Solve the system of linear equations using ELIMINATION. Write your final solution as an ORDERED PAIR.
5x-3y=x1
2x-y=2
Answers
Answer:
The solution to the system of equations becomes:
(x, y) = (7, 12)
Step-by-step explanation:
Given the system of equations
\(5x - 3y = -1\)
\(2x - y = 2\)
Solving using the Elimination Method
\(\begin{bmatrix}5x-3y=-1\\ 2x-y=2\end{bmatrix}\)
Multiply 5x - 3y = - 1 by 2: 10x - 6y = -2
Multiply 2x - y = 2 by 5: 10x - 5y = 10
\(\begin{bmatrix}10x-6y=-2\\ 10x-5y=10\end{bmatrix}\)
subtraction operation
\(10x-5y=10\)
\(-\)
\(\underline{10x-6y=-2}\)
\(y=12\)
so the system of equations becomes
\(\begin{bmatrix}10x-6y=-2\\ y=12\end{bmatrix}\)
Therefore, the value of y = 12
For 10x - 6y = -2 plug in y = 12
10x - 6y = -2
10x - 6(12) = -2
10x - 72 = -2
10x = -2+72
10x = 70
dividing both sides by 10
10x/10 = 70/10
x = 7
Therefore, the value of x = 7
Thus, the solution to the system of equations becomes:
(x, y) = (7, 12)
Related Questions
in order to estimate the mean 30-year fixed mortgage rate for a home loan in the united states, a random sample of 14 recent loans is taken. the average calculated from this sample is 7.35%. it can be assumed that 30-year fixed mortgage rates are normally distributed with a population standard deviation of 0.6%. compute 90% and 99% confidence intervals for the population mean 30-year fixed mortgage rate.
Answers
a) The 90% confidence intervals for the population mean 30-year fixed mortgage rate is (0.0762, 0.0708)
b) The 99% confidence intervals for the population mean 30-year fixed mortgage rate is (0.07394, 0.07306)
Given,
Mean fixed mortgage rate = 30
Random sample, n = 14
Sample mean, x = 7.35% = 0.0735
Population Standard Deviation, σ = 0.6% = 0.006
We have to compute 90% and 99% confidence interval for the population mean;
Here,
Formula to find confidence interval for population standard deviation;
x ± tₙ₋₁, ∝/2 σ/√2
Now,
a) Significance Level, ∝ = 1 - 0.90 = 0.1
Critical Value, tn-1 ∝ = t₂₇, ₀.₀₅ = 1.703
Now, the 90% confidence intervals for the population mean 30-year fixed mortgage rate will be:-
0.0735 ± (1.703) 0.006/√14
= 0.0735 ± 0.0027
= (0.0735 + 0.0027, 0.0735 - 0.0027)
= (0.0762, 0.0708)
b) Significance Level, ∝ = 1 - 0.99 = 0.01
Critical Value, tn-1 ∝ = t₂₇, ₀.₀₀₅ = 0.2771
Now, the 99% confidence intervals for the population mean 30-year fixed mortgage rate will be:-
0.0735 ± (0.2771) 0.006/√14
= 0.0735 ± 0.00044
= (0.0735 + 0.00044, 0.0735 - 0.00044)
= (0.07394, 0.07306)
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the random variable x is known to be uniformly distributed between 70 and 90. the probability of x having a value between 80 to 95 is group of answer choices 0.05 0.5 0.75 1
Answers
The probability of x having a value between 80 to 95 is 0.75.
The probability of x having a value between 80 to 95 can be determined by calculating the proportion of the total range of x that falls within that interval. Since x is uniformly distributed between 70 and 90, the probability can be obtained by dividing the width of the desired interval (15) by the width of the entire range of x (90 - 70 = 20).
Using the formula for probability in a uniform distribution, we have:
Probability = (width of interval) / (width of range)
Probability = 15 / 20
Probability = 0.75
Therefore, the probability of x having a value between 80 to 95 is 0.75.
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The random variable x is known to be uniformly distributed between 70 and 90. the probability of x having a value between 80 to 95 is group of answer choices (a)0.05 (b)0.5 (c)0.75 (d)1
three ratios that are equivalent to 11:111:111, colon, 1.
Answers
Answer:
sdsadasdads121
Step-by-step explanation:
Answer:
22:222:222
33:333:333
44:444:444
Step-by-step explanation:
22:222:222
33:333:333
44:444:444
This means ratios which when reduced give us 11:111:111
HOPE THIS HELPED
Simplify 4 x + 3 y 2 − 7 z 4 + 5 z 4 + 11 − 4 x + y 2
Answers
Answer:
\(4y {}^{2} - 2z {}^{4} + 11\)
Step-by-step explanation:
\(1. \: (4x - 4x) + (3y {}^{2} + y {}^{2} ) + ( - 7z {}^{4} + 5z {}^{4} ) + 11 \\ 2. \: 4y {}^{2} - 2z {}^{4} + 11\)
I need answers for this.
