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3 years ago

Determine if the set of ordered pairs is a relation or a function.

1 answer:

3 0

to be a function, each input can have only one output. For these points, each x has only one y, so it it a function. A relation, just describes x to y, so it is both

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Colton has 32 blue marbles and 24 white marbles. If he wants to put them in identical groups without any left over, what is the

Alja [10]

The awnser is 50 because 32 divided by 47 is 50

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3 years ago

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Find slope. <br>a. 4<br>b. -1/4<br>c. 1/4<br>d-4

Ganezh [65]

Answer:

1/4

Step-by-step explanation:

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3 years ago

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How to find horizontal and vertical asymptotes from equations?

julsineya [31]

This is how u would find horizontal and vertical asymptotes

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3 years ago

2. Given a quadrilateral with vertices (−1, 3), (1, 5), (5, 1), and (3,−1):

zlopas [31]

<h2>Explanation:</h2>

In every rectangle, the two diagonals have the same length. If a quadrilateral's diagonals have the same length, that doesn't mean it has to be a rectangle, but if a parallelogram's diagonals have the same length, then it's definitely a rectangle.

So first of all, let's prove this is a parallelogram. The basic definition of a parallelogram is that it is a quadrilateral where both pairs of opposite sides are parallel.

So let's name the vertices as:

$A(-1,3) \\ \\ B(1,5) \\ \\ C(5,1) \\ \\ D(3,-1)$

First pair of opposite sides:

<u>Slope:</u>

$\text{For AB}: \\ \\ m=\frac{5-3}{1-(-1)}=1 \\ \\ \\ \text{For CD}: \\ \\ m=\frac{1-(-1)}{5-3}=1 \\ \\ \\ \text{So AB and CD are parallel}$

Second pair of opposite sides:

<u>Slope:</u>

$\text{For BC}: \\ \\ m=\frac{1-5}{5-1}=-1 \\ \\ \\ \text{For AD}: \\ \\ m=\frac{-1-3}{3-(-1)}=-1 \\ \\ \\ \text{So BC and AD are parallel}$

So in fact this is a parallelogram. The other thing we need to prove is that the diagonals measure the same. Using distance formula:

$d=\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^2} \\ \\ \\ Diagonal \ BD: \\ \\ d=\sqrt{(5-(-1))^2+(1-3)^2}=2\sqrt{10} \\ \\ \\ Diagonal \ AC: \\ \\ d=\sqrt{(3-1)^2+(-5-1)^2}=2\sqrt{10} \\ \\ \\$

So the diagonals measure the same, therefore this is a rectangle.

5 0

3 years ago

A series of three? separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers. Each

Nadya [2.5K]

Answer:

$312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$

Step-by-step explanation:

We have been given that a series of 3 separate, adjacent tunnels is constructed through a mountain. Its length is approximately 25 kilometers.

Each of the three tunnels is shaped like a half-cylinder with a radius of 5 meters.

Since we know that volume of a semicircular or a half cylinder is half the volume of a circular cylinder.

$\text{Volume of a semicircular cylinder}=\frac{\pi r^2h}{2}$ , where,

r = Radius of cylinder,

h = height of the cylinder.

Upon substituting our given values in volume formula we will get,

$\text{Volume of a semicircular cylinder}=\frac{\pi (5\text{ km})^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*25\text{ km}^2*25\text{ km}}{2}$

$\text{Volume of a semicircular cylinder}=\frac{\pi*625\text{ km}^3}{2}$

$\text{Volume of a semicircular cylinder}=\pi*312.5\text{ km}^3$

$\text{Volume of a semicircular cylinder}=981.74770\text{ km}^3$

Therefore, the volume of earth removed to build the three tunnels is $312.5\pi \text{ km}^3\approx 981.75\text{ km}^3$ .

4 0

3 years ago