(08.01) Two lines, A and B, are represented by the following equations: Line A: 3x + 3y = 12 Line B: x + y = 4 Which statement is true about the solution to the set of equations? It is (12, 4). There are infinitely many solutions. It is (4, 12). There is no solution.
Answers
Answer: There are infinitely many solutions.
Step-by-step explanation:
Given, Two lines, A and B, are represented by the following equations:
Line A: 3x + 3y = 12
Line B: x + y = 4
By comparing to the equations \(a_1x+b_1x=c_1\) and \(a_2x+b_2x=c_2\) respectively , we have
\(a_1=3,\ b_1=3\ \ \&\ c_1=12\\\\a_2=1,\ b_2=1\ \ \&\ c_2=4\)
Now , \(\dfrac{a_1}{a_2}=\dfrac{3}{1},\ \dfrac{b_1}{b_2}=\dfrac{3}{1},\ \&\ \dfrac{c_1}{c_2}=\dfrac{12}{4}=\dfrac{3}{1}\)
i.e. \(\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}\)
It implies the gives lines are co-incident (linearly dependent).
That means it has infinitely many solutions.
So, the correct answer is "There are infinitely many solutions.".
Related Questions
A grocery store recently sold a bag of peanuts for $0.76 and a bag of Pikachu's for $3.68 at the end of the day 50 bags of peanuts and Pikachu's were sold for a total of 128 point 52 how many bags of each were sold
Answers
Answer:
31 Pikachu bags were sold.
19 peanut bags were sold.
Step-by-step explanation:
Let's set up an equation of the total revenue of the day, where x is the number of Pikachu's sold.
We know that the number of Peanuts sold is 50-x (as the total needs to be 50)
We know that the total revenue is:
Number of Pikachus * Cost per Pikachus + Number of Peanuts * Cost per Peanuts
Using our definitions above:
Total Revenue = x * $3.68 + (50-x) * $0.76
We know that the revenue needs to be $128.52.
$128.52 = x * $3.68 + (50-x) * $0.76
Let's remove the $ signs.
128.52 = x * 3.68 + (50-x) * 0.76
Multiplying both 50 and -x with 0.76, "expanding" the parenthesis.
128.52 = x*3.68 + 50*0.76 - x*0.76
128.52 = x*3.68 + 38 - 0.76*x
Subtracting 38 from both sides
90.52 = 3.68*x - 0.76*x
We can simplify the right side.
90.52 = 2.92*x
We can divide both sides by 2.92:
31 = x
And flip it:
x = 31
So 31 Pikachus were sold (remember we claled that x), and as we know, the number of peanut bags sold is
50-x = 50-31 = 19
31 Pikachu bags were sold.
19 peanut bags were sold.
\( \LARGE{ \boxed{ \rm{ \pink{Solution:}}}}\)
Let the number of peanut bags be x
Then, Number of pikachu bags = 50 - x
Given,
Cost of each peanut bag = $0.76Cost of each pikachu bag = $3.68Then,
⇛ Total cost he gets from peanut bag = $0.76 × x
⇛ Total cost he gets from pikachu bag = $3.68(50 - x)
According to question,
⇛ $0.76x+ $3.68(50 - x) = $128.52
Solving this equation,
⇛ 0.76x + 184 - 3.68x = 128.52 (Removed $ symbol)
⇛ 184 - 2.92x = 128.52
⇛ 184 - 128.52 = 2.92x
⇛ 55.48 = 2.92x
Flipping the equation,
⇛ 2.92x = 55.48
⇛ x = 55.48 / 2.92
⇛ x = 19
Then,
⇛ 50 - x = 50 - 19 = 31
\( \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: peanut \: bags = 19}}}}}\)
\( \large{ \therefore{ \boxed{ \rm{ \purple{No. \: of \: pikachu \: bags = 31}}}}}\)
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Solve the following equations.
1.) 1/5x - 2 = -3
2.) 15 = 10 - x/4
3.) x/3 - 12 = -2
4.) x/-2 + (-6) = 6
Answers
Answer:
-5-2030-24Step-by-step explanation:
Solve the following equations.
1.) 1/5x - 2 = -3
2.) 15 = 10 - x/4
3.) x/3 - 12 = -2
4.) x/-2 + (-6) = 6
1/5x - 2 = -3
1/5x = -1
x = -1 : 1/5
x = -1 × 5
x = -5
15 = 10 - x/4
5 = -x/4
x = -5 : 1/4
x = -5 × 4
x = -20
x/3 - 12 = -2
x/3 = 10
x = 10 × 3
x = 30
x/-2 + (-6) = 6
x/-2 - 6 = 6
x/-2 = 12
x = -24
Write and solve an equation that represents the following math sentence.
Twenty-four equals the sum of 10.5 and the quotient of a number and 4.5.
24 = 10.5 + 4.5m; m = 60.75
24 = 10.5 + 4.5m; m = 3
24 equals 10.5 plus m over 4.5; m = 3
24 equals 10.5 plus m over 4.5; m = 60.75
Answers
Answer:
24 = 10.5 + 4.5m; m = 60.75
Step-by-step explanation:
Answer:
24=10•5+4•5m؛m=60•75
24=10•5+4•5m؛m=
24 equal 10•5plus m over 4•5؛m=
24 equal 10•5 plus m over 4•5؛m=60•
Step-by-step explanation:
When you reverse the digits in a certain two-digit number you increase its value by 9. What is the number if the sum of its digits is 5?
Answers
Use r = 2 and r = 5 to determine if the two expressions are equivalent.
r + 4(2 + r) – 12 8 + 2r – 6
Complete the statements.
When r = 2, the first expression is
.
When r = 2, the second expression is 6.
When r = 5, the first expression is 21.
When r = 5, the second expression is
.
The expressions are not equivalent.
Answers
When r =5 the 2nd is 12
Jackie has a circular shaped table. She wants to paint the circular top. If the radius of the circle is 3 feet, what is the area of the table top?
18.84 square feet
28.26 square feet
56.52 square feet
9.42 square feet
Answers
area of circle :- π r²
\( \frac{22}{7} \times 3 \times 3 \: ft {}^{2} \\ \frac{22}{7} \times 9 {ft}^{2} \\ \frac{198}{7} = 28.26 {ft}^{2} \)
Answer:
A.
Step-by-step explanation:
The formula (i believe) is:
A = 2r\(\pi\)
A = 2(3)(3.14)
A = (6)(3.14)
A = 18.84
The answer i got is 18.84
hope this helps :)
A rectangular poster has an area of 504 square centimeters. The width of the poster is 14 centimeters. How long is the poster?
Answers
Answer:
36 sq. cm.
Step-by-step explanation:
We find area by multiplying the length by the width of the poster. But now, in your question we want to find the length of the poster. We are given the area, 504 square centimeters, and the width, 14 centimeters. Since multiplication and division are inverse operations, we will do the opposite of multiplication, division, to find the quotient, the length of the poster. 504 divided by 14 can be written like this: 504 / 14. 504 / 14 = 36 sq. cm. We can check our answer by multiplying 36 and 14 to get 504. So, we know our answer is correct.
Answer:
i think it is 514
Step-by-step explanation:
Wondering if you can help again..?
Answers
Answer:
try 65
Step-by-step explanation:
google calculator bud
I know because I’m built DIFFERENT
5.7 - 14.
a. 43
b. 19.7
c.-8.3
d. -19.7
Answers
Answer:
c
Step-by-step explanation:
5.7 -14 = -8.3
5.7 going back 14 is -8.3
how far was 14.5 from 14.4
Answers
Answer:
.1
Step-by-step explanation:
14.5-14.4=.1
Explanation:
Sample Answer: Make a table with inputs showing the number of bottles of water and outputs showing the total cost of the water. Use 1, 2, 3, and 4 bottles for the inputs. Find the corresponding outputs. Plot the ordered pairs in the table of the form (input,output).
