All categories

3 years ago

In the standard (x, y) coordinate plane, what is the slope of the line joining the points (3,7) and (4,−8)?

1 answer:

4 0

$(3,7) \ and \ (4,-8)\\ \\ First \ find \ the \ slope \ of \ the \ line \ thru \ the \ points \: \\ \\ m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} } \\ \\m=\frac{-8-7}{4-3} = \frac{-15}{1}=-15 \\ \\Now \ use \ y = mx + b \ with \ either \ point \ to \ find \ b, \ the \ y-intercept \ : \\ \\ y=mx+b \\ \\7=-15*3+b\\ \\7=-45 +b \\ \\b=7+45\\ \\b=52 \\ \\ y= - 5x+52 \ is \ the \ answer
$

You might be interested in

URGENT help me please

WARRIOR [948]

Answer:

i have the same thing that im confused on

Step-by-step explanation:

confused help-

6 0

3 years ago

The miles-per-gallon obtained by the 1995 model Z cars is normally distributed with a mean of 22 miles-per-gallon and a standard

AlekseyPX

Answer:

0.42074

Step-by-step explanation:

In this question, we are asked to calculate the probability that a car will get less than 21 miles per gallon.

This is P(x < 21)

z = 21-22/5 = -1/5 = -0.2

Therefore the probability of getting less than 21 miles per gallon will be;

P(x<21) = P (z < -0.2)

= 0.42074

4 0

3 years ago

Tony wants to put a total of at least x stamps in 3 albums. If he puts 42 stamps in the first album and 58 stamps in the second

Pavel [41]

The answer is possibly B

6 0

3 years ago

Read 2 more answers

Evaluate the limit with either L'Hôpital's rule or previously learned methods.lim Sin(x)- Tan(x)/ x^3x → 0

Vsevolod [243]

Answer:

$\dfrac{-1}{6}$

Step-by-step explanation:

Given the limit of a function expressed as $\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}$ , to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

$= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)$

Step 2: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the function

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\$

Step 3: substitute x = 0 into the resulting function

$= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)$

Step 4: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\$

$= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)$

Step 6: Apply L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

$= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\$