The value of x is found as 3 using the method of substitution.
What is the method of substitution?The substitution method is a straightforward method for algebraically solving a system of linear equations and determining variable solutions. It entails determining the value of x-variable in aspects of y-variable using the first equation and afterwards substituting or fixing the value of x-variable with in second equation, as the name implies.For the given expression, use substitution method to solve.
2x + y = 7 ........eq 1
y = 2x - 5 ........eq 2
Substitute the value of y from eq 2 in eq 1.
2x + 2x - 5 = 7
Solving;
4x = 7 + 5
4x = 12
x = 3
Thus, the value of x is found as 3.
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1. Write a matrix to represent the system.
2a - 3b = 6
a + b = 2
O [2 -3 6]
[ 1 1 2]
O [2 1 -3]
[1 6 2]
O [a b 6]
[a b 2]
O [2a -3b 6]
[a b 2]
2. Write the system of equations represented by the matrix.
[0 1 2 4]
[-2 3 6 9]
[1 0 1 3]
O x + 2y = 4
-2x - 3y + 69 = 0
x + y = 3
O x + 2y = 4
-2x - 3y + 6 = 9
x + y = 3
O y + 2z = 4
-2x + 3y + 6z = 9
x + z = 3
O x + 2z = 4
-2x - 3y + 6 = 9
x + y = 3
Please help, I'm so confused. Xd Brainliest to whoever is correct!
From the relations between matrices and system of equations, we have that:
1. The matrix is:
[tex]\left[\begin{array}{ccc}2&-3&6\\1&1&2\end{array}\right][/tex]
2. The system is:
y + 2z = 4.-2x + 3y + 6z = 9.x + z = 3.What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the numeric values of each variable, according to the relations built in the problem.
There are multiple ways to represent a system, and one way is using matrices, in which:
The first n - 1 rows represent the coefficients of the input variables.The last row represents the results of the operations.For item 1, the system is:
2a - 3b = 6a + b = 2.Hence the matrix is:
[tex]\left[\begin{array}{ccc}2&-3&6\\1&1&2\end{array}\right][/tex]
In item b, we have the matrix and want to build the system, hence:
y + 2z = 4 (first element of 0, which is the coefficient of x for the first equation).-2x + 3y + 6z = 9.x + z = 3. (second element of 0, which is the coefficient of y for the third equation).More can be learned about a system of equations at https://brainly.com/question/24342899
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18 hours: one day (ratio)
Answer:
It's 3.4
Step-by-step explanation:
get sum of 18 and 24
=42
18/42=3/7
24/42=4/7
Take the numerators which are 3and4
What form is the number 750,000 written in?
A: Expanded
B: Standard
Answer:
A. standard form.
Step-by-step explanation:
Standard form = 750,000
Expanded form = 700,000 + 50,000
1. 2(x-4) + 4 = 16.
Melissa and Kristina are solving the same equation:
The table below shows their FIRST step in solving the
Melissa says:
In Step 1 of solving this problem, I will divide
everything in the equation by 2 to get:
(x-4) +2=8
Kristina says:
In Step 1 of solving this problem, I will multiply 2 by
each term inside the parenthesis to get:
2x 8+4 = 16
1a) Mrs. Chow gives them both full credit for completing the problem correctly. How is this possible?
*We already know they arrive at the same correct answer. How else can you explain why both methods work?
It is possible that Mrs. Chow gives them both full credit for completing the problem correctly because they correctly used relevant properties of equality
How to solve Algebra Word Problems?We are given the algebraic expression as;
2(x - 4) + 4 = 16
Now according to Melissa, her first step is to divide everything by 2 to get; (x - 4) + 2 = 8
Now, what Melissa has done is to use division property of equality to get that solution.
Whereas, Kristina solved the fitrst step by expanding the bracket to get;
2x - 8 + 4 = 16
Kristina used the algebraic property known as distributive property of equality.
Since they both used correct properties of equality, then they are both correct.
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Fifth graders at a school write a paper about a historical person for a contest. There are $5$ classes of $25$ students and $1$ class of $28$ students participating in the contest. Use the expression $5\times25+28$ to find how many students participate in the contest.
A school's fifth graders prepare a paper about a historical figure for a contest. The total number of students who participated in the contest is 153.
Given that,
A school's fifth graders prepare a paper about a historical figure for a contest.
The contest is being competed in by $5 classes of $25 students and $1 classes of $28 students.
We have to calculate the number of students who enter the contest.
We get
=5×25+1×28
Multiply the terms
=125+28
Adding the terms
=153
Therefore, the total number of students who participated in the contest is 153.
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49 Jessica skated 4 laps in 82 seconds. Which of the following is an equivalent rate of skating??A6 laps in 120 secondsB10 laps in 205 secondsC 6 laps in 130 secondsD10 laps in 215 seconds
ANSWER
B. 10 laps in 205 seconds
EXPLANATION
If we write the rate of laps to seconds as a fraction we have:
[tex]\frac{4}{82}=\frac{2}{41}[/tex]I simplified the fraction and got 2/41. An equivalent rate must give the same simplified fraction. For option B:
[tex]\frac{10}{205}=\frac{2}{41}[/tex]We can reduce both rates to the same rate: 2 laps every 41 seconds. Therefore, these two rates are equivalent.
ASAP PLEASE!! The points H, I, J and K all lie on the same line segment, in that order, such that the
ratio of HI: IJ: JK is equal to 1: 3: 1. If HK = 25, find HJ.
The value of HJ in the line segment = 20
How to find the value of HJ?
Points H, I, J, K lie on the same line segment in order.
HI : IJ : JK = 1: 3: 1
HK = 25
Let us consider the ratios,
Let H I = x
Let IJ = 3x
Let JK = x
⇒In the line segment,
HK = HI+ IJ+ JK
25 = x +3x +x
25 = 5x
x = 5
⇒In the line segment,
HJ = HI +IJ
HI = x
IJ = 3x
HJ = HI +IJ
= x + 3x
= 4x
= 4*5
HJ = 20
What is a line segment?
An area of a line that can connect two points is known as a line segment. Any portion of a line with two endpoints is referred to as a line segment. A line segment has a set length as opposed to a line.Both metric measurements, such as milli meters and centimeters, as well as conventional units, such as feet or inches, can be used to measure the length of a line segment.To learn more about line segments, refer:
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1. Evaluate the expression. Give your answer as a mixed number in simplest form.
11/12 + 5/6
Answer: 1 3/4
Step-by-step explanation:
1. find common denominator
11/12+10/12=21/12
2. simplify
21/12=7/4= 1 3/4
a certain ceiling is made up of tiles. Every square meter of ceiling requires 10.75 tiles .fill in the table with the missing values
Answer:
1) 1 m² = 10.75 tiles
2) 10 m² = 107.5 tiles
3) 9.3 m² of tiles = 100 tiles
4) a m² = 10.5a tiles
Step-by-step explanation:
The table is missing and so i have attached it.
From the question, we are told that each square meter of ceiling requires 10.75 tiles. Thus on the first row;
1 m² = 10.75 tiles
The second row of the table shows 10 m² of tiles.
Thus, by proportion, 10 m² of tiles will require; 10 × 10.75 tiles = 107.5 tiles
The third row shows us 100 tiles required.
Since 10.75 tiles is for 1 m² , then by proportion, we can find the square meters of tiling of 100 tiles. Thus;
100 tiles will use; 100 × 1/10.75 = 9.3 m² of tiles
The fourth row shows us square meter of tiles to be a.
Thus by proportion, number of tiles required for this square meter of tile is;
a × 10.75/1 = 10.75a tiles
Divya and Miguel were asked to find an explicit formula for the sequence 80, 40, 20, 10,..... which one of them is right?
The explicit formula for the sequence is aₙ = 80 (0.5)ⁿ⁻¹
Given,
The sequence = 80, 40, 20, 10, ...
We have to find the explicit formula for the above sequence.
Explicit formula for a sequence: aₙ = a₁ (r)ⁿ⁻¹
That is,
a₁ = first term
r = common ratio
Lets check:
The sequence is 80, 40, 20, 10,....
a₁ = 80
a₂ = 40
a₃ = 20
a₄ = 10
Now, lets find the common ratio:
a₂/a₁ = 40/80 = 1/2
a₃/a₂ = 20/40 = 1/2
a₄/a₃ = 10/20 = 1/2
That is, the common ratio, r for the sequence is 1/2 which equals 0.5
Then, the explicit formula for the sequence is aₙ = 80 (0.5)ⁿ⁻¹
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10) Convert 6 inches to centimeters
Which of the following equations represents the parabola with vertex at (3, 2) and directrix y = 4?
a (x − 3)2 = −8(y − 2)
b (x + 3)2 = 8(y + 2)
c (y − 2)2 = −4(x − 3)
d (y + 2)2 = 4(x + 3)
The equation of parabola is (x − 3)² = −8(y − 2).
What is parabola?A parabola is a U-shaped curve that is drawn for a quadratic function, f(x) = ax²+ bx + c. The graph of the parabola is downward (or opens down), when the value of a is less than 0, a < 0. The graph of parabola is upward (or opens up) when the value of a is more than 0, a > 0.
Given:
Vertex = (3, 2)
Directrix, y =4
line of symmetry is the Y value in the vertex = 2
directrix, y= 2 - p
p = -2
and, a= 1/4p = -1/8
and, focus = (3, (2-2)) = (2, 0)
Now, equation of parabola
y= -1/8 (x- 3)² + 2
-8y = (x- 3)² + 2
(x − 3)² = −8(y − 2)
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the graph of linear function f is shown on the grid. what is zero of the function?
The zero of a function is the value of x of the point on which the value of y is equal to zero.
You can observe in the graph the such a point is the point (1,0).
Hence, the zero of the function is x = 0
the sides of a triangle are xcm,x+3cm and 10cm. If x is a whole numberof x, find the highest value of x
Highest possible whole number is 3.
What is properties of triangle?A triangle has three sides, three angles, and three vertices, which are its characteristics. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property. Any two triangle sides can add up to a length that is longer than the third side.
Given Data
Sum of length of any two sides of a triangle is always equal to the third side.
For sides a, b and c
We must have, a + b > c
Sides of triangle are x, x +3 and 10cm
So,
x + x+ 3 > 10
2x > 10 - 3
2x> 7
x > [tex]\frac{7}{2}[/tex]
Possible values of x are 3.5, 3, and so on.
Highest possible whole number is 3.
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Tyler bought 8 chicken wings for $16.00. If Tyler spent $46.00, how many chicken
wings did he buy?
Answer:
Step-by-step explanation:
23. 16 divided by 8 is 2, which means he spent 2 dollars on 1 wing. So 46 divided by 2 is 23.
For 46 dollars, Tyler can buy 23 chicken wings.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given that, Tyler bought 8 chicken wings for $16.00.
To find the number of chicken wings, first find the cost of one chicken wing and to find number of chicken wings divide total cost by cost of one chicken wing.
So, the cost of each chicken wing is 16/8
= $2
So, the cost of each chicken wing is 2 dollars.
Tyler spent $46.00 on chicken wings.
Number of chicken wings = 46/2
= 23
So, the number of chicken wings are 23.
Therefore, Tyler can buy 23 chicken wings for $46.
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Is 141/47 a repeating decimal
the answer is no.
because 47 times 3 gives 141
where 3 is a non-decimal
Answer:
141/47 Is not a repeating decimal.
Step-by-step explanation:
141 ÷ 47 Is not a repeating decimal because 47 × 3 = 141
f(x) = 6x³ - 23x² - 6x + 8 if (x-4)
Answer:
(x - 4) (2x - 1)(3x + 2)
Step-by-step explanation:
Dividing:
x - 4)6x^3 - 23x^2 - 6x + 8 (6x^2 + x- 2 <----Quotient
6x^3 -24x^2
x^2 - 6x
x^2 - 4x
-2x + 8
-2x + 8
6x^2 + x - 2
= 6x^2 - 3x + 4x - 2
= 3x(2x - 1) + 2(2x - 1)
= (3x + 2)(2x - 1)
im so done with math
Please help I know it’s only 10 points but please
Answer:
The average change is -0.7 per hour.
Step-by-step explanation:
-2.8/4
Suppose that prices increase 2.5% each year for 10 years. How much will a jacket that costs 100 today cost in 10 years?
Answer:
$125
Step-by-step explanation:
Find out what the percentage increase is in ten years.
2.5%->change to decimal thingy (divide by 100) 0.025 then multiply it by the total amount of years(10): 0.025(10)= 0.25- 25%
The cost percentage in 10 years is 25%
Next multiply your new percentage by the jacket's original cost: 0.25(100)=25
So $25 is the amount that the jacket has increased over ten years
Add 25 to 100 to fin the cost of the jacket in 10 years.
Kinda a confusing explanation but the answer is right.
Three students were scheduled to give book reports in 1 hour.
After the first report, 2/3 hour remained (HINT: this means the first persons' report was 1/3 of an hour)
The next report took 1/6 hour. What fraction remained?
When we add or subtract fractions, we always have to make sure that all the fractions involved have a common denominator.
Solving the Question
We're given:
After the first report, [tex]\dfrac{2}{3}[/tex] hours remainedThe second report took [tex]\dfrac{1}{6}[/tex] hours remainedTo find the fraction representing the remaining time, subtract [tex]\dfrac{1}{6}[/tex] from [tex]\dfrac{2}{3}[/tex]:
[tex]\dfrac{2}{3}-\dfrac{1}{6}[/tex]
⇒ Make both denominators the same; multiply [tex]\dfrac{2}{3}[/tex] by [tex]\dfrac{2}{2}[/tex] to change its denominator to 6:
[tex]= \dfrac{4}{6}-\dfrac{1}{6}\\\\= \dfrac{3}{6}[/tex]
⇒ Simplify the fraction:
[tex]= \dfrac{1}{2}[/tex]
Therefore, [tex]\dfrac{1}{2}[/tex] the hour remained.
Answer[tex]\dfrac{1}{2}[/tex] the hour remained
a researcher studies a group of 25 preschool children in order to answer questions about the entire population of preschool children. what general categories of statistical techniques will this researcher be using?
The researchers use inferential statistics.
Inferential statistics uses measurement from a sample, comparing groups and making generalizations about the large population. Inferential statistics are based on a test statistic calculated based on a formula. The test statistic along with degrees of freedom to determine the difference between the study population. With inferential statistics, the researcher will draw conclusions from extrapolations.
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In a certain chemical, the ratio of zinc to copper is 4 to 17. A jar of the chemical contains 374 grams of copper. How many
grams of zinc does it contain?
Answer:
88 g
Step-by-step explanation:
zinc : copper
4 : 17
? : 374
374 ÷ 17 = 22
22 × 4 = 88
Sierra hiked to the 5½ mile marker. She then hiked 3
more miles. At noon she hiked back to where she started.
How many miles did Sierra hike in total?
Answer:
17 miles
Step-by-step explanation:
5 1/2 + 3= 8 1/2 x 2 = 17
The coordinates of the point Rare (9, -9) and the coordinates of point S are
(9, 10). What if the distance, in units, between the point R and point S?
Answer:
Formula for length between coordinates is given as √(x1-x2)²+(y1-y2)², which x and y being the coordinates of the points.
Length of RS = √(9-9)²+(-9-10)²
= √0+(-19)²
= √361
= 19 units
Answer:
RS = 19 unitsStep-by-step explanation:
Given pointsR(9, - 9) and S(9, 10)Since both of the points have same x- coordinate of 9, the distance between the points is the absolute value of the difference of y-coordinates:
RS = | - 9 - 10| = | - 19| = 19 unitsMajid can walk at spped of 6km/h. How far can he walk in 30 min.
( Give me steps please )
Answer: 3 km
Step-by-step explanation: (included in picture) the 0.5 represents 30 minutes because 30 minutes is 0.5 of an hour. the x represents how far Majid can walk in 30 minutes
Calculate the mean to the following data set.
7, 13, 6, 2
Answer: 7
Step-by-step explanation: 7 + 13 = 20
20 + 6 = 26
26 + 2 = 28
28/4 = 7
Answer:
Mean = 7
Step-by-step explanation:
[tex]\boxed{\sf Mean=\dfrac{\textsf{sum of all the numbers}}{\textsf{amount of numbers}}}[/tex]
Given data set: 7, 13, 6, 2
Therefore:
[tex]\implies \sf Mean=\dfrac{\textsf{7+13+6+2}}{4}=\dfrac{28}{4}=7[/tex]
Nicholas has nickels, dimes and quarters that total $12.30. The number of dimes is 3 more than twice the number of nickels, and the number of quarters is three times the number of nickles. how many coins of each kind does he have?
Using a system of equations, the amounts of each coin that he has is given as follows:
Nickels: 12.Dimes: 27.Quarters: 36.System of equationsThe variables to the system of equations are given as follows:
Variable x: number of nickels.Variable y: number of dimes.Variable z: number of quarters.Nicholas has nickels, dimes and quarters that total $12.30, hence, considering the value of each coin:
0.05x + 0.1y + 0.25z = 12.30.
The number of dimes is 3 more than twice the number of nickels, hence:
y = 2x + 3.
The number of quarters is three times the number of nickles, hence:
z = 3x.
Then we can solve for x as follows:
0.05x + 0.1y + 0.25z = 12.30.
0.05x + 0.1(2x + 3) + 0.25(3x) = 12.30.
x = 12. (nickels)
Then the other amounts are as follows:
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In a recent survey, 2/3 of the lions said that
they were happy to serve as King of the
Forest, while another 1/9 thought it was way
too much responsibility. If 14 lions gave one of
these two answers, how many lions were
surveyed in total? Make sure your answer is
fully reduced.
The total number of lions that were surveyed is 18.
How to calculate the value?It should be noted that based on the information given in the survey, 2/3 of the lions said that they were happy to serve as King of the forest, while another 1/9 thought it was way too much responsibility and 14 lions gave one of these two answers.
The total lions that were surveyed will be illustrated thus:
Let the total number of lions be x.
Therefore, (2/3 + 1/9)x = 14
= 7x/9 = 14
Cross multiply
7x = 9 × 14
x = (9 × 14) / 7
x = 9 × 2
x = 18
Therefore, the total number of lions is 18.
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Help please. ASAPPP!
Answer:
Step-by-step explanation:
f(15) = F(75-2times 5)
Answer: f(15) = F(75-2times 5)
Step-by-step explanation: f(15) = F(75-2times 5)