Answers
9514 1404 393
Answer:
{ (-441/23, 433/23) }
Step-by-step explanation:
The "cross-multiplication method" is usually shown as follows:
1. rewrite the equations in general form: ax +by +c = 0
2. write the coefficients in two row in the order b, c, a, b.
3. form three products, each being the number in the first row times the number to its right in the second row. That is, b1·c2, c1·a2, a1·b2
4. form three more products, each being the number in the second row times the number to its right in the first row. That is, b2·c1, c2·a1, a2·b1
5. form three differences, subtracting the products of step 4 from those of step 3. Call these differences d1, d2, d3. (For example, d1=b1c2-b2c1.)
6. The values of x and y satisfy the equations ...
x/d1 = y/d2 = 1/d3
which is to say, ...
x = d1/d3, and y = d2/d3
_____
For your equations, we can rewrite them as ...
11x +12y -15 = 012x +11y +23 = 0Then our rows of coefficients are ...
[tex]\begin{array}{cccc}12&-15&11&12\\11&23&12&11\end{array}[/tex]
And our differences are ...
d1 = 12(23) -11(-15) = 441
d2 = -15(12) -23(11) = -433
d3 = 11(11) -12(12) = -23
The relations between x and y are ...
x/441 = y/-433 = 1/-23
so, x = -441/23 and y = 433/23
The solution set is one ordered pair: { (-441/23, 433/23) }.
_____
Additional comments
The final solution is identical to the formula arrived at using Cramer's Rule. Calling this the "cross-multiplication method" avoids any discussion of matrices and determinants.
Related Questions
A teacher assigns 5 points for a correct answer and -2 points for an incorrect answer and 0 points for leaving the questioned unanswered. What is the score for Mohit who had 22 correct answers and 15 incorrect answers and 7 unanswered questions?
Answers
Answer:
Mohit has a score of 80
Step-by-step explanation:
Answer: Mohit got a scoe of 70
Step-by-step explanation: had this question on my assigment
What is the factored form of the binomial expansion?
256x4 − 1,536x3y + 3,456x2y2 − 3,456xy3 + 1,296y4
(4x – 6y)3
(4x – 6y)4
(16x – 36y)3
(16x – 36y)4
Answers
The factored form of the binomial expansion of 256x4 − 1,536x3y + 3,456x2y2 − 3,456xy3 + 1,296y4 is (4x-6y)^4
Answer:
B
Step-by-step explanation:
State the degree of the polynomial.
3x2y + 4xy + 1 − 5x4y − 6y,
Answers
Answer:
The degree of the given polynomial is 5
Step-by-step explanation:
The degree of a polynomial is the highest of the degrees of its monomials with non-zero coefficients.
The degree of a monomial is the sum of the exponents of the variables that appear in it.
We have the following polynomial:
[tex]3x^2y + 4xy + 1 - 5x^4y - 6y[/tex]
Degree of the first monomial: 2+1=3
Degree of the next monomial: 1+1=2
Degree of the next monomial: 0
Degree of the next monomial: 4+1=5
Degree of the next monomial: 1
Thus, the degree of the given polynomial is 5
Beth wants to paint the four walls of her rectangular bedroom. Her room is 10 feet wide, 13 feet long, and 8 feet high. She will not paint her rectangular door, which is 3 feet wide and 7 feet high. What is the total area of the walls that Beth needs to paint?
A. 347 square feet
B. 368 square feet
C.578 square feet
D. 1019 square feet
E. 1040 square feet
Answers
Answer:
D; 1019 square feet
Step-by-step explanation:
10 x 13 x 8 = 1040 square feet
3 x 7 = 21 square feet
1040 - 21 = 1019 square feet (:
Answer:
10x13 is 130
130x8 is 1040
Step-by-step explanation:
Help!
Let f(x)= 7x² + 4x and g(x) = -9x -- 2. What function represents a new function, h(x), for which h(x)=(f+g)(x)
a. h(x)= -2x² + 2x
b. h(x) = 7x2 + 5x - 2
c. h(r)= -2x² + 4x - 2
d. h(x) = 7x- 5x - 2
Answers
Answer:
Option D
Step-by-step explanation:
h(x) = (f+g)(x) = f(x) + g(x)
= 7x² + 4x +(-9x-2)
= 7x² -5x -2
Explain in your own words what happens when a car's tires are changed from the original size to a LARGER size. How is the odometer affected? How is the speedometer
affected?
Answers
Answer:
Step-by-step explanatin
it affects it because your going from smaller tires witch make it easier to make turns go faster things like that when you put bigger tires on the car it is gonna raise the car and have a whole differnt outlook
For a certain race, 4 teams were allowed to enter 3 members each. A team earned 9 – n points whenever one of its members finished in nth place, where 1 ≤ n ≤ 8. There were no ties, disqualifications, or withdrawals. If no team earned more than 10 points, what is the least possible score a team could have earned?
A) 0
B) 1
C) 2
D) 3
E) 4
Answers
Answer:
D. 3 Points
Step-by-step explanation:
Given
[tex]Members = 3[/tex]
[tex]Point = 9 - n[/tex]
[tex]1 \leq\ n \leq 8[/tex]
Required
Determine the least possible score
The least point a member of a team can get is when n = 8.
i.e.
[tex]Point = 9 - n[/tex]
[tex]Point = 9- 8[/tex]
[tex]Point = 1[/tex]
To get the least score, each of the 3 members must have 1 point each.
So:
[tex]Total = 3 * 1[/tex]
[tex]Total = 3[/tex]
Town M is 282 feet below sea level. Town R is 679 feet above sea level. How much higher, in feet is Town R than M?
Answers
Given parameters:
Elevation of Town M = 282ft
Elevation of Town R = 679ft
Unknown:
How much higher is Town R than M = ?
Solution:
Town M lies below the sea level whereas Town R is above the sea level.
Graphically:
Town R 679ft
↑
↑
↑
↑
↔↔↔ Sea level
↓
↓
Town M 282ft
Town R is 282ft + 679ft higher than Town M = 961ft
Convert 50.0 mL to liters. Use the appropriate significant figures
Answers
Answer:
50 ml = 0.050 liters
Step-by-step explanation:
The solution is:
The mass/volume percent = 16/50 x 100% = 32%
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Explanation
Given:
Mass of NaCl, m = 16.0 g
Volume of solution, v = 50.0 mL
What to find:
The mass/volume percent.
Solution
The mass/volume percent of the solution can be calculated using the formula below
The mass/volume percent = mass/volume x 100%
so, we get,
The mass/volume percent
= 16/50 x 100%
= 32%
Hence, The mass/volume percent is 32%.
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complete question;
Calculate the mass/volume percent (m/v) of 16.0 g NaCl in 50.0 mL of solution.Express your answer to three significant figures.
2 2/3 divided by 1 1/3
Answers
Answer:
2
Step-by-step explanation:
Answer:
It is 2
Step-by-step explanation:
I do not have a true explanation its just quick math to my brain.
Pls help me. I need help
Answers
Answer:
x= horizontal y=vertical55 in feet and inches
Answers
Answer:
1 foot 8 inches
Step-by-step explanation:
A painter charges a flat fee of $100 and $35 per hour (for up to 8 hours), h, that he spends painting. This relationship can be represented by the function f(h)=100+35h where f(h) represents the total amount the painter charges.
Answers
Answer:
I don't know
Step-by-step explanation:
But the question you asked i think you have add and stuff
Lines ℓ and m are intersected by transversal t. ℓ ∥ m. Lines l and m are horizontal with l above m and intersected by transveral t. Angles 1, 2, 3, and 4 are formed where t intersects l with 1 and 3 above l from left to right and 2 and 4 below it. Angles 5, 6, 7, and 8 are formed where t intersects m with angles 5 and 7 above line m from left to right and 6 and 8 below it. If m∠4 = 105, what is m∠5?
Answers
Answer:
<5 = 105 degrees
Step-by-step explanation:
From the description given, since line l is parallel to m then <4 is alternate to <5 and two alternate angles are equal, if thst is the case
<4 = <5 (alternate angle)
Since <4 = 105 degrees, hence m<5 = 105 degrees
Simplify
(sec ∅ - 1)(sec ∅+ 1)
Answers
Answer:
[tex]tan^2(x)[/tex]
Step-by-step explanation:
[tex](sec(x)-1)(sec(x)+1)\\sec^2(x) - 1\\\frac{1}{cos^2(x)} -1\\\frac{1-cos^2(x)}{cos^2(x)} \\\frac{sin^2(x)}{cos^2(x)}\\ \\tan^2(x)[/tex]
Sarah is doing research on the average age of first-year resident physicians. She wants her estimate to be accurate to within 1 year. From past studies, she knows the population standard deviation is 8.265. How many first-year residents must she survey to be 95% confident?
Answers
Answer: The number of first-year residents she must survey to be 95% confident= 263
Step-by-step explanation:
When population standard deviation ([tex]\sigma[/tex]) is known and margin of error(E) is given, then the minimum sample size (n) is given by :-
[tex]n=(\dfrac{z^*\sigma}{E})^2[/tex], z* = Two-tailed critical value for the given confidence interval.
