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3 years ago

Describe how to find the sums -4 + 2 and -4 + ( -2 ) on a number line

Mathematics

1 answer:

ivolga24 [154]3 years ago

4 0

Answer:

For the first one, you go from -4 on the number line and move 2 spaces to the right to get -2. For the second one, you start at -4 again and then you move to the left 2 spaces since your subtracting.

Step-by-step explanation:

-viridiancat4, an 8th grader :)

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What best describes the asymptote of an exponential function of the form f(x)=b^x?

horrorfan [7]

It depends on the value of b

Exponential functions are defined for positive values of the base [ŧex] b [/tex]. Also, they're not defined if $b=1$ , or at least let's say that this is a trivial case, since it is the constant function 1.

Case 0<b<1:

If the base sits between 0 and 1, the exponential function is constantly decreasing. The explanation is quite intuitive, assume for the sake of simpleness that b is rational. If it sits between 0 and 1, it means that it can be written as a fraction p/q, with p<q. So, if you give a large exponent to b, you obtain

$\frac{p^x}{q^x},\quad p^x \ll q^x \text{ as } x \to \infty$

On the other hand, if you consider negative exponents, you switch numerator and denominator and then raise to the same exponent the fraction q/p, which gets larger and larger.

So, if 0<b<1, we have

$\lim_{x \to -\infty} b^x = \infty,\qquad \lim_{x \to \infty} b^x = 0$

and thus 0 is a horizontal asymptote as x tends to (positive) infinity.

Case b>1:

This case is very similar, except all roles are inverted. Now you start with a fraction p/q where p>q. So, with positive, large exponents you get

$\frac{p^x}{q^x},\quad p^x \gg q^x \text{ as } x \to \infty$

And as before, negative exponents switch numerator and denominator, so the fraction becomes q/p and thus you have

$\lim_{x \to -\infty} b^x = 0,\qquad \lim_{x \to \infty} b^x = \infty$

So, again, 0 is a horizontal asymptote, but this time for x tending towards negative infinite.

6 0

3 years ago

Read 2 more answers

Ayo runs a fairground game.In each turn, a player rolls a fair dice numbered 1 - 6 and spins a fair spinner numbered 1 - 12.It c

aksik [14]

Using the definition of expected value, it is found that Ayo can be expected to make a profit of £55.8.

The <em>expected value</em> is given by the <u>sum of each outcome multiplied by it's respective probability.</u>

In this problem:

The player wins $6, that is, Ayo loses £6, if he rolls a 6 and spins a 1, hence the probability is $\frac{1}{6} \times \frac{1}{12} = \frac{1}{72}$ .

The player wins $3, that is, Ayo loses £3, if he rolls a 3 on at least one of the spinner or the dice, hence, considering three cases(both and either the spinner of the dice), the probability is $\frac{1}{6} \times \frac{1}{12} + \frac{1}{6} \times \frac{11}{12} + \frac{5}{6} \times \frac{1}{12} = \frac{1 + 11 + 5}{72} = \frac{17}{72}$

In the other cases, Ayo wins £1.40, with $1 - \frac{18}{72} = \frac{54}{72}$ probability.

Hence, his expected profit for a single game is:

$E(X) = -6\frac{1}{72} - 3\frac{17}{72} + 1.4\frac{54}{72} = \frac{-6 - 3(17) + 54(1.4)}{72} = 0.2583$

For 216 games, the expected value is:

$E = 216(0.2583) = 55.8$

Ayo can be expected to make a profit of £55.8.

To learn more about expected value, you can take a look at brainly.com/question/24855677

6 0

3 years ago

Find the slope of line passing through the two points, (7, 1) and (-2, 1).

Mamont248 [21]

Answer: m = 0

Step-by-step explanation:

Slope (m) = y2 - y1/,x2 - x1 : meaning increase in y divided by increase in x . it can also be written as ∆y/∆x

y1= 1, y2 = 1, x1 = 7, x2 = -2

Substitute for those values in the equation above

m = 1 -1/-2 - 7

= 0/-9

Therefore,

m = 0

The slope of the line passing through those coordinates = 0

3 0

4 years ago

ZABD and ZDBC are supplementary angles.

adell [148]

x=54°

Answer:

x+126=180 supplementary

x=180-126

x=54

4 0

3 years ago

Which solid figure has one polygon base

Dahasolnce [82]

Answer:

the answer your looking for is a pyramid

Step-by-step explanation:

8 0

3 years ago