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2 years ago

An apple falls from a tree that is 21 feet tall. What is the height

Mathematics

1 answer:

Alexeev081 [22]2 years ago

4 0

Answer:

Use the vertical motion model, h = -16t^2 + 21 , t=1 second

h = -16(1) ^2 + 21

h = 5 feet

Step-by-step explanation:

Just plug in the time with t to get your answer in height

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Peter wants to cut a rectangle of size 6x7 into squares with integer sides. What is the smallest number of squares he can get

Semmy [17]

He can cut 5 squares, by making 1 4 × 4, 2 3 × 3 and 2 2 × 2 squares.

5 0

2 years ago

The quotient of 9 3/4 and 5/8

suter [353]

Answer:

15.6

Step-by-step explanation:

$9\frac{3}{4} = \frac{39}{4}$
Plug 39/4 in: 39/4 ÷ 5/8
39/4 ÷ 5/8 = 39/4 × 8/5
39/4 × 8/5 = 312/20
$\frac{312}{20} = 15.6$

I hope this helps!

4 0

2 years ago

Read 2 more answers

A circle has diameter of 11cm

dlinn [17]

Since length of diagonal ( $Diagonal= 9.9cm$ ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without touching the edge of the circle.

Step-by-step explanation:

Here we have , A circle has diameter of 11 cm A square has side length of 7 cm . Use Pythagoras’ Theorem to show that the square will fit inside the circle without touching the edge of the circle . Let's find out:

We know the concept that for any square to fit inside the circle without touching the edge of circle , diagonal of square must be less than diameter of circle . Let's find out length of diagonal by using Pythagoras Theorem :

$Hypotenuse ^2 = Perpendicular^2+Base^2$

For a square , $Perpendicular = base = side$

⇒ $Diagonal^2 = 2(side)^2$

⇒ $Diagonal= \sqrt{2}(side)$

⇒ $Diagonal= \sqrt{2}(7)$

⇒ $Diagonal= 9.9cm$

Since length of diagonal ( $Diagonal= 9.9cm$ ) is less than diameter of circle ( 11 cm ) , Therefore , the square will fit inside the circle without ruching the edge of the circle.

5 0

2 years ago

According to an informal poll in Glenview 1/3

Talja [164]

Answer:

Percent form: 41.65%

Fraction form: $\frac{833}{2000}$

Step-by-step explanation:

33% of men support John Smith.

67% of women support John Smith.

Lets say, for instance, that there are 20 polled individuals -- 10 women and 10 men.

However, since 1.5 times as many men voted as women, we have to apply our poll to 15 men and 5 women.

33% of the 15 men makes 5 men who voted for Smith and 10 who did not.

67% of the 5 women makes 3.33 women who voted for Smith and 1.67 who did not.

Add these numbers together.

8.33 total voters were cast for John Smith, while 11.67 were not.

Now, divide 8.33 by 20 and multiply by 100 to obtain a percentage.

$\frac{8.33}{20} \\.4165\\41.65$

41.65% of voters voted for John Smith according to the results of the poll.

7 0

2 years ago

A rectangular sheet of metal has identical squares cut from each corner. The sheet is then bent along the dotted lines to form a

Reika [66]

The correct answer is:

3 inches.

Explanation:

We will use the Rational Roots Theorem to solve this.

First we can divide both sides of the equation by 4 in order to simplify it:

$\frac{4x^3-72x^2+320x}{4}=\frac{420}[4} \\ \\x^3-18x^2+80=105$

In order to solve this, we want the polynomial set equal to 0. To do this, subtract 105 from both sides:

$x^3-18x^2+80x-105=105-105 \\x^3-18x^2+80x-105=0$

The Rational Roots Theorem says that if p/q is a root of the polynomial, then p is a factor of the constant term and q is a factor of the leading coefficient. The constant term is -105. Drawing a factor tree, we find that the factors of this number are 1, -1, 3, -3, 5, -5, 7, -5, 15, -15, 21, -21. The leading coefficient is 1; its only factor is 1. This means p/q must be a whole number, and can be any of the factors of 105.

Using synthetic division, we try 1 in the box:

1 | 1 -18 80 -105

_______ 1__ -17___63__

1 -17 63 -42

Since there is a remainder, this is not a root. Trying -1,

-1 | 1 -18 80 -105

_______-1__ 19 _-99_

1 -19 99 -204

This is not a root; in fact, it shows us that none of the negatives will be a factor, as the absolute values increase as we complete the synthetic division.

Trying 3,

3 | 1 -18 80 -105

________3__-45___105_

1 -15 35 0

Since there is no remainder, 3 is a root, and is the answer we are looking for.

3 0

2 years ago

Read 2 more answers