Answers
10. This system has one solution with coordinates (1, -2)
11. This system has one solution with coordinates (0,-3)
12. This system has one solution with coordinates(-1, -2)
13. This system has no solution.
14. This system has no solution.
16. This system has one solution with coordinates (0,-4)
How to determine the co-ordinates of system of equations?To determine the co-ordinates of a system of equations, the first step is to eliminate any redundant equations in the system.This is done by subtracting or adding equations that are already represented in the system.Once this is done, the system of equations can be set up in matrix form to find the co-ordinates.To do this, one must represent the equations as a matrix by representing the coefficients of each variable as the elements of the matrix.Once the matrix is set up, the inverse of the matrix can then be used to solve for the co-ordinates of the system.This can be done using Gaussian Elimination, Cramer's Rule, or another method.Once the inverse of the matrix is found, one can then multiply it by the vector of the constants in the equations and the resulting vector will contain the co-ordinates of the system.According to question:-
10. y = x - 3 ------- 1
y = -5x + 3 ------- 2
substitute 1 in 2,
x - 3 = -5x + 3
x = 1
y = 1 - 3 = -2
y = -2
The co-ordinates is (1,-2)
11. y = -3
substitute in y = x-3
-3 = x - 3
x = 0
The co-ordinates is (0,-3)
12. y = 4x + 2 --------- 1
y = -2x - 4 ------------2
Substitute 1 in 2,
4x + 2 = -2x - 4
6x = -6
x = -1
substitute x = -1 in 2
y = -2
The co-ordinates is (-1, -2)
13. y = x - 6 -----1
y = x+ 2 -------2
It has no solution, so there is no co-ordinates.
14. x + y = 4
3x + 3y = 12
It has no solution, so there is no co-ordinates.
16. 2x + 3y = 12 ------1
2x - y = 4 --------2
from 2 we rewrite the equation as y = 2x-4
Sub in eq 1
2x + 3(2x-4) = 12
2x + 6x - 12 = 12
8x = 24
x = 3
y = 2
The co-ordinates is (3,2)
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Related Questions
Kim paid $33 for 2 shirts and $48 for 3 shirts including a fixed shipping fee assuming the same function applies to any numbers of shirts bought how much in dollars would 1 shirt cost before the shipping fee
Answers
Answer:
33=2x+y, 48=3x+y
Step-by-step explanation:
Sorry my internet isn't working well. Go to math-way and put that in and it will give you the answer :)
Describe a sequence of transformation that maps triangle DOG onto triangle CAT
Answers
The transformation of the function is given by reflection along y axis and a translation of 5 units up
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the transformation be represented as A
Now , the equation will be
Let the triangle be represented as ΔODG
Now , the coordinates of ΔODG is
O = O ( -1 , -2 )
D = D ( -5 , -3 )
G = G ( -2 , -4 )
Now , the transformed triangle is ΔACT
The coordinates of ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Now , on reflecting the triangle ΔODG along y axis , we get
When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse
So , the coordinates of triangle O'D'G' , we get
O' = O' ( 1 , -2 )
D' = D' ( 5 , -3 )
G = G' ( 2 , -4 )
Now , translating the triangle ΔO'D'G' up by 5 units , we get
The y coordinate of the triangle gets incremented by 5
So ,
A = O' ( 1 , -2 + 5 )
C = C ( 5 , -3 + 5 )
T = T ( 2 , -4 + 5 )
And , the coordinates of the triangle ΔACT is
A = A ( 1 , 3 )
C = C ( 5 , 2 )
T = T ( 2 , 1 )
Hence , the transformation is reflection along y axis and followed by translation of 5 units up
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A can of carrots weighs 15/16 of a pound. One serving of carrots is ¼ of a pound. How many servings are in the can of carrots?
Answers
Answer:
Step-by-step explanation:
How many carrots are in a can? is that the question ? :DDDDD
15/16 and 1/4 = 4/16 sooo
4*3 = 12
so three full servings and one that is 3/4 full
so 3
Mr. Mason paints his fence on Monday, Tuesday, Wednesday, and Thursday. It takes him a total of 6 2/4 hours to paint his fence. Write a digit in each box to show how many hours he could have painted each day.
Answers
Rudy says that the sum of the measures of the exterior angles of a regular hexagon is 720°. Is Rudy correct? Why or why not?
Answers
Answer:
Yes, Rudy is correct
Explanation:
Number of sides of a hexagon = 6
The sum of all interior angles of a polygon with n sides = (n-2)*180
Here, since a regular hexagon has 6 sides, n = 6
= (6 - 2)*180
= 4*180
= 720 degrees
Hope it helps :)
Have a great day!
Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
(Use the correct operation or combination of operations to solve the problem)
Answers
She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.
What are the different types of profit?Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.
number of bracelets sold for $12 each=9
number of bracelets sold for $8 each=14
Total profit=9x12+8*14=$220
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__________ are designed so that the objective of the test is not apparent to the test taker. A. Projective tests B. Source errors C. MMPI tests D. 16PF tests Please select the best answer from the choices provided A B C D
Answers
Projective tests are created so that the test taker cannot tell what they are testing for.
What is Projective tests?Projective tests are created so that the test taker cannot tell what they are testing for.A personality test used in psychology is called a projective test. This kind of test provides answers to confusing situations, phrases, or visuals. Unconscious motivations or attitudes are disclosed by asking the person a question or giving them a stimulus that is unclear. Projective exams are designed to enlighten individuals about sentiments, wants, and conflicts that are not readily apparent to them. Psychoanalysts try to find unconscious feelings that might be behind a person's troubles in life by evaluating responses to ambiguous stimuli. Projective testing is mostly used to evaluate personality functioning.To learn more about Projective tests refer to:
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HOW TO DO THIS QUESTION PLEASE
Answers
Answer:
b = -10
c = 25
Step-by-step explanation:
Since the only solution to x is 5 that mean answer will look something like this:
(x-5) (x-5) = 0
x(x-5) -5(x-5)
x^2 -5x -5x + 25
x^2 -10x + 25
This is same as x^2 + bx + c = 0
where b is -10 and c is 25
Type the correct answer in each box. Use numerals instead of words. Find the missing side and angle measures in triangle ABC. Round your answers to the nearest tenth. Scalene triangle ABC with side AC labeled 23 and side BC labeled 15. Angle A measures 40 degrees. The measure of angle B is approximately . The measure of angle C is approximately . The length of side AB is approximately
Answers
The measures of the angles of the triangles are
The measure of ∠B = 80.3°
The measure of ∠C = 59.7°
The length of side AB = 20.2 units
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measure of side AC = 23
The measure of side BC = 15
The measure of ∠A = 40°
From the law of sines , we get
( sin A ) / a = ( sin B ) / b = ( sin C ) / c
Substitute the value of A and a in the equation , we get
sin ( 40 )° / 15 = sin B / 23
On simplifying the equation , we get
sin B = ( 23/15 ) x sin ( 40 )°
Now , m∠B = 80.27°
So , the measure of angle ∠B = 80.3°
And ,
The interior angles of a triangle is 180°
So , The measure of angle ∠C = 180° - ( 80.3° + 40° )
On simplifying the equation , we get
The measure of angle ∠C = 59.7°
Now ,
From the law of cosines , c² = a² + b² - 2ab ( cos C )
Substitute the value of a , b and cos C in the equation , we get
c² = 15² + 23² - 2 ( 15 ) ( 23 ) cos ( 59.7 )°
On simplifying the equation , we get
c² = 225 + 529 - 348.12363
c² = 405.87
Taking square roots on both sides of the equation , we get
c = 20.156
c = 20.2 units
Therefore, the measure of side AB = 20.2 units
Hence , the measures angles of triangle is solved
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Choose the type of variation that relates the variables in the table.
Answers
Answer:
Multiply the x by 5 to get the y
Which equation is the slope intercept form of this equation?
y - 4 = -2 (x – 5)
a- x = - 2y + 3
b- 2x + y = 6
c- y = -2x + 14
d- y – 4 = -2x + 10
Answers
Answer:
C
Step-by-step explanation:
Y - 4 = -2x + 10 Multiply -2 to the inside the brackets
Y = -2x + 14 Add the 4 over
State who is correct
And
Describe the mistake the other student made
Answers
Answer:
Sebastian is correct
Step-by-step explanation:
George is wromy because where he had to simplify:
+ 5 - 8 ( which is the same as - 8 + 5 ), he added the two numbers (5 and 8) which is not supposed to be so. He should have rather subtracted the 8 from the five which will be + 5 - 8 = 3. This then makes Sebastian correct as he subtracted the two numbers.
how to solve x-y+x/2 (if x=10, y=1)
Answers
=14 bc 10-1=9 and 10/2 = 5 so 5+4 =9
When Juan commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 31 minutes and a standard deviation of 4.5 minutes. Using the empirical rule, what percentage of his commutes will be between 22 and 40 minutes?
Answers
Answer: 95%
Step-by-step explanation:
i kinda slayed
Using the empirical rule, for normal distribution is 68 % of his commutes will be between 23.5 and 32.5 minutes
What is normal distribution?The normal distribution is a probability distribution used to calculate probability for continuous variables.
Here, we have,
to find what percentage of his commutes will be between 23.5 and 32.5 minutes using the empirical rule:
Now, since gabriel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes, we need to find the percentage of his commutes will be between 23.5 and 32.5 minutes using the empirical rule.
First, we need to find how many standard deviations away from the mean each value is using the z-score
Z = (x - μ)/σ where
x = value,
μ = mean and
σ = standard devation
For x = 23.5, we have
Z = (x - μ)/σ
Z = (23.5 - 28)/4.5
Z = -4.5/4.5
Z = -1
Z = -1σ
Also, for x = 32.5, we have
Z = (x - μ)/σ
Z = (32.5 - 28)/4.5
Z = 4.5/4.5
Z = 1
Z = 1σ
So, we have that -1σ ≤ (x - μ) ≤ 1σ
So, the values between 23.5 and 32.5 minutes lie within one standard deviation.
Using the empirical rule, this is 68 % of the values.
So, 68 % of his commutes will be between 23.5 and 32.5 minutes
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complete question:
when gabriel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 28 minutes and a standard deviation of 4.5 minutes. using the empirical rule, what percentage of his commutes will be between 23.5 and 32.5 minutes?
*HELP PLEASE*
In circle J with HJK = 146", find the HLK.
A) 214°
B) 73°
C) 292°
D) 46.5°
Answers
Answer:
B. 73°
Step-by-step explanation:
Find the volume of each solid. Round to the nearest tenth if necessary. Use 3.14 for or
22/7
A : 14.7 m3
B : 3.7 m3
C : 4.7 m
D : 6.7 m3
Answers
Answer:
1.1^2 = 1.21
1.21 x 3.14 = 3.7994
3.7994 x 2.9 = 11.01826
11.01826 divided by 3 = 3.67275333333 rounded = 3.7 m3
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a Question 18 options: A) kite. B) trapezoid. C) hexagon. D) parallelogram.
Answers
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram.
Option (d) is the correct choice.
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
A parallelogram has the following qualities:
The opposing sides are equally spaced and parallel.
Angles on either side are equal.
The following or neighboring angles are supplemental.
All of the angles will be at right angles if any one of them is a right angle.
The two diagonals cut across one another.
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[tex]4x ^{2} \: 6xy \: 8y ^{2} [/tex]
Answers
Answer:
[tex]192x ^{3} y ^{3} [/tex]
Use the distributive property to simplify the expression
6(8x+5)
Answers
Step-by-step explanation:
6(8x+5)
Use the distributive property to multiply 6 by 8x+5.
48x+30
Hope it Helps!
Fill in the blank: If a number is located to the left
of another number on the number line, that
number is ____ the other number
Answers
Answer:
smaller/ less than
Answer:
less than
Step-by-step explanation:
On a number line, the values go from least to greatest, left to right. So if you go towards the left, the number is decreasing.
What is the solution to the pair of simultaneous equations 2x y 5 3x 2y 4?
Answers
The solution to the pair of simultaneous equations 2x + y = 5 and 3x - 2y = 4 is (2, 1).
A system of linear equations is a set of two or more equations which includes common variables. The solution to a system of equations, is the value of the unknown variables used in the equations that satisfies both equations.
Given two linear equations in x and y,
2x + y = 5 (equation 1)
3x - 2y = 4 (equation 2)
Use substitution method to find its solution. Express the first equation as y in terms of x and substitute the value of y to the second equation.
