Solve the system of linear equations using any method you choose:
-6x + 3y = 18
10x - y = 4
Answers
9514 1404 393
Answer:
(x, y) = (1.25, 8.5)
Step-by-step explanation:
I choose to put these equations into reduced general form, then use the "cross multiplication method" to solve.
2x -y +6 = 0
10x -y -4 = 0
d1 = 2(-1) -10(-1) = 8
d2 = -1(-4) -(-1)(6) = 10
d3 = 6(10) -(-4)(2) = 68
Solutions are ...
x = d2/d1 = 10/8 = 1.25
y = d3/d1 = 68/8 = 8.5
The solution is (x, y) = (1.25, 8.5).
_____
Additional comment
I like a graphing calculator for a quick and easy solution. When the values are not integers, I like an algebraic solution to see what the exact values are.
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The "cross multiplication method" is similar to Cramer's rule in that determinants of pairs of coefficients are computed. If you look up this method, videos will show you a variation that is slightly different. Here, we determined d1, d2, and d3 as the 2×2 determinant of the coefficients in adjacent columns of the array you get from the general form equations with the first column repeated:
[tex]\begin{array}{cccc}2&-1&6&2\\10&-1&-4&10\end{array}[/tex]
In each pair, the determinant is the difference between the product of numbers on the down-diagonal and the product of numbers on the up-diagonal.
The determinants relate to the x- and y-values by ...
1/d1 = x/d2 = y/d3 ⇒ x = d2/d1, y = d3/d1
There is a Vedic solution method for linear equations that is similar to this, but starts from equations in standard form. As a consequence, the cross-differences are done in a different order.
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Standard form: ax +by = c
General form: ax +by +c = 0
Related Questions
Matthew poured 28 quart of lemonade from a pitcher into a smaller container. There was 58 quart left in the pitcher. What amount of lemonade did Matthew originally have in the pitcher?
Answers
Answer:
86 quarts
Step-by-step explanation:
If you took away 28 quarts and were left with 58 quarts then you add the two numbers to get 86 quarts which is what you started with.
Someone pls help me with these worksheets.
(Please answer properly, if u don't know, just ignore it)
Answers
Answer:
i wrote answer of the question 1 to 4 but i don't know the answer to 5
Answer: 1) (3,0) 2) (4,2) 3) (5,1) not sure about 4 and 5
1) (3,7/2) 2) (1,-4) 3) (-3,2) im bad at word problems, sorry.
Step-by-step explanation: all i can say without sounding confusing is divide on both sides!! <3
It is predicted that the value of a home will decrease by a rate of 4.6% annually due to a recent recession. Today, the value of the home is $185,000. What is the predicted value of the home in 6 years?
Answers
Answer:
$139 463.95
Step-by-step explanation:
100% - 4.6% = 95.4%
95.4% ÷ 100 = 0.954
0.954 --> decimal multiplier
$185 000 × 0.954^6 = $139 463.95
Hope this helps! <3
What is the answer to, one half of 9?
Answers
4.5
Step-by-step explanation:
One half of 9 = 9/2 = 4.5
Order the fallowing numbers from least to greatest put the lowest number on the left. -4 , 2 , -1, 3
Answers
Answer:
-4,-1,2,3
Step-by-step explanation:
Cliff earns $15 for each hour that he works as a television sales person plus an additional $10 for each television that he sells which of the following represents the amount cliff earns , in dollars, if he sells n television and works h hours ?
Answers
Answer:
15h+10n
Step-by-step explanation:
You forgot to list the equations.
10 * n = 10n = $ paid for amount of televisions sold
15 * h = 15h = $ paid for hours worked
15h + 10n = Total amount paid
The answer for n television sold and h hours working is 15h +10n.
Expression:
An expression is an algebraic or mathematical statement in which some variable and constant are arranges with any algebraic operations
Given that
Cliff earned for one hour = $15
Therefore for h hours = 15h
Also he earned additional for each television sold = $10
Therefore for n television sold = 10n
How to add the algebraic terms?Here 15h and 10n are two algebraic numbers because there is constants 15 and 10 and variables h and n are multiplied simultaneously.
Therefore the total earning is the addition of both
15h + 10n
The final answer is 15h + 10n
Learn more about expression here-
https://brainly.com/question/4344214
#SPJ2
60 is the product of Javier's age and 5
Translate this sentence into an equation
Answers
Answer:
J= Javiers age
5J=60
5J/5= 60/5
J= 12
Check:
5(12)= 60
60=6p
Step-by-step explanation:
see answer
hope this helps
Do you think you could use a multiply a 4 digit number by a 1 digit number
Answers
Answer:
line them up straight with the bottom number and the top number.
