A ball is dropped from a treetop 256 feet above the ground. How long does it take to hit the ground? (s = 16t2)
4 seconds
8 seconds
16 seconds

Answer:

a) -22, b)14 c) -3

Step-by-step explanation:

a) -19+3(-13+4*3)

= -19+3*(-13+12)

= -19+3*(-1)

= -22

b) | -7(2)|

= | -7*2|

= -14

c) 15-3 | -4-2|

= 15-3* (-6)

= 15-18

= -3

Easy way to do this, divide 24 with 3, you will get 8. That means 8 is 1/3 of 24. To get 2/3 you just add 8+8 which equals to 16

Answer:

36

Step-by-step explanation:

Any number on top, like 6^2 is multiply the number by itself accordingly to the number on top. For example, if it is 6 to the 4th, then you multiply 6 by itself 4 times, and you will get 1296. Squaring is a number multiplying to itself according to the exponet.

Answer:

14.4 units

Step-by-step explanation:

In Trigonometry

\(\cos \theta =\frac{Adjacent}{Hypotenuse}\\\)

In Triangle DEF,

\(\cos F =\dfrac{EF}{DF}\\\cos 26^\circ =\dfrac{EF}{16}\\EF=16 \times \cos 26^\circ\\=14.4$ units (correct to the nearest tenth).\)

Answer:

60°

Step-by-step explanation:

The triangle ABC is a equilateral triangle with all side lengths measures equal to each other so the angle measures would be same and equal as well

Answer:

change your pfp and ill give u the answer

Step-by-step explanation:

Answer:

x = 17.5 degrees

Step-by-step explanation:

So with this, it gives you the angle measure and the terms for that angle measure for Angle EDC. Since these are equal, set them equal to each other.

2x+10 = 45

Move over the 10

2x = 35

Divide by 2

x = 17.5 degrees

That's all.

Answer:

7

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

\(ax^{2} + bx + c, a\neq0\).

This polynomial has roots \(x_{1}, x_{2}\) such that \(ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})\), given by the following formulas:

\(x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}\)

\(x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}\)

\(\Delta = b^{2} - 4ac\)

In this question:

The height of the rock after t seconds is given by the following equation:

\(H(t) = -16t^2 + 96t + 112\)

How long will it take in seconds for the rock to hit the ocean?

This is t for which:

\(H(t) = 0\)

So

\(-16t^2 + 96t + 112 = 0\)

Simplifying by -16

\(t^2 - 6t - 7 = 0\)

So a quadratic equation with \(a = 1, b = -6, c = -7\)

\(\Delta = b^{2} - 4ac = (-6)^2 - 4*1*(-7) = 36 + 28 = 64\)

\(t_{1} = \frac{-(-6) + \sqrt{64}}{2*1} = 7\)

\(t_{2} = \frac{-(-6) - \sqrt{64}}{2*1} = -1\)

Since time is a positive measure, it will take 6 seconds for the rock to hit the ocean, and the answer is 7.

Answer:

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

  h + s = 88

  h - s = 54

Subtracting the second equation from the first gives ...

  (h +s) -(h -s) = (88) -(54)

  2s = 34 . . . . . simplify

  s = 17 . . . . . . . divide by 2

  h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

5(y-2)

Step-by-step explanation:

(look at screenshot)

The solution of the expression (y⁴ - 16) /(y + 2) ÷ (y² + 4) / 5 will be;

⇒  5 (y - 2)

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (y⁴ - 16) /(y + 2) ÷ (y² + 4) / 5

Now,

Solve the expression as;

⇒ (y⁴ - 16) /(y + 2) ÷ (y² + 4) / 5

⇒((y²)² - 4²) /(y + 2) ÷ (y² + 4) / 5

Since, we know that;

⇒ a² - b² = (a - b) (a + b)

So, We get;

⇒ (y² - 4) (y² + 4)/(y + 2) ÷ (y² + 4) / 5

⇒ (y² - 4) (y² + 4)/(y + 2) × 5 / (y² + 4)

⇒ (y² - 4) /(y + 2) × 5

⇒ 5 (y² - 4) /(y + 2)

⇒ 5 (y - 2) (y + 2)/(y + 2)

⇒  5 (y - 2)

Thus, The solution of the expression (y⁴ - 16) /(y + 2) ÷ (y² + 4) / 5 will be;

⇒  5 (y - 2)

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Answer:

a = 4

b = 5

c =6

Step-by-step explanation:

i hope it helps

the answers are absolutely correct

Answer:

0.55x10= 5.50

Step-by-step explanation:

Answer:

were fired up

Step-by-step explanation:

The exponential function that passes through the point (-1, 1/7) for the given interval is f(x) =  7ˣ.

