MATHEMATICS MIDDLE SCHOOL

Given: AP=AQ, BP=BQ, CP=CQ

Prove: A, B and C are collinear.

Answers

Answer 1

Answer:

Solution:

Given: In the given figure, where there are pair of Quadrilateral, in which AP=A Q, BP=B Q, C P=C Q .

To Prove : A, B and C are collinear.

Construction: Join AC , the point where it intersects P Q is M.

Proof:

AP=A Q, C P=C Q,

So, the quadrilateral A P C Q is a kite.→→If in a quadrilateral One pair of adjacent sides are equal, then the quadrilateral is a kite.

As we know in a kite Diagonals bisect each other at right angles.

∠AMP=∠A M Q=∠CM P=∠C M Q=90°

Also, BP=B Q, C P=C Q.

So, the quadrilateral B P C Q is a kite.

∠B MP=∠B M Q=∠CM P=∠C M Q=90°

As you can see that , 1. ∠AMP +∠CM P=90°+90°=180°→→Shows Point A and C are in line.------------(1)

2. ∠B MP +∠CM P=90°+90°=180°→→→Shows Point B and C are in line.------------------(2)

Combining (1) and (2),

Shows that point A, B,C lie in a line.

It means Points A, B,C are Collinear.

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Manny made 4 pizzas to share among himself and 6 friends How much pizza will each person get?

Answers

Well in maths terminology for sharing is dividing:

4 pizzas' ÷ 6 friends
Slight algebra form 4p÷6f ⇔ equation
↑
= 1.2
I don't know how this is possible but each friend got one and a 1/2 pizzas'
Hope this helps :)

Jerry borrowed $4,000 for 5 years at 6% simple interest rate. How much interest is that?

Answers

Use I = Prt
where
I = Interest
P = Principal = $4,000
r = interest rate = 6% = 0.06
t = time = 5 years

I = $4,000 × 0.06 × 5 = $1,200

Jerry borrowed $1,200 for 5 years. Hope this helps!

In this question one has to look forward to the information's already given. Based on those given information's the answer to the question can be easily determined.
Principal amount = $4000
Time for which money is borrowed = 5 years
Rate of interest = 6%
Then
Amount of Interest = Principal * Rate * Time
   = 4000 * 6% * 5
   = 4000 * 6/100 * 5
       = 40 * 30
   = 1200 dollars
So the amount of interest that needs to be given is 1200 dollars. I hope the naswer and the procedure is clear enough for you to understand.

randy Driven 54 miles he consumed 2 gallons of gas.So If he consumed 4 gallons of gas how many miles did he drive

Answers

Twice more! 108 gallons of gas

Divide 54 by 2 and then Multiply by 4 ☺️

Write the inequality;
Eight less than a number is greater than 0 and less than or equal to 1.

Answers

1>N-8>0 the sign in between the 1 and the n should have a line under it

If log10 y = 2. what does y equal?

Answers

Answer:

$log_(10) (100) = 2$

Step-by-step explanation:

Here, the given expression is:

$log_(10) (y) = 2$

Now, by logarithm rules, we know

if $log_(b)(x) = z$

, then x = $b^(z)$

Comparing here, b = 10 and z = 2

⇒ y = $10^(2) = 100$

or, $log_(10) (100) = 2$

GuYS PLEASE HELP I WILL MARK AS BRAINIEST IF YOU EXPLAIN WELL. ANYWAYS, SOLVE EACH EQUATION BY FACTORING. R^2+9R+8=0 SO MY QUESTION IS HOW DO I DO THIS PLEASE HELP

Answers

To factor the equation, you can start by note that leading coefficient is 1 so factor would looks like (R + ?)(R + ?) = 0 because 1*1 = 1

And we know that 1*8 = 8 and 1 + 8 = 9 so then we have (R + 8)(R + 1)=0

Now we can split factors into two equations: R+8 = 0 or R+1 = 0.

Solve both equation and we get R = -8 or R = -1

I will try my best to assist you with your problem.

We need to factor the equation, so you must start by note that leading coefficient is 1 so factor would looks like (R + ?)(R + ?) = 0 because 1*1 = 1

And we know that 1*8 = 8 and 1 + 8 = 9 so then we have (R + 8)(R + 1)=0

Now we can split factors into two equations: either R+8 = 0 R+1 = 0.

Solve both equation and we get R = -8 or R = -1

Hope I helped!

Good Luck!

⛈

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y 2; r t ’ r i n than STEELE thud 8. Draw an example of 3 shape that has at least one right angle my one angle less than a right angle and one angle greater than a right angle Label the angles

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