A person standing at the edge of a cliff 48 feet tall throws a ball up and just off the cliff with an initial upward velocity of 8 feet per second. What is the maximum height of the ball? When will the ball hit the ground?



The ball will be at its highest at ___


feet.



The ball will hit the ground at t =___


second(s)

Answer:

x² = 81 , x = ± 9

x² - 18x = 7 : x = 9 ± √(22)

Step-by-step explanation:

x² = 81

simply take the square root of both sides

x = ± 9

x² - 18x = 7

This question is a bit more complicated as there is a variable with a power as well as a variable with no power. To solve for x we are going to have to put the equation in quadratic form then solve using the quadratic equation

x² - 18x = 7

put the equation in quadratic form by subtracting 7 from both sides so that the equation is equal to 0

x² - 18x - 7 = 0

we can now solve for x using the quadratic equation

recall the quadratic equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

where the value of a,b and c are derived from the equation

remember the equation is in quadratic form ax² + bx + c = 0

so ax² + bx + c = 0 : x² - 18x - 7 = 0

knowing this we can assign variables, a = 1 , b = -18 and c = -7

now we plug in the variables into the quadratic equation

recall equation : [tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex]

a = 1 , b = -18 and c = -7

plug in values

[tex]x=\frac{-(-18)+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]

remove parenthesis

[tex]x=\frac{18+\sqrt{(-18)^2-4(1)(-7)} }{2(1)}[/tex]

simplify exponent

[tex]x=\frac{18+\sqrt{324-4(1)(-7)} }{2(1)}[/tex]

simplify multiplication in square root and on denominator

[tex]x=\frac{18+\sqrt{324+28} }{2}[/tex]

simplify addition

[tex]x=\frac{18+\sqrt{352} }{2}[/tex]

simplify radical

[tex]x=\frac{18+4\sqrt{22} }{2}[/tex]

simplify fraction

[tex]x=9+or-\sqrt{22}[/tex]

and we are done!

The only true statement that compares the two functions is:

B: The solution to f(x)=g(x) is 1

Here we have the functions:

f(x) = |x - 3| + 1

g(x) = 2x + 1

First, let's find the solution for:

f(x) = g(x)

|x - 3| + 1 = 2x + 1

|x - 3| = 2x

Notice that we have two options, x = 3:

|3 - 3| = 2*3

0 = 6  (x = 3 is not a solution)

And x = 1:

|1 - 3| = 2*1

2 = 2  (x = 1 is a solution).

Now to get the y-value where the graphs intersect, we just evaluate one of the functions in the solution we found above;

f(1) = |1 - 3| + 1  = 2 + 1 = 3

The graphs intersect when y = 3.

Then we conclude that the only true statement is:

B: The solution to f(x)=g(x) is 1

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

Answer:

The answer is that they both payed $9.00.

Step-by-step explanation:

The both payed $60.00, and 30% of that is $18.00.

( $60.00*.03=$18.00)

$18.00 divided by two (two people, James and Sarah) is $9.00.

So they both payed $9.00 individually.

Answer:

  (x, y) = (1 7/9, -2 1/9)

Step-by-step explanation:

If all you want is a solution, an appropriate calculator can provide that. The attachment shows the result of using a graphing calculator. (We have to know the fraction equivalents of the decimal values shown.)

The solution to the system is ...

  (x, y) = (1 7/9, -2 1/9)

__

The solution is approximately (2, -2).

Answer:

A because a prism is the only solid they can be used in that way

Then the maximum value of both the quadratic functions is the same. Then the correct option is A.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadratic functions f(x) and g(x) are described as follows:

f(x) = −4x² + 5

x     g(x)

0       0

1         1

2       5

3        1

4       0

The value of x for which f(x) will be maximum

[tex]\begin{aligned} \dfrac{d}{dx} \ f(x) = 0\\\\\dfrac{d}{dx} \ (-4x^2 + 5) = 0\\\\-8x =0\\\\x = 0 \end{aligned}[/tex]

Then the maximum value of f(x) will be

f(x) = −4(0)² + 5

f(x) = 5

Then the maximum value of both the functions is the same.

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

The maximum values is the same for both functions.

Step-by-step explanation:

I took the test on flvs and got it right. And it should be correct too on other places like flvs. Hope this helps.

(please don't report me for advertisement of other websites. I believe how I have put it doesn't break that rule.)

Answer:

the first one

Step-by-step explanation:

absolute value is a number's distance from zero, so distance from zero can not possibly be negative. Therefore, |4x-2|=-6 has no solution.

Answer:

It would be the first one because there is no value of x that makes the equation be true since an absolute value can never be negative.

Step-by-step explanation:

Hope this helps:)....if don't help then sorry for wasting your time and may God bless you:)

hi my name not Jeff. ok?

Step-by-step explanation:

hi im not jeff

Answer:

The thickness of the paper doubles each fold: it's an exponential growth.

Step-by-step explanation:

Answer:

2/2 = 1

Step-by-step explanation:

Slope intercept equation:

y2 - y1 / x2 - x1 = slope

Answer:

Step-by-step explanation:

The value of the quadratic equation is given by the formula. Then the value of x is 0.8968 and negative 2.23.

It is the method to separate the polynomial into parts and the parts will be in multiplication. And the value of the polynomial at this point will be zero.

The equation for the expression is given below.

