What is the measure of the smallest angle?<br> A 53<br> B 57<br> C 63<br> D 63

To determine the height of a pine tree, you measure the shadow cast by the tree and find it to be 20 feet long. Then you measure

Otrada [13]

Answer:

Height of the pine tree = 60 in.

Step-by-step explanation:

Since, triangle formed by the tip of the tree and tip of the shadow of the tree will be similar to each other,

By the property of similarity, corresponding sides of the similar triangles will be proportional.

$\frac{x}{20}=\frac{36}{d}$

If d = 12 inches,

$\frac{x}{20}=\frac{36}{12}$

x = $\frac{20\times 36}{12}$

x = 60 in.

Therefore, height of the pine tree will be 60 in.

7 0

3 years ago

*URGENT I WILL MARK BRANLIEST*

Monica [59]

Answer:

P = 10y + 4

Step-by-step explanation:

P = 2L + 2W

P = 2(4y) + 2(y + 2)

P = 8y + 2y + 4

P = 10y + 4

3 0

4 years ago

We define the relation =m (read "equal mod m") on Z x Z to be the set: {(p,q): m|(p-q)}. Please show work.

Slav-nsk [51]

Step-by-step explanation:

a) Give two pairs which are in the relation $\equiv \mod 4$ and two pairs that are not.

As stated before, a pair $(x,y)\in \mathbb{Z}\times\mathbb{Z}$ is equal mod m (written $x\equiv y\mod m$ ) if $m\mid (x-y)$ . Then:

x=0 and y=4 is an example of a pair $\equiv \mod 4$
x=0 and y=1 is an example of a pair $\not \equiv \mod 4$

b) Show the $\equiv \mod m$ is an equivalence relation.

An equivalence relation is a binary relation that is reflexive, symmetric and transitive.

By definition $\equiv \mod m$ is a binary relation. Observe that:

Reflexive. We know that, for every m, $m\mid 0$ . Then, by definition, $x\equiv x \mod m$ .
Symmetry. It is clear that, given x,y and m such that $m\mid (x-y)$ , then $m\mid (y-x)$ . Therefore $x\equiv y \mod m \iff y\equiv x \mod m$
Transitivity. Let x,y,z and m such that $x\equiv y \mod m$ and $y\equiv z \mod m$ . Then, $m\mid (y-x)$ and $m\mid (z-y)$ . Therefore:

$m\mid [(y-x)+(z-y)] \implies m\mid (z-x) \implies x\equiv z \mod m$ .

In conclusion, $\equiv \mod m$ defines an equivalence relation.

6 0

3 years ago

Casie jumped off of a cliff into the ocean while on vacation. Her height as a function of time is modeled by the equation h = −1

erastova [34]

It takes Casie 3.5 seconds to hit the water.

3 0

3 years ago

Algebra 2 question. Which complex number lies in the shaded triangle in this graph?

Nadusha1986 [10]

The complex number are formed by a real part and an imaginary part.

The imaginary part is indicated with the letter i.

2i is only imaginary, so it is not complex

i - 1 is complex but is out of the triangle.

1 - i indeed is complex and is inside the triangle

2 - 3i is complex but is out of the triangle.

So, the answer is 1 - i

3 0

3 years ago

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What is the measure of the smallest angle? A 53 B 57 C 63 D 63