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2 months ago

Time =(distance)/speed

Time taken by the raft going with the current to travel x miles is:

12/x hours

Time taken by the raft going against the wind is:

7/y

Total time taken for both raft is 4 hours thus:

12/x+7/y=4

hence the answer is:

D. x/12 + y/7 = 4

Time taken by the raft going with the current to travel x miles is:

12/x hours

Time taken by the raft going against the wind is:

7/y

Total time taken for both raft is 4 hours thus:

12/x+7/y=4

hence the answer is:

D. x/12 + y/7 = 4

Question

Aaron borrows $150 from his friend Austin. He promises to pay back the money in 4 monthly installments. Each month he wants to pay half the amount he paid the previous month. Assuming Austin does not charge any interest, how much should Aaron pay the first month to repay the money as scheduled?

Solution 1

Assume first month's price is x

The Equation :

x+1/2x+1/4x+1/8x = 150

Multiply every term by 8 to get whole numbers

8x+4x+2x+x = 1200

15x = 1200

x = 80

Solution 2

This can be expressed by,Â

80 + 40 + 20 + 10 = 150

80 + 40 + 20 + 10 = 150

Question

Solve the system using substitution or elimination and describe your steps. Be sure to verify your solution. â€¢ x = y - 3 2x + y = 12

Solution 1

x = y - 3

2x + y = 12

substituteÂ x = y - 3Â into 2x + y = 12

2x + y = 12

2(y - 3Â )+ y = 12

2y - 6 + y = 12

3y - 6 = 12

3y = 18

Â y = 6

substitute y = 6 intoÂ x = y - 3 to find x

x = y - 3

x = 6 - 3

x = 3

answer

x = 3 and y = 6

2x + y = 12

substituteÂ x = y - 3Â into 2x + y = 12

2x + y = 12

2(y - 3Â )+ y = 12

2y - 6 + y = 12

3y - 6 = 12

3y = 18

Â y = 6

substitute y = 6 intoÂ x = y - 3 to find x

x = y - 3

x = 6 - 3

x = 3

answer

x = 3 and y = 6

Question

For what value of c will this function have one zero?
f(x) = X^2 +c

Solution 1

XÂ² + c is actually a quadratic function.

And xÂ² + c = 0,Â it usually has two zeros which are solutions.

But for when c = 0,

xÂ² + c = 0

xÂ² + 0 = 0

xÂ² = 0

Taking the square root of both sides.

x = 0.Â Here it only has one zero.

So the function xÂ² + c,Â only has one root forÂ c = 0.

And xÂ² + c = 0,Â it usually has two zeros which are solutions.

But for when c = 0,

xÂ² + c = 0

xÂ² + 0 = 0

xÂ² = 0

Taking the square root of both sides.

x = 0.Â Here it only has one zero.

So the function xÂ² + c,Â only has one root forÂ c = 0.

Question

What is the surface area of a conical grain storage tank that has a height of 43 meters and a diameter of 14 meters? Round the answer to the nearest square meter. A. 1,100 square meters
B. 1,112 square meters
C. 2,507 square meters
D. 2,605 square meters

Solution 1

We know that

[surface area of the cone]=pi*rÂ²+pi*r*l

whereÂ

r is the radius

l is the slant height

lÂ²=hÂ²+rÂ²

h=43 m

r=14/2---> 7 m

lÂ²=43Â²+7Â²----> lÂ²=1898--------> l=43.57 m

[surface area of the cone]=pi*7Â²+pi*7*43.57----> 1111.53 mÂ²----> 1112 mÂ²

**the answer is the optionÂ **

**Â ****B. 1,112 square meters**

[surface area of the cone]=pi*rÂ²+pi*r*l

whereÂ

r is the radius

l is the slant height

lÂ²=hÂ²+rÂ²

h=43 m

r=14/2---> 7 m

lÂ²=43Â²+7Â²----> lÂ²=1898--------> l=43.57 m

[surface area of the cone]=pi*7Â²+pi*7*43.57----> 1111.53 mÂ²----> 1112 mÂ²

Question

Beatrice buys a dishwasher for her new house. The price of the dishwasher is D dollars, and she pays an additional 2% tax. Match the expressions to their correct meanings for Beatrice.

Solution 1

The total amount of $ that this person will have to pay for the dishwasher is given by 1.02D (dollars).

