Just by adding the second row to the first one in the matrix, we can see that the solution of the system of equations is x = 0.5 and y = 20.
How to solve the system of equations?
Here we have the system of equations:
300x - y = 130
200x + y = 120
And we want to solve it using a matrix equation. Remember that we could add the two rows, subtract them, etc to remove one of the variables.
Here is really simple to see that if we add the two rows (or the two equations, depending on how you see the system) the variable y will be removed.
Then we can add the second row to the first one to get.
(300x + 200x) + (-y + y) = (130 + 120)
Now our matrix will look like:
500x + 0y = 250
200x + y = 120
With the first row we can find the value of x, it just is:
x = 250/500 = 0.5
And with taht we can find the value of y:
200*0.5 + y = 120
100 + y = 120
y = 120 - 100 = 20
Just by adding two rows, we can see that the solution of the system of equations is x = 0.5 and y = 20.
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Writing Explain how you can find the range of the inverse of f(x)=√x-1 without finding the inverse itself.
Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}
Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}
Finding the Inverse Function but not the Inverse Function's Domain and Range
First, we must determine the domain and range of the original function f in order to determine the domain and range of an inverse function (x).
1.Find the function's domain and range.
Assume that the domain of the function f(x) is [0,∞),{x|x≥0}
Assume that the range of the function f(x) is [-1,∞),{y|y≥-1}
2. Substitute Domain for Range and Range for Domain
The domain of the calulated function f^-1(x) is [-1,∞),{x|x≥-1}
f^-1(x) calculated function (x) the interval for range is [0,∞),{y|y≥0}
∴Domain of inverse of f(x)=√x -1 is [-1,∞),{x|x≥-1}
Range of inverse of f(x)=√x -1 is [0,∞),{y|y≥0}
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4t^2+2 + 4t^2-2
what is the sum?
Answer: its 8t²
Step-by-step explanation:
Answer:
Sum = 8t²
Step-by-step explanation:
Let's solve the problem,
→ 4t² + 2 + 4t² - 2
→ (4t² + 4t²) + (-2 + 2)
→ 8t² + 0 = 8t²
Hence, the answer is 8t².
Find the area of the shape below.
9 cm
11 cm
6 cm
15 cm
Answer:
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Step-by-step explanation:
1. At the ice cream shop, there are 14 shakes
sold for every 6 malts. Record the ratios
below.
b. malts to total
The ratio of malts to the total ice creams is 3:10 .
Ratio is defined as the fraction which defines the relationship between two quantities .
Ratio is denoted by a:b such that it can also be written as a/b where a and b are co-prime. Ratio can also be denoted as a decimal but mostly it is represented as fraction in its lowest terms
Now the given ice cream shop has 14 shakes that are sold for every 6 malts.
Hence when 14 shakes are sold total number of ice cream sold is
14+6 = 20 .
Now we have to find the ratio of the malts to the total number of ice creams
∴ malts : ice creams = 6 : 20
Reducing to lowest terms we get :
ratio = 3:10
Hence the ratio of malts to total ice cream is 3:10
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Simplify each expression. Rationalize all denominators. √48 +2√27 +5√12
The simplify of the expression is [tex]20 \sqrt{3}[/tex].
Fixing an equation manner that we ought to discover the fee of the variable, with the aid of the use of homes of actual numbers and combining like terms, which make the equation true. Simplifying an algebraic expression manner that we most effectively need to lessen the expression by means of the use of properties of actual numbers and mixing like phrases.
The square root of 2 hundred in its simplest radical form is 10√2. If we know the high factorization of quite a number, we can write the radical shape of the rectangular root of that variety. As a result, the high factorization of 2 hundred is two × 2 × 2 × five × five. As a result, the square root of 200 within the handiest radical shape has to be 10√2.
Simplify genuinely manner to make it easy. In arithmetic, genuinely or simplification is reducing the expression/fraction/trouble in an easier shape. It makes the hassle easy with calculations and fixing.
[tex]\sqrt{48} +2 \sqrt{27} + 5\sqrt{12}[/tex]
[tex]\sqrt{48} = 4\sqrt{3}[/tex]
[tex]2 \sqrt{27} = 6\sqrt{3}[/tex]
[tex]5\sqrt{12} = 10 \sqrt{3}[/tex]
[tex]4\sqrt{3} +6 \sqrt{3} + 10 \sqrt{3}[/tex]
[tex]= 20 \sqrt{3}[/tex]
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2
21. --x-5 = y; (9,-11)
3
answer is y=x+216 and -6.
In the question, the expression is given 221--x-5=y;(9-11)3
An equation is said to be linear equation in two variables if it is in the form of ax + by + c=0, where a, b & c are real numbers and a and b respectively, are not equal to zero. For example, 10x+4y = 3 and -x+5y = 2 are linear equations in two variables.
Unique Solution:
For the given linear equations in two variables, the solution will be unique , if and only if they intersect at a point.
No Solution:
For the given linear equations in two variables, the given system of equations has no solution if lines of two linear equations are parallel.
Infinitely many solution:
For the given linear equations in two variables, the given system of equations has infinitely many solution if lines of two linear equations coincident.
Two consecutive minus signs have the same mathematical meaning as a single plus sign .
221+x-5=y,(9-11).3
x+216=y
Subtract 216 from both sides of the equation,
x+216-216=y-216
x=y-216
replace x with y-216 in the expression
(9-11).3
subtract 11 from 9
-2.3
Multiply -2 by 3
-6
Hence, Final answer is y=x+216 and -6.
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what is 4
7
10
− 9
=
The value of -4(7/10) - 9(7/15) is -85 / 6.
What is a mixed fraction?A fraction represented with its quotient and remainder is a mixed fraction.
For example:
3 4/5 is a mixed fraction, where 3 is the quotient, and 4 is the remainder.
We have,
-4(7/10) - 9(7/15)
Convert each term into a proper fraction.
4 7/10 = (40+7) / 10 = 47 / 10
9 7/15 = (135 + 7) / 15 = 142 / 15
Now,
= -47 / 10 - 142 / 15
The LCM of 10 and 15 is 30
= [3 x (-47) - (2 x 142)] / 30
= (-141 - 284) / 30
= -425 / 30
We can divide by a common factor of 5
= - 85 / 6
Thus the value of -4(7/10) - 9(7/15) is -85 / 6.
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The complete question is
Evaluate -4(7/10) - 9(7/15)
Which of the following is an example of the associative property of multiplicaition?
1. 7 • (3 + 5) = 21 + 35
2. 7 • (3 • 5) = 7 • (5 • 3)
3. 7 • (3 • 5) = (7 • 3) • 5
4. 7 • ⅐ = 1
The example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5
How to determine the example of the associative property of multiplication?The associative property of multiplication states that
(a * b) * c = a * (b * c)
Using the above equation as a guide, we have the following equation
7 • (3 • 5) = (7 • 3) • 5
The above equation is the option (3) of the associative property of multiplication
Hence, the example of the associative property of multiplication is 7 • (3 • 5) = (7 • 3) • 5
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use deductive reasoning to write a formula for the perimeter P of a regular polygon with n sides
for each side is S
The perimeter P is mathematically given as
P=[Number of sides of regular polygon] * [Length of each side]
This is further explained below.
What is a formula for the perimeter P of a regular polygon with n sides for each side is S?Generally, The formula for calculating the perimeter of a regular polygon is ns.
Having said that; The formula for the number of sides of a regular polygon is n.
The length of each side is equal to one unit.
Find:The formula for calculating the perimeter of a regular polygon
Hence
The formula for calculating the perimeter of a regular polygon is as follows:
Perimeter = [Number of sides of regular polygon] * [Length of each side]
In conclusion, The formula for calculating the perimeter of a regular polygon is
P= [Number of sides of regular polygon] * [Length of each side]
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3ײ + 8 × - 8 - 5× ² - 10 please solve and give a solution tthankyou!! asap!!
Answer:
-2x²+8x-18
not sure if the x's are multiplication or x but this what I got.
Answer:
-2x² + 8x - 18Step-by-step explanation:
3ײ + 8 × - 8 - 5× ² - 10 please solve and give a solution tthankyou!! asap!!
3x² + 8x - 8 - 5x²- 10 =
-2x² + 8x - 18
Bertie has 3494 comic books he wants them in groups of 8 how many comics would be left over after putting them in groups of 8
Answer: 6 would be left
Step-by-step explanation: divide 3494 by 8
There will be 6 comics left over after putting them in groups of 8
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Bertie has 3494 comic books he wants them in groups of 8.
∴ The no. of groups can be obtained if we divide the total number of books by no. of books in each group which is,
= (3494/8).
= 438×8 + 6.
So, There will be 6 comics left over after putting them in groups of 8.
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One of Ted’s jobs at home is to pump gas for his family’s sedan and truck. When he fills up the sedan with 12 gallons of gas, he notices that it costs him $50.04. Write an equation using the unit rate from #27. #27 is $4.17.
The equation that can be formed with the unit and total costs of filling up the Sedan with 12 gallons of gas is 12p = 50.04, where p = 4.17.
What is an equation?An equation is a mathematical statement that expresses two equal variables.
Equations use the equation sign (=).
Data and Calculations:The quantity of gas per the Sedan's tank = 12 gallons
The unit cost of a gallon of gas = $4.17
The total cost of filling 12 gallons with gas = $50.04
In equation form, the expression can be written as:
12p = 50.04
Where p = 4.17
Thus, the equation of the total cost is 12p = 50.04, where p = 4.17.
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Find the domain, points of discontinuity, and x - and y - intercepts of each rational function. Determine whether the discontinuities are removable or non-removable. y=6-3 x / x²-5 x+6
The domain of given points are :
IR x ≠ 2, 3
Points of discontinuity - x = 2 ( removable/hole )
x = 3 ( non removable / asymptote )
x - intercept = 2/3 , y - intercept = 1
What is rational functions ?Any function that can be expressed as a polynomial divided by a polynomial is said to be rational. The domain of a rational function is the set of all numbers except the zeros of the denominator since polynomials are defined everywhere. First example: f(x) = x/ (x - 3).
CALCULATIONy = 6-3x/[tex]x^{2}[/tex]-5x+6
= -3(x-2)/[tex]x^{2}[/tex]-3x-2x+6
= -3(x-2)/x(x-3)-2(x-3)
= -3(x-2)/(x-2)(x-3)
The domain of given points are :
IR x ≠ 2, 3
Points of discontinuity - x = 2 ( removable/hole )
x = 3 ( non removable / asymptote )
x-intercept :
0=-3(x-2)
-3x+2=0
2=3x
x=2/3
y - intercept :
-3( 0-2)/(0-2)(0-3)
y = 1
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What is the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin?
The image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)
How to determine the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin?The point is given as
Point = (10, 10)
The scale factor is given as
k = 1/2 centered at the origin
The image after a dilation by the scale factor is calculated as
Image = Point * k
This gives
Image = (10, 10) * 1/2
Evaluate
Image = (5, 5)
Hence, the image of (10,10) after a dilation by a scale factor of 1/2 centered at the origin is (5, 5)
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This IS MY LAST QUESTION PLEASE ANYTHING YALL
Answer:
The correct answer is the last choice
Step-by-step explanation:
You see that the pattern is increasing by 4 each step. If start at -5 and back up 4 three more times to get to the starting number, you will be at -17
Which line has an equation of y = negative 5 x + 4 in slope-intercept form?
The correct option is (d).
d) (2,-6) & (4,-16)
Now, To find the correct option that is equivalent to this equation, we can begin by narrowing down the given options.
Since, The slope contains a negative number, that's mean the second point must have a lower y value than the first x value.
Hence, By using this criteria, we can eliminate the first and the third option.
Now, we can check the second and fourth option as;
We can test using by putting in values.
Let's plug in the point values to check whether they work:
Hence, For option 2:
y = -5x + 4
-24 = -5(4) + 4
-24 = -20 + 4
-24 ≠ -16
And, For option 4:
y = -5x + 4
-16 = -5(4) + 4
-16 = -20 + 4
-16 = -16
Therefore, The correct option is option (d).
The complete question is this;
Which line has an equation of y= -5x+4 in slope intercept form?
A line passing through the points -
a) (1,9) & (3,19)
b) (2,-14) & (4,-24)
c) (1,1) & (3,11)
d) (2,-6) & (4,-16)
What is the sum of measures of the interior angles of a pentagon
The sum of the interior angles of the pentagon is the 540°.
According to the statement
We have to find that the sum of measures of the interior angles of a pentagon.
So, For this purpose, we know that the
A pentagon is a geometrical shape, which has five sides and five angles.
From the given information:
the sum of measures of the interior angles of a pentagon
Then
A pentagon is a geometrical shape, which has five sides and five angles.
and
we have to know that the
Pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°.
Then
The sum of the interior angles of the pentagon is the 540°.
So, The sum of the interior angles of the pentagon is the 540°.
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The value of the digit 2 in the number 42,780 is 10 times the value of the digit 2 in which number?
426135 is the number in which the value of 2 is 10 times the value of 2 in 42780.
Given:
The number = 42,780
Here, the place value of 2 is 2000 or 2 thousand.
Let's check all the options for the right answer.
There is only one option with 2 in it.
That is option c 426135
We have given that, the value of 2 should be 10 times the value of 2 in 42780.
That is, 2000 x 10 = 20000.
The value of 2 in 426135 is 20000 or 2 ten thousand.
Thus, 426135 is the number in which the value of 2 is 10 times the value of 2 in 42,780.
Rest of the options are incorrect.
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The question is incorrect and the corrected question is given below.
The value of the digit 2 in the number 42,780 is 10 times the value of the digit 2 in which number?
The options are 34,651 or 146,703 or 426,135 or 510,400
My school's debate club has 12 members. How many ways are there to pick two groups of two club members to debate against each other, if no one can be part of both groups?
Answer: Or you could make six groups of 2 so that way no one is on the same team.
Step-by-step explanation: I hope I'm explaining this right because I don't fully get your question ;)
How many inverse variation functions have (2,3) as a solution?
According to the question, solution for the inverse variation function. Using standard concept which defines inverse variation function is as follows:
Inverse variation function: [tex]yx=k[/tex]
Therefore, the number of inverse variation function which has[tex](2,3)[/tex] as a solution is : one
What is inverse variation function?
Inverse variation function defines the relationship which are in inverse function. Like, direct variation define direct relationship between the two variables. In inverse variation function, one variable is inversely related to the another variable.
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You are selling lemonade for $1.50, a bag
of kettle
dog for $2.50 at a fair. Write and simplify an
corn for $3, and a hot
of money you receive when p people buy
expression for the amount
one of each item.
Answer:
I don't understand you hear me
Which quadratic inequality does the graph below represent?
Answer:
3rd option, y<=x^2-3
Step-by-step explanation:
y<=x^2-3 is the graph of the function. The vertex of the graph is (0, -3), so when x=0, y=-3. Also, for every x-coordinate, the shaded region is below the corresponding y-coordinate. For example, when x=0, the shaded area for that x-coordinate is below y=-3.
Three friends eat lunch together. The bill comes to 21 plus 10% tax.if they split the bill and tax evenly, then how much will each person owe?
Each person will owe $7.7
How to calculate the amount each person will pay ?Three friends eat lunch together
The bill accumulates to $10 plus a 10% tax fee
If they split the bill and and tax evenly
The amount each person will pay can be calculated as follows
21 × (1+10/100) /3
= 21 × (1+0.1)/3
= 21 × 1.1/3
= 23.1/3
= 7.7
Hence each person will pay $7.7
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Graph g(x) = |x + 3|.
The graph shows an upward opening v-shaped graph with a vertex at negative 3 comma 0, which passes through negative 4 comma 1 and negative 2 comma 1.
The graph shows an upward opening v-shaped graph with a vertex at 3 comma 0, which passes through 2 comma 1 and 4 comma 1.
The graph shows an upward opening v-shaped graph with a vertex at 0 comma 3, which passes through negative 1 comma 4 and 1 comma 4.
The graph shows an upward opening v-shaped graph with a vertex at 0 comma negative 3, which passes through negative 1 comma negative 2 and 1 comma negative 2.
I’ll give Brainly :)
The graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)
How to graph the equation of the function?The equation of the function is given as; g(x) = |x| - 3
The above function is an absolute value function.
The parent function of an absolute value function is; f(x) = |x|
This means that the function f(x) is translated to get to function g(x)
In this case, the function is f(x) is translated down by 3 units to get to function g(x)
So, the graph of g(x) is gotten by translating the function f(x) = |x| down by 3 units to get to function g(x)
See attachment for the graph of g(x)
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Answer: its c
Step-by-step explanation:
plug in 0 to the equation and you get (0,3)
What is (f⁰g)(-3) for the functions f and g defined in Problem 3 ?
f(g(-3)) = f(6) = 9.
For composing functions like this, we'll work from the inside out. First, find g(-3) by plugging x = -3 into the function g(x):
g(x) = |x - 3|
g(-3) = |-3 - 3|
g(-3) = |-6|
g(-3) = 6
Now we can replace g(-3) with 6 in the function composition to get f(g(-3)) = f(6). Find f(6) by plugging x = 6 into the function f(x):
f(x) = x + 3
f(6) = 6 + 3
f(6) = 9
So, f(g(-3)) = f(6) = 9.
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Solve each equation.
log 2 x+log x=11
log 2x + log x = 11 => x = 223600, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
log (2x) + log (x) = 11
=> log [(2x)(x)] = 11 (as log (a) + log (b) = log (ab))
=> log (2x²) = 11
Since, generally the base of log is 10, raising them to 10
=> [tex]10^{log_{10}(2x^{2})} = 10^{11}[/tex]
=> 2x² = 10¹¹
=> x² = [tex]\frac{10^{11}}{2}[/tex]
=> x = [tex]10^{5}\sqrt{\frac{10}{2}} = 10^{5}\sqrt5[/tex]
=> x = 10⁵ (2.2360)
=> x = 223600
Hence, log 2x + log x = 11 => x = 223600, by properties of logarithm.
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10. Murphy and Naryam do their math homework together. When they find 9- (-8), they get different answers. Murphy claims the difference is 17. Naryam claims the difference is -1. a. Who is correct? Murphy b. What error likely led to the incorrect answer?
Answer:
Naryam
Step-by-step explanation:
Murphy is incorrect because when subtracting integers, you have add the addictive inverse of the others. (keep, change, change) which would lead to the equation of 9 + 8. What Murphy did wrong is subtract 9 and -8 without finding -8 addictive inverse.
Which coordinates represent P1 and P2 respectively in the coordinate plane below .
Answer:
P1 - (4,2) P2 - (-2,1)
Step-by-step explanation:
You write the point as (x,y) so just put the numbers from the graph into their correct positions
Answer:
[tex]p_{1}(4,2)[/tex] and [tex]p_{2} (-2,1)[/tex]
Step-by-step explanation:
Latitude and longitude are broken into degrees, minutes, seconds and directions, starting with latitude. For instance, an area with coordinates marked 41° 56' 54.3732” N, 87° 39' 19.2024” W would be read as 41 degrees, 56 minutes, 54.3732 seconds north; 87 degrees, 39 minutes, 19.2024 seconds west.
hich of the following ratios is not equivalent to 7 : 3? Multiple choice question. A) 14 : 3 B) 14 : 6 C) 21 : 9 D) 28 : 12
Answer:
C
Step-by-step explanation:
because the 21:9 is break to the smallest form which is C
Please help me I need help
Answer: divide 22/2
Step-by-step explanation:
Answer:
Divide 22/2
Step-by-step explanation:
22/2 is 11, a whole number.
Simplifying:
(22/2)*(3/9)*4
11*(3/9)*4
11*(1/3)*4
Solving:
11*(1/3)*4
11*4=44 44/3=14 2/3
(22/2)*(3/9)*4=44/3 or 14 2/3