What are the zeros of the polynomial function?

A new company spent $9,399.74 on 24 tablets for their employees. How much did each tablet cost? Round your answer to the nearest

Nitella [24]

$391.655 or $391.66 per table

8 0

3 years ago

Read 2 more answers

Write a system<br> of linear inequalities represented by the graph.

Helga [31]

2,3 or 4,1 either one

6 0

2 years ago

A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
$A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4$

We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$

3 0

2 years ago

Jocelyn and Madelyn go to the movie theater and purchase refreshments for their friends.

Alik [6]

let's make p stand for popcorn and d for drinks. Using those variables, we can create our equations:

2p + 3d = 18.25

4p + 2d = 27.50

From this, we can use substitution or elimination to solve:

For substitution, in the second equations, we could factor out a 2, divide both sides by 2, and then move the left over 2p to the other side to isolate d to put into the first equation.

For elimination, we can multiply the first equation by -2 so that we can remove the 4p and focus on solving for d.

I'll be using elimination in this case:

-2(2p + 3d = 18.25) --> -4p - 6d = -36.50

-4p - 6d = -36.50

4p + 2d = 27.50

-4d = -9.00

d = 2.25

4p + 2 * 2.25 = 27.50

4p + 4.50 = 27.50

4p = 23.00

p = 5.75

Now let's check our answer:

2 * 5.75 + 3 * 2.25 = 18.25

11.50 + 6.75 = 18.25

18.25 = 18.25

So drinks cost $2.25 and popcorn $5.75

7 0

2 years ago

Need help with this pls <br> (Show work pls!!)

Aleksandr-060686 [28]

This is my first time on this app but this question doesn’t look to hard i’m ok at math but not that good at showing my work

Isosceles triangles have to equal sides

and each side is 5 cm greater than the base

you know the perimeter is 46

i would use basic algebra

x = base

46 = 2(x +5) + x

the 2(x +5) is the equal sides

46 = 2(x+5) + x

using distributive property

46 = 2x + 10 + x

add the common variable

46 = 3x + 10

now it’s easy

3x = 46 - 10

3x = 36

x = 36 / 3

x = 12

now that we got x (base)

we know that the equal sides are 5 cm longer than the base

12 + 5 = 17

since there are 2 sides and they are equal they are both 17

so each side of the triangle would be
1. 17 cm
2. 17 cm
3. 12 cm

to check you should be able to add them all together and get 46

17 + 17 + 12 = 46

7 0

3 years ago