Answer: all real numbers
Step-by-step explanation:
YES I WILL GIVE BRAINLIST
Which of the following systems of equations has exactly one solution?
Question 1 options:
2x+y=10y=−2x+8
2x+4y=102(x+2y)=10
2(2x+1)=yy=2x+8
y=10−2xy=−2x+7
Which of the following systems of equations has infinitely many solutions?
Question 4 options:
2x+7x+y=6y=9x+6
y=5x+7y=2x+8
y=x+42y=2x+8
7x−y=10y=6x+8
Answer:
Question 1) Option C: 2(2x+1) = y, y = 2x + 8.
Question 4) Option C: y = x + 4, 2y = 2x + 8
Step-by-step explanation:
Definitions:Perpendicular LinesThe graph of perpendicular lines will show an intersection of two lines at a single point, forming 90° adjacent angles. Since perpendicular lines intersect at exactly one point, then it means that they will have one solution. Additionally, perpendicular lines have negative reciprocal slopes for which multiplying the slopes of both lines result in a product of -1.
Coinciding LinesLines that have the same slope and y-intercept. Therefore, they are equivalent equations that will result in an infinitely many solutions. The graph of these lines will coincide on top of each other, as if they are the same line. The systems of linear equations that result in an infinitely many solutions are dependent and consistent. They are dependent if they have an infinite number of solutions, and consistent because they have at least one solution.
Parallel linesParallel lines have the same slope. A systems of linear equations whose graph involve parallel lines have no solution, as there is no point of intersection between those two lines. Therefore, parallel lines have no solution, making it an inconsistent system.
Question 1:We must transform these equations in its slope-intercept form, y = mx + b, which will allow us to easily determine the type of lines a given system has based on their slopes.
Option A:Equation 1: 2x + y = 10
Equation 2: y = −2x + 8
Transform Equation 1 to slope-intercept form:
2x + y = 10
Subtract 2x from both sides:
2x - 2x + y = - 2x + 10
y = -2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Since Equations 1 and 2 have the same slope, but different y-intercepts, then it means that they are parallel lines that have no point of intersection.
Option B:
Transform both equations to slope-intercept form:
Equation 1: 2x + 4y = 10
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ This is the slope-intercept form of Equation 1.
Equation 2: 2(x+2y) = 10
Distribute 2 into the parenthesis:
2(x+2y) = 10
2x + 4y = 10 ⇒ It is clear at this point that this equation matches Equation 1. Thus, the slope-intercept form of Equation 2 will be the same:
[tex]\large\bf\sf{y\:=\:-\frac{1}{2}x\:+\:\frac{5}{2}}[/tex] ⇒ Slope-intercept form of Equation 2.
It turns out that Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. Therefore, they have coinciding lines and have infinitely many solutions.
Option C:Transform both equations to slope-intercept form:
Equation 1: 2(2x+1) = y
y = 4x + 2 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 2x + 8
Option D:Equation 1: y = 10 − 2x
y = − 2x + 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = −2x + 7
Since Equations 1 and 2 have the same slope, but different y-intercept, then it means that they are parallel from each other.
Answer for Question 1:Out of all the given four options, Option C seems to be the correct answer, since the given system has varying slopes and y-intercept. Therefore, the correct answer for Question 1 is Option C: 2(2x+1) = y, y = 2x + 8.
Question 4:For Question 4, I will not elaborate as thoroughly as in Question 1 since I'll be using the same techniques.
Option A)Equation 1: 2x+ 7x + y = 6
Combine like terms:
2x+ 7x + y = 6
9x + y = 6
Subtract 9x from both sides:
9x - 9x + y = - 9x + 6
y = - 9x + 6 ⇒ Slope-intercept form of Equation 1.
Equation 2: y = 9x + 6
Option A Explanation:
Equations 1 and 2 have different slopes and the same y-intercept. This implies that they will have a point of intersection = one solution. However, they don't have perpendicular lines because their slopes are not negative reciprocal of each other. Hence, Option A is not a valid answer for question 4.
Option B)Equation 1: y = 5x + 7
Equation 2: y = 2x + 8
Option B explanation:
Similar to Option A, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option B is not a valid answer for question 4.
Option C)Equation 1: y = x + 4
Equation 2: 2y = 2x + 8
Transform Equation 2 to Slope-intercept form:
Divide both sides by 2 to isolate y:
[tex]\displaytext\mathsf{\frac{2y}{2}\:=\:\frac{2x\:+\:8}{2}}[/tex]
y = x + 4 ⇒ This is the slope-intercept form of Equation 2.
Option C explanation:
Equations 1 and 2 are equivalent, as they have exactly the same slope and y-intercept. They also have coinciding lines, having infinitely many solutions.
Therefore, Option C is the correct answer for Question 4.Option D)
Equation 1: 7x − y = 10
y = 7x - 10 ⇒ This is the slope-intercept form of Equation 1.
Equation 2: y = 6x + 8
Option D explanation:
Similar to Option B, Equations 1 and 2 have different slopes and varying y-intercepts. Since they are not parallel from each other, and do not have coinciding lines, then Option D is not a valid answer for question 4.
say I like English debating but it takes too long sometimes. but replace English with math
I like Math debating but it takes too long sometimes. This is so because mathematics, despite being an exact science, provides several alternatives to reach the same final result.
Thus, for example, a probability percentage can be obtained by means of a binomial formula or by means of a cross multiplication calculation, where both results will be correct.
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Answer:
oh my god
Step-by-step explanation:
1\4-2\5
plese help and thank
you
Answer:
3/20
Step-by-step explanation:
3/20 I sure, Just trying this one
Help!?! I have no clue how to solve it :/
Line FG passes through points (0, 2) and (3, 2). Line F′G′ is formed by dilating line FG by a factor of 2 about the origin. Which statement is true? Group of answer choices Line F′G′ is the original line. Line F′G′ passes through the origin. Lines FG and F′G′ are parallel to each other. Lines FG and F′G′ are perpendicular to each other.
Answer:
See the picture, it explains the correct choice is CStep-by-step explanation:
a) Line F′G′ is the original line. Falseb) Line F′G′ passes through the origin. Falsec) Lines FG and F′G′ are parallel to each other. TRUEd) Lines FG and F′G′ are perpendicular to each other. FalseCallum says that every number is greater than its opposite. Do you agree?
Answer:
I disagree with Callum because the opposite of -1 is 1 and a positive number is greater than a negative number. If Callum wants to be right then he has to say every positive number is greater than its opposite in order to be true.
Step-by-step explanation:
please help im failing
Statement
∠1 = ∠2
Reason(1): l║m, Corresponding angles are congruent
Reason(2): Corresponding angles are congruent (Postulate)
Hope this can help
We have to prove how j||k?
As <1=<2 Theya are opposite interior angles .<1 and <4 are corresponding angles so they are equal .Hence
J||K Proved4x+3+3=-2
help asappl
Answer:
x = − 2
Step-by-step explanation:
What is the time difference between usa and england?
Answer:
-5 hours
Step-by-step explanation:
does the graph represent a function? yea or no
Answer:
no
Step-by-step explanation:
It is not because it does not pass the vertical line test.
****************************************************************
This is the vertical line test:
Imagine a vertical line that starts at the left side of the graph, at x = -8, and is moving right to x = 8. If at any time in the vertical line's movement from left to right, it intersects more than 1 point of the relation simultaneously, then the relation is not a function.
******************************************************************
Here, when the vertical line is x = -7, the vertical line intersects points (-7, 4) and (-7, 6) simultaneously. That means this relation does not pass the vertical line test, and it is not a function.
a farmer takes 1 week to fill 6 bins of squash. At this rate,how long will it take to fill 360 bins
Answer:
60 weeks
Step-by-step explanation:
Setup a proportion.
[tex] \frac{weeks}{bins} \frac{1}{6} = \frac{w}{360} [/tex]
cross multiple
[tex]6w = 360[/tex]
now divide by 6
[tex] \frac{6w}{6} = \frac{360}{6} [/tex]
[tex]w = 60[/tex]
Answer/Step-by-step explanation:
Important Information:
1 Week to fill 6 Bins
Question to answer:
How Long will it takes to fill 360 Bins
Solution/Explanation:
360 Divided by 6 =
60 Week
Graph the linear function w(x) = 3/5x + 2
Answer:
Coordinates or points would be (0,2), (1,2.6) (2,3.2) (3,3.8)
Step-by-step explanation:
Formula
w(x) = 3/5x +2 in each coordinate I have a x so for example 3.
I would rewrite this as 3/5(3) + 2
w(x) = 3/5x +2
w(3) = 3/5(3) + 2
y = 1.8 + 2
y = 3.8
Consider Brainiest
how can you solve this (3/4 - 1/5)
Answer:
11/20
Step-by-step explanation:
Help me please i beg you please
Using Pythagorean theorem
[tex]\\ \sf\longmapsto x^2=26^2-10^2[/tex]
[tex]\\ \sf\longmapsto x^2=676-100[/tex]
[tex]\\ \sf\longmapsto x^2=576[/tex]
[tex]\\ \sf\longmapsto x=24ft[/tex]
Find the perimeter. Simplify your answer.
Answer:
16c-6
Step-by-step explanation:
(7c-6)+(6c-10)+(3c+10)=?
7c-6+6c-10+3c+10=?
Collect like terms.
16c-6-10+10
Add and subtract.
16c-6
Hope this helps :)
A line has this equation y=1/4x+6
Write an equation for the perpendicular line that goes through (5,-6)
Francis's rectangular lawn has a length of 2x + 1 feet and a width of x + 1 feet. She plants a square garden with a side length of x + 2 feet
in the lawn. What is the area of the lawn not covered by the garden?
Answer:What is the slope of the line through (-5,-10)(−5,−10)left parenthesis, minus, 5, comma, minus, 10, right parenthesis and (-1,5)(−1,5)left parenthesis, minus, 1, comma, 5, right parenthesis?
Step-by-step explanation:
Answer:x^2-x-3
Step-by-step explanation:
step 1-find area of rectangular lawn
(2x+1)(x+1)=2x^2+3x+1
step 2-find area of garden
(x+2)(x+2)=x^2+4x+4
step 3- subtract the two
=x^2-x-3
Elliot purchased 3 trick cameras and 4 fake snakes and spent a total of $40. Kaci bought 7 trick cameras and 8 fake snakes, and her total was $85. Let x be the price of the trick cameras and let y be the price of the snakes.
It can be deduced that the price of the trick cameras will be $5 and the price of the snakes will be $6.25.
Based on the information given, the equation to solve the question will be:
3x + 4y = 40 ...... i
7x + 8y = 85 ...... ii
Multiply equation i by 7
Multiply equation ii by 3
21x + 28y = 280
21x + 24y = 255
Subtract the equations
4y = 25
y = 25/4 = 6.25
Since 3x + 4y = 40
3x + 4(6.25) = 40
3x + 25 = 40
3x = 40 - 25.
3x = 15
x = 15/3 = 5
Therefore, the price of the trick cameras will be $5 and the price of the snakes will be $6.25.
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https://brainly.com/question/25771535
Your poster was sold for 4250 pesos. You want to share this money with your two siblings. You and your younger sibling will each receive ¼ of the amount and the rest will be for your oldest sibling. How much money will each of you receive?
For 0° ≤ x < 360°, what are the solutions to cos(x/2) – sin(x) = 0?
A{0°, 60°, 300°}
B{0°,120°, 240°}
C{60°, 180°, 300°}
D{120°,180°, 240°}
Precalc
Answer:
the answer is c
Step-by-step explanation:
cos30 = sin60
then cos30 - sin 30 = 0
c is the only choice which can satisfy in the problem
PLEASE HELP ASAPPPPPP
Answer:
150 miles/ per hour
Step-by-step explanation:
because it's per hour you find the 1
go up the one and you can see it's halfway between 100 and 200
so 150 m/hour
Given a polygon with 14 sides, find the sum of the measures of its interior angles.
Can you help me plzzzzzzz
Answer:
Step-by-step explanation:u have to add x+6 = ur answer there u go
1The lengths of pregnancies are normally distributed with a mean of 271 days and a standard
deviation of 20 days. If 64 women are randomly selected, find the probability that they have a mean
pregnancy between 271 days and 273 days.
A) 0.2881
B) 0.5517
C) 0.2119
D) 0.7881
[tex]probablity = \frac{271}{273} \\ = 0.99267399267[/tex]
The lines represented by the equations 5y - x = 5 and y - x = 1 are
Answer:
Same line
Step-by-step explanation:
5y - x = 5 y - 1/5x = 1
5y = x + 5 y = 1/5x + 1
5y/5 = x/5 + 5/5
y = 1/5x + 1
12 liters to quarts rounded to nearest hundredth
Answer:
12.6
Step-by-step explanation:
have a wonderful day :)
A survey was given to a random sample of 80 residents of a town to determine
whether they support a new plan to raise taxes in order to increase education
spending. Of those surveyed, 40 respondents said they were in favor of the plan.
Answer:
sorry i dont quite understand your question .
Ratio would be 1/2 or 50:100 in terms to 40:80
Step-by-step explanation:
if this was more or less of a GOVT question for history or law class then the answer would be " If no candidate for president receives an absolute majority of the electoral votes, pursuant to the 12th Amendment, the House of Representatives is required to go into session immediately to choose a president from among the three candidates who received the most electoral votes. "
Mrs. Wright needs to purchase bottles of water for Fall Festival. She can purchase 18 bottles for $3.69 or 24 bottles for 5.94? Which is the Best Buy?
Answer:
24 bottles for $5.94.
Step-by-step explanation:
hope that helps, have a great day!!
4(x+6)=3x-7 please could you help me
Hello!
Let's use the Distiributive property:
4(x+6)
4x+24
4x+24=3x-7
Move all the variables to the left:
4x-3x=-7-24
x=-31
Hope this helps!
~Just a determined gal
#CarryOnLearning
[tex]MysteriousNature[/tex]
8. Expand, then simplify: (2 Points) (2a – 3) (a2 + 3a - 5)
Hello
just a second
people reading this please complete because you will help me a lot.
I am an Indian girl my name is Lamer and am 13 years old.
I Just got this new device after working at a farm for 2 years.
I used to use brainly at my friend device she had money to buy brainly plus.
I cant please help me get points so I can get good marks and my dad let me complete my education instead of getting married.