All categories

3 years ago

Can someone please tell me what the range is?

Mathematics

1 answer:

ipn [44]3 years ago

8 0

Answer: y > -1.5 which is the same as y > -3/2

==========================================================

Explanation:

As x goes off to negative infinity, the term 3^x gets closer to 0.

So the expression 0.5*(3^x - 3) approaches 0.5*(0-3) = 0.5*(-3) = -1.5 = -3/2

The y value will never actually get to -1.5 because 3^x never actually reaches 0. It only gets closer and closer.

So the range is the set of possible y outputs such that y > -1.5 or y > -3/2

This means the horizontal asymptote is y = -3/2 or y = -1.5 which is the horizontal "electric fence" of sorts that the function curve gets closer to, but never touches.

You might be interested in

The height of a triangle is 3cm less than twice the base. The area is 10cm2

Kamila [148]

Answer:

The base is 4cm and the height is 5cm.

Step-by-step explanation:

This is a solve the system question. Call H the height of the triangle and B the base. The question tells us:

$H=2B-3$

and

$\frac{B \times H}{2}=10$

Sub the first equation into the second (as H is already isolated). You will end up with a quadratic equation - solve that any way you wish (e.g. quadratic formula). I've provided the factored form below which shows you the roots:

$\frac{B(2B-3)}{2}=10\\\frac{2B^2-3B}{2}=10\\2B^2-3B=20\\2B^2-3B-20=0\\(2B+5)(B-4)=0\\B= - \frac{5}{2},4$

In this question, we take B=4. You can't have a negative side length so the other answer is eliminated. Now sub the value for B into either of the original equations. I'll use the first, again because H is already isolated:

$H=2(4)-3\\H=8-3\\H=5$

3 0

3 years ago

3(4x + 2)<br> Pleaseee helppppp meeeeeee

zlopas [31]

Answer:

12x + 6

Step-by-step explanation:

3(4x + 2)

you distribute the 3 to 4x and 2

12x + 6

hope this helps

5 0

3 years ago

What is the equation in point−slope form of the line passing through (−2, −5) and (2, 3)?

Sloan [31]

Hi,

m = (y-y₀)/(x-x₀)
m = (-5-3)/(-2-2)
m = -8/-4
m = 2

For point (2,3) ⇒ x₀ = 2 and y₀ = 3

y-y₀ = m(x-x₀)
y-3 = 2(x-2)

For point (-2,-5) ⇒ x = -2 and y = -5

-5-3 = 2(-2-2)
-8 = 2(-4)
-8 = -8 ⇒ True

Answer:

C. The equation is y-3 = 2(x-2)

8 0

3 years ago

A car dealership has three locations, all about the same size, within the city. The graph shows last month's sales figures for o

BabaBlast [244]

Answer: C

Step-by-step explanation: 8 (1/3) 16 (2/3) 24 (3/3)

7 0

3 years ago

Determine whether statement (3) follows from statements (1)

larisa [96]

Answer: Law of Detachment

Step-by-step explanation:

1) If you swim (p), you must use earplugs (q)

2) Roy swims (p)

3) Roy must use earbuds (q)

4 0

3 years ago