X-2y=5 2x-4y=10
Put both equations in slope-intercept form
Solve the systems of equations by substitution
Solve the systems of equations by graphing
ONE HUNDRED POINTS HURRY
Answers
Step-by-step explanation:
X-2y=5 ; 2x-4y=10
• x - 2y = 5 • 2x -4y = 10
-2y = -x+5 -4y= -2x +10
y1 = ½x - 5/2 y2 = ½x -5/2
• => y1 = y2
½x -5/2 = ½x -5/2
the systems have no solution
• graph as attached
Answer:
[tex]\textsf{Equation 1}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
[tex]\textsf{Equation 2}: \quad y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
True for all x (infinitely many solutions)
Step-by-step explanation:
Slope-intercept form of a linear equation:
[tex]y = mx + b[/tex]
(where m is the slope and b is the y-intercept)
Given equations:
[tex]\begin{cases}x-2y=5\\2x-4y=10\end{cases}[/tex]
To put both equations in slope-intercept form, rearrange both equations to make y the subject:
Equation 1
[tex]\implies x-2y=5[/tex]
[tex]\implies x-2y+2y=5+2y[/tex]
[tex]\implies x=5+2y[/tex]
[tex]\implies x-5=5+2y-5[/tex]
[tex]\implies 2y=x-5[/tex]
[tex]\implies 2y \div 2=(x-5) \div 2[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Equation 2
[tex]\implies 2x-4y=10[/tex]
[tex]\implies 2x-4y+4y=10+4y[/tex]
[tex]\implies 2x=10+4y[/tex]
[tex]\implies 2x-10=10+4y-10[/tex]
[tex]\implies 4y=2x-10[/tex]
[tex]\implies 4y \div 4=(2x-10) \div 4[/tex]
[tex]\implies y=\dfrac{1}{2}x-\dfrac{5}{2}[/tex]
Therefore, both equations are the same as they have the same slope and y-intercept.
As both equations are the same, this system of equations is called an equivalent system.
To solve a system of equations by substitution, substitute one equation into the other:
[tex]\implies \dfrac{1}{2}x-\dfrac{5}{2}= \dfrac{1}{2}x-\dfrac{5}{2}[/tex]
As both sides are equal, the solution is true for all x.
The solution to a graphed system of equations is the point(s) of intersection.
When graphing the given system of equations, as the lines are the same, they will be on top of each other. They are called coincident lines and have infinitely many solutions since the lines have the same slope and same y-intercept.
Learn more about systems of equations here:
https://brainly.com/question/21447811
https://brainly.com/question/27357423
Related Questions
Can someone help me with this ?
Answers
Answer:
Step-by-step explanation:
the side opposite of K is JL.
explanation:
Zachary earns $5 per hour, and he makes a $20 bonus.
His equation is shown in red on the graph, y = 5x + 20.
Maisy earns $7.50 per hour, and she makes a $5 bonus.
Her equation is shown in blue on the graph, y = 7.50x +
5.
After how many hours do they earn the same amount of
money? Where do you see this on the graph?
Answers
Answer:
6 hours
we see it at the x value of 6 on the graph
Step-by-step explanation:
I graphed it too using desmos then located the point where they cross, the solution point, and it was at the x value of 6 and they will have made $50 by the way in case you wanted to know that too so we see that on the graph at the point (6,50) is where they make the same amount of money.
math is hard
I'll mark someone the brainlyest
Answers
Answer:
1/w^6 or w^-6
Step-by-step explanation:
You add the two exponents
I recommend putting 1/w^6
Please mark brainliest
The expected value of the number of points for one roll is
A) 0
B) 3
C) 6
Answers
Answer:
A) 0
Step-by-step explanation:
got right on assignment
If $36.25 in tax is added to the price of an item, what was the original price in dollars of the item?
$400
$500
$483.33
$600
Answers
What is the probability of flipping a coin 12 times and getting heads 3 times?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
1/4
Step-by-step explanation:
We put 3 /12 which is 1/4 simplified
Glad I could help!!1
Find the square roots of the following numbers. Give the steps correctly.
\sqrt {19.9 }
Please give me the answer .
Answers
Answer:
the sqare root of 19.9 is 4.46094160464
Which of the following is a non linear equation?
i) x/3 = 12
ii) x + 1 = 6
iii) x + y + z = 17
iv) x y + x/y = 3
Answers
Answer:
Option (iv) is correct.
Step-by-step explanation:
The linear equation is the equation in which the degree of the equation is 1.
(i) x/3 = 12
As the degree of equation is 1, so, it is a linear equation.
(ii) x + 1 = 6
As the degree of equation is 1, so, it is a linear equation.
(iii) x + y + z = 17
As the degree of equation is 1, so, it is a linear equation.
(iv) x y + x / y = 3
x y^2 + x = 3 y
The degree of equation is 3, so the equation is non linear.
For what value of k is the expression x4+kx2+36 a perfect square?
Answers
Answer:
12
Step-by-step explanation:
Because if you see clearly that is the only answer that makes the most sense!
The value of m is the expression x⁴ + mx² + 64 a perfect square will be 16.
What is a perfect square trinomial?A perfect square trinomial formulation can be created by taking the binomial equation's squared. If and then only if a trinomial satisfying the criterion b² = 4ac has the form ax² + bx + c, it is indeed a perfect square.
The equation is given below.
⇒ x⁴ + mx² + 64
Then the value of a, b, and c will be 1, m, and 64, respectively. Then the equation will be given as,
b² = 4ac
m² = 4 x 1 x 64
m² = 265
m² = 16²
m = 16
The value of m is the expression x⁴ + mx² + 64 a perfect square will be 16.
More about the perfect square trinomial link is given below.
brainly.com/question/16615974
#SPJ3
complete question:
For what value of m is the expression x4+mx2+64 a perfect square?
Drag each length to match it to an equivalent length. 2 yards 5 inches returned to choices list. 2 feet 8 inches4 yards9 feet2 yards 5 inches Length Equivalent Length 32 inches 77 inches 144 inches 3 yards
Answers
Answer:
2 yards 5 inches will be equivalent to 77 inches
Step-by-step explanation:
Given length -
2 yards 5 inches
One yard has 36 inches
Two yards will have 2*36 = 72 inches
Thus, 2 yards 5 inches will sum up to 72 inches + 5 inches = 77 inches
Hence, 2 yards 5 inches will be equivalent to 77 inches
Answer:
3 yards = 9 feet
77 inches = 2 yards 5 inches
48 inches = 1 yard 1 foot
32 inches = 2 feet 8 inches
I hope this helped!! <3
Verona is solving the equation -3+4x=9. In order to isolate the variable term using the addition property of equality, which number should she add to both sides of the equation?
Answers
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Step-by-step explanation: he should add 3 because then you have 4x=12 and that simplifies to x=3
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Answer:
(5x + 16) + 102 + 92 + 100 = 360
(5x + 16) + 294 = 360
-294 -294
5x + 16 = 66
-16 -16
5x = 50
Divide by 5 on both sides.
x = 10 degrees
A quadrilateral will always equal 360 degrees
A triangle will always equal 180 degrees.
The scatterplot below shows the relationship between the height, in inches, and the shoe size of each of 10 students in a class. Students' Heights and Shoe Sizes 69 Height Based on the scatterplot, what ordered pair represents the outlier in the data? O (67, 7) O (8.5, 65) O (7.67) O (65,8.5)
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What is the missing term?
Answers
Answer:
Missing term = 6x
Step-by-step explanation:
We got:
=> 4x by multiplying +4 and x (x * 4 = 4x)
=> 12 by multiplying +4 and +3 (4 * 3 = 12)
=> 2x² by multiplying 2x and x (2x * x = 2x²)
Similarly we will get the "missing term" by multiplying 2x and +3
=> Missing term = 6x, (2x * 3 = 6x)
Hope this helps!
Reasoning : 2x • 3 = 6x
Luke randomly selects 25 students from his school and asks each of them how many minutes they read each night to find out how much, on average, students at his school read. This represents which type of data collection
Answers
Answer:
Simple random sampling
Step-by-step explanation:
Luke wants to study average minutes students read each night. For that matter, he has selected a 'sample' of 25 students from entire 'population' of students in school.
He has selected the sample students randomly, for collecting data related to minutes of study each night. He also collects data from them directly ie with primary contact with them.
So, primary data collection, simple random sampling - has been used as a type of data collection.
What is the shape of this distribution
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Could I please get brainliest answer?
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
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Answer:
810
Step-by-step explanation:
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Write the equation of the line in fully simplified slope-intercept form.
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Answer:
y=-1/2x-1
Step-by-step explanation:
What part of the circle is shown?
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Answer:
Diameter
Step-by-step explanation:
The diameter is a straight line through the centre of a circle.
Hope this helps :)
♡BRAINLIEST TO RIGHT ANSWER♡
------Find the surface area of the figure, round your answer to the nearest hundredth if necessary <3
5.1 in
1 in
Answers
Answer:
19.47
Step-by-step explanation:
if the radius Is 1 and height is 5.1
formulas of a triangular prism
Answers
Answer: Triangular prisms have their own formula for finding surface area because they have two triangular faces opposite each other. The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.?
Step-by-step explanation:
"How much does it cost for a ticket to ride the subway from Station A to Station B?"
Is this an statistical question or its not an statistical question?
Answers
1 In triangle MNP the measure of angle NPM is 80° and the measure of angle MNP is 22.5°.
What is the measure of angle PMN in degrees?
Answers
Answer:
77.5°
Step-by-step explanation:
Recall that the sum of angles in a triangle is 180 degrees.
Given the triangle MNP with the measure of angle NPM is 80° and the measure of angle MNP is 22.5°
Then
angles NPM + MNP + PMN = 180 degrees
This means that
80 + 22.5 + PMN = 180
102.5 + PMN = 180
Collect like terms
PMN = 180 - 102.5
= 77.5°.
Professor Turner wrote the expression below on the chalkboard for his team at the Research Center. He asked the scientists there to write an equivalent expression that eliminated the parentheses.
Answers
Answer:
12x + 18y + 6z + 4x - 4z
Step-by-step explanation:
Given the expression : 3(4x + 6y + 2z) + 4(x – z)
To eliminate the parenthesis ; we use the distributive property :
3(4x + 6y + 2z) + 4(x – z) becomes ;
3*4x + 3*6y + 3*2z + 4*x + 4*-z
12x + 18y + 6z + 4x - 4z
Hence,
12x + 4x + 18y + 6z - 4z
16x + 18y + 2z
please help i give all my points
Answers
where is the drip at?
Here's the number line what fraction of 1 foot is 3 inches what fraction of one yard is 3 inches explain
Answers
Answer:
1/4 and 1/12
Step-by-step explanation:
We know that
1 foot = 12 inches
therefore, 1 inch = 1/12 foot
hence, 3 inches = 3/12 foot
= 1/4.
Therefore, the required fraction is = 1/4
Similarly,
1 yard = 36 inches
This implies 1 inch = 1/36 yard
Hence, 3 inches = 3/36 = 1/12
Therefore, the required fraction = 1/12
A cable 27 feet long runs from the top of a utility pole to a point on the ground 16 feet from the base of the pole. How tall is the utility pole?
Answers
Answer: 31.38
Step-by-step explanation:
you can always remember a*2+b*2=c*2
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1. {26, 21, 28, 31, 9, 28, 16, 18, 21, 23, 29, 24, 19, 22, 25, 28}
Find the mean.
Find the Medium
Find the mode(s)
Find the range
Answers
Mean=23
Median=21.5 its a hard one to do so yeah
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90%in the SIMPLEST form
Answers
Answer:
[tex]90\% = \frac{90}{100} \\ = \frac{9}{10} = 0.9[/tex]
Answer:
The simplest form of
90/100
is
9/10
Step-by-step explanation:
Find the GCD (or HCF) of numerator and denominator
GCD of 90 and 100 is 10
Divide both the numerator and denominator by the GCD
90 ÷ 10
100 ÷ 10
Reduced fraction:
9
10
Therefore, 90/100 simplified to lowest terms is 9/10.
Find the discriminant of 3x^2 - 10x = -2
I don't know what a discriminant is help