Hence, 728 kilograms of sugar is used in this month.
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Diya earned a 36 out of 80 on a test. Her teacher offered extra credit that would allow Diya to double her score. What score could she earn if she completes the extra credit?
Diya could earn 72 marks out of 80 after getting the extra credits.
What are extra credits in School?Teachers employ extra credit for a variety of reasons. For example, it may be felt that students who are highly capable may benefit from an additional challenge that might not be suitable as required work for all students. Extra credit may also be used as a way to allow a student to improve their grade after a weak performance earlier in a course. In both of these cases, extra credit can promote differentiated instruction by factoring in optional work in the assessment of student performance.
Given here: Diya scores 36 out of 80 on a test.
Also, her teacher gives her extra credit with which she could double her marks.
If Diya doubles her marks then her total marks would be 72
Therefore the increase in her marks is 72-36=36
She could earn another 36 credits.
Thus her score after the extra credit is equal to 72
Hence, Diya could earn 72 marks out of 80 after getting the extra credits.
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now, set up an integral to compute the volume of this solid, then evaluate it to find the volume of the solid: V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx an integral that gives the volume of the solid is:
The volume of the solid is equal to 96 cubic units.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
Set up an integral to compute the volume of the solid.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx
Rewrite the integral with a function of x in terms of a single power of x.
V= Integral (from x=2 to x=-4) of (8-x^2-2x)^2 dx = ∫(8-x^2-2x)^2 dx
= 1/3*∫(24-6x^2-12x)dx
Integrate the function.
= 1/3*[24x-2x^3-6x^2] from x=2 to x=-4
Evaluate the integral to find the volume of the solid.
= 1/3*[(-6)-(-140)-(-136)]
= 1/3*(288)
= 96 cubic units
The volume of the solid is equal to 96 cubic units.
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If the sun is 69° above the horizon, find the length of the shadow cast by a building 91 ft tall. Round your answer to the nearest tenth.
If the sun is 69° above the horizon, the length of the shadow cast by a building 91 ft tall
How to find the length of the shadow?You should understand that the length of the shadow is the distance between a point to the foot of the tenth
This makes an angle of depression, with 69 degrees
Remember that the angle on top of the tenth is 90-69 = 21 degrees
therefore, using the trigonometrical ratio
We have Tan∅ = opposite of adjacent
Tan 21⁰ = x/9
x= 9*tan 21⁰
x = 9*0.3839
The distance is 3.45
Therefore the length of the shadow cast by a building is approximately 3.5 feet long
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Can someone explain to me why the answer is 90 and not 1080? I think it has to do with the inches and ft. But I don’t remember how you solve it.
Answer:
You are correct
Step-by-step explanation:
You are correct sir. They want the answer in feet, so everything on that triangle has to be converted into feet.
There are 12 inches in a foot. If we do 108/12 we get 9 feet.
a movie theater has 7 shows a day 4 days per week and 11 shows a day 2 days per week together how many shows in 6 days
The movie theater will have 50 shows in 6 days
To find the total number of shows in 6 days, we need to calculate the number of shows for each type of day (4 days per week with 7 shows per day and 2 days per week with 11 shows per day) and then add them together.
First, let's calculate the number of shows for the 4 days per week with 7 shows per day:
4 days per week x 7 shows per day = 28 shows per week
Next, let's calculate the number of shows for the 2 days per week with 11 shows per day:
2 days per week x 11 shows per day = 22 shows per week
Now, we can add the number of shows for each type of day together to find the total number of shows in 6 days:
28 shows per week + 22 shows per week = 50 shows in 6 days
We used multiplication to calculate the number of shows per week for each type of day (by multiplying the number of days by the number of shows per day) and then added the two results together to find the total number of shows in 6 days.
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a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side.
Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
A triangle's third side must be longer than the difference between the other two sides' lengths and shorter than the total length of the other two sides. The two side lengths in this situation are 18 and 26. The third side must be greater than 8 because the difference between them is 8. The third side must be less than 44 because the total length of the first two sides equals 44. Therefore, the third side length might be any side length between 8 and 44.Since the longest side cannot be longer than the total of the other two sides, the third side's potential lengths range from 8 to 44.
