All categories

4 years ago

A rectangular sheet of paper is folded diagonally from A to C what is the length of side B

Mathematics

1 answer:

sveta [45]4 years ago

7 0

Answer:

AC = $\sqrt{AB^2 + BC^2}$

Step-by-step explanation:

Here we have to draw the figure.

When the rectangle is folded A to C. we get a right triangle.

Here we have to use the Pythagorean theorem to find the side lenght of B.

The sides length of B is AC.

By the Pythagorean theorem, the sum of the squares of the sides is equal to the square of the hypotenuse.

Therefore,

AC^2 = AB^2 + BC^2

Taking the square roots on both sides, we get

AC = $\sqrt{AB^2 + BC^2}$

You might be interested in

baherus [9]

Answer: see proof below

<u>Step-by-step explanation:</u>

Given: cos 330 = $\frac{\sqrt3}{2}$

Use the Double-Angle Identity: cos 2A = 2 cos² A - 1

$\text{Scratchwork:}\quad \bigg(\dfrac{\sqrt3 + 2}{2\sqrt2}\bigg)^2 = \dfrac{2\sqrt3 + 4}{8}$

Proof LHS → RHS:

LHS cos 165

Double-Angle: cos (2 · 165) = 2 cos² 165 - 1

⇒ cos 330 = 2 cos² 165 - 1

⇒ 2 cos² 165 = cos 330 + 1

Given: $2 \cos^2 165 = \dfrac{\sqrt3}{2} + 1$

$\rightarrow 2 \cos^2 165 = \dfrac{\sqrt3}{2} + \dfrac{2}{2}$

Divide by 2: $\cos^2 165 = \dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \bigg(\dfrac{2}{2}\bigg)\dfrac{\sqrt3+2}{4}$

$\rightarrow \cos^2 165 = \dfrac{2\sqrt3+4}{8}$

Square root: $\sqrt{\cos^2 165} = \sqrt{\dfrac{4+2\sqrt3}{8}}$

Scratchwork: $\cos^2 165 = \bigg(\dfrac{\sqrt3+1}{2\sqrt2}\bigg)^2$

$\rightarrow \cos 165 = \pm \dfrac{\sqrt3+1}{2\sqrt2}$

Since cos 165 is in the 2nd Quadrant, the sign is NEGATIVE

$\rightarrow \cos 165 = - \dfrac{\sqrt3+1}{2\sqrt2}$

LHS = RHS $\checkmark$

4 0

3 years ago

I need help with this problem

serious [3.7K]

i’m not sure imma look stuff up and get back to you tho

3 0

3 years ago

Identify the explanatory and response variables in the following situation:

zhannawk [14.2K]

Negative correlation refers to an inverse relationship between two variables. When one variable increases, the other decreases.

The variables are latitude and average temperature.

The explanatory variable is latitude and the response is the average temperature. Choice B.

As the latitude increases, the average temperature decreases. This is a strong negative correlation of between the two variables.

3 0

3 years ago

Read 2 more answers

A store had homemade sweaters on sale for $20 off the original price. Aunt Ethel jumped at the bargain and bought a sweater for

Harrizon [31]

Original price would be $675

$20 multiply 15 to get $300 being taken off.

add 300 to 375 you get $675

8 0

3 years ago

The length of a rectangle is 6 in. more than the its width. the perimeter of the rectangle is 24 in. what is the length of the r

photoshop1234 [79]

The answer is 3, 3+3+9+9 = 24

6 0

3 years ago