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3 years ago

15

What is the GCF of 81 and 180?

1 answer:

IgorC [24]3 years ago

4 0

Answer:

9

Step-by-step explanation:

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The coordinate grid shows points A through K. What point is a solution to the system of inequalities? y ≤ −2x + 10 y > 1 over

vlabodo [156]

Answer:

A, C, D and K

Step-by-step explanation:

First, plot the solution set to the system of two inequalities.

The inequality $y\le -2x+10$ determines solid line and bottom shaded region under this line.

The inequality $y>\dfrac{1}{2}x-2$ determines dotted line and top shaded region under this line.

The intersection of these two regions is the solution set to the system of two inequalities.

Points A, C, D and K belong to this region.

4 0

3 years ago

Pam has 90 m of fencing to enclose an area in a petting zoo with two dividers to separate three types of young animals. The thre

andrew-mc [135]

Answer:

The area function is

$A=\frac{135}{2}x-\frac{9}{2}x^2$ .

The domain and range of A is $(0,15m)$ and $(0, 253.125 m^2]$ .

Step-by-step explanation:

The given length of fencing is $90 m$ .

Let the length and width of each pen be $x$ and $y$ respectively as shown in the figure.

As there are 3 pens, so, the total area,

$A= 3 xy \;\cdots (i)$

From the figure the total length of fencing is $6x+4y$ .

Here, for a significant area for the animals, $x>0$ as well as $y>0$ as $x$ and $y$ are the sides of ben.

From the given value:

$6x+4y=90\;\cdots (ii)$

$\Rightarrow y=\frac {45}{2}-\frac{3x}{2}$

Now, from equation (i)

$A=3x\left(\frac {45}{2}-\frac{3x}{2}\right)$

$\Rightarrow A=\frac{135}{2}x-\frac{9}{2}x^2\;\cdots (iii)$

This is the required area function in the terms of variable $x$ .

For the domain of area function, from equation (ii)

$x=15-\frac{2y}{3}$

$\Rightarrow x$ [as y>0]

So, the domain of area function is $(0,15m)$ .

For the range of area function:

As $x \rightarrow 0$ or $y\rightarrow 0$ , then $A\rightarrow 0$ [from equation (i)]

$\Rightarrow A>0$

Now, differentiate the area function with respect to $x$ .

$\frac {dA}{dx}=\frac{135}{2}-9x$

Equate $\frac {dA}{dx}$ to zero to get the extremum point.

$\frac {dA}{dx}=0$

$\Rightarrow \frac{135}{2}-9x=0$

$\Rightarrow x=\frac{15}{2}$

Check this point by double differentiation

$\frac {d^2A}{dx^2}=-9$

As, $\frac {d^2A}{dx^2}$ , so, point $x=\frac{15}{2}$ is corresponding to maxima.

Put this value back to equation (iii) to get the maximum value of area function. We have

$A=\frac{135}{2}\times \frac {15}{2}-\frac{9}{2}\times \left(\frac {15}{2}\right)^2$

$\Rightarrow A=253.125 m^2$

Hence, the range of area function is $(0, 253.125 m^2]$ .

4 0

3 years ago

here is a list of numbers. 7,12,16,20,27,40,56,64. a work out the difference between the two square numbers in the list. b work

poizon [28]

Answer:

see below

Step-by-step explanation:

7,12,16,20,27,40,56,64

The square numbers are 16 = 4^2 and 64 = 8^2

The difference is 64 - 16 =48

The cube numbers are 27 = 3^3 and 64 = 4^3

64 - 27 =37

4 0

3 years ago

Read 2 more answers

How many solutions does the system of equations have?

SIZIF [17.4K]

The answer is d) none because substituting -1/4x + 5/3 for y in the first equation gives 3x - 3x + 5/3 = 20 so 5/3 = 20 which is not true.

8 0

3 years ago

Why does the shape of the distribution of the weights of russet potatoes tend to be symmetrical?

Sergio [31]

Answer:

Mean ≈ Median

6 0

3 years ago

Read 2 more answers