A hiker climbs a 5-mile trail up a mountain in 2 hours. On the return trip downhill, she walks the same trail and returns to her starting point in 1 hour. What was her average rate of speed, in miles per hour, for the entire trip?

Answer:

Correct option: C.

(Both Joey and Nolan)

Step-by-step explanation:

The step Joey did is:

Add 7x to both sides of the equation

Then, he got:

13x - 42 + 7x = 18 - 7x + 7x

20x - 42 = 18

The step Nolan did is:

Add 42 to both sides of the equation

Then, he got:

13x - 42 + 42 = 18 - 7x + 42

13x = 60 - 7x

So both of them used correctly the addition property of equality in the first step of their work.

Correct option: C.

Answer:

√3 - 1

Step-by-step explanation:

(1+√3)(2-√3)=2-√3+2√3-3=√3 - 1

Answer:

[tex]-1+\sqrt{3}[/tex]

Step-by-step explanation:

[tex](1+\sqrt{3} )(2-\sqrt{3} )[/tex]

[tex]2-\sqrt{3} +2\sqrt{3} -3[/tex]

[tex]-1+\sqrt{3}[/tex]

Answer:

4 pounds

Step-by-step explanation:

The ratio of pounds of dog bones to dollars is 1:1/4. Multiplying this by 4 to get to 1 dollar leaves you with 4 pounds of dog bones. Hope this helps!

Answer:

22 bagssss i am right because i did 4 time 4 times 1 and got 16 and then i divided that by 0.75 and got 21.33333 and since you can't get a 0.3333333 of a bag you have to get one extra so it would be 22

Step-by-step explanation:

Answer:

the range of the function is ∞

Answer:

S(x)= 10+2^x

Step-by-step explanation:

The correct function which represents the number of members in the science club after x weeks is,

S (x) = 10 + 2ˣ

We have,

The science club is experiencing a growth in membership.

On average, they are seeing 2 new members sign up each week.

Here, they started with 10 members.

Hence, The function S (x) which represents the number of members in the science club after x weeks is,

S (x) = 10 + 2ˣ

Where, x is number of weeks.

Therefore, The function is,

S (x) = 10 + 2ˣ

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Answer: not very sure but i think that may be 5

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

you see we need to make pairs and then we divide each one by square numbers and I have given picture

Answer:

Yes, the number 16,641 is a perfect square.

Step-by-step explanation:

16641 is the 129th perfect square number

__________________________________________

1 2 9    

1 1 66 41    

1        

22  66      

44      

249  22 41    

22 41    

258   0    

Number = 16641

Square Root = 129

________________________________

Step-1 :

Make pair of digits of given number starting with digit at one's place. Put bar on each pair.

1 66 41    

Step-2 :

Now we have to multiply a number by itself such that the product ≤ 1

Here 1×1=1≤1, So divisor is 1 and quotient is 1. Now do the division and get the remainder.

 1        

1 1 66 41    

1        

0        

Step-3 :

Now , we have to bring down 66 and quotient 1 is multiplied by 2 becomes 2, which is starting digit of new divisor

 1        

1 1 66 41    

1        

2  66      

Step-4 :

2 should be the digit at one's place of new divisor because when 22 is multiplied by 2 we get 44.

So new divisor is 22 and next digit of quotient is 2. Now do the division and get the remainder.

 1 2      

1 1 66 41    

1        

22  66      

44      

22      

Step-5 :

Now , we have to bring down 41 and quotient 12 is multiplied by 2 becomes 24, which is starting digit of new divisor

 1 2      

1 1 66 41    

1        

22  66      

44      

24  22 41    

Step-6 :

9 should be the digit at one's place of new divisor because when 249 is multiplied by 9 we get 2241.

So new divisor is 249 and next digit of quotient is 9. Now do the division and get the remainder.

 1 2 9    

1 1 66 41    

1        

22  66      

44      

249  22 41    

22 41    

0    

Answer: 129 (proof 129^2) = 16,641 or 129 x 129 = 16,641

______________________________

Second Solution shortcut:

A perfect square is a number that can be expressed as the product of two equal integers.

The only way to accurately calculate if a number is a perfect square is to find the factors. Before we go through the trouble of finding the factors, there is a quick trick you can use to help determine if you need even need to do the extra work.

