All categories

3 years ago

Erin writes the set of ordered pairs below. The set represents a function.

1 answer:

7 0

Point A shows that she is incorrect.
With functions, you can perform the "straight line test through each point. If the line goes through both points, you know it's not a function.
If we plotted point A, it'd fail the straight line test because the given point (-6, 7) already has -6 as an x value.
Hope this helps!

You might be interested in

I will give 5 points

ikadub [295]

Use the sum of cubes factoring rule

$a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

to transform the left hand side into the right hand side.

$\frac { \sin^{3} \theta + \cos^{3} \theta } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\\frac { (\sin \theta + \cos \theta)(\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta) } { \sin \theta + \cos \theta } = 1 - \sin \theta \cdot \cos \theta\\\\$

$\sin^2 \theta - \sin \theta \cdot \cos\theta + \cos^2 \theta = 1 - \sin \theta \cdot \cos \theta\\\\(\sin^2 \theta + \cos^2\theta)- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta\\\\1- \sin \theta \cdot \cos\theta = 1 - \sin \theta \cdot \cos \theta \ \ \checkmark\\\\$

Throughout the entire process, the right hand side stayed the same.

On the last step, I used the pythagorean identity.

8 0

2 years ago

Solve for x in the equation x2 - 12x+ 36 = 90

12345 [234]

Answer:

6 + 3 $\sqrt{10\\}$ or 6 - 3 $\sqrt{10\\}$

Step-by-step explanation:

x^2 - 12x + 36 = 90

x^2 - 12x - 54 = 0

x = $\frac{-b +/- \sqrt{b^{2} + 4ac }}{2a}$

a = 1, b= -12, c= -54

6 + 3 $\sqrt{10\\}$ or 6 - 3 $\sqrt{10\\}$

6 0

3 years ago

A person invests $1,150 in an account that earns 5% annual interest compounded continuously. Find when the value of the investme

AfilCa [17]

Answer:

11.1 years

Step-by-step explanation:

The formula for interest compounding continuously is:

$A(t)=Pe^{rt}$

Where A(t) is the amount after the compounding, P is the initial deposit, r is the interest rate in decimal form, and t is the time in years. Filling in what we have looks like this:

$2000=1150e^{{.05t}$

We will simplify this first a bit by dividing 2000 by 1150 to get

$1.739130435=e^{.05t}$

To get that t out the exponential position it is currently in we have to take the natural log of both sides. Since a natural log has a base of e, taking the natual log of e cancels both of them out. They "undo" each other, for lack of a better way to explain it. That leaves us with

ln(1.739130435)=.05t

Taking the natural log of that decimal on our calculator gives us

.5533852383=.05t

Now divide both sides by .05 to get t = 11.06770477 which rounds to 11.1 years.

7 0

3 years ago

Sarah uses a recipe to make 2 gallons of juice. Two of the containers she plans to use to store the juice have a capacity of one

Allisa [31]

Answer:

14 pint containers.

Step-by-step explanation:

First we have to convert gallon to quart.

2 gallons = 8 quarts

There are 2 containers that added up to 1 quart, so let's subtract the one quart from the 2 gallons(8 quarts), leaving behind 7 quarts.

The conversion between quarts and pints are 1qt=2pt, according to the key you provided. Then 7 quarts will equal to 14 pints. And therefore, she will need 14 pint containers.

4 0

3 years ago

Determine how long it will take an object to rotate through 6.9 revolutions at an angular velocity of 3.1 radians per second. Us

gregori [183]

Answer: 13 . 99 seconds

Step-by-step explanation:

The formula to find how long it will take an object to rotate through 6.9 revolutions at an angular velocity is given as :

t = 2π x number of revolutions / angular velocity

Therefore :

t = 2π x 6.9 / 3.1

t = 2 x 3.142 x 6.9 / 3.1

t = 43.3596/3.1

t = 13. 98696774194

to the nearest tenth

t = 13. 99s

7 0

3 years ago