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2 years ago

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A family needs to build fencing around their rectangular home and square swimming pool, depicted below. A rectangle labeled home

has its right side labeled (2 + 5 x) yards and its bottom side labeled (3 + 10 x) yards. The square, labeled pool, is smaller than the rectangle. One of its sides is labeled (2x) yards.

2 answers:

Black_prince [1.1K]2 years ago

6 0

Answer: The total amount of fencing they need can be written as 38x + 10.

If x = 5;

The family needs 160 yards of fencing for their home.

The family needs 40 yards of fencing for their pool.

i just did the assignment and git it right

hope this is helpful (:

Andrej [43]2 years ago

5 0

Answer:

The total amount of fencing they need can be written as

38 x + 10.

If x = 5;

The family needs 160 yards of fencing for their home.

The family needs 40 yards of fencing for their pool.

Step-by-step explanation:

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The diagram shows a cube of side length 4 inches. A is a vertex of the cube, while B and C are located on opposite edges of the

Nikolay [14]

Answer:

we will get an isosceles triangle as a result.

Step-by-step explanation:

when the point A is joined to B and C we will get the side AB and AC of equal length.

length of AB and AC could be calculated easily with the help of pythagorean theorem where the base and perpendicular are of length 4in and 1in .

when we will cut a plane including the the points A,B and C we will get a triangle whose sides AB and AC are equal but BC would be of distinct length.

Hence, the resultant figure will be an isosceles triangle.

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2 years ago

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Tony is 4 years younger than his brother josh and two years older than his sister Cindy. Tony also has a twin brother, Evan. All

Sholpan [36]

Let Tony's age = x

He is 4 years younger than his brother Josh, so Josh's age would be x + 4

He is 2 years older than his sister, so her age would be x - 2

He has a twin, which would be the same age, so the twins age is also x

They all add together to equal 66, so you get:

x + x + x+4 + x-2 = 66

Simplify:

4x +2 = 66

Subtract 2 from both sides:

4x = 64

Divide both sides by 4:

x = 64/4 = 16

Tony is 16 years old.

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2 years ago

Alan, Bill, and Calvin are playing a game with collectible cards. At the moment, Alan has 11 less than 2 1/2 times the number of

kramer

Bill has 12 cards. I figured this out by making a table and drawing an equation:

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2 years ago

A store sells 8 colors of balloons with at least 28 of each color. How many different combinations of 28 balloons can be chosen?

Len [333]

Answer:

(a) $Selection = 6724520$

(b) $At\ most\ 12 = 6553976$

(c) $At\ most\ 8 = 6066720$

(d) $At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

Step-by-step explanation:

Given

$Colors = 8$

$Balloons = 28$ --- at least

Solving (a): 28 combinations

From the question, we understand that; a combination of 28 is to be selected. Because the order is not important, we make use of combination.

Also, because repetition is allowed; different balloons of the same kind can be selected over and over again.

So:

$n => 28 + 8-1$ $= 35$

$r = 28$

$Selection = ^{35}^C_{28$

$Selection = \frac{35!}{(35 - 28)!28!}$

$Selection = \frac{35!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29*28!}{7!28!}$

$Selection = \frac{35*34*33*32*31*30*29}{7!}$

$Selection = \frac{35*34*33*32*31*30*29}{7*6*5*4*3*2*1}$

$Selection = \frac{33891580800}{5040}$

$Selection = 6724520$

Solving (b): At most 12 red balloons

First, we calculate the ways of selecting at least 13 balloons

Out of the 28 balloons, there are 15 balloons remaining (i.e. 28 - 13)

So:

$n => 15 + 8 -1 = 22$

$r = 15$

Selection of at least 13 =

$At\ least\ 13 = ^{22}C_{15}$

$At\ least\ 13 = \frac{22!}{(22-15)!15!}$

$At\ least\ 13 = \frac{22!}{7!15!}$

$At\ least\ 13 = 170544$

Ways of selecting at most 12 =

$At\ most\ 12 = Total - At\ least\ 13$ --- Complement rule

$At\ most\ 12 = 6724520- 170544$

$At\ most\ 12 = 6553976$

Solving (c): At most 8 blue balloons

First, we calculate the ways of selecting at least 9 balloons

Out of the 28 balloons, there are 19 balloons remaining (i.e. 28 - 9)

So:

$n => 19+ 8 -1 = 26$

$r = 19$

Selection of at least 9 =

$At\ least\ 9 = ^{26}C_{19}$

$At\ least\ 9 = \frac{26!}{(26-19)!19!}$

$At\ least\ 9 = \frac{26!}{7!19!}$

$At\ least\ 9 = 657800$

Ways of selecting at most 8 =

$At\ most\ 8 = Total - At\ least\ 9$ --- Complement rule

$At\ most\ 8 = 6724520- 657800$

$At\ most\ 8 = 6066720$

Solving (d): 12 red and 8 blue balloons

First, we calculate the ways for selecting 13 red balloons and 9 blue balloons

Out of the 28 balloons, there are 6 balloons remaining (i.e. 28 - 13 - 9)

So:

$n =6+6-1 = 11$

$r = 6$

Selection =

$^{11}C_6 = \frac{11!}{(11-6)!6!}$

$^{11}C_6 = \frac{11!}{5!6!}$

$^{11}C_6 = 462$

Using inclusion/exclusion rule of two sets:

$Selection = At\ most\ 12 + At\ most\ 8 - (12\ red\ and\ 8\ blue)$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 170544+ 657800- 462$

$Only\ 12\ red\ and\ only\ 8\ blue\ = 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = Total - Only\ 12\ red\ and\ only\ 8\ blue$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 6724520 - 827882$

$At\ most\ 12\ red\ and\ at\ most\ 8\ blue = 5896638$

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2 years ago

A bug was running along a number line at a speed of 11 units per minute. It never changed its direction. If at 7:15 pm it was at

Ne4ueva [31]

7:15-7:20 is 5 minutes
If every one minute is 11 units then it would be 5x11=55
If it was at point 100 it would now be at point 100+55=155
Answer: point 155
Hope this is correct and helps :)

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2 years ago

Read 2 more answers