Which equation represents a line that passes through (2,-2) and has a slope of 3?

Identify the type of function represented by... please help

Vladimir [108]

Answer:

Exponential decay.

Step-by-step explanation:

You can use a graphing utility to check this pretty quickly, but you can also look at the equation and get the answer. Since the function has a variable in the exponent, it definitely won't be a linear equation. Quadratic equations are ones of the form ax^2 + bx + c, and your function doesn't look like that, so already you've ruled out two answers.

From the start, since we have a variable in the exponent, we can recognize that it's exponential. Figuring out growth or decay is a little more complicated. Having a negative sign out front can flip the graph; having a negative sign in the exponent flips the graph, too. In your case, you have no negatives; just 2(1/2)^x. What you need to note here, and you could use a few test points to check, is that as x gets bigger, (1/2) will get smaller and smaller. Think about it. When x = 0, 2(1/2)^0 simplifies to just 2. When x = 1, 2(1/2)^1 simplifies to 1. Already, we can tell that this graph is declining, but if you want to make sure, try a really big value for x, like 100. 2(1/2)^100 is a value very very very veeery close to 0. Therefore, you can tell that as the exponent gets larger, the value of the function goes down and gets closer and closer to zero. This means that it can't be exponential growth. In the case of exponential growth, as the exponent gets bigger, your output should increase, too.

3 0

3 years ago

Ella already knew 5 appetizer recipes before starting culinary school, and she will learn 2 new

Natalija [7]

A = 2w+5

example: on week three, she would have the recipes from the other weeks that you have to account for as well as the extra five

2(3)+5=11 so A would equal 11 by week three.

Use multiplication because it is essentially repeated addition.

2(from week 1) + 2(from week 2) + 2(from week 3) + 5(prior to school) =11

5 0

3 years ago

Surface Area of the pyramid

hichkok12 [17]

Answer:

C

Step-by-step explanation:

the total surface area of such a pyramid is the sum of 5 areas :

1 bottom square (8×8)

4 side triangles

the area of a triangle is

baseline × height / 2

now, we know the baseline of the 4 triangles, but what is their height (at least we know, all 4 have the same height, as the pyramid is totally regular) ?

the height of the side triangles is the slant height of the pyramid (the distance from the middle of a sideline to the top of the pyramid).

we get this by imagining a right-angled triangle inside the pyramid :

one leg is the inner height of the pyramid.

the second leg is the connection on the bottom square from the base of the inner height to the middle point of a sideline). this is half the length of a sideline.

and the baseline (Hypotenuse) is the slant height of the pyramid.

we can use Pythagoras

c² = a² + b²

with c being the Hypotenuse (side opposite of the 90° angle).

slant height² = 7² + (8/2)² = 49 + 4² = 49 + 16 = 65

slant height = sqrt(65) = 8.062257748... in

so, we get a areas

bottom square = 8×8 = 64 in²

a side triangle = 8×sqrt(65)/2 = 4×sqrt(65) =

= 32.24903099... in²

all 4 side triangles = 4×32.24903099... =

= 128.996124... in²

and we get as total surface area

64 + 128.996124... = 192.996124... in² ≈ 193.00 in²

8 0

2 years ago

Annalee hammered in nail into a piece of wood each time she hammer the nail it went to 1/8 Inch deeper into the word if she hamm

mash [69]

Answer: 0.5 inch

Step-by-step explanation:

Given

On hammering nail advances $\frac{1}{8}\ inch$ each time

Annalee hammered 4 times

So, total advancement of nail= $4\times \dfrac{1}{8}=\dfrac{1}{2}\ inch$

3 0

3 years ago

***Question is on the picture

RUDIKE [14]

Answer:

M(4, -3)

Step-by-step explanation:

Reflecting over the x-axis is simple:

If the x is positive, the reflection would be negative and vice versa.

In this case, the <em>y </em>isn't affected since it's only reflecting over the x-axis.

So, M is at the coordinates (4, -3)

5 0

3 years ago