To find the exponential function that passes through the points (-1, 1/7), we can use the general form of an exponential function, which is:

f(x) = aˣ

where;

First, we can use the given point (-1, 1/7) to find the value of "a". Substituting these values into the equation, we get:

1/7 = a⁻¹

To solve for "a", we can take the reciprocal of both sides of the equation and simplify:

7 = a

Now that we have found the value of "a", we can substitute it into the general form of the exponential function to get the specific function for this interval:

f(x) = 7ˣ

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The complete question is below:

(-1, 1 / 7)

Find the exponential function f(x) = aˣ of this interval.

f(x) =

Since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

Similar triangles are triangles with corresponding sides that have the same ratio.

Thus:

AD is parallel to BC (bases of a trapezoid are parallel)

Therefore:

∠ACB = ∠CAD (alternate interior angles)

This implies that, ΔABC ~ ΔACD by AA similarity theorem.

Thus:

AC/DA = CB/AC

Substitute

AC² = 12 × 27

AC = √324

AC = 18 m

Therefore, since ΔABC and ΔACD are similar triangles, therefore the length of AC is 18 m.

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Answer:

-6 +8d -2c

Step-by-step explanation:

\(\frac{-2}{5} (15 -20d +5c) = \frac{-2}{5} \times 15 - \frac{-2}{5}\times20d +\frac{-2}{5}\times5c = -6 + 8d -2c\)

Step-by-step explanation:

Hello,

I hope you mean to cancel the common factor that exists in numerator and denominator,right.

so, Let's look for the common factor,

here, the expression is,

=4(x-2)/ (x+5)(x-2)

so, here we find the common factor is (x-2)

now, we have to cancel it. And after cancelling we get,

=4/(x+5)

Note:{ we cancel the common factor if the common factors are in multiply form.}

Hope it helps

Answer:

ss

Step-by-step explanation:

s

A set of two or more linear equations involving the same set of variables make up a linear system of equations, which is the type of system of equations in question.

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Answer:

(x-3)^2+(y-4)^2=6^2

Step-by-step explanation:

(x-3)^2+(y-4)^2=6^2

The sοlutiοn οf the given prοblem οf unitary methοd cοmes οut tο be  fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

The well-knοwn straightfοrward apprοach, actual variables, and any relevant infοrmatiοn frοm the initial and specialist questiοns can all be used tο finish the assignment. Custοmers may be given anοther chance tο try the gοοds in respοnse. If nοt, significant expressiοn in οur understanding οf prοgrams will be lοst.

Here,

We must figure οut hοw many pairs οf sunglasses must be sοld tο cοver the fixed and variable cοsts in οrder tο reach the break-even pοint.

Assume that X sunglasses must be sοld tο break even.

Fixed cοst plus variable cοst equals tοtal cοst.

Selling price x Number οf units sοld equals tοtal revenue.

The tοtal revenue and entire expense are equal at the break-even pοint.

Thus, we can cοnstruct the equatiοn:

Fixed cοst plus variable cοst multiplied by the selling price equals the quantity sοld.

=>  $9.44 X = $748,374 + $2.19 X

=>  $9.44 X - $2.19 X = $748,374

=>  $7.25 X = $748,374

=>  X = $748,374 / $7.25

=>   X = 103,184

Therefοre, fοr Met Manufacturing tο turn a prοfit, 103,184 sunglasses must be sοld.

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Answer:

Step-by-step explanation:

A)   We can find half of the width of the surface by applying pythagorean theorem on the right angled triangle formed by three points which are the center of the circle, the point on the circle where the the endpoints of the width and the radius meet, and the midpoint of the width.

let radius=r, width=w

\(r^2=(w/2)^2+(3.4-2.1)^2\\\), since the distance between the origin and the midpoint of the width is 3.4m-2.1m.

