The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
How to resolve a system of linear equations
In this problem we find a system of three linear equations with three variables, which can be resolved by several methods. In this case, we shall use the method of substitution. First, clear the variable x in the third equation:
x = 4 - 3 · y
Second, substitute x in the first two equations:
3 · (4 - 3 · y) + 2 · y - z = 8
12 - 9 · y + 2 · y - z = 8
- 7 · y - z = - 4
2 · (4 - 3 · y) + 2 · z = - 4
8 - 6 · y + 2 · z = - 4
- 6 · y + 2 · z = - 12
Third, clear z in the first equation derived in the previous step:
z = 4 - 7 · y
Fourth, substitute z in the second equation derived in the second step:
- 6 · y + 2 · (4 - 7 · y) = - 12
- 6 · y + 8 - 14 · y = - 12
- 20 · y = - 20
y = 1
Fifth, calculate y and x:
z = 4 - 7 · 1
z = - 3
x = 4 - 3 · 1
x = 1
The solution of the system of linear equations is (x, y, z) = (1, 1, - 3).
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Jane is 3 years older than Mary. Mary is twice as old as Kay. If Kay is x years how old is jane
Jane is 2x+3 years old. (answer)
In this case, we can use Kay as the base/foundation in this problem. Kay is x years old. Mary is twice as old as Kay, making Mary 2 times x or 2x. We are solving for Jane. Jane is 3 years older than Mary, who we know is 2x. We can add on 3 years making the final expression for Jane's age: 2x+3. Since we do not know Kay's age, or x, we cannot solve this problem any further.
An architectural company is trying to test the effectiveness of its promotional activity by looking at how many designs for
new buildings it sells each year.
Year Sales
2012 23
2013 18
The company assumes its promotional activity is less effective, which is why sales decreased. However, there could be many
confounding factors. Which of the following is not a possible confounding factor?
The factor that is not a possible confounding factor is B. the expected sales for the year 2014.
What is a confounding factor?A confounding factor is a third variable that influences or explains both the independent and dependent variables.
The independent variable here is the year while sales are the dependent variable.
However, confounding factors could include the number of new buildings constructed in 2013, which was not factored in by the architectural company and the state of the economy in 2013.
Thus, the expected sales for the year 2014 cannot be a confounding variable for the decreased sales in 2013 because it cannot explain the 2013 performance.
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Question Completion:A. the number of new buildings constructed
B. the expected sales for the year 2014
C the state of the economy
PLEASE HELP I WILL GIVE BRAINLIST Graph the line with slope 1/3 passing through the point (2, -3)
Answer:
steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts steadfast hearts
3 meters of cloth is the ratio of 3:7
When given 3 meters of cloth and it is to be divided in a ratio of 3:7 then one part will have 0.9 meters and the other will have 2.1 meters.
How to divide cloth by ratio?The first thing to do is to find the denominator of the ratio by summing the two numbers in the ratio:
= 3 + 7
= 10
The first part of the cloth would be:
= 3 / 10 x 3 meters
= 0.3 x 3 meters
= 0.9 meters
The second part of the cloth would be:
= 7 / 10 x 3 meters
= 0.7 x 3
= 2.1 meters
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Alison is training for a marathon, Last week, she ran 26 miles in 208 minutes, If she runs at that speed a, How long would it take her to run 15 miles?b. How far could she run in 20 minutes?c. How fast is she running in miles per minute? In miles per hour?
Answer:
Answers below
Step-by-step explanation:
To find per 20 miles
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 40 (to get miles per 20 min)
= 20 miles / 160 minutes
_____________________________________________
To find per 15 miles
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 30 (to get miles per 15 minutes)
= 15 miles / 120 minutes
_____________________________________________
To find miles per minute
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 8 (to get miles per minute)
= 0.125 miles / 1 minute
_____________________________________________
To find miles per hour
= 26miles/ 208minutes / 26 (to simplify)
= 1mile / 8minutes / 2 (to simplify)
= 1/2mile / 4 minutes x 15 (to get miles per hour)
= 7.5 miles / 60 minutes
based on the equation 5×x+860=2×x+380, you can say
The value of x is -160.
An equation in which the power of any variable is not more than one is called a linear equation.
Here, we are given a linear equation as follows-
5 × x + 860 = 2 × x + 380
⇒ 5x + 860 = 2x + 380
Let us solve the given equation-
Subtracting 2x from both sides, we get
5x - 2x + 860 = 2x - 2x + 380
3x + 860 = 380
Subtracting 860 from both sides-
3x + 860 - 860 = 380 - 860
3x = -480
dividing both sides by 3,
3x/3 = -480/3
x = -160
Thus, the value of x comes out to be -160.
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An online poll of 6,000 residents of Washington, DC showed that 79% agreed with the statement "Employers should be required to pay men and women the same salary for the same job." An online poll of 4,800 residents of Atlanta revealed that 74% agreed with the same statement.
A button hyperlink to the SALT program that reads: Use SALT
(b)
How many successes were there in the Washington sample?
How many failures were there in the Washington sample?
(c)
Calculate a 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement (DC − Atlanta). (Use a table or technology. Round your answers to three decimal places.)
Step-by-step explanation:
Results of the Assembly elections in five States are indeed a shot in the arm for the Bharatiya Janata Party (BJP), which won in all four States where it was in power. The Hindu editorial captures the broad trends that emerge out of these results. Prime Minister Narendra Modi has said these results have sealed the outcome of the 2024 Lok Sabha elections too in the BJP’s favour. He said people have rejected caste and dynastic politics.
b. The number of successes in the Washington sample were 4740 .
The number of failures in the Washington sample is 1,260
c. the 95% confidence interval for the true difference in population proportions between the people of Washington, DC, and the people of Atlanta who agree with the statement "Employers should be required to pay men and women the same salary for the same job" is 0.018 to 0.068.
How do we calculate?(b) Number of successes and failures in the Washington sample:
Total number of respondents in the Washington sample: 6,000
Percentage who agreed with the statement: 79%
Number of successes = 79% of 6,000
= 0.79 * 6,000
= 4,740
Number of failures = Total - Number of successes
= 6,000 - 4,740
= 1,260
(c)
confidence interval = (p1 - p2) ± Z * √((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2))
p1 = Proportion of successes in the Washington sample
p2 = Proportion of successes in the Atlanta sample
n1 = Size of the Washington sample
n2 = Size of the Atlanta sample
Z = Z-score for the desired confidence level = 1.96
confidence interval = (0.79 - 0.74) ± 1.96 * √((0.79 * (1 - 0.79) / 6000) + (0.74 * (1 - 0.74) / 4800))
confidence interval = 0.05 ± 1.96 * √((0.79 * 0.21 / 6000) + (0.74 * 0.26 / 4800))
confidence interval = 0.05 ± 1.96 * √(0.00013815 + 0.0001244583)
confidence interval = 0.05 ± 1.96 * √(0.0002626083)
Lower bound of the confidence interval (DC - Atlanta)
= 0.05 - 0.0317226549
= 0.018
Upper bound of the confidence interval (DC - Atlanta)
= 0.05 + 0.0317226549
= 0.068
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You measure a foam roller in the shape of a cylinder. The foam roller has a diameter of 5.9375 inches and a height of 53.5 inches. About how many cubic inches of foam were used to make the roller?
Answer:
Volume V ≈ 1481.3269 cubic inches
Step-by-step explanation:
Volume V of a cylinder is given by the formula
V = πr²h where r = radius of the base of the cylinder and h the height
Here we are given the diameter, d = 5.9375 inches
Radius r = d/2 = 5.9375/2 = 2.96875 in
Height h = 53.5 in
V = π x 2.9685² x 53.5 ≈ 1481.3269 cubic inches
Answer V ≈ 1481.3269 cubic inches
What are all the solutions to the equation 10x4 + 30x3 + 35x2 = 0? 0, StartFraction 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, StartFraction negative 3 + i StartRoot 5 EndRoot Over 2 EndFraction, StartFraction negative 3 minus i StartRoot 5 EndRoot Over 2 EndFraction. 0, 6 + 2 i StartRoot 5 EndRoot, 6 minus 2 i StartRoot 5 EndRoot. 0, negative 6 + 2 i StartRoot 5 EndRoot, negative 6 minus 2 i StartRoot 5 EndRoot.
The solutions to the equation 10x⁴ + 30x³ + 35x² as required in the task content are; 0, (-3 + i√5)/2, and (-3 - i√5)/2.
What are all the solutions to the equation 10x⁴ + 30x³ + 35x² = 0 as given in the task content?It follows from the task content that the given equation is; 10x⁴ + 30x³ + 35x² = 0.
Hence, to find all the solutions of the equation, one must factorise the expression on the left hand side so as to obtain the factors as follows;
10x² (x² + 3x +3.5) = 0
Hence, we have;
10x² = 0; x = 0 OR
x² + 3x +3.5 = 0.
Hence, it follows from the quadratic formula that the roots/zeroes of x in the equation above can be evaluated as follows;
x = {-b±√(b²-4ac)}/2a
hence, by comparison, we have;
x = {-3±√(9-14)}/2
x = (-3 ± √-5)/2
x = (-3 ± i√5)/2
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6x + 4y = 36 when x
= 3 and y = 4 explain the solution satisfies the open sentence
Answer:
Undefined
Step-by-step explanation:
Plugging in 3 for x and 4 for y we get:
6(3) + 4(4) = 36
multiplying we get
18 + 16 = 36
34 = 36
which is not true.
if this was helpful pls give me brainliest <3
'DesTunes is a new music streaming service.
Write an equation to represent each scenario, where x represents the number of months and y represents the total charge.
Scenario 1: DesTunes charges adults $15 per month.
The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represents the number of months and y represents the total charge.
Scenario 1: DesTunes charges adults $15 per month.
Hence:
y = 15x
Scenario 2: DesTunes charges students a $20 sign-up fee and $5 per month, hence;
y = 5x + 20
The equation that represent scenario 1 is y = 15x while the equation that represent scenario 2 is y = 5x + 20
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38 Points pls help Evaluate the expression (2 + 2) (3) × 5 - 3.
Answer:
4/9
Step-by-step explanation:
Find the quotient.
h6 ÷ h
Answer:
6
Step-by-step explanation:
Possibly 6 but if not let me know
Answer:
6
Step-by-step explanation:
the h's cancel out
Need help asap math !
Answer:
7/10 = 0.7 = 70%
25/100 = 0.25 = 25%
56/100 = 0.56 = 56%
Step-by-step explanation:
Factor as the product of two binomials. x 2 + 3 x − 4
Answer:
[tex](x-1)(x+4)[/tex]
Step-by-step explanation:
Given:
[tex]x^2+3x-4[/tex]
The best way to write a polynomial with three terms as a product of binomials is to FACTOR!
The middle number is 3 and the last number is -4.
Factoring means we want something like
[tex](x+?)(x+?)[/tex]
We need two numbers that...
ADD together to get 3 and
MULTIPLY together to get -4
Test the numbers -1 and 4:
[tex]-1+4=3\\(-1)4=-4[/tex]
These are the right numbers! Now, I can write them as factored binomials!
[tex](x-1)(x+4)[/tex]
Find the area of the triangle
3 m
8 m
Answer:
3×8 =24
24÷2=12
Area of triangle=12m²
Step-by-step explanation:
3×8 =24
24÷2=12
3x + 1 > 2x - 3 > x - 13
Answer:
x> - 4
Step-by-step explanation:
In order to solve these simultaneous inequalities, we need to write them as two separate inequalities, and find the values of x that satisfy both of them.
China generated 237.188 billion kilowatt-hours (kWh) of wind energy in 2018. The population in China in 2018 was 1.379 billion. What was the wind energy generated per capita? Give your answer to the nearest hundredth.
Answer:
172 kilowatts.
Step-by-step explanation:
Energy : 237.188 billion = 237,188,000,000 = 2.37188 × 10¹¹
People : 1.379 billion = 1,379,000,000 = 1.379 × 10⁹
Divide both values : 2.37188 ÷ 1.379 = 1.72; 10¹¹ ÷ 10⁹ = 10² ⇒ 1.72 × 10² or 172 kilowatts.
Need help with this problem
Answer:
I could be wrong, but I think you got right in the beginning 107°, but go with your gut feeling. Wish you the very best <3
Answer: x=73 degrees, z=73 degrees, y=107 degrees
Step-by-step explanation:
y=107 degrees because y and 107 degrees are congruent angles
z=x because z and x are congruent angles
x+y=180 ==> x and y are supplementary angles that are placed on a straight line(the straight line is 180 degrees and is called a straight angle.)
x+107=180
x=73 degrees
z=x
z=73 degrees
Carlos is paid $17.90 per hour regularly. If he worked 45 hours last week, what was his gross pay? Carlos is paid at time-and-a-half for overtime.
Answer:
$ 850.25
Step-by-step explanation:
I will assume anything over 40 hours is 'overtime'
total pay will be
regular pay + overtime pay
17.90 * 40 hr + (17.90 * 1.5)(5hr) = $ 850.25
I just need the answer for C. Please answer quick this is due tmr morning!! worth 20 points and brainliest
Answer:
The answer is 7 for C.
Step-by-step explanation:
7+7=14 and 7x7=49
The diamond just asks for numbers that make up a pattern for the two given numbers.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Write the least common multiple of 7 and 14.
Answer:
14
Step-by-step explanation:
To work out the lowest common multiple, we first:
List multiples of both numbersFind the first similarity7, 14, 21, 28...
14, 28...
The common multiples of 7 and 14 are 14, 28 etc, but the LEAST (or lowest) common multiple is 14.
Hope this helps.
How much it’s 27+ 0.185
Answer: 27.185
Step-by-step explanation:
Hi there!
If you just want to add 27+0.185, the answer is 27.185.
You just have to add 27+0.185 (what I think of for this question is just adding the 27 to it).
Hope this helps! Have a great day!
Diego made the shape on the left, and Elena made the shape on the right. Each shape uses 5 circles.
Answer:
Options 2-5
Step-by-step explanation:
1. False, since the designs aren't identical.
2. True, both circles have a radius of 1.
3. True, you can translate the circles in Diego's design up to that they are all tangent to each other to make Elena's design.
4. True, both circles have diameter 10.
5. True, simlar logic to 2 and 4
Hall dimensions 200m by 85m. Diagram office wall scale 1:40. What are the dimensions of floor space in cm
The dimensions of floor is 500 cm by 212.5 cm
HOW TO FIND DIMENSION OF HALL ?Multiply the width and length of each rectangle to find its area. The areas of each rectangle are then added up to determine the total area. In the event that your room is L-shaped, for instance, this can be split into two rectangles. Additionally, this method still works in a complicated room.
CALCULATION500 cm by 212.5 cm
Given :
The main arena hall has dimensions 200 m by 85 m.
On a large diagram on the office wall the scale is 1:40.
Length of arena hall = 200 m
Scale is 1:40
So, the length of the floor =
Since 1 m = 100 cm
So, 5 m = 100*5 = 500 cm
Width of arena hall = 85 m
So, width of floor =[tex]\frac{85 * 1}{40}[/tex] = 2.125m
Now 1 m = 100 cm
So, 2.125 m = 212.5 cm
Thus the dimensions of floor is 500 cm by 212.5 cm
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Gabriel is deciding between 2 different movie streaming sites to subscribe to. Plan 1 costs $22 per month plus $1 per movie watched. Plan 2 cost $14 per month plus $3 per movie watched. Create a system of equations to represent this situation. Use the graph below and explain how many movies x would cause the 2 plans would have an equal monthly cost
Using linear functions, it is found that 4 movies would cause the two plans to have an equal monthly cost.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.For the functions in this problem, we have that:
The fixed cost is the intercept.The cost per movie is the slope.Hence the cost functions are given as follows:
C1(x) = 22 + x.C2(x) = 14 + 3x.The costs will be the same when:
C1(x) = C2(x).
Hence:
22 + x = 14 + 3x
2x = 8
x = 4.
4 movies would cause the two plans to have an equal monthly cost.
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Please help I will give you brainliest
Answer:
$7.4
each bag of milk cost $7.4
Answer: $7.4
Step-by-step explanation: i did this and i remember it!
How are ratios, rates, and unit rates used to solve problems?
Answer:
The Ratios, Rate and unit rate are used to solve many real-world problems.
Step-by-step explanation:
As a ratio is a comparison of two numbers or measurements.
A rate is also a ratio in which the two terms are in different units.
A unit rate means a rate for one of something
solving systems by substitution (algebra 2)
7x + y = 12
y = 4x - 21
Answer:
x = 3, y = -9
Step-by-step explanation:
plug y=4x-21 into 7x+y=12 to get
7x + (4x-21) = 12 -> 11x -21 = 12 -> 11x = 33 -> x = 3
plug x=3 into y=4x-21 to get
y = 4(3) - 21 = 12 - 21 = -9
6) Convert the following equivalent scales to ratios.
(i) 1cm=20m
Answer:
[tex]1cm = 20 \times 100 \\ = 2000cm \\ 1cm = 2000cm[/tex]