A system of linear equations is shown below. 2x + 4y = 10 3x – y = 8 marla is attempting to prove that by replacing 2x + 4y = 10 with a different equation it will sometimes produce a new system of equations with the same solution. marla plans on multiplying 2x + 4y = 10 by 2 and then adding the results to the equation 3x – y = 8 in order to create a new equation. marla claims that the new equation that she will replace 2x + 4y = 10 with is 7x + 7y = 12. is marla correct?
Answers
.. 7x +7y = 28
Marla has incorrectly calculated the constant as 12. It should be 28.
No, Marla is not correct. The correct new equation is 4x + 8y = 20.
Explanation:No, Marla is not correct. To create a new equation that represents the same system of equations, we need to perform the same mathematical operation on both sides of the equation. In this case, Marla multiplied the left side of the equation by 2, but not the right side. To maintain equality, we need to multiply both sides of the equation by the same constant. Therefore, the correct new equation would be 4x + 8y = 20.
Related Questions
John bought 6 dumplings for $3.00.
Let x represent the number of dumplings purchased, and let y represent the total cost.
Graph the line that represents the proportional relationship.
Answers
Serena paid $194.99 for a game system and then bought two equally-priced games. If she spent a total of $284.97, what is the price, p, of one game? Enter your answer in the box.
Answers
$89.98 / 2 = $44.99
Serena bought two equally priced game at a price of $44.99 each and the total money spent in buying all three games is $284.97.
Given information:
The price Serena paid for buying the first game is $194.99
The overall price Serena paid for buying three games is $284.97
Let, the price of one of the two equally priced game is [tex]\bold{P}[/tex]
As, the price of second and third game is equal, we can consider the combined price of second and third game.
Thus , the equation formed according to the information given in the question is:
[tex]\bold{194.99+2P=284.97}[/tex]
Solve, the above equation in order to find the price of one game.
[tex]2P=284.97-194.99\\\2P=89.98}\\{P=44.99}[/tex]
Hence, the price of one game in two equally priced game is $44.99
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1. J. Cole is a successful Hip-Hop recording artist. He has a record contract that pays him $20,000 a month plus an additional $12 for each album that he sells. Last month he earned $24,800. Write an equation to express the money J. Cole earned last month. Let "x" represent the number of albums.
2. How many albums did J. Cole sell last month?
Answers
Payment per album = $12
Total earned last month = $24,800
Part (a): Expression for money earned last month
Let x be number of albums last month. Then,
Total earning = Fixed payment + Variable payment
That is,
24,800 = 20,000 + 12*x
24,800 = 20,000 + 12x
Part (b): Number of albums last month
This involves solving for x in the expression derived in part (a) above.
24,800 = 20,000 + 12x
24,800 - 20,000 = 12
12x = 4,800
x = 4,800/12 = 400 albums
Anybody have a real answer for the question?
Answers
now, notice, ∡y and ∡x are "linear angles", therefore
x + y = 180
y = 180 - x.
Jordan is 4 feet 8 inches tall, her mother is 5 ft 10 inches tall, how much taller is Jordan's mother than Jordan? Give your answer in feet and inches.
Answers
Perpendicular lines AB and CD intersect at point E. If m∠AED = x + 20, what is the value of x?
A.) 160
B.) 110
C.) 90
D.) 70
Answers
What is the relation between the graphs of f(x)=x^2 and g(x)=x^2+6?
a.
the graph of g(x) is a translation of the graph of f(x) up 6 units
c.
the graph of g(x) is a translation of the graph of f(x) right 6 units
b.
the graph of g(x) is a translation of the graph of f(x) left 6 units
d.
the graph of g(x) is a translation of the graph of f(x) down 6 units
Answers
Answer:
I think it is the first one
Step-by-step explanation:
Please give brainliest
Write two operations in order that you would use to solve the equation 3x - 2=7 then solve the equation
Answers
3x = 7 + 2
3x = 9
x = 9/3
x = 3
You first subtract 2 from both sides, so 2-2=0 & 7-2=5
3x=5
Then you divide 3 from both sides to get “X” alone, 3x/3= 1x (but the the one is invisible so it equal “X”) and then 5/3= 1.66666..
So the answer to this problem is
X=1.6
WILL GIVE BRAINLIEST ANSWER!!! PLEASE HELP!!! 12 POINTS!!!!!!!
The formula for the volume, V, of a right rectangular pyramid is one-third its base length, l, times its base width, w, times its height, h. Which of the equations below are equivalent to the formula described?
-----Note: more than one must be used-----
ANSWER OPTIONS:
* l = V over 3hw
* w = V over 3lh
* l = 3V over wh
* h = 3Vl over w
* w = 3V over lh
* h = V over 3lw
Answers
h l w = 3V
l = 3V / w h Which is the third choice.
h = 3V / l w
w = 3V / h l - which is the fifth choice
The third and fifth are equivalent to the formula described.
What is the value of x in the triangle?
Answers
We’re going to use Cosine because the angle and sides given are Adjacent and Hypotenuse- which goes with the CAH part of SOH CAH TOA.
Cos(18) = x/25
Multiply both sides by 25
25cos(18) = X = 23.776
So x = 23.776 cm
I hope this Helps!
And that gives you... x = 23.776 cm
helppppppppppppppppppppppppppppppp
Answers
a (x) = 3x + 1
b (x) = root (x-4)
Making the composition
b (a (x)) = root ((3x + 1) -4)
Rewriting:
b (a (x)) = root (3x-3)
b (a (x)) = root (3 (x-1))
Answer:
The domain of the function is:
x> = 1
Equivalently:
[1, inf)
Factor x2 – 3x – 28. Identify the values that should be written to complete the X diagram. On the top: On the bottom: On the sides: Rewrite the expression using the numbers on the sides of the X diagram. Use double grouping to factor the four terms. x2 – 3x – 28 =
Answers
= x^2 -7x +4x -28
= x(x -7) +4(x -7)
= (x +4)(x -7)
-28
-3
-7 and 4
(x-7)(x+4)
NEED HELP ASAP
What are the restrictions of:
(n^2 -6) / (n^2 -2)
5 and 2
+/- SQRT5 and +/- SQRT2
5 and -2
Answers
We have then that in this case the values are:
(n ^ 2 -2) = 0
Clearing n we have:
(n ^ 2) = 2
n = + / - sqrt (2)
Answer:
the restrictions are:
n = + / - sqrt (2)
Find the area of the triangle. Round the answer to the nearest tenth.
A.
7.8 square units
B.
8.9 square units
C.
19.3 square units
D.
38.5 square units
Answers
So the closest answer is C. 19.3
Hope this helps :)
Answer:
19.3 square units .
Step-by-step explanation:
∠D=∠F=52°
Opposite sides of equal angles are equal .
So, DE=EF =6.3
Now sum of all angles of triangle is 180°
So, ∠D+∠F+∠E = 180°
52°+52°+∠E =180°
104°+∠E =180°
∠E =180°-104°
∠E =76°
Now to find the length of DF we will use law of cosines
[tex]c^2=a^2+b^2+2(a)(b) Cos E[/tex]
[tex]DF^2=DE^2+EF^2+2(DE)(EF) Cos E[/tex]
[tex]DF^2=6.3^2+6.3^2+2(6.3)(6.3) Cos 76^{\circ}[/tex]
[tex]DF^2=79.38+79.38 (0.2419)[/tex]
[tex]DF^2=98.582[/tex]
[tex]DF=\sqrt{98.582}[/tex]
[tex]DF=9.9[/tex]
Now we are supposed to find the area of triangle
To calculate the area of given triangle we will use the heron's formula :
[tex]Area = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where [tex]s = \frac{a+b+c}{2}[/tex]
a,b,c are the side lengths of triangle
Now substitute the values :
[tex]s = \frac{6.3+6.3+9.9}{2}[/tex]
[tex]s =11.25[/tex]
[tex]Area = \sqrt{11.25(11.25-6.3)(11.25-6.3)(11.25-9.9)}[/tex]
[tex]Area = 19.2907[/tex]
Hence the area of the triangle is 19.2907 ≈19.3 square units .
The perimeter of an isosceles triangle is 14 cm. One of its sides is twice longer than another of its sides. Find all sides of the triangle.
Answers
The side that is twice longer than another side make it equal 2*a.
So the total of the 3 sides would equal 14
4a = 14
So 2 sides = 3.5 and the third side = 7.
3.5 + 3.5 + 7 = 14
Answer:
Step-by-step explanation:
2.8, 5.6, 5.6
Melina has 4 sheets of wacky face sticker individually from the sheet. She then divides them evenly into 3 piles to give to friends. How many stickers are in each pile?
Answers
SEE THE ATTACHED IMAGE.
For this case what we must do is first find the total number of stickers.
We have then:
(4) * (24) = 96
Then, we must organize the stickers in three piles.
We have then:
(96) / (3) = 32
Answer:
in each pile are 32 stickers
The answer explains how to divide 4 stickers into 3 piles, resulting in 1 sticker each.
