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3 years ago

How many solutions does the system have?

Mathematics

1 answer:

klio [65]3 years ago

4 0

it have manny solution it depand on a method u are using

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

Catherine reads 7 1/2 pages of mystery book in 9 minutes. What is her average reading rate in pages per minute?

ki77a [65]

7 1/2 pages divided by 9 minutes is 5/6 pages per minute.

4 0

3 years ago

Beth can swim 2 laps in 7 minutes what is Beth rate in minutes per lap

Bond [772]

The answer is 1 lap/3.5 minutes

4 0

3 years ago

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1100 students attend Ridgewood Junior High School. 4% of students bring their lunch to school everyday. How many students brough

Triss [41]

Answer:

the answer is 44 students.

Step-by-step explanation:

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3 years ago

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Special right triangles 45-45-90 & 30-60-90 formula!!<br> finding missing side lengths

nordsb [41]

The formula you need to know is that the side opposite of the 30° angle is always half the hypotheneus. For example in question 2 X should be 6 since 3 is opposite side of the angle 30°. In a 45 45 90 triangle, it is important to know that the straight sides are always the same length (since they are the same angle). For example in question 9, v is also 9√2.

When you have two sides, you can figure out the third side with a² + b² = c² since they are all right triangles. Good luck

4 0

3 years ago