MATHEMATICS HIGH SCHOOL

The length of line segment AK is 640 meters. ∆ABC, ∆CDF, and ∆FJK are similar, and 2AC = CF = 2FK. The first pillar is 20 meters tall. What is the area of ∆CDF

Answers

Answer 1
Answer: A to K = 640 meters

2AC = CF = 2FK


2AC = 2(160) = 320
CF = 320
2FK = 2(160) = 320

AC = 160
CF = 320
FK = 160
AK    640

BG = 20 m ; Area = (160m*20m) / 2 = 3,200/2 = 1,600 m²

20:160 = x : 320
20*320 = 160x
6,400 = 160x
6,400/160 = x
40 = x

Area of CDF = (320m*40m) / 2 = 12,800 / 2 = 6,400 m²
Answer 2
Answer:

Answer:

what that other guy said

sorry just here for the points

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Two groups separately performed an experiment by tossing a coin in the air. Group A performed 50 trials and group B performed 100 trials. Each group recorded the results in the table below:Group Heads Tails
A 30 20
B 52 48


What conclusion can be drawn about the number of trials and the probability of the coin landing on heads or tails?

Answers

Theoretical probability;
Head = 1/2 or 50%
Tail = 1/2 or 50%

Group     Heads      Tails      Total
A                30          20          50
B                52          48        100

Experimental probability:
Group A: 
Heads : 30/50 = 60%
Tails: 20/50 = 40%

Group B:
Head: 52/100 = 52%
Tails: 48/100 = 48%

Experimental probabilities of Group B is closer to the theoretical probabilities.

A school custodian waxed the gymnasium floor that measured 20 feet by 20 feet. How many square feet did she have to wax?

Answers

Hey there, all you do is multiply 20 by 20, 20×20=400. Therefore, the answer is 400 square feet.

What is the axis of symmetry of the function f(x) = –(x + 9)(x – 21)?The axis of symmetry is x =

Answers

f ( x ) =  - ( x + 9 ) ( x - 21 ) =
= - ( x² - 21 x + 9 x - 189 ) =
= - x² + 21 x - 9 x + 189 =
= - x² + 12 x + 189
This is a quadratic function and its axis of symmetry is:
x = - b / 2a,  where: a = - 1 and b = 12
x = - 12 / 2·(-1) = - 12 / (- 2) = 6
Answer: x = 6

The axis of symmetry is x = 6

Further explanation

Discriminant of quadratic equation ( ax² + bx + c = 0 ) could be calculated by using :

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

\large {\boxed {x = (-b)/(2a) } }

Given:

f(x) = - (x + 9)(x - 21)

f(x) = - (x^2 - 21x + 9x - 189)

f(x) = - (x^2 - 12x - 189)

f(x) = -x^2 + 12x + 189

The axis of symmetry is

x = (-b)/(2a)

x = (-12)/(2(-1))

x = (-12)/(-2)

\large {\boxed {x = 6} }

Learn more

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number , Axis , Symmetry , Function

. 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:

brainly.com/question/16410393

#SPJ3

A spinner and 2 cards are shown below:A spinner with 7 equal sectors is shown in the figure. The colors Green, Red, Orange, Violet, Pink, Yellow, and Blue are marked on it. The arrow points at the red color. Two cards are shown on the right side. The colors Purple and Green are marked on them.

Sophie spins the spinner and picks up a card without looking. What is the probability that the spinner stops at red and a green card is selected?

1 over 49
1 over 16
1 over 14
1 over 2

Answers

P(red AND green card) = P(red) * P(green card)

P(red) = 1/7 (i.e. one color out of total of seven)
P(green card) = 1/2 (i.e. one card out of two)

P(red AND green card) = 1/7 * 1/2 = 1/14

Answer:

Hence, probability that the spinner stops at red and a green card is selected is:

1 over 14

Step-by-step explanation:

It is given that a spinner and two cards are selected.

A spinner has 7 colors in it:

Green,Red,Orange, Violet, Pink, Yellow, and Blue are marked on it.

Two cards are shown on the right side. The colors Purple and Green are marked on them.

Now we are asked to find the probability that the spinner stops at red and a green card is selected.

Let A  denotes the event that the arrow stops at red.

and B denote the event that a green card is selected.

Now, we have to find:

P(A∩B)

Where P denotes the probability of an event.

As we know that event A and event B are independent.

Hence,

P(A∩B)=P(A)×P(B)

Now,

P(A)=1/7

( Since we have 7 choices out of which only one sector has red color)

Similarly,

P(B)=1/2

( since we have just two cards and one card is green).

Hence,

P(A∩B)=(1/7)×(1/2)=1/14

Hence, probability that the spinner stops at red and a green card is selected is:

1 over 14

Inverse operations 15x+8=6

Answers

Answer:

1 step. multiplayer with 8 and find their sum the difference between the temperature recorded on llllll
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