How many sides can two congruent angles share

Answers

Answer 1

Answer: 8 i think the answer

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. Let A = (−2, 4) and B = (7, 6). Find the point P on the line y = 2 that makes the total distance AP + BP as small as possible.

Answers

Answer:

P(1,2)

Step-by-step explanation:

There are 2 points.

A(-2,4) and B(7,6)

the point P on the y=2 can also represented as P(x,2)

We can use the distance formula to find the distances AP and BP

$\text{dist} = √((x_1 - x_2)^2 + (y_1 - y_2)^2)$

for AP: A(-2,4) and P(x,2)

$AP = √((-2 - x)^2 + (4 - 2)^2)$

$AP = √((-2 - x)^2 + 4)$

$AP = √((-1)^2(2 + x)^2 + 4)$

$AP = √((2 + x)^2 + 4)$

for BP: B(7,6) and P(x,2)

$BP = √((7 - x)^2 + (6 - 2)^2)$

$BP = √((7 - x)^2 + 16)$

the total distance AP + BP will be

$√((2 + x)^2 + 4)+√((7 - x)^2 + 16)$ (plot is given below)

Our task is to find the value of x such that the above expression is small as possible. (we can find this either through plotting or differentiating)

If you plot the above equation, the minimum point of the curve will be clearly visible, and it will be at x = 1. Hence, the point P(1,2) is such that the total distance AP + BP is as small as possible.

Final answer:

The point P that makes the total distance AP + BP smallest on the line y=2 is given by the x-coordinate of the midpoint of A and B because the shortest distance is in a straight line. Therefore, the point P is (2.5, 2).

Explanation:

To find the point P on the line y = 2 that makes the total distance AP + BP the smallest, you need to recall that the shortest distance between two points is a straight line. So, ideally, we want to find a point P (x,2) that is on the same vertical line (or x-coordinate) that intersects the line AB at the midpoint.

Step 1: Find the midpoint of A and B. The midpoint M is obtained by averaging the x and y coordinates of A and B: M = ((-2+7)/2 , (4+6)/2) = (2.5, 5).

Step 2: Since line y = 2 is horizontal, the x-coordinate of our point P will stay the same with the midpoint x-coordinate. Therefore, P has coordinates (2.5, 2).

So, the point on the line y = 2 that makes the total distance AP + BP as small as possible is P (2.5, 2).

Learn more about Point here:

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Factor: 21x^3+6x^2+7x+2 I will give Brainliest to the first person :) please show all work

Answers

Answer:

(3x^2+1)*(7x-2)

Step-by-step explanation:

(1): "x2" was replaced by "x^2". 1 more similar replacement(s).

STEP

Equation at the end of step 1

(((21 • (x3)) - (2•3x2)) + 7x) - 2

STEP

Equation at the end of step

(((3•7x3) - (2•3x2)) + 7x) - 2

STEP

Checking for a perfect cube

3.1 21x3-6x2+7x-2 is not a perfect cube

Trying to factor by pulling out :

3.2 Factoring: 21x3-6x2+7x-2

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: 7x-2

Group 2: 21x3-6x2

Pull out from each group separately :

Group 1: (7x-2) • (1)

Group 2: (7x-2) • (3x2)

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

Add up the two groups :

(7x-2) • (3x2+1)

$8000 is borrowed at 6.2% p.a. Simple interest for 4 years.What is the total amount owed over 4 years??

Answers

The total amount owed after 4 years is $8000 plus the simple interest:

$8000 + $8000(0.062)(4) = $9984

A politician wants to distribute campaign flyers to 8000 homes in his district. The color flyers cost him $0.08 each, and the black and white flyers cost $0.05 each. He has $500 to spend on printing. What is the maximum number of color flyers he can buy (and still deliver flyers to all 8000 homes)?

Answers

Given:
8000 homes
color flyers : $0.08 each
black and white flyers : $0.05 each
budget of $500

c + b = 8,000
0.08c + 0.05b = 500

c = 8,000 - b
0.08(8,000 - b) + 0.05b = 500
640 - 0.08b + 0.05b = 500
-0.03b = 500 - 640
-0.03b = -140
b = -140 / -0.03
b = 4,667 black and white flyers

c = 8,000 - b
c = 8,000 - 4,667
c = 3,333 colored flyers

0.08(c) + 0.05(b) = 500
0.08(3,333) + 0.05(4,667) = 500
266.64 + 233.35 = 500
499.99 = 500
500 = 500

Length and breadth of a rectangular field is 5 : 3. If the breadth of rectangle is 60m, find the length of the rectangle.

Answers

Answer:

Step-by-step explanation:

Given data

Ratio of length to breadth is 5 : 3

hence in fraction form it is 5/3

the breadth of rectangle is 60m

let the length be x

5/3= x/3

cross multiply we have

5*3= 3x

15= 3x

divide both sides by 3

x= 15/3

x= 5m

Hence the length is 5m

How to change 4.1 into a decimal?

Answers

Well you can't change 4.1 into a decimal because it's already a decimal with a decimal point included in it, so there's really no point of asking that question when you've already done it yourself! Just wanted to notify you on that point.

You can't change it to a decimal because it is already a decimal.

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