Answers
Answer:
18, 24, 8, 3
Step-by-step explanation:
8a = 42 - 18
8a = 24
a = 24 / 8
a = 3
To check, plug 3 into the equation
8(3) = 42-18
24 = 24
Answer:
8a = 42 - 18
8a = 24
a = 24 ÷ 8
a = 3
Step-by-step explanation:
To find the steps to the equation, we must solve the equation.
Step 1: Subtract 18 from both sides.
\(8a = 42 - 18\) \(8a = 24\)Step 2: Divide both sides by 8.
a = 24 ÷ 8 a = 3Therefore, the answers are 18, 24, 8, and 3.
Have a lovely rest of your day/night, and good luck with your assignments! ♡
a ______ is a descriptiion of the approach that is used to obtain samples from a population prior to an data collection activity.
A.
population frame
B.
sampling weight
C.
sampling plan
D.
probability interval
Answers
The correct answer is option C. A sampling plan refers to a detailed strategy for obtaining a sample from a population for the purpose of data collection.
It describes the precise procedures needed to choose the sample, determine the members of the sample, and gather the data.
The sampling strategy should take into account the type of sampling design, sample size, sampling process, and the methods to be employed for data collecting.
The strategy for implementing sampling should be outlined in the plan, along with instructions on how to make sure the sample is representative of the population, how to prevent bias in the sampling process, and how to make sure the data gathered is of high quality.
A good sampling plan should provide a clear and consistent method for gathering data and be founded on basic statistical concepts.
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brainliest, 100 points, and its multiple choice!!!!
Answers
Answer:
Answer is C
(-2,3)
Step-by-step explanation:
Answer:
(-8, 18)
Step-by-step explanation:
To solve this system of equations using elimination, we want to eliminate one of the variables by adding or subtracting the two equations.
One way to do this is to multiply the second equation by a constant that will make the coefficient of x the same as in the first equation. In this case, we can multiply the second equation by -5, which will give us:
-15x - 10y = -60
Now we can add this equation to the first equation:
5x + 2y = -4
-15x - 10y = -60
-10x - 8y = -64
Dividing both sides by -2, we get:
5x + 4y = 32
Now we have one equation with only x and y, so we can solve for either variable.
Let's solve for y by subtracting 5x from both sides:
5x + 4y = 32
-5x = -5x
4y = 32 - 5x
Dividing both sides by 4, we get:
y = (32 - 5x) / 4
Now we can substitute this expression for y into one of the original equations to solve for x. Let's use the first equation:
5x + 2y = -4
5x + 2[(32 - 5x) / 4] = -4
Multiplying both sides by 4, we get:
20x + 2(32 - 5x) = -16
Simplifying, we get:
20x + 64 - 10x = -16
10x = -80
x = -8
Now we can substitute this value of x into either of the equations to solve for y. Let's use the first equation again:
5x + 2y = -4
5(-8) + 2y = -4
-40 + 2y = -4
2y = 36
y = 18
Therefore, the solution to the system of equations is (x, y) = (-8, 18).
3. determine whether the given functions form a fundamental solution set to an equation x’(t) = ax. if they do, find a fundamental matrix for the system and give a general solution.
Answers
Here c1 and c2 are constants determined by the initial conditions. To determine whether the given functions form a fundamental solution set to the equation x’(t) = ax, we need to check if they are linearly independent and if they satisfy the equation. Let the given functions be f1(t) and f2(t).
First, we need to check if they satisfy the equation x’(t) = ax. We have:
f1’(t) = a f1(t) and f2’(t) = a f2(t)
This shows that both f1(t) and f2(t) satisfy the equation.
Next, we need to check if they are linearly independent. To do this, we can form a matrix with the two functions as its columns and take its determinant.
| f1(t) f2(t) |
| f1’(t) f2’(t) |
Expanding the determinant, we get:
f1(t) f2’(t) - f2(t) f1’(t) = W(t)
where W(t) is the Wronskian of f1(t) and f2(t). If W(t) is not identically zero, then f1(t) and f2(t) are linearly independent and form a fundamental solution set.
Therefore, if W(t) is not identically zero, we can find a fundamental matrix for the system as follows:
| f1(t) f2(t) |
| f1’(t) f2’(t) |
And the general solution can be written as:
x(t) = c1 f1(t) + c2 f2(t)
where c1 and c2 are constants determined by the initial conditions.
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Fill in the blanks to express the quantities given in ratio language. Ratios must be
expressed in simplest form.
Number of Animals in the Pet Store:
Animal Count
16 cats
8 dogs
For every __ cats in the pet store, there are __dogs.
Answers
Which are factors of 18? Check all that apply. 1 2 3 4 8
Answers
Answer:
1 2 3
Step-by-step explanation: 1 times 18, 2 times 9, 3 times 6
Given that a box has 4 blue marbles, 3 red marbles, and 5 yellow marbles, use the probability formulas to answer the following questions. What is the probability of drawing a blue marble? Drawing a marble that is not red? Drawing a red and yellow marble at once? Drawing a red or blue marble? Drawing a red marble, put it back, and then drawing a yellow marble? Drawing a yellow marble, keeping it, and then drawing another yellow marble? Drawing a yellow marble, given that a red marble was drawn on the first draw and not replaced?
Answers
Answer:
CHUPAPI MUNYNYOStep-by-step explanation:
MESHEPO MESHEEPOOgiving 30 points pls help
Answers
Answer:
8.66
Step-by-step explanation:
The formula for the perimeter of a triangle is the sum of the length of all the sides of a triangle.
P = π + √10 + √5 = 3.14 + 3.162 + 2.36 = 8.662 or 8.66
If you draw a marble replace it, and then draw another , then what is the probability of choosing two yellow marbles?
Answers
Answer:
if ur marble count is 6 then
Step-by-step explanation:
First off, the probability of choosing a yellow marble the first time would be 3 out of the 6 total marbles which simplifies to 1/3
Then you have to multiply this probability by the second chance of picking a yellow marble
1/3 * 1/3
1/9
Solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure you include all steps needed to solve for ∠A
Answers
Answer:
∠A=123°.
Step-by-step explanation:
From the given figure it is clear the CD and CE are two tangent lines on circle with center A.
Radius is perpendicular to the tangent at the point of tangency.
\(\angle ADC=90^{\circ}\)
\(\angle AEC=90^{\circ}\)
Smaller arc DE = (5x-2)°
It means central angle DAE is (5x-2)°.
\(\angle DAE=(5x-2)^{\circ}\)
Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.
\(\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}\)
\(90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}\)
\((7x+5)^{\circ}+180^{\circ}=360^{\circ}\)
\((7x+5)^{\circ}=360^{\circ}-180^{\circ}\)
\((7x+5)^{\circ}=180^{\circ}\)
\(7x+5=180\)
\(7x=175\)
\(x=25\)
The value of x is 25.
\(\angle A=5x-2=5(25)-2=125-2=123^{\circ}\)
Therefore, the measure of ∠A is 123°.
I purchased 3.4 pounds of apples for $7.29. What is the cost per pound? I need the answer fast.
Answers
Answer:
The answer is $2.14 per pound of apples.
Step-by-step explanation:
7.29/3.4= roughly 2.14.
Answer:
is 24.786
Step-by-step explanation:
multiply the numbers and that's how you get your answer and I use my calculator so I know the answer is 24.786
pls help i don’t understand this
Answers
1(5x-7u=-7)
1(-2x+3y=2)
3x-4y=5
what is the slope of this line? y=x+12
Answers
Answer:
its slope is 1
Step-by-step explanation:
The complex numbers $z_1$ and $z_2$ are such that $|z_1| = 5,$ $|z_2| = 13,$ and
\[13z_1 - 5z_2 = 27 - 99i.\]find $z_1 z_2.$
Answers
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
How to determine two complex numbers based on their norms and a given operation
In this question we must derive two complex numbers such that the following conditions are fulfilled:
a² + b² = 5² (1)
c² + d² = 13² (2)
13 · (a + i b) - 5 · (c + i d) = 27 - i 99 (3)
If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):
13 · (4 - i 3) - 5 · (5 + i 12)
52 - i 39 - 25 - i 60
27 - i 99
By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.
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help please i need asap
Answers
Answer:
Yes, no, no, no, Yes
Step-by-step explanation:
Which is the best estimate of 90/7 divided by 1 3/4? 2 6 12 24
Answers
Answer:
6 is the best estimate.
Step-by-step explanation:
(90/7) / (1 & 3/4) == (90/7) / (7/4) == (90/7) * (4/7) == 360/49 > 7.
Choose 6 as your best approximation.
prime, incorporated, purchases $100,000 in construction machinery on january 1, year 1. the useful life is estimated to be 8 years, and the residual value is estimated to be $20,000. if the company uses the double-declining-balance method, the asset will reach its residual value in the ____ year.
Answers
If the company uses the double-declining-balance method, the asset will reach its residual value in the 9th year. We can find the solution in the following manner.
Under the double-declining-balance method of depreciation, the depreciation rate is twice the straight-line rate, and the book value is multiplied by the depreciation rate each year. The formula for calculating the depreciation expense is:
Depreciation expense = (2 / Useful life) x Book value at the beginning of the year.