Try these steps first:

A number that is a perfect square never ends in 2, 3, 7 or 8. If your number ends in any of those numbers, you can stop here because your number is not a perfect square.

Obtain the digital root of the number. The digital root essentially is the sum of all of the digits. If you're lost, don't worry, we'll go over each step in more detail below.

All possible numbers that are a perfect square have a digital root of 1, 4, 7, 9.

Let's try it...

Step 1:

What is the last number of 16,641? It is this number: 16641. The answer is 1. Is 1 in the list of numbers that are never perfect squares (2, 3, 7 or 8)?

Answer: NO, 1 is not in the list of numbers that are never perfect squares. Let's continue to the next step.

Step 2:

We now need to obtain the digital root of the number. Here's how you do it:

Split the number up and add each digit together:

1 + 6 + 6 + 4 + 1 = 18

If the answer is more than one digit, you would add each digit of the answer together again:

1 + 8 = 9

What is the digital root of number 16,641?

Answer: 9

Step 3:

So now we know the digital root of 16,641 is 9. Is 9 in the list of digital roots that are always a square root (1, 4, 7 or 9)?

Answer: YES, 9 is in the list of digital roots that are always perfect squares. We can conclude that 16,641 could be a perfect square!

Factoring

OK, so now we know that 16,641 could be a perfect square. We have to find the factors of the number to be sure.

Here are all of the factors of 16,641:

1 x 16,6413 x 5,5479 x 1,84943 x 387129 x 129

Highlighted in orange above is the factor combination that makes 16,641 a perfect square. Do you see why? A number can only be a perfect square if the product of two exactly the same numbers is equal to the original number.

Here's the proof: 129 x 129 = 16,641

Answer:

C

Step-by-step explanation:

C is the correct answer because the other 3 points are not correct when you put the numbers into the equation.

y = 16 + 0.5x

20 = 16 + 0.5(8)

20 = 20

Answer:The opposite sides are parallel.

They have four right angles.

Step-by-step explanation: I know it because we all learn it in 5 grade.

Answer:

[tex]5660[/tex]

Step-by-step explanation:

Rounded to the nearest tenth.

Answer:

5660

Step-by-step explanation:

When finding the nearest 10 u need to start counting from the last figure your zeros and tenth(10) start it

Answer:

1) If the coefficent of any variable is zero then the answer of the variable is 0.

2) There are two answers in a system of equations.

Answer:

A

Step-by-step explanation:

r^2 = (x - k)^2 + (y - h)^2

Work Shown:

(h,k) = (2,-2) is the center. So h = 2 and k = -2

r = 4 is the radius. We go 4 units from the center C to point P

Therefore,

(x-h)^2 + (y-k)^2 = r^2

(x-2)^2 + (y-(-2))^2 = 4^2

(x-2)^2 + (y+2)^2 = 16

Answer:

Step-by-step explanation:

These are the values we will need:

  f(-5) = (-5)^2 -7(-5) +6 = 25 +35 +6 = 66

  f(4) = 4^2 -7(4) +6 = 16 -28 +6 = -6

  g(-5) = -5 -1 = -6

  g(4) = 4 -1 = 3

__

(f+g)(-5) = f(-5) +g(-5) = 66 +(-6)

(f+g)(-5) = 60

__

(f-g)(4) = f(4) -g(4) = -6 -3

(f-g)(4) = -9

Answer:

[tex]\frac{7}{9}[/tex] OR 77.78%

Step-by-step explanation:

So, we first need to find out how many numbers fit the "less than 29 or odd" group.

This would be: 1, 2, 3, 5, 15, 21, and 29, which is a total of 7 numbers.

Next, we figure out the total amount of numbers in the population.

This would be: 1, 2, 3, 5, 15, 21, 29, 38, and 500, which is a total of 9 numbers.

Finally, we put the first number (7) over the total (9) = [tex]\frac{7}{9}[/tex]

[tex]\frac{7}{9}[/tex] is now able to be written in a percentage, if you need.

The probability is [tex]\frac{7}{9}[/tex] OR 77.78%

Answer:

The missing factor is (9s+1)

Step-by-step explanation:

The missing factor is (9s+1) because of the following

(9s^2 + s) + (18s+2)

If we factor out s from 9s^2+s, we get s(9s+1).