3x² + 4x = 6

3x² + 4x - 6 = 0

we know that the formula

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

Then we have

[tex]x = \dfrac{-4 \pm \sqrt{4^2-4*4*(-6)}}{2*3}\\\\x = \dfrac{-4 \pm \sqrt{112}}{6}\\\\x = 0.8968, \ -2.23[/tex]

More about the factorization link is given below.

https://brainly.com/question/6810544

The length of the segment AB is the number of units on AB, and the length of segment AB is 14.4 units

The points are given as:

A = (-1,7)

B = (11,-1)

The length of the segment is then calculated using:

AB = √(x₁ - x₂)² + (y₁ - y₂)²

So, we have:

AB = √(-1 - 11)² + (7 + 1)²

Evaluate the exponent

AB = √144 + 64

Evaluate the sum

AB = √208

Evaluate the exponent

AB = 14.4

Hence, the length of segment AB is 14.4 units

Read more about length at:

https://brainly.com/question/2217700

#SPJ1

Answer:

a₄ = 75

Step-by-step explanation:

using the recursive formula and a₁ = 5 , then

a₂ = 2a₁ + 5 = 2(5) + 5 = 10 + 5 = 15

a₃ = 2a₂ + 5 = 2(15) + 5 = 30 + 5 = 35

a₄ = 2a₃ + 5 = 2(35) + 5 = 70 + 5 = 75

Answer:

[tex]a_4=75[/tex]

Step-by-step explanation:

Given:

[tex]\implies a_2=2(a_1)+5=2(5)+5=15[/tex]

[tex]\implies a_3=2(a_2)+5=2(15)+5=35[/tex]

[tex]\implies a_4=2(a_3)+5=2(35)+5=75[/tex]

Answer:

[tex]\bf Area= 90\;in[/tex]

Step-by-step explanation:

Area of ABCD = L * W

[tex]\bf 6\times 12[/tex]

[tex]\bf 72 \;in^2[/tex]

Area of EFGC:- L * W

[tex]\bf 6 \times 3[/tex]

[tex]\bf 18\; in^2[/tex]

Now, the area of the combind rectangles:-

ABCD + EFGC

[tex]\bf 72+18[/tex]

[tex]\boxed{\bf 90\; in}[/tex]

The value of logarithm expression 2log₅(5x³) + (1/3)log₅(x² + 6) is simplified as log₅[{25x⁶}{∛(x² + 6)}].

Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.

The logarithmic expression is given as

[tex]2\log _55x^3 + \dfrac{1}{3} \log _5(x^2 +6)[/tex]

We know that formulas

[tex]a \log b = \log b^a\\\\\log a + \log b = \log ab[/tex]

Then we have

[tex]\rightarrow \log _5(5x^3)^2 + \log _5(x^2 +6)^{1/3}\\\\\rightarrow \log _525x^6 + \log _5\sqrt[3]{(x^2 +6)}\\\\\rightarrow \log _5 25x^6 (\sqrt[3]{(x^2 +6)})[/tex]

More about the logarithm link is given below.

https://brainly.com/question/7302008

Answer:

D) As the amount of nutrients in the soil increases, the rate of plant growth increases.

Step-by-step explanation:

When there is more nutrients in the soil it makes the plant healthier and grow more. Also all of the other ones have no correlation to eachother or effect on another.

Answer:

80+40x

Step-by-step explanation:

-5x2(2x2-4x-12)

-10(2x2-4x-12)

-20-20+40x+120

-40+120+40x

80+40x

Answer:

a= 1/b-c

Step-by-step explanation:

Answer:

21sqrt(6)

Step-by-step explanation:

Hope it helps......

Answer:

12a −24b −4

Step-by-step explanation:

Answer:

i think its between 2-5

Step-by-step explanation:

Answer:

that would be -3 becuase it's the least negative out of all the choices

Step-by-step explanation:

Answer:

Step-by-step explanation:

In Isosceles triangle base angles (angles oppoiste to equal sides) are congruent.

x + x + 98 = 180 {Angle sum proeprty of triangle}

   2x + 98 = 180   {Subtract 98 from both sides}

        2x = 180 - 98

       2x  = 82      {Divide both sides by 2}

        x   = 82/2

x = 41

Answer:

x = 41°

Step-by-step explanation:

An isosceles triangle has 2 opposite sides equal.

Therefore the angle opposite x is also x

Hence:

x + x + 98° = 180° (angles in a triangle add up to 180°)

2x + 98° = 180°

2x = 180° - 98°

2x = 82°

2x/2 = 82°/2

x = 41°

The statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.

A number line is drawn with numbers equally spaced or sections running the length of it.

A number line should be drawn horizontally and can be extended in any direction indefinitely.

The number line shows the number of crackers lies between 7 and 13. Which is numerically as 7,8,9,10,11,12,13.The number of the digit on the number line skewed is 7.

Hence statement must be true according to the box plot if the data is skewed, and the lowest number of crackers in a package was 7. Option C is correct.

To learn more about the number line refer to the link;

https://brainly.com/question/13189025

Answer:

the answer is C

Step-by-step explanation:

Because im js swag

Answer:

x≈3.35, or the square root of 11.

Step-by-step explanation:

Use the pythagorian therom. 3²+1.5²=x²

(Half of 3 is 1.5 and the line splits it in half)

Answer:

Step-by-step explanation:

A cube has 6 faces. Area of one face is 4x². To find the total suface area of cube, multiply 4x² by 6

Area of cube = 6 * 4x²

                      = 24x²