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Kipish [7]
3 years ago
15

What is the GCF of 81 and 180?

Mathematics
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
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