For 95% confidence level , z* = 1.96
As, [tex]\sigma[/tex] = 8.265, E = 1
So, [tex]n= (\dfrac{1.96\times8.265}{1})^2 =(16.1994)^2\\\\= 262.42056036\approx263\ \ \ [\text{Rounded to the next integer}][/tex]
Hence, the number of first-year residents she must survey to be 95% confident= 263
Calculate the slope between the points: (4, -3) and (4,7)
a
m=-1.25
b
m=undefined
C
m=0.5
m=0
Answers
Answer:
B
Step-by-step explanation:
Slope = 10/0 = undefined
ASAP!! If quadrilateral PQRS is a square, what are the coordinates of point E?
Answers
Answer:
E - (28, 25)
Hope this helps!
PLEASE HELP!
You invest $1000 in an account that has an annual interest rate of 4%, compounded monthly for 12 years. What is the equivalent interest rate and how many times will the money be compounded?
0.33% and 1 time
3% and 4 times
3% and 144 times
0.33% and 144 times
Answers
Answer:
The final balance is $1,612.23.
The total compound interest is $612.23.
Step-by-step explanation:
The required equivalent interest rate and money compounded is 0.33% and 144 times respectively. Option b is correct.
Equivalent interest rate for 4% and how many times the money will be compounded to be determine.
What is arithmetic?In mathematics it deals with numbers of operations according to the statements.
Here, the equivalent interest rate = 4%/12
= 1/3
= 0.33%
Now, number of times money compounded = 12 years
= 12 x 12 months
= 144
Thus, the required equivalent interest rate and money compounded is 0.33% and 144 times respectively.
Learn more about arithmetic here:
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which are the possible size lengths of a triangle?
Answers
Answer:
All of those which summed are more that the third side, so the second is the only possible answer.
Step-by-step explanation:
4+8 = 12 which is greather than 10
Answer:
D
Step-by-step explanation:
you need to be able to add all the numbers up and divide by three. D is the only one that makes sense because 8+10=18 18+18=36 36/3=12
Evaluate g(2) =
[tex]g(2) =[/tex]
Answers
Step-by-step explanation:
question is not clear
The triangles shown below must be congruent.
True or false
Answers
Answer:
true
Step-by-step explanation:
they're not dilated in anyway.
Hey, I need help with a math question. thank you <3
Answers
Answer:
B
Step-by-step explanation:
4> 9 + 10
whats the anwsers?
Answers
Answer:
4>19
The statement is false 4 is not bigger than 19.
Which of the following equations have the same solution as 3x-5=5x×11
Answers
Answer:
-5=2x+11
Step-by-step explanation:
Y
Solve the equation, justify
each step with an algebraic
property
50 + 3x = 7x- 2
Answers
Answer:
13
Step-by-step explanation:
Step 1:
50 + 3x = 7x - 2 Equation
Step 2:
50 = 4x - 2 Subtract 3x on both sides
Step 3:
52 = 4x Add 2 on both sides
Step 4:
x = 52 ÷ 4 Divide
Answer:
x = 13
Hope This Helps :)
Add 2 to 50
Add 7x to 3x
solve for x ! I need help
Answers
Answer:
x = 47°
Step-by-step explanation:
This is an exterior angle property, one of the properties in a triangle. The exterior angle theorem states that if a triangle's side gets an extension, then the resultant exterior angle would be equal to the sum of the two opposite interior angles of the triangle.
Answer:
x=45.6
Step-by-step explanation:
(2x-2)+x+45=180
Combine like terms.
3x+43=180
Subtract 43 on both sides.
3x+43=180
-43 -43
3x=137
Divide by 3 on both sides.
3x=137
/3 /3
x=45.6
(I'm not sure if it's right because it's a decimal, but...)hope this helps!!!!! Have an amazing day c:
HELP ILL AWARD BRAINLIEST
Answers
Answer:
Think about it
Step-by-step explanation:
If you made $20 in 2 hrs you made $10 per hour
To find out how much you make per certain number of hrs multiply $10 by the number of hours
The equation is y = 10x + 0 <-- this is also answer to number 4
10x is the constant of proportionality I think.
5 hours: 50 dollars
8 hours: 1600 dollars
I don’t know the rest but I hope this helped for part of it at least:)
Which of the following is equal to 5/7-4/7 (a) 0 (b) 1 (c) undefined (d) 1/7
Answers
Answer:
It's 0.142857
Step-by-step explanation:
Answer:
your answer is d.1/7
Step-by-step explanation:
all you have to do is subtract 5-4 which is 1 then add 7 as the denominator
6x-5=4x+1
x=6
x=0.5
x=2
x=3