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3 years ago

Graph each function.

Mathematics

1 answer:

artcher [175]3 years ago

7 0

Answer:

Step-by-step explanation:

We can recognize that the parent function for all of these graphs is going to be y=x^2. What this means is that we can graph y=x^2 and then apply transformations to it to get to all of these new graphs.

1. y = -x^2 + 5

We can see that the coefficient of the x^2 term is negative which tells us that the graph will now open downwards.

We also know that we are adding 5 on the outside of the argument which means it affect vertical shift. Therefore, we will be moving 5 units up.

2. y = x^2 - 4

We can see that the only change made to this equation is subtracting 4 on the outside of the squared part of the equation. Again, this signifies vertical movement, but since it's negative we will be moving the entire y = x^2 graph down 4 units.

3. y = -x^2 - 1

What do you notice about this graph?

- negative coefficient

- subtracting 1 outside of the argument

What do these mean?

- negative coefficient: opens downwards

- subtracting 1: move entire y = x^2 graph down 1 unit

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The number of customers that visit a local small business is 51,200 and has been continuously declining at a rate of 3.8% each y

Hunter-Best [27]

Answer:

Final amount of customers =30141.44

Step-by-step explanation:

Amount of customer remaining

A= p(1-r/n)^(nt)

P= initial amount of customers

R= rate but it's a negative rate

N= number of times

T= number of years

A= final amount of customers

A= p(1-r/n)^(nt)

A= 51200(1-0.038/14)^(14*14)

A= 51200(1-0.0027)^196

A= 51200(0.9973)^196

A= 51200(0.5887)

A= 30141.44

6 0

3 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$