All categories

11 days ago

Which linear inequality is represented by the graph?

Mathematics

2 answers:

zzz [4K]11 days ago

6 0

The graph illustrates the linear equality represented by $\boxed{{\mathbf{y>3x+2}}}$ , which corresponds to $\boxed{{\mathbf{OPTION B}}}$ .

Additional details:

A line is shown to pass through the points $\left({0,2}\right)$ and $\left({-3,-7}\right)$ in Figure 1 below.

The slope of the line connecting points $\left({{x_1},{y_1}}\right)$ and $\left( {{x_2},{y_2}}\right)$ can be computed as follows:

$m=\frac{{{y_2}-{y_1}}}{{{x_2}-{x_1}}}$ ...........(1)

In this case, the slope is represented by $m$ , while the points are $\left({{x_1},{y_1}}\right)$ and $\left({{x_2},{y_2}}\right)$ .

Replace $0$ with ${x_1}$ , $2$ with ${y_1}$ , $-3$ with ${x_2}$ , and $-7$ with ${y_2}$ in equation (1) to find the slope for the line through points $\left({0,2}\right)$ and $\left({-3,-7}\right)$ .

$\begin{aligned}m&=\frac{{-7-2}}{{-3-0}}\\&=\frac{{-9}}{{-3}}\\&=3\\\end{aligned}$

Consequently, the slope is $3$ .

The equation for a line in point-slope form with slope $m$ that passes through $\left({{x_1},{y_1}}\right)$ is given as follows:

$y-{y_1}=m\left({x-{x_1}}\right)$ ...........(2)

By substituting $0$ for ${x_1}$ , $2$ for ${y_1}$ , and $3$ for $m$ in equation (2), the equation of the line can be derived.

$\begin{aligned}y-2&=3\left({x-0}\right)\\y-2&=3x\\y&=3x+2\\\end{aligned}$

Thus, the value for $y$ turns out to be $3x+2$ .

Noting that the shaded area in Figure 1 exists above the line represented by $y=3x+2$ , a greater than sign is employed instead of equality.

Therefore, the linear inequality depicted is $y>3x+2$ , as seen in Figure 2 below.

Consequently, four options are provided below.

$\begin{aligned}{\text{OPTION A}}\to &y3x+2\hfill\\{\text{OPTION C}}\to &yx+2\hfill\\\end{aligned}$

Since OPTION B corresponds to the derived equation $y>3x+2$ .

Thus, the graph shows the linear equality of $\boxed{{\mathbf{y>3x+2}}}$ , aligning with $\boxed{{\mathbf{OPTION B}}}$ .

To explore further:

1. Which classification best describes this system of equations?

2. What is the value of $x$ in the equation $x-y=30$ when $y=15$ ?

3. What are the values of x?

Response Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Coordinate Geometry

Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, inequality

PIT_PIT [3.9K]11 days ago

5 0

Answer: The graph corresponds to the inequality y > 3x + 2

Step-by-step explanation:

A linear inequality is similar to a linear equation, but it consists of inequality symbols (<, >, ≤, ≥) rather than the equal sign (=).

In the question, the linear inequality is depicted through a graph.

The line in the graph intersects the point (-3,-7).

Now, let’s evaluate which option meets the conditions of this point.

1) y < 3x + 2 implies the line should be y = 3x + 2.

⇒ -7 = 3(-3) + 2.

⇒ -7 = -9 + 2 ⇒ -7 = -7, which holds true.

2) y > 3x + 2, which is analogous to the first.

3) y < x + 2 means the line should be y = x + 2.

⇒ -7 = -3 + 2.

⇒ -7 = -1, which is false.

4) y > x + 2 parallels the third scenario.

Thus, options 3) and 4) cannot represent the required linear inequality.

From options 1) and 2), option 2) is the correct linear inequality since the graph indicates shading above the line, suggesting y (>) must be greater. [Conversely, for y (<) to be lower, the shading would be below the line.]

Consequently, the correct linear inequality presented by the graph is 2) y > 3x + 2.

