Please answer the following questions pertaining to the functions. Show your work! Given the equation 2x-3y=12
A) Determine if the solution(s) if the equation is paired with 3x+2y=31
B) Determine if the solution(s) if the equation is paired with 6x-9y=11
C) What types of slopes do parallel lines have?
Answers
Answer:
below
Step-by-step explanation:
A) 3x+2y=31 is line perpendicular with 2x-3y=12, slope= -3/2 vs 2/3 and intersect at (9 ,2)
B) 6x-9y=11 parallel to 2x-3y=12, has same slope of 2/3, no intersect
C) they have "positive type of slopes" to form parallel lines
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Answer:
A) (x, y) = (9, 2)
B) no solution
C) the same slope
Step-by-step explanation:
A) In the attached, the given equation is graphed in red. The paired equation is shown in blue. They intersect at the point (9, 2), which is the solution to this system of paired equations.
__
B) The line is parallel to its paired line, so there is NO SOLUTION.
__
C) Parallel lines have the same slope.
_____
Additional comments
A graphing calculator provides a quick and easy solution to a system of equations. There are many calculators and apps and on-line sites that can solve a system of equations for you.
For the pair of equations in part A, you can eliminate the y-variable by adding 2 times the first equation to 3 times the second equation:
2(2x -3y) +3(3x +2y) = 2(12) +3(31) ⇒ 13x = 117 ⇒ x = 9
Substituting in the first equation gives ...
2(9) -3y = 12 ⇒ 6 -y = 4 ⇒ y = 2
__
For the paired equation in part B, the ratio of the x- and y-coefficients is 6/-9 = -2/3, the same as it is for the given equation. The constants are different (even after dividing the second equation by 3), so the lines are parallel (not coincident). This means the system of paired equations has no solution.
Related Questions
A flying carpet flies 2.4 miles with the wind in the same amount of time it flies 1.4 miles against the wind. The wind speed is 4 mph. What is the speed of the flying carpet in still air?
Answers
Answer:
[tex]15.2~mph[/tex]
Step-by-step explanation:
Let the time flown by the flying carpet be [tex]t[/tex]. Then, we have that [tex](2.4)/t=(1.4)/t+2*4[/tex].
We multiply both sides of the equation by [tex]t[/tex] to get [tex]2.4=1.4+8t[/tex].
We subtract [tex]1.4[/tex] from both sides to get [tex]1=8t[/tex].
We divide both sides of the equation by [tex]t=1/8[/tex].
We know that the speed of the flying carpet in still wind is the average of the rates of the speed of the flying carpet with the wind and against the wind.
The speed with wind is [tex](2.4)/(1/8)=19.2[/tex]mph.
The speed against wind is [tex](1.4)/(1/8)=11.2[/tex]mph.
The speed in still wind is [tex](19.2+11.2)/2=(30.4)/2=15.2[/tex].
Therefore, the answer is [tex]\boxed{15.2~mph}[/tex] and we're done!
The speed of the flying carpet in still air is 15.2 mph
Let x represent the speed of the flying carpet in still air, and t represent the time.
Speed = distance/time
Since the wind speed is 4 mph, hence:
When flying with the wind:
x + 4 mph = 2.4/t (1)
When flying against the wind:
x - 4 mph = 1.4/t (2)
Dividing equation 1 by 2 gives:
(x + 4) / (x - 4) = 2.4/1.4
1.4x + 5.6 = 2.4x - 9.6
x = 15.2 mph
The speed of the flying carpet in still air is 15.2 mph
Find out more at: brainly.com
Picture below! Help plz. Will give brainilest!!!!!!!!!!!
Answers
This is because 1/10 equal 0.-
Step-by-step explanation:
7.1
7⅒(C).
hope this helps you.
please help with maths asap
Answers
[tex]5 {x}^{2} + 3 {x}^{2} + 6x = 3x - 6x + 9x[/tex]
find out x please fast please fast
Answers
Answer:
[tex]5 {x}^{2} + 3 {x}^{2} + 6x = 3x - 6x + 9x \\ 8 {x}^{2} + 6x = - 3x + 9x \\ 8 {x}^{2} + 6x = 6x \\ 8 {x}^{2} = 6x - 6x \\ 8 {x}^{2} = 0 \\ x = 0 \\ thank \: you[/tex]
What are some decimals for 9/2 other than 4.5
Answers
Answer:
1.4953
Step-by-step explanation:
You will need to break down 4.5
4√5
1.4953
sorry if it’s blurry
Answers
Answer:
surface area = side × side × 6
so answer is...
