Answers
The solution to the systems are (1, 1), (-3, -1), (1, -2), (2, -1), (7, -1) and (-2, 2)
How to determine the solution to the system?System 1
In this case, the system of equations is given as
y = -3x + 4
y = 3x - 2
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, 1)
So, the solution is (1, 1)
System 2
In this case, the system of equations is given as
y = x + 2
x = -3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (-3, -1)
So, the solution is (-3, -1)
System 3
In this case, the system of equations is given as
4x + y = 2
x - y = 3
Next, we plot the graph of the system of equations
In this case, the point of intersection of the equations represent the solution to the system
From the graph, the lines intersect at (1, -2)
So, the solution is (1, -2)
System 4
We have
y = 4x - 9
y = x - 3
Substitute y = 4x - 9 in y = x - 3
4x - 9 = x - 3
Evaluate the like terms
3x = 6
So, we have
x = 2
Recall that:
y = x - 3
So, we have
y = 2 - 3
y = -1
So, the solution is (2, -1)
System 5
We have
x + 7y = 0
2x - 8y = 22
Make x the subject in x + 7y = 0
x = -7y
Substitute x = -7y in 2x - 8y = 22
-14y - 8y = 22
Evaluate the like terms
-22y = 22
So, we have
y = -1
Recall that:
x = -7y
So, we have
x = -7(-1)
x = 7
So, the solution is (7, -1)
System 6
We have
-7x + 2y = 18
6x + 6y = 0
Make x the subject in 6x + 6y = 0
x = -y
Substitute x = -y in -7x + 2y = 18
7y + 2y = 18
Evaluate the like terms
9y = 18
So, we have
y = 2
Recall that:
x = -y
So, we have
x = -2
So, the solution is (-2, 2)
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Related Questions
HELP PLEASEEEEEEEEEEEEEEEE
Answers
Answer:
1[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
To find the answer, we divide the number of apples by the number of bags. This means we do 7 ÷ 4
7 ÷ 4 = 1.75
1.75 in fraction form is 1[tex]\frac{3}{4}[/tex]
Answer:
7 bags dived by 4=7/4=1 3/4 is your answer
Which of the following is correctly written in Standard Form?
y= 4/5x +4
4x- 3y = 6
4/5x + 2y = 6
-4.2 + 2y =8
Answers
9514 1404 393
Answer:
(b) 4x- 3y = 6
Step-by-step explanation:
Standard form is ...
ax +by = c
where a, b, c are mutually prime integers and a > 0. (If a=0, then b>0.)
__
A: slope-intercept form with variables on both sides of the equal sign.
B: standard form
C: coefficients aren't integers
D: coefficients aren't integers; leading coefficient is negative.
Answer:
4x- 3y = 6
Step-by-step explanation:
The cost of bottles of vitamins varies
directly with the number of vitamin
tablets in a bottle. A bottle of 50 vitamin
tablets costs $12. What is the cost in
dollars of a bottle of 75 vitamin tablets?
Answers
Answer:
find cost of one vitamin tablet first
50/12 = 4.2
therefore $4.2 is the cost for one tablet
now to find the cost of 75 vitamin tablets we just need to multiply the cost of one tablet with 75.
75*4.2=315
therefore the cost of a bottle of 75 vitamin tablets is $315
At a candy store each bag holds 0.75 pounds. A box with 12 pounds of candy is being put into ,b, bags. How many bags of candy is this?
Answers
Answer:
17 bags is correct
Step-by-step explanation:
12 / 75 is equal to 17.14
Solve it below:
...............
Answers
Answer:
i.+25
ii.+18
iii.-10
Step-by-step explanation:
hope this helps
Answer and step-by-step explanation:
We need to show the increase or decrease in Andre's money by representing it through a number.
i. His uncle gave him $25 as a present
This would be +$25
ii. He earned $18 dollars tutoring
This would be +$18
iii. He spent $10 on a book
This would be -$10
Find the simple interest on the following amounts:
a K4000 invested at 6% p.a. for 4 years
b K23 000 invested at 6.5% p.a. for 8 years
K580 borrowed at 5% p.a. for 9 months
inte
с
500
Answers
Answer:
a. Simple interest = K960
b. Simple interest = K11,960
c. Simple interest = K261
Step-by-step explanation:
Given the following data;
a. Principal = K4000
Interest rate = 6%
Time = 4 years
To find the simple interest;
Mathematically, simple interest is calculated using this formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is simple interest.
P is the principal.
R is the interest rate.
T is the time.
Substituting into the equation, we have;
[tex] S.I = \frac {4000*6*4}{100} [/tex]
[tex] S.I = \frac {4000*6*4}{100} [/tex]
[tex] S.I = \frac {96000}{100} [/tex]
S.I = K960
b. Principal = K23 000
Interest rate = 6.5%
Time = 8 years
To find the simple interest;
[tex] S.I = \frac {PRT}{100} [/tex]
Substituting into the formula, we have;
[tex] S.I = \frac {23000*6.5*8}{100} [/tex]
[tex] S.I = \frac {1196000}{100} [/tex]
S.I = K11,960
c. Principal = K580
Interest rate = 5%
Time = 9 months
To find the simple interest;
[tex] S.I = \frac {580*5*9}{100} [/tex]
[tex] S.I = \frac {26100}{100} [/tex]
S.I = K261
A jacket is priced $35.99, and is on sale for 25% off. What is the sale price of the jacket?
Answers
Answer:
The answer is $27
Step-by-step explanation:
This answer is pretty simple. All you have to do is multiply 35.99 x 0.25. This will get you the numeral 8.99... That is the discount. Next you will take the total amount and subtract it with the discount.
35.99 - 8.99 = 27
That is the sale price of the jacket.
I hope this answer helped you in some way. I would really appreciate it if you could check out my channel The Game Rater or soon to be Nitro Studios (based on when you see this). Anyways, I still thank you for reading this side note and it is completely up to you if you want to check out my channel. Thank you.
-Nitroid444inasmuch as 76543 is greater than 43765 help pleace
Answers
Answer:
32778
Step-by-step explanation:
76543-43765=32778
Natalie budgets $146 for yoga training. She buys a yoga mat for $10 and spends $9 per day on yoga classes. Which inequality represents the number of days, d, that Natalie can take classes and stay within her budget?
A 146 ≤ 9d + 10
B 146 ≥ 9d + 10
C 146 ≤ 10d + 9
D 146 ≥ 10d + 9
Answers
Answer:
The answer should be letter D (146 ≥ 10d + 9)
Step-by-step explanation:
Christie's Auction sold a painting for
$24,500. It charges all buyers a 15%
premium of the final bid price. How much
did the bidder pay Christie's?
Answers
X$. 15%
X=24,000•15/100
X=3,675 premium
24,000-3,675=20,825$ bidder pay Christine.
The price that bidder pays to Christie's is $2130.4.
What is percentage?A percentage is a value that indicates 100th part of any quantity.
A percentage can be converted into a fraction or a decimal by dividing it by 100.
And to convert a fraction or a decimal into percentage, they are multiplied by 100.
Given that,
The price for which painting is sold is $24,500.
The percentage of premium price of the final bid is 15%.
Suppose the price paid by the bidder be x.
Then, as per the question the following equation can be written for the price of painting,
x + 15% of x = 24500
=> x + (15/100)x = 24500
=> 115x/100 = 24500
=> x = (24500 × 100) ÷ 115
=> x = 2130.43
Hence, the amount paid to Christie's is $2130.4.
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The owner of the Texans football team wants to paint their red, white, and blue logo on the side of a building at their training facility. However, the existing paint, which would comprise the background for the logo, is beginning to deteriorate. The owner is considering re-painting the building with a special weatherproof paint prior to adding the logo. If the special background paint costs $1.25 per square foot, how much money will the owner have to spend on the paint for the background
Answers
Answer:
$393.75
Step-by-step explanation:
cost of special background paint = $1.25 per square foot
Area of background = area of triangle + area of rectangle
= 1/2 ( b*h) + L * B
= 1/2 ( 5 * 6 ) + 5 * 4 = 15 + 20 = 35 yd^2
Given that 1 yd^2 = 9 ft^2
35 yd^2 = ( 9 * 35 ) ft^2
Hence area of background = 315 ft^2
Cost = 315 * 1.25 = $393.75
Each square on the grid represents 1 square yard. What is the area of the octagon?
A.49 sq yd
B.41 sq yd
C.36 sq yd
D.39 sq yd
Answers
Answer:
B. 41 sq yd
hope this answer helps you......
The heights, in inches, of five players on a basketball
team are 68, 70, 76, 71, and 70. What is the mean
height, in inches, of these players?
A)76
B)72
C)71
D)70
Answers
Answer:
C) 71
Step-by-step explanation:
To find the mean you must first add all the numbers:
68 + 70 + 76 + 71 + 70 = 355.
After that you divide the number you got by how many numbers are in the set.
There are five players so we divide the number by 5
355/5 = 71
Therefore, it is 71.
-mZ2 = 30. Find m24.
Answers
The radius of a circle is changing at the rate of 1/π inches per second. At what rate, in square inches per second, is the circle’s area changing when the radius is 5 inches?
Answers
Answer:
10 square inches per second.
Step-by-step explanation:
The radius of the circle is given by the equation:
r(t) = (1/π in/s)*t
Where time in seconds.
Remember that the area of a circle of radius R is written as:
A = π*R^2
Then the area of our circle will be:
A(t) = π*( (1/π in/s)*t)^2 = π*(1/π in/s)^2*(t)^2
Now we want to find the rate of change (the first derivation of the area) when the radius is equal to 5 inches.
Then the first thing we need to do is find the value of t such that the radius is equal to 5 inches.
r(t) = 5 in = (1/ in/s)*t
5in*(π s/in) = t
5*π s = t
So the radius will be equal to 5 inches after 5*π seconds, let's remember that.
Now let's find the first derivate of A(t)
dA(t)/dt = A'(t) = 2*(π*(1/π in/s)^2*t = (2*π*t)*(1/π in/s)^2
Now we need to evaluate this in the time such that the radius is equal to 5 inches, we will get:
A'(5*π s) = (2*π*5*π s)*((1/π in/s)^2
= (10*π^2 s)*(1/π^2 in^2/s^2) = 10 in^2/s
The rate of change is 10 square inches per second.
(2x + y)2 – (3x – 2y)2 + (x – 4y)(x + 4y
11
Answers
Answer:
Step-by-step explanation:
(a+ b)² = a² + b² + 2ab
(2x + y)² = (2x)² + y² + 2*2x *y
= 4x² + y² + 4xy
(a- b)² = a² + b² - 2ab
(3x - 2y)² = (3x)² + (2y)² - 2*3x *2y
= 9x² + 4y² - 12xy
(a - b)(a +b) = a² - b²
(x - 4y(x + 4y) = x² - (4y)²
= x² - 16y²
(2x + y)² - (3x - 2y)² + (x - 4y)(x +4y)
= 4x² + y² + 4xy - (9x² + 4y² - 12xy) + x² - 16y²
= 4x² + y² + 4xy - 9x² - 4y² + 12xy + x² - 16y²
= 4x² - 9x² + x² + y² - 4y² - 16y²+ 4xy + 12xy
= -4x² - 19y² + 16xy
I need to give the slope but I don’t know how someone help!
Answers
Answer:
-4/2
Step-by-step explanation:
rise over run
goes down -4 "rises"
moves over 2 runs
NO SCAM LINKS.
please reply ASAP PLEASEEEE
Answers
Answer:
B
Step-by-step explanation:
No LINK Easy math please help is this liner y=2\x +1 explain please too
Answers
Answer:
It is not linear
Step-by-step explanation:
If you plug that function into Desmos graphing Calculator, you can see there are two leparate lines and they are not straight.
Find the value of "x"
Answers
Simplify 8(x + 7) + 8 over 3(x + 5) + 9
Answers
Answer:
8/3
Step-by-step explanation:
First you simplify 8(x+7) +8, which is 8x +64. then you simplify 3(x+5)+9, which is 3x+24. To simplify 8x+64 over 3x+24 is easy, because you just get rid of the x's, and divide by eight. So that's 8/3
Answer:
8/3
Step-by-step explanation:
First you simplify 8(x+7) +8, which is 8x +64. then you simplify 3(x+5)+9, which is 3x+24. To simplify 8x+64 over 3x+24 is easy, because you just get rid of the x's, and divide by eight. So that's 8/3
Amy needs to estimate how many students at her school like online testing. She needs to create a random sample of students. How should Amy collect her sample? Select two that apply.
O Amy should ask every 10th person leaving the school at the end of the day.
O Amy should ask 3 people at every table in the cafeteria
O Amy should ask her 10 closest friends.
O Amy should ask the 35 students in her honors math class
O Amy should ask the 50 students in the computer club.
Answers
The answer should be the second one and 4th
ASAP Please!
Enter the amplitude of the function. f(x)=5cosx
Answers
Amplitude of f(x)=5cosx
= 5
what's an amplitude example?The amplitude of a periodic variable is a measure of its change in a single period. The amplitude of a non-periodic signal is its magnitude as compared with a reference value. there are numerous definitions of amplitude, which can be all functions of the magnitude of the differences between the variable's extreme values.
It refers to most displacement from the equilibrium that an object in periodic motion show. as an example, a pendulum swings through its equilibrium point (straight down), and then swings to a maximum distance away from the center.
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Write (3i-2/3)-(6i-5) as a complex number in standard form.
A.(13/3-9i)
B.(13/3-3i)
C.(17/3-3i)
D.(13/3+9i)
E.13 - i
Answers
Answer:
(13/3+9i)
Step-by-step explanation:
narvella cut 1/2 of a pumpkin pie into 5 equal servings. what fraction of the whole pie is each of these servings?
a : 1/4
b : 1/2
c : 1/10
d : 1/8
Answers
Answer:
C. 1/10
Step-by-step explanation:
Which is a true statement about the graph of Y= -1/3x -6?
A) The graph slants downward as you move from left to right.
B) The graph passes through the Y-axis at (0, 6).
C) The graph passes through the origin.
D) The graph does not pass through Quadrant II.
Answers
Answer:
A
Step-by-step explanation:
The slope is negative so the line is high on the left and low on the right, slanting downward
Determine the measure of side AC. Round to the nearest tenth.
Answers
Answer:
Solution given:
sin 52°=perpendicular/base
sin52°=AB/AC
AC=12/sin52°=15.23is your answer
Which of the following expressions are equivalent to −5.93+(−8.62)+5.93?
Answers
Answer:
A, B, C, DStep-by-step explanation:
−5.93 + (−8.62) + 5.93 =−5.93 - (8.62 - 5.93) = B−(5.93 + 8.62) + 5.93 = C−5.93 −8.62 - (- 5.93) = D-8.62 AAll options Except E
Because
From question
The expression yields -8.62 after 5.93 gets cancelled outBut in E
-5.93-(8.62+5.93)Results one -5.93 more so 5.93 doesn't get cancelled out
r + 12 = 86
what does r equal ?
Answers
86 - 12 = 74
74 + 12 = 86
Answer:
86-12 is 74 so r=74
hope it helps
if 15% of x is 12. what is x?
Answers
Answer:
Step-by-step explanation:
80
Answer Explanation: 12 ÷ 15%
12 ÷ (15 ÷ 100)
(100 × 12) ÷ 15
1,200 ÷ 15
80