All categories

3 years ago

The system of equations graphed below has how many solutions?

Mathematics

1 answer:

Artist 52 [7]3 years ago

5 0

Answer: C) 0

The lines are parallel. They never cross. To have a solution, the lines need to intersect. Each intersection is a solution. That's why there are no solutions here. The system is inconsistent.

Note how the slopes are both 1/2 while the y intercepts are different. Parallel lines have equal slopes but different y intercepts.

You might be interested in

Fedex typically deleviers 2,400 packages per day and uses 75 trucks for delivery. If the number of trucks used per day is propor

irina1246 [14]

Answer:

Step-by-step explanation:

8 0

3 years ago

Cynthia Besch wants to buy a rug for a room that is 24 ft wide and 33 ft long. She

qaws [65]

<h3>Answer: 16 ft by 25 ft</h3>

=========================================================

Explanation:

Refer to the diagram below.

The outer dimensions 24 ft and 33 ft shrink down to 24-2x ft and 33-2x ft respectively. This subtraction of 2x is due to subtracting two copies of x per side.

The carpet has area of (24-2x)(33-2x)

Cynthia can afford to buy 400 sq ft of carpet

So we set 400 equal to that previous expression and solve for x

(24-2x)(33-2x) = 400

24(33-2x) - 2x(33-2x) = 400

792-48x - 66x + 4x^2 = 400

4x^2 - 114x + 792 = 400

4x^2 - 114x + 792-400 = 0

4x^2 - 114x + 392 = 0

From here, use the quadratic formula to isolate x.

Plug in a = 4, b = -114, c = 392

$x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-114)\pm\sqrt{(-114)^2-4(4)(392)}}{2(4)}\\\\x = \frac{114\pm\sqrt{6724}}{8}\\\\x = \frac{114\pm82}{8}\\\\x = \frac{114+82}{8} \ \text{ or } \ x = \frac{114-82}{8}\\\\x = \frac{196}{8} \ \text{ or } \ x = \frac{32}{8}\\\\x = 24.5 \ \text{ or } \ x = 4\\\\$

The two possible solutions are x = 24.5 and x = 4

But if x = 24.5, then 24 - 2x = 24 - 2*24.5 = -25 which isn't possible. We cannot have a negative width or negative length for the carpet.

Luckily x = 4 does work since

24 - 2x = 24 - 2*4 = 16

33 - 2x = 33 - 2*4 = 25

Both results are positive.

Therefore, the carpet has dimensions of <u>16 ft by 25 ft</u>

Check: 16*25 = 400, so the answer is confirmed

5 0

2 years ago

g Bonus: Assume that among the general pediatric population, 7 children out of every 1000 have DIPG (Diffuse Intrinsic Pontine G

patriot [66]

Answer:

0.9586

Step-by-step explanation:

From the information given:

7 children out of every 1000 children suffer from DIPG

A screening test designed contains 98% sensitivity & 84% specificity.

Now, from above:

The probability that the children have DIPG is:

$\mathbf{P(positive) = P(positive \ | \ DIPG) \times P(DIPG) + P(positive \ | \ not \DIPG)\times P(not \ DIPG)}$ $= 0.98\imes( \dfrac{7}{1000}) + (1-0.84) \times (1 - \dfrac{7}{1000})$