Question

Step-by-step solution for: (âˆš2+âˆš10)^2

Solution 1

Note:Â âˆša * âˆšaÂ = a

Â Â Â Â Â Â âˆša * âˆšbÂ = âˆšab

(âˆš2 + âˆš10)Â²Â =Â (âˆš2 + âˆš10)(âˆš2 + âˆš10)

Â Â Â Â Â Â Â Â Â Â =Â âˆš2(âˆš2 + âˆš10) + âˆš10(âˆš2 + âˆš10)

Â Â Â Â Â Â Â Â Â Â = Â âˆš2*âˆš2 + âˆš2*âˆš10 + âˆš10*âˆš2 + âˆš10*âˆš10

Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 2Â Â Â + âˆš20Â + âˆš20 + 10

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â (2 + 10) + (âˆš20 + âˆš20)

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 12 +Â 2âˆš20

âˆš20 = âˆš(4 *5) = âˆš4 * âˆš5 = 2âˆš5

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 12 +Â 2âˆš20Â = 12 + 2(2âˆš5)

Â Â Â Â Â Â Â Â Â Â Â = 12 + 4âˆš5

Â Â Â Â Â Â âˆša * âˆšbÂ = âˆšab

(âˆš2 + âˆš10)Â²Â =Â (âˆš2 + âˆš10)(âˆš2 + âˆš10)

Â Â Â Â Â Â Â Â Â Â =Â âˆš2(âˆš2 + âˆš10) + âˆš10(âˆš2 + âˆš10)

Â Â Â Â Â Â Â Â Â Â = Â âˆš2*âˆš2 + âˆš2*âˆš10 + âˆš10*âˆš2 + âˆš10*âˆš10

Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 2Â Â Â + âˆš20Â + âˆš20 + 10

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â (2 + 10) + (âˆš20 + âˆš20)

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 12 +Â 2âˆš20

âˆš20 = âˆš(4 *5) = âˆš4 * âˆš5 = 2âˆš5

Â Â Â Â Â Â Â Â Â Â Â =Â Â Â Â 12 +Â 2âˆš20Â = 12 + 2(2âˆš5)

Â Â Â Â Â Â Â Â Â Â Â = 12 + 4âˆš5

Question

If 2x2 â€“ 13x + 20 = (2x â€“ 5)(x â€“ 4), which equation(s) should be solved to find the roots of 2x2 â€“ 13x + 20 = 0? Check all that apply. A. 2x â€“ 5 = 0
B. x + 4 = 0
C. 2x â€“ 5 = x â€“ 4
D. 2x + 5 = 0
E. x â€“ 4 = 0

Solution 1

Hence, the Â correct options are:

**A. 2x-5 = 0**

**and Â E. x-4 = 0**

We are given a factorization of a polynomial function as:

The roots of the equation are the possible value of x such that the polynomial function is zero at that point.

i.e. we have to find x such that:

which could also be written as:

Hence, the equation that satisfy this equation is:

**Hence, the Â correct options are:**

**A. 2x-5 = 0**

**and Â E. x-4 = 0**

Solution 2

2x^2 â€“ 13x + 20

= (2x â€“ 5)(x â€“ 4)

to find roots of 0 thenÂ (2x â€“ 5)(x â€“ 4) = 0

then (2x â€“ 5) = 0 and (x â€“ 4) = 0

answer

A. 2x â€“ 5 = 0

E. x â€“ 4 = 0

= (2x â€“ 5)(x â€“ 4)

to find roots of 0 thenÂ (2x â€“ 5)(x â€“ 4) = 0

then (2x â€“ 5) = 0 and (x â€“ 4) = 0

answer

A. 2x â€“ 5 = 0

E. x â€“ 4 = 0

Question

Find the zeros of the function by using the Quadratic Formula:
f(x) = X^2 +7x + 9

Solution 1

X= x(2)+7x+9Ã—=

2(x)+7x+9x=

9x+9x=

Ã—=18

2(x)+7x+9x=

9x+9x=

Ã—=18

Question

In his new living room, Kirk installed carpeting on 1/2 of the floor and tile on another 1/4 of the floor. What fraction of the floor is now covered by either carpet or tile?

Solution 1

To find the total amount of floor covered add the amount of carpeting and tiling together. So 1/2 = 2/4, then 1/4 + 2/4 = (1 + 2) / 4 = 3/4. 3/4 of Captain Kirk's floor is covered.

Question

A holding pen for cattle must be square and have a diagonal length of 84 84 meters. a. find the length of a side of the pen.
b. find the area of the pen.

Solution 1

We know that

Applying the Pythagoras Theorem

cÂ²=aÂ²+bÂ²

in a square

a=b

c is the diagonal-----> 84 m

cÂ²=2aÂ²--------> aÂ²=cÂ²/2-----> aÂ²=84Â²/2-----> aÂ²=3528-----------> a=âˆš3528 m

the answer part a) is

âˆš3528 m or 59.40 m

the area of the pen is aÂ²------> 3528 mÂ²

**the answer Part b) isÂ **

**3528 mÂ²**

Applying the Pythagoras Theorem

cÂ²=aÂ²+bÂ²

in a square

a=b

c is the diagonal-----> 84 m

cÂ²=2aÂ²--------> aÂ²=cÂ²/2-----> aÂ²=84Â²/2-----> aÂ²=3528-----------> a=âˆš3528 m

the answer part a) is

âˆš3528 m or 59.40 m

the area of the pen is aÂ²------> 3528 mÂ²

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