The solutions are (4.5, 4.5) and (6, 3).
Here,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
We have to solve the equations.
What is Expression?
Expression in math is defined as the collection of the numbers, variables and functions by using signs like addition, subtraction, multiplication, and division
Now,
The equations are;
x + y = 9
x²- 3xy + 2y² = 0
Since, x + y = 9 ⇒ y = 9 - x
And, solve the equation as;
x²- 3xy + 2y² = 0
x²- 2xy - xy + 2y² = 0
x (x - 2y) - y (x - 2y) = 0
(x - y) (x - 2y) = 0
(x - y) = 0 or (x - 2y) = 0
For, (x - y) = 0
Given, x + y = 0
Hence, Solve equation (x - y) = 0 and (x + y) = 9 we get;
2x = 9
x = 4.5
And, y = 4.5
For (x - 2y) = 0
x = 2y put in equation (x + y) = 9 we get;
(x + y) = 9
2y + y = 9
3y = 9
y = 3
And, x = 6
Therefore, The solutions are (4.5, 4.5) and (6, 3).
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Solutions are (4.5,4.5) and (6,3)
What are Quadratic equations ?
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).
Given,
x + y = 9 => y = 9-x equation 1
x^2 - 3xy + 2y^2 = 0 equation 2
(x - y)(x - 2y)=0
x - y = 0 or x - 2y = 0
1. Equating x-y=0 and x + y = 9,
x + y = 9
x - y = 0
2x = 9
x = 4.5
y = 4.5
because y = x
2. Equating x - 2y = 0 and x + y = 9,
2x + 2y = 18
x - 2y = 0
3x = 18
x = 6
y = 9 - x = 3
therefore, possible solutions are (4.5,4.5) and (6,3)
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I need help asap!! (Fractions)
Answer:3 5/7
Step-by-step explanation:
Answer: A ----------------3 5/7
A town's population is . 57,900 About 75 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 60,600 . It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
The populations of both towns would be equal in nine months.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Let's assume that both town's populations will be equal in x months.
After x months, the population of the first town is given by
200x - 75x + 57,900
The population of the second town after x months is given by
60,600 - 175x
In order for the population of both towns to be equal, we have
200x - 75x + 57,900 = 60,600 - 175x
This is the required equation that represents the given situation.
200x - 75x + 57,900 = 60,600 - 175x
Rearrange the likewise terms and apply arithmetic operation
200x - 75x + 175x = 60,600 - 57,900
300x = 2700
x = 2700/300
x = 9
Therefore, the populations of both towns would be equal in nine months.
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If f (x) = 3x^4+5, then what is the remainder when f (x) is divided by x+4?
The remainder when polynomial function is divide by linear function is 773.
Given that the polynomial functon f(x)=3x⁴+5 and the linear function is x+4.
As it is given that we have to find the remainder the polynomial
f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4.
f(x)=3x⁴+5 .......(1)
g(x)=x+4 .......(2)
We know the remainder theorem that when a polynomial f(x) is divided by a linear expression (x−a), the remainder will be f(a).
From equation (2), we have a linear expression.
Now, on simplifying equation (2) to obtain the zero of g(x), we get
g(x)=x+4=0
x+4=0
Now, on comparing (x+4) and (x−a), we get
a=-4 ......(3)
Here, we have to get the value of f(a).
Now, using the remainder theorem, we can say that to get the remainder when the polynomial f(x)=3x⁴+5 is divided by g(x)=x+4, we have to replace x by -4 in the polynomial f(x)=3x⁴+5, we get
f(-4)=3(-4)⁴+5
f(-4)=3(256)+5
f(-4)=768+5
f(-4)=773
Therefore, the remainder when the polynomial f(x)=3x⁴+5 is divided by the linear expression g(x)=x+4 is 773.
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PLEASE HELP ME THANK YOU
Answer:
number 2. A
number 3. C
number 4. B
Step-by-step explanation:
if the answer's are correct then comment or like
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 777 points less than 222 times as many points as Carlos. Fabio scored 313131 points in the game.
Write an equation to determine the number of points (c) Carlos scored in the last game.
Find the number of points Carlos scored in the last game.
Considering the definition of an equation and the way to solve it, the number of points Carlos scored in the last game is 19.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.
The solution of a equation means determining the value that satisfies it. To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing:
"C" the number of points Carlos scored."F" the number of points Fabio scored.and knowing that in the last game, Fabio had 7 points less than 2 times as many points as Carlos, the equation to determine the number of points Carlos scored in the last game is:
2C - 7= F
Fabio scored 31 points in the game. So you get:
2C - 7= 31
Solving:
2C= 31 + 7
2C= 38
C= 38 ÷ 2
C=19
Finally, the number of points Carlos scored in the last game is 19.
