Justin Bieber's sand castle is 180 cm tall but the wind is

Provide reasons for the proof. Given line h is parallel to line k. line j is perpendicular to line h. Prove line j is perpendicu

dusya [7]

Answer: Provided.

Step-by-step explanation: We are given two lines 'h' and 'k' which are parallel to each other. Also, there is another line 'j' that is perpendicular to line 'h'.

We are to prove that line 'j' is perpendicular to line 'k'.

Let, m, n and p be the slopes of lines 'h', 'k' and 'j' respectively.

Now, since line 'h' and 'k' are parallel, so their slopes will be equal. i.e., m = n.

Also, lines 'h' and 'j' are perpendicular, so the product of their slopes is -1. i.e.,

m×p = -1.

Hence, we can write from the above two relations

n×p = -1.

Thus, the line 'j' is perpendicular to line 'k'.

Proved.

8 0

3 years ago

Joe has 4/5 as much money as bob. Tim has $50 more than joe. Rita has $150, which is $35 more than bob. How much money does tim

lesantik [10]

Rita = $150

Bob = $150 - $35 = $115 Bob has $115

Joe = $115 divided by 5 = $23 $23 x 4 = $92 Joe Has $92

Tim = Has $50 more then joe, $92 + $50 = $142 Tim has $142

3 0

3 years ago

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

Es The measure of an interior angle of a regular polygon is 120°. What is the measurb of each exterior angle? The polygon has

Troyanec [42]

The measure of each exterior angle is 60° and the polygon has 6 sides ⇒ 4th answer

Step-by-step explanation:

In a regular n-side polygon: