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3 years ago

x = y - 3 x + 3y = 13 What is the solution to the system of equations? A) (1, 4) B) (4, 1) C) (7, 4) D) (2.5, 5.5)

1 answer:

6 0

X+ 3y = 13
(y - 3) + 3y =13
4y - 3 = 13
4y -3 + 3 = 13+3
4y = 16
4y/4 = 16/4
y=4

x = 4 - 3
x = 1

A) (1, 4)

Check x+3y =13
1+ 3(4) =13
1 + 12=13
13=13

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Pearl's Biking Company manufactures and sells bikes. Each bike costs £40 to make, and the company's fixed costs are £5000. In ad

____ [38]

Answer:

R(x) =300·x - 2·x²

C(x) = £5000 + £40 × x

The break even points are 23.47 and 106.53 or 23 and 107 bikes

Step-by-step explanation:

Given that the price function P(x) = 300 -2·x

Cost per bike = £40

The revenue function R(x) is given by bike price × total number of bikes manufactured and sold

∴ R(x) = P(x)×x = (300 - 2·x)×x = 300·x - 2·x²

The company's cost function, C(x) is Fixed cost + cost to produce each bike × total number of bikes produced

∴ C(x) = £5000 + £40 × x

The break even point is given by the relation;

Total revenue - total cost = 0

That is, break even point is R(x) - C(x) = 0

300·x - 2·x² - (5000 + 40·x) = 0

-2·x²+260·x-5000 = 0 or 2·x²- 260·x + 5000 = 0

Factorizing, we have;

(x - (65 -5√69))(x - (65 +5√69))

Solving gives x = 23.47 or 106.53

Therefore, the break even points are 23.47 and 106.53.

That is the company is profitable when they produce less than 23 bikes or more than 107 bikes.

3 0

3 years ago

Kent and Bradley both work at a car dealership. Kent makes $10/hour + 3% on the amount of sales he completes. Bradley only makes

Masteriza [31]

Answer: There is difference of $660 in their paychecks.

Step-by-step explanation:

Since we have given that

Number of hours in one week they worked = 40

Amount of sales = $78000

Kent makes $10 per hour plus 3% on the amount of sales .

So, the equation for Kent becomes,

$10\times 40+\frac{3}{100}\times 78000\\\\=400+3\times 780\\\\=400+2340\\\\=\$2740$

Similarly, Bradley only makes $7 per hour but he makes 4% on the amount of his sales .

So, the equation for Bradley becomes,

$7\times 40+\frac{4}{100}\times 78000\\\\=280+4\times 780\\\\=280+3120\\\\=\$3400$

hence, the difference between of their paychecks is given by

$\$3400-\$2740\\\\=\$660$

Therefore, there is difference of $660 in their paychecks.

3 0

2 years ago

Please help! Very confused,

Alex777 [14]

The answer is probably c

8 0

3 years ago

Read 2 more answers

Find the distance between the two points. Round to the nearest tenth if necessary. (6, 11), (0, 3) a. 10 b. 14 c. 15 d. 100

lorasvet [3.4K]

Answer: option a

Step-by-step explanation:

You must apply the formula for calculate the distance between the two points. which is shown below:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Therefore, keeping on mind that the points given in the problem are (6, 11), (0, 3), when you substitute values into the formula shown above, you obtain that the distance between these two points is the following:

$d=\sqrt{(0-6)^2+(3-11)^2}\\d=10$

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2 years ago

Read 2 more answers

What power of 10 is used to write the number

Anastasy [175]

Answer: Seventh power of 10

Step-by-step explanation:

X > 1 so exponent will be positive and decimal point moves left. At each point divide X by 10, add 1 to exponent of 10. Exponent starts at zero.

Each time you move the decimal point one to left, you have divided the number by 10, so you have to compensate by multiplying the 10^n factor by 10, say 10 × 10^3 = 10×10×10×10 = 10^4.

12345678 = 12345678 × 10^0

= 1234567.8 × 10^1

= 123456.78 × 10^2

= 12345.678 × 10^3

= 1234.5678 × 10^4

= 123.45678 × 10^5

= 12.345678 × 10^6

= 1.2345678 × 10^7

Each time you move decimal to right, you have multiplied the number by 10, so you have to compensate by dividing the 10^n by 10, subtracting one from exponent.

0.000123 × 10^0 = 0.00123 × 10^-1

= 0.0123 × 10^-2 = 0.123 × 10^-3 = 1.23 × 10^-4

10^-2 / 10 = (1/(10×10)) / 10 = 1/(10×10×10) = 10^-3

6 0

3 years ago