Solve the following system of equations graphically on the set of axes below. y=3x−3 , x+y=5
Answers
Answer:
x=2, y=3
Step-by-step explanation:
First, graph both equations on a rectangular coordinate system (see attached screenshot). Then, simply figure out where these two lines intersect. Since they intersect at (2,3), x=2 and y=3.
Plugging these values in the equations for x and y, you can see if these are the correct answers:
(3)=3(2)-3, (2)+(3)=5
Since both of these are true, you have the right answer.
Hope this helps!
Two linear equation has their solutions on the points where they intersect each other.
The solution of the given system of equations is:
x = 2, y = 3.
How to determine the solution of system of linear equations graphically?Each linear equation represents a straight line.
If both the given lines intersect at one point, then that point's coordinate is the solution of the given system of the equations.
If both the given lines are parallel, then there is no intersection and thus no solution.
If both the lines are coincident(that is, lying over each other fully), then there are infinite points of intersection, as they touch each other on infinite points, and thus infinite solutions to the given system of equations exist.
Using method of substitution to solve the system of equations:[tex]y = 3x-3\\ x+y = 5 [/tex]
Substituting the value of y from first equation in the second equation, we get:
[tex]x + y = 5\\ x + (3x-3) = 5\\ x+3x = 5+3\\ 4x = 8 \\ x = 2\\ [/tex]
Thus, putting this value of x in first equation, we get:
[tex]y = 3x - 3\\ y = 3 \times 2 - 3\\ y = 6-3\\ y = 3[/tex]
Thus, the system has one solution and it is x = 2, y = 3.
Using graphing, we can see that point of intersection is (x,y) = (2,3)
Learn more about solutions of system of linear equations:
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Related Questions
900 students attend Ridgewood Junior High School. 5% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answers
Answer:
180 students brought their lunch to school on Thursday
Step-by-step explanation:
We are told that out of 900, 5% of the students brought their lunch to school everyday
So the number that brought their lunch on Thursday will be;
5% of 900
= 5/100 * 900 = 180
WILL GIVE BRAINLIEST
WHAT IS 2+2
RIGHT AWNSER WINS/ HINT 4+18
Answers
Answer:
2+2=4
4+18=22
Step-by-step explanation:
What is the value of cos(x/2) if tan x=1/2 and x is in quadrant III
Answers
Answer:
Step-by-step explanation:
The value of cos(x/2) is required.
The required value is [tex]\cos(x/2)=-\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
TrigonometryThe given value is
[tex]\tan x=\dfrac{1}{2}[/tex] where x is in quadrant III.
From trigonometric identities we have
[tex]\sec^2x=1+\tan^2x\\\Rightarrow \sec^2x=1+(\dfrac{1}{2})^2\\\Rightarrow \sec^2x=\dfrac{5}{4}\\\Rightarrow \cos^{2}x=\dfrac{4}{5}\\\Rightarrow \cos x=\dfrac{2}{\sqrt{5}}[/tex]
If x lies in quadrant III then x/2 lies in quadrant II.
Cos is negative in quadrant III so,
[tex]\cos x=-\dfrac{2}{\sqrt{5}}=-\dfrac{2\sqrt{5}}{5}[/tex]
[tex]\cos \dfrac{x}{2}=\pm \sqrt{\dfrac{1+\cos x}{2}}\\ =\pm\sqrt{\dfrac{1-\dfrac{2\sqrt{5}}{5}}{2}}\\ =\pm\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
Since, x/2 lies in the second quadrant and cos (x/2) is negative.
The required value is [tex]-\sqrt{\dfrac{5-2\sqrt{5}}{10}}[/tex]
Learn more about trigonometry:
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Find the sum of the complex numbers.
(3 + 5i) + (10 + 71)
O A. 13 + 121
O B. 7 + 121
O
C. 13 + 2i
O D. 7 + 21
Answers
Answer:
A
Step-by-step explanation:
(3 + 5i) + (10 + 7i) =
3 + 5i +10 + 7i =
3 + 10 + 5i + 7i =
13 + 12i
What is the degree-measure of an angle travelled by the minute hand from 3:05pm to 3:50pm?
Answers
Answer:
270°
Step-by-step explanation:
We know that a full circle is 360°, the shape of a clock, and that the clock is divided into 12 different sections.
Our equation would be: 360 ÷ 12 = 30
3:05 is at the 1 hand and 3:50 is at the 10 hand. Subtract 1 from 10 and you get 9.
