MATHEMATICS HIGH SCHOOL

The end zone of a football field is 10 yards deep and 53 yards across. Between the two end zones is the playing field, which is 100 yards long and 53 yards wide. What is the length of the diagonal from the back of one end zone to the back of the other?

Answers

Answer 1
Answer: When you put the pieces of the field together, you have a rectangle that's 53 yards
wide and 120 yards long.

When you draw the diagonal, it divides the field into two right triangles.Each one
has legs with lengths of 120 yards and 53 yards.  The diagonal of the field is the
hypotenuse of both right triangles.

(120)² + (53)² = (the hypotenuse)²

14,400 + 2,809 = (the hypotenuse)²

17,209 = (the hypotenuse)²

The diagonal (hypotenuse) = √17,209 = 131.183... yards (rounded)

I guess that's the longest straight line it is possible to run on a football field
while staying in bounds.

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What is A2 – (B + C) in simplest form?A=8x2 – 25x + 7
B=8x2– 25x + 11
C=10x2 – 25x + 7
D=10x2 – 25x + 11

A, B, and C are polynomials, where:
A = 3x – 4
B = x + 7
C = x2 + 2

Answers

A2 - (B + C) = (3x - 4)2 - ((x + 7)+ (x2 + 2))
A2 - (B + C) = 9x2 - 24x + 16 - (x2 + x + 9)
A2 - (B + C) = 9x2 - 24x + 16 - x2 - x - 9
A2 - (B + C) = 8x2 - 25x + 7

So, the answer is
A:
8x2 – 25x + 7

Answer: 8x^2 - 25x + 7

Step-by-step explanation:

Here, A = 3x - 4, B = x + 7 and C = x^2 + 2

A^2 - (B + C)= (3x-4)^2-(x+7+x^2+2)     ( By putting the values)

= (3x)^2+ (4)^2- 2* 3x* 4- x- 7 - x^2 -2    ( solving the brackets)

=  9x^2+ 16 - 24x - x- 7 - x^2 -2

=  8x^2- 25x + 7        ( By operating like terms)

⇒ A^2 - (B + C) = 8x^2- 25x + 7

Thus, Option A is correct.

What is 238,854 rounded to the nearest hundred

Answers

238,854 rounded to the nearest hundred is 238,900~

Convert the equation from standard to slope-intercept form.
10x – 2y = -6

Answers

Answer:

The answer would be y = 5x + 3

Step-by-step explanation:

If 5 is increased to 8 , the increase is what percent of the original number?

Answers

Answer:

60%

Step-by-step explanation:

5*1.60=8

Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 mph. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 mph. How many hours did it take the first plane to travel to the destination?Let x represent the number of hours that the first plane traveled.
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the number of hours in the second box.

Answers

First plane: 496x
Second plane:  558( x - 1/2) 

Equation: 496x = 558( x - 1/2) 

Solving  x = 9/2 ,  or  x = 4.5 hours.

Hope this helps.

If 3x^2-2x+7=0,then (x-1/3)^2= please help with detailed steps because i dont really understand it. I know the answer is -20/9 but please explain

Answers

Answer:

-(20)/(9)

Explanation:

A quadratic function is a kind of function with highest degree 2 .  Standard form of the quadratic equation : tex]ax^2+bx+c=0[/tex]

Further explanation:

Consider the given quadratic equation : 3x^2-2x+7=0  

First we divide both sides  by 3 , we get

x^2-(2)/(3)x+(7)/(3)=0--------(1)

Compare this equation to x^2+2ax+a^2 , we have

2a=(-2)/(3)  

\Rightarrow\ a=(-1)/(3)  [divide both sides by 2]

Now using the completing the squares method , Add and subtract ((-1)/(3))^2 to the left side in (1), we get

x^2-(2)/(3)x+((-1)/(3))^2-((-1)/(3))^2+(7)/(3)=0  

It can be written as

(x^2-2((1)/(3))x+(1)/(3))^2)-(1)/(9)+(7)/(3)=0  

Use identity x^2-2ax+a^2=(x-a)^2, we have

(x-(1)/(3))^2)+(7(3)-1)/(9)=0  

(x-(1)/(3))^2)+(20)/(9)=0  

Subtract (20)/(9) from both the sides , we get

(x-(1)/(3))^2)=-(20)/(9)

Therefore, the value of (x-(1)/(3))^2)=-(20)/(9)

Learn more :

Keywords :

Quadratic equation, standard form, completing squares method, Polynomial identities.

For this case we have the following polynomial:

3x^2-2x+7=0

To solve the problem, we must complete squares.

The first step is to divide the entire expression by 3.

We have then:

(3)/(3)x^2-(2)/(3)x+(7)/(3)=0

The second step is to place the constant term on the right side of the equation:

(3)/(3)x^2-(2)/(3)x=-(7)/(3)

The third step is to complete the square:

(3)/(3)x^2-(2)/(3)x + (-(1)/(3))^2=-(7)/(3)+ (-(1)/(3))^2

Rewriting we have:

x^2-(2)/(3)x + (1)/(9)=-(7)/(3)+ (1)/(9)

(x-(1)/(3))^2 = -(20)/(3)

Answer:

By completing squares we have:

(x-(1)/(3))^2 = -(20)/(3)
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