2x + y = 5 (equation 1)
y = 5 - 2x
3x - 2y = 4 (equation 2)
3x - 2(5 - 2x) = 4
3x - 10 + 4x = 4
Combining all terms containing the variable x on one side and the constants on the other side of the equality, and solve for x.
3x - 10 + 4x = 4
7x = 14
x = 2
Substitute the value of x in the first equation and solve for y.
y = 5 - 2x
y = 5 - 2(2)
y = 5 - 4
y = 1
Hence, the solution of the given system of equations is (2, 1).
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Steve, a restaurant owner, pays $2.75 per
pound for organic lettuce. He also pays
$50 for the lettuce to be delivered to his
restaurant. About how many pounds of
lettuce can Steve purchase &nd have
delivered for $220?
Answers
Answer: About 62 pounds of organic lettuce
2.75x+50=220
Solve for x
x=61.81(repeating)
PLEASE HELPP
If A and B are supplementary angles and
m/B = 54, find m/A.
Answers
Answer:
m∠A=126°
Step-by-step explanation:
Supplementary means that they add up to 180°.
Therefore we can do 180-54 to get 126° for the m∠A.
Hope this helped! :)
The light blue askes for the word form, the green says g= -1, the yellow askes for possible solutions, the purple wants how you shade the number line.
Please help!!!!!!!!!!!!!!!!!!!!!
Answers
Answer: get yio colors straightv
Step-by-step explanation:
A car on a Ferris wheel with a radius of 20 feet. To the nearest foot, how far does the car travel over an angle of pi/3 radians? (Include the unit of measure in your response.)
Answers
Answer:21
Step-by-step explanation:
The car on a Ferris wheel with a radius of 20 feet. travels a distance of 125.6 feet
In order to determine the distance that the car has travelled, we will use the formula for calculating the circumference of a circle expressed as:
C = 2πr
r is the radius of the fairy wheel
Given the following parameters
radius = 20 feet
Substitute into the formula of the circumference:
[tex]C = 2(3.14)(20)\\C = 40(3.14)\\C = 125.6 feet[/tex]
This shows that the car on a Ferris wheel with a radius of 20 feet. travels a distance of 125.6 feet
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How do you describe a logarithmic function?
Answers
A logarithmic function is a type of inverse function.
A logarithmic function is a type of inverse function that is commonly used in mathematics and science. It is typically written in the form of y = log base b (x), where b is the base of the logarithm, and x is the input value. The most common bases for logarithms are 10 (common logarithm) and e (natural logarithm).
The logarithmic function is the inverse of the exponential function with base b. This means that if y = log base b (x) then x = b^y
One way to describe a logarithmic function is to say that it represents the exponent to which the base number must be raised in order to produce the input value x. For example, log base 10 of 100 is 2, because 10^2 = 100.
Another way to describe a logarithmic function is to say that it is a way of expressing very large or small numbers in a more manageable form. For example, instead of expressing a number like 10^9 as 1 billion, it can be expressed as 9 using a logarithm to base 10.
It is also important to note that logarithmic function have some key characteristics such as:
The domain of a logarithmic function is x>0, since the logarithm of a non-positive number is undefined.
The range of a logarithmic function is all real numbers.
The graph of a logarithmic function has a vertical asymptote at x=0, since the logarithm of a non-positive number is undefined.
A logarithmic function is increasing over its domain and concave down.
The x-intercept of the graph is (1,0), since the logarithm of 1 is always 0.
Overall, logarithmic functions are mathematical tools that allow us to simplify the representation and manipulation of very large and small numbers, and are used in many areas of science and engineering.
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Need help with this dilation tyyy
Answers
Answer:
Scale Factor: 2
Step-by-step explanation:
Need more information?
Visit MathWareHouse.com
Hope this was helpful! Thank you & have an awesome day! =)
Which statement correctly describes this picture?
Answers
Because there, TY is show as a ray with one end point only. And PR is a lone segment.
find three fifth of Ghana cedis 200
Answers
Answer:
Hi.
three fifth of 200 is 120.
Anyone know this? I’m a wee bit brain dead any help is appreciated
Answers
I hope this helps :)
Answer:
I believe this is the only answer I got from you bro.
hope it helps.