The table shows the distance that two trains are from Center Station at various times of the day.

Miles From Center Station
Time of day
Train 1
Train 2
11:30
13
7
12:00
31
27
12:45
58
57

How do the speeds of the trains compare?
Train 1 is traveling 1 mile per hour faster than train 2.
Train 1 is traveling 6 miles per hour faster than train 2.
Train 2 is traveling 4 miles per hour faster than train 1.
Train 2 is traveling 5 miles per hour faster than train 1.

Answer:

a² + b² = 68

a3 + b3 = 520

Step-by-step explanation:

Given :

a + b = 10 (1)

ab = 16 (2)

A. Find a² + b²

(a + b)² = a² + 2ab + b² (3)

Substitutite the values of (1) and (2) into (3)

(10)² = a² + 2(16) + b²

100 = a² + 32 + b²

Subtract 32 from both sides

100 - 32 = a² + b²

a² + b² = 68

B. a^3 + b^3

(a + b)^3 = a^3 + b^3 + 3ab(a + b)

(10)^3 = a^3 + b^3 + 3*16(10)

1000 = a^3 + b^3 + 480

a^3 + b^3 = 1000 - 480

a3 + b3 = 520

Answer: 531441

Step-by-step explanation:

Answer:shrinking

Step-by-step explanation:

Answer:

bringing iron in

Step-by-step explanation:

hoped this helped let me know if it did

Answer:

does that mean x=-2? because if so then:

F(x)=36

Step-by-step explanation:

(-2-4)^2

-6^2

36

F(x)=36

Answer:

38/3

Step-by-step explanation:

3/2a-8=11      

3/2a=19     add 8 to each side

i forget the rest of the steps smh

Answer:

38/3

Step-by-step explanation:

3/2A-8=11

3A/2=11+8

3A/2=19 CROSS MULTIPLY

3A=38

A=38/3

Answer:

(n)*(x+y)(x-y)

Step-by-step explanation:

First of all, you take the n out, and then you use the formula of x²- y² and it will equal to (x+y)(x-y).

Answer:

n(x+y)(x−y)

Step-by-step explanation:

1. To factor this equation, first, you can see that both the x^2 and the y^2 have an n next to them.  So, you can take out the n.  You get this: n(x^2-y^2)

2. After you take the n out, you can also factor the (x^2-y^2) since they are both squared (to the second power).  To do this, you simply split the two apart and make sure to include the negative.  You get this, the final answer:

n(x+y)(x-y)

3. You can check it by multiplying out the answer, and once multiplied out, you get the original expression of x^2n-y^2n.

Hope this helped!  Feel free to ask any questions :)

Answer:

M=(-2,2)

Step-by-step explanation:

Xm= -4 + 0/2 --> -4/2

Ym= 7 + -3/2 --> 4/2

Answer:

38.08mph

Step-by-step explanation:

The question tells us that the speed of

Speed of boat = 35mph

Wind blowing = 15mph

We have to use the pythagorean theorem in other to find the resulting speed.

So,

Speed² = 35² + 15²

Such that

Speed = √35² + 15²

Speed = sqr(1225 + 225)

Speed = sqr(1450)

Speed = 38.08

The approximate resulting speed of the boat is therefore 38.08mph

Answer:

Angle2 is supplementary to Angle8.

If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8.

This refers to the type of angle where two different angles are said to have equal measure on their corresponding sides.

With this in mind, we can see that based on the two horizontal parallel lines are intersected by a third line, there is a third line that intersects the top line and forms four angles.

Hence, if If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8 because the sum of either angles is 180 degrees.

Read more about congruent angles here:
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Answer:

5 times 3

Step-by-step explanation:

you do 5 time 3. it is 15

Given that:

Membership  feet to play indoor soccer at the Sun Oaks Club = $100

Hourly rate = $10

To find:

The function f represents the  cost of playing soccer at Sun Oaks.

Here, fixed cost is $100.

Let the number of hours of playing be t.  So, total variable cost is $10t.

Total cost = Fixed cost + Variable cost

[tex]f(t)=100+10t[/tex]

So, the required function is [tex]f(t)=100+10t[/tex].

Now, if the hourly rate were halved. Then,

Hourly rate [tex]= \$ \dfrac{10}{2} = \$ 5 [/tex]

So, total variable cost is $5t and total cost function is

[tex]g(t)=100+5t[/tex]

So, the required function is [tex]g(t)=100+5t[/tex].

