Simplify. √24 A √38 B √212 C √26 D √46

Does the system have one solution, no solution, or infinitely many? Use your substitution to justify your answer

Taya2010 [7]

Answer: It has one solution. The solution is (x,y) = (-4,-3)

Add up the equations doing so straight down

x + -x = 0x = 0 so the x terms go away

2y + 2y = 4y

-10 + (-2) = -12

We end up with 4y = -12 so y = -3 after you divide both sides by 4. Use this y value to find the value of x

x+2y = -10

x + 2(-3) = -10

x - 6 = -10

x = -10+6

x = -4

The single solution is (x,y) = (-4,-3)

As a check, plug this solution into each equation to see if you get a true statement or not. Let's do so with the first equation

x+2y = -10

-4 + 2(-3) = -10

-4 - 6 = -10

-10 = -10 .... true

and then the second equation

-x+2y = -2

-(-4) + 2(-3) = -2

4 - 6 = -2

-2 = -2 .... true

both equations are true, so the solution is confirmed

4 0

2 years ago

A community theater uses the function p (d) = (-4d+40) (d−40) to model the profit (in dollars) expected in a weekend when the ti

fomenos

The theater make the maximum profit at d = $25. Then the maximum profit of the theatre is $ 900.

<h3>What is differentiation?</h3>

The rate of change of a function with respect to the variable is called differentiation. It may be increasing or decreasing.

A community theater uses the function P(d) = (− 4d + 40) (d − 40) to model the profit (in dollars) expected on a weekend when the tickets to a comedy show are priced at d dollars each.

Then the maximum profit of the theatre will be

The function is P(d) = (− 4d + 40) (d − 40)

Differentiate the function with respect to d and put it equal to zero for maximum or minimum profit.

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= 0\\\\\dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) &= 0\\\\(-4d+40) -4 (d-40) &= 0\\\\-8d + 200 &= 0\\\\d &= 25 \end{aligned}$

Then the checking for maximum or minimum, again differentiate, we have

$\begin{aligned} \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(- 4d + 40) (d - 40) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= \dfrac{\mathrm{d} }{\mathrm{d} d}(-8d + 200) \\\\\dfrac{\mathrm{d} }{\mathrm{d} d}P(d) &= -8\\\\ \dfrac{\mathrm{d} }{\mathrm{d} d}P(d) & < 0\end{aligned}$

The value is less than zero hence maximum value will occur at d = 25.

Then maximum profit will be

P(d) = (− 4×25 + 40) (25 − 40)

P(d) = (− 100 + 40) (−15)

P(d) = (− 60) (− 15)

P(d) = $ 900

More about the differentiation link is given below.

brainly.com/question/24062595

#SPJ1

7 0

1 year ago

The wingspans of a common species of housefly are normally distributed with a mean of 5mm and a standard deviation of 0.5mm. Sup

Anuta_ua [19.1K]

Answer:

Approximately Normal

Step-by-step explanation:

Since the population is normally distributed, the sampling distribution of the sample mean will also be normally distributed, even when the sample size is small.

6 0

1 year ago

Whats your favorite color? (free points) :)

aniked [119]

Answer:

My favourite color is The Red and White;)

What's yours?

don't forget to like and mark me

6 0

2 years ago

Read 2 more answers

Find the inverse of Y=2x-6