If we factor out 2 from 18s+2, we get 2(9s+1)

putting these together, we get s(9s+1) + 2(9s+1). Factoring out the common term of 9s+1, we get (9s+1)(s+2). therefore, the missing factor is 9s+1

-2 1/5

at least I think so lol

Answer:

10x - 15

Step-by-step explanation:

let Emily's be x hrs

Abbey = 3x-5 hrs

Nathan = 2 *  Abbey's time= 2(3x-5)

= 6x-10 hrs

Expression= x + 3x-5 + 6x-10 = 10x - 15 hrs

Therefore, 10x - 15 is the EXPRESSION THAT DENOTES THE TOTAL NUMBER OF HOURS SPENT FOR DOING HOMEWORK COLLECTIVELY.

Answer:

2

Step-by-step explanation:

12-2= m(2+3)

m= 10/5=2

Answer:

see below

Step-by-step explanation:

7. The similar rectangles are W and Z.

8. EF = 18 * 1.8 = 32.4

9. BD = 20 / 2.5 = 8.

Answer:

40%

Step-by-step explanation:

You can plug in 100 as the price of the radio to see how much the price decreased.

20% off of 100 will make it $80.

Then, with the 25% discount, it will be worth $60.

So, $40 was taken off, and 40÷ 100 is 0.4, so the overall percentage reduction was 40%

Answer:

When comes to initial value, x is equals to 0.

So x = 0 is substitute into the function.

In Indices Law, any values to the power of 0 will be 1.

So the initial value of function will be :

[tex]f(x) = a( {b}^{x} )[/tex]

[tex]f(0) = a \times {b}^{0} [/tex]

[tex]f(0) = a \times 1[/tex]

[tex]f(0) = a[/tex]

Answer:

42 Seats.

Step-by-step explanation:

If Arnold is in the second row and there are 5 rows behind him, there are 7 rows because 2 + 5 equals 7.

So then, you multiply 6 times 7 since there are 7 rows and 6 seats in each row. And that equals 42.

Answer:

b:42

Step-by-step explanation:

Answer:

D. 120

Step-by-step explanation:

1/3*360= 120

Option D

The answer choice which could be used to make a bow with the least amount remaining is; 1 2/5 yards.

It follows from the task content that the amount of ribbon remaining in each case can be evaluated as follows;

For 1 2/5 yards: 1 2/5 - 1 1/3 = 1/15. renders only 1/15 a yard to waste.

For 1 and 1/6 yards would render a waste of 1 1/6 yards since it is not possible to make a ribbon out of it.

1 2/10 yards would render a waste of 1 and 1/5 yards since it is not possible to make a ribbon out of it.

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Answer:

XZ

Step-by-step explanation:

Line segments are straight lines, not curves.

The only line is XZ, the rest are arcs

Answer:

Step-by-step explanation:

I believe that it’s yz

Answer:

9 students

Step-by-step explanation:

5/9 of 18 is 10

Answer:

6 Chickens

Step-by-step explanation:

Let  H represent the number of horses and  C represent the number of chickens. Since there are 32 legs altogether this means that on equation to use would be given by:

2C  +  4 H  =  32     (Eq. 1)

Another equation can be made from the fact that there are 11 heads or 11 animals altogether which can be written as:

C  +  H  =  11    (Eq. 2)

From Eq. 2, solve for the number of chickens:

C  +  H  =  11

C   =  11  - H    (Eq. 3)

Substituting Eq. 3 in Eq. 1, the number of horses can be determined:

2 C  +  4 H  =  32

2 ( 11  −  H )  +  4 H  =  32

22   −  2 H  +  4 H  =  32

2H  =  32  − 22

2 H  = 10

H = 5               Eq.4

Putting Eq.4 in Eq.1

2C + 4*5 =  32

2C = 32 - 20

2C = 12

C = 12/2

C = 6

Answer:

[tex]\frac{11}{13}[/tex]

Step-by-step explanation:

There are 4 aces and 4 kings.

[tex]\frac{8}{52} =\frac{2}{13}[/tex]

Now just subtract that from 1.

[tex]\frac{11}{13}[/tex]