Answers
Answer:
(a, b, c) = (-3, -2, -4)
Step-by-step explanation:
You want to solve the system of 3 equations in 3 variables shown in the attached figure.
SolutionThe easiest solution is one provided by a suitable calculator (attached). It tells you ...
a = -3b = -2c = -4The "work" is entering the problem into the calculator.
Ad hocWe notice the sum of 'a' coefficients is zero, so we can add the three equations to get ...
(4a +5b -6c) +(-3a -2b +7c) +(-a +4b +2c) = (2) +(-15) +(-13)
7b +3c = -26 . . . . . simplify
Multiplying the third equation by 4 and adding that to the first equation gives ...
4(-a +4b +2c) +(4a +5b -6c) = 4(-13) +(2)
21b +2c = -50 . . . . . simplify
Now, we have two equations in two unknowns.
Multiplying the first equation above by 3 and subtracting this last equation eliminates the b term to give ...
3(7b +3c) -(21b +2c) = 3(-26) -(-50)
7c = -28 . . . . . simplify
c = -4 . . . . . . . divide by 7
Using this in the first "ad hoc" equation, we can find b:
7b +3(-4) = -26
7b = -14 . . . . . . . . add 12
b = -2 . . . . . . . . divide by 7
And the values of b and c can go into the last of the original equations to give ...
-a +4(-2) +2(-4) = -13
-a = 3 . . . . . add 16
a = -3 . . . . . multiply by -1
The solution is (a, b, c) = (-3, -2, -4).
__
Additional comment
The given solution is "ad hoc" because we decide how we're going to approach the solution based on the coefficients we see. Here, we are solving by "elimination," performing as little arithmetic as possible.
The third equation suggests we could make a substitution for 'a':
a = 4b +2c +13
That substitution would give a different set of equations in 'b' and 'c' than the ones shown above.
The second attachment shows a graphical solution to the system. It shows (a, b, c) = (-3, -2, -4). The graphing program requires the use of x and y instead of 'a' and 'b' for the variables.
Four methods of solving the system have been described. Take your pick. The calculator solution was the easiest, requiring each number to be entered once.
Related Questions
Which of the following are accurate descriptions of the distribution below? (4 BRAINLIEST!!!)
Choose all answers that apply:
(Choice A)
The distribution has an outlier.
(Choice B)
The distribution has a gap from 20 to 29 states.
(Choice C)
None of the above
Answers
Answer:
B
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
A jar contains 3 blue marbles and 2 red marbles.
A marble is randomly selected from the jar and replaced, and then a second marble is chosen.
The probability that a blue marble was chosen both times is _____%.
Answers
The probability that a blue marble was chosen both times is 60%.
We have given that,
Type the correct answer in the box. Use numerals instead of words.
A jar contains 3 blue marbles and 2 red marbles.
A marble is randomly selected from the jar and replaced, and then a second marble is chosen.
What is the random probability?The probability distribution for a random variable describes how the probabilities are distributed over the values of the random variable.
3+2=5.
3/5 is the blue marble.
You may also say 6/10.
It is likely you will pull out a blue marble.
0.6×100=60
Therefore, The probability that a blue marble was chosen both times is 60%.
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Answer:
The ANSWER on top is WRONG
the correct answer is 36%
Step-by-step explanation:
I got it right on Edmentum
Hook me up with a 5 star and a thanks :)
Chris made a solid by joining two identical rectangular prisms as picture blow. The overall dimensions of the composite solid are 20 centimeters (cm) by 18 centimeters by 15 centimeters. What is the surface area, in square centimeters, of a single prism?
PLEASE, don’t answer if you don’t know the answer to the question. Whoever answers correctly will get Brainliest!
Answers
Answer:
B
Step-by-step explanation:
Base area = (base x width) = 20 x 18 = 360 cm^2
Base perimeter = (base + width) x 2 = (20 + 18) x 2 = 76 cm
lateral surface = (base perimeter x height) = 76 x 15 = 1140 cm^2
Surface area = (base area x 2) + lateral surface = (360 x 2) + 1140= 1860 cm^2
surface area of a single prism = 1860 / 2 = 930 cm^2
does anyone know what this is?!?! describe the transformation that occurs
Answers
Answer: see below...
Step-by-step explanation:
1. Reflection across the y axis.
2. Translation by a vector (0, -6): 0 units to the right/left, 6 units down.
Answer:
Step 1 is a reflection across the y- axis.
Step 2 is a translation 6 units down.
Step-by-step explanation:
Bob's Gift Shop sold 550 cards for Mother's Day. One salesman, Anand, sold 4% of the cards sold for Mother's Day. How many cards did Anand sell?
Answers
22 cards were sold by the Anand.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Bob's Gift Shop sold 550 cards for Mother's Day.
One salesman, Anand, sold 4% of the cards sold for Mother's Day.
We need to find the number of cards sold by Anand
Convert 4% to decimal by dividing 4 by 100
4/100=0.04
Now multiply 0.04 with 550
0.04×550
22
Hence, 22 cards were sold by the Anand.
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Work out
m
and
c
for the line:
y
=
9
x
Answers
Answer:
Find answers below.
Step-by-step explanation:
The equation isn't explicitly stated or well written. Thus, we would assume two (2) case scenario for the equation of line by altering the signs.
Scenario 1;
y = 9 + x
Mathematically, the equation of a line is given by the formula;
Equation of straight line is y = mx + c
Where;
m is the slope.
x and y are the points
c is the intercept.
Comparing the two equations, we have;
y = mx + c = 9 + x
Constant, c = 9
Slope, m = 1
Scenario 2.
y = 9 - x
y = mx + c = 9 - x
Constant, c = 9
Slope, m = -1
Eva works at a sandwich shop.she works between 10 and 20 hours each week.Last week Eva worked 18 hours and made $144.she wants to know how much she will make for working different number of hours
Answers
Answer:
$8/hour
Step-by-step explanation:
For each hour worked, she makes $8/hour (144/18). So depending on how many different hours worked, she will earn $8 x hours worked.
Answer:
$8
Step-by-step explanation:
The legislature in a state has 50 seats. Apportion these seats to the five counties below using Lowndes' method.
County Population Seats Received
Adams 71,000
Grant 483,000
Colton 224,000
Davis 406,000
Hayes 444,000
Answers
Answer: hi
Step-by-step explanation:
To apportion the 50 seats using Lowndes' method, you will need to follow these steps:
Calculate the apportionment ratio for each county by dividing the population of the county by the total population of the state.
Multiply the apportionment ratio for each county by the number of seats to be apportioned. This will give you the initial allocation of seats for each county.
Distribute the remaining seats (if any) to the counties with the largest remainders (the difference between the initial allocation of seats and the whole number of seats). If there are multiple counties with the largest remainders, distribute the seats among these counties based on their remainders.
Here is the apportionment for the five counties using these steps:
County Population Apportionment Ratio Initial Allocation Seats Received
Adams 71,000 0.088 4.4 4
Grant 483,000 0.591 28.9 29
Colton 224,000 0.274 13.7 14
Davis 406,000 0.500 25.0 25
Hayes 444,000 0.547 27.4 27
Total 1,928,000 50 50
So using Lowndes' method, Adams County would receive 4 seats, Grant County would receive 29 seats, Colton County would receive 14 seats, Davis County would receive 25 seats, and Hayes County would receive 27 seats.
I need someone to explain this step by step. I have a test very soon.
Answers
9514 1404 393
Answer:
D. Infinitely many solutions
Step-by-step explanation:
To compare two linear equations, it is handy to have them in the same for. It doesn't really matter what that form is. You generally want to reduce the equations as far as possible by removing any common factors from the coefficients.
Here, we can put both equations into standard form: ax +by = c.
First equation:
y = -3x +5 . . . . given
3x +y = 5 . . . . add 3x
Second equation:
6x +2y = 10 . . . . given
3x + y = 5 . . . . divide by 2
These two equations are now identical. That means they describe the same line, so any (x, y) pair that satisfies one of these equation will also satisfy the other one (obviously). That means there are an infinite number of points these lines have in common, an infinite number of solutions.
__
More about number of solutions
Above is one of the possibilities.
Another possibility is that the left side looks the same, but the right side is different. For example, ...
3x +y = 5
3x +y = 4
The ratios of the coefficients of x and y are the same (a:b = 3:1). That means these lines have the same slope and they are the equations of parallel lines. They do not intersect, so this set of equations will have no solutions.
Another suitable form for comparing the slopes is slope-intercept form. The above two equations in that form would be ...
y = mx + b
y = -3x +5
y = -3x +4 . . . . . . same slope, different y-intercept
__
If the equations are different (except as just noted), there is one solution. Lines with different slopes must cross somewhere. They will cross exactly once.
the width of a rectangle is 2 m less than the length. if the area of the rectangle is 48sq meters. what is the length and width
Answers
Then the width=v-2
Area= length x width
48= v(v-2)
48= v^2 -2v
v^2 -2v -48=0
(v-8)(v+6)=0
then v= 8 and v=-6
Since length cannot be negative so v=8
And width=v-2
= 8-2=6
So length= 8 m
Width= 6 m
determine if each liners function is a direct variation. If it is state the constant of variation.
Answers
The liners function are not direct variation
What is a direct variation?The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation.
For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation
If b is directly proportional to a, then k is the constant of variation and the value of k = b/a for all value of b and a
In the problem, the variables are compared as follows
feet = k * sec
k = feet / sec
For the first values, k = 33 / 3 = 11
For the second values, k = 36 / 6 = 6
since 11 ≠ 6 the function is not a direct variation
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The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2.
1. x = -1, y = 29
2. x = 8, y = 11
Answers
1) The equation is:
y = -29/x
And when we evaluate in x = 2, we get y = -14.5
2) The equation is:
y = 88/x
And when we evaluate in x = 2, we get y = 44
How to find the equation between x and y?We know that the variables x and y vary inversely, then the equation between these variables will be something like:
y = k/x
Where k is a constant.
