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2 years ago

Write the interval (5, 100] as an inequality and using set notation

1 answer:

7 0

An inequality is a statement that shows relation between two values, when the two values are not equal.
The inequality is opposite than equality.
So, the interval (5,100] means that it contains all number from number 5 (not and 5) till 100, including 100. We can see this from the bracket's type.
For a value x in this interval we can write the inequality:
5<x<=100
x is bigger than 5 , and smaller or equal 100

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Write the exact value of the side length of each square. If the value is not a whole number, estimate the length.

Savatey [412]

Given:

The area of the squares are given.

To find:

The exact side length or estimate side length of the square.

Solution:

We know that, the area of a square is

$A=a^2$

Where, a is the side length of the square.

$a=\sqrt{A}$

Area of the square is 100 square units. So, the side length is:

$a=\sqrt{100}$

$a=10$

Therefore, the side length is 10 units.

Area of the square is 95 square units. So, the side length is:

$a=\sqrt{95}$

It is not exact. We know that $\sqrt{81}$ .

Therefore, the side length is between 9 and 10.

Area of the square is 36 square units. So, the side length is:

$a=\sqrt{36}$

$a=6$

Therefore, the side length is 6 units.

Area of the square is 30 square units. So, the side length is:

$a=\sqrt{30}$

It is not exact. We know that $\sqrt{25}$ .

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3 years ago

How do i find the shorted distance between the point and the line

m_a_m_a [10]

Answer:

5 units

Step-by-step explanation:

3x + 4y = 8

4y = -3x+8

y = -3/4+2

The shortest distance between a point and a line is the perpendicular line.

Slope of the perpendicular line: 4/3 and point (-3,-2)

b = -2-(4/3)(-3) = 2

Equation of the perpendicular line: y=4/3x+2

y is equal y

4/3x+2= -3/4x+2

4/3x +3/4x = 2-2

x = 0

Plug x=0 into one of the equations to find y

y = 4/3(0) + 2

y = 2

(0,2) and (-3,-2)

Distance = sqrt [(-3-0)^2 + (-2-2)^2]

Sqrt (-3)^2+ (-4)^2

Sqrt 25 = 5

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2 years ago

Yanka [14]

Answer:

6 units down

Step-by-step explanation:

Transformation is the movement of a point from its original position to a new position. If an object is transformed, all the point making the object is also transformed. There are four different transformations: Reflection, dilation, translation and rotation.

If y = f(x), y = f(x) + k is a translation k units up if k > 0 and is a translation k units down if k < 0

Given that the parent function is an absolute value represented by:

y = |x|

Therefore comparing y = |xl - 6 with y = f(x) + k, k < 0, therefore this is a translation of 6 units down

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2 years ago