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3 years ago

How many solutions does this system have?

Mathematics

1 answer:

zhenek [66]3 years ago

5 0

Answer:

A. None

General Formulas and Concepts:

<u>Algebra I</u>

Perpendicular Lines/Intersecting Lines have 1 solution.
2 identical Lines have infinitely many solutions.
Parallel Lines have no solution.

Step-by-step explanation:

According to the graph, we see that we have 2 parallel lines. Therefore, there will be no solution.

You might be interested in

Five more than three times a number is that number increased by 40. What is the number

rewona [7]

Let the number be n.

Then 3n+5 = n+40
Combining like terms, we get

2n = 35, and so n = 35/7, or 17 1/2.

6 0

3 years ago

A city council consists of seven Democrats and five Republicans. If a committee of four people is selected, find the probability

Hoochie [10]

Answer:

The probability of selecting two Democrats and two Republicans is 0.4242.

Step-by-step explanation:

The information provided is as follows:

A city council consists of seven Democrats and five Republicans.
A committee of four people is selected.

In mathematics, the procedure to select k items from n distinct items, without replacement, is known as combinations.

The formula to compute the combinations of k items from n is given by the formula:

${n\choose k}=\frac{n!}{k!\times (n-k)!}$

Compute the number of ways to select four people as follows:

${12\choose 4}=\frac{12!}{4!\times (12-4)!}=495$

Compute the number of ways to selected two Democrats as follows:

${7\choose 2}=\frac{7!}{2!\times (7-2)!}=21$

Compute the number of ways to selected two Republicans as follows:

${5\choose 2}=\frac{5!}{2!\times (5-2)!}=10$

Then the probability of selecting two Democrats and two Republicans as follows:

$P(\text{2 Democrats and 2 Republicans})=\frac{21\times 10}{495}=0.4242$

Thus, the probability of selecting two Democrats and two Republicans is 0.4242.

6 0

2 years ago

For what values of x is the trinomial 2x^2-x+55 equal to the square of binomial x+5

jeka94

Answer:

x = 6 , 5. For these values of x they are equal.

Step-by-step explanation:

2x² - x + 55 =(x +5)²

2x² - x + 55 = x² + 2*x*5 + 5²

2x² - x + 55 = x² + 10x + 25

2x² - x + 55 - x² - 10x - 25 = 0

2x² - x² - x - 10x + 55 - 25 = 0

x² - 11x + 30 = 0

x² -6x - 5x + 30 = 0

x(x - 6) - 5(x - 6) = 0

(x - 6)(x - 5) = 0

x - 6 = 0 ; x - 5 = 0

x = 6 ; x = 5

7 0

3 years ago

Read 2 more answers

An airplane flies at a constant speed. It can travel a distance (d) of 1,800 kilometers in 2 hours (t).

ss7ja [257]

D = 900t

because if you want to simplify t (2 hours) into one then you divide 1800 by 2 and that gives you the constant of proportionality (slope) of 900. Using this information you can write the expression d = 900t.

8 0

3 years ago

A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend

anyanavicka [17]

Answer:

The equation of Grant's path is y = 4 - x over 2 ⇒ 2nd answer

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the slope of the line
b is the y-intercept (value y at x = 0)

The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∵ Grant's path is a line from point A to point B

∴ The equation of AB represents Grant's path

Lets find the slope of AB using the formula of the slope above

∵ A = (8 , 0)

∵ B = (-4 , 6)

∴ $x_{1}$ = 8 and $x_{2}$ = -4

∴ $y_{1}$ = 0 and $y_{2}$ = 6

∵ $m=\frac{6-0}{-4-8}=\frac{6}{-12}$

∴ $m=-\frac{1}{2}$

Substitute the value of m in the form of the equation

∵ y = m x + b

∴ y = $-\frac{1}{2}$ x + b

∵ b is the value of y at x = 0

∵ y = 4 at x = 0 ⇒ from the figure

∴ b = 4

∴ y = $-\frac{1}{2}$ x + 4

We can write $-\frac{1}{2}$ x as $-\frac{x}{2}$

∴ y = $-\frac{x}{2}$ + 4

- Switch the two terms of the right hand side

∴ y = 4 - $\frac{x}{2}$

The equation of Grant's path is y = 4 - $\frac{x}{2}$

4 0

3 years ago