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Naya [18.7K]
3 years ago
8

2x+3y=12 and y=x+1.5 in substitution form

Mathematics
1 answer:
Sonbull [250]3 years ago
4 0

Answer:

(1.5, 3)

Step-by-step explanation:

Given the 2 equations

2x + 3y = 12 → (1)

y = x + 1.5 → (2)

Substitute y = x + 1. 5 into (1)

2x + 3(x + 1.5) = 12 ← distribute and simplify left side

2x + 3x + 4.5 = 12

5x + 4.5 = 12 ( subtract 4.5 from both sides )

5x = 7.5 ( divide both sides by 5 )

x = 1.5

Substitute x = 1.5 into (2) for corresponding value of y

y = 1.5 + 1.5 = 3

Solution is (1.5, 3)

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Number 2 help me plz
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Answer:

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7. Convert the subtraction problem into an addition problem.<br> 10- (-5)
dalvyx [7]

Answer:

10 + 5

Step-by-step explanation:

If you are subtracting a negative then it become adding a positive. A way to remember this is because it has matching socks.

7 0
3 years ago
In the diagram below, what is the relationship between the number of triangles and the perimeter?
Eduardwww [97]

The perimeter "P" is equal to the length of the base of one triangle multiplied by the "n" number of triangles in the figure plus two times the length of another side. The equation for the perimeter is P = 5n + 14.

We are given triangles. The triangles are arranged in a certain pattern. The length of the base of each triangle is equal to 5 units. The length of the other two sides is 7 units each. We conclude that all the triangles are isosceles. We need to find the relationship between the number of triangles and the perimeter of the figure. Let the perimeter of the figure having "n" number of triangles be represented by the variable "P".

P(1) = 14 + 5(1)

P(2) = 14 + 5(2)

P(3) = 14 + 5(3)

We can see and continue the pattern. The relationship between the perimeter and the number of triangles is given below.

P(n) = 14 + 5n

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3 0
1 year ago
NEED HELP FOR THIS QUESTION
const2013 [10]

Answer:

(a) A = 0.00278787878787878x

(b) B = 0.00235294117647058x + 3

(c) The answers are as follows:

<u>For buying by credit card</u>

For 700 BWP: Cost = A = £1.95

For 800 BWP: Cost = A = £2.23

For 800 BWP: Cost = A = £2.79

<u>For buying from a Bureau de Change</u>

The equation (4) is used as follows:

For 700 BWP: Cost = B = £4.65

For 800 BWP: Cost = B = $4.88

For 1000 BWP: Cost = B = £5.35

(d) You would have to buy 6,897.54 pulas for the cost to be the same whether you use a credit card or cash.

Step-by-step explanation:

(a) by credit card

For the exchange rate, we have:

8.25 BWP = £1 ⇒ 8.25 / 8.25 BWP = £1 / 8.25 = 1.00 BWP = £0.121212121212121

The expression can therefore be written as follows:

A = £0.121212121212121 * r * x ................. (1)

Where;

A = cost (including commission) of buying a particular number of Botswana pulas by credit card

r = commission on a credit card transaction = 2.3%, or 0.023

x = the number of pulas bought

Substituting for r into equation (1), we have:

A = £0.121212121212121 * 0.023 * x

A = 0.00278787878787878x ................. (2)

Equation (2) is the expression.

(b) from a Bureau de Change

For the exchange rate, we have

8.5 BWP = £1 ⇒ 8.5 / 8.5 BWP = £1 / 8.5 = 1.00 BWP = 0.117647058823529

B = (£0.117647058823529 * r * x) + F ................. (3)

Where;

B = cost (including commission) of buying a particular number of Botswana pulas by from a Bureau de Change.

r = commission charged by Bureau de Change. = 2%, or 0.02

x = the number of pulas bought

F = fee = £3

Substituting for r and F into equation (3), we have:

B = (£0.117647058823529 * 0.02 * x) + £3

B = 0.00235294117647058x + 3 ................. (4)

Equation (4) is the expression.

c. Evaluate each of these expressions for 700 BWP, 800 BWP, and 1000 BWP respectively.

<u>For buying by credit card</u>

The equation (2) is used as follows:

For 700 BWP: A = £0.00278787878787878 * 700 = £1.95

For 800 BWP: A = £0.00278787878787878 * 800 = £2.23

For 800 BWP: A = £0.00278787878787878 * 1000 = £2.79

<u>For buying from a Bureau de Change</u>

The equation (4) is used as follows:

For 700 BWP: B = (£0.00235294117647058 * 700) + £3 = £1.65 + £3 = £4.65

For 800 BWP: B = (£0.00235294117647058 * 800) + £3 = £1.88 + £3 = $4.88

For 1000 BWP: B = (£0.00235294117647058 * 1000) + £3 = £2.35 + £3 = £5.35

d. Hazard a guess as to the number of pulas you would have to buy for the cost to be the same whether you use a credit card or cash.

This can be calculated by equating equations (2) and (4) and then solve for x as follows:

0.00278787878787878x = 0.00235294117647058x + 3

0.00278787878787878x - 0.00235294117647058x = 3

x(0.00278787878787878 - 0.00235294117647058) = 3

x0.0004349376114082 = 3

x = 3 / 0.0004349376114082

x = 6,897.54 pulas

Therefore, you would have to buy 6,897.54 pulas for the cost to be the same whether you use a credit card or cash.

5 0
3 years ago
You are analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur. As p
kvasek [131]

Answer:

0.784

Step-by-step explanation:

Given that you are  analyzing the allele frequencies for fur color in a population of squirrels where black fur is dominant to red fur.

As part of your research, you collect the following data:

Total individuals: 1,000

Red fur individuals: 216

So black fur individuals = 1000-216\\=784

p2 = proportion of black fur individuals to total individuals

= \frac{784}{1000} \\=0.784

4 0
3 years ago
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