9 · 30 = 270, so our angle is 270°
I hope this helped, please mark Brainliest, thank you!
WILL MARK BRAINLIEST!!! Can someone help me wit dis question?
Given y = 9x - 4, what is the y-intercept?
a.) 4
b.) -4
c.) 9
Answers
Answer:
B.) -4
Step-by-step explanation:
y=mx+b
b is equal to the y-intercept.
Answer:
-4
Step-by-step explanation:
The slope intercept form is y = mx + b.
m = slope
b = y-intercept
since b = -4, the y-intercept is -4
Simplify 7 +(-3). (1 point)
Answers
Answer:
4
Step-by-step explanation:
7-3=4
Answer:
7-3=4
Step-by-step explanation:
Im not quite sure if this is what you were asking for but here
In ABC the measure of the largest angle 32 less than 3 time the smallest angle the measure of the middle angle is 8 more than half the measure of the largest angle . What is the measure of the middle angle?
Answers
Answer: The measure of the middle angle = 52°
Step-by-step explanation:
Let x = Smallest angle.
largest angle = [tex]3x-32[/tex]
Middle angle= [tex]8+\dfrac12 (3x-32)[/tex]
Sum of all angles in a triangle is 180 degrees.
So, Smallest angle+ largest angle+ Middle angle = 180°
[tex]\Rightarrow\ x+8+\dfrac12 (3x-32)+3x-32=180\\\\\Rightarrow\ 4x-24+\dfrac{3x}{2}-16=180\\\\\Rightarrow\ \dfrac{2\times4x+3x}{2}-40=180\\\\\Rightarrow\ \dfrac{11x}{2}-40=180\\\\\Rightarrow\ \dfrac{11x}{2}=220\\\\\Rightarrow\ x=\dfrac{220\times2}{11}\\\\\Rightarrow\ x= 40[/tex]
Now , Middle angle= [tex]8+\dfrac12 (3(40)-32)=8+\dfrac12 (120-32)[/tex]
[tex]=8+\dfrac12 (88)\\\\=8+44\\\\=52[/tex]
Hence, the measure of the middle angle = 52°
ill mark brainlest if right
Answers
Answer:
I am super sure its A and C
Hope this helps :D
Is 0.000027 greater than 270?
Answers
Answer:
no because it is lower than 1 and 270 is higher
Answer:
No, because 0.000027 is a decimal. Any decimal with 0. *something* will be less than one. 27 is more than one. Thus, the statement is false.
The total charge on 4 particles is −36 units. All the particles have the same charge.
need asap What is the charge on each particle?
−9 units
−8 units
8 units
9 units
Answers
Answer:
-9
Step-by-step explanation:
If you multiply 9x4 you get 36. its minus 36 so therefor it has to be -9
Hope this helps :) <3
Suppose a system of equations was solved my elimination and the resulting equation was 0=3. Which of the following statements is/are true.
a. The slopes of the two equations in the system are the same but their y-intercepts are different.
b. The system is an independent system.
c. The graphs of the two equations would intersect at the point (0,3).
Answers
Answer:
a. The slopes of the two equations in the system are the same but their y-intercepts are different.Step-by-step explanation:
The system resulting in equation 0=3 means:
There is no solutionThe lines are parallel as no intersectionCorrect choice is:
a. The slopes of the two equations in the system are the same but their y-intercepts are different.*15 points* any help would be appreciated plz
Answers
Answer:
70 degrees because all of the angles in a triangle add up to 180 degrees150 degrees because the adjacent angle is 30 degrees110 degrees because the adjacent angle is 70 degrees50 degrees because angle 5 would also have to be 50 in order for all of the angles on that line to be 180 degreesStep-by-step explanation:
I hope this helps!!!!
Please help this is due today :)
Answers
(Remember rise/run)
The full equation would be 1/2+1
Please do for me thank you I am
Answers
4.) top row: 1, 2, 4, 6, 8, 10
bottom row: 25, 50, 100, 150, 200, 250
5.) top row: 1, 2, 4, 6, 8, 10
bottom row: 50, 100, 200, 300, 400, 500
An advertisement reads “All Books 28 Percent Off.” A best-selling novel is originally priced at $18.99. About how much money will Gio save if he buys the novel on sale?
$2
$6
$10
$14
Answers
Answer:
6 dollars i think
Step-by-step explanation:
Answer:
Gio will save about $6.
Step-by-step explanation:
You would convert 28% to a decimal which is 0.28 and then multiply 0.28 by $18.99 and you would get $5.3172 which is closest to $6 so it would be B. about $6
The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is
Y+ 7 = -
-- (x-10). What
is the standard form of the equation for this line?
O 2x - 5y = -15
2x - 5y = -17
2x + 5y = -15
2x + 5y = -17
Save and Exit
Answers
Answer:2x-5y=-15
Step-by-step explanation:
A delivery driver earns $221 for 17 hours of work. Assuming he is paid by the hour, how much will he earn in 12 hours?
Answers
Answer:
156
Step-by-step explanation:
221/17=13
13*12=156
Answer:
$156
Step-by-step explanation:
221/17=x/12
221*12=17x
2652=17x
156=x
Please help me out!
Answers
Choose 3 values that would make this inequality true. 9 - n ≥ 4
Answers
Answer: Could be 0,1,2,3,4,5
Step-by-step explanation: 9-n has to be greater or equal to four. 9 minus 4 is five. So all of the answers must be positive numbers that are less than five.
Please help!! I have to find x and y!!
Answers
Answer:
X= 17.5
Step-by-step explanation:
the outside of the triangle always = 180
so you need to add up all the sides and equal to 180
5x+35+x+5+2x=180
add like terms
8x+40=180
get the x alone
x=17.5
Mass = 65 kg
Acceleration = 0.3 m/s2
Force =
Answers
Answer: 19.5 N
Step-by-step explanation:
Answer:
The answer is 19.2N
Step-by-step explanation:
F=m a
F=64*0.3=19.2N
An art teacher needs to cut out squares of paper for an art project from a left-over sheet of paper measuring 72 x 104 inches. What size would the biggest possible square be with sides of whole number length?
Answers
Answer:
7488 inches
Step-by-step explanation:
I think that this is the correct answer. The reason is that you have to multiply 72 x 104. I´m not 100% sure.
The required maximum area of the biggest possible square is with sides of a whole number length of 7396 inches².
What is surface area?The surface area of any shape is the area of the shape that is faced or the Surface area is the amount of area covering the exterior of a 3D shape.
Here,
Area of the leftover sheet = 72 × 104 = 7488 inches²
area of the square = 7488
a² = 7488
a = 86.53
Somehow, for the biggest possible square to be with sides of whole number length,
The area is given as,
= 86²
= 7396 inches²
Thus, the required maximum area of the biggest possible square be with sides of whole number length 7396 inches².
Learn more about the surface area here:
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#SPJ2
Simplify (1/2)4. Plz answer fast
Answers
Answer: 2
Step-by-step explanation: 1/2 x 4 = 4/2 = 2/1 = 2.
URGENT HELP! VIEW PICTURE
Answers
Answer:
it 2
Step-by-step explanation:
I think it’s 3(n/5)
Explanation:
The graph of f(x) = 2x + 3 shifts 10 units to the right when it is replaced with the graph of f(x) = 2x − k. What is the value of k?
Answers
Answer:
k=7
Step-by-step explanation:
when entering values of x in the function, it is observed that for k = 7 the results of f (x) displace 10 units. For this see the attached table. Therefore, for this case, the correct answer is k = 7 and the way to solve it is to substitute values of x in the given functions and see the results of f (x).I attach results.
Are the lines parallel? 2x + 3y = 6 and 2x + 3y = 10
Answers
Answer:
the fact that this dosen´t the question like
Step-by-step explanation:
Please answer for a and b
Answers
Answer:
a
Step-by-step explanation:
a
Answer:
Step-by-step explanation:
a can't be an integer
8/√2 doesn't reduce to an integer. It will give you 4*√2 * √2/√2 = 4√2
-√18/√2 = -√(3*3*2)/√2 = -3(√2)/√2 = -3
At best you will get 4√2 - 3
a = 4√2
b = - 3
Edit
b is correct. the answer for b = -3
a can't be done giving an integer answer. My best guess is 4 but that is not the correct answer. You could write it as (4 - 3)√2
My advice to you is to present it to your instructor and see what he/she comes up with.
Solve the equation. a4−56=−12 a=
Answers
Explanation is in the picture
-0.59x+0.39x=5.8 I need help
Answers
Answer: x = -29
Step-by-step explanation:
-0.59x+0.39x=5.8
Collect like terms
-0.2x = 5.8
Divide both sides of the equation by -0.2
x = -29
Response to user in comments:
-0.59+0.39=-0.2 that is a fact
-0.2/-0.2=1 that is a fact
5.8/-0.2= - 29 that is a fact
These are the facts about the steps of the equation. Solving Steps for Solving the Equation