All categories

3 years ago

1. Which is the graph of the function y = −3(2)^x?

Mathematics

2 answers:

qaws [65]3 years ago

7 0

Last picture is the correct one

Leni [432]3 years ago

6 0

Answer:

Step-by-step explanation:

y = − 3 ( 2 ) x

Exponential functions have a horizontal asymptote. The equation of the horizontal asymptote is

y = 0 .

Horizontal Asymptote:

y = 0

You might be interested in

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

dsp73

Answer:

The required sequence is $a_n=20(\frac{1}{2})^{n-1}$ . The average rate of change from n = 1 to n = 3 is -7.5.

Step-by-step explanation:

From the given graph it is clear that the sequence is a GP because the all terms are half of their previous terms.

Here, $a_2=10,a_3=5,a_4=2.5,a_5=1.25$

$r=\frac{a_3}{a_2}=\frac{5}{10}=\frac{1}{2}$

The common ratio of GP is 1/2.

$r=\frac{a_2}{a_1}$

$\frac{1}{2}=\frac{10}{a_1}$

$a_1=20$

The first term of the sequence is 20.

The formula for sequence is

$a_n=a(r)^{n-1}$

Where a is first term and r is common difference.

The required sequence is

$a_n=20(\frac{1}{2})^{n-1}$

The formula for rate of change is

$m=\frac{f(x_2)-f(x_1)}{x_2-x_1}$

The average rate of change from n = 1 to n = 3 is

$m=\frac{f(3)-f(1)}{3-1}$

$m=\frac{5-20}{3-1}$

$m=\frac{-15}{2}=-7.5$

Therefore the required sequence is $a_n=20(\frac{1}{2})^{n-1}$ . The average rate of change from n = 1 to n = 3 is -7.5.

8 0

4 years ago

Read 2 more answers

Help please.........

Tanya [424]

Answer:

y = 4.5 x

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Three black beads, two red beads, and a yellow bead are arranged in a line. What is the probability that no black bead is adjace

shtirl [24]

Answer:

Probability of no black bead is adjacent to the yellow bead is = 0.966

Step-by-step explanation:

First to arrange all the beads without restrictions = 6! = 720

Probability the black bead is adjacent to Yellow bead = 4!/6! = 24 /720

= 0.0333

Probability of no black bead is adjacent to the yellow bead is

= 1- Probability the black bead is adjacent to Yellow bead

= 1-0.033

= 0.966

6 0

4 years ago

Help me please asap I need to know fully how to solve this problem

vivado [14]

Consider the absolute value, because we only worry about the quadrant later.

$\text{Consider: } sin(A) = |-\frac{\sqrt{3}}{4}|$
$sin(A) = \frac{\sqrt{3}}{4}$

Thus, we know that the hypotenuse has a length of 4 units, and the side opposite the angle, A is √3, because this is the nature of the sine function in relation to its triangular component.

The missing side can be found using Pythagoras' Theorem:
4² - (√3)² = x²
16 - 3 = x²
13 = x²
x = √13

$\therefore tan(A) = \pm \sqrt{\frac{3}{13}}$

Since angle A is in the third quadrant, the tangent function will produce a positive angle.

$tan(A) = \sqrt{\frac{3}{13}}$
$\text{Rationalise the denominator: } \frac{\sqrt{3}}{\sqrt{13}} \cdot \frac{\sqrt{13}}{\sqrt{13}}$

$tan(A) = \frac{\sqrt{39}}{13}$

7 0

4 years ago

What is the distance between (10, 6) and (-2, -3)

Helga [31]

Answer:

15 units.

Step-by-step explanation:

The distance between the points (x1, y1) and (x2, y2) is

√(x1-y1)^2 + (y1-y2)^2))

So here it is:

√(10- -2)^2 + (6- -3)^2)

= √(144+81)

= √225

= 15.

4 0

4 years ago