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(7x10^9)(5.3x10^2). Write this in scientific Notation
The required answer would be 3.7×10¹⁰ which is written in the form of scientific notation.
What is the Scientific Notation?Scientific Notation is a way of writing down in the easy form of very large or very small numbers.
We have been given that expression as:
⇒ (7×10⁹)(5.3×10²)
⇒ 7×5.3 ×10⁹×10²
We have to add exponents of tens and apply the multiplication operation between 7 and 5.3,
⇒ 37 ×10⁹⁺²
⇒ 3.7×10⁻¹ ×10¹¹
⇒ 3.7×10¹⁰
Hence, the required answer is 3.7×10¹⁰ which is expressed in scientific notation.
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The equation y = 2.50x determines the total cost, y, of buying x carnival tickets. Use the drop-down menu to complete the sentence.
According to the equation, 15 carnival tickets would cost.
.
The cost of 15 carnival tickets is 37.5 dollars.
How to use the equation to find the cost of 15 ticket ?The equation y = 2.50x determines the total cost, y, of buying x carnival tickets.
where
x = number of carnival tickety = total costTherefore, according to the equation, the cost of 15 carnival ticket can be calculated as follows:
y = 2.50x
where
x = 15
Hence,
y = 2.50 × 15
y = 37.5 dollars
Therefore, the cost of 15 carnival tickets is 37.5 dollars.
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Of the numbers 0.4761, 0.04761, 0.4671, and 0.04671, which is the largest?
Answer:
0.4761
Step-by-step explanation:
It is in the 10ths place making it bigger than 0.04761 and 0.04671
Then in the hundreths place for 0.4761 7 is bigger than the 6 in in the hundreths place of 0.4671, so the answer is
0.4761
This question is throwing me off track. Help?
Solve 1/3x + 6/5 = 3/5
The slashes means that it is a fraction btw! Thanks so much if you do help me :)
Answer:
x= -9/5
Step-by-step explanation:
I hope this helps!
Which fractions have the same value as -1/4 please help
(different question and look at picture)
Answer:
-1/4 ,-(-1/-4) and 1/-4 are the answers please
prove that if all of the 2n subsets of a set containing 2n 1 are equal, then all elements of set n are equal
when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).
Take the power set. It has 2^(2n+1) members.
Replace any member which has n+1 or more elements with its complements.
Now the power set has members, which have n or fewer elements, and each such member appears twice.
Therefore, when multiplicity is removed, you get 2^(2n+1)/2 members, which is 2^(2n).
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What is the domain and range for first graph
We need to know about domain and range of a graph to solve this problem. The domain is (-∞,5) and the range is (-∞,2).
The domain of a function is the input values that the function can take. The range is the set of values that can be the possible output of the function. The domain of a graph are the values that are on the x-axis and the range is on the y-axis. The arrow means that the graph goes on till infinity, a solid sphere means that the graph ends at that point and the ending point is included in the function, a hollow sphere means the graph ends at that point and the ending point is not included in the function. In the graph in the question, along x-axis the values on left goes on till negative infinity and on right the domain is open at 5. For range along y-axis, the range on the left side goes on till negative infinity and on the right it is open at 2.
Therefore we see that the domain of the graph is (-∞,5) and the range is (-∞,2).
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If ∠DEG is 8 times m∠FEG, what is m∠DEG?
Answer:
160
Step-by-step explanation:
180 (a straight angle's degrees) /9 = 20
20 * 8 = 160
Check:
160 + 20 = 180
Find the 8th term of the geometric sequence shown below. 6x,18x^4,54x^7
please help
The 8th term of the geometric sequence is 13122x^22
Explicit form of a geometric sequenceThe explicit form of a geometric sequence is expressed according to the equation;
Tn = ar^n-1
where
r is the common ratio
a is the first term
n is the number of terms
Given the sequence below;
6x,18x^4,54x^7
r = 18x^4/6x
r = 3x^3
a = 6x
n = 8
Substitute to have:
T8 = 6x(3x^3)^8-1
T8 = 6x (3x^3)^7
T8 = 13122x^22
Hence the 8th term of the geometric sequence is 13122x^22
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Make c subject of the formula
πc² =A
Answer: c=[tex]\sqrt{A/\pi}[/tex]
Step-by-step explanation:
πc²=A
c²=A/π
c=[tex]\sqrt{A/\pi}[/tex]
In an AP the 9th Term is 2 times the 4th Term and the 12th Term is 78. What is the sum of the first twenty terms?
The sum of the first twenty terms of the given AP is 1380.
An arithmetic progression is given in this problem.Let the first term of the AP be "a".Let the common difference between the terms of the AP be "d".Let the term in the "n" position be denoted by t(n).t(n) = a + (n-1)*dIt is given that the 12th term is 78.t(12) = a + 11d78 = a + 11dThis is equation 1.It is given that the 9th term is twice the 4th term.t(9) = 2*t(4)a + 8d = 2(a + 3d)a + 8d = 2a + 6da = 2dThis is equation 2.Solving equations 1 and 2, we get the values of "a" and "d".The value of "a" is 12 and "d" is 6.The sum of the first "n" terms of an AP is given by the formula :S(n) = (n/2)[2a + (n-1)d]We need to find the sum of the first 20 terms.S(20) = (20/2)[2*12 + 19*6]S(20) = 10*(24 + 114)S(20) = 10*138S(20) = 1380To learn more about common difference, visit :
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determine whether the data are qualitative or quantitative. the colors of automobiles on a used car lot
The data is qualitative one.
Qualitative Data:
Qualitative data consists of Labels, Attributes, Descriptions
This type of data is observed not measured
Examples: Colors, categories, appearances, dogs, etc.
Basically it considers the qualities of the data.
Quantitative Data:
Quantitative data Consists of numbers or counts in the data.
This type is mainly focused on the measurement. Which means it only consider the quantities.
Examples: Length, height, area, speeds, dollar amounts, ages, etc.
Given,
The colors of automobiles on a used car lot.
Here we need to determine the given data is qualitative or quantitative.
Based on the definition of the qualitative or quantitative,
We conclude that the given data is qualitative.
Because it describe the quality of the car.
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f(x)=x+5
g(x)=\sqrt 3x+1
find f/g and f-g then give their domains using interval notation
[tex] \frac{f(x)}{g(x)} = \frac{x + 5}{ \sqrt{3x + 1} } [/tex]
[tex]x ∈ \: \: ] \frac{ - 1}{3} ,∞[[/tex]
[tex]f(x) - g(x) = x + 5 - \sqrt{3x + 1} [/tex]
[tex]x ∈ \: \: [ \frac{ - 1}{3} ,∞[[/tex]
PLS HELP ASAP!!
Three less than the quotient of a number and two has a result of thirteen. What would the solution be? Please only place the number.
Thanks a ton!!!
The solution of the of the expression is as follows:
x = 32How to find solution to expression?Three less than the quotient of a number and two has a result of thirteen.
Therefore,
let
the number = x
The quotient of the number and two = x / 2
Therefore,
x / 2 - 3 = 13
add 3 to both sides
x / 2 - 3 = 13
x / 2 - 3 + 3 = 13 + 3
x / 2 = 16
cross multiply
x = 2 × 16
x = 32
Therefore, the solution of the of the expression is as follows:
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What are the solutions to the equation
w squared
=
36
? Select all that apply.
−
18
6
−
9
−
6
18
9
Answer:-4
Step-by-step explanation:
100 points, please help
In 8-11, write a justification for each conclusion.
Answer:
8. Supplementary means that two angles add up to 180 degrees (straight line). For the justification, I would simply write "def. of supplementary angles."
9. Equilateral means that all sides equal. For the justification, I would simply write "def. of equilateral triangle."
10. In a circle, all radiuses equal in length. TC and ZC are both radiuses. For the justification, I would simply write "def. of radius."
11. A midpoint divides a line segment in half. For the justification, I would simply write "def. of midpoint."
PLS HELPP IM LOST
1: Find the missing Statements #3, #7, and #8 in the Algebraic Proof below.
2: What are the missing statements for #4 and #6?
Answer:
#3: -2 = 2y - 8
#7: 3 = y
#8: y = 3
#4: Angle1 + Angle2 = Angle ABC
#6: Angle 1 and Angle 2 are supplementary
Step-by-step explanation:
6y - 2 = 8y - 8
8 - 2 = 8y - 6y
6/2 = 2y/2
3 = y
y = 3
#35 i
Find the measure of the exterior angle.
to
38°
The measure of the exterior angle is
Answer:
128°
Step-by-step explanation:
The three INTERIOR angles of the triangle are 90 38 and 52° ( they sum to 180 °)
52 ° and 'x' form a straight line = 180 ° so x = 128°
Answer:
128
Step-by-step explanation:
Add the two farthest angles, 90 and 38, so that's 128
brainliest pls
4(r-2+y) distribute to creat an equivalent expression with the fewest symbols possible
Answer: 4r-8+4y
Step-by-step explanation: Distribution is when you multiply every term inside the parantheses by the outside term. So 4(r-2+y)=4(r)+4(-2)+4(y). This is the same as 4r-8+4y. Since none of these are like terms we have the fewest symbols possible.
Which weight represents the 65th percentile?
The 65-th percentile is approximately 83.8 ounces.
A number at or below which a particular percentage falls in its frequency distribution, or a score below which a given percentage falls, is known as the k-th percentile in statistics. The 50th percentile, for instance, is the score at or below which 50% of the distribution's scores can be found.
The 50-th percentile is called the median.The 25th and 75th percentile is called the lower and upper percentile respectively.Mean of a data-set is the measure of central tendency which denotes the average of the data.The standard deviation denotes the fluctuations of the data from the central tendency.The percentile can be calculated by using the formula
Percentile Value = μ + zσ where
z is the z-score , μ is the mean and σ is the standard deviation.
Here the percentile that is to be calculated is 65.
So we take the value that is closest to 0.65 from the z-table.
We get the value of the data to be 0.39
Now putting the values in the equation we get:
Percentile Value = μ + zσ
or, Percentile Value = 83 + (0.39 × 2)
or, Percentile Value = 83.78
or, Percentile Value ≈ 83.8
Hence the 65th percentile value of the function is given by 83.8 .
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the federal helium reserve held about 20 billion cubic feet of helium in 2010 and is being depleted by about 1.9 billion cubic feet each year. a . give a linear equation for the remaining federal helium reserves in billions of cubic feet, r , in terms of t , the number of years since 2010. r ( t )
The linear equation for the remaining Federal Helium Reserves, r(t) = 20 -1.9t
There is 20 billion cubic feet of Helium in 2010. Helium is depleted by about 1.9 billion cubic feet each year.
Let 'r' denotes the remaining Federal Helium Reserves in billions of cubic feet.
Let 't' denotes the number of years since 2010.
We have to find a linear equation to represent the depletion of Helium through years since 2010. A linear equation will have two variables, one dependent and one independent variable. Here, let 'r' be the dependent variable and 't' be the independent variable.
Then the amount of Helium depleted in 't' years = 1.9t
So, the remaining Helium in the Federal Helium Reserve since 2010 = 20 - 1.9t.
Thus, r(t) = 20 - 1.9t
This is a linear equation because it depends on only one variable, 't'.
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HELP FOR BRAINLIEST! A rectangle solid has a length of 16, a width of 20 and a total surface area of 4480. What is the total surface area of a similar rectangular solid with a width of 10?
Given: A is between B and C. if AB =x+2, BC=4x-7 , and AC =2x-1 , find x and AC
If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x=8 and AC=15 units.
Given,
That A is between B and C.
AB= x+2
BC= 4x-7
AC= 2x-1
Then,
BC = AB+AC
4x-7= x+2+2x-1
4x-7= 3x+1
4x-3x=1+7
x=8
Then the length of the line AC is
AC= 2x-1
AC= 2×8-1 =15 units
Hence, If A is between B and C, and AB=x+2, BC=4x-7 and AC=2x-1, then the x= 8 and AC= 15 units
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Pablo mixes 3 units of white paint and 1 unit of black oaint to make gray paint. What two equations show the relationship between units of white paint and unites of black paint
(ANSWER QUICK PLEASE) 1. Kasey noticed that the distribution of candy bars in the variety bags of candy bars is always the same. There are three times as many Twix Bars as Milky Ways. There are 5 fewer snickers than there are Twix.
Answer:
Let's call the number of Twix bars "x".
Since there are three times as many Twix bars as Milky Ways, the number of Milky Ways is x / 3.
And, since there are 5 fewer Snickers bars than there are Twix bars, the number of Snickers bars is x - 5.
So, the total number of candy bars can be found by adding the number of each type of candy bar:
x + x / 3 + x - 5 = total number of candy bars
Combining like terms, we get:
5x / 3 - 5 = total number of candy bars
To find the value of x, we can solve this equation for x.
5x / 3 = total number of candy bars + 5
5x / 3 = total number of candy bars + 5
5x = 3(total number of candy bars + 5)
5x = 3(total number of candy bars) + 15
5x = 3(total number of candy bars) + 15
5x - 15 = 3(total number of candy bars)
5x - 15 = 3(total number of candy bars)
(5x - 15) / 3 = total number of candy bars
So, the total number of candy bars can be found by dividing (5x - 15) by 3. The value of x represents the number of Twix bars, and the rest of the candy bars can be found using the relationships described in the problem.