7 × 7 × 6 = 294 cm²
Step-by-step explanation:
brainliest plz
What is the answer to my question?
Answers
t=3,&y=5....................
Answer:
D
Step-by-step explanation:
-8+(3)=-5
-2(5)-2=-12
Given a function f(x)=2x^2+3, what is the average rate of change of f on the interval [2, 2+h]?
Answers
Answer:
4x+2h
Step-by-step explanation:
The average rate of change of a continuous function,
f
(
x
)
, on a closed interval
[
a
,
b
]
is given by
f
(
b
)
−
f
(
a
)
b
−
a
So the average rate of change of the function
f
(
x
)
=
2
x
2
+
1
on
[
x
,
x
+
h
]
is:
A
r
o
c
=
f
(
x
+
h
)
−
f
(
x
)
(
x
+
h
)
−
(
x
)
=
f
(
x
+
h
)
−
f
(
x
)
h
...
.
.
[
1
]
=
2
(
x
+
h
)
2
+
1
−
(
2
x
2
+
1
)
h
=
2
(
x
2
+
2
x
h
+
h
2
)
+
1
−
2
x
2
−
1
h
=
2
x
2
+
4
x
h
+
2
h
2
−
2
x
2
h
=
4
x
h
+
2
h
2
h
=
4
x
+
2
h
Which is the required answer.
Additional Notes:
Note that this question is steered towards deriving the derivative
f
'
(
x
)
from first principles, as the definition of the derivative is:
f
'
(
x
)
=
lim
h
→
0
f
(
x
+
h
)
−
f
(
x
)
h
This is the function we had in [1], so as we take the limit as
h
→
0
we get the derivative
f
'
(
x
)
for any
x
, This:
f
'
(
x
)
=
lim
h
→
0
4
x
+
2
h
=
4
x
Someone please hurry and answer number one will give brainlyst
Answers
Answer:
put them in desmos and graph them
1. En una biblioteca quieren comprar una computadora que
cuesta $989.99. Hasta ahora recibieron $311.25 en donaciones.
Aproximadamente, ¿cuánto dinero más se necesita para comprarla?
Answers
Answer:
678.74
that might be the question since I don't really understand what it says really
solve pls brainliest
Answers
Answer:
simply 8c = 128
The gas tank of a certain car contains 13 gal when the driver of the car begins a trip. For each mile driven by the driver, the amount of gas in the tank decreases by 0.025 gal.
a. Write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven.
b. Use your equation to find the number of gallons in the tank after 180 miles are driven.
Answers
Answer:
a. write a linear function for the number of gallons of gas in the tank in terms of the number of miles driven.
2.
A cube has a volume of 7 to the third cubic centimeters. What is its surface area?
الم
Answers
Answer:
294
Step-by-step explanation:
since the area is 7^3, the cube's side length is 7
SA = 6*7^2 = 294
Simplify: (4 – 5) – (13 – 18 + 2).
Answers
Answer:
(4 – 5) – (13 – 18 + 2)
= -1-(13+2-18)
= -1-(15-18)
= -1-(-3)
= -1+3
= 2Answer:
(4-5)-(13-18+2)
(-1)-(-3)
-1+3
2
hope this helps u
help me with this question nowww pleasee
Answers
Answer:
Down Here ↓↓↓↓↓
Picture Attached
Step-by-step explanation:
P is 1 1/4 units to the left of 0
R is 3/4 units to the left of 0
Q is 1/4 units to the right of 0
S is 1/4 units to the left of 0
-Chetan K
pls simplify n answer me please guys help
Answers
Answer:
i) 4
ii) -216
please give brainliest
WILL MARK BRAINLIEST IF CORRECT❤️❤️
Simplify the expression -5+i/2i
Step by step
Answers
Answer:
For complex numbers,
a + bi and a - bi
they have the interesting property that if you add them you get the real number 2a
and if you multiply them , because of the difference of square pattern, you get a^2 - b^2 i^2
But since i^2 = -1, we end up with a real number as a product.
e.g. 6 - 5i and 6 + 5i are conjugates of each other
sum = 6-5i + 6+5i = 12
product = 36 - 25i^2
= 36 -(-25) = 61
Your question is even easier, since the denominator is a monomial instead of a binomial, so we just have to multiply by i/i
Also I believe, according to the answer, that you have a typo, and you meant
(-5+i)/(2i)
= (-5+i)/(2i) *i/i
= (-5i + i^2)/2i^2)
= (-5i +i^2)/-2
= (-5i - 1)/-2
= (1 + 5i)/2 or they way they have it: 1/2 + 5i/2
Greenpoint is 12 miles due north of the airport, and Arlington is due east of the airport. If the distance between Greenpoint and Arlington is 13 miles, how far is Arlington from the airport?
