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xenn [34]
2 years ago
12

Solve t/he system of linear equations given by x + y = 1 and ax − by = c, where a, b, c are real numbers. Note: The solution in

this case will not be numbers but formulas containing a, b, and c. Need help ASAP!!
Mathematics
1 answer:
Phantasy [73]2 years ago
8 0

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

x + y = 1 → (1)

ax - by = c → (2)

In (1) subtract y from both sides

x = 1 - y → (3)

Substitute x = 1 - y into (2)

a(1 - y) - by = c ← distribute left side

a - ay - by = c ( subtract a from both sides )

- ay - by = c - a ( multiply through by - 1 )

ay + by = a - c ← factor out y from each term on the left side

y(a + b) = a - c ← divide both sides by (a + b)

y = \frac{a-c}{a+b} ← substitute into (3)

x = 1 - \frac{a-c}{a+b} = \frac{a+b}{a+b} - \frac{a-c}{a+b} = \frac{a+b-a+c}{a+b} = \frac{b+c}{a+b}

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In Omak the sales tax is 8.4%. What is the total cost including tax Aakel spent on a $48 purchase?
Vikki [24]

Answer:

$52.03

Step-by-step explanation:

1. Approach

To solve this problem, first one needs to calculate the sales tax, then one must add that to the amount spent on the purchase. To calculate sales tax, one must convert the percent to decimal form, this can be done by dividing the percent by 100. Then one will multiply the decimal by the amount spent.

2. Find the tax

As states above; to calculate sales tax, one must convert the percent to decimal form, this can be done by dividing the percent by 100. Then one will multiply the decimal by the amount spent.

<u>a. convert percent to decimal</u>

8.4 / 100 = 0.084

<u>b. multiply the decimal by the amount spent</u>

48 * 0.084 = 4.032

The amount spent on sales tax is, $4.032

3. Find the total amount spent

Now all one has to do is add the amount spent in tax by the amount spent on the purchase.

48 + 4.032 = 52.032

Since money is only spent rounded to the second decimal point, one has to round the number;

52.03

6 0
2 years ago
Solve for x: |x − 2| + 10 = 12 (1 point)
True [87]

Answer:

I think that would be 1

Step-by-step explanation:

Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.

6 0
2 years ago
Read 2 more answers
At a toy factory, toy cars are produced on an assembly line. It takes 2.054 s to attach each of the four wheels. It takes 3.652
IrinaK [193]
Add together the time it takes to put on the four wheels and the hood.
2.054s +3.652s = 5.704s

multiple this answer by 42

5.706s times 42= 239.652s


answer number two is correct
8 0
3 years ago
A uniform bar of length l and weight w is attached to a wall with a hinge that exerts a horizontal force hx and a vertical force
maria [59]
The answer is Hx = ½ Wsin θ cos θ
The explanation for this is:
Analyzing the torques on the bar, with the hinge at the axis of rotation, the formula would be: ∑T = LT – (L/2 sin θ) W = 0
So, T = 1/2 W sin θ. Analyzing the force on the bar, we have: ∑fx = Hx – T cos θ = 0Then put T into the equation, we get:∑T = LT – (L/2 sin θ) W = 0
4 0
4 years ago
A certain element has a half life of 2.5 billion years. a. You find a rock containing a mixture of the element and lead. You det
sashaice [31]

Answer:

Step-by-step explanation:

For a first order decay, fraction remaining = 0.5n where n = number of half lives elapsed.

fraction remaining = 55% = 0.55

0.55 = 0.5n

log 0.55 = n log 0.5

-0.2596 = -0.301 n

n = 0.8625 = # of half lives elapsed

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b)  0.15 = 0.5n

log 0.15 = n log 0.5

-0.824 = -0.301 n

n = 2.74 half lives

2.5 billion years/half life x 2.74 half lives = 6.85 billion years = age of rock

7 0
3 years ago
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