the difference of 5.189 and 2.94

The time taken by the rock to reach the lake below is 5.123 sec

t= 5.123 sec

A quadratic equation is an algebraic expression of the second degree in x. The quadratic equation in its standard form is [tex]ax^{2} +bx+c=0[/tex] where a, b are the coefficients, x is the variable, and c is the constant term.

It is given that,

H= [tex]-16t^{2} +32t+256[/tex], which represent the height of the rock

Also, we have given that the height of the cliff is 256 feet.

Now to find the time taken by the rock, take H=0

[tex]-16t^{2} +32t+256[/tex]=0

[tex]-16(t^{2} -2t-16) = 0[/tex]

[tex]t^{2} -2t-16 = 0[/tex]

[tex]t= \frac{-(b)\pm\sqrt{(b)^{2}- 4 *a*c } )}{2*a}[/tex]

From above equation, a=1, b=-2, c=-16

So,

[tex]t= \frac{-(-2)\pm\sqrt{(-2)^{2}- 4 *1*(-16) } )}{2*1}[/tex]

[tex]t= \frac{2\pm\sqrt{(4+64 } )}{2}[/tex]

[tex]t= \frac{2\pm\sqrt{(68 } )}{2}[/tex]

There will be two value one with positive [tex]t= -2+\sqrt{(68 } )[/tex] and another with negative [tex]t= -2-\sqrt{(68 } )[/tex]

We will neglect negative value because time can't be negative.

[tex]t= \frac{2+\sqrt{(68 } )}{2}[/tex]

[tex]t= \frac{2+8.246}{2}[/tex]

[tex]t= \frac{10.246}{2}[/tex]

t= 5.123 sec

The time taken by the rock to reach the lake below is t= 5.123 sec

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Answer:

4•(7^4)

Step-by-step explanation:

You would first do 7^4, and get 2401.

You would then multiply 2401 by 4, and get 9604.

Hope this helps! Added steps to solve it just in case :)

Answer:

[tex]4*7^{4}[/tex]

Step-by-step explanation:

The Exponential Notation is:

"A method of simplifying the writing and handling of very large or very small numbers."

The word "Exponential" comes from the word "Exponent"

So we have 1 four and 4 sevens and they are all being multiplied by each other.

Our operation: Multiplication

Our first number in the equation: 4

Our second number in the equation: 7 to the fourth power or [tex]7^{4}[/tex]

Our final answer: [tex]4*7^{4}[/tex]

I hope this helps!

Have a great day! :)

Answer:

39.74 %

Step-by-step explanation:

12 years - 11.5  = .5 years

.5 / 1.9 = .2631 S.D   above the mean

  From z-score table this corresponds to .6026

          60.26 are BELOW this life span

             39.74 % are above 12 years

Answer:

12.25.

Step-by-step explanation:

1) the formula of the volume given in the condition is:

V=2*2/7*10x.

2) If V=70, then

2*2/7*10x=70, where x=12.25.

Answer:

(10x)(7/4)(2)=70

=10x=70/7/4/2

=10x=20

x=2

Answer: 2

Step-by-step explanation:

Answer:

x=7 and y=3

Step-by-step explanation:

Step: Solve x−3y=−2 for x:

x−3y=−2

x−3y+3y=−2+3y(Add 3y to both sides)

x=3y−2

Step: Substitute3y−2for x in x+3y=16:

x+3y=16

3y−2+3y=16

6y−2=16(Simplify both sides of the equation)

6y−2+2=16+2(Add 2 to both sides)

6y=18

6y

6

=

18

6

(Divide both sides by 6)

y=3

Step: Substitute3foryinx=3y−2:

x=3y−2

x=(3)(3)−2

x=7(Simplify both sides of the equation)

Answer:

x=7 and y=3

Answer:

Step-by-step explanation:

2x = 14

x = 7

7 + 3y = 16

3y = 9

y = 3

(7, 3)

answer is A

The line graph (C) represents the data representation on the line plot option (C) is correct.

A line graph is a graph made up of segments of straight lines that connect the depicted data points.

We have data shown in the table:

The data set value 11 repeated two times, so two dots we will see on the line plot.

The data set value 11(1/2) repeated one time, so one dot we will see on the line plot.

The data set value 11(3/4) repeated two times, so two dots we will see on the line plot.

The data set value 12 repeated two times, so two dots we will see on the line plot.

Similarly, we can check for others.

Thus, the line graph (C) represents the data representation on the line plot option (C) is correct.

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Answer:

  256.10

Step-by-step explanation:

You want the original price given the total amount is 307.32 and the tip rate is 20%.

Adding a tip multiplies the original price by (1 +tip rate). We can divide the total amount by this factor to find the original price:

  307.32/(1+0.20) = 256.10

The original price was 256.10.

<95141404393>

Isolating the absolute value term, we find

|x| + 5 ≤ 1   ⇒   |x| ≤ -4

However, the absolute value function maps every number x to a non-negative number, so |x| ≤ -4 is impossible and there is no solution to the inequality.

Answer:

1548 unit^2

Step-by-step explanation:

The area each of the 2 bases

= width * height

=  17 * 12

= 204 unit^2

2 have area 408 unit^2

Area of the lateral rectangles = 2 * 13 * 19 = 494 unit^2

Area of the top and bottom  rectangles = 2 * 17 * 19 = 646 unit^2

Total surface area = 408 + 494 + 646

= 1548 unit^2.

To solve this problem, we have to write out the simple harmonic motion equation and then use the respective formula to solve. The maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

The given equation of the simple harmonic motion is

[tex]x = 3.5sin(\frac{\pi}{2t} + \frac{5\pi}{4})\\[/tex]

Data;

Solving this

[tex]\frac{dx}{dt} = \theta = -3.5 * \frac{\pi}{2} cos (\frac{\pi }{2}t + \frac{5\pi}{4})\\[/tex]

Let's calculate the maximum velocity.

