Danielle’s retirement income is $90,000. Assuming it is 70% of his final salary, what was her final salary

The table below shows the distance d(t) in feet that an object travels in t seconds: t (seconds) d(t) (feet) 2 64 4 256 6 576 8

Thepotemich [5.8K]

Answer:

128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds

Step-by-step explanation:

The average rate of change is another way to say slope.

slope = (y2-y1)/(x2-x1)

= (576-64)/(6-2)

= (512/4)

=128 ft/s

This represents the change in ft per second, or the average speed the object is going during the time period.

5 0

3 years ago

Read 2 more answers

Item 11

marysya [2.9K]

Answer:

4 ft higher

Step-by-step explanation:

Since the ladder is 10 ft long and its top is 6 feet high(above the ground), we find the distance of its base from the wall since these three (the ladder, wall and ground) form a right angled triangle. Let d be the distance from the wall to the ladder.

So, by Pythagoras' theorem,

10² = 6² + d² (the length of the ladder is the hypotenuse side)

d² = 10² - 6²

d² = 100 - 36

d² = 64

d = √64

d = 8 ft

Since the ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up.

Now, let x be the distance the top of the ladder is moved, the new height of top of the ladder is 6 + x. Since the base moves twice the distance the top of the ladder moves up, the new distance for our base is 8 - 2x(It reduces since it gets closer to the wall).

Now, applying Pythagoras' theorem to the ladder with these new lengths, we have

10² = (6 + x)² + (8 - 2x)²

Expanding the brackets, we have

100 = 36 + 12x + x² + 64 - 32x + 4x²

collecting like terms, we have

100 = 4x² + x² + 12x - 32x + 64 + 36

100 = 5x² - 20x + 100

Subtracting 100 from both sides, we have

100 - 100 = 5x² - 20x + 100 - 100

5x² - 20x = 0

Factorizing, we have

5x(x - 4) = 0

5x = 0 or x - 4 = 0

x = 0 or x = 4

The top of the ladder is thus 4 ft higher

7 0

3 years ago

In point slope form: passes through (1, -3), slope = -1?

sleet_krkn [62]

Answer:

y + 3 = -1(x-1)

Step-by-step explanation:

sub (1, -3) and slope = -1:

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

Topic: Coordinate Geometry

If you would like to venture further, you can check out my Instagram page (learntionary) where I post notes and mathematics tips. Thanks!

5 0

3 years ago

HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

sasho [114]

Answer is 54^2.

since there are triangles in this one, it is easier to do this. all you have to do is make boxes in and since there are angles, outside the lines. like this picture.

the orange is 1
red and dotted is 2
blue is 3
purple is 4(a regular box which should be easy to count.

all you have to do is add up all the boxes within the boundaries.
boundary 1: 12
boundary 2: 18
boundary 3: 6
boundary 4: 36

now when the boundary has a triangle in it (1, 2, & 3) divide the number you got in half or 2.
boundary 1: 6
boundary 2: 9
boundary 3: 3

the ractangle box doesn't not get divided.
boundary 1: 6
boundary 2: 9
boundary 3: 3
boundary 4: 36

add all the numbers you got now for each boundary and that would be your area squared.

6+9+3+36=54^2

so your final answer is 54^2.

i hope this helps you.

3 0

3 years ago

Anyone know this ion get it ??

ehidna [41]

Answer:

D.

Step-by-step explanation:

So the question is asking which set of inequalities and given point represent the graph. The point it gives is (-3,1) on the graph. That already narrows your choices down to B and D. Now, the easiest way to see the answer is look at the y axis. In the equation y=mx+b, b is the value on the y axis. We see on the y axis that the equations pass through positive 1 and 2. D adds 1 and 2 the equations, so it would produce that graph.

5 0

3 years ago