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The complete question is
a triangle has one side length of 26 and another side length of 18. select all of the possible lengths of the third side potential lengths range from 8 to 44?
8-3(4-4)+2*4*6 :< i need help man
Answer:
[tex]\sf 56[/tex]Step-by-step explanation:
[tex]\sf 8-3(4-4)+2*4*6[/tex]
[tex]\sf 8-(3)(0)+(2)(4)(6)[/tex]
[tex]\sf 8-0+(2)(4)(6)[/tex]
[tex]\sf 8+(2)(4)(6)[/tex]
[tex]\sf 8+(8)(6)[/tex]
[tex]\sf 8+48[/tex]
[tex]\sf 56[/tex]
Ann and leila are driving separate cars to New York. They begin the trip with full gas tanks. The amount of gas (in gallons) remaining in the tank of each car depends on the number of miles driven, as shown below.After 225 miles driven, which car will have less gas remaining?After how many miles will the tanks contain the same amount of gas? If the number of miles driven is less than this, which car will have more gas remaining?
After 180 miles both the cars' tanks contain same amount of gas.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
Given that, Ann and Leila are driving separate cars to New York. They begin the trip with full gas tanks.
From the given graph,
After 360 miles Ann's car has 2 gallons of gas.
After 180 miles both the cars' tanks contain same amount of gas.
When they travelled less than 180 miles, Leila's car has more gas.
Therefore, after 180 miles both the cars' tanks contain same amount of gas.
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Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 6.00 inches at the top and a height of 10.0 inches. At the instant when the water in the container is 8.00 inches deep, the surface level is falling at a rate of 0.9 in./sec. Find the rate at which water is being drained from the container.
The rate at which the water flow from the given volume is 21.72 in³/sec
What is rate at which the water flowTo find the rate at which water is being drained from the container, we first need to find the rate at which the water level is falling and then use that to calculate the volume of water being drained per unit of time.
We know that the surface level is falling at a rate of 0.9 inches per second and that the container has the shape of an inverted right circular cone. The volume of a cone is given by the formula:
V = (1/3) * π * r^2 * h
Where V is the volume, π is pi (approximately 3.14), r is the radius of the base, and h is the height of the cone.
We can use this formula to find the volume of the container when the water level is 8 inches. The radius at this point is 6 * (8/10) = 4.8 inches and the height is 8 inches.
V = (1/3) * π * (4.8 inches)^2 * 8 inches = 193.02 inches³
Now that we know the volume of the container when the water level is 8 inches, we can use the rate at which the water level is falling (0.9 inches per second) to find the rate at which the water is being drained.
The rate at which water is being drained = rate of change of volume / rate of change of height = dV/dt = dV/dh * dh/dt = -dV/dh * dH/dt
Where dV/dh is the derivative of volume with respect to height, dH/dt is the rate of change of height.
-dV/dh = -(1/3) * π * (4.8 inches)^2 = -24.13 in³
dH/dt = -0.9 inches/sec
The rate at which water is being drained = -dV/dh * dH/dt = -24.13 * -0.9 inches/sec = 21.72 in³/sec
So the rate at which water is being drained from the container is 21.72 in³/sec
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A piece of material measures 38 inches. Courtney cuts the piece of material into two pieces. One piece measures 19 inches. Write an addition equation that could be used to find the length, m, of the other piece of material.
Answer:
As a whole, the piece first measured 38 inches. No matter how many times you cut it, all of the pieces will still add up to 38 inches. You know that 19 inches is the length of one of the two pieces, so all you need to find is the other unknown piece. Add the two together, with m being the unknown length.
19+m=38
If you want to solve the equation, just subtract 19 from both sides.
19+m=38
m=19
the price of a new car is 23% more than the price of a 3-year old car. if the price of the new car was $12,400, what is the price of the 3-year old car?
Answer: To find the price of the 3-year old car, we need to determine how much less it is than the new car, which is 23% of the price of the new car.
