Here is the graph for one equation in a system of equations:
a. Write a second equation for the system so it has infinitely many solutions.
b. Write a second equation whose graph goes through (0,1) so the system has no solutions
c. Write a second equation whose graph goes through (0,2) so the system has one solution at (4,1)
Answers
1) The equation that has infinitely many solution is y = -8/11·x + 4
2) The equation of the graph that has no solution is y = -8/11·x + 1
3) The equation of the line that has only one solution is y = -1/4·x + 2
Step-by-step explanation:
1) The points on the graph are;
(0, 4), and (5.5, 0)
The slope of the line defined by the given two points, we have;
(0 - 4)/(5.5 - 0) = -40/55 = -8/11
the equation of the straight line graph in point and slope form, we have;
y - 4 = -8/11 × (x - 0)
y - 4 = -8/11·x
For the equation for the system that has infinitely many solution, we have;
y = -8/11·x + 4
2) For the equation whose graph foes through the point (0, 1) and the system has no solution, we have;
An equation that has no solution with the equation y = -8/11·x + 4, is parallel to y = -8/11·x + 4, and therefore, the slope are equal
Therefore, the equation whose graph foes through the point (0, 1) and the system has no solution, in point and slope form is given as follows;
y - 1 = -8/11 × (x - 0)
y - 1 = -8/11·x
The equation of the graph that has no solution is therefore;
y = -8/11·x + 1
3) For the equation of the graph that goes through the point (0, 2), and has a common solution with the system at (4, 1), we have;
The slope of the graph is (1 - 2)/(4 - 0) = -1/4
The equation of the line that has only one solution with the system in point and slope form is given as follows;
y - 2 = -1/4×(x - 0)
y - 2 = -1/4·x
The equation of the line that has only one solution in standard form is therefore;
y = -1/4·x + 2
The second equation for the system so it has infinitely many solutions is [tex]y=-\dfrac{3}{4}x+1[/tex] and the second equation whose graph goes through (0,2) so the system has one solution at (4,1) is [tex]\rm y = -\dfrac{1}{4}x+2[/tex] and this can be determined by using the point-slope form of the line.
Given :
The graph of the line that passes through the points (4,1) and (0,4).
The equation of the line that passes through the points (4,1) and (0,4) is given by:
[tex]\dfrac{y-1}{x-4}=\dfrac{4-1}{0-4}[/tex]
Cross multiply in the above equation.
-4(y - 1) = 3(x - 4)
-4y + 4 = 3x - 12
3x + 4y = 16
[tex]\rm y = 4-\dfrac{3x}{4}[/tex] --- (1)
a) The second equation for the system so it has infinitely many solutions is given by:
Multiply equation (1) by 2 in order to determine the second equation.
[tex]\rm 2\times \left(y = 4-\dfrac{3x}{4}\right)[/tex]
[tex]\rm 2y = 8 - \dfrac{3x}{2}[/tex]
b) The second equation that passes through (0,1) and has a slope of -3/4 is given by:
[tex](y-1)=-\dfrac{3}{4}(x)[/tex]
[tex]y=-\dfrac{3}{4}x+1[/tex]
c) The second equation whose graph goes through (0,2) so the system has one solution at (4,1) is given by:
[tex]\dfrac{y - 2}{x-0}=\dfrac{1-2}{4-0}[/tex]
Cross multiply in the above equation.
4(y - 2) = -1(x)
4y - 8 = -x
[tex]\rm y = -\dfrac{1}{4}x+2[/tex]
For more information, refer to the link given below:
https://brainly.com/question/2263981
Related Questions
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Priya wrote 320 for the value of 906 +3. Check her answer by multiplying it by 3. What product do you get and what does it tell you about Priya's answer?
correct answer is 302**
Answers
Answer:
Her mistake is that she wrote a two in the tenths place and zero in the ones place.
Step-by-step explanation:
3 can't go into zero so she had to write a zero in the tenths place. And 3 can go into 6 two times so she must write a 2 in the ones place.
