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2 years ago

Which graph shows the solution to the system of linear inequalities? x + 3y > 6 y ≥ 2x + 4 PLEASE HELP

Mathematics

2 answers:

Vadim26 [7]2 years ago

4 0

Answer:

Last Graph is the Answer

Step-by-step explanation:

Andrei [34K]2 years ago

3 0

Answer:

x + 3y > 6

Step-by-step explanation:

Find two points that satisfy x + 3y = 6 and draw a DASHED line through them.

It is greater than so shade the section ABOVE that line.

Using the intercept method, the two points I chose are: (0, 2) & (6, 0)

y ≥ 2x + 4

Find two points that satisfy y = 2x + 4 and draw a SOLID line through them.

It is greater than so shade the section ABOVE that line.

The two points I chose are: (0, 4) & (1, 6)

The solution is where the shaded sections overlap.

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Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s.

vampirchik [111]

The correct answer is:

This is the average number of days the house stayed on the market before being sold for $150,000.

Explanation:

f(p) is defined as the average number of days a house stays on the market before being sold for price p (given in $1000).

We want f(150); this means p=150. Since p is in thousands of dollars, this means the price of the house was $150,000.

This means f(150) is the average number of days the house stayed on the market before being sold for $150,000.

4 0

2 years ago

Read 2 more answers

A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

$f (x,y,z) = xy + 2xz + 2yz$ ------ (1)

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

6 0

2 years ago

Which equation is the inverse of (x minus 4) squared minus two-thirds = 6y minus 12?

mario62 [17]

Answer:

The correct option is option B.

Step-by-step explanation:

The given function is

$(x - 4)^{2} - \frac{2}{3} = 6y - 12$

We can rearrange the function as

$(x - 4)^{2} - \frac{2}{3} = 6y - 12$

⇒ 3(x - 4)² - 2 = 18y - 36

⇒ 3(x - 4)² = 18y - 34

⇒ $(x - 4)^{2} = 6y - \frac{34}{3}$

⇒ $x - 4 = \pm \sqrt{6y - \frac{34}{3}}$

⇒ $x = 4 \pm \sqrt{6y - \frac{34}{3}}$

Therefore, the inverse function will be, $y = 4 \pm \sqrt{6x - \frac{34}{3}}$

Therefore, the correct option is option B. (Answer)

7 0

2 years ago

Read 2 more answers

On a state map, a cartographer plots Geocity at coordinates (5, 8) and Shapetown at coordinates (11, 16). How far is it from Geo

Eddi Din [679]

We can solve for the distance between Geocity to Shapetown using the formula for the distance between two points which is shown below:
d² = (x2-x1)²+(y2-y1)²
Such as we have two points:
Geocity (5,8)
Shapetown (11,16)

Solving for the distance, we have:
d² = (11-5)² + (16-8)²
d² = 6² + 8²
d = 10

The answer is 10 units.

7 0

2 years ago

All of the following are equivalent except _____. A:5 over 4. B:1.25. C:12.5%. D:125%.

earnstyle [38]

Hello, there!

5/4 = 1.25

So, we know that the answer is not A or B.

1.25 = 125%

Now, we know that the answer is not D ether.

So, the answer must be C.

I hope I helped!

Let me know if you need anything else!

~ Zoe

3 0

2 years ago

Read 2 more answers