Which instructions did you include in your explanation? Check all that apply.
Identify the input.
Identify the output.
Create a table for four input values.
Plot the points from the table.
Answers
The instructions that you would include in your explanation are:
Identify the output.
Create a table for four input values.
Plot the points from the table.
The instructions to be includedIn the given question, a series of instructions are provided. To properly explain your process, you have to explain how you got the output. There is no need of explaining the input as they are already provided.
Next, you will Show how you created the table and why you created it in that way. Finally, indicate how the points were plotted on the table. An explanation such as this will help anyone to follow through.
Learn more about ordered pairs here:
https://brainly.com/question/1528681
#SPJ1
Answer:1 to 2
2 to 4
Step-by-step explanation:
Plz answer the pic, I need help with this math
Answers
Answer:
63
Step-by-step explanation:
width x length = area of rectangle
7 x 9 = 63 square feet
Answer:
63
Step-by-step explanation:
Area= length x weigth
Area= 9ft x 7ft
Area= 63ft square
⚠️(Math 8th grade) HELP PLZZZ⚠️
Answers
Answer:
Your answer is: C) y=-2x+2
I am 100% sure!!
Step-by-step explanation:
Hope this helped : )
PLEASEE HURRY AND HELP ME NO WRONG ANSWERS :( !!!!!!!!!!
LOOK AT THE IMAGES BELOW !!!!!!!!!!!!!
Answers
Answer:
Hello, for the first one, the answer should be (C) 3
The following transformation is an enlargement, meaning it would get bigger. Meaning that the scale factor increases by 3.
2x3=6
3x3=9
Therefore, the scale factor is (C) 3.
#5: The answer is (D): 4
Since this is an enlargement, we have to determine what ? x 6 = 24 is. Since the height of the photo is 6, we can conclude that 6 x 4 = 24.
Therefore, the answer is (D): 4
Hope this helped! Sorry for the complications <33
a squirrel digs 4 holes in 5 minutes how many holes does it dig in 15 minutes?
Answers
Answer:
12 holes
15=5.4 you can also use mateay for this
Alicia was stacking unit cubes with side lengths of 12 inch to make a larger cube, but she did not have time to finish. If she used the given length, width, and height of the stack so far, what will be the volume of Alicia′s cube when it is finished?
Answers
Cube, length= 12in (cubes are the same length on each side)
So 12•12•12
= 1,728in for just 1 cube
Volume of 1 cube=1,728in(cubed)
Im assuming that a bigger cube would be 4 cubes together or 8 cubes.
So for 4 cubes together it would be 1,728•4 = 6,912in(cubed)
For 8 cubes together it would be
1,728•8= 13,824in(cubed)
Robin wants to buy a membership at a carwash this summer so that she can keep her car clean. She compared deals from Speedy Clean Carwash and Sudsy Bubbles Carwash to decide which membership to get. Robin arranged the information in the tables below.
How many times will Robin need to wash her car to spend the same amount at both carwashes?
P.S.: I attached the table below:)
Answers
Determine the value of h in the equation h minus three eighths equals two eighths.
A: one eighth
B: six eighths
C: two eighths
D: five eighths
Answers
PLEASE ANSWER QUESTION
Answers
Answer:
Zero
Step-by-step explanation:
because, if the Discriminant of f is positive, it intersects the x-axis twice; if it’s negative, it intersects the x axis 0 times, but if it intersects the x axis or touches it in 1 point, then the Discriminant is 0!
As you can see in this graph, the x-axis and parabola only touch/intersect in 1 point, so the Discriminant of f is zero
Hope this helps!
Answer: Discriminant is zero
Step-by-step explanation:
If negative, the vertex of the graph will be above the x-axis, if positive it will be below the x-axis, and zero if it is directly on the x-axis.
Can someone please solve this for me on paper and explain it? I'm offering 30 points? This is a Sixth-grade level question.
Answers
Answer:
Where is the Question? Are you joking around or a you for real
IM TIMEDDD HELP!! Which shows a rational number plotted correctly on a number line?