Answer:

The correct option is;

1

Step-by-step explanation:

A line in geometry is an array of points that lay on the path of a ray and extends along the ray path in both directions infinitely, while a point in geometry marks a location

Therefore, given that the points A and B are on the same line, and are therefore on the same ray that gives the direction of the line, the number of distinct lines that can contain the both A and B, given that the original line extends to infinity in both direction is 1.

Answer:

I think B option is correct ..I m 95% sure

Answer:i

the correct option is A

First we have to convert the 3 whole 8 /33 into a fraction so the method to do that is 33*3 =99 and then 99 +8 = 107 .The denominator will remain the same so we get 107 /33.Now by dividing 107 by 33 we get 3.242424

Answer:

x = -1/6, x = -0.16

Step-by-step explanation:

Answer:

True- She needs $3 more. She will not have enough money to buy everything. The cost is $28.

False- She has $3 left over.

Step-by-step explanation:

2 pounds of burgers for $3 each is $6

1 bag o bun equals $2

5 bags of chips for $4 each is $20

$20 + $6 +$2 = $28

She only had $25 to spent, so she doesn't have enough money and needs to 3 more dollars.

Answer: x = 16

Step-by-step explanation:

PQ = 26

PM = 1/2 PQ (M is midpoint of PQ)

PM= 1/2x + 5 = 1/2 * 26

or x = 2(13 - 5) = 16

The value of x is 16 units.

The midpoint of a line is the point which divide a given line in two equal parts.The formula for midpoint is Mₓ = (x₁ + x₂)/2 and Mₙ = (y₁ + y₂)/2.

(here y is replaced by n).

According to the given question Given M is the midpoint of PQ with PM = 1/2x + 5 and PQ = 26 and we have to find x.

As M is the midpoint of PQ with PM = 1/2x + 5 then MQ can also be represented by 1/2x + 5.

We know

PM + MQ = PQ

1/2x + 5 + 1/2x + 5 = 26.

x + 10 = 26.

x =16.

learn more about lines here :

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Answer:

-3

Step-by-step explanation:

40=16-8r

Subtract 16 from both sides.

24=-8r

Now divide by -8

-3=r

Answer:

-3= r

Step-by-step explanation:

40= 16- 8r

subtract 16 from both sides

40-16= 16 - 16 -8r

24= -8r

divide both sides by -8

24/-8 = -8r/-8

-3= r

Answer:

32 classmates and each classmate pays $19 per ticket. This is a multiplication problem. We can solve this a couple of ways:

  32

*19

-------

288

320

-------

608

Another way is to realize 19 is nearly 20, multiply 32 by 20 and then subtract 32:

 32

*20

------

640

640

-32

-----

608

So, the answer is $608

Answer:

$608

Step-by-step explanation:

The answer is $608 because each ticket costs $19 and 32 students are going to the fair. Therefore, it's 32 x 19 = 608.

Hope this helps!

Answer:

(5,1)

Step-by-step explanation:

if macs house if it’s 1/2 of the distance from Nate house to the park then half the distance of 10,2 is 5,1

The required coordinate of the max location is (4, 3).

Given that,
Nate wants to visit his friend max before going to the park. Nate's house is located at (-2,4), while the park is located at (10,2).
To find the location of macs house if it’s 1/2 of the distance from Nate's house to the park.

The midpoint is that point the line whose distance from both the ends of the line is equal.

Here,
Max lies 1/2 the distance of Nate and Park,
Location of max is given by,
= 10 - 2 / 2 and 4 + 2 / 2
= 8 / 2 and 6 / 2
= 4 and 3
Location of max is (4, 3)

Thus, the required coordinate of the max location is (4, 3).

Learn more about midpoints here:
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Answer:

102.66666667 feet/ seconds

Step-by-step explanation:

From the question, we are told to convert 70 miles per hour to feet per second.

Step 1

1 mile = 5280 feet

70 miles = x feet

Cross Multiply

1 mile × x feet = 5280 feet × 70 miles

x feet = 5280 feet × 70 miles

x feet = 369600 feet

Hence, 70 miles = 369600 feet

Step 2

We convert 369600 feet/ hour to feet per second

60 seconds = 1 minute

60 minutes = 1 hour

1 hour = 60 × 60

= 3600 seconds.

