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FromTheMoon [43]

3 years ago

6

Bradley bought 2 cakes for his class Valentines's party. There are 23 students in his class. How much cake will each student rec

eive?

1 answer:

Cloud [144]3 years ago

4 0

So 2 divded into 23 parts =2/23 which is simplest form

so each person will recieve 2/23 of a cake

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the distance a car travels can be found using the formula d=rt, where d is the distance in miles, r is the rate of speed in mile

ICE Princess25 [194]

Answer:

35 miles

Step-by-step explanation:

d=(70)(.5)

d=35 miles

8 0

3 years ago

Read 2 more answers

Surface Area of a sphere, A grapefruit with C = 14cm.

9966 [12]

Surface area SA: $4\pi r^2$
Circumference C: $2\pi r$ dividing this you get $7=\pi r$ and $r= \frac{7}{\pi}$

Now let's input the radius $r$ into the Surface area formula...
$4\pi r^2\rightarrow 4\pi(\frac{7}{\pi})^2=4\pi(\frac{49}{\pi^2})=\frac{196}{\pi}$

3 0

3 years ago

The price dark roasted coffee beans is $11 per pound.

Mademuasel [1]

If the change in the number of pounds is p, the change in the cost will be $11c.
This is because each pound costs $11.

8 0

4 years ago

Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x3 − 6x2 − 15x + 2 (a) Find the interval on which

Burka [1]

Answer:

a) $(-\infty, -1) \cup (5, \infty)$

b) $(-1,5)$

Step-by-step explanation:

The first step to solve this question is finding the roots of the derivative of x.

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}$

$\bigtriangleup = b^{2} - 4ac$

In this question:

$f(x) = x^{3} - 6x^{2} - 15x + 2$

So

$f'(x) = 3x^{2} - 12x - 15$

Finding the roots:

$3x^{2} - 12x - 15 = 0$

Simplifying by -3

$x^{2} - 4x - 5 = 0$

So $a = 1, b = -4, c = -5$

Then

$\bigtriangleup = (-4)^{2} - 4*1*(-5) = 36$

$x_{1} = \frac{-(-4) + \sqrt{36}}{2} = 5$

$x_{2} = \frac{-(-4) - \sqrt{36}}{2} = -1$

So the function can be divided in three intervals.

They are:

Less than -1

Between -1 and 5

Higher than 5

In which it increases and which it decreases?

Less than -1

Lets find the derivative in a point in this interval, for example, -2

$f'(x) = 3x^{2} - 12x - 15$

$f'(-2) = 3*(-2)^{2} - 12*(-2) - 15 = 21$

Positive.

So in the interval of $(-\infty, -1)$ , the function increases.

Between -1 and 5

Will choose 0.

$f'(x) = 3x^{2} - 12x - 15$

$f'(0) = 3*(0)^{2} - 12*(0) - 15 = -15$

Negative.

So in the interval of $(-1,5)$ , the function decreases.

Higher than 5

Will choose 6.

$f'(x) = 3x^{2} - 12x - 15$

$f'(6) = 3*(6)^{2} - 12*(6) - 15 = 21$

Positive

So in the interval of $(5, \infty)$ , the function increases.

(a) Find the interval on which f is increasing.

Using interval notation

$(-\infty, -1) \cup (5, \infty)$

b) Find the interval on which f is decreasing.

$(-1,5)$

5 0

4 years ago

Solve each inequality of -4x -2<8

FromTheMoon [43]

<span>-4x -2<8
Add 2 to both sides
-4x<10
Divide -4 on both sides
Final Answer: x > -10/4 or -2 1/2 *Both answers are equivalent to each other.
</span>

6 0

3 years ago