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3 years ago

What is the range of the function in this table?

Mathematics

2 answers:

bekas [8.4K]3 years ago

5 0

Answer: A) 1, 2, 4

Step-by-step explanation:

The range of a function is every y value.

Tju [1.3M]3 years ago

5 0

Answer:

A. {1, 2, 4}

Step-by-step explanation:

Well let’s take a step back,

What is range?

Range is the amount of y-value son a graph or table.

So the range is (1, 4, 2)

You might be interested in

The population of Earth is estimated to be 7.4 billion people, or 7,400,000,000. What is this number in scientific notation?

Nitella [24]

Answer:

7.4 x 10 to the 9th power

Step-by-step explanation:

At the end of numbers, there is a decimal point. when writing in function notation, you bring the point to the left or to the right depending on if it is a negative or a positive number

in this problem, you are dealing with a positive number, so bring the decimal point to the left. count how many numbers it takes to get in between, in this number, 7 and 4. it takes 9 spaces to the left. now the decimal point has been moved, your number goes from 7,400,000,000 to 7.4 x 10 to the 9th power(7.4 x 10^9)

7 0

3 years ago

A right triangle has side lengths a, b, and c as shown below.

Musya8 [376]

Answer:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Step-by-step explanation:

Given that

A right triangle has side lengths a, b, and c

Because you did not attached photo of the right triangle so I will assume that:

Side a is the adjacent (A)
Side b is the opposite (O)
Side c is the hypotenuse (H)

(Please have a look at the attached photo)

To solve for the trigonometric functions of x, we need to recall the ratios they represent as shown below.

$\sin x = \frac{O}{H}\\\cos x = \frac{A}{H}\\\tan x = \frac{O}{A}$

EX: the sine of x is equal to the side opposite of angle x over the hypotenuse. Hence, we have the expressions of the trigonometric functions as shown below:

$\bold{\sin x = \frac{b}{c}}\bold{\\\cos x = \frac{a}{c}}\bold{\\\tan x = \frac{b}{a}}$

Hope it will find you well

4 0

3 years ago

PLZ HELP, DUE TONIGHT!! Find the values of a and b such that f(x) is continuous at x=

Goryan [66]

Answers:

a = 2 and b = -4

============================================================

Explanation:

Let's define the three helper functions

f(x) = ax^2 - b
h(x) = 6
j(x) = 5ax+b

which are drawn from the piecewise function. The g(x) function will change depending on what the input is.

If x < 1, then g(x) = f(x).
If x = 1, then g(x) = h(x)
If x > 1, then g(x) = j(x)

Since we want g(x) to be continuous at x = 1, this must mean the three functions f(x), h(x), j(x) must have the same output value when the input is x = 1.

Because h(x) = 6 is a constant function, the output is always 6 regardless of the input. Therefore, we want f(x) and j(x) to have 6 as their output when x = 1. Or else, the pieces won't connect.

Plug x = 1 into the f(x) function to get

f(x) = ax^2 - b

f(1) = a(1)^2 - b

f(1) = a - b

Set this equal to the desired output of 6 and we end up with the equation a-b = 6. Solving for 'a' leads to a = b+6.

------------

We'll use the same idea for j(x)

j(x) = 5ax + b

j(1) = 5a(1) + b

j(1) = 5a + b

5a+b = 6

5(b+6) + b = 6 ... plug in a = b+6; solve for b

5b+30+b = 6

6b+30 = 6

6b = 6-30

6b = -24

b = -24/6

b = -4

Which then leads to,

a = b+6

a = -4+6

a = 2

------------

Since a = 2 and b = -4, we go from this

$g(x) = \begin{cases}ax^2-b, \ \ x < 1\\6, \ \ x = 1\\5ax+b, \ \ x > 1\end{cases}$

to this

$g(x) = \begin{cases}2x^2+4, \ \ x < 1\\6, \ \ x = 1\\10x-4, \ \ x > 1\end{cases}$

Meaning

f(x) = 2x^2+4 and j(x) = 10x-4

You should find that plugging x = 1 into each of those two functions leads to 6 as the output.

The graph is shown below. Note the red graph f(x) is only drawn when x < 1. Similarly, j(x) is only drawn when x > 1. The orange point represents h(x) which only happens when x = 1. So as the name implies, the piecewise function g(x) is composed of pieces of the three functions f(x), h(x), j(x).

3 0

3 years ago

Expression 7 + 9/4 can also be written in the form ofc÷a^b . A = b= c=

Arlecino [84]

<h3>Answer: a = 37, b=2 and c=2.</h3>

Step-by-step explanation: Given expression 7 + 9/4.

Let us simplify given sum of fractions by taking common denominator, we get

$\frac{7}{1} +\frac{9}{4}$

Common denominator is 4.

Therefore, multiplying top and bottom of 7/1 by 4, we get

$\frac{7\times 4}{1\times 4} +\frac{9}{4} = \frac{28}{4} +\frac{9}{4}$ .

We got same denominators,

So, combining top numbers, we get

$\frac{28+9}{4}=\frac{37}{4}$

We can read 37/4 as 37 divided by 4.

Therefore, 37 ÷ 4.

Let us write 4 as the power of 2.

$4= 2^2.$

37 ÷ $2^2$

On comparing c÷a^b and 37 ÷ 2^2, we can see..

5 0

4 years ago

Shelley plans to enclose the patio with fencing. If fencing costs $5 per meter, how much will it cost to enclose the patio?

mixer [17]

Answer:

$120

Step-by-step explanation:

<u><em>The complete question is</em></u>

Shelley designed the patio below, in which one side of the patio is a wall of the house. The length of each side of a square on the grid represents 3 meters.

Shelley plans to enclose the patio with fencing. If fencing costs $5 per meter, how much will it cost to enclose the patio?

$40

$60

$120

$180

<u><em>The picture in the attached figure</em></u>

Find the perimeter of the patio in units (without the wall of the house)

$P=(6+12+6)=24\ m$