A cube has a volume of 125 cubic feet. What is the length of each side of the cube

a nut mixture of peanuts and macadamia nuts at a small fair is $1.00 per pound of peanuts and $3.26 per pound of macadamia nuts.

Studentka2010 [4]

This answer seems really hard but just don't overthink it. You pretty much don't have to do any math. It took me forever to do this because I was thinking so hard but i re-read it and the answer was right infront of me.

1.00p + 3.26n = $248.52

6 0

3 years ago

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Kendra dives off a diving board into the water and then comes back up to the surface. Her dive can be modeled by the equation: ,

MAVERICK [17]

Answer:

1. 6 feet

2. 6.25 feet

3. 1 feet

4. 6 feet

Step-by-step explanation:

The equation is : $h(x)=x^2-7x+6$

1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.

So, substituting x = 0 in the equation, we get

$h(0)=0^2-7(0)+6$

$=0-0+6$

$=6$

So, the diving board is 6 feet above the surface of the water.

2. From the equation, we known that it is a parabola and the vertex is minimum.

It is the minimum height which represents the depth Kendra dives into the water.

So the $x$ coordinate of the vertex is = $\frac{-b}{2a}$

Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,

a = 1 and b = -7

∴ x coordinate = $\frac{-(-7)}{2 \times 1}$

$\frac{7}{2}=3.5$

Now substituting to find f(x),

$h(3.5)=(3.5)^2-7(3.5)+6$

= -6.25

Therefore, the diver dives 6.25 feet below the water surface.

3. The horizontal distance from the board the diver enters into the water.

This is the y-intercept and it is the value of x when h(x)=0.

∴ $0=x^2-7x+6$

Factorizing, we get $(x-1)(x-6)=0$

∴ $x=1 \text{ or}\ x=6$

So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.

4. We know that the equation given has $\text{two}$ x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height $h(x)=0$ . The height is the water surface level.

The first x intercept represents the points where Kendra dives into the water.

And the second x intercept is the point where Kendra comes out of the water surface. This this is $x=6$ for $h(x)=0$ .

Thus Kendra dives out of the water surface at 6 feet from the board.

3 0

2 years ago

A scientist measure change in the temperature of chemical solution at the start of the experiment , the solutions is at temperat

zhannawk [14.2K]

Answer:

The temperature of the chemical solution after t hours is $-14.96-2.9t\;^{\circ}C$

Step-by-step explanation:

Given that the initial temperature of the chemical solution, $T_0= -14.96^{\circ}C$ .

The rate of decreasing temperature, $R = 2.9^{\circ}C/ hour$

So, after t hours, the temperature of the chemical solution will decrease by $Rt=2.9t^{\circ}C$ .

So, the temperature of the chemical solution after t hours,

$T=T_0-Rt \\\\\Rightarrow T = -14.96-2.9t\;^{\circ}C$

Hence, the temperature of the chemical solution after t hours is $-14.96-2.9t^{\circ}C$ .

4 0

3 years ago

4th grade conversions please help!!

MAVERICK [17]

6 inches of yarn make 1 bracelet.

5 feet of yarn make how many bracelets?

1 foot = 12 inches
5 feet = 12 * 5 inches = 60 inches

6 inches of yarn make 1 bracelet
60 inches of yarn make x bracelets

6/1 = 60/x

Cross multiply

6x = 60

x = 10

60 inches yarn make 10 bracelets.

6 0

4 years ago

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Danielle’s text messaging plan costs 7$ for the first 700 messages and 30 cents for each additional text message. If she owes 18

Artemon [7]

Answer:

738 messages

Step-by-step explanation:

Use the given information to set up an equation. 7 is constant and 0.3 per message, with a total of 18.40.

0.3x + 7 = 18.4

Now solve for x

0.3x = 11.4

x = 38

She sent 38 messages over the standard 700, meaning she sent a total of 738 messages in the month of October

7 0

3 years ago