[tex]V_m = \frac{3.5\pi}{2}[/tex]

This is only possible when cos θ = -1

The maximum kinetic energy is

[tex]K_m = \frac{1}{2}mv_m^2 = \frac{1}{2}* \frac{500}{1000} * (\frac{7\pi}{4} )^2\\K_m = 7.56J[/tex]

The maximum kinetic energy is 7.56J

The maximum potential energy can be calculated as

[tex]\omega^2 = \frac{k}{m} \\k = \omega^2 m \\k = \frac{\pi^2}{4} * \frac{500}{1000}\\ k= 1.254 N/m[/tex]

Using the value of spring constant, we can find the maximum potential energy

[tex]P.E = \frac{1}{2}kx^2\\P.E = \frac{1}{2} * 1.234 * 3.5^2\\P.E = 7.56J[/tex]

The maximum potential energy is 7.56J

The maximum mechanical energy is equal to the sum of maximum potential energy and the maximum kinetic energy.

[tex]ME = P.E + K.E\\ME = 7.56J[/tex]

The reason ME is equal to 7.56J is because when x is at maximum, v = 0 and makes kinetic energy equal to zero.

ME = 7.56J

From the calculations above, the maximum kinetic energy, maximum potential energy and the maximum mechanical energy is equal to 7.56J.

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Pull terms out from under the radical, assuming positive real numbers.

56

Have a good one :)

A circular cake pan that measures 8 inches across and 2 inches high. thus, the volume of a circular cake pan is 100.84 cubic inches.

The volume of the circular shape can be calculated as the product of the area and the height.

Given; a circular cake pan that measures 8 inches across and 2 inches high.

The radius will be 4.

The area of the circle = [tex]\pi r^{2}[/tex]

[tex]\pi \times 4^2\\\\3.14\times 16\\\\50.24[/tex]

The volume of a circular cake pan = area x height

                                                     [tex]50.24 \times 2\\ \\100.48[/tex]

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Answer:

Area = 1

Step-by-step explanation:

I;ve attached my work below

Hope it helps, Let me know if you have any questions/concerns !

Have a nice rest of your day :)

Answer:

tobe specific, it is 53.33%, but if you want just a whole #, it is 53%

Answer:

53.33%

Step-by-step explanation:

or 53% if rounded to the nearest whole

Answer:

Give performance an unfair advantage

Answer:

interferances of the blood preser

Step-by-step explanation:

I can only solve no.2

Step-by-step explanation:

CAB=ABC(ISCOSCELES TRIANGLE)

SO REPRESENT THEM BY X BECAUSE YOU DON'T KNOW THEM

THEIR SUM =180

SO,CAB+ABC+ACB=180

SUBSTITUTE THEIR VALUES

X+X+120=180

2X+120=180

2X=180-120

2X=60

[tex] \frac{2x}{2x} = \frac{60}{2 } [/tex]

cancel

so x is 30 degrees

Trust me

Answer:

Step-by-step explanation:

25 + 14 / (5-3)

25 + 14 / 2

25 + 7

32

Answer: Mean - 93.8571428571, round however you need to

Median - 75

Mode - 65

Range - 205

Step-by-step explanation: Order the numbers first. 45,65,65,75,77,80,250.

Find the mean. 45 + 65 + 65 + 75 + 77 + 80 + 250 is 657. Divide by 7 is 93.8571428571.

Median is middle. It is 75.

Mode is the most common. - 65

Range is the highest subtracted by the lowest. 250 - 45 is 205.

Answer:

Step-by-step explanation:

This question is based on the of expression. Therefore, the correct option is (A) that is, .

Given:

Expression :

We have to determined the expression is equivalent to the given expression.

According to the question,

It is given, to be assume that denominator does not equal zero.

Now by given expression, i.e.

Now, divide denominator by numerator we get,

Therefore, the correct option is (A) that is,

The measurements that would work for the box is 10cm for the length, 15cm for the width and 5cm for the height.

The candy box has the shape of a rectangular prism. A rectangular prism is a is a three-dimensional shape with six faces, twelve sides and six verticies.

Volume = length x width x height

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Answer: 2 and 4

Step-by-step explanation: They both have 3 x's

Answer:

Okay the mode means the most repeating number.

So if you write this all out:

1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4

You can now see that 3 is the most repeating number.

So 3 is the mode.

Step-by-step explanation:

Hope this helps!

From your neighborhood softie :)

Answer:

[tex]x=\sqrt{15,} -5[/tex]

Step-by-step explanation:

Answer:

140kilo in 1hr and 280kilo in 2hr and 420kilo in 3hr and 28kilo in 20 min.

Answer:

45,40,35,30,25,20,15...

Step-by-step explanation:

The common difference equals:

-5

The sum of the sequence equals:

150

The explicit formula of this sequence is:

a_n=45+(n-1)*(-5)

The recursive formula of this sequence is:

a_n=a_((n-1))-5

The nth terms:

45,40,35,30,25,20,15...

Hope this helps

Give brainliest :)

Considering the parabolic equation, the equation for the directrix is given by x = 4.9375.

The equation of a horizontal quadratic function, of vertex (h,k), is given by:

(y - k)^2 = 4p(x - h)

The directrix is given by:

x = h - p.

In this problem, the equation is given by:

(y - 2)² = 0.25(x - 5).

Hence h = 5, p = 0.25/4 = 0.0625, hence the directrix is:

x = h - p = 5 - 0.0625 = 4.9375.

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