Choose the graph that matches the following system of equations 4x +2y=-2 x-3y=24
Answers
4x + 2y = -2 represents the red line.
x - 3y = 24 represents the blue line.
The solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
What is system of equations?"It is a finite set of equations for which we find the solution."
For given question,
We have been given a system of equations.
4x +2y = -2 ................(i)
x - 3y = 24 ................(ii)
From equation (ii),
x = 24 + 3y .............(iii)
Substitute this value of x in equation (i)
⇒ 4(24 + 3y) +2y = -2
⇒ 96 + 12y + 2y = -2
⇒ 14y = -98
⇒ y = -7
Substitute this value of y in equation (iii)
⇒ x = 24 + 3(-7)
⇒ x = 24 - 21
⇒ x = 3
Therefore, the solutions of the above system of equations is x = 3 and y = -7 and the graph of above system of equations is as shown below.
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Related Questions
solve the equation c²=4
Answers
Answer:
c = 2, c = -2
Step-by-step explanation:
The question is asking us to solve the equation [tex]\sf{c^2=4}[/tex].
To solve it, we take the square root of each side. Note that once we do this, we will have 2 solutions.
[tex]\sf{\sqrt{c^2}=\sqrt{4}}[/tex]
[tex]\sf{c=2,c=-2}[/tex]
Therefore, this equation has two solutions, which are c = 2 and c = -2.
What is the domain when a function has an imaginary number?
Answers
A function that has imaginary numbers would have a domain that consists a range of numbers on the horizontal axis. Since the horizontal axis represents real numbers, hence the domain of the function (providing there's no limitation) is all the numbers on the horizontal axis
what is the midpoint coordinates of segment HX H(13,8) X(-6,-6)
Answers
[tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
so the midpoint of HX is the mdpoint of (13,8) and (-6,-6)
which is
[tex](\frac{13-6}{2},\frac{8-6}{2}=[/tex]
[tex](\frac{7}{2},\frac{2}{2}=[/tex]
[tex](3.5,1)[/tex]
the midpoint is (3.5,1)
What is 12/7 written as a mixed number in simplest form
Answers
----- = 1----
7 7
Hope this helps
What is 60% of 7?????
Answers
60% = 0.60
7*0.6 = 4.2
Find the length of LM
Answers
solve for the 20 points
Answers
t + 1.24 = 5.8
t + 1.24 (-1.24) = 5.8 (-1.24)
t = 4.56
hope this helps
Answer:
t=4.56
Step-by-step explanation:
t+1.24=5.8
t=4.56
Can somebody help me with this one?
Answers
p = sticker price (in dollars)
Note: the sticker price is what the customer pays after the discount
Another note: This is ignoring any taxes or other fees
We're told that the sale price is the result of taking 10% off the sticker price. This means...
sale price = (sticker price) - (10% of sticker price)
s = p - 0.10*p
s = 1*p - 0.10*p
s = (1 - 0.10)*p
s = (0.90)*p
s = 0.90*p
So the expression for the sale price is 0.90*p where p is the sticker price in dollars.
Note: this means that the sale price is 90% of the sticker price.
----------------------------------------
Now plug in the sticker price p = 80 to find the sale price s
s = 0.90*p
s = 0.90*80
s = 72
The sale price is $72 which is what the customer will pay (if we ignore any taxes or other fees).
I need help 2/3 - 4/10
Answers
Tony started a blanket business. He purchased a sewing machine and some fabric to get started, and then sold each blanket for the same price. The expression −450+12x represents the profit that Tony has earned based on the number of blankets sold.
Which expression represents the total amount Tony earns from selling blankets?
12x
12
−450+12x
x
Answers
The answer is a.
12x
what is the square root of 61 to the nearest integer?
Answers
8
work:
take the square roots around 61.
the square root of 8 is 64,
the square root of 7 is 49.
61 is closer to 64.
Integers cannot be fractions, so the answer of 7.8 is rounded up to 8!
hope this helps, have a great day!
Solve for c.
a(c + b)=d
Just show how I would need to move the equation to solve for c :)
Answers
Optional:
c = d/a - ba/a = (d-ba)/a
Wastewater is filling barrels at the rate 7 quarts per hour.The recycling facility picks up 25 full barrels each trip, and each barrel hold 48 quarts of wastewater. How many days are between each pickup
Answers
25 *48 = 1200 total quarts
1200/7 = 171.43 hours
171.42/24 = 7.14 days
so every 7 days
What is the conclusion in this conditional statement?
If a square has a perimeter of 8 units, then its sides have a length of 2 units each.
the square has a perimeter of 8 units
the sides of the square have a length of 2 units each
Submit
Answers
The conclusion in the given conditional statement is that the sides of the square have a length of 2 units each. This is deduced from the formula for the perimeter of a square (P = 4 × side length), and the given perimeter of 8 units.
Explanation:The conclusion in the conditional statement "If a square has a perimeter of 8 units, then its sides have a length of 2 units each" is the sides of the square have a length of 2 units each.
In a conditional statement, the "if" part is known as the hypothesis and the "then" part is the conclusion. Given that a square's perimeter is the sum of the lengths of all four sides, we can show this through an equation: P = 4 × s, where P represents the perimeter and s the length of one side. Since the perimeter is given as 8 units, we can solve for s by dividing the perimeter by 4: 8 units = 4 × s, which simplifies to s = 2 units. Therefore, each side of the square must be 2 units long.
Final answer:
The conclusion in this conditional statement is that the sides of the square have a length of 2 units each.
Explanation:
The conclusion in this conditional statement is:
The sides of the square have a length of 2 units each.
In a conditional statement of the form 'if A, then B', the conclusion (B) is the statement that follows 'then'. In this case, the conclusion states that the sides of the square have a length of 2 units each.
Mary invests £12000 into a savings account. The account pays 1.5% compound interest per year
Answers
Answer:
Value of her investment after 2years is £12,362.7
Step-by-step explanation:
The question is incomplete, here is the complete question.
"Mary invests £12000 in a savings account. The account pays 1.5% compound interest per year. Work out the value of her investment after two years"
Using the relationship:
A = P(1+r/100)^n
Where P is the principal = amount invested = £12000
r is the compound interest = 1.5%
n is the time = 2years
A is the amount compounded after n years
A = 12000(1+1.5/100)²
A = 12000(1+0.015)²
A = 12000(1.015)²
A = 12000(1.03)
A = 12362.7
Value of her investment after 2years is £12,362.7
Is this answer correct? If not what is the correct answer
Answers
Let 's assume AD=x,DC=6-x.
Using angle nisector theorem:
AD/DC=AB/AC
==> x/(6-x)=8/10
==>10x=48-8x
==>18x=48
==>x=48/18
==>x=24/9=2+2/3 (2.666666666.....)
Answer is false, the correct answer is 2 2/3
Answer:
no
Step-by-step explanation:
If 3.485 ÷ 5.1 is written in long division form as so that the divisor is written as a whole number, where should the decimal point be placed in the dividend
Answers
What are the coordinates of the point (2, −3) after a counterclockwise rotation of 90° about the origin?
(3, 2)
(−3, −2)
(−2, 3)
(−3, 2)
Answers
Answer:
(2,-3) changes to (3,2)
A is correct.
Step-by-step explanation:
Given: The point (2, −3) after a counterclockwise rotation of 90° about the origin.
[tex]R_{90\circ}(x,y)\rightarrow (-y,x)[/tex]
Rotation is counterclockwise about origin.
[tex](x,y)\rightarrow (-y,x)[/tex]
We are given coordinate
[tex](2,-3)\rightarrow (3,2)[/tex]
We can see in diagram also. Please see the attachment for rotation.
Hence, (2,-3) changes to (3,2)
Answer:
Point would be (3,2).
Step-by-step explanation:
Given: point (2, −3) after a counterclockwise rotation of 90° about the origin.
To find: What are the coordinates after rotation.
Solution: We have given that point (2, −3).
By transformation rotation 90° (x,y)→→→(-y,x).
Then point (2, −3) would be (-(-3),2) .
Then (3 ,2)
Therefore, Point would be (3,2).
Find the value of the variable and YZ if Y is between X and Z. XY= 11, YZ=4c, XZ=83
Answers
Answer: The required value of the variable c is 18 and that of YZ is 72.
Step-by-step explanation: Given that Y is in between X and Z, where
XY= 11, YZ=4c and XZ=83.
We are to find the value of the variable c and YZ.
Since the point Y is in between X and Z, so we must have
[tex]XY+YZ=XZ\\\\\Rightarrow 11+4c=83\\\\\Rightarrow 4c=83-11\\\\\Rightarrow 4c=72\\\\\Rightarrow c=\dfrac{72}{4}\\\\\Rightarrow c=18.[/tex]
And,
[tex]YZ=4c=4\times 18=72.[/tex]
Thus, the required value of the variable c is 18 and that of YZ is 72.
The given problem is a segment addition problem in geometry. It can be solved by creating an equation based on the Segment Addition Postulate, simplifying and solving it to find the value of the variable c equal to 18. Substituting this value into the equation for YZ gives a result of 72.
Explanation:The subject of this question is a segment addition problem in geometry. From the given values, we can create an equation based on the Segment Addition Postulate, which states that the length of the whole line segment (XZ in this case) is equal to the sum of the lengths of the two segments it is split into (XY and YZ in this context).
With XZ = 83, XY = 11, and YZ = 4c, the equation becomes XY + YZ = XZ, or 11 + 4c = 83. To solve for the value of the variable c, subtract 11 from both sides, giving 4c = 72. Finally, divide each side by 4 to find that c = 18.
To find the value of YZ, substitute c = 18 back into the YZ equation: YZ = 4c = 4*18 = 72.
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The sum of two consecutive integers is 47. what is the product of these integers?
Answers
The two consecutive integers that sum up to 47 are 23 and 24, and their product is 552.
The question involves finding two consecutive integers whose sum is 47 and subsequently determining their product. To solve this, let's denote the smaller integer as n, which means the next consecutive integer will be n + 1. Since the sum is 47, we set up the equation n + (n + 1) = 47.
This simplifies to 2n + 1 = 47. To find the value of n, we subtract 1 from both sides to get 2n = 46, and then divide both sides by 2, yielding n = 23. Therefore, the two consecutive integers are 23 and 24. To find the product of these integers, we multiply them together: 23 imes 24 = 552.
What is the domain of 2x+5
Answers
hope this helps
What unit of measure would you use to measure length of piece of paper?
Answers
I need help please!!!! Jon buys t shirts online for his friends. the table below shows the cost including the shipping fee. write a verbal description that describes the relationship
Answers
so equation
c = 3 + 12t
if t = 1 then c(cost) = 3 + 12(1) = 3 + 12 = 15
if t = 2 then c(cost) = 3 + 12(2) = 3 + 24 = 27
if t = 3 then c(cost) = 3 + 12(3) = 3 + 36 = 39
if t = 4 then c(cost) = 3 + 12(4) = 3 + 48 = 51
Examine the work shown. Explain the error and find the correct result.
2(4 – 16) – (–30)
2(–12) – (–30)
24 – (–30)
54
Answers
The error is in third step where 2(–12) is -24 and not 24 thus the correct result is 6.
What is an expression?An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.
Now the given expression is,
2(4 – 16) – (–30)
solving the bracket,
2(–12) – (–30)
expanding the bracket we get,
-24 – (–30)
this is the error in the given work where 2(–12)– (–30) = 24– (–30)
Thus open the bracket,
-24 + 30
solving we get,
6
which is the correct answer.
Thus, the error is in third step where 2(–12) is -24 and not 24 thus the correct result is 6.
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Evaluate. 62+(3⋅4)−24 Enter your answer in the box. plz help mehh someone out there ty
Answers
74-24=50
The value of expression 62+(3⋅4)−24 is 50
What is PEMDAS ?
A rule of operations explains the correct order in which math expressions should be evaluated, and we can remember those steps using PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Here, the expression is given as 62+(3⋅4)−24 now using PEMDAS rule to solve this expression first by solving under bracket terms 3x4 = 12 and then adding 62 and 12, then subtract it by 24 to get the final answer.
62+(3⋅4)−24
62 + 12 -24
74 - 24
50
Therefore, the value of expression 62+(3⋅4)−24 is 50
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What is the slope of a line that is parallel to the line shown?
Answers
Parallel lines have the same slope, so if we find the slope of the line shown, the slope of the line parallel to it will be the same.
To find the slope, we find the rise divided by the run, or the change in x values divided by the change in y values.
slope = m = (y1 - y2)/(x1 - x2) = (3-2)/(0-3) = 1/(-3) = -1/3
Therefore, the slope is -1/3, and so the slope of the parallel line is also -1/3.
Your answer is -1/3.
Hope this helps!
Find the equation of the line in slope-intercept form that passes through (2, 7) and (-1, 5).
Answers
Jennifer and Margaret have to make brownies for a bake sale. Jennifer can bake a dozen brownies in 20 minutes and Margaret can bake 15 brownies every half hour. Jennifer bakes for 1 hour and 40 minutes and Margaret bakes for 2 hours. How many brownies do the girls have for the sale altogether?
Answers
Find the common ratio for the following sequence 9,6,4
Answers
The common ratio for the sequence is 2/3
Finding the common ratio for the sequenceFrom the question, we have the following parameters that can be used in our computation:
Sequence: 9,6,4
The common ratio for the sequence is calculated using
Ratio = T2/T1
substitute the known values in the above equation, so, we have the following representation
Ratio = 6/9
Evaluate
Ratio = 2/3
Hence, the common ratio is 2/3
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PLEASE HELP!!
(x-7)^3 (x+2)^2 (x-13) <0