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Makovka662 [10]

3 years ago

13

This table shows how the cost of Dana’s birthday party depends on the number of guests. What is the price per guest?

1 answer:

krok68 [10]3 years ago

6 0

Answer:

it would be 60

Step-by-step explanation

4*5= 20

8*5=40

12*5= 60

We multiply by 5 because if we divide 20/4=5, 40/8=5, 60/12=5.

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Two trains travel a 160 km track each day. The express travels 10 km h^-1 faster and take 30 minutes less time than the normal t

aniked [119]

Let s = the speed of the slower train in km/hrs+10 = the speed of the faster train in km/hrLet t = time in hrs for the slower train to go 160 kmt-5 = time in hrs for faster train to go 160 km---------------Slower train:(1)
160=s.t

Faster train:(2) 160=(s+10) .(t-.5)From (1)(1) t=160/s
use the relations given in following screenshot and then use quadratic equation.

4 0

4 years ago

What is <img src="https://tex.z-dn.net/?f=15%5E%7B2%7D" id="TexFormula1" title="15^{2}" alt="15^{2}" align="absmiddle" class="la

umka21 [38]

Amayo943,

Remember that with exponents you have to multiply the number of exponets by the same number it's in for example: $1^2 = 1 \times 1$ In this case you need to know that:

$15^2 = 15 \times 15$
$15 \times 15 = 225$
$=225$

Therefore your answer is "225."

Hope this helps!

5 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

SOMEONE ANSWER QUICK!!

aleksandrvk [35]

Answer:

3/4 of a pizza leftover.

Step-by-step explanation:

2 7/12 + 2/3 = 3 1/4

4 - 3 1/4 = 3/4

so 3/4 of 1 pizza is left.

6 0

3 years ago

Simplify the expression 4x3 2x3

Fittoniya [83]

Answer:

onc

Step-by-step explanation:

3 0

2 years ago