A ball dropped from the roof of a 120 foot high building took 4 seconds to reach the ground. What was the average speed of the ball during its fall?

A
480 feet per second
B
124 feet per second
C
30 feet per second
D
130 feet per second

Answer:

Step-by-step explanation:

It's a simple question as we know:

y-y1=m(x-x1)

y-20=12(x-3)

y=12x-36+20

y=12x-16

Now, your line is in slope intercept form you can compare it with

y=mx+c

m=12 and c=16. You can also put your point to verify your answer.

Answer:

Y = 10.25 or 10.247

Step-by-step explanation:

Alright So use the Formula A^2 + B^2 = C^2

You have one leg and the hypotenuse so first you are going to find 19 ^2 = 361.

Next, you need to find 16^2 = 256.

Last but not least, you subtract the leg from the hypotenuse, which equals 361-256=105

Finally, you take 105 and find its square root.

And depending on how far you round it down, your answer would be 10.25(that is in tenths), or 10.247(which is rounded to hundredths)

Hope this helps!

did you get ittttt???

please help me out

Answer:

$267.5

Step-by-step explanation:

7% of 250=17.5. 250+17.5=267.5

Answer:

267.5

Step-by-step explanation:

250+7%=267.5

Hope this helps :)

Answer:

-2/x

Step-by-step explanation:

simplified is y = -x/2 - 6

Perpendicular slopes are just reciprocals of the original slope, so just flipp the original slope around to be the complete opposite.

Example if slope= -2, the reciprocal= -1/2

Just flip the numerator with the denominator for perpendicular slope

Answer:

C

Step-by-step explanation:

AE = 14.6 I think. If I'm wrong, use whatever number it is.

Sin(x) = 5/14.6

Sin(x) = 0.3425

x = Sin-1 (0.3425)

x =20.03

Now the other larger triangle has an acute angle of 90 -20.03 =  69.97

===================

Cos(69.97) = 13.1/DE

DE = 13.1/cos(69.97)

DE = 38.25

9514 1404 393

Answer:

  x = 10√3

Step-by-step explanation:

The Pythagorean theorem tells you ...

  FB^2 = BC^2 +CF^2

  FA^2 = FB^2 +BA^2

Substituting for FB^2, we have ...

  FA^2 = BC^2 +CF^2 +BA^2 = x^2 +x^2 +x^2

  FA^2 = 3x^2

  FA = x√3 = 30 . . . . take the square root and substitute for FA

  x = 30/√3

  x = 10√3

Answer:

Solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

Step-by-step explanation:

We need to solve the inequality: [tex]x - 2 > 2x + 12[/tex] and find value of x

Solving the inequality

[tex]x - 2 > 2x + 12[/tex]

First of all, we will add 2 on both sides

[tex]x - 2+2 > 2x +12 +2\\x>2x+14[/tex]

Now, add -2x on both sides of inequality

[tex]x-2x>2x+14-2x\\-x>14[/tex]

Now, multiply both sides by -1, when multiplying by negative number, the inequality is reversed i.e. > will become <

[tex]-1*-x<14*-1\\x<-14[/tex]

So, solving the inequality: [tex]x - 2 > 2x + 12[/tex] we found the value of x: [tex]\mathbf{x<-14}[/tex]

Option D is correct option.

Answer:

52 students or 51

Step-by-step explanation:

Answer:

The one on the graph

Step-by-step explanation:

Answer:

t ≤ − 4

Step-by-step explanation:

Answer: t ≤ -4

Step-by-step explanation:

rearrange the problem 24-(-6*t)≤0  Pull out like factors :24 + 6t  =   6 • (t + 4)

Divide both sides by 6    Subtract  4  from both sides t ≤ -4

Answer:

D

Step-by-step explanation:

Because pi never ends.

Hence, D (π) is a irrational number.

The expression to represent the net yardage is 30.5x+12.9y.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, gain 25x yards, gain 0.9y yards lose 12y yards and lose 5.2x yards.

Now, net yardage

= 25x+0.9y+12y+5.5x

= 30.5x+12.9y

Therefore, the expression to represent the net yardage is 30.5x+12.9y.

To learn more about an expression visit;

https://brainly.com/question/28170201.

#SPJ2

Answer: It number 4

Step-by-step explanation:

Answer:

a) h = 15

b) x = 4

Step-by-step explanation:

a) set up a proportion:

  5 = h

   8     24

cross-multiply:

8h = 120

h = 15

b) x + 5 = x + 5 + 15

   5x + 1    5x + 1 + 35

cross-multiply:

(x + 5)(5x + 36) = (5x + 1)(x + 20)

5[tex]x^{2}[/tex] + 61x + 180 = 5[tex]x^{2}[/tex] + 101x + 20

180 = 40x + 20

160 = 40x

x = 4

Answer:

[tex]\displaystyle y = x^{-\frac{2}{3}}[/tex]

Step-by-step explanation:

Logarithms

Some properties of logarithms will be useful to solve this problem:

1. [tex]\log(pq)=\log p+\log q[/tex]

2. [tex]\displaystyle \log_pq=\frac{1}{\log_qp}[/tex]

3. [tex]\displaystyle \log p^q=q\log p[/tex]

We are given the equation:

[tex]\displaystyle \log_{2}(x) = \frac{3}{ \log_{xy}(2) }[/tex]

Applying the second property:

[tex]\displaystyle \log_{xy}(2)=\frac{1}{ \log_{2}(xy)}[/tex]

Substituting:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(xy)[/tex]

Applying the first property:

[tex]\displaystyle \log_{2}(x) = 3(\log_{2}(x)+\log_{2}(y))[/tex]

Operating:

[tex]\displaystyle \log_{2}(x) = 3\log_{2}(x)+3\log_{2}(y)[/tex]

Rearranging:

[tex]\displaystyle \log_{2}(x) - 3\log_{2}(x)=3\log_{2}(y)[/tex]

Simplifying:

[tex]\displaystyle -2\log_{2}(x) =3\log_{2}(y)[/tex]

Dividing by 3:

[tex]\displaystyle \log_{2}(y)=\frac{-2\log_{2}(x)}{3}[/tex]

Applying the third property:

[tex]\displaystyle \log_{2}(y)=\log_{2}\left(x^{-\frac{2}{3}}\right)[/tex]

Applying inverse logs:

[tex]\boxed{y = x^{-\frac{2}{3}}}[/tex]

Answer:

3/10 shade 3 in

Step-by-step explanation:

Answer:

Quotient : 3x² + 5x + 1

Step-by-step explanation:

Answer:

9 years ( approximately)

Step-by-step explanation:

900(1.03)^t = 1200

(1.03)^t= 1.33

( 1.03)^t= ( 1.03)^9

So, t= 9

Answer:

A. 35°C.

Step-by-step explanation:

35 C (Celsius), converted to F (Fahrenheit), would be 95. Which would make it a hot day.

So, you answer is 35°c.

Answer:

<XWY= 180-23

Step-by-step explanation:

angles on a straight line add up to 180!

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Answer:

7 / 15= 0.47

Step-by-step explanation:

9514 1404 393

Answer:

  4)  6x

  5)  2x +3

Step-by-step explanation:

We can work both these problems at once by finding an applicable rule.

  [tex]\text{For $f(x)=ax^n$}\\\\\lim\limits_{h\to 0}\dfrac{f(x+h)-f(x)}{h}=\lim\limits_{h\to 0}\dfrac{a(x+h)^n-ax^n}{h}\\\\=\lim\limits_{h\to 0}\dfrac{ax^n+anx^{n-1}h+O(h^2)-ax^n}{h}=\boxed{anx^{n-1}}[/tex]

where O(h²) is the series of terms involving h² and higher powers. When divided by h, each term has h as a multiplier, so the series sums to zero when h approaches zero. Of course, if n < 2, there are no O(h²) terms in the expansion, so that can be ignored.

This can be referred to as the power rule.

Note that for the quadratic f(x) = ax^2 +bx +c, the limit of the sum is the sum of the limits, so this applies to the terms individually:

  lim[h→0](f(x+h)-f(x))/h = 2ax +b

__

4. The gradient of 3x^2 is 3(2)x^(2-1) = 6x.

5. The gradient of x^2 +3x +1 is 2x +3.

__

If you need to "show work" for these problems individually, use the appropriate values for 'a' and 'n' in the above derivation of the power rule.

Answer:

2*2=4

Step-by-step explanation:

Answer:

5.25x + 55 is greater than or equal to 399

Step-by-step explanation:

55 is a fixed amount of money that Amelia already has so that will be added to the part of the eqaution: 5.25x.

Her total should be greater than or equal to $399

Answer:

x = 41

Step-by-step explanation

9^2 + 40^2 = x^2

81 + 1600 = 1682

square root of 1681 = 41

x = 41