A line that passes through (3, 1) and (0, -3)
Answers
Ms. Mary spent $192 less than Ms.Mona on supplies for their class. Together they spent a total of $988. How much did each person spend?
Answers
Answer:
Ms. Mona and Ms. Mary spent $590 and $398 respectively.
Step-by-step explanation:
Total spent= $988
Ms. Mary +Ms. Mona= $988
Since Ms. Mary spent $192 less than Ms. Mona,
(Ms. Mona -$192) +Ms. Mona= $988
2(Ms. Mona)= $988 +$192
2(Ms. Mona)= $1180
Amount Ms. Mona spent
= $1180 ÷2
= $590
Since Ms. Mary spent $192 less than Ms. Mona,
amount Ms. Mary spent
= $590 -$192
= $398
Alternatively, since the total spending is $988,
amount Ms. Mona spent
= $988 -$590
= $398
How long would it take to earn Php 8,000 on a principal of Php 20,000 at 5% simple interest rate?
Answers
The length of time it would take the given principal to become Php 8,000 is 8 years.
The formula that would be used to determine the length of time it would take Php 20000 to accumulate an interest of Php 8000 can be determined using this formula:
Time = Interest earned / (principal x interest rate)
8000 / (20,000 x 0.05)
= 8 years
To learn more about simple interest, please check: brainly.com/question/9352088?referrer=searchResults
16. In April, Harry received his phone bill and found that he was charged $40 for 120
minutes of talking. In May, Harry received his phone bill and found that he was
charged $50 for 140 minutes of talking
Part A: Find the rate that Henry is charged for each minute of use.
a. $2 per minute
b. $1 per minute
C. $5 per minute
d. $0.50 per minute
Part B: Describe an equation in point slope form for calculating the cost (y) based on
minutes of use (x)
Answers
Step-by-step explanation:
A. Take two pairs of points:
(120, 40) and (140, 50)Find the rate of change:
(50 - 40)/(140 - 120) = 10/20 = 0.5This is the rate, $0.50 per minute
B. Take one pair of points (120, 40) to show the relationship between number of minutes and the cost:
y - 40 = 0.5(x - 120)1. This yield sign has equal sides and a perimeter of 136 cm. How long is each side?
Answers
Answer:
45 1/3 cm
Step-by-step explanation:
A yield sign is a triangle so it has 3 sides.
If the perimeter is 136 cm meaning 3x = 136 because all the sides are equal so you can multiple the length of each side by 3 to find the perimeter
3x = 136
x = 136/3
x = 45 1/3
each side is about 45 1/3 cm
Dita adds 2 oz of milk to an 18 oz cup of coffee that is 10% milk. What is the percentage of milk in the resulting mixture?
SHOW YOUR WORK!
Answers
Increasing the amount of milk in the coffee increases the percentage of milk in the cup of coffee.
The resulting mixture is 19% milkReasons:
The known quantities are;
The volume of milk Dita adds to an cup of coffee = 18 oz
The percentage of milk in the cup of coffee = 10%
Required:
The percentage milk in the resulting mixture.
Solution:
Initial amount of milk initially in the cup of coffee = 10% × 18 oz = 1.8 oz
The total amount of milk in the resulting mixture = 2 oz + 1.8 oz = 3.8 oz
Volume of the resulting mixture = 2 oz + 18 oz = 20 oz
The percentage of milk in the resulting mixture is therefore;
[tex]\displaystyle \mathrm{Percentage \ of \ milk = } \frac{3.8}{20} \times 100 = 19\%[/tex]
The resulting mixture is 19% milk.
Learn more here:
https://brainly.com/question/22599498
Evaluate : X + 2 ( x -20) (4)
for x = 10
Answers
Answer:
x + 2 ( x - 20 )( 4 ) = -70
Step-by-step explanation:
hope this helps. . .<3
Which equation represents a line which is parallel to the line y=1/5x -1
5x +y =3
X+ 5y =10
5y - x = -20
5x - y = -3
Answers
9514 1404 393
Answer:
(c) 5y - x = -20
Step-by-step explanation:
When the x- and y-terms are on the same side of the equation, the slope of the line will be ...
m = -(coefficient of x)/(coefficient of y)
So, the slopes of the offered choices are ...
a) -5/1 = -5
b) -1/5
c) -(-1)/5 = 1/5 . . . . . parallel to given line
d) -5/-1 = 5
The lines will be parallel when their slopes are the same. The slope of the given line is the coefficient of x, 1/5. Choice C has the same slope.
whats the answer can someone answer please
Answers
Answer:
b
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
3 is being distributed into x and 3 inside the parenthesis. So it is distributive property.