1) First we know that when x = -1, y = 29, replacing these values we will get:
29 = k/-1
-1*29 = k
-29 = k
Then the equation is:
y = -29/x
If now we evaluate in x = 2, we will get:
y = -29/2
y = -14.5
2) Now we know that x = 8 and y = 11, replacing these we get:
11 = k/8
11*8 = k
88 = k
So the equation is:
y = 88/x
If now we replace x by 2, we will get:
y = 88/2 = 44
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Liam sorted music albums in his collection into three genres as shown
Genre
Rock
Country
Holiday
Count
7
3
5
Which statements identify correct ratios for the album collection Select all that apply
The ratio of holiday music albums to the entire collection is 5:10.
The ratio of rock music albums to country music albums is 7 to 3.
The ratio of rock music albums to holiday music albums is 5 to 7
The ratio of country music albums to the entire collection is 1 to 5.
There is 1 holiday music album for every 3 albums in the collection
Answers
5 + 23 ÷ 4 = Which operation would you do first:
A: Addition
B: Exponents
C: Division
LINKS WILL GET REPORTED
Answers
bcuz pemdas
what is the equation of four less thrice a number and two will result to forty six
Answers
Answer:
4 - b x 2 = 46
Step-by-step explanation:
Henry believes that if you square the expression x^4 The result will be x^16. Is Henry correct? (Help please)
Answers
What is this number in standard form? 19 thousands, 6 hundreds, 12 tens, 5 ones Your answer
Answers
Answer:
19,725
Step-by-step explanation:
For the graphed exponential equation, calculate the average rate of change from x = −3 to x = 0.
A. -1/3
B. -5/8
C. -4/5
D. -7/3
Answers
Answer:
D)
Step-by-step explanation:
f(-3) = 2
f(0) = -5
[f(-3) - f(0)] ÷ -3-0
[2-(-5)] / -3
7/-3
A shop has a sale of 15% off all items in stock.
If the original price of a dress is £40 what would be its sale price?
Answers
Answer:
The sale price is 34 euros.
Step-by-step explanation:
40 * .85 (100% - 15% = 85% or .85) = 34
HELP ME ON THIS PLEASEEEE!!!
The sum of Jahiem and his sister's age is 21. If Jahiem is 7 years older than his
sister, write and solve a system of equations using ) to represent Jahiem's age and s
to represent his sister's age
Answers
Step-by-step explanation:
ANSWER He is 14 and she is 7 because 21 - 7 is 14
Find the missing angle measure. Round to the nearest degree. cos 0 = 0.9563
Answers
The measure of the missing angle is 17 degrees.
Cosine as an example of trigonometric functions.Trigonometry is a method that can by used to solve questions involving the application of functions. Some examples of trigonometric functions are: Sine, Cosine, Tangent, Secant, Cotangent etc.
Now considering the given question, we are to find the measure of the missing angle. We have;
cos θ = 0.9563
where θ is the missing angle the value of which is to be determined.
Thus, divide both sides of the expression by cos to have;
cos θ/ cos = 0.9563. cos
θ = cos^-1 0.9563
θ = 17.0 degrees
Therefore, the value of the missing angle is 17 degrees.
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Khan Academy Question pls answers only
Answers
Answer: 0
Step-by-step explanation:
When x = 6, y = 0 [since the graph passes through (6,0)].;
the length of a rectangular frame is 15 inches and the width of 8 inches. what is the length of a diagonal of this Fram inches
Answers
Answer:
using the phytogaran theory we get 17 inch as the length of the diagonal
Answer:
sorry just a sec
Step-by-step explanation:
maybe 9?
Find all REAL zeros of f(x) = x3 – 4x2 - 15x + 18
Answers
Answer:
Move 18 18 to the left side of the equation by adding it to both sides. x3 ...
Find an equivalent expression 3xy + 4x + 8 + (-2)
Answers
Answer:
3 x y + 4 x + 6 and x (3 y + 4) + 6
Step-by-step explanation:
What is the value of x?
Answers
9514 1404 393
Answer:
54
Step-by-step explanation:
The external angle is half the difference of the subtended arcs.
x° = (136° -28°)/2 = 108°/2
x = 54
Please help me with this faster if you know please?!!!
Answers
Answer:
22%
Step-by-step explanation:
************************************
Answer:
81%
Step-by-step explanation:
The total number of Large drinks: 27
The probability that a customer orders a Hot and Large drink if the customer ordered a Large is the ratio of the number of Hot and Large drinks to the number of Large drinks:
22/27 = 0.8148 = 81.48%
Find the value of x, if x,3,5 and 15 are proportional,
Answers
Answer:
» x : 3 :: 15 : 5
» x = 15
3 5
» x = 15 × 3
5
» x = 3 × 3
» x = 9
Step-by-step explanation:
PLSS HELP WILL GIVE BRAINLIEST TIMED QUESTION
What is m
Answers
Answer:
Step-by-step explanation:
The answer is 46
Rose bushes are planted in a line on both sides of a path. The distance between the
bushes is 2 meters. What is the largest number of rose bushes that can be planted if
the path is 20 meters long?