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3 years ago

I don't get this. (write a linear function f with the given values)

Mathematics

2 answers:

ELEN [110]3 years ago

6 0

Answer:

$f(x) = 1/2*x$

Step-by-step explanation:

Linear functions are functions of the form "f(x) = a * x + b" where 'a' and 'b' are constants (numbers) and x is the input.

In this problem, you are given the inputs and outputs of the function. Since you know it is linear, you begin thinking about what number you can multiply on the left to get the value on the right.

-4 / 2 = -2

-2 / 2 = -1

0 / 2 = 0

We find that dividing x by 2 gives the correct output. Dividing by 2 is the same as multiplying by 1/2. Therefore, we have found the answer!

f(x) = 1/2 * x

Nataly [62]3 years ago

3 0

Answer:

f(x) = (1/2)x

Step-by-step explanation:

f(x) = mx + b

m is the slope

b is the y-intercept

m = rise/run

for every run of 2 in x

f(x) rises 1

m = 1/2

The y-intercept occurs when x = 0

from the table f(0) = 0

b = 0

Therefor

f(x) = (1/2)x + 0

f(x) = (1/2)x

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Graphs of the following equations are straight lines except :

meriva

Answer:

Step-by-step explanation:

D. This contains an x^2 and is called a parabola ( curved line like a U).

4 0

3 years ago

Find the equation of a line with a slope of 13/2 that passes through the point (−2, — 10).

Darya [45]

Answer: $y=\frac{13}{2} x+3$

Step-by-step explanation:

Remember the point-slope equation which is $y-y_{1} = m(x-x_{1} )$ where $(x_{1} , y_{1} )$ is your point and $m$ is your slope.

Given that we substitute what you have:

$y-(-10) =\frac{13}{2} (x - (-2))$

Minus and minus give us positive:

$y+10 =\frac{13}{2} (x +2)$

Multiply slope into the parenthesis:

$y+10= \frac{13}{2}x + \frac{13}{2}*2\\$

Calculate it:

$y+10= \frac{13}{2}x +13$

Isolate the $y$ by subtracting 10 from both sides:

$y=\frac{13}{2} x + 13 -10$

Your final equation is:

$y=\frac{13}{2} x +3$

Hope this makes sense!

And here's the graph to prove that the line actually goes through the point $(-2,-10)$ :

3 0

2 years ago

You are putting a rectangular hot tub on your back porch. It is 6 feet long, 5 feet wide, and 3 feet deep. How much will it cost

sleet_krkn [62]

It costs $ 3.4 to fill the hot tub

<h3>Solution:</h3>

Given that, You are putting a rectangular hot tub on your back porch

The rectangular hot tub is of shape cuboid

The volume of cuboid is given as:

$\text{Volume of cuboid } = length \times width \times height$

It is 6 feet long, 5 feet wide, and 3 feet deep

Therefore,

length = 6 feet

width = 5 feet

height = 3 feet

Thus volume of rectangular hot tub is:

$volume = 6 \times 5 \times 3 = 90$

Thus volume of rectangular tub is $90 ft^3$

Convert feet to gallons

We know that,

1 cubic feet = 7.48052 gallon

Therefore,

90 cubic feet = 7.48052 x 90 = 673.247

Thus gallons of water tub can hold is 673.247 gallons

Given that it costs $ 5 per 1000 gallons

1000 gallons = $ 5

Therefore,

1 gallons = $ $\frac{5}{1000}$

Find for 673.247 gallons

673.247 gallons = $\frac{5}{1000} \times 673.247 = 3.366235 \approx 3.4$

Thus it costs $ 3.4 to fill the hot tub

5 0

3 years ago

A combination lock has 25 numbers on it. How many different 3-digit lock combinations are possible if no digit can be repeated?

IgorC [24]

Answer:

The number of ways is 13,800 ways

Step-by-step explanation:

In this question, we are tasked with calculating the number of ways to form 3-digits codes from 25 different numbers given that no repetition is allowed.

Now, for the first digit, we have all the 25 numbers completely wanting to take a spot. Now, in how many ways can we choose a single out of 25, that would be 25 ways

Now, we have 24 numbers left, and we are trying to pick one, the number of ways this can be done is 24 ways also

for the last digit, we have 23 numbers and we are selecting just one, the number of ways this can be done is 23 ways too

Thus, the cumulative number of ways would be 25 * 24 * 23 = 13,800 ways

7 0

3 years ago

Could you help with a Algebra problem (unions and intersections)? Got stuck on this ninth one.

Roman55 [17]

1) If A c B matches with c. then A ∪ B = B
2) If B c A matches with e. then A ∩ B = B
3) A ∪ Ø matches with d. A
4) A ∩ Ø matches with a. Ø
5) B ∪ Ø matches with b. B

6 0

3 years ago