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2 years ago

The area of the base of a square notepad is 2.25 square inches. What is the length of one side of the base of the notepad?

Mathematics

1 answer:

scoundrel [369]2 years ago

4 0

Answer:

1.5 inches

Step-by-step explanation:

Because the base of the notepad is a square, that means that each side of the base would be equal. Since the area is 2.25 square inches, and each side would have to be equal, the equation to solve would be x*x = 2.25, or x^2=2.25. So, you just take the square root of both sides, and x=1.5 inches. Each side of the notepad would be 1.5 inches.

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What is the vertex for the following quadratic? f(x)=2(x - 4)^2 -8

Ghella [55]

Answer:

vertex = (4, - 8 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

f(x) = (x - 4)² - 8 ← is in vertex form

with (h, k ) = (4, - 8 ) ← coordinates of vertex

6 0

3 years ago

What is the mean of the set of data given below? 13 8 9 6 10 8

olga_2 [115]

Answer:

Mean = The numbers added up and divided by the number of numbers.

Step-by-step explanation:

= (13 + 8 + 9 + 6 + 10 + 8) / 6

= 54 / 6

= 9

The mean is 9.

8 0

2 years ago

Drake rolls two fair number cubes. 1 2 3 4 5 6 1 1 2 3 4 5 6 2 2 4 6 8 10 12 3 3 6 9 12 15 18 4 4 8 12 16 20 24 5 5 10 15 20 25

e-lub [12.9K]

Wouldn’t it be 2/15 chance because there is only two fifteens

7 0

3 years ago

Read 2 more answers

You need to design a rectangle with a perimeter of 14.2 cm. The length must be 2.4 cm. What is the width of the

irina1246 [14]

Part (a)

<h3>Answer: 2(2.4+w) = 14.2</h3>

--------------

Explanation:

L = 2.4 = length

W = unknown width

The perimeter of any rectangle is P = 2(L+W)

We replace L with 2.4, and replace P with 14.2 to get 14.2 = 2(2.4+w) which is equivalent to 2(2.4+w) = 14.2

========================================================

Part (b)

<h3>Answer: w = 4.7</h3>

--------------

Explanation:

We'll solve the equation we set up in part (a)

2(2.4+w) = 14.2

2(2.4)+2(w) = 14.2

4.8+2w = 14.2

2w = 14.2-4.8

2w = 9.4

w = 9.4/2

w = 4.7

The width must be 4.7 cm.

4 0

2 years ago

What is a solution to the equation 3 / m + 3 - M / 3 - M equals m^2 + 9 / m^2-9?

Mnenie [13.5K]

Answer: Last option.

Step-by-step explanation:

Given the equation:

$\frac{3}{m+3}-\frac{m}{3-m}=\frac{m^2+9}{m^2-9}$

Follow these steps to solve it:

- Subtract the fractions on the left side of the equation:

$\frac{3(3-m)-m(m+3)}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{9-3m-m^2-3m}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}\\\\\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{m^2-9}$

- Using the Difference of squares formula ( $a^2-b^2=(a+b)(a-b)$ ) we can simplify the denominator of the right side of the equation:

$\frac{-m^2-6m+9}{(m+3)(3-m)}=\frac{m^2+9}{(m+3)(m-3)}$

- Multiply both sides of the equation by $(m+3)(3-m)$ and simplify:

$\frac{(-m^2-6m+9)(m+3)(3-m)}{(m+3)(3-m)}=\frac{(m^2+9)(m+3)(3-m)}{(m+3)(m-3)}\\\\-m^2-6m+9=\frac{(m^2+9)(3-m)}{(m-3)}$

- Multiply both sides by $m-3$ :

$(-m^2-6m+9)(m-3)=\frac{(m^2+9)(3-m)(m-3)}{(m-3)}\\\\(-m^2-6m+9)(m-3)=(m^2+9)(3-m)$

- Apply Distributive property and simplify:

$(-m^2-6m+9)(m-3)=(m^2+9)(3-m)\\\\-m^3-6m^2+9m+3m^2+18m-27=3m^2+27-m^3-9m\\\\-m^3-3m^2+27m-27+m^3-3m^2+9m-27=0\\\\-6m^2+36m-54=0$

- Divide both sides of the equation by -6:

$\frac{-6m^2+36m-54}{-6}=\frac{0}{-6}\\\\m^2-6m+9=0$

- Factor the equation and solve for "m":

$(m-3)^2=0\\\\m=3$

In order to verify it, you must substitute $m=3$ into the equation and solve it:

$\frac{3}{3+3}-\frac{3}{3-3}=\frac{3^2+9}{3^2-9}\\\\\frac{3}{6}-\frac{3}{0}=\frac{18}{0}$

<em>NO SOLUTION</em>

7 0

2 years ago