MATHEMATICS MIDDLE SCHOOL

In the standard (x,y) coordinate plane, what are the coordinates of the midpoint of a line segment whose endpoints are (–3,0) and (7,4) ?A. (2,2)
B. (2,4)
C. (5,2)
D. (5,4)
E. (5,5)

Answers

Answer 1
Answer: A(x_A;\ y_A);\ B(x_B;\ y_B)\n\nmidpoint\ AB:\left((x_A+x_B)/(2);\ (y_A+y_B)/(2)\right)\n\n-------------------\n\n(-3;\ 0);\ (7;\ 4)\n\nmidpoint:\left((-3+7)/(2);\ (0+4)/(2)\right)\to\left((4)/(2);\ (4)/(2)\right)\to(2;\ 2)\n\nAnswer:A

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If arc AD = 130° and arc AB = arc CD = 80°, what is the measure of ∠APD?

Answers

Answer:

(B)

Step-by-step explanation:

Given: It is given that arc AD=130° and arc AB=arc CD=80°.

To find: The measure of ∠APD.

Solution: It is given that arc AD=130°⇒m∠AOD=130° (The measure of the central angel is equal to the intercepted arc)

Also, arc AB=arc CD=80°⇒m∠AOB=m∠DOC=80° (The measure of the central angel is equal to the intercepted arc)

We know that the sum  of the central angles is equal to 360°, thus

m∠AOD+m∠AOB+m∠BOC+m∠COD=360°

⇒130°+80°+m∠BOC+80°=360°

⇒290°+m∠BOC=360°

⇒m∠BOC=360°-290°

⇒m∠BOC=70°

Now, since  (The measure of the central angel is equal to the intercepted arc), therefore arcBC=70°.

Also, we know that Angle Formed by Two Secants is half of the DIFFERENCE of Intercepted Arcs, therefore

m{\angle}APD=(1)/(2) (arcAD-arBC)

Substituting the values, we get

m{\angle}APD=(1)/(2) (130-70)

⇒m{\angle}APD=(60)/(2)

⇒m{\angle}APD=30^(\circ)

Thus, the measure of ∠APD is 30°.

Hence, option B is correct.

Answer:

the answer is 25

Step-by-step explanation:

1/2(130-80)

If (s-3)^2=0, what is the value of (s+3) (s+5)?

Answers

Here,

(s-3)²=0

→s-3=0

→s=3

Substituting s=3 in,

(s+3)(s+5)

=(3+3)(3+5)

=(6)(8)

=48

You finish washing 3/4 of your windows in an hour and a half. At that rate, how much longer will it take you to finish washing all the windows?If you are washing the windows at a rate of 1/4 every 30 minutes, you need only 30 minutes to finish washing the remaining one-fourth.

Answers

It would take about to hours to wash all the windows.
2 hours to finish whole thing

but 1/4 = 30 min

A blimp is 1500 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 72.9° and 34.1°, how far apart are the two stadiums to the nearest meter?

Answers

Answer:

The distance between both stadiums is:

2215.49 m - 461.46 m =1754.03 m

Step-by-step explanation:

Look at the attached picture:

Lets say that the stadium on the left is stadium 1 and stadium 2 is on the right.

Using the angle property of alternate angles the angle above stadium 1 is 72.9°  and the angle above the stadium 2 is 34.1°

By using trigonometric function of tangent we solve it as:

We know that tanθ = opposite / adjacent

Therefore,

tan  72.9°=1500/ adjacent

Now

adjacent = 1500/tan 72.9°

adjacent = 461.46 m

Solve for next angle:

Tan 34.1°=1500/ adjacent

adjacent = 1500/tan 34.1°

adjacent = 2215.49 m

Therefore the distance between both stadiums is:

2215.49 m - 461.46 m =1754.03 m ....

What is the value of 1 raised to the power of any exponent? What is the value of 0 raised to the power of any nonzero exponent? Explain.Please help me.

Answers


You can easily do this one on your own.

-- Pick up a pencil and find a piece of paper.

-- Multiply ' 1 ' by itself, two or three or ten or a million times.

That means like (1 x 1 x 1 x 1 x 1 x 1 . . .).  What do you get ?


-- Multiply 'zero' by itself, two or three or ten or a million times.

That means like (0 x 0 x 0 x 0 x 0 x 0 . . . . . ).  What do you get ?

What two numbers multiply together and equal 16 and add together and equal -2?

Answers

There is a solution, but you might not have learned how to do it yet
in middle school.

If you've learned to use the quadratic formula to solve a quadratic equations,
then you can do this.

The first requirement says: ' x ' times ' y ' = 16
The second requirement says: (x + y) = -2

Take the second requirement, and subtract ' x ' from each side:

y = -x - 2

Substitute this into the first requirement:

' x ' times (-x - 2) = 16

Eliminate parentheses:

-x² - 2x = 16

Subtract 16 from each side:

-x² - 2x - 16 = 0

Multiply each side by -1:

x² + 2x + 16 = 0

Solve this with the quadratic formula, and you get two solutions,
which are the two numbers that satisfy both requirements.

The numbers are

-1 + √-15

-1 - √-15

Check:

-- Product: (-1 + √-15) times (-1 - √-15) = 1 + 15 = 16

-- Sum = -1 + √-15 -1 - √-15 = -2

They work. 
yay
None, because both numbers must be negative in order to get a positive answer, or both positive. However, -2 means that there is at least one negative number, or two negative numbers. the only option : -1+(-1)= -2. So there is no real solution.
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