All categories

3 years ago

Write an equation of a ine in slope-intercept form that passes through a point (4,-6) and has a slope of -3.

Mathematics

1 answer:

Sindrei [870]3 years ago

7 0

Answer:

y= -3x +6

Step-by-step explanation:

<u>slope-intercept form</u><u>:</u>

y=mx +c, where m is the slope and c is the y-intercept.

Given that the slope is -3, m= -3.

Susbt. m= -3 into the equation:

y= -3x +c

Since the line passes the point (4, -6),

(4, -6) lies on the line and must therefore satisfy the equation. Thus, susbt. (4, -6) into the equation to find the value of c.

y= -3x +c

when x=4, y= -6,

-6= -3(4) +c

-6= -12 +c

c= 12 -6

c= 6

Hence, the equation of the line is y= -3x +6.

You might be interested in

The average speed to go by car from home to college is 30 miles per hour. The average speed to go back home from college is 20 m

Levart [38]

Answer:

24 mph for both 60 miles and 40 miles.

Step-by-step explanation:

We need to find how long it takes to get to college and from it.

Speed x time (x) = Distance (60)

30x = 60

x=2

It takes two hours to get to college

20x = 60

x = 3

It takes 3 hours to get back. It's a total of 5 hours, 2 hours at 30mph and 3 at 20. Now we need to find the average

30+30+20+20+20=120

120/5= 24

The average speed for the round trip is 24.

To do the second part, we follow the same process, but replace 60 with 40 for distance.

30x=40

x= 1.33

20x=40

x=2

We can add the total distance and divide by total time to find the average.

The total distance is 80. Time is 3.33

80/3.33=24

The average speed is still 24.

3 0

3 years ago

Find and simplify each of the following for

WINSTONCH [101]

Answer:

(A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

(B) f(x + h) - f(x) = 8xh + 4h² - 6h

Step-by-step explanation:

* Lets explain how to solve the problem

- The function f(x) = 4x² - 6x + 6

- To find f(x + h) substitute x in the function by (x + h)

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) = 4(x + h)² - 6(x + h) + 6

- Lets simplify 4(x + h)²

∵ (x + h)² = (x)(x) + 2(x)(h) + (h)(h) = x² + 2xh + h²

∴ 4(x + h)² = 4(x² + 2xh + h²) = 4x² + 8xh + 4h²

- Lets simplify 6(x + h)

∵ 6(x + h) = 6(x) + 6(h)

∴ 6(x + h) = 6x + 6h

∴ f(x + h) = 4x² + 8xh + 4h² - (6x + 6h) + 6

- Remember (-)(+) = (-)

∴ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

* (A) f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

- Lets find f(x + h) - f(x)

∵ f(x + h) = 4x² + 8xh + 4h² - 6x - 6h + 6

∵ f(x) = 4x² - 6x + 6

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - (4x² - 6x + 6)

- Remember (-)(-) = (+)

∴ f(x + h) - f(x) = 4x² + 8xh + 4h² - 6x - 6h + 6 - 4x² + 6x - 6

- Simplify by adding the like terms

∴ f(x + h) - f(x) = (4x² - 4x²) + 8xh + 4h² + (- 6x + 6x) - 6h + (6 - 6)

∴ f(x + h) - f(x) = 8xh + 4h² - 6h

* (B) f(x + h) - f(x) = 8xh + 4h² - 6h

- Lets find $\frac{f(x+h)-f(x)}{h}$

∵ f(x + h) - f(x) = 8xh + 4h² - 6h

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh + 4h^{2}-6h}{h}$

- Simplify by separate the three terms

∴ $\frac{f(x+h)-f(x)}{h}=\frac{8xh}{h}+\frac{4h^{2} }{h}-\frac{6h}{h}$

∴ $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

* (C) $\frac{f(x+h)-f(x)}{h}=8x+4h-6$

4 0

3 years ago

A multiple choice test is composed of 10 questions. Each question has four possible answers, only one of the four possible answe

kompoz [17]

Answer:

Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:

$X \sim Binom(n=10, p=0.25)$

And the expected value is given by:

$E(X) = np =10*0.25 = 2.5$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

Let X the random variable of interest "Number of correct anwers on the tet", on this case we now that:

$X \sim Binom(n=10, p=0.25)$

And the expected value is given by:

$E(X) = np =10*0.25 = 2.5$

4 0

3 years ago

I don’t understand??

wlad13 [49]

Answer:

$\huge\boxed{\sf x = 10}$

Step-by-step explanation:

Hypotenuse = x

Base = 4

Perpendicular = $\sqrt{84}$

<u>Using Pythagoras Theorem:</u>

$\sf H^2 = P^2 + B^2\\\\ x^2 = (\sqrt{84} )^2 + (4)^2\\\\x^2 = 84 + 16\\\\x^2 = 100\\\\Taking \ sq \ root \ on \ both \ sides\\\\x = 10\\\\\rule[225]{225}{2}$

Hope this helped!

7 0

3 years ago

Write in standard form y=-3x+4 through (0,-1)

aev [14]

Y= -3x +4
So from the equation we can tell that m is 3 .

(0,-1)
(x, y)

0 = x
-1 = y

M = 3

Y = mx+ c
Just insert it
-1 = 3(0) + c
-1 = c

So thts mean the answe is y = 3x-1

4 0

4 years ago