Answers
Three teams, A, B and C, play in a competition.
games won by A: games won by B = 4:3
games won by B: games won by C = 5:2
Team B has won 30 games.
In total, how many games have the three teams won?
Answers
ANSWER:
43
Explanation:
A : B : C
4 : 3
5 : 2
A × B → 4 × 5 = 20
B × B → 3 × 5 = 15
B × C → 3 × 2 = 6
A : B : C
20 : 15 : 6
B = 15 = 30
what of teams A and C together?
If 15 = 30games, what about 26games?
Cross multiply.
15 × 26 =13
30
So, games won by Team B + games won by Teams A and C
30games + 13games
=43games.
Answer:
82
Step-by-step explanation:
Alonzo buys cheese from the local farmers market the graph below shows the cheese cost in cents versus its weight in ounces use the graph to answer the questions
Answers
Answer:
35 cents per 1oz
Step-by-step explanation:
there is a slope of 1 so the cost of 1 oz is equal to (1,1)
aisha has 9 pizzas. she is serving each person at the party 3/4 of a pizza how many people can she serve
Answers
Answer:
12 peopleStep-by-step explanation:
hope it helps youUse factoring to solve the equation X(x-32)=0
Answers
You have two terms (0) and (x - 32). And anything multiplied by 0 is 0 so one of those terms has to equal zero.
x = 0
x - 32 = 0
x - 32 + 32 = 0 + 32
x = 32
Which of the following functions is graphed below?
Answers
Answer:
A
Step-by-step explanation:
vertex is (-3,-4)
so inside the absolute value bars need to be postive 3 and the four has to be -4.
Find the slope of the line.
Answers
Answer:
slope = 3
Step-by-step explanation:
rise/run = 3/1 = 3
Find the equation of the line that passes through the point:
(-5, -3) with a slope of 2
Answers
Answer:
y=2x+7
Step-by-step explanation:
find (-5,-3)
use the slope to find the y intercept
intercept is (0,7)
use formula y=mx+b to plug in numbers
(slope is m and y intercept is b)
y=mx+b
y=2x+7
Brainliest?Please?
c. The tires on a mining truck are 14 ft tall.
Radius=
Diameter=
Circumference=
Answers
Radius= 14/2 = 7
circumference = 2(3.14) r
circumference = 43.98
The length of the side of a square whose area is 225 m² is _____.
Answers
Answer:
15
Step-by-step explanation:
Answer: 15
Step-by-step explanation:
you would have to find the square root of 225 and this is 15 so if you do 15x15 you will get 225
and if you need to find the perimeter you add up all the sides
15x4=60
The perimeter of a square is 60
1 side length of a square: 15
Hope this helped :)
PERIOD 2. Which of the dot plots shows a skewed distribution? A. !!! 1.1 12 1.3 1.4 1.5 1.6. 17 1.8 19 B. N +.... 2 2.5 3 3.5 4 4.5 5 5.5 6. 0.5 1 1.5 11 12 13 14 15 9 10 16 18 17 (D. 2.1 14 15 16 17 1.8 20 11 12 13 1.9
Answers
Answer: A.
Step-by-step explanation: There are a few outliers in A which would generally distort the shape of a dot plot where a majority would be clustered around the mean, and the points off to the side would fall far away from the mean making it skewed right in this situation.
52 – 2g = 30
Complete the missing value in the solution to the equation.
(8.
)
Answers
Answer:
The answer is 5
Step-by-step explanation:
Since we already know what x we can just substitute it.
5(8)-2y=30
5 times 8 is 40
40-2y=30
Subtract 40 on both sides:
-2y=-10
Divide -2 on both sides:
y=5
Hope this helps!
And who is your bias for BTS?
(Edit) answer is 5 I guess
Answer:
g=11
Step-by-step explanation:
What I did was Isolate the variable by dividing each side by factors that don't contain the variable.
Set the equation equal to zero and factor the left side.
The factor answer would be 2(−g+11)=0
find (x+55)°
find (3x-5)°
find x
Answers
Answer:
x = 30
Step-by-step explanation:
The two angles are congruent so they have the same value
3x-5 = x+55
Subtract x from each side
3x-5 -x = x+55-x
2x-5 = 55
Add 5 to each side
2x-5+5 = 55+5
2x= 60
Divide each side by 2
2x/2 = 60/2
x = 30
You would get
x=40
Your answer