Answer: The system of equations have many solutions and the correct options are A,B and D.
Explanation:
The given equations are,
[tex]2x+y=5[/tex] ..... (1)
[tex]3y=15-6x[/tex] .... (2)
Simplify the second equation.
[tex]3y+6x=15[/tex]
[tex]3(y+2x)=15[/tex]
Divide both sides by 3.
[tex]2x+y=5[/tex]
It is same as equation (1). Since equation (1) and (2) are same, therefore all the points lies on the line or which satisfies the equation are the solution of the given system of equations.
Test the points whether the point lies on the line or not.
Check for point A(6,-7).
[tex]2(6)+(-7)=5[/tex]
[tex]5=5[/tex]
LHS and RHS are equal, therefore the point A is the solution of the system of equations.
Check for point B(2,1).
[tex]2(2)+(1)=5[/tex]
[tex]5=5[/tex]
LHS and RHS are equal, therefore the point B is the solution of the system of equations.
Check for point C(-2,-9).
[tex]2(-2)+(-9)=5[/tex]
[tex]-13=5[/tex]
LHS and RHS are not equal, therefore the point C is not the solution of the system of equations.
Check for point D(-4,13).
[tex]2(-4)+(13)=5[/tex]
[tex]5=5[/tex]
LHS and RHS are equal, therefore the point D is the solution of the system of equations.
Therefore the options A,B and D are correct.
The points (6, –7), (2, 1), and (–4, 13) satisfies the equation and hence, will be the solution of the equation. The correct solution for this system is A, B, and D.
Given:
The given system of linear equations is,
[tex]2x + y = 5\\3y = 15 - 6x[/tex]
Equate the y coefficient of the equations and write them as,
[tex]6x + 3y = 15\\6x+3y = 15[/tex]
The given system of equation is the same equation and hence, will have infinite solutions.
Now, the solution of equation from the given options can be found by putting each point in the equation and checking for its satisfaction of the equation.
So, try All the points given. Point A(6,-7) Where x=6, y=-7
Put in equation.
[tex]-7+2(6)=5\\-7+12=5\\5=5[/tex]
Hence LHS=RHS
Point B(2,1), Where x=2, y=1
Put in equation.
[tex]1+2(2)=5\\1+4=5\\5= 5[/tex]
Hence, LHS= RHS
Point C(-2,-9), Where x=-2, y=-9
Put in equation.
[tex]-9+2(-2)=5\\-9-4=5\\-13\neq 5[/tex]
Hence LHS[tex]\neq[/tex]RHS
Point D(-4,13)
Where x=-4, y=13
Put in equation.
[tex]13+2(-4)=5\\13-8=5\\5=5[/tex]
Hence, LHS= RHS
Therefore, points (6, –7), (2, 1), and (–4, 13) satisfies the equation and hence. will be the solution of the equation.
Learn more about coordinate geometry here
https://brainly.com/question/21391578
which statement about the equation is true?
x + 2 = x + 4
a. one solution
b. no solution
c. multiple solutions
Answer:
The correct option is b) no solution.
Step-by-step explanation:
Consider the provided equation,
[tex]x + 2 = x + 4[/tex]
We need to find the solution of the above equation.
Subtract x from both the sides as shown.
[tex]x-x+2=x-x+4[/tex]
[tex]2=4[/tex]
Which is false.
As 2 is not equal to 4.
Hence, the provided equation has no solution.
Thus, the correct option is b) no solution.
a beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40%. for what price does the salon sell each bottle
The price the salon sells each bottle is 6.3 if a beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40%.
What is percentage?It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
It is given that:
A beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40%.
From the question:
= 40% of 4.50
= 1.8
= 1.8 + 4.5 = 6.3
Thus, the price the salon sells each bottle is 6.3 if a beauty salon buys bottles of styling gel for 4.50 per bottle and marks up the price by 40%.
Learn more about the percentage here:
brainly.com/question/8011401
#SPJ2
One-eighth of the 32 students in the class went abroad for fall break. How many students went abroad?
divide 32 by 8
32/8 = 4 students went abroad
What is the domain and range of the function shown in the graph?
how many even numbers are between 32 and 60. (not including 32 & 60)
I need some help plz!
Enter in the missing numbers to create equivalent ratios.
2:5
Blank:10
6: Blank
Blank:25
order greatest to least for the following 2.007, 2.714, 2.09, 2.97
25 exponent 9 is grewter then (5 exponent 4) and a exponent 2 next to the parentheses
6,700 rounded to nearest thousand
What statement makes the open sentence 1.2 = 3x true?
1.) x = 0.4
2.) x = 1.8
3.) x = 2.5
4.) x = 3.6
I am very confused XD
Also if you could tell me how you got the answer I would appreciate it :)
Which of the following shows the factors of 2y^2 - 2y - 4? Select one of the options below as your answer: A. (2y - 4)(y - 1) B. (2y - 4)(y + 1) C. (2y - 2)(y - 2) D. (2y - 2)(y + 2)
a backpack manufacturer produces an internal frame pack and an one hour and let y represent the number of external frame packs produced in one hour.Then the inequalities x+3y<=18,2x+y<=16,x>=0 and y>=0 describe the constraints for manufacturing both packs.Use the profit function f(x,y)=50x+80y and the constraints given to determine the maximum profit for manufacturing both packpacks for the given constraints
The maximum, 1280, occurs at (0,16).
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The inequality is,
x + 3 < 18
x < 15
And,
2x + y < 16
y < - 2x + 16
Now, you can see the constraint, x + 3 < 18 doesn't even enter into calculating the feasible region because the constraint, 2x + y < 16 really identifies the region.
Now, We can Check the value of the function at the three vertices as:
At (0,0):
f(x, y) = 50x + 80y = 0
At (8, 0);
f(x, y)=50x+80y
f (8, 0) = 400
At (0, 16);
f(x, y ) = 50x+80y
f (0, 16) = 1280
Thus, The maximum, 1280, occurs at (0,16).
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ3
What transformation is represented by the rule (x, y)→(−y, x)?
A. reflection across the x axis
B. rotation of 90 degrees clockwise about the origin
C. reflection across the y axis
D. rotation of 180 degrees about the origin
Answer:
The answer is D, an 180 rotation about the origin
Step-by-step explanation:
I just did the test and got it right :)
the table shows how far four students walked in 5 minutes. how far did they walk together. 3/4, 1/2,2/3,3/4.
To find the total distance walked by the four students, add their individual distances together.
Explanation:To find the total distance walked together, you need to add up the distances each student walked. The distances given are represented as fractions. To add fractions, first make sure the denominators are the same. In this case, the denominators are already the same, so you can add the numerators together. So, 3/4 + 1/2 + 2/3 + 3/4 = 15/12.
Simplify the resulting fraction by finding the greatest common divisor of the numerator and the denominator, which is 3. Divide both the numerator and denominator by 3 to get the final answer: 15/12 ÷ 3/3 = 5/4.
Therefore, the students walked a total distance of 5/4 or 1 1/4.
Learn more about Addition of fractions here:https://brainly.com/question/14427715
#SPJ2
How do I solve this question?
Dori and Malory are tracking their steps taken as a health goal. Dori leaves her house at 12:00 p.m. and walks at 50 steps per minute. Malory leaves her house at 12:20 p.m. and walks at 90 steps per minute. At what time will Malory's steps catch up to Dori's steps?
In the recent year, 26.6% of all registered doctors were female. If there were 54,200 female registered doctors that year, what was the total number of registered doctors? Round the answer to the nearest whole number.
what is the answer to a/164363 -10 = 10
Express the following number using expanded form, unit form, and word form: 625.25
when multiplying and subtracting fractions ... 5/6-3/4
Write in exponent form and word form. 10x10x10x10x10x10
What is 0.04 divided by 10
Which property of equality would you use to solve the equation 14x=56
The division property of equality is used to solve equality 14x = 56 where x = 4.
What is equality?In mathematics, equality is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
The given equality is,
14x = 56
Using division property of equality,divide both side by 14
14x/14 = 56/14
Solving we get,
x = 4
Thus, the division property of equality is used to solve equality 14x = 56 where x = 4.
To learn more about property of equality:
https://brainly.com/question/4597952
#SPJ2
Cara likes candles. She also likes mathematics and was thinking about using algebra to answer a question that she had about three of her candles. Her taller candle is 16 centimeters tall. Each hour it burns makes the candle lose 2.5 centimeters in height. Her short candle is 12 centimeters tall and loses 1.5 centimeters in height for each hour that it burns. Cara’s middle candle is 15 cm tall and burns at a rate of 2.25 centimeters in height for each hour that it burns. When will all candles be the 6cm tall?
All three candles will be 6 centimeters tall after 4 hours of burning.
To determine when all three candles will be 6 centimeters tall, we can set up equations for each candle and solve for the time it takes to reach the desired height.
For the taller candle, we can set up the equation:
16 - 2.5t = 6,
where t represents the number of hours.
Similarly, for the shorter candle:
12 - 1.5t = 6.
And for the middle candle:
15 - 2.25t = 6.
Simplifying each equation, we have:
-2.5t = -10,
-1.5t = -6,
-2.25t = -9.
Solving for t in each equation, we find:
t = 4 for the taller candle,
t = 4 for the shorter candle,
t = 4 for the middle candle.
To learn more about the equation;
https://brainly.com/question/12788590
#SPJ2
Shawn wants to model the number 13,450 using base ten blocks how many large cubes flats and longs does he need model the number
2m-2x=x+n. solve for x.
Your teacher divides your class into two groups and then randomly chooses a leader for each group the probability that you are chosen to be a leader is 1÷12 the probability that both you and your best friend are choosing is 1÷132 is your best friend in your group explain
Answer:
1 DIVIDED BY 12 IS 1 SO SAME THING WITH 1 DIVIDED 132 IS 132 SO ADD THEM AND YOU SHOULD GET YOUR ANSWER PS i dont know the answer
Step-by-step explanation:
No, my best friend is not in my group.
Let's break down the probabilities to determine if your best friend is in your group. The probability that you are chosen as a leader is [tex]\frac{1}{12}[/tex]. Let’s denote your best friend by BF. Given that the probability that both you and best friend are chosen as leaders is [tex]\frac{1}{132}[/tex], we need to check if BF is in your group.If your best friend is in your group, then there is only one leader to be chosen from this group. Hence, the probability that you and your best friend are chosen from the same group would be calculated by selecting the group leader and then the remaining leader from the other group.In this scenario, the probability of you and your best friend being chosen as leaders would typically depend on the group size and configuration.Since the probability of you both being chosen is [tex]\frac{1}{132}[/tex], this indicates that you are more likely not in the same group. If BF were in the same group, the probability would be calculated based on how likely both members are to be from the same group, considering the overall class size and number of groups.Thus, given the probability details, we can conclude that your best friend is not in the same group as you.A fish market bought two swordfish at a rate of $13 per pound the cost of the larger fish was 3 times as great as the cost of the smaller fish the total cost of the two fish was $3,952 how much did each fish weigh
what is 9x-7=-7 in two step show your work
9x-7 = -7
step 1 = add 7 to each side
9x = 0
step 2 divide both sides by 9
x = 0/9 = 0
A line contains the points (−26, −37) and (−32, −61) . What is the slope of the line in simplified form?
I got -4 for my answer, but I don't know if this is right. Please help!!XD
The slope of the line is "4".
Given:
[tex](x_1 , y_1 )= (-26, -37)[/tex][tex](x_2, y_2) = (-32,-61)[/tex]As we know the formula for finding the slope will be:
→ [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
By substituting the values, we get
→ [tex]= \frac{-61-(-37)}{-32-(-26)}[/tex]
→ [tex]= \frac{-61+37}{-32+26}[/tex]
→ [tex]= \frac{-24}{-6}[/tex]
→ [tex]=4[/tex]
Thus the answer above is right.
Learn more:
https://brainly.com/question/1833315