369600 feet/ 1 hour = 369600 feet/3600 seconds

= 102.66666667 feet/ seconds

Therefore, 70 miles per hour is equivalent to 102.66666667 feet/ seconds

Answer:

10 times greater, because 10x10=100

Step-by-step explanation:

Answer:

b = y - mx

Step-by-step explanation:

Given

y = mx + b ( subtract mx from both sides )

y - mx = b

Answer:

2

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

i just did the question on my test!

Answer:

80=x+y

Step-by-step explanation:

The maximum amount of glasses is 80; the solution cannot be more than 80; the number of glasses of lemonade and of iced tea cannot be more than 80 total.  

Answer:

your weight loss will help your child get through to your doctor if your child is a si and he's a doctor or 6or a child or an adult or an adult child and you can get in the way I want

When something is bisected, it is cut into two equal halves.

We know that SV cut RST into two parts.

Those two parts are RSV and VST

RSV = 64 and VST = 64

RST = RSV + VST = 64 + 64 = 128

The correct answer should be 128

Answer:

I.128

Step-by-step explanation:

Since SV bisected angle RST, the angle is split in two by equal parts, therefore RSV + VST = RST

64 + 64= 128

128°= RST

Answer:

[tex]f(x)=2x^{2}-3[/tex]

[tex]D=(-\infty,\infty)[/tex]

[tex]R=[-3,\infty)[/tex]

x-intercepts: [tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]

y-intercept: (0,-3)

f(3)=15

Step-by-step explanation:

A quadratic function is any polynomial function whose greatest power is a 2, so [tex]f(x)=2x^{2}-3[/tex] is a nice example of it.

For the domain, as a rule, polynomial functions that have positive whole degrees will be defined for all real  numbers, so:

[tex]D=(-\infty,\infty)[/tex]

When talking about quadratic functions, its range will happen from the lowest point (in this case the vertex) to it's highest point (in this case infinity)

In order to find the vertex, we can use the following formula:

[tex]x=-\frac{b}{2a}[/tex]

which is used for quadratic equations in standard form:

[tex]y=ax^{2}+bx+c[/tex]

In this case a=2, b=0 and c=-3, so we get:

[tex]x=-\frac{0}{2(2)}=0[/tex]

Now we know that the range will happen at x=0, so we substitute:

[tex]f(0)=2(0)^{2}-3=-3[/tex]

so the range will be:

[tex]R=[-3,\infty)[/tex]

For the x-intercepts we need to set the given function equal to zero so we get:

[tex]2x^2-3=0[/tex]

and solve for x:

[tex]2x^{2}=3[/tex]

[tex]x^{2}=\frac{3}{2}[/tex]

[tex]x=\pm \sqrt{\frac{3}{2}}[/tex]

which can be rationalized to:

[tex]x=\frac{\sqrt{6}}{2}[/tex] and [tex]x=-\frac{\sqrt{6}}{2}[/tex]

so the x-intercepts are located at:

[tex](\frac{\sqrt{6}}{2},0)[/tex] and [tex](-\frac{\sqrt{6}}{2},0)[/tex]

For the y-intercept, we need to set x=0 so we get:

[tex]f(0)=2(0)^{2}-3[/tex]

[tex]f(0)=-3[/tex]

So the y-intercept is located at:

(0,-3)

and finally, in order to get f(3) we must substitute x for 3 so we get:

[tex]f(3)=2(3)^{2}-3[/tex]

f(3)=15

Answer:

Midpoint of XY = ( - 5, - 3)

Step-by-step explanation:

[tex]Midpoint \: of \: XY \\ = \bigg( \frac{ - 2 + ( - 8)}{2}, \: \frac{3 + ( - 9)}{2} \bigg) \\ = \bigg( \frac{ - 2 - 8}{2}, \: \frac{3 - 9}{2} \bigg)\\ = \bigg( \frac{ - 10}{2}, \: \frac{ - 6}{2} \bigg)\\ Midpoint \: of \: XY = ( - 5, \: - 3)[/tex]

Answer:

[tex]MP = (5,3)[/tex]

Step-by-step explanation:

[tex]MP= (\frac{x_1+x_2}{2}) (\frac{y_1+y_2}{2} )\\MP= (\frac{7+3}{2}) (\frac{11+-5}{2} )\\MP= (\frac{10}{2}) (\frac{6}{2} )\\MP= (5,3)[/tex]