Martin will ride his bike from his aunts house. He has two different routes he can take. One route goes up and down hill. The other route avoids the hill by going around the edge of the hill. How do you think the routes will differ. What do you think about the relationship of speed and time?

Answer:

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{15}[/tex]

Step-by-step explanation:

Given

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2[/tex]

Required

Solve:

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2[/tex]

Simplify 6/10

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = (\frac{3}{5})^3 * (\frac{5}{9})^2[/tex]

Express 9 as 3^2

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = (\frac{3}{5})^3 * (\frac{5}{3^2})^2[/tex]

Apply law of indices

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3}{5^3}* \frac{5^2}{(3^2)^2}[/tex]

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3}{5^3}* \frac{5^2}{3^4}[/tex]

Express as a sing;e fraction

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{3^3*5^2}{5^3*3^4}[/tex]

Apply law of indices:

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5^{3-2}*3^{4-3}}[/tex]

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5^1*3^1}[/tex]

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{5*3}[/tex]

[tex](\frac{6}{10})^3 * (\frac{5}{9})^2 = \frac{1}{15}[/tex]

Answer:

There were 24 females and 36 men on the bus

Step-by-step explanation:

To find the amount of females on the bus you multiply the 60 passengers by 0.4 to mimic the 40% and you get 24. So there were 24 females and to find the men you simply subtract 24 and 60 to get 36

Answer:

multiply the dividend denominator by the divisor numerator to make a new denominator:

7 x 6

3 x 5

 =    

42

15

Thus, the answer to 7/3 divided by 5/6 in fraction form is:

42

15

To make the answer to 7/3 divided by 5/6 in decimal form, you simply divide the numerator by the denominator from the fraction answer above:

42/15 = 2.8

The answer is rounded to the nearest four decimal points if necessary.

42/15 can be simplified to 14/5.

14/5 is an improper fraction and should be written as 2 4/5.

Step-by-step explanation:

42/25 = 2 4/5 = 2.8 is the value of 7/3 divided by 5/6 .

Here, we have,

given that,

7/3 divided by 5/6

so, we get,

7/3 / 5/6

=7/3 x 6/5

multiply the dividend denominator by the divisor numerator to make a new denominator:

7 x 6/3 x 5

= 42/15

Thus, the answer to 7/3 divided by 5/6 in fraction form is:

42/15

To make the answer to 7/3 divided by 5/6 in decimal form, we simply divide the numerator by the denominator from the fraction answer above:

42/15 = 2.8

The answer is rounded to the nearest four decimal points if necessary.

42/15 can be simplified to 14/5.

14/5 is an improper fraction and should be written as 2 4/5.

Learn more about the Division here:

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Answer:

Step-by-step explanation:

The answer is A

Answer:

Step-by-step explanation:

Use the law of cosines:

Apply to the given triangle and solve for x:

Answer:

22

Step-by-step explanation:

94-6 divided by 4

Answer:

LOOK BELOW IN STEP-BY-STEP

Step-by-step explanation:

First, do $94.00 times 4 which is $376

Then, take away 6 dollars from $376 which is $370

Hope that helped!!!

Complete question is;

Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet jane at the end of her run. Use the pythagorean theorem to write an equation for the distance janes trainer bikes

Answer:

x = √(12² + 16²)

Step-by-step explanation:

We are told that;

She bikes from health club to South = 16 miles

From South to West = 12 miles

Her trainer bikes from the health club to meet her at the end which is west.

I have attached a diagram showing this movement in form of a triangle.

From the diagram I attached, I have depicted the distance the trainer bikes as x.

Using pythagoras theorem;

x² = 12² + 16²

x = √(12² + 16²)

Answer:

a) translation

Step-by-step explanation:

We have two lines on the map.

One is given by g(x) = -x + 1, and the other is f(x) = x + 1.

The change from f to g is given by:

[tex]g(x) = f(-x)[/tex]

Which represents a translation in the function.

Answer:

3 cups = 348 calories

Step-by-step explanation:

Step 1

Let the calories in one cup be represented as C

Therefore

3/4 x C = 87 calories

C = 87 X 4 / 3 = 116

unit rate is 116 calories per cup.

Step 2- Solving the number of calories in 2 cups

1 cup serving = 116 calories

2 cups servings = 116 x 2= 232 calories

116 x 3 = 348 calories

Credit: tutorAnne

Answer:

(-4)^10

Step-by-step explanation:

When doing this sort of problem, we multiply the exponents.

This is the power rule.

Answer:

8+12x^4/x^2

Step-by-step explanation:

i know im right!

Answer:

16/x + 6

Step-by-step explanation:

Edge 2021

Answer:

length= 3.7 ft.

Step-by-step explanation:

T= (square root of length) * k

1.8 seconds = (square root of 3) * k

k= 1.8 seconds / (square root of 3)

a.) T= (square root of 11) k

substituting k:

T=(square root of 11) * 1.8 seconds / (square of 3)

T= 3.4 seconds

b.) 2 seconds = (square root of length) k

substituting k:

2 seconds =(square root of length) 1.8 seconds / (square root of 3)

Divide the equation by 1.8 seconds / (square root of 3):

2 seconds / [1.8 seconds / (square root of 3)] = (square root of length)

10(square root of 3) / 9 = (square root of length)

square both sides:

100/7 ft= length

length= 3.7 ft.

Hope this helps.

Answer:

5.5 cm

(Rounded up)

Answer:

20 %  40%  60% 80% 90% is the numbers you're missing.

Step-by-step explanation:

10 ,20, 30, 40, 50, 60, 70,  80, 90, 100. The numbers underlined is what you're missing and their in order. 10-100.

Answer:

25-7

Step-by-step explanation:

"Substitute for": Replace x with ____

Since it is given that x = 25 -y, we can replace the x in 5x + y = 10 with 25 - y by the substitution property of equality.

Answer:

The expression to substitute for x is: 25-y, as said in the first equation

Step-by-step explanation:

Not sure if you need to solve for the variables, but here:

To find y:

Put 25-y in place of x.

You will get:

5(25-y) + y = 10

Use the Distributive Property and multiply 25 and y by 5:

125 - 5y + y = 10

Combine like terms (the y's):

125 - 4y = 10

Put like terms on the same side (move the 125 to the right side of the equal sign by subtracting 125 from both sides:

-4y = -115

Divide both sides by -4:

y = 28.75 (or 28-3/4)

To find x:

Substitute 28.75 for y in either equation.

First equation:

x= 25 - 28.75

x= -3.75

Second equation:

5x + 28.75 = 10

Subtract 28.75 from both sides:

5x = -18.75

Divide both sides by 5:

x = -3.75

Answer: [tex]x=\sqrt{18}[/tex]

Step-by-step explanation:

We can use Pythagorean's Theorem for the triangle on the bottom. The resulting answer will give the side length of the square.

[tex]3^2+3^2=\sqrt{18}[/tex]

Answer:

Y = 4 and X = -6 ,  So the equation would be 4 + -6

Step-by-step explanation:

Look at were the line go across the numbers in Line Y and Line X this will help you understand more. And i also answered first :)

Answer:

y=3/2x+4

Step-by-step explanation:

First we find the slope.

To find the slope, we use this equation:

x2-x1/y2-y1=slope

So, we just need to pick any two points on the line.

(0, 4) and (3, 6)

3-0/6-4

3/2

The slope is 3/2.

Now, all we need to find is the B in y=3/2x+B

B is also known as the y intercept.

Since the line passes through 4 when x=0, the y intercept is 4.

So the equation is:

Y=3/2x+4

Answer:

n < 2

Step-by-step explanation:

Answer: Look at the explanation please.

Step-by-step explanation:

The first thing you would do is distribute the 2 to the n and the 3.