To find out how many stickers are in each pile:
Count the total number of stickers = 4 sheets x 1 sticker per sheet = 4 stickers.Divide the total number of stickers evenly into 3 piles: 4 stickers ÷ 3 piles = 1 sticker in each pile.Let A = 40. If B is complement of A, and C is a supplmenet of B, what is B+C?
A. 60
B. 150
C. 180
D. 210
Answers
Explanation:
Complementary angles add upto 90 degrees and supplementary angles add to 180 degrees
Given A=40
B = Complement of A =90-40 =50
C = Supplement of B = 180-50 =130
Therefore B+C = 50 +130 =180.
Triangle ABC is similar to triangle FGH. Angle A measures 42 degrees. Angle B measures 19 degrees. Find the measure of angle H.
42
19
119
29
Answers
Let's find the angle C:
∠C=180-42-19=119
Then ∠H=119
Answer: 119 degrees
Each of two trapezoidal prisms has a volume of 120 cubic centimeters. the prisms have no dimensions in common. give possible dimensions for each prism.
Answers
If the height of one trapezoid is 4, the area would need to be 30. I wrote out the formula for area of a trapezoid (h (b1+b2)/2) and solved for 30. I multiplied both sides by 2 and saw that I needed a 60 from the sun of my 2 bases and the height of the trapezoid base. I used 2 for the height and 20 and 10 as the 2 bases.
For the second trapezoid, I used 6 as the height of the prism. This left me with 20 as the area. I used the same formula above and found that I needed to get 40. I used 5 as the height of the trapezoid and 1 and 7 as the two base lengths. Hope this helps!!
Find two consecutive integers whose product is 24 more than three times the first integer
Answers
x+1= second consecutive integer
Product means multiply, so we'll multiply x by x+1. More than means to add and 3 times is multiplication.
x(x + 1)= 3x + 24
use distributive property to multiply x by everything in parentheses
(x*x) + (x*1)= 3x + 24
x^2 + x= 3x + 24
subtract 3x from both sides
x^2 - 2x= 24
subtract 24 from both sides
x^2 - 2x - 24= 0
factor the expression
(x-6)(x+4)= 0
x-6=0
x=6
x+4=0
x=-4
If x= 6 is the first integer, x+1= 7 is the second integer
If x= -4 is the first integer, x+1= -3 is the second integer
Hope this helps! :)
In this activity, you'll calculate a probability and use it to predict the result of repeating a simple chance-based trial many times.
You are in charge of the casino night game area at a fundraising event. In one of the games, called Odd Odds, the player rolls two six-sided dice. The player gets points if the product of the two numbers rolled is odd. So, success in the game depends on the chances of getting an odd number for the result.
1)Find the number of outcomes in the sample space, n(S), of the trial of this game.
2)List and count all the outcomes for event E, in which the product of the two numbers rolled is odd.
3)Find the probability of getting an odd number. In this case, you will calculate the probability, P(E), of event E, in which the product of the two numbers rolled is odd. Write the probability as a fraction reduced to lowest terms and as a decimal correct to two places.
Answers
Answer:
Step-by-step explanation:
They are saying the player gets points if the PRODUCT of the two numbers rolled is odd not the SUM So the answer should be
(1,3) (1,5) (3,1) (3,3) (3,5) (5,1)(5,3)(5,5) which is 9 out of 36 which would be 1/4 or 0.25
Final answer:
In this activity, the student needs to calculate the number of outcomes in the sample space, list and count the outcomes for event E, and find the probability of getting an odd number.
P(E) = 9/36 = 1/4 = 0.25.
Explanation:
To find the number of outcomes in the sample space (n(S)) of the trial, we need to consider all the possible combinations of rolling two six-sided dice. Since each die has six sides, the total number of outcomes for each die is 6. To find the total outcomes in the sample space, we multiply the outcomes for each die: n(S) = 6 * 6 = 36.
In this game, we are interested in the outcomes where the product of the two numbers rolled is odd. To list and count these outcomes, we need to consider the combinations where one or both of the numbers rolled is odd. By listing all the possible outcomes, we have: (1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5). There are 9 outcomes for event E.
To find the probability of getting an odd number, we need to divide the number of outcomes for event E by the total number of outcomes in the sample space. P(E) = 9/36 = 1/4 = 0.25.
If sec a = 5/4 and a is an angle in quadrant iv find the value of cos a
Answers
sec a = 5/4
sec(a)=1/cos(a)
then
cos (a)=1/sec(a)
cos (a)=1/(5/4)=4/5---> is positive because the function cos is positive in IV quadrant
the answer is cos(a)=4/5
Four bars of soap cost $1.12. What would you pay for 2 dozen bars? (1 dozen=12)
Answers
Multiply the above equation by 6.
