20 points

Two mountain bikers are riding on a 35-mile trail. Abel started at the beginning of the trail and is riding at a rate of 14
miles per hour. Neal started 6 miles ahead of Abel and is riding at a rate of 11 miles per hour. When will the boys be
at the same point on the trail?
If Abel's journey is represented by the equation d = 14t, where d represents the total distance and t represents time
in hours, what equation represents Neal's journey?

Answer:

4.25

Step-by-step explanation:

Answer:

I will give you the explanation, figure out the answer.

Step-by-step explanation:

For this expression, you need to distribute 27 into the expression inside the parantheses.

Distributing will look like this:

(27 x 2p) + (27 x 4e) + (27 x 10p) + (27 x 20)

Now to get the simplified version of this expression, you just need to multiply and combine like terms!

Answer:

4

Step-by-step explanation:

Answer:

The secret number is 93.

Answer: I think 12...

Step-by-step explanation:

Answer:

Step-by-step explanation

[tex]\frac{4x - y}{2} = 5[/tex]

4x - y = 5 × 2

4x - y = 10

4x = y + 10

x = [tex]\frac{y + 10}{4}[/tex]

hope this helps

Answer:

$31.50

Step-by-step explanation:

If the value fell by 30%, then the game is worth 70% of its' original value. So:

45 x 70%=45 x .7=31.5......................

Answer:

12,435 bats

Step-by-step explanation:

We need to figure out how many bats were produced.

First let's write the equation. Cost is $28 for each bat, and we start with fixed expenses of $58,780

y=28x + 58780

We are given y, total expenses at 406,960

so 406,960 = 28x + 58780

subtract 58780 from both sides

406,960 - 58,780 = 28x

348,180 = 28x

divide both sides by 28

12,435 = x

This means they produced 12,435 bats.

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Answer:

32000 grams

Step-by-step explanation:

The weight of a 32 kg child in pounds is 70.56 pounds.

What is Measurement unit?

A measurement unit is a standard quality used to express a physical quantity. Also it refers to the comparison between the unknown quantity with the known quantity.

Given that;

The weight of baby = 32 kg

Now,

Since, 1 kg = 2.205 pounds

So, We convert the weight of baby from kg to pounds as;

1 kg = 2.205 pounds

32 kg = 32 x 2.205 pounds

         = 70.56 pounds.

Thus, The weight of a 32 kg child in pounds is 70.56 pounds.

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Answer:

Step-by-step explanation:

Sum of infinite GP is:

The second term is:

Eliminate r in the system:

Compare the two equations and solve for a:

Multiply both sides by 16a:

a = 8 - 6√2 = -0.4852 ⇒ r = -0.5/a = -0.5/-0.4852 = 1.03 > 1

Answer:

Statement F is true

Step-by-step explanation:

Let x represent number of yoga classes

Let y represent total cost

Let m represent the additional fee per yoga class

Let b represent the membership fee

y=mx+b

Notice that after every 2 classes, the price goes up by 7.5 so m=7.5/2

m=3.75

Thus the first statement is true

Note you can also find the membership fee if you plug this in with some points

y=mx+b

67.5=3.75(6)+b

b=45 so membership fee is $45

Answer:

22 people

Step-by-step explanation:

49 - 5 = 44 cupcakes

44 ÷ 2 =  22 people

Answer:

D: Add 4; 1, 5, 9​

Step-by-step explanation:

Firstly, we can look at the preceding sequence: -15, -11, -7, and -3. It's pretty much impossible to be subtract 4, since -15 - 4 = -19, and it only goes downhill from there, deviating from the original sequence. Hence, the front sequence should be following the pattern of add 4.

Now, to decide between B and D, all you have to do is add 4 to the last term of the sequence to continue it. In this case, that would be -3 + 4 = 4 - 3 = 1. Hence, we can instantly identify the correct option is D: Add 4; 1, 5, 9​.

Hope this helped!

Answer:

D is the answer: 4, 1, 5, 9

Step-by-step explanation:

Answer:

[tex]\displaystyle \frac{118}{125}[/tex]

Step-by-step explanation:

Trigonometry

Calculate

[tex]\sin (3\sin^{-1}(2/5))[/tex]

We use the formula for the sine of triple angle:

[tex]\sin 3x=3\sin x-4\sin^3 x[/tex]

And recall:

[tex]\sin \sin^{-1}x=x[/tex]

For this problem, we set:

[tex]x=\sin^{-1}(2/5)[/tex]

Thus:

[tex]\sin 3x=3\sin (\sin^{-1}(2/5))-4\sin^3 (\sin^{-1}(2/5))[/tex]

[tex]\displaystyle \sin 3x=3*\frac{2}{5}-4\left(\frac{2}{5}\right)^3[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-4*\frac{8}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6}{5}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{6*25}{125}-\frac{32}{125}[/tex]

[tex]\displaystyle \sin 3x=\frac{150-32}{125}[/tex]

[tex]\mathbf{\displaystyle \sin 3x=\frac{118}{125}}[/tex]

Answer:6.875

Step-by-step explanation:

Answer:

Ethan sold more

Step-by-step explanation:

2/3 and 1/4

Simplify to 8/12 and 4/12

8/12 is more

9514 1404 393

Answer:

Step-by-step explanation:

a) You go about this by using the given equation.

  Left + Right = Total

  JK + KL = JL

  (2x -3) + 11 = 4x

  8 = 2x . . . . . simplify, subtract 2x

  4 = x . . . . . . divide by 2

__

b) JL = 4x = 4·4

  JL = 16

Answer:

C

Step-by-step explanation:

Answer:351.86 cc( approximately)

Step-by-step explanation:

The volume of the material = External volume - internal volume

= π3^2×50-π 2.6^2×50

=351.86

The volume of the material by the pipe is 351.86 cc.

The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it

V = πr²h

where 'r' is the radius of the base (circle) of the cylinder

'h' is the height of the cylinder

Given that the external and the internal radius of a cylindrical pipe are 3 cm and 2.6cm respectively

The length of the pipe is 50 cm

External volume = π(3)²×50 = 1413.71 cc

internal volume = π (2.6)²×50 = 1061.85

The volume of the material = External volume - Internal volume

The volume of the material = 1413.71 - 1061.85

The volume of the material = 351.86 cc

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Answer:

a) $450 per week, because you have room to earn more money because the average is sales is $2397.26 per week which the commission for option one would be is $227.74 which means on average people get $ 342.74, so $450 every week is a much higher salary.

b) The differace is that option 1 has the potential to increase by you selling more you can make more but in option 2 you know you will get $450 a week every week and that you would need to sell well above average to make more than $450

Step-by-step explanation

2.5 cups = 5servings

x cups = 8servings

2.5*8 = 5*x

20 = 5x

divide both sides by the coefficient of x

20/5 = 5x/5

4 = x

i.e x = 4

Answer:

We should attempt synthetic division to find when

x

3

−

k

x

2

+

2

k

x

−

15

x

−

3

has a remainder of

0

, which would signify that it is a factor of the polynomial.

The synthetic substitution would be set up as:

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

−−−

−−−

−−−

|

0

Treating the synthetic division like any other synthetic division problem, we see that

3

−

∣

∣

∣

1

−

k

2

k

−

15

−−−

−−−

3

−−−−−−−−

−

3

k

+

9

−−−−−−−−

−

3

k

+

27

−−−−−−−−−

1

−

k

+

3

−

k

+

9

|

0

If the remainder equals

0

, then we know that

−

3

k

+

27

+

(

−

15

)

=

0

Solve this to see that

k

=

4

.

Thus,

(

x

−

3

)

is a factor of

x

3

−

4

x

2

+

8

x

−

15

.

Answer:

2/5

Step-by-step explanation:

(2,2) and (7,4) 4-2/7-2=2/5

Step-by-step explanation:

x+y=17 (First equation)

x-y=3 (Second equation)

Solving Equation (i)

x+y=17

x=17-y(First equation)

Putting value of x in equation (ii)

x-y=3

x=3+y

17-y=3+y

17=3+y+y

17=3+2y

2y=17-3

y=14/2

y=7

Putting value of y in equation(i)

x=17-y

x=17-7

x=10