A 13 foot board is cut into two pieces. If one piece is x feet long express the other length in terms of x

Answers

Answer 1
Answer: Since the foot board is 13 feet long, it can be said that the sum of the two pieces is 13. If one piece is x, the other piece can be expressed as the difference of 13, the total length of the foot board, and x, the length of the first piece. Hence, the other piece, in mathematical terms, is expressed as 13-x.

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Abigail was skateboarding home when the wheel axle of her skateboard broke. She had already traveled two thirds of the way home and had to walk the rest of the way. Walking the rest of the way home took her twice as long as it took her to ride her skateboard. How many times faster is Abigail on her skateboard than she is walking?

Answers

Answer:

The number of times faster Abigail is on her skateboard than she is walking is 4 times

Step-by-step explanation:

The information given are;

Abigail was skateboarding home (let the distance home = D)

The distance Abigail had traveled when her skateboard broke = 2/3 of D

The distance of the rest (remaining) of the way home = 1 - 2/3 of D = 1/3 of D

The time Abigail took in walking the rest of the way home = 2 × t, Time it will take on the skateboard

Given that t is the time it takes Abigail to arrive home on skateboard alone, we have;

Speed = (Distnce)/(Time)

Speed on skate board, S_t = Distance/Time = D/t

Therefore, the time it took Abigail to travel two thirds (2/3) of D is given as follows;

Time= (Distnce \ covered)/(Speed ) = ((2)/(3) D)/(S_t)  =  ((2)/(3) D)/((D)/(t) )  = (2)/(3) D * (t)/(D)  =  (2)/(3) t

The total time it took Abigail to get to her home = Time of walking + Time on skateboard

The question also states that he total time it took Abigail to get to her home by walking and skateboarding because her skateboard broke = 2×t

Therefore, the total time it took Abigail to get to her home = 2×t = Time of walking + Time on skateboard = Time of walking + (2)/(3) t

Which gives;

2×t = Time of walking + (2)/(3) t

Time of walking = 2 * t -(2)/(3) t = (4)/(3) t

∴ The time Abigail walked 1/3·D = (4)/(3) t

Abigail walking speed is then

Walking \ speed= (Distnce \ covered \ walking)/(Time \walking) = ((1)/(3) D)/((4)/(3) t)  = ((D)/(3) )/((4 \cdot t)/(3) ) = (D)/(3) } * {(3)/(4 \cdot t) } = (D)/(4 \cdot t) }

To compare how many times faster is Abigail on her skateboard than she is walking, we divide the expression (formula) for the speed of skateboarding with the (formula) for the speed of walking as follows;

The \ number \ of \ times \ faster = ((D)/(t) )/((D)/(4 \cdot t) )} = (D)/(t)  * (4 \cdot t)/(D) } = 4

The number of times faster is 4 that is Abigail is four times faster on her skateboard than she is walking.

The base of a cube is parallel to the horizon. A plane cuts through the cube creating a pentagon-shaped cross section. Which kind of plane could it be? A. a vertical plane cutting two adjacent edges of the base B. a vertical plane cutting two opposite edges of the base
C. a slanting plane cutting two adjacent edges of the base
D. a slanting plane containing exactly one edge of the cube

Answers

I think the answer is C. a slanting plane cutting two adjacent edges of the base. I thought of the Pentagon building in Washington where it also has a pentagon-shaped cross section. 

Answer:

C. a slanting plane cutting two adjacent edges of the base

Step-by-step explanation:

The base of a cube is parallel to the horizon. A plane cuts through the cube creating a pentagon-shaped cross section. The plane could be - a slanting plane cutting two adjacent edges of the base.

Two large numbers of the Fibonacci sequence are F49 = 7,778,742,049 and F50 = 12,586,269,025. What is the approximate value of the quotient ?

Answers

 Two large numbers of the Fibonacci sequence are F497778742049 and F50=12586269025.

Simplify 7(n - p) + 5p.

Answers

7(n - p) + 5p
7n - 7p + 5p
7n - 2p 
7(n-p) +5p
remove (  ) and distribute 7
7n-7p+5p
combine like terms
7n-2p

hope this helps

What is the value of this expression when c=4 c^3/2

Answers

Answer:

8

Step-by-step explanation:

c ^ 3/2

Let c = 4

4 ^ 3/2

Rewriting 4 as 2^2

2 ^2 ^3/2

We know that a^b^c = a^(b*c)

2 ^(2*3/2)

2 ^3

8

therightansweris8.

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The sum of two numbers is 26 and their difference is 20.find each of the numbers.

Answers

23 and 3
23 + 3 = 26 and 23 - 3 = 20
(1) x+y= 26 
 (2 ) x-y= 20 from here we can find : x= 20+y
We replace the ''x'' we found from (2) to the (1)
20+y+y=26
2y= 26-20
2y=6
y=3
x= 20+y = 23
Prove: 23+3 = 26 and 23-3 = 20