\(-(w/2)^2=(3.4-2.1)^2-r^2, r=2.1\\-(w/2)^2=(1.3)^2-(2.1)^2\\-(w/2)^2=1.69-4.41\\-(w/2)^2=-2.72\\w/2=\sqrt{2.72}\\w=2*\sqrt{2.72}\\w=3.3 meter\)

B) we can find the other depth of oil which can give the same surface area of oil if the now empty part of the cylinder is filled with oil and the now filled part of the cylinder is empty, so the other possible depth for the same surface area of oil is the diameter of the circle minus 3.4 meters:

diameter=4.2 meter, 4.2 meter-3.4 meter:

0.8 meter depth

a. The width (x) of the oil surface is approximately 5.348 meters.

b. Another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.

a) Here, we have to calculate the width (x) of the oil surface, we need to find the length of the chord of the circular cross-section at the top of the oil tank.

We can use the formula for the length of a chord in a circle when the depth and radius are known.

Given that the radius (r) of the circular cross-section is 2.1 meters and the depth (d) of the oil is 3.4 meters, the width (x) can be calculated as follows:

x = 2 * √(r * d)

x = 2 * √(2.1 * 3.4)

x = 2 * √(7.14)

x ≈ 2 * 2.674

x ≈ 5.348 meters

So, the width (x) of the oil surface is approximately 5.348 meters.

b) Now, let's find the other depth of oil that would give the same surface width (x = 5.348 meters).

We can rearrange the formula to solve for the depth (d):

x = 2 * √(r * d)

Divide both sides by 2:

x/2 = √(r * d)

Square both sides:

(x/2)² = r * d

Now, plug in the given values (x = 5.348 meters and r = 2.1 meters) and solve for d:

(5.348/2)² = 2.1 * d

2.674² = 2.1 * d

7.145076 = 2.1 * d

Divide by 2.1:

d ≈ 7.145076 / 2.1

d ≈ 3.402417

So, another depth of oil that would give the same surface width (x ≈ 5.348 meters) is approximately 3.402417 meters.

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do 180-32=148 and then do 148÷2=74

Answer:

$2971.9

Step-by-step explanation:

2000*(1+2%)^20 = 2971.895

The tax amount is $16.48 and the tax rate is 16.8%

If the tax rate is an increase of an X percent, and x is the decimal form of that percentage, then the factor by wich a price increases is (1 + x)

Here we know that the cost of theitem is $98 and the selling price (after the the tax is applied, is $111.48

Then we can write:

111.48 = 98*(1 + x)

Solving that for x we will get:

111.48/98 - 1 = x = 0.168

Writting that as a percentage we get:

0.168*100% = 16.8%

And the value of the tax alone is given by the difference between the two prices:

$114.48 - $98 = $16.48

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Answer:

0

Step-by-step explanation:

1. Substitute the values in: \(2^0 - (-1)^2\)

2. Evaluate the expression:  \(2^0 = 1\), \((-1)^2 = 1\), which means that 1 - 1 is 0

Therefore, 0 is the answer.

The sentence that contains filler is: D. This set also includes heroes like Obi-Wan Kenobi and Anakin Skywalker, both of whom come fully-equipped with their signature lightsabers and Jedi robes. Option D

In this sentence, the phrase "also includes heroes like Obi-Wan Kenobi and Anakin Skywalker" acts as a filler. The main purpose of this phrase is to provide additional information about the set and highlight the inclusion of popular characters from the Star Wars franchise. It doesn't directly contribute to the core information about the set's features or components.

The other sentences (A, B, and C) provide specific details and descriptions about the LEGO set, such as the number of pieces, minifigures, droids, and features like the opening top hatch and cockpit. They directly convey important information about the set itself without any filler or additional unnecessary information.

In marketing or promotional contexts, fillers are often used to enhance the appeal of a product or create excitement by mentioning well-known or desirable elements that may not be directly relevant to the core features. The filler in sentence D serves to attract fans of Obi-Wan Kenobi and Anakin Skywalker by emphasizing their presence in the set and the inclusion of their iconic weapons and attire.

Option D

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Answer:D

Step-by-step explanation: