Substitution method of solving a system of equations replaces the variable with a value while elimination method of solving a system of equations removes the variable from the equations.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
example:
Given two equations: x + 3y = 7 and 2x - 4y = 24, find the solution.
Using substitution method, express one equation to an equation of one of its variables(in terms of the other variable).
x + 3y = 7 ⇒ x = 7 - 3y
Substitute it to the other equation and solve for y.
2x - 4y = 24
2(7 - 3y) - 4y = 24
14 - 6y - 4y = 24
-10y = 10
y = -1
Substitute the value of y in any of the equations and solve for x.
x = 7 - 3y
x = 7 - 3(-1)
x = 7 + 3
x = 10
Hence, the solution is (10 , -1).
Using elimination method, multiply the first equation by 2 so that if we add or subtract it to the second equation, a variable will be removed.
x + 3y = 7 ⇒ 2x + 6y = 14
Subtracting equation 2 from equation 1,
2x + 6y = 14
2x - 4y = 24
0x + 10y = -10
y = -1
Substitute the value of y in any of the equations and solve for x.
x + 3y = 7
x + 3(-1) = 7
x = 7 + 3
x = 10
Hence, the solution is (10 , -1).
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O Rachel was checking the weight of a gold nugget and a piece of fool's gold. Together
they weighed 120.5 grams. If the fool's gold was 23.90 grams, how much did the gold
nugget weigh?
Answer:
96.6
Step-by-step explanation:
120.5 subtracted by 23.90 give you how much the gold nugget weight.
Find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of miles per hour. speed (miles per hour) 4245 4649 5053 5457 5861 frequency
47.4 is the mean of the data summarized in the given frequency distribution.
What is a frequency distribution?
The number of times a value appears in a dataset is its frequency. The pattern of frequencies for a variable is known as a frequency distribution. The frequency with which each potential value of a variable appears in a dataset.speed m f m*f
42-45 43.5 22 957
46-49 47.5 14 665
50-53 51.5 7 360.5
54-57 55.5 4 222
58-61 59.5 2 119
Total 49 2323.5
mean = 2323.5/49 = 47.4
The computed mean is not close to the actual mean because the difference between the means is more than 5%.
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21. x ≥-1
y> -2 on a graph
Answer:
perhaps it is 7.09809809876 or it might be 5.437437437, a recursive number.
Step-by-step explanation:
i might be
Font
Paragraph
F
Unit Test, Part 2: Working with Data
Answer the questions. When you have finished, submit this assignment to your teacher by the due date for full
credit
Fy
Total score: of 20 points
Answer:
Styles
(
(Score for Question 1: of 9 points)
1. The data set shows the fuel efficiencies, in miles per gallon, of the vehicles featured in a car-buying guide.
26 31 40 28 19 23 35 38 43 46 28 30
(a) What is the five-number summary of the data set?
(b) What is the range of the data set? Show your work
(c) What is the interquartile range (IQR) of the data set? Show your work.
The data set's interquartile range (IQR) is 12 and the data set's range is expressed as a five-number summary at 46.
Interquartile range: what is it?The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics. The middle 50%, fourth spread, or H-spread are further names for the IQR.The discrepancy between a data set's 75th and 25th percentiles.
ACCORDING TO GIVEN STATEMENT;
Firstly, arrange the data.
19 23 26 28 28 30 31 35 38 40 43 46
a) 5 number summary
-min value = 19
- Q1= (26+28/2) = 27
- Q2/ Median = (30+31/2)= 30.5
- Q3= (38+40/2)= 39
- Max value= 46
b) range= max value-min value
∴46-19= 21
c)interquartile range = Q3-Q1
= 39-27
=12
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Need help finding x please
Answer:
[tex]x = \frac{64}{3} [/tex]
Step-by-step explanation:
Based on the given conditions:
[tex] \frac{x}{32} = \frac{12}{12 + 6} ⟹ \frac{x}{32} = \frac{12}{18} [/tex]
Cross multiply the above
[tex]18x = 384 [/tex]
Divide both sides by 18 to find the value of x
[tex]x = \frac{384}{18} [/tex]
Therefore:
[tex]x = \frac{64}{3} [/tex]
create two different infinite geometric series that each have a sum of 8
Two different infinite geometric series that each have a sum of 8 are 32 + 32(3) +32(3)² + 32(3)³ + ................. and 24 + 24(2) + 24(2)²+ 24(3)³+ .............
What is an infinite geometric series?An Infinite geometric series is the sum of the infinite terms and these terms have constant ratio between successive terms.
Let us take first term of the infinite series be a and r be the constant ratio between successive terms. Then formula for such geometric series be a+ar+ar²+ar³+.............
And sum of such series is ,S =a/(1+r)
We have to find two infinite geometric series with sum S = 8
Let us take a=24 and r=2
Then sum, S = [tex]\frac{24}{2+1} =\frac{24}{3}=8[/tex]
Therefore such series will be:
24 + 24(2) + 24(2)²+ 24(3)³+ .............
Another possibility for sum 8 will be with a =32 and r=3
Then the sum, S = [tex]\frac{32}{3+1} =\frac{32}{4}=8[/tex]
Therefore another such infinite geometric series will be
32 + 32(3) +32(3)² + 32(3)³ + .................
Thus, two different infinite geometric series that each have a sum of 8 are 24 + 24(2) + 24(2)²+ 24(3)³+ ............. and
32 + 32(3) +32(3)² + 32(3)³ + .................
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Smiling is a facial expression of happiness or contentment. In math, what is the expression that represents the quotient of 3 and 3 less than a number?
A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.
The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).
What is an expression?A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms. In order to help establish the order of operations and other elements of logical syntax, mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. An expression can be used in algebra to represent a value, and that value may rely on the values given to the variables that appear in the expression.Depending on the semantics associated with the expression's symbols, this value is determined.Let, x be a number
So the expression is, 3/(x - 3)
A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific norms.
The expression that represents the quotient of 3 and 3 less than a number is 3/(x - 3).
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Solve each equation. 3(2 z+1)=35
The solution of the given linear equation in one variable 3(2z +1) = 35.
According to the given question.
We have a linear equation in one variable 3(2z + 1) = 35.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Therefore, the solution of the given linear equation in one variable is given by
3(2z + 1) = 35
⇒ 6z + 3 = 35 (by distributive rule)
⇒ 6z = 35 - 3 (subtracting 3 from both the sides)
⇒ 6z = 32
⇒ z = 32/6 (dividing both the sides by 6)
⇒ z = 16/3
Hence, the solution of the given linear equation in one variable 3(2z +1) = 35.
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if the coffee is hot then you shouldn't drink it
Answer: Yes only if is is so hot it will burn yout tung but you dont want cold coffe so
Step-by-step explanation:
Answer:
Step-by-step explanation:
I agree with the first answer but maybe people like cold brews, i know i do. also people on here be asking the craziest questions bro like i just answered "what are your thoughts about brainly being a dating app" i was like what ;-;
What set of reflections and rotations would carry rectangle ABCD onto itself?
Reflect over the y-axis, reflect over the x-axis, rotate 180°
Rotate 180°, reflect over the x-axis, reflect over the line y = x
Reflect over the x-axis, rotate 180°, reflect over the x-axis
Rotate 180°, reflect over the y-axis, reflect over the line y = x
Answer:
2 line is the answer to the questions
PART 2!!
Topic: Addition and Subtraction of polynomials
Directions: Simplify each rational expressions
Step-by-step explanation:
4.
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{a - b}{a + b} [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{(a - b)(a - b)}{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab}{ {a}^{2} - {b}^{2} } - \frac{ {a}^{2} - 2ab + {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - ( {a}^{2} - 2ab + {b}^{2} ) }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{5ab - {a}^{2} + 2ab - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] = \frac{7ab - {a}^{2} - {b}^{2} }{ {a}^{2} - {b}^{2} } [/tex]
[tex] \: [/tex]
5.
[tex] = \frac{5}{n + 5} + \frac{4n}{2n + 6} [/tex]
[tex] = \frac{5}{n + 5} + \frac{4n}{2(n + 3)} [/tex]
[tex] = \frac{5}{n + 5} + \frac{2n}{n + 3} [/tex]
[tex] = \frac{5(n + 3) + 2(n + 5)}{ {n}^{2} + 8n + 15 } [/tex]
[tex] = \frac{5n + 15 + 2n + 10}{ {n}^{2} + 8n + 15} [/tex]
[tex] = \frac{7n + 25}{ {n}^{2} + 8n + 15} [/tex]
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Let's solve these problems ~
Problem 1 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ {a}^{2} - {b}^{2} } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab}{ (a + b)(a - b) } - \dfrac{a - b}{a + b} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b)(a - b)}{ (a + b)(a - b) } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a - b) {}^{2} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - (a {}^{2} - 2ab + {b}^{2} ) {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5ab - a {}^{2} + 2ab - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{7ab - a {}^{2} - {b}^{2} {}^{} }{ {a}^{2} - b {}^{2} } [/tex]
Problem 2 ~[tex]\qquad \sf \dashrightarrow \: \dfrac{5}{n + 5} + \dfrac{4n}{2n + 6} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{5(2n + 6) + 4n(n + 5)}{(2n + 6)(n + 5)} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{10n +30 + 4n {}^{2} + 20n}{2n {}^{2} + 10n + 6n +30} [/tex]
[tex]\qquad \sf \dashrightarrow \: \dfrac{4n {}^{2} + 30n + 30}{2n {}^{2} + 16n + 30} [/tex]
[ taking 2 common out ]
[tex]{ \qquad \sf \dashrightarrow \: \dfrac{2n {}^{2} + 15n + 15}{n {}^{2} + 8n + 15}} [/tex]
if t+t = 0
what is the answer
Answer:
t = 0
Step-by-step explanation:
t + t = 0 , that is
2t = 0 ( isolate t by dividing both sides by 2 )
t = [tex]\frac{0}{2}[/tex] = 0
Answer:
t=0
Step-by-step explanation:
t+t is 0 and since were not given any numbers for t its automatically 0
Identify a pattern and find the next three numbers in the pattern. 5,3,1,-1, . . .
The next three numbers of the sequence are -3, -5, -7,........
What is an arithmetic progression?An arithmetic progression, or AP, is a series in which the next term is derived from the previous one. by modifying the previous word with a constant d known as the common difference. The arithmetic progression is if the first term of the series is a, a + d, a + 2d, a + 3d, ...
The given pattern forms an Arithmetic progression (A.P.)
The sequence is - 5 , 3, 1, -1, -3, -5, -7,........
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Emma and Ben each have some money.
Hafid has no money.
Emma gives £8 to Hafid.
Ben gives £3 to Hafid.
Now they all have the same amount of money.
How much did Emma have to begin with
Emma initially had £19 as the amount of money she initially had at the beginning
How to calculate the amount of money that Emma has ?Emma gives £8 to Hafid
Ben gives £3 to Hafid
The total amount of money that Hafid can be calculated by adding Emma and Ben's money together.
= 3 + 8
= 11
They all have the same amount of money.
Emma initial amount can be calculated by adding 11 and the amount of money Emma gives to Hafid
= 11+8
= 19
Hence Emma initially had £19
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90 points! Can someone please explain what ie substitution in the work? I dont get it. My teacher is asking me to not substitute but I dont know what that is. I would really appreciate an answer!
Answer:
x=5/11 | x=6, A
Step-by-step explanation:
For the first question- 3(4-2x)=-x+1
Use algebra to solve
1. 3(4-2x)=-x+1 Distribute
2. 12-6x=-x+1 Seperate like terms
3. 12-1=6x-x Combine
4. 11=5x
5. x=5/11
For the second babysitting question, since we want to multiply the combined hours worked by 9 (the amount of money per hour, the equation should be A. Use algebra to find the hours.
1. 9(5+x)=99 Distribute
2. 45+9x=99
3. 9x=54
4. x=54/9
5. x=6
I NEED HELP THIS IS DUE TODAY
Answer:
B is the correct answer:)) explanation up top
There are n socks, 3 of which are red, in a drawer. what is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12 ?
n=4 is the value of if, when 2 of the socks are chosen randomly, the probability that they are both r e d i s 12.
What is the probability in simple terms?
Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.Number of socks = n .
Number of red socks = 3 .
Given
3C2nC2=12
⇒nC2=3×2=6
⇒n=4
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A store pays $10 for a blanket. The markup is 35%. What do they sell it for?
Alma is making bionicos at a food stand. She has 15 strawberries and 30 grapes. She plans to use all the strawberries and grapes, as well as some other fruits. Alma wants to know the greatest number of identical bionicos she can make.
The greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.
It is required to find the solution.
What is greatest common factor (GCF)?The greatest common factor (GCF) of a set of numbers is the largest factor that all the numbers share. The greatest common divisor of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers.
Given:
In total, there are 15 strawberries and 30 grapes.
To find the greatest number of identical arrangements, first we need to find the greatest common factor of 15 and 30.
According to given question we have
GCF of (15,30) = 15
Therefore, the greatest number of identical arrangements is 1 arrangements of 15 strawberries and 2 grapes.
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ALGEBRA The Ross Family drove 300 miles to visit their grandparents. Mrs. Ross drove 70 miles per hour for 65% of the trip and 35 miles per hour or less for 20% of the trip that was left. Assuming that Mrs. Ross never went over 70 miles per hour, how many miles did she travel at a speed between 35 and 70 miles per hour?
A 195
B 84
C 21
D 18
She has driven 84 miles at speeds ranging from 35 to 70 miles per hour.
The correct option is B.
What exactly is algebra in mathematics?Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we use variables such as x, y, and z in addition to numbers. In algebra, signs are employed.
According to the given information:She drove 70 miles per hour for 65% of the journey hour.
So she covered = ((65)*100)*300
= 195 miles.
The remaining distance is 300 – 195 = 105 miles.
She drove just under 35 miles per hour for the remaining 20% of the route.
So she covered. = ((20)/100)*105
or 21 miles
So, totally she covered 195 +
21 or 216 miles at 70 miles per hour maybe less than 30 miles per hour However, since the trip is 300 miles long, this same remaining distance becomes 300 - 216 or 84 miles.
She has driven 84 miles at speeds ranging from 35 to 70 miles per hour.
The correct option is B.
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Suppose you toss a coin four times. What is the probability of getting four tails?
Answer:
1/16
Step-by-step explanation:
Coin toss
probability 1/2×1/2×1/2×1/2 = 1/16
You are designing a house with three 3-foot windows across the back. There are 4 feet
between the edge of the house and the end windows. The total width of the house is 33
feet. How far apart are the windows?
The windows of house are 8 feet apart distance.
As we are provided with the the total width of house is 33 feet and 4 feet distance between the edge of the house and the end windows
So the space available for the windows is total width of the house minus the distance between the edge of the house and the windows from both the sides = 33 - 2(4) = 33-8 = 25 feet
The length of the windows to be inserted is the product of number of windows and their side = 3 × 3 = 9 feet
The total distance between the windows can be find out by reducing the distance covered by windows from the area available for windows = 25feet - 9 feet = 16 feet
There are three windows, so there will be only 2 gaps whose length is 16 feet / 2 = 8 feets
Hence, the windows of the house are 8 feet apart
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The expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped. What is the distance the object falls during each time?
0.25 second
If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet
Given,
The expression of distance in feet that an object falls = [tex]16t^{2}[/tex]
Where t is the time seconds
Then the time = 0.25 second
Substitute the values in the expression = [tex]16(0.25)^{2}[/tex]
=1 feet
Hence, If the expression 16t² models the distance in feet that an object falls during the first t seconds after being dropped then the distance the object falls during 0.25 second time is 1 feet
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Evaluate the expression for the given value of the variable 4|3x-1| - |9x+6| ; x=-5
Answer: 5
Step-by-step explanation:
4|3x-1| - |9x+6| ; x=-5
Insert 5 into the x's
4|3(5)-1| - |9(5)+6|
Multiply the 5's
4|(15)-1| - |(45)+6|
Now add/subtract within the absolute values
4|14| - |51|
Get rid of the absolute vaules
4(14) - 51
Multiply 4(14) = 56
56 - 51 = 5
Given:
A={1,2,3,4,5,6,7,8,9,10}
B={2,4,6,8,10}
C={1,3,5,7,9}
1.A ꓵ C=
2.B ꓵ C=
3.A ꓵ B=
4.A U B=
5.B U C=
6.A U C=
7.A - C=
8.B - C=
9.A - B=
10.C - A=
Answer:
The answers are as follows:
A ꓵ C = {1, 3, 5, 7, 9}B ꓵ C = 0A ꓵ B = {2, 4, 6, 8, 10}A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}B U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A U C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}A - C = {2, 4, 6, 8, 10}B - C = {2, 4, 6, 8, 10}A - B = {1, 3, 5, 7, 9}C - A = 0I hope they helpKendra and her horse completed the barrel racing in 15.839 seconds. What is this number rounded to the nearest tenth?
Answer:
15.8
Step-by-step explanation:
To round to nearest tenth we only go so far as the first decimal place. If the second decimal digit is less than 5 we leave that number as it is otherwise we increase it by 1
In 15.839, the second decimal digit is 3 so we get 15.8
(If it had been 15.864 then it would be 15.9)
If the distance between Earth and the Sun is actually 150,000,000 kilometers, how far apart are Earth and the Sun when using the 1:93,000,000 scale model?
The scaled distance using the given scale factor is; 1.613 units
How to use the scale model?
We are given;
Distance between Earth and the sun = 150, 000, 000 km
Now, we are given that the scale model that represents Distance between Earth and the sun is 1:93,000,000.
This means that 1 unit represents 93000000 kilometers. Thus;
The scaled distance using the given scale factor is;
150,000,000/93,000,000 = 1.613 units
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is 8.141141114 a ratinial number
Based on the number given of 8.141141114, it is NOT a rational number.
What is a rational number?A rational number refers to one that does not extend to infinity after the decimal. Some rational numbers will extend to infinity but they will have repeating numbers such as 0.3333333333.
The number 8.141141114, is not a rational number because it extends into infinity and the numbers after the decimal point are nonrepeating.
In conclusion, 8.141141114 is not a rational number.
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Factor each expression completely.
3 x²-75
The area of Miki's room is x²+8 x+12 square feet. A gallon of paint will cover an area of x²+6 x+8 square feet. Which expression gives the number of gallons of paint that Miki will need to buy to paint her room?
F. x+6 / x+4
G. x-4 / x-6
H. x+4 / x+6
J. x-4 / x+6
The expression that gives the number of gallons of paint that Miki will need to buy to paint her room is F. (x + 6) / (x + 4)
Expression:
Expression are the mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given,
The area of Miki's room is x²+8 x+12 square feet. A gallon of paint will cover an area of x²+6 x+8 square feet.
Here we need to find the expression that gives the number of gallons of paint that Miki will need to buy to paint her room .
The number of gallons of paint required to paint the room is calculated by dividing the expression.
Then we get,
=> [tex]\frac{x^{2} +8 x+12}{x^2+6x+8}[/tex]
Factor the numerator and the denominator to simplify the fraction.
So, the factors of
=> x² + 8x + 12 = (x+6) (x+2)
and the factors of
=> x² + 6x + 8 = (x+4) (x+2)
When we apply the factors instead of the given expression,
Then we get,
=> [tex]\frac{(x+6)(x+2)}{(x+4)(x+2)}[/tex]
After the simplification we get,
=> (x +6) / (x + 4)
So, the option is F. (x+6) / (x+4) is the correct expression that gives the number of gallons of paint that Miki will need to buy to paint her room .
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