24 bars = $6.72 . . . . . . the cost for 2 dozen bars.
Average Monthly Temperature Month Temperature January 45 degrees February 42 degrees March 54 degrees April 62 degrees May 78 degrees June 85 degrees July 92 degrees August 94 degrees September 89 degrees October 78 degrees November 65 degrees December 54 degrees The average monthly temperatures for the city of Mathville are given in the chart above. One year was particularly warm, and the average temperature each month increased by 5°. What did this do to the average yearly temperature? A) The average remained the same. B) The average increased by 5°. C) The average decreased by 5°. D) The average increased by 60°.
Answers
x------------> the average yearly temperature
if One year was particularly warm, and the average temperature each month increased by 5°
in one year the temperature increased------->5*12-----> 60°
so
[the new average yearly temperature]=x+(60)*12-------> x+5°
therefore
the answer is the option
B) The average increased by 5°.
f(x)=9x^3+2x^2-5x+4 and g(x)=5x^3-7x+4 what isf(x)-g(x)
Answers
f(x) - g(x) = 4x³ + 2x² + 2x
Explanation:
We are given that:
f(x) = 9x³ + 2x² - 5x + 4
g(x) = 5x³ - 7x + 4
We want to get the value of f(x) - g(x). This means that we will simply subtract g(x) from f(x) as follows:
f(x) - g(x) = 9x³ + 2x² - 5x + 4 - (5x³ - 7x + 4)
f(x) - g(x) = 9x³ + 2x² - 5x + 4 - 5x³ + 7x - 4
f(x) - g(x) = 9x³ - 5x³ + 2x² - 5x + 7x + 4 - 4
f(x) - g(x) = 4x³ + 2x² + 2x
Hope this helps :)
What is the value of y in the parallelogram below?
Answers
Answer:
The answer is the option B
[tex]23\°[/tex]
Step-by-step explanation:
we know that
In a parallelogram consecutive angles are supplementary
so
In this problem
[tex]5y\°+65\°=180\°[/tex]
Solve for y
[tex]5y\°=180\°-65\°[/tex]
[tex]y=115\°/5=23\°[/tex]
Answer:
23
Step-by-step explanation:
just took the test
Sandra got a 3/27 balloon mortgage and her initial payments were $945. She decided to refinance her balloon payment with a 30-year mortgage and her new payments were $937. What is the total financed cost she paid for her house?
Answers
Sandra got a 3/27 balloon mortgage and her initial payments were $945.
This means Sandra paid $945 per month for 3 years. Total payment made in 3 years = 945*3*12 = $34,020
Later, she decided to refinance her balloon payment with a 30-year mortgage. Her new payments were $937.
Payment made under mortgage = 937 * 30 * 12 = $337,320
The total financed cost she paid for her house = $34020 + $ 337320 = $371340
Hope this helps..!!
Thank you :)
Part 1.] Find the value of x in [tex]4,000( 1.5^{x})=25,000[/tex]. Show your work.
Part 2.] Use the domain {½ , 1, 2, 4, 8} to plot the points on the graph for the given equation. The grid marks represent one unit, the horizontal red line represents the x-axis, and the vertical red line represents the y-axis. [tex]y= log_{2} x[/tex]
Answers
[tex] \frac{4000(1.5^{x}) }{4000} = \frac{25000}{4000} [/tex]
[tex]1.5^{x} = \frac{25}{4} [/tex]
Now we can use logarithms to bring down the variable:
[tex]ln(1.5^{x} )=ln( \frac{25}{4}) [/tex]
[tex]xln(1.5)=ln( \frac{25}{4}) [/tex]
[tex]x= \frac{ln( \frac{25}{4}) }{ln(1.5)} [/tex]
[tex]x=4.52[/tex]
Part 2. Lets use the domain (x values) to find the range (y values):
[tex]log_{2} (\frac{1}{2})=-1 [/tex]
[tex]log_{2} (1)=0 [/tex]
[tex]log_{2} (2)=1 [/tex]
[tex]log_{2} (4)=2 [/tex]
[tex]log_{2} (8)=3 [/tex]
Finale lets put the points together and draw our graph:
Which example best represents balanced forces
Answers
The forces are equal and opposite, the book remains at rest, representing a state of balanced forces.
Balanced forces occur when the net force acting on an object is zero, meaning that the forces are equal in magnitude and opposite in direction. As a result, the object remains in a state of equilibrium and does not accelerate.
One example that best represents balanced forces is:
A book resting on a table.
When a book is placed on a table, it doesn't move because the force of gravity pulling it down (its weight) is balanced by the normal force exerted by the table, pushing the book upward.
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Which graph shows a proportional relationship? help!!