We can start by finding the value of 23% of the price of the new car, which is: $12,400 x 0.23 = $2,832
Now we know that the price of the 3-year old car is $2,832 less than the price of the new car. To find the price of the 3-year old car, we subtract $2,832 from the price of the new car: $12,400 - $2,832 = $9,568
So the price of the 3-year old car is $9,568.
Step-by-step explanation:
QUICK!!! WHAT IS -2 2/5 times -1/3
(Please show work)
Select the correct answer. An archway is modeled by the equation y = -2x2 + 8x. A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0. If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, at what distance from the ground level is point B? A. 8 units B. 6 units C. 5 units D. 3 units
Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Using the quadratic equation the distance of point B from the ground level is D. 3 units
What is an equation?An equation is a mathematical function that shows the relationship between two variables.
How to find the distance of point B from the level ground?Since an archway is modeled by the equation y = -2x² + 8x.
A rod is to be placed across the archway at an angle defined by the equation x − 2.23y + 10.34 = 0.
If the rod is attached to the archway at points A and B, such that point B is at a higher level than point A, we desire to find the distance of point be from the ground. To do this , we proceed as follows.
Since we have the equations
y = -2x² + 8x and x - 2.23y + 10.34 = 0Substituting y into the second equation, we have
x - 2.23y + 10.34 = 0
x - 2.23(-2x² + 8x) + 10.34 = 0
x + 4.46x² - 17.84x + 10.34 = 0
4.46x² - 16.84x + 10.34 = 0
To find the points a and B, we solve for x where both equations intersect.
So, using the quadratic formula, we solve for x
[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex] where a = 4.46, b = -16.84 and c = 10.34
So, substituting the values of the variablers into the equation, we have that
[tex]x = \frac{-(-16.84) +/-\sqrt{(-16.84)^{2} - 4\times4.46\times10.34} }{2\times4.46}\\= \frac{16.84 +/-\sqrt{283.5856 - 184.4656} }{8.92}\\= \frac{16.84 +/-\sqrt{99.12} }{8.92}\\= \frac{16.84 +/-9.96 }{8.92}\\x = \frac{16.84 + 9.96 }{8.92} or x = \frac{16.84 - 9.96 }{8.92}\\x = \frac{26.8}{8.92} or x = \frac{6.88}{8.92}\\x = 3.004 or x = 0.771[/tex]
Since B is higher, we take the higher value x = 3.
So, the distance of point B from the ground level is D. 3 units
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Quadrilateral EFGH is a rhombus.
Which additional fact would prove that
EFGH is a square?
O A) EG ~ FH
O BEG 1 FH
O C) EG bisects LFEH
O DILFEH ~ LFGH
The additional fact that would prove that
EFGH is a square is D) IFLEH ~ LFGH.
What is a quadrilateral?A quadrilateral is a plane figure with four edges and four corners, also known as vertices. The quadrilateral's four vertices or corners all have angles.
If a quadrilateral is a rhombus, that means opposite sides are congruent, but it does not mean that all angles are congruent. In order to prove that EFGH is a square, we need to show that all angles are congruent. The statement "IFLEH ~ LFGH" implies that all angles in the quadrilateral are congruent, since it states that opposite angles are congruent, which is one of the defining characteristics of a square. Therefore, statement D is the correct answer.
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Sarah ordered 37 shirts that cost $9 each. She can sell each shirt for $16. She sold 30 shirts to customers. She had to return 7 shirts and pay a $3 charge for each returned shirt. Find Sarah's profit.
Sarah's profit, given the shirts sold, the cost of the shirts, and the shirts returned, can be found to be $ 126
How to find the profit ?First, find Sarah's cost :
= Cost to buy the shirts + cost to return the shirts
= ( 37 x 9 ) + ( 7 x 3)
= 333 + 21
= $ 354
The revenue made from selling the shirts was :
= 30 x 16 per shirts
= $ 480
Sarah's profit is therefore:
= 480 - 354
= $ 126
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in the x y coordinate plane, which of the following points must lie on kx + 3y + 6 if k = -1/2
Answer:
honestly, I got no idea. I can tell you though - go us Desmos kid. it'll help you more than any person in this platform.
don't thank me
Step-by-step explanation:
Desmos
use Desmos
please solve quickly! (15 points)
Answer:
Step-by-step explanation:
36
(
x
+
3
)
2
(
x
−
3
)
2
Select all ratios equivalent to 7:6.
