Sixteen blocks are needed to build a four-step double staircase like

The table below represents a linear function in the equation represents a function. table numbers are X: -1,0,1. f(x): -3,0,3. G

Alexxx [7]

A)
SLOPE OF f(x)
To find the slope of f(x) we pick two points on the function and use the slope formula. Each point can be written (x, f(x) ) so we are given three points in the table. These are: (-1, -3) , (0,0) and (1,3). We can also refer to the points as (x,y). We call one of the points $( x_{1} , y_{1} )$ and another $( x_{2} , y_{2} )$ . It doesn't matter which two points we use, we will always get the same slope. I suggest we use (0,0) as one of the points since zeros are easy to work with.

Let's pick as follows:
$( x_{1} , y_{1} )= (0.0)$
$( x_{2} , y_{2} )= (1.3)$

The slope formula is: $m= \frac{y_{2} - y_{1} }{ x_{2}- x_{1} }$
We now substitute the values we got from the points to obtain.
$m= \frac{3-0}{ 1-0 } = \frac{3}{1}=3$

The slope of f(x) = 3

SLOPE OF g(x)
The equation of a line is y=mx+b where m is the slope and b is the y intercept. Since g(x) is given in this form, the number in front of the x is the slope and the number by itself is the y-intercept.

That is, since g(x)=7x+2 the slope is 7 and the y-intercept is 2.

The slope of g(x) = 2

B)
Y-INTERCEPT OF g(x)
From the work in part a we know the y-intercept of g(x) is 2.

Y-INTERCEPT OF f(x)
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. This point will always have an x-coordinate of 0 which is why we need only identify the y-coordinate. Since you are given the point (0,0) which has an x-coordinate of 0 this must be the point where the line crosses the y-axis. Since the point also has a y-coordinate of 0, it's y-intercept is 0

So the function g(x) has the greater y-intercept

5 0

3 years ago

On Monday, I bought 1 dog and 3 cats for a total cost of $7.75. On Tuesday, 1

Zina [86]

Answer: The cats cost more

also there is a typo

Step-by-step explanation:

I bought 1 dog and 3 cats a total cost of $7.75. the three cats cost more so in all the cats must cost 3.56$

4 0

3 years ago

Which is the graph of f(x) = (x + 3)(x – 2)?

vodka [1.7K]

Looks like this
Everything in one picture

4 0

3 years ago

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I need help with #61 to #64 ASAP please and thank you …. Could someone please help me with it… I need to get it done ASAP

aivan3 [116]

Problem 61

The nth triangular number is

T(n) = n(n+1)/2

I'll rewrite this into

T(n) = 0.5n(n+1)

The triangular number right after this is

T(n+1) = 0.5(n+1)(n+2)

I replaced every n with n+1 and simplified

Let's see what we get when we add up the two expressions

T(n) + T(n+1)

0.5n(n+1) + 0.5(n+1)(n+2)

0.5n^2+0.5n + 0.5(n^2+3n+2)

0.5n^2 + 0.5n + 0.5n^2 + 1.5n + 1

n^2+2n+1

(n+1)^2

This shows that the sum of any two consecutive triangular numbers results in a square number

Here's a few examples

0+1 = 1
1+3 = 4
3+6 = 9
6+10 = 16
10+15 = 25

Note each sum is a perfect square, which visually would plot out a square figure.

For quick reference, the set of the first few triangular numbers is {0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55,...}

<h3>Answer: Square number</h3>

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Problem 64

Let's say we go with n = 5.

This means,

T(n) = 0.5n(n+1)

T(n-1) = 0.5(n-1)(n-1+1)

T(n-1) = 0.5n(n-1)

T(5-1) = 0.5*5(5-1)

T(4) = 10

This says that when n = 5, the 4th triangular number is 10

Triple that result and add on n = 5

3*T(4) + n = 3*10+5 = 35

This result is beyond obvious which category of figurate number it belongs to. It's not a triangular number since it's not in the form n(n+1)/2. It's not a square number either.

Through a bit of trial and error, you should find it's a pentagonal number

Pentagonal numbers are of the form n(3n-1)/2

If you plugged n = 5 into that, it leads to 35

n(3n-1)/2 = 5*(3*5-1)/2 = 5*14/2 = 70/2 = 35

The diagram shown below represents the first few pentagonal numbers. The number of blue dots corresponds to the pentagonal number itself. Note the equal spacing when dealing with dots on each segment (eg: some interior blue dots are midpoints, others are quarter points, etc.)

<h3>Answer: Pentagonal number</h3>

8 0

2 years ago

Four circles, each with a radius of 2 inches, are removed from a square. What is the remaining area of the square? (16 – 4π) in.

anyanavicka [17]

Since 4 circles are circumscribed by a square, then the side length of the square is 8

So the area of the square is 8^2 = 64

The area of 4 squares is 4 * pi*2^2 = 16pi

So the answer will be 64 - 16pi

6 0

3 years ago

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