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3 years ago

10

Find the slope and y intercept of the line represented by each table

1 answer:

d1i1m1o1n [39]3 years ago

5 0

5. m=3 because 6/2 is the slope. b= 1

6. m= -4 because -20/5 is the slope. b= 140

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Simplify the expressions.<br><br> i32 = <br><br> i25 = <br><br> i86 = <br><br> i51 =

maw [93]

Simplify the expression using the definition of an imaginary number i = sqrt -1

i32 = 1

i25 = i

i86 = -1

i51 = -i

3 0

3 years ago

Find the arc length for arcs of circles as follows:

Sauron [17]

Answer:

≈ 11.78 in

Step-by-step explanation:

The arc length is calculated as

arc = circumference of circle × fraction of circle

= 2πr × $\frac{\frac{\pi }{4} }{2\pi }$ ( cancel 2π on numerator/ denominator )

= 15 × $\frac{\pi }{4}$

= $\frac{15\pi }{4}$

≈ 11.78 in ( to 2 dec. places )

6 0

2 years ago

If I’m asked to simplify an expression does that mean I shorten it or solve it?

DochEvi [55]

Answer:

Solve it

Step-by-step explanation:

When you're asked to simplify an expression it means to solve it.

4 0

3 years ago

Read 2 more answers

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

What is the simplified form of x+8/4-x+5/4

kap26 [50]

Answer:

Step-by-step explanation:

x+ 8/4 -x+ 5/4

= x+2+-x +5/4

Combine Like Terms:

x+2+-x+ 5/4

(x+x)+ ( 2 +5/4)

= 13/4

5 0

3 years ago

Read 2 more answers