Consider two congruent square prisms each rectangular face of prism A has a width of 2x+3 and each rectangular face of prism B had a length of 4x+6 if each rectangular face of prism A has and area of 25x+25 what is the volume of prism B (round to the nearest whole number)
Answers
Answer:
Step-by-step explanation:
prism A side area is square of side length
(2x + 3)² = 25x + 25
4x² + 12x + 9 = 25x + 25
4x² - 13x - 16 = 0
x = (13 ±√(13² - 4(4)(-16))) / (2(4))
positive answer is
x = (13 +√425)/8 which is approximately 4.20194...
so side length of B is
4((13 +√425)/8) + 6 which is approximately 22.80776...
Volume is side length cubed
V = (4((13 +√425)/8) + 6)³ which is approximately 11,864.4643...
V = 11,864 units³
The following statement is from the contract Peter signed with his Homeowner's Association (HOA).
"Overnight parking on community streets is prohibited. For the purpose of this contract, 'overnight' will be defined as the hours between 11:00 p.m. and 4:00 a.m. The HOA will monitor overnight parking not less than once every calendar week with nightly patrols by community security.
"In the event a car is found parked on community streets overnight and that ownership of the offending car can accurately be verified as a community homeowner, the homeowner will receive one (1) written warning asking him or her to correct the situation. A second and third infraction by the same homeowner, whether or not it is with the same car, will result in a monetary fine as permitted by CC&R guidelines and HOA bylaws. Further infractions (past 3) will result in monetary fines in addition to the towing of the car at the homeowner's expense."
Because of the extremely low ground effects and body profile on his racing car, Peter is unable to drive his car off of the street and onto the driveway. He has parked on the street overnight for the past five weeks. He has received one written warning and one monetary fine from the HOA. What consequences should Peter expect after this week's security check?
a.
His car will be towed.
b.
He will receive another monetary fine.
c.
He will receive a monetary fine and his car will be towed.
d.
A "boot" will be place on his car to prevent him from driving it.
Answers
Determine the number of solutions to the the equation: 2 (x - 3) + 9 = 5 + x - 1
Answers
Answer:
2×-6+9=5+×-1
2×-×=5-1+6-9
×=1
Solve it ( i'll select u as brainlist )
Answers
Answer:
b is ur answer
Step-by-step explanation
hope this helps :)
please help asap and please give real answers
Answers
Answer:
x = 2, x = - 5
Step-by-step explanation:
To factor it, you can split the middle term to get:
x² - 2x + 5x - 10 = 0
Then, you can factor the first two and the last two to get:
x (x - 2) + 5(x - 2) = 0
And if you divide both sides by (x - 2) you get:
(x - 2) (x + 5) = 0
Finally, this can be solved by the Zero Product Property which states that if x*y=0, then x and/or y has to be equal to 0. If you apply it to the eqaution you get:
x - 2 = 0, x + 5 = 0
which results in:
x = 2, x = - 5
A line is reflected. Which of these could be the result?
Answers
b bcause i knew it and i mean i have a 5.0 gpa
32 is 40 percent of what number? A 12.8 B 128 C 114 D 124
Answers
Answer: C
.Step-by-step explanation:
it was right for me so if its wrong im sorry :)
June earned $ 75 last week. April earned $25. June earnings were how many times greater than April
Answers
Answer:
3 times
Step-by-step explanation:
75÷25=3 times greater than April
Find the inverse function of f informally.
Answers
Answer:
What is f?
Step-by-step explanation:
A basket containing 150mangoes cost 450 find the selling price of an orange if it is to be sold at a profit of 5%
Answers
Answer:
The selling price cost 472.5
Step-by-step explanation:
Let's find the profit first.
To find that, let's turn 5% to decimal form.
5 % = 0.05
Then, lets multiply it to the initial price which is 450
450 * 0.05 = 22.5
So the profit costs 22.5
Now, let's add the profit to the initial cost to find the selling price
450 + 22.5 = 472.5
That's it.
Please please help please help me help please help me
Answers
A rectangular photograph has an area of 48 square inches. If the width of the photograph is 8 inches less than its height, find the dimensions of the photograph
The height of the photograph is
Answers
Answer:
H= 12, W=4
Step-by-step explanation:
let H = height
let H-8 = width
We know that the area of the rectangle is A = H*W
now we substitute the statements we have made:
H(H-8) = 48
H^2 - 8H - 48 = 0
Simplify:
(H-12)(H+4) = 0
So now we have 2 options H = -4 or H = 12, having a -ve number as height does not make sense so we use 12.
We know that width is H-8 so now we do 12-8 which is 4.
Therefore width is 4 and height is 12.
Convert to an exponential equation.
In 17 = 2.8332
Answers
Answer:
17 = e^2.8332
Step-by-step explanation: