The solution of the system of equations is x = 1 and y = -1.
What is a two-variable linear equation?
If an equation is written in the form ax + by + c=0, where a, b, and c are real integers and the coefficients of x and y, i.e., a and b, respectively, are not equivalent to zero, it then is said to be a linear equation in 2 factors. Examples of two-variable linear equations are 10x+4y = 3 and -x+5y = 2.
SOLUTION TO WORK OUT
the equations are resolved
8x + 3y = 5 & 3x − 2y = 5
EVALUATION
The equations in the given system are
8x + 3y = 5 - - - - - - - (1) (1)
3x − 2y = 5 - - - - - - - (2) (2)
Equation 1's two sides multiplied by two gives us
16x + 6y = 10 - - - - - - (3) (3)
Equation 2's two sides are multiplied by three to get
9x - 6y = 15 - - - - - - (4) (4)
Equation 3 and Equation 4 together give us
25x = 25
⇒ x = 1
Equation 1 is completed when x = 1.
8 + 3y = 5
⇒ 3y = 5 - 8
⇒ 3y = - 3
⇒ y = - 1
FINAL RESPONSE
Consequently, the needed answer is x = 1 and y = - 1.
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PLEASE HELP PLSSS
Given the coordinates below, determine if ΔFGH and ΔJKL are congruent. If they are, give the reason, if they aren't choose "not congruent".
F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)
*enter your lengths to the NEAREST TENTH
FG=
GH=
FH=
JK=
KL=
JL=
ARE THE TRIANGLES CONGRUENT BY
SSS
SAS
OR
NOT CONGRUENT
Hence, the two triangles have the same side length so they are congurent triangles.
What is the congurency?
The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes, they remain equal.
Here given triangles are
In Δ[tex]FGH[/tex] and Δ[tex]JKL[/tex] are congruent. If they are, give the reason, if they aren't choose "not congruent".
[tex]F(-5, 10), G(-2, 2), H(-9, -7), J(0, -5), K(9, 2), L(-8, -2)[/tex]
We know the distance formula
ie., [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Length in between [tex]FG[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-2-(-5))^2+(2-10)^2}\\\\d=\sqrt{(-2+5)^2+(2-10)^2}\\\\d=\sqrt{(3)^2+(-8)^2}\\\\d=\sqrt{9+64}\\\\d=\sqrt{73}[/tex]
Length in between [tex]GH[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-9-(-2))^2+(-7-2)^2}\\\\d=\sqrt{(-9+2)^2+(-7-2)^2}\\\\d=\sqrt{(-7)^2+(-9)^2}\\\\d=\sqrt{49+81}\\\\d=\sqrt{130}[/tex]
Length in between [tex]HF[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-5-(-9))^2+(10-(-7))^2}\\\\d=\sqrt{(-5+9)^2+(10+7)^2}\\\\d=\sqrt{(4)^2+(17)^2}\\\\d=\sqrt{16+289}\\\\d=\sqrt{305}[/tex]
Length in between [tex]JK[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(9-0)^2+(2-(-5))^2}\\\\d=\sqrt{(9)^2+(2+5)^2}\\\\d=\sqrt{(9)^2+(7)^2}\\\\d=\sqrt{81+49}\\\\d=\sqrt{130}[/tex]
Length in between [tex]KL[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-8-9)^2+(-2-2)^2}\\\\d=\sqrt{(-17)^2+(-4)^2}\\\\d=\sqrt{289+16}\\\\d=\sqrt{305}[/tex]
Length in between [tex]LJ[/tex] is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\d=\sqrt{(0-(-8))^2+(-5-(-2))^2}\\\\d=\sqrt{(0+8)^2+(-5+2)^2}\\\\d=\sqrt{(8)^2+(-3)^2}\\\\d=\sqrt{64+9}\\\\d=\sqrt{73}[/tex]
Therefore, [tex]FG[/tex]≅[tex]LJ-GH[/tex]≅[tex]JK-HF[/tex]≅[tex]KL[/tex]
Hence, the two triangles have the same side length so they are congurent triangles.
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Lupita ride a taxi that charge a flate rate of $6. 75 plu $3. 20 per mile. If the taxi charge lupita $40. 03 in total for her trip , how many mile i her ride ?
Based on the charged amount, Lupita drove 8.76 miles.
Let us assume the number of miles rode bh Lupita be x. Forming the equation now -
Total charge = flat rate + cost per mile × number of miles
Keep the values in above mentioned equation to find the value of x
40.03 = 6.75 + 3.20×x
Rewriting the equation with respect to x
3.20x = 40.03 - 6.75
3.20x = 33.28
Shifting 3.20 to Right Hand Side of the equation
x = 33.28 ÷ 3.20
Performing division on Right Hand Side of the equation
x = 8.76 miles
Thus, Lupita drove 8.76 miles.
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Please help me out with this
Answer:
6\sqrt3
Step-by-step explanation:
Since 30-60-90 tri, small side is 6.
This means x=[tex]6\sqrt3[/tex]
Answer:
[tex]x = 6\sqrt{3}[/tex]
Step-by-step explanation:
Utilize the trigonometric ratio cosine.
[tex]\cos(30\textdegree ) = \dfrac{x}{12}[/tex]
Solve for x by multiplying both sides by 12.
[tex]12\cos(30\textdegree ) = x[/tex]
[tex]12\left(\dfrac{\sqrt{3}}{2} \right) = x[/tex]
[tex]x = 6\sqrt{3}[/tex]
A segment in the complex plane has a midpoint at â€"1 i. if the segment has an endpoint at â€"5 â€" 7i, what is the other endpoint? â€"9 â€" 15i â€"3 â€" 3i â€"2 â€" 4i 3 9i
The other midpoint is 3+9i in the given complex plane.
Given that,
We know that the middle point is: (-1+i)
And the end point is: (-5-7i)
We know that the formula to find the middle point is:
(x1+ x2 /2, z1+z2/2)
We wish to find the point x1,z1
So we can write the following equation
x1 + (-5)/2 = -1 --------> 1
and
z1 + (-7i)/2 = i ----------->2
Now we clear x1 from equation (i) and clear z1 from equation (ii)
For equation (i) we have:
-2 = x1 -5
x1 =3
For equation (ii) we have:
2i = z1 - 7i
z1 = 9i
Then the initial point is: 3+9i
So, The other endpoint is 3+9i
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Define a variable and write an algebraic expression for each phrase.
two points fewer than 3 times the number of points scored before
The variable that can be used to represent the number of points scored before is x and the algebraic expression is (3x - 2).
How to write algebraic expression?Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
let
Number of points scored before = x3 times the number of points scored before
= 3 × x
= 3x
two points fewer than 3 times the number of points scored before
= 3x - 2
Other examples of algebraic expression are:
2t - 5 + 3t
65x + y - 8y + 5x
In conclusion, the expression can be written in algebra form as 3x - 2
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A test has 20 questions.
If Peter gets 80\%80% correct, how many questions did peter miss?
Which symbol correctly compares these two fractions?
6/10 ? 5/7
A. <
B. =
C. >
Answer:
A. <
Step-by-step explanation:
Hope this helps! ^^
Answer:
>
Step-by-step explanation:
2/5 is greater than 7/10. Therefore, the best symbol to compare the two would be the greater than symbol, >.
Write the equation of the line that passes through (7,- 4) and
(-1, -2) in slope-intercept form.
help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
In 2001, 150 000 students were expected to enroll at the institution.
For the 2018 academic year, 468000 students are anticipated to enroll at the
How can the population size be calculated?The size of a population refers to its total number of members. The average person count per unit of area or volume is referred to as population density.
a. The formula to solve the question is as follows:
y = 123.1(1.069)x.
Hence x is the amount of time that was passed.
2001 - 1998 = 3y = 123.1 (1.069)³y
= 123.1 x 1.2216115y = 150.4
In 2001, the school is expected to have 150000 students enrolled.
b. 2018
The distinction x, or the variation between the years we are to calculate, must be considered:
x = 2018 - 1998
= 20.y = 123.1 x (1.069)²⁰y
= 123.1 x 3.798y
= 467.5468
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How do you find the mean absolute deviation on a number line?.
We can find the mean absolute deviation by the dot plot of the number line.
The mean absolute deviation is the average of all the variations in a dataset. It can be defined as a measure of finding out spread out the values of a dataset are from the mean. The mean is calculated by adding the absolute deviations and dividing the sum by the number of values in the data set.
Absolute mean deviations can be represented graphically on a number line from a dot plot. These dot plots can be used to find out the mean absolute deviation on a number line.
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What is square figure in math?.
Square is the geometrical figure with certain properties which distinguishes from other geometrical figures.
What is square ?In geometry, a square is a two-dimensional plane shape with four equal sides and four equal angles that add up to 90 degrees. The characteristics of a rectangle and a square are somewhat similar, although a rectangle only has its opposite sides equal. As a result, a rectangle is only referred to as a square if its four sides are of the same length.
Square
Number of sides = 4Number of vertices = 4Area = Side2Perimeter = 4(Side)Below is a list of a square's key characteristics:
The inner angles are all equal to 90 degrees.The square's four sides are equal to each other or congruent.The diagonals of the square cut each other at a 90° angle, and the opposite sides of the square are parallel to one another.There is an equal distance between the square's two diagonals.4 sides and 4 vertices make up the square.The square is split along its diagonal into two identical isosceles triangles.The square's sides are smaller than the diagonal lengthTo learn more about Square, visit:
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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $45 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $250, how many hours did the plumber work? Write and solve an equation to determine the number of hours worked by the plumber.
I need an answer asap
Answer: 4.1 hours (4 hours and 6 minutes)
Equation: 250=50x+45
Step-by-step explanation:
The equation would be: 250=50x+45
x represents the number of hours worked
Next, solve your own equation: 250=50x+45
205=50x
4.1=x
PLEASE HELP I need to pass
1. Suppose a graph passes the horizontal line test: No horizontal line can be
drawn that touches the graph in more than one location. Does this mean that
the graph represents a function? If not, is there anything special about a graph
that passes the horizontal line test? Share your ideas with a classmate.
2. Dotty and Lionel are making a graph comparing a car's age with its gas
mileage. Dotty says the graph should show discrete points because the car's
age is stated in whole numbers of years. Lionel says they should make a
continuous line because age increases gradually, like time. Which student do
you agree with and why?
3. Write two linear functions, f(x) and g(x). For example, f(x) = 3x - 7 and
g(x)=-2x+5. Then see whether f(x) - (-g(x)) is equivalent to f(x)+ g(x). Hint
To find -g(x), just change the signs of all the terms in g(x) Discuss whether
1. When a function passes the horizontal line test, we can infer that its inverse is both known and exists.
You can use the vertical line test to determine whether an expression is actually a function; if it succeeds, it is. If the graph does, in fact, pass the vertical line test before passing the horizontal line test, it is a function. If it also passes the horizontal line test, it is a one-to-one function, which means there is a unique x-coordinate value for every unique y-coordinate value. Only one-to-one functions have an inverse expression that is also a function.
Graph:
A graph is a logical visual representation of any data in mathematics. The correlation between the variable values is depicted on the graph. A graph is used in graph theory to depict a group of items that are interconnected in some way. In essence, the vertices or nodes of the objects are mathematical notions, and the edges are representations of the connections between the nodes. In mathematics and statistics, many graph types are used to visually display data. The study of points and lines is the focus of the field of graph theory. It is a branch of mathematics with a focus on graph analysis. The mathematical truth is clearly illustrated in this artwork. Relationships are studied using the graph theory.
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2. Which of the following is the simplified form of the
expression 5(x-3)-3x+10?
F. 2x-5
G. 5x+7
H. 8x-5
J. 12x+10
K. 22x
Answer:
F is the correct answer
Step-by-step explanation:
5x-15-3x+10
2x-5
Valentina is cycling down a hill fast. To be most efficient, should Valentina use a gear on the back wheel that has a small diameter or a large diameter? Explain.
Valentina should use a gear on the back wheel that has larger diameter to be more efficient
Further explanations to why using larger diameterThe problem deals with circumference of the wheel.
Circumference is a function of diameter such that: A larger wheel will have a larger circumference and a smaller wheel will have a smaller circumference
The wheel is assumed to be a circle and equation of circumference of a circle is pi * diameter
Gear has the function of rotating the wheel when a gear makes a initiates one revolution of the wheel
say wheel x, diameter = 5 and wheel y, diameter = 10
distance covered by one revolution = circumference
circumference of x = pi * 5 = 5pi
circumference of y = pi * 10 = 10pi
comparing both shows that wheel y will cover double the distance of x hence more efficient.
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12▸ A road has a gradient of 1/15 for 90 m. Then there is a horizontal section 130 m long. The final section has a gradient of 1/25 for 200 m. a Find the total height gained from start to finish. b What is the average gradient from start to finish?
The total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
What is an average gradient?
The gradient of a straight line drawn between two points is the average gradient between the two points.
Here, we have
A road has a gradient of 1/5 for 90 m.
Horizontal section 130 m long
The final section has a gradient of 1/5 for 200 m.
First, we will find the total height gained from start to finish
Total height from start to finish = 90 ×1/5 +200 × 1/5
= 18 + 40
Total height from start to finish =58 m
The average gradient from start to finish = 58/(90 + 130 +200)
= 58/420
= 29/210
Hence the total height gained from start to finish is 58m and the average gradient from start to finish is 29/210
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In 2012 there were approximately 800 elves working at the North Pole. A survey found that 88% of these elves enjoyed their work conditions.
Answer:
704 people out of 800
Step-by-step explanation:
88% of 800= 704
Simplify x raised to the negative second power over y raised to the fourth power.
y raised to the fourth power over x raised to the negative second power
y raised to the fourth power over x raised to the second power
1 over the quantity x raised to the second power times y raised to the fourth power end quantity
−x2y4
Answer:
Step-by-step explanation:
(x 2 y) 4 = x2*4 y 1*4 = x 8 y4
An exponent raised to another exponent means to multiply the exponents. If a number does not have a visible exponent, then it is an implied 1.
The required simplified form of the expression is 1 / (x² · y⁴) which is the correct answer would be an option (D).
How to use laws of exponents?When multiplying similar bases, keep the base and add the exponents the same. When comparing one power to another, keep the base constant and multiply the exponents. Keep the base constant when dividing like bases and subtract the denominator exponent from the numerator exponent.
Simplify x raised to the negative second power over y raised to the fourth power.
The expression is given in the question below as:
x⁻² / y⁴
The expression can be simplified as follows:
⇒ x⁻² / y⁴
⇒ (1 / x²) / (y⁴)
⇒ 1 / (x²) · y⁴)
⇒ 1 / (x² · y⁴)
Therefore, the simplified form of the expression is 1 / (x² · y⁴).
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the aquarium has 3 more yellow fish than green fish. 60% of the fish are yellow. how many green fish are in the aquarium? show your work.
The number of green fish are in the aquarium is 6.
Given that,
The aquarium has 3 more yellow fish than green fish.
60 percent of the fish are yellow.
Let us assume the green fishes be x and the yellow fishes are y.
Total no of fished = x + y.
And, y = x + 3
Based on the above information, the calculation is as follows:
Now, put y = x + 3
So,
60%(y+x)=y
[tex]\frac{60}{100}(x+3+x)=x+3[/tex]
60(2x+3)=100(x+3)
120x + 180 = 100x + 300
20x = 120
x = 6
Hence the number of green fishes are x=6
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there is a total of 85 tiles work out the number of blue tiles
The number of blue tiles is 68.
Given:
Red tiles = 1/5 of the total
Total tiles = 85
Red tiles = 1/5*85
= 17.
Number of blue tiles = total tiles - red tiles
= 85 - 17
= 68.
Therefore the number of blue tiles is 68.
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A photocopier take 8 econd to make 20 copie. How long will it take to make 45 copie?
Given that a photocopier takes 8s to make 20 copies and we need to find out how long would it take to make 45 copies .
This can be solved using Unitary Method as ,
To make 20 copies it takes 8 s.
To make 1 copy it would take 8/20 s
Hence to make 45 copies it would take 8/20*45 = 18s
And we are done!
Answer:
45 copies = 18 seconds
Step-by-step explanation:
Time taken to make 1 copy,
→ Total time ÷ Total copies
→ 8 ÷ 20
→ 8/20 seconds
Then the time taken for 45 copies,
→ 45 × (8/20)
→ (45 × 8)/20
→ 360/20
→ 18 seconds
Hence, time taken is 18 seconds.
How do you find the average of 1 to 100?.
The first 100 natural numbers are 1,2,3,...,100 is 50.5.
An average is a single number chosen to represent a group of numbers; it is typically the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.
We know that the sum of the first n natural numbers is = 2n(n+1)
Therefore, the sum of the first 100 natural numbers is = 2×100(101)
=200(101)=20200
Hence, the sum of the first 100 natural numbers is = 20200 = 101
200
Hence, the average of the first 100 natural numbers is = 101 = 50.5
2
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Solve the equation 7x-27<8
Answer:
x < 5
Step-by-step explanation:
Joey has 42 marbles. He has 7 times as many marbles as Sam has. How many marbles does Sam have? *
Answer:
Sam has 6 marbles
Step-by-step explanation:
42 ÷ 7 = 6
7 times means that whatever Joey has it is sams × 7. so to find answer we the do reserve.
PLS HELP WITH THIS MATH
When we multiply the given inequality that is [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex], then we get the required equation as [tex](\frac{-x+5}{2x+6}) ; x[/tex] ≠ [tex]-3,3,-2,-5[/tex]
What is multiplication of inequalities ?If you multiply one side of an inequality by a number, you can multiply the other side of the inequality by the same number .
What is the condition of inequality ?The denominator should not be 0 that is the value of x .
Given: [tex](\frac{x^{2} - 25}{2x^{2} +10x +12})(\frac{x+6-x^{2} }{x^{2} +2x-15})[/tex]
On solving ,we get
[tex]=(\frac{(x+5)(x-5)}{2(x+2)(x+3)}) (\frac{(-1)(x-3)(x+2)}{(x-3)(x+5)})[/tex]
Since denominator cannot be equal to zero.
Therefore x ≠ -2, x ≠ -3
and x ≠ 3, x ≠ -5
So ,x ≠ -2,-3,3,-5
It is the condition for x .
On cancelling common terms ,we get
[tex]=(\frac{(-1)(x-5)}{(2)(x+3)})[/tex]
[tex]=(\frac{-x+5}{2x+6})[/tex]
This is the required equation obtained .
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‼️‼️‼️‼️‼️‼️SOMEONE PLEASE HELP IM BAD AT MATH PLS ITS URGENT ‼️‼️‼️‼️
Answer:
I agree due to everything stated there everything is perpendicular and is equal to the each other.
PLEASE GIVE BRAINLIEST THANK YOU!!!
What is the area of trapezoid ABCD? A (-3,2) B (1,5) C (7,-3) D (0,-2)
The area of the given quadrilateral trapezoid ABCD with vertices A (-3,2) B (1,5) C (7,-3) D (0,-2) will be 37.5 square units.
What is quadrilateral?A quadrilateral is a geometrical 2d shape with four sides, each side being connected and making a close polygon.
In other words, a quadrilateral is a polygon in which four sides, such as a trapezoid, square, and parallelogram, are quadrilateral.
As per the given quadrilateral as trapezoid,
The area of the trapezoid = 1/2 x (sum of parallel length) x perpendicular
The given trapezoid has been drawn below,
The length associated to two points (x₁, y₁) and (x₂, y₂) is given by the formula;
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
The smaller parallel line = 5 unit
Bigger parallel line = 10 unit
Perpendicular distance = 5 unit
Area = 1/2 x (5 + 10) x 5 = 37.5 unit square.
Hence "The area of the given quadrilateral trapezoid ABCD with vertices A (-3,2) B (1,5) C (7,-3) D (0,-2) will be 37.5 square units".
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Solve for the side or angle in the right triangles below. Show all of your work....
1)
X
12
18°
2)
25
10
The side and angle is in the right angle triangle respectively x = 3, 68°.
What is a right angle triangle?
A right triangle, also known as a right-angled triangle, is a triangle with one angle that is a right angle (i.e., a 90-degree angle) and two perpendicular sides.
We have,
[tex]1) Opposite = x, \ Adjustment = 12, \ \theta = 18.\\\\2) Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
How to determine the angle in a right angled triangle,
[tex]Sin (\theta ) = \frac{Opposite}{Hypotenuse}[/tex][tex]Tan (\theta ) = \frac{opposite}{adjacent}[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]1) \ Opposite = x, Adjustment = 12, \ \theta = 18.[/tex]
[tex]cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(\theta)}[/tex]
[tex]Hypotenuse = \frac{Adjacent}{cos(18)}[/tex]
[tex]= 12.61755[/tex]
[tex]Opposite = \sqrt{Hypotenuse^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{12.6175466908592 - 122}[/tex]
[tex]= \sqrt{15.202484496012}[/tex]
∴ [tex]Opposite(x) = 3.89904[/tex]
[tex]2) \ Opposite = 25, \ Adjustment = 10, \ \theta = ?.[/tex]
[tex]Hypotenuse = \sqrt{{Opposite^{2} - Adjacent^{2} }[/tex]
[tex]= \sqrt{25^{2} + 10^{2} }[/tex]
[tex]= \sqrt{725} \\\\= \ 26.92582 \ = \ 5\sqrt{29}[/tex]
[tex]\theta =\ sin^{-1} {\frac{Opposite }{Hypotenuse} }[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]\theta = \ sin^{-1} (\frac{25}{26.92} )[/tex]
[tex]= sin^{-1} (0.92847669088526)[/tex]
[tex]\theta = \ 68[/tex]°
Hence, The side and angle is in the right angle triangle respectively x = 3, 68°.
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08,
Watch help video
Determine if the following system of equations has no solutions, infinitely many
solutions or exactly one solution.
No Solutions
One Solution
5x + 4y = -3
-5x - 4y = 3 Infinitely Many Solutions
One solution: 3x- 5y = 8; 5x - 3y = 2
3x + 2y = 8; 4x +3y = 1
What are types of solution?The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. other words, the set of all feasible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.Different Approaches to Solving Linear EquationsThe set of linear equations can have one of three different sorts of solutions. As follows:Unique solutionNo soulutioninfinite Number of Solutionsacc to our question-
One solution:3x- 5y = 8; 5x - 3y = 23x + 2y = 8; 4x +3y = 1No solution:3x - 2y = 3; 6x - 4y = 13x - 4y = 2; 6x - 8y = 1Infinitely solutions:3 x - 6y = 3; 2x - 4y = 2learn more about solutions click here:
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You rotate a triangle 270° counterclockwise about the origin. Then you translate its image 2 units right and 1 unit down. The vertices of the final image are (0, 2), (8,-1), and (5,-2). What are the vertices of the original triangle?
The vertices of the original triangle are:
(-3,-2) , (0,6) and (1,3)
Given,you rotate a triangle 270° counterclockwise about the origin.
Then you translate its image 2 units right and 1 unit down.
The vertices of the final image are (0, 2), (8,-1), and (5,-2).
we are asked to find the vertices of the original triangle =?
Before translating the image of final image 2 units right and 1 unit down.
the vertices of the triangle is:
(0-2,2+1) → (-2,3)
(8-2,-1+1) → (6,0)
(5-2 , -2+1) → (3,-1)
{translate the final image 2 units left, 1 unit up again}
then before rotate 270° counterclockwise.
the vertices of the triangle is:
(-2,3) → (-3,-2)
(6,0) → (0,6)
(3,-1) → (1,3)
{rotate 270° clockwise again }
Hence the vertices of the original triangle is:
(-3,-2) (0,6) and (1,3)
Hence we get the required vertices of the triangle.
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