You might be interested in

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 1

AnnZ [3900]

Question:

Which statement is accurate concerning the function’s discontinuities $f(x) = \frac{x-5}{3x^2-17x-28}$

A) There are gaps at x = 7 and.

B) Asymptotes exist at x = 7 and.

C) Asymptotes exist at x = –7 and.

D) Gaps are present at (–7, 0) and.

Answer:

B) Asymptotes exist at x = 7 and $(x = \frac{-4}{3})$

Step-by-step explanation:

Given:

$f(x) = \frac{x-5}{3x^2-17x-28}$

Goal:

Identify the correct statement

$f(x) = \frac{x-5}{3x^2-17x-28}$

We need to factor the denominator first.

$f(x) = \frac{x-5}{(3x+4)(x-7)}$

To express x in terms of (3x+4) and (x-7):

3x + 4 =

3x = -4

Divide both sides by 3:

$x = \frac{-4}{3}$

x - 7

x = 7

Next, evaluate the limit when $(x = \frac{-4}{3})$ and at (x = 7)

lim f(x) as $(x = \frac{-4}{3})$ = ±∞

lim f(x) as (x=7) = ±∞

Since both scenarios result in the denominator approaching zero, they represent asymptotes.

Thus, asymptotes are found at $(x = \frac{-4}{3})$ and x=7

Option B is determined to be correct

6 0

3 days ago

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –

Zina [3917]

Answer:

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

Step-by-step explanation:

Given the inequality is -3(2x - 5) < 5(2 - x)

First, simplify both sides:

∵ -3(2x - 5) = -3(2x) + -3(-5)

Remember that (-)(-) results in (+)

Thus, -3(2x - 5) = - 6x + 15

∵ 5(2 - x) = 5(2) + 5(-x)

Remember that (+)(-) results in (-)

Then, 5(2 - x) = 10 - 5x

Now we have: - 6x + 15 < 10 - 5x

Subtract 15 from both sides

So: - 6x < -5 - 5x

Add 5x to both sides

Thus, - x < - 5

Note that since the coefficient of x is negative, we reverse the inequality sign when dividing both sides by it

∵ The coefficient of x is -1

Therefore, dividing both sides by -1 gives us x > 5

The accurate representations are:

- 6x + 15 < 10 - 5x ⇒ 3rd option

A circle is open at 5 with a bold line extending right from 5 ⇒ 4th option (see diagram)

7 0

1 day ago

Read 2 more answers

SALES Cars and trucks are the most popular vehicles. Last year, the number of cars sold was 39,000 more than three times the num

PIT_PIT [3949]

Given :

Miki possesses 104 nickels and 88 dimes. She intends to sort her coins into sets where each set has an equal count of both nickels and dimes.

Last year, 216,000 cars were sold.

To Find :

An equation that can identify the number of trucks, t, sold the previous year.

Solution :

Let t represent the quantity of trucks sold and c represent the cars sold.

The statement indicates that the quantity of cars sold exceeded three times the trucks sold by 39,000.

Thus,

$c=3t+39000\\\\t=\dfrac{c-39000}{3}$

Plugging the value of c = 216000 into the equation above yields :

$t=\dfrac{c-39000}{3}\\\\t=\dfrac{216000-39000}{3}\\\\t=59000$

This gives us the solution we seek.

8 0

16 days ago

A ballpark sells bags of popcorn for $1 each and bags of peanuts for $2 each. Hector will buy x bags of popcorn and y bags of pe

tester [3938]

Answer:

Hector will purchase 6 bags of peanuts and 2 bags of popcorn.

Step-by-step explanation:

His plan includes buying 6 peanut bags for a total of $12 and 2 popcorn bags totaling $2. He aimed for 8 bags of snacks overall, with a maximum budget of $14. Hope this is helpful!!!:)

6 0

3 days ago

What does distributions from owners int non adr mean?

AnnZ [3900]

Distributions from owners refer to payments that business owners take out from profits the firm earns, commonly issued as dividends. An ADR, or American Depositary Receipt, is a type of stock bought and sold within the U.S. market that represents a specific number of shares in a foreign company. Therefore, the owner’s payments do not originate from the ADR shares.

5 0

13 days ago