All categories

2 years ago

The demand for coffee is given by the following equation, where QD stands for the quantity demanded and P stands for price.

Mathematics

1 answer:

mart [117]2 years ago

4 0

Using linear function concepts, it is found that the slopes and intercepts of the functions are given as follows:

a) -4.

b) P = 25.

c) 2.

d) P = 5.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The demand is given by:

D = 100 - 4P.

Hence the slope is of -4. The demand is equals to zero when:

100 - 4P = 0 -> P = 25.

The supply is given by:

QS = -10 + 2P.

Hence the slope is of 2. The supply is equals to zero when:

-10 + 2P = 0 -> P = 5.

More can be learned about linear function concepts at brainly.com/question/24808124

#SPJ1

You might be interested in

−8 3/4÷2 1/6 please show me ur work

nalin [4]

Answer:

- 4 1/26

Step-by-step explanation:

<u>Solving in steps:</u>

- 8 3/4 ÷ 2 1/6 =
- 35/4 ÷ 13/6 =
- 35/4 × 6/13 =
- 35/2 × 3/13 =
- 105/26 =
- 4 1/26

6 0

3 years ago

Which equation does not represent a function? A) y = 2x + 3 B) x = 4y + 7 C) 6x - 5y = 8 D) y2 = -5x - 8

marin [14]

D. It is not a function because there are multiple outputs for one input.

4 0

3 years ago

Read 2 more answers

Which of the following statements are true regarding functions? Check all that apply. A.The vertical line test may be used to de

BigorU [14]

The answer o this question would be:
<span>A.The vertical line test may be used to determine whether a function is one-to-one
</span><span>D. The horizontal line test may be used to determine whether a function is one-to-one.

Vertical and horizontal line test can be used to find out whether the function, not one-to-one. The test is done by making a horizontal line (for horizontal line test) or vertical line( for vertical line test). If there are no 2 or more points of the graph that touch the line in both tests, then the function would be one-to-one</span>

6 0

3 years ago

Read 2 more answers

In a class of 40 students, 20% are females. How many males are in the class?

Vadim26 [7]

Answer:

In a class of 40 students, 20% are females. How many males are in the class?

ANSWER

= 32

6 0

2 years ago

Read 2 more answers

2/7m-1/7=3/14 help this is so confusing

Free_Kalibri [48]

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

<h3>Further explanation</h3>

A case about one variable linear quations. We have to solve the equation to get the variable m. Let's isolate the variable m alone at the end of the process on one side of the equation, until the variable will be equal to a value on the opposite side.

We add $\frac{1}{7}$ to both sides:

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get:

$\frac{2}{7}m = \frac{5}{14}$

We divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$ :

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

We simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

In the form of mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Check the solution into the equation:

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

Quick steps in summary:

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

$\frac{2}{7}m = \frac{5}{14}$

$m = \frac{5}{14} \times \frac{7}{2}$

$m = \frac{35}{28}$

$\rightarrow \boxed{ \ m = \frac{5}{4} \ }$

$\rightarrow \boxed{ \ m = 1 \frac{1}{4} \ }$

$\rightarrow \boxed{ \ m = 1.25 \ }$

Note:

The important thing to do is how to manipulate both sides of the equation with the algebraic properties of equality such as:

adding,
subtracting,
multiplying, and/or
dividing both sides of the equation with the same number.

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation. In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
turn fractions into mixed fractions or decimal forms.

Let's practice a lot until you get used to and know which operations should be done first.

<h3>Learn more</h3>

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

<h3>Answer details </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, substract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal, brainly

6 0

4 years ago