The ratios equivalent to 7:6 can be expressed as a) 14 : 12
What does the idea of ratios mean?The concept that will be used here is ratio. The proportion is an equation that demonstrates how two ratios are equivalent, but the notion of ratio defines us to compare two quantities.
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
From the ratios equivalent to 7:6 which can be written as 7/6
Then we consider option A , 14/12 = 7/6 ( divide the denominator and numerator by factor of 2.
Option B; 2 : 18 = 2/18 = 1/9
option C : 28 : 26 = 16/ 13
option D : 30 : 25 = 6/5
Therefore, option A is correct.
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Missing options:
a) 14 : 12
b) 2 : 18
c) 28 : 26
d) 30 : 25
What is the equation of the line that passes through the point (8, 4) and has a slope
of o?
The equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.
What is the slope intercept?
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
The line passing through the point (8, 4) and having a slope of 0 is a horizontal line which is parallel to the x-axis. The slope (m) of this line is 0.
The point-slope form of this line would be:
(y - 4) = 0(x - 8)
Simplifying this, we get:
y = 4
Hence, the equation of the line passing through the point (8, 4) and having a slope of 0 is y = 4.
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How the expressions are equivalent
Equivalent equations are algebraic equations that are having identical roots or solutions
What are Equivalent Expressions?Equations in algebra with the same roots or solutions are said to be equivalent. An analogous equation is one that is created by adding or removing the identical number, symbol, or expression from both sides of an equation. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value.
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
To determine which complex expression is the simple expression's equivalence:
Give any coefficients a distribution:
a(bx±c)=abx±ac
X-terms and constants should be combined with any other like terms on either side of the equation.Put the terms in the same order, with the x-term typically coming before the constants.The two phrases are equal if and only if each of their terms is the same.To know more about Equivalent expressions, refer to:
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Find the measure of the angle. Round to the nearest degree
Answer:
59.036
Step-by-step explanation:
tanΘ = opposite/adjacent
Θ =tan⁻¹(opposite/adjacent)
tan⁻¹(10/6) - 59.03624347
Find the plane determined by the intersecting lines.
L1 x= -1 + 3t y = 2+2t z=1-t
L2 x=1-4s y=1+2s z=2-2s
In a plane, intersecting lines are any two or more lines that cross each other. The point of intersection is the common point shared by all intersecting lines.
What are Intersecting Lines?In a plane, intersecting lines are those that cross one another three times or more. The point of intersection is the shared location between all intersecting lines that exists on all intersecting lines.Point O represents the point of intersection where lines P and Q meet in this instance.Specifications of intersecting linesWhen two or more lines intersect, they always do so at the same location.Any angle may be used to intersect the lines. Always more than 0° and less than 180° is the angle that is generated.Vertical angles are created by two intersecting lines. There is a common vertex between the opposing vertical angles (which is the point of intersection).Vertical angles a and c are equivalent in this case. Additionally, b and d have equal vertical angles and are vertical angles.A plus D equals a straight angle of 180 degrees.To Learn more About intersecting lines refer To:
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please help will mark BRAINLIEST
The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°
What exactly is the degree formula?
Yes, we can use the radian-to-degree formula to convert a negative radian to a degree. Degrees = Radians 180 / is the formula, and it may be used for both positive and negative values. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees).
These are referred to as parallels. A circle of latitude is an imaginary ring that connects all places that share a parallel. The Equator is the 0 degree latitude line. Each parallel is one degree north or south of the Equator, with 90 degrees north and 90 degrees south respectively.
Hence, The sum of the angles formed on the same side of the transversal which are inside the two parallel lines is always equal to 180°
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Tyrone put 1/3 teaspoon of salt in a batch of cookie dough. He thought that might not been enough salt, so he added another 1/4 teaspoon. How much salt did Tyrone use in total?
Answer:
7/12 of salt.
1/4 + 1/3 =
1/3 + 1/4 =
4/12 + 3/12 = 7/12.
Step-by-step explanation:
Hope it helps! =D