MATHEMATICS HIGH SCHOOL

One day, a person went to a horse racing area. Instead of counting the number of humans an horses, he conuted 74 heads and 196 legs. How many humans and horses were there?A.
37 humans and 98 horses
B.
24 horses and 50 humans
C.
31 horses and 74 humans
D.
24 humans and 50 horses




99 POINTS

Answers

Answer 1
Answer: A human has 1 head and 2 legs.
A horse has 1 head and 4 legs.

Let's make two equations from what we know.

There were a total of 74 heads.
There were a total of 196 legs.

Let's call humans 'x' and horses 'y'

The total number of heads were 74.
Humans have 1 head, and so do horses.

Our first equation is:
x + y = 74

There were a total of 196 legs. 
Humans have 2 legs, and horses have 4 legs.

Our second equation is:
2x + 4y = 196

Our two equations are:

x + y = 74
2x + 4y = 196

We need to solve this system of equations to find out how many humans and horses were at this racing event.

Multiply the first equation by 2.

2(x + y) = 2(74)
2x + 2y = 148

Our two equations are:

2x + 2y = 148
2x + 4y = 196

Subtract the first equation from the second equation.

2x - 2x + 2y - 4y = 148 - 196
2y - 4y = 148 - 196
-2y = - 48

Divide both sides by -2

y = 24

That means that there were 24 horses.

We can plug back in y = 24 into our first equation to find out how many humans there were.

x + y = 74
x + 24 = 74
x + 24 - 24 = 74 - 24
x = 50

There were 50 humans.

At the horse racing event, there were 24 horses and 50 humans.

Your final answer is B. 24 horses and 50 humans.
Answer 2
Answer: 50 +24 =74 heads  50 x 2 = 100 human legs 4 x 24 = 96 horse legs 100 + 96 =196 legs total. So b will be your final answer.

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A bicycle is on sale at $12 more than half of the regular price. If the sale price is $75, find the regular price.

Answers

The regular price of the bicycle will be $126.

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a bicycle is on sale at $12 more than half of the regular price and the selling price is $75.

The regular price of the bicycle will be calculated as below:-

( P / 2 ) + 12 = 75

P  + 24 = 150

P = 150 - 24

P = 126

Therefore, the regular price of the bicycle will be $126.

To know more about an expression follow

brainly.com/question/723406

#SPJ2
so 12 more than half the regular price.
let's let p be the original price.

(1)/(2) p + 12 = 75
right?
Now you just have to solve from there.

A leatherback sea turtles was swimming at 850 below sea level. He went 165 meters and then descendes 165 meters. Draw a number line to show the change in position of the sea turtles from depth it was swimming. What integer represents the sea turtles change in position?

Answers

Answer:

0

Step-by-step explanation:

Initial. Position = (- 850) below sea level

Upward movement = 165m

Deownward movement (descent) = (165m

Change in position : net change

Upward movement + downward movement

(165 + (-165)m = (165 - 165)m = 0

-4 is less than or equal to x, and 0 is greater than x

Answers

Answer:

4\leq x \leq 0

Step-by-step explanation:

Find the product of (4x − 3)(2x2 − 7x + 1).8x3 − 22x2 + 17x− 3

8x3 + 8x2 + 4x − 3

8x3 − 34x2 + 25x − 3

8x3 − 42x2 + 25x − 3

Find the product of 2x4(4x2 + 3x + 1).

8x6 + 6x5 + 2x4

8x8 + 3x4 + 2x4

2x4 + 6x5 + 8x6

6x6 + 5x5 + 3x4



Which statement shows that when two polynomials 4x + 6 and 2x2 − 8x demonstrates the closure property when multiplied?

8x3 − 20x2 − 48x is a polynomial

8x3 − 20x2 + 48x may or may not be a polynomial

8x2 − 32x2 − 14x is a polynomial

8x3 − 32x2 + 14x may or may not be a polynomial

Answers

The correct answers are:

(1)~8x^3 -34x^2 + 25x -3 ~~(Option C)

(2) ~ 8x^(6) + 6x^(5) + 2x^4 ~~(Option A)

(3) ~ 8x^3 - 20x^2-48x ~~ is a polynomial (Option A)

Explanations:

(1) Given Expression:

(4x-3)(2x^2-7x + 1)

Now simplify as follows:

4x(2x^2 - 7x + 1) - 3(2x^2 - 7x + 1) \n8x^3 - 28x^2 + 4x - 6x^2 + 21x - 3 \n8x^3 -34x^2 + 25x -3

Therefore, the correct answer is 8x^3 -34x^2 + 25x -3(Option C)

(2) Given Expression:

2x^4(4x^2 + 3x + 1)

Now simplify as follows:

2x^4(4x^2 + 3x + 1) \n2x^4(4x^2) + 2x^4(3x) + 2x^4(1) \n8x^((4+2)) + 6x^((4+1)) + 2x^4 \n8x^(6) + 6x^(5) + 2x^4

Therefore, the correct answer is 8x^(6) + 6x^(5) + 2x^4(Option A)

(3) Given Data:

Polynomial one: 4x + 6

Polynomial two: 2x^2-8x

First multiply both polynomials:

(4x + 6) * (2x^2-8x) \n(4x) * (2x^2-8x) + (6) * (2x^2-8x) \n8x^3-32x^2+12x^2-48x \n8x^3-20x^2-48x

Now as we can see, if we multiply two polynomials, the resultant expression is also a polynomial. Therefore, it does demonstrate the closure property (closed set). Hence, the correct answer is 8x^3-20x^2-48x ~~(Option A)
1. The correct answer among the choices provided is 8x3 − 34x2 + 25x − 3.
2. The correct answer among the choices provided is 8x6 + 6x5 + 2x4.
3. The correct answer among the choices provided is 8x3 − 20x2 − 48x. It is a polynomial.

What is 6.4X10 to the 8th power meters per second, in kilometers per hour???

Answers


(6.4 x 10^8 meter/sec) x (1 km / 1,000 meter) x (3,600 sec/hour) =

       (6.4 x 10^8 x 3,600 / 1,000)  km/hour  = 

                            177-7/9 km/hour
 

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2?a) (x-3)^2 = 20(y-1)
b) (y-1)^2 = 20(x-3)
c) (y-1)^2 = -20(x-3)
d) (x-3)^2 = 20(y-1)

Answers

Answer with Step-by-step explanation:

We have to find:

the standard form of the equation of the parabola that has a vertex of (3, 1) and a directrix of x = –2

General form of Parabola that opens left or right:

(y−k)²=4p(x−h)

Vertex =(h,k)  

Directrix: x=h−p

Here, h=3,k=1 and h-p=-2  i.e. p=h+2=5

Hence, equation of parabola in this case equals

  (y-1)²=4×5(x-3)

i.e. (y-1)²=20(x-3)

Hence, correct option is:

b)  (y-1)²=20(x-3)
Hello,

Remenber:
if S=(0,0) y²=2px then F=(p/2,0 and d:x=-p/2


Let's pose
x'=x-3
y'=y-1 axes passing by the point (3,0) in base (x,y) and (0,0) in base (x',y')

y'²=2p'x'
d': x'=-5=-p'/2 ==> p'=10 and y²=20x'
Returning in base (x,y) : (y-1)²=20(x-3)

Answer B
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