MATHEMATICS MIDDLE SCHOOL

Is the gcf of any two even numbers is always even?

Answers

Answer 1
Answer: Yes because only odd numbers go into the whole number

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What is the area of the shape shown?92 square centimeters

378 square centimeters

486 square centimeters

798 square centimeters

Answers

Answer:

B: 378 cm^2

Step-by-step explanation:

22 * 24 = 528

528 - (10 * 15) = 378

Answer:

378 B  

Step-by-step explanation:

Hopes that help Thanks

Draw a quadrilateral with only one set of parallel lines

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Draw a trapezoid because the top and bottom are parallel but not the sides
A trapezoid. It has parallel side on the left and right side. On the top it's short and on the bottom the line is longer

chad buys peanuts in 2 pound bags. he repackage them into bags that hold 5/6 pounds pound of peanuts. how many 2 pound bags of peanuts should chad buy so that he can fill 5/6 pounds bags without having any peanuts left over?

Answers

he needs to buy three bags

Two ants are at a common point at time t=0, the first ant starts crawling along a straight line at the rate of 4 ft/min. Two minutes later, the second ant starts crawling in a direction perpendicular to that of the first, at a rate of 5 ft/min. How fast is the distance between them changing when the first insect has traveled 12 feet? Thank you!

Answers


I looked at this just before going to bed, and it ruined my night, worrying
about it. Then, this morning, when I actually set pencil to paper, it turned
out not to be such a vicious limbic twister.

You DO need to know how to take a chain derivative, though.  I must say,
I'm surprised to see this much Calculus at the middle school level.  Maybe
it's MY problem, but I just can't see a way to do it without this derivative,
so I'll just show you how I did it:

The ants begin together, and crawl out along the legs of a right triangle.

-- The first one moves at 4 ft/min, so after 't' minutes, he's 4t-ft from
the vertex.  The question concerns what happens when this one has
covered 12-ft.  That will happen in (12/4) = 3 minutes after he starts out.

-- The second one starts out 2-min later, and moves at 5-ft/min. So,
after 't' minutes, he's  5(t-2) ft  from the vertex.

-- The distance between them is the hypotenuse of the right triangle.
The square of the distance is the sum of the squares of the legs:

            D² = (4t)² + [ 5(t-2) ]²

We're actually going to need to know how far apart they are after 3 minutes,
so let's do that now.

           D² = (4 x 3)² + (5 x 1)² = (12)² + (5)² = 144 + 25 = 169

           D = √169 = 13-ft apart, after the first  guy has covered 12 feet.
     We will need this shortly.

OK.  Now, let's simplify the equation for the distance between them,
(as we get ready to differentiate it).

             D² = (4t)² + [ 5(t-2) ]²

             D² = 16t² + (25) (t² - 4t + 4)

             D² = 16t² + 25t² - 100t + 100

             D² = 41t² - 100t + 100

The question asks "How fast is the distance between them changing . . . ? ",
and we know that this is the derivative of 'D' with respect to 't' .  It's easy to
take the derivative of the right side of the equation, but what about the derivative
of ' D² ' ?   That's the part that I'm not so sure about in middle school, so I'll just
give it to you:

     (Derivative of D²) is [ (2D) times (derivative of D) ] .

Now we can take the derivative of each side of the equation:

     (2D) x (derivative of D) = 82 t - 100 .

                derivative of D = (82 t - 100) / (2D)

That's how fast the distance between them is changing at any time 't' .

After 3 minutes, we calculated 'D' earlier.  It's 13-ft

               derivative of D = [ (82 x 3) - 100 ] / (2 x 13)

                                       =     146               /      26  

                                       =      5.615  feet per second.

Are you confident ?  Do you trust me?
I'm not confident at all, and I don't trust myself.
The best I can suggest is for you to go through this and look for my mistakes,
or better yet, sit down with your teacher and go through it for mistakes.
That'll help you think about it and understand it, even if my work is wrong.
Ok, so I'll be quantizing time here to get you the most accurate result I can give you.

What you have to know is that:

D=\sqrt { { x }^( 2 )+{ y }^( 2 ) }

Also:

t=time snapshot (in minutes)

x=distance first ant has travelled

y=distance second ant has travelled (perpendicular to the first ant)

D=distance between both ants

--------------------------------------

Now, when:

t=0, x=0, y=0, D=0

t=1, x=4, y=0, D=4

t=2, x=8, y=0, D=8

t=3, x=12, y=5, D=13

Now we quantize time and find the tangent line (slope) between two points on the distance vs time graph at t=3 and t=3.000001, knowing that distance is represented by feet and time is represented in minutes.

When t=3.000001, x=12.000004, y=5.000005 D=13.00000562...

Now we find the slope on the distance vs time graph between the points (3,13) and (3.000001, 13.00000562).

m=\frac { 13.00000562-13 }{ 3.000001-3 } \n \n =\frac { 281 }{ 50 }

So, at the point (3,13) on the distance vs time graph, the two ants are moving away from each other at approximately 5.62 feet per minute.

Notations you may require to understand problem in the attachment below.

If f(x) = 3x + 2, find f(4)

Answers

f(4)=3(4)+2
f(4)=12+2
f(4)=14

PLZ HELP Kim wants to know how many families in her small neighborhood of 70 homes would participate in a neighborhood sports event. She put all the addresses in a bag and drew a random sample of 35 addresses. She then asked those families if they would participate in the sports event. She found that 15% of the families would participate in the event. She claims that 15% of the neighborhood families would be expected to participate in the sports event. Is this a valid inference? A. Yes, this is a valid inference because she took a random sample of the neighborhood
B. Yes, this is a valid inference because the 35 families speak for the whole neighborhood
C. No, this is not a valid inference because she asked only 35 families
D. No, this is not a valid inference because she did not take a random sample of the neighborhood

Answers

C. No because she only asked 35 families
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