Simplify: 3 · 3^2 + 8 ÷ 2 − (4 + 3)

The coordinate plane below represents a city.

alex41 [277]

Answer:

Part A) The system of inequalities is

$x\geq2$ and $y\geq2$

Part B) In the procedure

Part C) The schools that Natalie is allowed to attend are A,B and D

Step-by-step explanation:

Part A: Using the graph above, create a system of inequalities that only contain points C and F in the overlapping shaded regions

we have

Points C(2,2), F(3,4)

The system of inequalities could be

$x\geq2$ -----> inequality A

The solution of the inequality A is the shaded area at the right of the solid line x=2

$y\geq2$ -----> inequality B

The solution of the inequality B is the shaded area above of the solid line y=2

see the attached figure N 1

Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities

Verify point C

C(2,2)

<em>Inequality A</em>

$x\geq2$ -----> $2\geq2$ ----> is true

<em>Inequality B</em>

$y\geq2$ ------> $2\geq2$ ----> is true

therefore

Point C is a solution of the system of inequalities

Verify point D

F(3,4)

Inequality A

$x\geq2$ -----> $3\geq2$ ----> is true

Inequality B

$y\geq2$ ------> $4\geq2$ ----> is true

therefore

Point D is a solution of the system of inequalities

Part C: Natalie can only attend a school in her designated zone. Natalie's zone is defined by y < −2x + 2. Explain how you can identify the schools that Natalie is allowed to attend.

we have

$y < -2x+2$

The solution of the inequality is the shaded area below the dotted line $y=-2x+2$

The y-intercept of the dotted line is the point (0,2)

The x-intercept of the dotted line is the point (1,0)

To graph the inequality, plot the intercepts and shade the area below the dotted line

see the attached figure N 2

therefore

The schools that Natalie is allowed to attend are A,B and D

6 0

4 years ago

Complete the sentences below the radius of a circle is _____ the length of its diameter. the diameter of a circle is ______ the

son4ous [18]

Answer:

Half; twice

Step-by-step explanation:

In a circle, the radius is said to be the distance from the center of the circle to any point on the edge of the circle, it is denoted as "r". The radius is called a radii if it is more than one.. The radius of a circle is half the length of the diameter of a circle because the diameter of a circle is the distance of the line that passes through the center of a circle touching both edges of the circle. It is denoted as "d".

Thus,

2r = d

r = d/2

For example, if the radius of a circle is 10cm, the diameter of the circle will be calculated as: d = 2 * 10 = 20cm. Which means if the radius is 10cm, diameter will be 20cm.

Therefore, the radius of a circle is half the length of its diameter. the diameter of a circle is twice the length of its radius

5 0

3 years ago

Is the square of an irrational number always irrational? Explain

iVinArrow [24]

<h2>Answer:</h2><h2><u>NOO</u></h2>

Step-by-step explanation:

<h3>For example, √3 is irrational, but (√3)2 = 3, which is rational.</h3>

HOPE IT HELP

7 0

3 years ago

Read 2 more answers

A furniture maker is building a bookshelf she needs to cut rectangular pieces of wood to a length of 5/12 foot and a width of 2/

jok3333 [9.3K]

We Know, Area = Length * Width
Here, L = 5/12
W = 2/3

Substitute it into the expression,
A = 5/12 * 2/3
A = 10/36
A = 5/18 ft²

So, the area of the wood would be 5/18 ft²

Hope this helps!

3 0

3 years ago

Given that a x 70 = b work out the value of<br>3b/a<br><br>Your final line should say, 3b/a = ...

Leto [7]

Answer:

$\frac{3b}{a} = 210$