In this case, the construction machinery has a useful life of 8 years and a cost of $100,000 with a residual value of $20,000. Therefore, the depreciable base is $80,000 ($100,000 - $20,000).
To calculate the depreciation expense for the first year, we use the formula:
Depreciation expense = (2 / 8) x $100,000 = $25,000
The book value at the beginning of year 2 is:
Book value = Cost - Accumulated depreciation
Book value = $100,000 - $25,000 = $75,000
To calculate the depreciation expense for year 2, we use the same formula:
Depreciation expense = (2 / 8) x $75,000 = $18,750
We continue to calculate the book value and depreciation expense for each year until the book value reaches the residual value of $20,000.
Year 1:
Book value = $100,000 - $25,000 = $75,000
Year 2:
Book value = $75,000 - $18,750 = $56,250
Year 3:
Book value = $56,250 - $14,063 = $42,187
Year 4:
Book value = $42,187 - $10,547 = $31,640
Year 5:
Book value = $31,640 - $7,910 = $23,730
Year 6:
Book value = $23,730 - $5,932 = $17,798
Year 7:
Book value = $17,798 - $4,450 = $13,348
Year 8:
Book value = $13,348 - $2,337 = $11,011
Year 9:
Book value = $11,011 - $1,674 = $9,337
Therefore, the asset will reach its residual value in Year 9.
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Please help, I’m not sure how to set this equation up. Want to donate to a better cause? Consider micro-lending. Micro-lending is a process where you lend directly to entrepreneurs in developing countries. You can start lending at $25. Kiva. Org boasts a 99% repayment rate. The average loan to an entrepreneurs is $388. 44 and the average loan amount is $261. 14. With a total amount loaned of $283,697,150, how many people are lending money if the average number of loans per lender is 8?
Answers
Approximately 234,314 people are lending money through Kiva.org.
To solve this problem, you can use the formula:
\(Total amount loaned = (average loan amount) x (number of loans) x\) \((number of lenders)\)
Let x be the number of lenders. Then we have:
Total amount loaned = $283,697,150
Average loan amount = $388.44
Number of loans = total amount loaned / average loan amount = $283,697,150 / $388.44 ≈ 729,464
Number of loans per lender = 8
Number of lenders = x
Using the formula, we get:
$283,697,150 = $388.44 x 729,464 x x / 8
Simplifying, we get:
x ≈ 234,314
Therefore, approximately 234,314 people are lending money through Kiva.org.
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Simplify 29-4.37+(-5.68)
Answers
Answer:
18.95
Step-by-step explanation:
I hope this is correct!
A gardener is planting flowers and would like for them to be in even rows. He has 12 rose bushes and 15 tulips. What is the greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows?
12
6
5
3
Answers
Answer:
Step-by-step explanation:
The factors of 12 and 15 common number is 3. You can do rows of 3 four times to get 12 rose bushes and rows of 3, five times to get 15 tulips.
4x3 = 12 and 5x3 = 15. This is how I understood the question.
Answer:
3
Step-by-step explanation:
the factors of 12 are
1,2,3,4,6,12
and the factors of 15 are
1,3,5,15
so the answer would be 3
( i did the quiz and got it right )
Find: tan A
1.8/10
2.6/8
3.10/6
4.8/6
Answers
Answer:
2. 6/8Step-by-step explanation:
6 * tan (A) = 8
tan⁻¹ (A) = 6/8
on a map, 1 inch equals 15 miles. two cities are 6 inches apart on the map. what is the actual distance between the cities?
Answers
1 inch= 15 miles
to find:the distance between the cities
solution:1 in/ 15 miles = 6 in/ x miles
applying cross products:
1 * x = 15 *6
x= 90
so, the distance betwixt the cities is 90 miles.
I need help solving this equasion
Answers
130+x=180
X=50
Angle on a straight line is 180°
So to get y it will be 180°-(60°+70)
Which is equal to 180°-130°= 50°
Y= 50°
Y and x are vertically opposite angles and vertically opposite angles are equal so therefore x=y and y=50° so x is also equal to 50° or also to find x you could do the same method as the way to find y. Angles 60°, 70° and x form a straight line. So 180°- (60°+70°)= 180°-130°=50°
X=50°.
If f(x) = 3x - 1 and g(x) = x + 2, find (f + g)(x)
A) 2x-3
B)3x-3
C)4x+1
D)2x-1
Answers
Answer:
C.
Step-by-step explanation:
Water come out of a pipe at a rate of 16 gallons per minute. How many gallons have come out after 4 minutes
Answers
Answer:
64 gallons
Step-by-step explanation:
Ask yourself; if
16gallons = 1minute
? = 4minutes
Cross multiply;
(16 × 4) ÷ (1) = 64
Help pls!!
given j || k given two angles that alternate exterior
Answers
Answer:
<2 and <7
<1 and <8
Step-by-step explanation: