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slava [35]
3 years ago
7

What is the equation of the line whose slope is 1/3 and y-intercept is -4?

Mathematics
1 answer:
faltersainse [42]3 years ago
3 0

Answer:

y=1/3x-4

Step-by-step explanation:

the slope-intercept format of the line is y=mx+b, where m is the slope and b is the y intercept.

we are given the slope (1/3) and the y intercpet (-4).

substitute the numbers into the equation

y=1/3x-4

the answer is y=1/3x-4

hope this helps!

You might be interested in
Suppose that 43% of a town's population have blue eyes, 46% have blonde hair, and 24% have both blue eyes and blonde hair. What
Varvara68 [4.7K]

We need to find the probability of the event:

having blue eyes or blond hair

This event is the union of the events:

A: having blue eyes.

B: having blond hair.

So, we need to find the probability P(A ∪ B). In order to do so, we can use the following formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

We know that the probability of the intersection of A and B (having both) is

P(A ∩ B) = 24%

Also:

P(A) = 43%

P(B) = 46%

Then, using those values into the above formula, we find:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

P(A ∪ B) = 43% + 46% - 24%

P(A ∪ B) = (43 + 46 - 24)%

P(A ∪ B) = 65%

3 0
1 year ago
[Will mark as brainliest]
Aleks04 [339]

The answer is: f^{-1} = 4x^2-3,\quad\text{for  } x \leq 0

The inverse of a function f(x) is another function, f^{-1}(x), with the following property:

f(f^{-1}(x)) = f^{-1}(f(x)) = x

In other words, the inverse of a function does exactly "the opposite" of what the original function does, and so if you compute them both in sequence you return to the starting point.

Think for example to a function that doubles the input, f(x)=2x, and one that halves it: f(x)= \frac{x}{2}. Their composition is clearly the identity function f(x)=x, since you consider "twice the half of something", or "half the double of something".

In general, to invert a function y=f(x), you have to solve the expression for x, writing an expression like x = g(y). If you manage to do so, then g is the inverse of f.

In your case, you have

f(x) = y = -\frac{1}{2}\sqrt{x+3}

Multiply both sides by -2 to get

-2y = \sqrt{x+3}

Square both sides to get

4y^2 = x+3

Finally, subtract 3 from both sides to get

x = 4y^2 - 3

Since the name of the variables doesn't really have a meaning, you can say that the inverse function is

f^{-1}(x) = 4x^2 - 3

As for the domain of the inverse function, remember what we said ad the beginning: if the original function goes from set A (domain) to set B (codomain), then the inverse function goes from set B (domain) to set A (codomain). This means that the inverse function is defined on an element in B if and only if that element belongs to the range of the original function, i.e. the set of the elements of the codomain b \in B such that there exists a \in A : f(a)=b. So, we need the range of f(x).

We know that the range of g(x)=\sqrt{x} is [0,\infty). When you transform it to g(x)=\sqrt{x+3} you simply translate the graph horizontally, so the range doesn't change. But when you multiply the function times -\frac{1}{2} you affect both extrema of the range, turning it into (-\infty,0], which you can simply write as x \leq 0

4 0
3 years ago
The location of point D is (7,1) the location of point F is (5,4). Determine the location of point E which is 1/3 of the way fro
IceJOKER [234]

Answer:

( 19/3 , 2 )

Step-by-step explanation:

Given in the question,

point D(7,1)

x1 = 7

y1 = 1

point F(5,4)

x2 = 5

y2 = 4

Location of point E which is 1/3 of the way from D to F

which means ratio of point E from D to F is 1 : 2

<h3>a : b</h3>

1 : 2

xk = x1 + \frac{a}{a+b}(x2-x1)

yk = y1 + \frac{a}{a+b}(y2-y1)

Plug values in the equation

xk = 7 + (1)/(1+2) (5-7)

xk = 19/3

yk = 1 + (1)/(1+2)(4-1)

yk = 2

6 0
3 years ago
100 points!
GenaCL600 [577]

Answer: If i was living there usually , The climate in Ancient Greece generally has hot summers and mild winters. Because it can get so hot, most people wore lightweight clothing throughout most of the year. They would put on a cloak or wrap during the colder days of the winter months. The environment would make a HUGE impact on the Greeks by teaching them how to collect food and survive in a harsh environment. Therefore, I would have to adapt to adapt to their environment efficiently. The environment also affected them because they had to learn to fish instead of hunt on

Step-by-step explanation: This is how I would do it.

6 0
3 years ago
Elena and Jada are 12 miles apart on a path when they start moving towards each other Elena runs at a constant speed of 5 miles
Leviafan [203]
If you really want to figure this out you make an equation to solve for the time
let's let
x = time from Elena to Jada and
x = time from Jada to Elena
12 then the equation
12 = 5x +3x
would help figuring out their distance say for one of them
12 = x(5+3)
12/8 = x
1.5 = x
1. 5 hours they will meet up
7 0
3 years ago
Read 2 more answers
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