Answer:
3
Step-by-step explanation:
First, we can start by multiplying the equation 2x - 3y = 12 by six to see where that gets us,
2x - 3y = 12 --> 12x - 18y = 72
12x - 18y = 72
5x + 6y = 18 (other equation)
We can notice that eliminating the y term would be the easiest to go about, so we want to find the number that we can multiply 6 by to get 18. That number is 3, so the factor is 3.
You can use the fact that non of 2 times 6 doesn't include 5 as factor.
There are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.
Those values of the factor are [tex]3[/tex] (for elimination of y) or [tex]-\dfrac{12}{5}[/tex] (for elimination of x)
How to find by what factor should we multiply the equations to eliminate a variable in a system of linear equations of two or more variables?Our aim in doing so is to make the coefficients of same variable equal and with opposite signs so that when we add the equations, that variable gets eliminated because of coefficient becoming zero.
For example, take the given equations and the factor by which Yumiko multiplied the second equation.
5x + 6y = 18
2x – 3y = 12 => 12x - 18y = 72 (since she multiplied this with 6)
Let she multiply the first equation with factor "p"
Then we will have the system as;
[tex]p \times 5x + p \times 6y = p \times 18\\12x - 18y = 72[/tex]
Adding both the equations, we get:
[tex](5p + 12)x + (6p - 18)y = 18p + 72[/tex]
Since there are two variables and since any one of them can be eliminated depending on the value of p, thus we have two cases:
Case 1: Eliminated variable is xThen we have coefficient of x = 0
or
[tex]5p + 12 = 0\\5p = -12\\p = -\dfrac{12}{5}\\[/tex]
Case 2: Eliminated variable is yThen we have coefficient of y = 0
or
[tex]6p - 18 = 0\\6p = 18\\p = \dfrac{18}{6} = 3[/tex]
Thus, there are two possible values of the factor by which if Yumiko multiplies the first equation and add the equations, a variable is eliminated.
Those values of the factor are [tex]3[/tex] or [tex]-\dfrac{12}{5}[/tex]
Learn more about system of linear equations here:
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Charlotte the turtle was born with 4 squares on her shell,
as in the first picture below. When she was 1 year old, 12
new squares appeared around the old squares, as in the
second picture below. Each year, a new group of squares
appeared around the old squares.
Answer:
Step-by-step explanation:
Tell whether the angles are adjacent or vertical. Then find the value of x.
Answer:
#3 is 74 and adjacent #4 is 29 and adjacent #5 is 48 and vertical
Step-by-step explanation:
just trust me i had the same questions
y = kx
In the equation, what does "k" represent?
Answer: it’s the number that stays the same
Step-by-step explanation: ex. y = 24(6x)
Find the circumference of each of the circles described below.
a. Radius of 3 inches
b. Diameter of 27 cm
Answer:
a) 18.85 or 19
b) 84.82 or 85
Mr. Jones surveyed his class to find out how many students feel that Math is their favorite subject. Based on these results, how many students would say that Math is their favorite subject if he asked all 150 students in the 6th grade class.
Answer:
im not sure
Step-by-step explanation:
I remember doing this but i forget
the question is in the image.(no links)
Answer:
I don't know but I think the answer is 3
PLEASE HELP...FAST :)!!
You are playing a game similar to shuffleboard, where you need to slide a puck into the light gray area of the board in order to score points. The board is surrounded by wood boards that keep the puck in the playing surface. An image of the board and its dimensions are shown below.
What is the probability that you slide the puck into the light gray area? Your answer may be written as a fraction or a decimal
The probability is ________________
The probability that one can slide the puck into the light gray area will be 0.72.
How to calculate the probability?From the information given, the board is surrounded by wood boards that keep the puck in the playing surface.
In this case, the probability that you slide the puck into the light gray area will be:
= 4feet/(4 feet + 1.5 feet)
= 4/5.5
= 0.72
Learn more about probability on:
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please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
Answer:
Side lengths- LK = 1.56 JK = 2.88
Step-by-step explanation:
Use tan for LK. Tan 26 = x/3.2, x = 1.56 to the nearest hundredth. Use cosine for JK. Cos 26 = x/3.2, x = 2.88 to the nearest hundredth.
PLS HELP!!!!!!
What is the solution of the system shown?
0 (2, 2)
O (2,3)
O (3,2)
Answer:
(3,2)
Step-by-step explanation:
Answer:
3.2
Step-by-step explanation:
help me with this math question please I'm giving away brainliests
Answer:
orangeeeeeee
Step-by-step explanation:
Marking brainliest pls help!!!!
Answer:
He would recognize Lincoln's accomplishments which a good amount was about his documents like the Emancipation document.
Step-by-step explanation:
Also, he did his "I have a dream" speech on the Lincoln Memorial.
