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svp [43]
3 years ago
14

Which system of inequalities is represented by the graph?

Mathematics
1 answer:
timofeeve [1]3 years ago
4 0

Answer:

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4 " is represented by the graph ⇒ D

Step-by-step explanation:

To find the answer let us find the equation of each line

Blue line:

∵ The line passes through points (5 , 0) and (0 , 2.5)

- Find the slope of the line

∵ m = Δy/Δx

∴ \frac{0-2.5}{5-0}=\frac{-2.5}{5}

∴ m = -0.5

- The form of the equation is y = m x  + b, where b is the

   y-intercept (value y at x = 0)

∵ y = 2.5 at x = 0

∴ b = 2.5

- Write the equation of the line

∴ y = - 0.5 x + 2.5

- Multiply both sides by 2

∴ The equation of the blue line is 2 y = - x + 5

- The shading is under the line and the line is solid, that means

  2 y is less than or equal - x + 5

∴ The inequality of the blue line is 2 y ≤ - x + 5

Red line:

∵ The line passes through points (3 , -5) and (0 , 4)

- Find the slope of the line

∴ m=\frac{-5-4}{3-0}=\frac{-9}{3}

∴ m = -3

∵ y = 4 at x = 0

∴ b = 4

- Write the equation of the line

∴ y =  -3 x + 4

∴ The equation of the red line is y = -3 x + 4

- The shading is below the line and the line is solid, that means

  y is less than or equal -3 x + 4

∴ The inequality of the red line is y ≤ -3 x + 4

Let us find which answer is the same with this system of inequalities

∵ 2 y ≤ - x + 5

- Add x to both sides

∴ x + 2 y ≤ 5 ⇒ same as the first inequality of answer D

∵ y ≤ -3 x + 4

- Add 3 x to both sides

∴ 3 x + y ≤ 4 ⇒ same as the second inequality of answer D

The system of inequalities " x + 2 y ≤ 5 and 3 x + y ≤ 4" is represented by the graph

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A microscope has a setting that magnifies an object so that it appears 100 times as large when viewed through the eyepiece. If a
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The length of the insect in the final image is \boxed{9.5\text{ centimeter}}.

Further explanation:

In the question it is given that if an object is viewed under a microscope then the object appears 100 times large than its original size.

It is given that the length of a insect is 0.095 centimeter.

This question is based on the concept of multiplication of decimals.

Consider the length of the insect as x\text{ cm}.

Since, the length of insect is 0.095 centimeter so, trhe value of x is 0.095.

As per the question the size of the final image is 100 times large as the original size so, the size of final image is calculated as follows:

\boxed{S=x\times 100}

Substitute 0.095 for x in the above equation.

\boxed{\begin{aligned}S&=x\times 100\\&=0.095\times 100\\&=9.5\end{aligned}}

From the above calculation it is concluded that the length of the insect in the final image is 9.5\text{ centimeter}.

Therefore, the length of the insect in the final image is \boxed{9.5\text{ centimeter}}.

Learn more:

1. Learn more about numbers brainly.com/question/4736384

2. Learn more about scientific notation of numbers brainly.com/question/4736384

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Simplification

Keywords: Microscope, insect, cenimeter, magnifies, 0.095cm, 100 times, eyepiece, viewed, 9.5cm, simplification, multiplication, decimals, final image.

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4+5=4m+1 what is m=?
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