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3 years ago

What is the rule/output?

Mathematics

2 answers:

tankabanditka [31]3 years ago

7 0

Answer:

The rule is y = 4x - 5.

Step-by-step explanation:

Notice that if we start with x = 1 and increase x by 1, we get 2. Simultaneously, y starts with -1 and becomes 3. Thus, the slope is m = rise / run = 4/1, or 4.

The rule is y = 4x - 5.

Check: Suppose we pick input 4 from the table. Does this rule produce output 11? Is 11 = 4(4) - 5 true? YES.

labwork [276]3 years ago

6 0

Answer:

y = 4x - 5

Step-by-step explanation:

Have you been taught to set up 2 equations and 2 unknowns?

That is actually the only way I could do this.

y = mx + b

x = 2

y = 3

3 = 2m + b

x = 1

y = -1

-1 = m + b Multiply by 2. That means that the m term will cancel.

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

-2 =2m +2b

<u>3 = 2m + b </u> Subtract

-5 = b

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

3 = 2m + b Substitute - 5 for b

3 = 2m - 5 Add 5 to both sides.

3+5= 2m-5+5 Combine

8 = 2m Divide by 2

8/2=2m/2

m = 4

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Write the rule for the linear function. Remember a function rule is written using f(x)

Marina CMI [18]

Answer:

The rule for the linear function will be:

$f(x) = -2x+5$

Step-by-step explanation:

We know that linear function can be represented using the slope-intercept formula

y = mx+b

where m is the slope and b is the y-intercept

Given the function is linear

Taking two points from the table to determine the slope

(1, 3)

(2, 1)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(1,\:3\right),\:\left(x_2,\:y_2\right)=\left(2,\:1\right)$

$m=\frac{1-3}{2-1}$

$m=-2$

Using the point-slope form of the line equation

$y-y_1=m\left(x-x_1\right)$

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (1, 3)

$y-y_1=m\left(x-x_1\right)$

$y - 3 = -2 (x-1)$

$y-3 = -2x+2$

adding 3 to both sides

$y-3+3 = -2x+2+3$

$y = -2x+5$

$f(x) = -2x+5$

Therefore, the rule for the linear function will be:

$f(x) = -2x+5$

4 0

3 years ago

HELP NO DECIMALS!!!!!!!! Please I need this done almost due....

nikklg [1K]

Answer: 432cm^3

Step-by-step explanation:

7 0

3 years ago

For her presentation on the Wonders of the World, Mary baked a square pyramid-shaped cake as pictured below. The slant height of

mihalych1998 [28]

Answer:

$V=196in^3$

Step-by-step explanation:

The volume of a pyramid is:

$V=\frac{A_{b}h}{3}$

where $A_{b}$ is the area of the base and $h$ is the height (the perpendicular measurement between base and highest point, not the slant height)

Since the base is a square, the area is given by:

$A_{b}=l^2$

where $l$ is the length of the side: $l=8in$ , thus:

$A_{b}=(8in)^2\\A_{b}=64in^2$

Now we need to find the height, for this we use the right triangle that forms with half of a square side (8in/2 = 4in), the slant height (10in), and the height.

In this right triangle, the slant height is the hypotenuse, the leg 1 is the unknown height, and leg 2 is half of the square side.

Using pythagoras:

$hypotenuse^2=leg1^2+leg2^2$