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Step-by-step explanation:
Directions: Answer the following questions, showing all pertinent work. Paul has a 40 ft. by 30 ft. pole barn on his farm that he wants to move. The southeast corner of the pole barn is currently located 50 ft. west and 25 ft. north of the stock tank where the cows get their water. Paul wants to move the pole barn so the southeast corner of the barn is located 80 feet east and 80 feet south of the stock tank. 1. Complete the transformation statement for moving Paul’s pole barn. (x, y)→(x + _______ , y + _______ ) —continue to the next page—
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Answer: (x + 130, y - 55)
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A new sweater cost $15.99.. If the sweater was on sale for 1/4 off it's price, about how much would you save?
Answers
Answer:
About $4
Step-by-step explanation:
You have about 16, divide it by 4 and that’s your answer
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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What is the area of figure?
• A. 320 square centimeters
• B. 608 square centimeters
• C. 448 square centimeters
• D. 560 square centimeters
Answers
Answer:
area of trapezium=1/2 ×20(38+18)=560cm²
Answer:
C. 448
Step-by-step explanation:
Since 38-18=20, you divide by 10 to find the base of the two triangles on the side. The height of the triangle is 16 and the formula is basexheightx1/2.
10x16x0.5=80
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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* * *
I don't want to confused anyone so I'll use this chance to explain the difference between linear and proportional.
In simple terms, proportional relationships has the y-intercept at 0. So proportional lines cross the origin (0,0) while linear lines just has to be a straight.
Hope I was able to help! Good Luck!
Answer:
The number of tickets and cost have a proportional relationship.
Step-by-step explanation:
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Answer:
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What is the relationship between <8 and <4? Select the TWO answers that apply. *pleasee helpp*
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Also, Prove that the median to the base of an isosceles triangle is also: the angle bisector of the angle from which it is drawn.
Please provide statement and reason proof. Would really appreciate it. Best Answer will get brainliest, and please don't spam stuff just for points. Thanks, and have a great day!
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Hey there!
The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent. The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle.
Let me know if you are still confused and need a better explination :)
Have a great day!
Answer:
The base angles theorem converse states if two angles in a triangle are congruent, then the sides opposite those angles are also congruent. The Isosceles Triangle Theorem states that the perpendicular bisector of the base of an isosceles triangle is also the angle bisector of the vertex angle. Let me know if you are still confused and need a better explanation :) Have a great day!
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Answer:
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Answer:
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Step-by-step explanation:
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Answer:
This the 2nd page
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Answers
Answer:
D
Step-by-step explanation:
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Answer:
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answer options
19 degrees
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Answers
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Answers
Answer:
6. 425
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9. 112
Step-by-step explanation:
6.
26*15=390
5*4=20
3*5=15
390+20+15=425
7.
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8.
4*8=32
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32-8=24
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8*8=64
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Answer:
I got the same answer as the other girl
Step-by-step explanation:
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Answer:
24
Step-by-step explanation:
Jasper plans to serve cheese and crackers as an appetizer at his next dinner party. He buys 0.8 pounds of cheddar cheese. If the cheese costs $5.35 per pound, how much does he spend?
Answers
Answer:
It might be 42.80
Step-by-step explanation:
5.35x0.8
The cost of 0.8 pounds of cheddar cheese is $4.28.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Jasper buys 0.8 pounds of cheddar cheese.
The cheese costs $5.35 per pound
So, cost of 0.8 pounds of cheddar cheese is
0.8×5.35
= $4.28
Therefore, the cost of 0.8 pounds of cheddar cheese is $4.28.
To learn more about the unitary method visit:
brainly.com/question/22056199.
#SPJ2
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Use the bar diagram to find the weight of Jade’s dog.
Answers
Answer:
13.3 or 13 and 3/10
Step-by-step explanation:
8.3 + 5 = 13.3
Answer:
41.4
Step-by-step explanation:
The problem says 5 times as much as her cat, so you have to do 8.3x5 which the answer is 41.4!
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answer options
55 degrees
75 degrees
110 degrees
120 degrees
Answers
Answer:
choice #1, 55 degrees
Step-by-step explanation:
180 = 70 +2x
2x = 110
x=55 degrees
Answer:
The answer is choice #1, 55 degrees
Step-by-step explanation:
180 = 70 +2x
2x = 110
110 divided by 2
=
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