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3 years ago

10

A bottle contains 120 fluid ounces

1 answer:

inessss [21]3 years ago

4 0

Answer:

B. 4.05 liters

Step-by-step explanation:

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The point (5,6) is the solution to which of the following systems of equations

VikaD [51]

Answer:

i dont know

Step-by-step explanation:

e

3 0

2 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

Show that the triangle below is not a right-angled triangle.

Paha777 [63]

Step-by-step explanation:

A right triangle is a triangle in which one of the angles is a 90∘ angle.

$(5x - 8) + (2x - 5) + (2x + 3) = 180 \\ 9x - 10 = 180 \\ 9x = 190 \\ x = \frac{190}{9} \\ x = 21.11$

$(5x - 8) =97.56 \\ (2x - 5) =37.22 \\ (2x + 3) =45.22 \\$

Since None of the angels is 90° , so the triangle is not a right triangle.

7 0

2 years ago

Please help me with this!

salantis [7]

The original area of a face would be a^2. Now that you added b to the edge, the new area of each face would be (a+b)^2. To find how much the are increased, subtract a^2 from (a+b)^2. $(a+b)^2-(a^2)= a^2+2ab+b^2-(a^2)= 2ab+b^2= b(2a+b)$ So the answer is b(2a+b)

6 0

2 years ago

Read 2 more answers

Help please thankssss

Bad White [126]

The answer to your question is r=6

8 0

9 months ago