All categories

1 year ago

A diagonal of a cube measures

Mathematics

1 answer:

Gennadij [26K]1 year ago

4 0

Answer: 7cm

Step-by-step explanation:

Use pythagorean theorum:

Variables:

Let the edge = A

Face diagonal (F) = 10cm

Inner diagonal (I) = sqrt(150) cm

A^2 = I^2 - F^2

A^2 = [sqrt(150)]^2 - 10^2

A^2 = 150 - 100

A^2 = 50

A = sqrt(50)

A = 7.0710678 cm

A = 7cm (to the nearest tenth)

so, length of an edge = 7cm

You might be interested in

Use the pythagorean Theorem to prove the three sides of the triangle are the three sides of a right triangle. Show all of your w

weeeeeb [17]

Answer:

$2^{2}$ + $(2\sqrt{3}) ^{2}$ = 4 + 4 * 3 = 16 = $4^{2}$

Step-by-step explanation:

The Pythagorean Theorem states that the two shorter sides of a right triangle squared and added together will equal the longest side (hypotenuse) of the right triangle squared. The longest side of this right triangle is 4, 4 squared is 16. The two shorter sides of the right triangle are 2 and $2\sqrt{3}$ , squared individually would be 4 and 12, and added together they also equal 16. These sides are a valid input for the Pythagorean Theorem, so these three sides are the sides of a right triangle. 2 and $2\sqrt{3}$ being the legs of the right triangle, and 4 being the hypotenuse.

6 0

3 years ago

Complete the table below.

Nana76 [90]

Angle 1 is 122 degrees bc of vertical angle
Angle 2 is 87 degrees bc of alt ext angle converse
Angle 3 93 degrees
Angle 4 is 58 degrees

7 0

2 years ago

Find all values of the angle θ (in radians, with 0 ≤ θ < 2π) for which the matrix a = cos θ −sin θ sin θ cos θ has real eigen

harina [27]

The matrix

$A=\begin{bmatrix}\cos\theta&-\sin\theta\\\sin\theta&\cos\theta\end{bmatrix}$

has eigenvalues $\lambda$ such that

$\det(A-\lambda I)=\begin{vmatrix}\cos\theta-\lambda&-\sin\theta\\\sin\theta&\cos\theta-\lambda\end{vmatrix}=0$

$(\cos\theta-\lambda)^2+\sin^2\theta=0$

$(\cos\theta-\lambda)^2=-\sin^2\theta$

$\cos\theta-\lambda=\pm\sqrt{-\sin^2\theta}$

$\lambda=\cos\theta\pm\sqrt{-\sin^2\theta}$

$\sin^2\theta\ge0$ for all values of $\theta$ , so we need to have $\sin\theta=0$ in order for $\lambda$ to be real-valued. This happens for

$\sin\theta=0\implies\theta=n\pi$

where $n$ is any integer, and over the given interval we have $\theta=0$ and $\theta=\pi$ .

4 0

2 years ago

AT THIS POINT I'M TIRED OF ASKING PLEASE DON'T ANSWER IF YOU DON'T KNOW I WILL GIVE BRAINIEST PLEASE I BEG YOU.

IgorC [24]

9514 1404 393

Answer:

$17.97

Step-by-step explanation:

It should be no surprise that the total cost is the sum of the costs of the items being purchased.

We can add the costs of repeated items into the sum several times, or we can use multiplication to find their cost. Most folks use multiplication to find the sum of repeated numbers.

milk + strawberries + bananas

= $3.49 + 2×$4.99 +6×$0.75

= $3.49 +9.98 +4.50

= $17.97

Jane spent $17.97 on these food ingredients.

_____

<em>Additional comment</em>

If you're paying attention, you see that this is what happens at the cash register every time you buy something at a store.

7 0

2 years ago

Read 2 more answers

There are 12 triangles and 3 squares what is the simplest ratio of squares to triangles?

FromTheMoon [43]

Answer:

Step-by-step explanation:

3:12 can be simplified to 1:4

7 0

2 years ago