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3 years ago

Assignment: Using Prime Factorization Investigation

Mathematics

1 answer:

damaskus [11]3 years ago

3 0

Answer:

3(2 +7)
9(3 +5)
16(2 +3)
15(2 +5)
8(11 +3)

Step-by-step explanation:

6 + 21 = 2·3 + 3·7 = 3(2 +7)
27 + 45 = 3^3 + 3^2·5 = 9(3 +5)
32 + 48 = 2^5 + 2^4·3 = 16(2 +3)
30 + 75 = 2·3·5 + 3·5^2 = 15(2 +5)
88 + 24 = 2^3·11 +2^3·3 = 8(11 +3)

In each case, the factor outside parentheses is the greatest common factor, the product of the prime factors common to both numbers. When the same factor has different powers, the least power is the common factor.

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3. Find the area of the shaded region. Leave your answer in terms of pi. (1 point)

anygoal [31]

ANSWER

$(4 - \pi) {ft}^{2}$

EXPLANATION

The area of the square is

${l}^{2}$

The length of the square is

$l = 2ft$

The area of the square is

$= {2}^{2} = 4 {ft}^{2}$

Area of the circle is

$= \pi \: {r}^{2}$

The radius of the circle is

$r = \frac{2}{2} = 1ft$

Area of circle is

$= \pi \: \times {1}^{2} = \pi {ft}^{2}$

The area of the shaded region is

$= (4 - \pi) {ft}^{2}$

5 0

3 years ago

Find the area. Round to the nearest hundredth if necessary

lara31 [8.8K]

Add 16.7m 4 times that should be the correct answer if not sorry

5 0

3 years ago

The density of a certain material is such that it weighs 9 kilograms for every 7 cubic feet of volume. Express this density in p

Vadim26 [7]

Answer:

1.641× 10^-3 pounds/ cubic inch

Step-by-step explanation:

Density= mass / volume

Mass of the material= 9 kilograms

Volume= 7 cubic feet

Density= 9/7= 1.286 kg/ ft^3

Density= 1.286 kg/ ft^3

To Convert to pounds per inch

1 kg/ ft^3 = 0.00128 pound / cubic inch

1.286 kg/ ft^3 = X pounds/ cubic inch

X=( 1.286 × 0.00128)

= 0.0016407087 pounds/ cubic inch

= 1.641× 10^-3 pounds/ cubic inch

Hence,this density in pounds per inch is 1.641× 10^-3 pounds/ cubic inch

5 0

3 years ago

NO LINKS!! Please help me with these graphs

Stella [2.4K]

Answer:

square: 9 square units
triangle: 24 square units

Step-by-step explanation:

Using a suitable formula the area of a polygon can be computed from the coordinates of its vertices. You want the areas of the given square and triangle.

<h3>Square</h3>

The spreadsheet in the first attachment uses a formula for the area based on the given vertices. It computes half the absolute value of the sum of products of the x-coordinate and the difference of y-coordinates of the next and previous points going around the figure.

For this figure, going to that trouble isn't needed, as a graph quickly reveals the figure to be a 3×3 square.

The area of the square is 9 square units.

<h3>Triangle</h3>

The same formula can be applied to the coordinates of the vertices of a triangle. The spreadsheet in the second attachment calculates the area of the 8×6 triangle.

The area of the triangle is 24 square units.

<em>Additional comment</em>

We have called the triangle an "8×6 triangle." The intention here is to note that it has a base of 8 units and a height of 6 units. Its area is half that of a rectangle with the same dimensions. These dimensions are readily observed in the graph of the vertices.

7 0

1 year ago

How can you write the equation for a linear function if you know only two ordered pairs for the function?

Vinvika [58]

1. m
2. One set of ordered pairs
3. b

To show why this is, I’m going to explain how to write the equation for a linear function with two random sets of ordered pairs - (1,0) and (5, 8).

First, find the slope. The formula for slope is m = (y2 - y1)/(x2-x1) where m is the slope and (x1, y1) and (x2, y2) are two sets of points.

This is why #1 is m. M is the letter used when finding slope.

To find m, I plug in the two sets of ordered pairs.

m = (8-0)/(5-1)
m = 8/4
m = 2

An equation for a line (linear function) is written in something called slope-intercept form. It looks like y = mx + b. m is the slope and b is the y-intercept (number y equals when x = 0). If m = 3 and b = 1, the equation would be y = 3x + 1.

Here, you have just solved for m and know it equals 2. Plug that value in for m.

y = 2x + b

To solve for b, plug one ordered pair in for x and y. I will use (1,0)

0 = 2(1) + b
0 = 2 + b
-2 = b

Now that you know b = -2, plug that in for b.
y = 2x - 2. Now you have the equation fo the line.

4 0

3 years ago