-3.5
-8
-6
4
-4
-2
0
2
21
2
-18
-20
-16
-14
-12
-10
-
1.00
-10
-6
-4
-2
0
4
2.
Answers
Please answer TwT I need it fasssssssst
Answers
Answer:
The answer is 56
Step-by-step explanation: Scroll down!!!!if needed
2*2=4
2*2=4
8*2=16
16*2=32
32
+16
____
48
+2+2+2+2=4
48
+8
___
56.
Therefore the answer is 56.
* means multiplication
+ means addition
= is equal to
Write 2 * 10^2 + 3 * 10^(-3) as a decimal.
Answers
Answer:
200.003
Step-by-step explanation:
2*10^2+3*10^(-3)=200.003
this answer can probably be simplified into a smaller decimal but I did this on a calculator
Need answer as fraction or however it is, need asap
Answers
Answer: 1 byte45 or 1^45
Step-by-step explanation:
Mackey invested some money in an account paying 6% interest for one year. She invested $1000 more than this amount in an account paying 8.5%. How much did she invest in total if the total interest earned in the year was $737.50?
Answers
Step-by-step explanation:
Let's assume the amount Mackey initially invested in the 6% account is x dollars.
According to the given information, Mackey invested $1000 more than x in the 8.5% account, which means she invested (x + $1000) dollars in that account.
The total interest earned from the 6% account would be 0.06x dollars, and the total interest earned from the 8.5% account would be 0.085(x + $1000) dollars.
The total interest earned in the year is given as $737.50, so we can set up the equation:
0.06x + 0.085(x + $1000) = $737.50
Simplifying the equation:
0.06x + 0.085x + 0.085($1000) = $737.50
Combining like terms:
0.145x + $85 = $737.50
Subtracting $85 from both sides:
0.145x = $737.50 - $85
0.145x = $652.50
Dividing both sides by 0.145:
x = $652.50 / 0.145
x ≈ $4500
Therefore, Mackey initially invested approximately $4500 in the 6% account, and she invested $1000 more, which means she invested a total of $5500.
$4500
$4500
$4500
$4500
Write your answer as either a whole number, a reduced improper fraction, or a decimal rounded to the hundredths place.
Answers
Answer:
x=15/8; x ≈ 1.88
Step-by-step explanation:
cross products
15=8x
Divide both sides by 8
x = 1.875 = 15/8
x ≈ 1.88
Find a common numerator like 45
8*5=45
5*8=45
Now do the same to the known top numbers
3*5=15
So now we have 15/40 and if we divide both the top and bottom number by 8 we get our answer
.
Which phrase matches the equation -3r + 5 = 28?
a The product of three times a number equals twenty-eight.
b The sum of three and a number times negative five gives twenty-eight.
c The product of negative three and a number plus five equals twenty-eight.
d The sum of negative five plus three times a number equals twenty-eight.
Answers
Answer:
b
Step-by-step explanation:
b The sum of three and a number times negative five gives twenty-eight
X Y
-7 0
0 1
What is the slope of the linear function represented in
the table?
*-7
07/1
01/1
07
Answers
the formula for slope is rise over run, or y1-y2 divided by x1-x2. we can choose either number as y1 or y2 but it needs to stay consistent with x
so let’s plug in from your table.
0-1 divided by -7 -0
(you could also do 1-0 divided by 0-(-7))
-1/-7 which equals 1/7
so, your slope is 1/7
I hope this helps! :)
i need help... .........TnT"
Answers
Answer:
c.
Step-by-step explanation:
c. is the answer
it maybe the answer
Answer:
The answer Is C
Step-by-step explanation:
If you think this is correct can you mark as brainliest? Plz it will be my first time ever
Which of the following describes a compound event?
Answers
Answer: B
Step-by-step explanation:
A compound event is the combination of two or more events. Letter b explains how you roll a dice 4 times. The rest of the letters are only talking about one event. letter b shows more than 1. So the answer is B. In general the answer for compound events have to be a event that includes something done more than once