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3 years ago

Find the length indicated

Mathematics

2 answers:

disa [49]3 years ago

8 0

Answer:

Step-by-step explanation:

K is the midpoint of JL, so half of 14is 7

defon3 years ago

3 0

Answer:

I think its 7 but im not sure

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El rodeo has 837 students , El rodeo has 78 more students than hawthorne how many students are there at Hawthorne school later h

elena-s [515]

The number of Elrodeo students is 837.

Let the number of students at Hawthorne be x.

"El rodeo has 78 more students than hawthorne"

this means that

837 = 78 + x
x = 837 -78 = 759

Answer: Hawthorne has 759 students

5 0

4 years ago

The temperature went from -12F to 18F how much did the temperature change?

Arturiano [62]

Answer:

Should be 30

-12-0=12

0-18=18

12+18=30

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

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:

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

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

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

3 years ago

A store is having a sale in which all items are reduced by 20% including tax. Jennifer paid $21 for a pair of shorts if the sale

Julli [10]

Answer:
original price of pants = $25

Explanation:
First, let's calculate the price of shorts after discount:
Assume that the price of shorts after the discount is x
Total payment = price of shorts + taxes

We know that:
total payment = $21
taxes = 5% = 0.05 of the price

This means that:
21 = x + 0.05x
21 = 1.05x
x = $20

Therefore, the price of the shorts is $20 after the discount

Now, we will get the price of the shorts before the discount:
Assume that the price of shorts before discount is y

We know that:
The discount was 20%
This means that Jennifer paid:
100% - 20% = 80% of the price of the shorts

Therefore:
80% of the price = $20
0.8y = 20
y = $25

This means that price of shorts before discount was $25

Hope this helps :)

7 0

3 years ago

Read 2 more answers

Question number 7 Give a reasonable domain and range for the function in this context

alina1380 [7]

Answer: D: [0, ∞)

R: [0, ∞)

Step-by-step explanation:

f(x) = 1.5x

x is the number of bottles

f(x) is the cost

Domain is the x-values. The least amount of bottles you can buy is 0 and the most you can buy is infinite (technically you can only buy the amount you can afford and the amount the store has to sell but for mathematical purposes you can buy an infinite amount)

So, the domain (D) is x = 0 to ∞ → D: [0, ∞)

Range is the y-values. The least and most amounts are based on the domain. Since the smallest x-value is 0, input that value into the equation to solve for f(x). Similarly, input the greatest x-value to solve for f(x).

f(x) = 1.5(0)

= 0

f(x) = 1.5(∞)

= ∞

So, the range (R) is f(x) = 0 to ∞ → R: [0, ∞)

3 0

4 years ago