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3 years ago

Write the equation of a line in point-slope form that has a slope of -1 and passes through the point (-2, 5).

1 answer:

7 0

$The\ point-slope\ form:y-y_1=m(x-x_1)\\----------------------\\m=-1;\ (-2;\ 5)\to x_1=-2;\ and\ y_1=5\\\\\boxed{y-5=-1(x-(-2))\to y-5=-(x+2)}$

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What is the units digit of 2 to the 50th power

11111nata11111 [884]

Notice that

$2^1=2$
$2^2=4$
$2^3=8$
$2^4=16$
$2^5=32$

so that for each power of 2, there is a pattern of period 4. This means that for integers $k\ge0$ , each of $2^{4k}$ , $2^{4k+1}$ , $2^{4k+2}$ , and $2^{4k+3}$ have the same units digit.

We can write $50=4(12)+2$ , and since $3=4(0)+2$ , it follows that $2^{50}$ and $2^3$ share the same units digits. So the units digit of $2^{54}$ is 8.

6 0

3 years ago

Consider the following function. f(x)=x^2+2x+1.

Gekata [30.6K]

Answer:

A) x² + 2x + 6

B) x² + 2x - 7

C) ¼(x²+2x+1))

D) 6x²+12x+6

E) -x²-2x-1

Step-by-step explanation:

A) f(x) + 5 =x²+2x+1 + 5

= x² + 2x + 6

B) f(x)-8,=x^2+2x+1-8

= x² + 2x - 7

C) ¼f(x) = ¼(x²+2x+1)

D) 6f(x) = 6(x²+2x+1) = 6x²+12x+6

E) -f(x) = -(x²+2x+1) = -x²-2x-1

4 0

3 years ago

How long will it take you to get home?

SVEN [57.7K]

It depends on where you are....

4 0

3 years ago

I need help with 11 and 12

Yakvenalex [24]

Answer:

Both are inverse pairs

Step-by-step explanation:

Question 11

$g(x)= 4 + \dfrac{8}{5}x$

(a) Rename g(x) as y

$y = 4 + \dfrac{8}{5}x$

(b) Solve for x :

$\dfrac{8}{5}x = y - 4$

(c) Multiply each side by ⅝

$x = \dfrac{5}{8}(y - 4) = \dfrac{5}{8}y - \dfrac{5}{2}$

(d) Switch x and y

$y = \dfrac{5}{8}x - \dfrac{5}{2}$

(e) Rename y as the inverse function

$g^{-1}(x) = \dfrac{5}{8}x - \dfrac{5}{2}$

(f) Compare with your function

$f(x) = \dfrac{5}{8}x - \dfrac{5}{2}\\\\f(x) = g^{-1}(x)$

f(x) and g(x) are inverse functions.

The graphs of inverse functions are reflections of each other across the line y = x.

In the first diagram, the graph of ƒ(x) (blue) is the reflection of g(x) (red) about the line y = x (black)

Question 12

h(x)= x - 2

(a) Rename h(x) as y

y = x - 2

(b) Solve for x:

x = y + 2

(c) Switch x and y

y = x + 2

(e) Rename y as the inverse function

h⁻¹(x) = x + 2

(f) Compare with your function

f(x) = x + 2

f(x) = h⁻¹(x)

h(x) and ƒ(x) are inverse functions.

The graph of h(x) (blue) reflects ƒ(x) (red) across the line y = x (black).

5 0

3 years ago

A computer is used to generate passwords made up of numbers 0 through 9 and lowercase letters. The computer generates 400 passwo

tamaranim1 [39]

The prediction for the number of passwords in which the first character is a vowel is 56 passwords.

<h3>How to find that a given condition can be modelled by binomial distribution?</h3>

Binomial distributions consist of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

$X \sim B(n,p)$

The probability that out of n trials, there'd be x successes is given by

$P(X =x) = \: ^nC_xp^x(1-p)^{n-x}$

The expected value and variance of X are:

$E(X) = np\\$

Given that the characters that can be used are numbers 0 through 9 and lowercase letters. Therefore, a total of 36 different characters are available.

Since we need to know the passwords made with vowels, therefore, the probability of a password in which the first character will be a, e, i, o, u is (5/36).

Now as the computer produces 400 passwords, therefore, the predicted value can be written as,

$E = np = 400 \times \dfrac{5}{36} = 55.5556 \approx 56$

Hence, the prediction for the number of passwords in which the first character is a vowel is 56 passwords.

Learn more about Binomial Distribution:

brainly.com/question/14565246

#SPJ1

5 0

2 years ago