Solve for y:
y - (-10) = -41
Answer:
y = -51
Step-by-step explanation:
Apply the - (-a) = a rule.
y + 10 = -41
Subtract 10 from both sides
y + 10 = -41
-10 -10
y = -51
simplify 4 -2y + (-8y) + 6.2
Answer:
-10y+10.2
hope this helps
have a good day :)
Step-by-step explanation:
Help on Math please and thank you
Answer:
the value of x to the nearest tenth is 12 * x
$450 at 7% for 2 years.
Answer:
63
Step-by-step explanation:
What is 5x-3 equal to
Answer:
-15
Step-by-step explanation:
Answer:
-15 hdbdudbdjsbakznzbzjzbzbz
When using the quadratic formula to solve 7x2 – 3x + 2 = 0, which number will be squared as part of the formula?
Answer:
The value of b will be squared
Step-by-step explanation:
Recall that the quadratic formula is [tex]x=\frac{-b\pm\sqrt{b^{2}-4ac } }{2a}[/tex]
You will see that the only squared coefficient is b.
Which of the following best describes a simple random sample?
A. Each member of the population has an equal chance of being chosen
B. Each member of the sample has an equal chance of being chosen
C. A percentage of the population is chosen
D. Randomly selected one person from the population
Trish had a square garden with side lengths of 8 feet. She expanded her garden to 10 feet by 8 feet. By how many square feet did she expand the area of her garden?
Answer:
[tex]16\:\mathrm{ft^2}[/tex]
Step-by-step explanation:
Trish's initial garden had an area of [tex]8\cdot8=64\:\mathrm{ft^2}[/tex]. After expanding her garden to be 10 feet by 8 feet, the garden has an area of [tex]8\cdot 10=80 \:\mathrm{ft^2}[/tex]. Therefore, the garden was expanded by [tex]80-64=\boxed{16\:\mathrm{ft^2}}[/tex]
WILL GIVE THANKS, BRAINIEST, AND 5 STARS! PLEASE HELP!
Answer:
30
Step-by-step explanation:
C(n) = 5n, 0 ≤ n ≤10 You would use this formula because 6 is greater than 0 but less than 10.
C(n) = 5n, 0 ≤ n ≤10 ← You can just ignore the 0≤ n ≤10 part.
C(6) = 5(6) Input the value 6 as x.
C(6) = 30
The answer is that 6 shirts costs 30 dollars.
does it represent the range, mode, median, or mean
Answer:
median
Step-by-step explanation:
in a box plot, it does not represent the mean, just so you know.
mode = largest number.
range = difference between largest number and smallest number
Meliah wants to make a gallon of punch. She uses 2 quarts of orange juice, 1 cup of lemon juice, and 2 1/2 pints of pineapple juice. How many cups of water should she add to make 1 gallon?
Answer:
2 cups of water
Step-by-step explanation:
Meliah wants to make a gallon of punch.
Note that
1 gallons = 16 cups
For Orange juice
She uses 2 quarts of orange juice,
1 quart = 4 cups
2 quarts = x
Cross Mulitiply
2 × 4 cups = 8 cups
For lemon juice
1 cup of lemon juice
For pineapple juice
2 1/2 pints of pineapple juice.
1 pint = 2 cups
2 1/2 pints = x
Cross Mulitiply
2 1/2 × 2 cups = 5 cups
Total number of cups
= 8 cups orange juice + 1 cup lemon juice + 5 cups of pineapple juice
= 14 cups
Hence, the number of cups of water she should add to make 1 gallon is calculated as:
16 cups - 14 cups
= 2 cups of water
Which table corresponds to the function y = -3x + 11?
Answer:
im not a 100% sure but i think its the 3rd one
The third table represents the linear function y = -3x + 11 so option (C) is correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given function,
y = -3x + 11
Put x = 0
y = -3 x 0 + 11 = 11
Put x = 1
y = -3(1) + 11 = 8
Put x = 2
y = -3 x 2 + 11 = 5
Since the values in table third are satisfied thus it will be correct.
Hence "The linear equation for the third table is y = -3x + 11.".
For more about the linear function,
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Which of the following tables of values represent a function ? Circle all that apply
Answer:
The last one
Step-by-step explanation:
An airplane is navigating a polygon-shaped course. Each turn is labeled with the measure of the external angle at the striped post. What is m<1
M<1 = ?
Answer:
100
Step-by-step explanation:
A rep hockey team has two goalies. Goalie A has a save percentage of 0.92 and Goalie B has a save percentage of 0.89. If goalie A plays 75 percent of the games and goalie B plays 25 percent of the games then: a) Determine the probability that a save has been made by either goalie A or goalie B. b) If a save has been made, what is the probability that is was goalie A? c) If a goal was let in, what is the probability it was goalie B?
Answer:
a) 0.9125
b) 0.756
c) 0.314
Step-by-step explanation:
The save percentage of Goalie A = 0.92
The save percentage of Goalie B = 0.89
The percentage of the games Goalie A plays = 75 percent
The percentage of the games Goalie B plays = 25 percent
a) The probability that a save has been made by either Goalie A or Goalie B
Therefore we get;
The probability that Goalie A made a save, P(A) = 0.92 × 0.75 = 0.69
The probability that Goalie B made a save, P(B) = 0.89 × 0.25 = 0.2225
For mutually exclusive events, we have;
P(A) or P(B) = P(A) + P(B)
∴ P(A) or P(B) = 0.69 + 0.2225 = 0.9125
The probability that a save has been made by either Goalie A or Goalie B, P(A) or P(B) = 0.9125
b) Where there are 10,000 attempts, made evenly in all games, we have;
The number of attempts made with Goalie A playing = 10,000 × 0.75 = 7,500
The number of saves Goalie A makes = 0.92 × 7,500 = 6,900
The number of saves for 10,000 attempt = (P(A) or P(B)) × 10,000 = 0.9125 × 10,000
The number of saves for 10,000 attempt = 9,125
∴ The probability that Goalie A saves = 6,900/9,125 ≈ 0.756
c) Out of the 2,500 attempts at Goalie B, the number of goals let in is given as follows;
P(Goal B) = 2,500 - 2,500 × 0.89 = 275
The number of goals let in by Goalie A, we have;
P(Goal A) = 7,500 - 7,500 × 0.92 = 600
Therefore, the total number of goals let in = 300 + 275 = 875
The probability that the goals was let in by Goalie B = 275/875 = 11/35 ≈ 0.314.
PLZ PLZ HELP WILL MARK BRAINLIEST Select ALL the correct answers. Select all the expressions that will include a remainder.
Answer: a, b, and finally d
Step-by-step explanation:
Whats 1/7 + 3/4 ?
Please help me?
Answer:
25/28
Step-by-step explanation:
28 is the greatest common factor, found by multiplying 7 by 4 (the denominators)
1/7 = 4/28
3/4 = 21/28
21/28 + 4/28 = 25/28
An Brainly Question:
Whats 1/7 + 3/4 ?
Answer:
25/28
Step-by-step explanation:
Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.
So, we multiply 1 by 4, and get 4, then we multiply 7 by 4 and get 28.
Let's add
1
7
+
3
4
Step 1
Can you add yet? Nope! The denominators don't match. We need a common denominator. So next we take both denominators and multiply them. Next, take each numerator and multiply it by the denominator of the other term.
So, we multiply 1 by 4, and get 4, then we multiply 7 by 4 and get 28.
1/7 times 4
Now for the second term. You multiply 3 by 7, and get 21, then multiply 7 by 4 and get 28.
3/4 times 7
We now have a new problem, that looks like this:
4
28
+
21
28
Step 2
Since our denominators match, we can add the numerators.
4 + 21 = 25
That gives us the sum, which is
25
28
Step 3
Now, do we need to simplify this fraction?
First, we attempt to divide it by 2...
Nope! So now we try the next greatest prime number, 3...
Nope! So now we try the next greatest prime number, 5...
Nope! So now we try the next greatest prime number, 7...
Nope! So now we try the next greatest prime number, 11...
Nope! So now we try the next greatest prime number, 13...
Nope! So now we try the next greatest prime number, 17...
Nope! So now we try the next greatest prime number, 19...
Nope! So now we try the next greatest prime number, 23...
Nope! So now we try the next greatest prime number, 29...
No good. 29 is larger than 25. So we're done reducing.
There you have it! Here's the final answer to 1/7 + 3/4
1
7
+
3
4
=
25
28
You ARE SUPPOSED TO BE IN BRAINLY.IN FOR 5th Grade and LESS
¿Cuál es el volumen en pulgadas cúbicas de una esfera cuya circunferencia mide 64 pulgadas?
Answer:
4445.18 pulgadas cúbicas
Step-by-step explanation:
Paso 1
La fórmula para la circunferencia de una esfera = 2πr
Circunferencia de una esfera = 64 pulgadas
Por eso,
64 = 2πr
Por lo tanto, encontramos r
Dividir ambos lados por 2π
64 / 2π = 2πr / 2π
r = 10.185916358 pulgadas
Radio r = 10.2 pulgadas
Paso 2
Volumen de una esfera
= 4/3 × π × r³
r = 10.2 pulgadas
Por lo tanto, 4/3 × π × (10.2) ³
= 4445.18 pulgadas cúbicas
Por lo tanto, el volumen en pulgadas cúbicas de una esfera = 4445.18 pulgadas cúbicas
Angie, Keisha and Chen shared 125 stickers among themselves. Keisha and Chen received an equal number of stickers and Angie received one less sticker. How many stickers did Keisha receive?
Answer:
42 stickers
Step-by-step explanation:
Let
x = number of stickers Keisha and chen received
x - 1 = number of stickers Angie received
Total stickers = 125
125 = x + x + (x - 1)
125 = 2x + x - 1
125 + 1 = 3x
126 = 3x
x = 126/3
x = 42 stickers
x = number of stickers Keisha and chen received = 42 stickers
x - 1 = number of stickers Angie received = 42 - 1 = 41 stickers