MATHEMATICS HIGH SCHOOL

a bowling ball is dropped from a height of 24 feet. write a function that gives the height h (in feet) of the bowling ball after t seconds

Answers

Answer 1

Answer:

Answer:

$h=16t^2$

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 32 ft/s²

$s=ut+(1)/(2)at^2\n\Rightarrow h=ut+(1)/(2)32* t^2\n\Rightarrow h=ut+16t^2$

Here, u = 0 so,

$h=0t+16t^2\n\Rightarrow h=16t^2$

The equation is $h=16t^2$

$24=16t^2\n\Rightarrow t=\sqrt{(24)/(16)}\n\Rightarrow t=1.22\ s$

Time taken by the ball to hit the ground is 1.22 seconds

Answer 2

Answer: gravity pulls at 32 feet per second so it would take .75sec to hit the ground now make an equation that can make this applicable so after .75 second T it would be at 0 feet H

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Graph the function represented by the equation y=3×2-6×-9
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Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?answers:
3x2 − 11x + 8 may or may not be a polynomial
3x2 − 11x + 8 will be a polynomial
3x2 − x + 4 may or may not be a polynomial
3x2 − x + 4 will be a polynomial

Answers

The correct answer is that 3x²-11x+8 will be a polynomial.

Explanation:
When we subtract polynomials, we combine like terms:
3x² is the only x² term we have.
We have -6x and subtract 5x from it; this gives us -11x.
We have 2 and subtract -6 from it; when we subtract a negative, we add the opposite, which means we have 2--6=2+6=8.

This gives us 3x²-11x+8. This is a polynomial, since it is made of monomials (none of the terms have a negative exponent or a radical sign).

Answer:

option (b) is correct.

we get a polynomial $3x^2-11x+8$

Step-by-step explanation:

Given : Polynomial 5x -6 and $3x^2-6x+2$ .

We have to choose out of given options which shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from $3x^2-6x+2$ .

We first subtract the polynomial

$\Rightarrow 3x^2-6x+2-(5x-6))$

$\Rightarrow 3x^2-6x+2-5x+6$

similar terms are terms having same variables with same degree.

Here, -6x and -5x are similar

and 2 and 6 are similar.

Adding similar terms, we get,

$\Rightarrow 3x^2-11x+8$

Polynomial is an algebraic expression that can involves variables with non negative integer terms and constants.

Thus, we get a polynomial $3x^2-11x+8$

Hence, option (b) is correct.

How many multiples of 9 are there between 100 and 2,000?

Answers

first of all, find the first number more than 100 that can divided by 9, and it's 108 (we'll call it as 'a') then, find the number less than 2000 that can divided by 9, it's 1.998 (we'll call it as 'Un')

Un = a + (n-1).b
1998 = 108 + (n-1).9
1998 = 108 + 9n -9
1899 = 9n
211 = n

and the total is
Sn = n/2 (a+un)
s211 = 211/2 (108+1998)
= 222.183

How many solutions does the system have?

{y=−3x+5
{y=x^2−3x+5

Answers

Hello here is a solution :
y= -3x+5 ...(1)
y = x² -3x+5 ... ( 2 )
-3x+5 = x² -3x+5
x² =0
x=0
y= -3(0)+5 = 5
the system have one solution (0;5)

Start at 200.Create a pattern that multiplies each number by 2.Stop when you have 5 numbers.

Answers

200, 400, 800, 1600, 3200

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0?

Answers

Answer: The required equation of the line is $4x+y=6.$

Step-by-step explanation: We are given to find the equation of the line that passes through (1, 2) and is parallel to the line whose equation is as follows:

$4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The slope-intercept form of the given line (i) is

$4x+y-1=0\n\n\Rightarrow 4x+y=1\n\n\Rightarrow y=-4x+1,$

where, slope of the line is, m = - 4.

Since parallel lines have equal slopes, so the slope of the new line that passes through the point (1, 2) is

m = - 4.

Therefore, the equation of the line will be

$y-2=m(x-1)\n\n\Rightarrow y-2=-4(x-1)\n\n\Rightarrow y-2=-4x+4\n\n\Rightarrow 4x+y=6.$

Thus, the required equation of the line is $4x+y=6.$

y=-4x+6
or if you need it in the original format
4x+y-6=0

What are the dimensions of the rectangle?

Answers

the dimensions would be 18 by 5.5. because you know the area is 99, and you know the area formula is length multiplied by width, you set the dimensions to 99, and continue to solve for x. then you plug the x value into the length’s dimension to get 18.

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