You will then get 2n+6-4<6

Next, you will have to subtract 6-4 and you will get 2

You will the have 2n+2<6

Subtract 2 from 2 to get 0 and from 6 to get 4.

Your left with 2n<4

Then, divide 2 from 2n and 2 from 4

Last, your answer will be n<2.

Graphing

Your graph would look like (from what I see in my book)

You have seven tick marks and in the middle will be 0.

From the left of 0 should have negative 1, 2, and 3

From the right of 0 would be positive 1, 2, and 3

On the top of 2 would be a open circle and an arrow going to the left.

Hope this helps :)

Answer:

A    27

Step-by-step explanation:

f(5) means x = 5, so substitute 5 into 1/9(3)^x

f(5) = 1/9(3^5) = 1/9(243) = 27

Answer:

27

Step-by-step explanation:

Answer:

23

Step-by-step explanation:

6/3 = x-5/9 simplify the first fraction

2= x-5/9 multiply both of the sides

18 = x-5/9 move it around correctly

-x=-5-18 calculate it

-x=-23 the negatives cancel out

x=23

3:1 is the answer

it is simplified

Answer: 1/4.5

Step-by-step explanation:

9/2=4.5

Answer:

[tex] {5}^{ \frac{5}{6}}[/tex]

Step-by-step explanation:

[tex]( \sqrt{5} )( \sqrt[3]{5}) \\ \\ = ({5}^{ \frac{1}{2} } ).({5}^{ \frac{1}{3} } ) \\ \\ = {5}^{ \frac{1}{2} + \frac{1}{3} } \\ \\ = {5}^{ \frac{3 + 2}{2 \times 3}} \\ \\ \huge \red{ \boxed{ = {5}^{ \frac{5}{6}} }}[/tex]

Answer:

As given,

Per hour cost of Jack's plumbing = $100

Also,

Al's plumbing charges = 75x + 50 where x = time in hours .

Now,

Al's plumbing cost for 4 hours:

Here , x = 4

⇒75x + 5 = 75(4) + 50 = 300 + 50 = 350

∴ we get

Al's plumbing cost for 4 hours = $350

Now,

As Jack cost for 1 hour = $ 100

⇒ For 4 hour = 4×$100 = $400

∴ we get

Jack's plumbing cost for 4 hours = $400

As we can see that

$ 400 > $350

⇒Jack's plumbing cost for 4 hours  >  Al's plumbing cost for 4 hours

Now,

Al's plumbing charges = 75x + 50 where x = time in hours .

For 1 hour

75x + 50 = 75(1) + 50 = 125

Al's 1 hour cost = $125

whereas Jack Plumbing cost for 1 hour  = $100

∴ we get

$125 > $100

⇒Al's 1 hour cost > Jack's 1 hour cost

Now,

Al's 2 hour cost

75x + 50 = 75(2) + 50 = 150 + 50 = 200

Al's 1 hour cost = $200

whereas Jack Plumbing cost for 2 hour  = $200

∴ we get

$200 =  $100

⇒Al's 2 hour cost = Jack's 2 hour cost

Now,

Al's 3 hour cost

75x + 50 = 75(3) + 50 = 225 + 50 = 275

Al's 1 hour cost = $275

whereas Jack Plumbing cost for 3 hour  = $300

∴ we get

$275 <   $300

⇒Al's 3 hour cost < Jack's 3 hour cost

Als0,

Jack's plumbing cost for 4 hours  >  Al's plumbing cost for 4 hours

∴ we get

We can not say that Als Plumbing charge less than Jacks Plumbing for all repair jobs.

Because the charge is fluctuating ,

For 1 hour , Aly' charge is grater whereas The 2 hour cost of Jack's is higher.

So, the Correct answer is - No, Al's Plumbing charge is not always less than Jacks Plumbing for all repair jobs.

Answer:

18

Step-by-step explanation:

90/5=18