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3 years ago

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Which of the sets of ordered pairs represents a function? A = {(−4, 5), (1, −1), (2, −2), (2, 3)} B = {(2, 2), (3, −2), (9, 3),

(9, −3)}
A Only A
B Only B
C Both A and B
D Neither A nor B

1 answer:

dangina [55]3 years ago

3 0

Answer:

D Neither A nor B

Step-by-step explanation:

In each relation, there are some x-coordinates that repeat, and whenever that happens, the relations are not functions.

I am joyous to assist you anytime.

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Another question like the last, please help!!!

gizmo_the_mogwai [7]

W(2) = 2^2 + 2 = 4 + 2 = 6
u(w(2)) = -x -2 = -6 - 2 = -8

answer: u(w(2)) = -8

5 0

3 years ago

The measure of one angle of an octagon is two times smaller that of the other seven angles. What is the measure of each angle?

Anestetic [448]

Answer:

7 of the angles measure 144 degrees each and one angle measures 72 degrees

Step-by-step explanation:

Let

x -----> represent the measures of the seven same-size angles,

x/2 ----> represent the measure of the one that is "two times smaller."

we know that

The sum of internal angles of a polygon can be calculated as:

$S=180^o(n-2)$

where

n is the number of sides of the polygon

In this case

n=8 (octagon)

substitute

$S=180^o(8-2)=1,080^o$

so

The linear equation that represent this problem is

$\frac{x}{2}+7x=1,080$

solve for x

$\frac{15x}{2}=1,080\\\\15x=2,160\\\\x=144^o$

so

$\frac{x}{2}=72^o$

therefore

7 of the angles measure 144 degrees each and one angle measures 72 degrees

7 0

3 years ago

A horse takes 3 steps to walk the same distance for which a goat takes 4 steps. Suppose 1 step of the dog covers 1/2 of a metre.

almond37 [142]

Answer:

The goat would cover <u>9 meters</u> in taking 24 steps.

Step-by-step explanation:

<u><em>There is a mistake in the question so the correct question is below:</em></u>

A horse takes 3 steps to walk the same distance for which a goat takes 4 steps. Suppose 1 step of the horse covers 1/2 of a metre. How many metres would the goat cover in taking 24 steps?

Now, to find the meters goat cover in taking 24 steps.

As 1 step of horse covers = $\frac{1}{2} \ meter.$

So, 3 step of horse covers = $\frac{1}{2} \times 3$ $=\frac{3}{2} =1.5\ meters.$

<u><em>Thus, 3 steps of horse covers = 1.5 meter</em></u><em>s.</em>

<em>As given, the horse takes 3 steps to walk the same distance for which a goat takes 4 steps.</em>

<u><em>So, the distance covers by goat in 4 steps = 1.5 meters.</em></u>

Now, to get the meters goat cover in taking 24 steps by using unitary method:

If, the distance cover by the goat in 4 steps = 1.5 meters

So, the distance cover by the goat in 1 step = $\frac{1.5}{4}$

Thus, the distance cover by the goat in 24 steps = $\frac{1.5}{4}\times 24$

= $\frac{36}{3}$

= $9\ meters.$

Therefore, the goat would cover 9 meters in taking 24 steps.

8 0

3 years ago

When solving an equation, Drew's first step is shown below. Which property justifies

Diano4ka-milaya [45]

Answer:

good luck...

Step-by-step explanation:

3 0

3 years ago

Use lagrange multipliers to find the shortest distance, d, from the point (4, 0, −5 to the plane x y z = 1

Varvara68 [4.7K]

I assume there are some plus signs that aren't rendering for some reason, so that the plane should be $x+y+z=1$ .

You're minimizing $d(x,y,z)=\sqrt{(x-4)^2+y^2+(z+5)^2}$ subject to the constraint $f(x,y,z)=x+y+z=1$ . Note that $d(x,y,z)$ and $d(x,y,z)^2$ attain their extrema at the same values of $x,y,z$ , so we'll be working with the squared distance to avoid working out some slightly more complicated partial derivatives later.

The Lagrangian is

$L(x,y,z,\lambda)=(x-4)^2+y^2+(z+5)^2+\lambda(x+y+z-1)$

Take your partial derivatives and set them equal to 0:

$\begin{cases}\dfrac{\partial L}{\partial x}=2(x-4)+\lambda=0\\\\\dfrac{\partial L}{\partial y}=2y+\lambda=0\\\\\dfrac{\partial L}{\partial z}=2(z+5)+\lambda=0\\\\\dfrac{\partial L}{\partial\lambda}=x+y+z-1=0\end{cases}\implies\begin{cases}2x+\lambda=8\\2y+\lambda=0\\2z+\lambda=-10\\x+y+z=1\end{cases}$

Adding the first three equations together yields

$2x+2y+2z+3\lambda=2(x+y+z)+3\lambda=2+3\lambda=-2\implies \lambda=-\dfrac43$

and plugging this into the first three equations, you find a critical point at $(x,y,z)=\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)$ .

The squared distance is then $d\left(\dfrac{14}3,\dfrac23,-\dfrac{13}3\right)^2=\dfrac43$ , which means the shortest distance must be $\sqrt{\dfrac43}=\dfrac2{\sqrt3}$ .

7 0

3 years ago