The height of an object that is dropped from the top of a tower is given by the expression −16t2 + 441, where t is the time in seconds.
(a) Factor this expression.

(b) Use a spreadsheet to determine how many seconds it takes the object to fall to a height of 377 feet. (Use 0.5-second intervals for t.)
t = BLANK sec

i need this fast

Answer:

i guess it might be x=7

Step-by-step explanation:

Answer:

1 , 2

Step-by-step explanation:

y = 2x --------------(I)

5x + y = 7 ------------(II)

Substitute y = 2x in equation (II)

5x + 2x = 7

7x = 7

Divide both sides by 7

x = 7/7

x = 1

Plugin x = 1 in (II)

y = 2*1

y = 2

Answer:

276.1875

Step-by-step explanation:

make me brainliest

Answer:

276

Step-by-step explanation:

jJHgplugouogoufuofogugup

Answer:

The derivative of f(x,y)=x2 y2 in the direction of the unit tangent vector of the curve r(t)=(cos t t sin t)i (sin t−t cos t)j, t>0 is 2x^2+2y^2

The area of the figure is 39ft²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles.

Area of a rectangle is expressed as ;

A = l × w

where l is the length and w is the width.

Dividing the shape into two;

The area of shape 1 = l× w

= 3× 7 = 21ft²

The area of shape 2 = l× w

= 6 × 3 = 18 ft²

therefore the total area = 21+18 = 39 ft²

therefore the area of the figure is 39ft²

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There are 70 ways to split 8 people into two teams of 4. There are 1680 ways to split 9 people into 3 teams of 3. There are 945 ways to choose 2 teams of 4 from 10 prospects.

To find the number of ways to split 8 people into two teams of 4, we can first choose the first team in $\binom{8}{4} = 70$ ways, and the second team will be the remaining 4 people.

To split 9 people into 3 teams of 3, we can first choose the first team in $\binom{9}{3} = 84$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{3} = 20$ ways. The final team will be the remaining 3 people.

To choose 2 teams of 4 from 10 prospects, we can first choose the first team in $\binom{10}{4} = 210$ ways. After this, we are left with 6 people, from which we choose the second team in $\binom{6}{4} = 15$ ways. However, since the order in which we choose the two teams does not matter, we must divide by 2 to get the final answer of $\frac{210 \cdot 15}{2} = 945$.

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Answer:

it can mean anything.... be more specific with your question

Step-by-step explanation:

Answer:

E

Step-by-step explanation:

NO

Answer:

if EG || HJ,

m GFD = 130°

Step-by-step explanation:

Because, m EFI = m GFD

( vertical opposite angles )

so, m GFD = 130°

The angle sum or difference identity can be used to find the exact value of the expression `cos 7π/12`.The exact value of `cos 7π/12` is `(1 + √3√2) / 2`.  

Identity cos (A + B) = cos A cos B - sin A sin B

Cos (A - B) = cos A cos B + sin A sin B

Let us use the identity `cos (A - B) = cos A cos B + sin A sin B

To get an expression of `cos 7π/12` that we can calculate.

7π/12 = π/3 + π/4`

cos 7π/12 = cos (π/3 + π/4)

cos 7π/12 = cos (3π/12 + 4π/12)

cos 7π/12 = cos (π/4) × cos (3π/12) + sin (π/4) × sin (3π/12)

cos 7π/12 = (1/√2) × (1/2) + (1/√2) × (√3/2)

cos 7π/12 = 1/2√2 + √3/2√2

Multiplying both numerator and denominator by

√2√2(cos 7π/12) = (1 + √3√2) / 2

∴ The exact value of `cos 7π/12` is `(1 + √3√2) / 2`.

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Answer:

????

Step-by-step explanation:

Answer:

where's the shape

Step-by-step explanation:

what's the length and width, maybe I can help

Answer:

4

Step-by-step explanation:

The coordinates of the y-intercept of the line is (0, 17)

Defining y-intercept before working out the coordinates for the equation. The y-intercept is the point where the line will intersect the y-axis on graph. Since the line intersects at y-axis, there will be no x-axis coordinate.

Hence, for calculation, the value of x will be zero. Keeping the value to find y-intercept.

y = 3×0 + 17

Performing multiplication on Right Hand Side

y = 0 + 17

Performing addition on Right Hand Side

y = 17

So, the coordinates are (0, 17).

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Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

A parabola has the form:

y = a*x^2 + b*x + c

Where a is the leading coefficient.

If a is positive, the parabola opens up.

If a is negative, the parabola opens down.

a is the factor that multiplies the part that grows the fastest in the equation, thus, if a is a larger value (in absolute value) then the parabola will grow faster (then the parabola will be narrow)

if a is smaller (again, in absolute value) the parabola will grow slower, then the parabola will be wider.

With this, we can conclude that:

a = -4

is the largest value of a in absolute value.

Then this corresponds to the thinner parabola (the one at the left)

a = -1

Is the middle value of a, then this corresponds to the graph of the middle

a = -0.25

Is the smallest absolute value of a, then this one corresponds to the widest graph (the first one at the left)

Answer:

well figure it out

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

the are is pi times radius times radius

so do the square root of 25, which is 5.

this means that the radius is 5

Answer:

five (5).

Step-by-step explanation:

Area of circle =pi r^2

given that area is 25pi

now equate both .....we get

25pi=pi r^2

25=r^2

r=5

Answer:

It will take 51 days for the flowering plant to be 2 feet tall.

Step-by-step explanation:

Lets say d are the Days. Lets make an equation. 2 feet is 24 inches.

11.25 + 0.25d = 24

-11.25                 -11.25

0.25d = 12.75

0.25    0.25

d = 51

Prime numbers from 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97. Composite Number from 1 to 100 are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, and 99.

It's important to note that 1 is not considered to be a prime number, it is considered a unit.

Prime numbers are considered to be the "building blocks" of numbers and are of particular interest to mathematicians, as they have many unique properties and uses. They are used in many areas of mathematics, such as number theory and cryptography, and are also used in many fields of science and engineering.

In conclusion, prime numbers are numbers that are divisible by only 1 and themselves, while composite numbers are numbers that can be divided by other numbers besides just 1 and themselves. From 1 to 100, there are 25 prime numbers and 75 composite numbers.

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The percentage change in multifactor productivity is approximately 36.15%.

To calculate the percentage change in multifactor productivity, we need to compare the productivity before and after the improvement in the production process. The multifactor productivity is calculated by dividing the output value by the input value.

Given data for the old process:

Number of workers: 11

Output per hour: 4,873 units

Materials cost per unit: $56

Worker wage per hour: $17

Selling price per unit: $102

Given data for the improved process:

Materials cost reduction per unit: $14

Workers reduced: 3

Let's calculate the multifactor productivity before and after the improvement:

Before the improvement:

Output value = Output per hour * Selling price per unit = 4,873 * $102 = $497,046

Input value = (Number of workers * Worker wage per hour) + (Materials cost per unit * Output per hour) = (11 * $17) + ($56 * 4,873) = $5,661 + $272,488 = $278,149

Multifactor productivity before = Output value / Input value = $497,046 / $278,149 ≈ 1.785

After the improvement:

Output value remains the same = $497,046

Input value = [(Number of workers - Workers reduced) * Worker wage per hour] + [(Materials cost per unit - Materials cost reduction per unit) * Output per hour]

= [(11 - 3) * $17] + ($42 * 4,873) = $119 + $204,666 = $204,785

Multifactor productivity after = Output value / Input value = $497,046 / $204,785 ≈ 2.43

Now, let's calculate the percentage change in multifactor productivity:

Percentage change = ((Multifactor productivity after - Multifactor productivity before) / Multifactor productivity before) * 100

= ((2.43 - 1.785) / 1.785) * 100

= (0.645 / 1.785) * 100

≈ 36.15

Therefore, Multifactor productivity has changed by about 36.15 percent.

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The weight of the Avery's lunch box using given weights is equal to 0.92 pounds (rounded to two decimal places).

Total weight of the backpack= 2 2/3 pounds

                                                = 8/3 pounds

The weight of the each book =7/8 pounds.

Let x be the weight of the lunch box in pounds.

An equation that represents the total weight in Avery's backpack,

2(7/8) + x = 8/3

To solve for x, simplify and solve for x,

⇒14/8 + x = 8/3

Multiplying both sides by 24 the least common multiple of 8 and 3 to clear the fractions,

⇒42 + 24x = 64

Subtracting 42 from both sides,

⇒24x = 22

Dividing both sides by 24,

⇒x = 22/24

Simplifying the fraction,

⇒x = 11/12

     =  0.92 pounds (rounded to two decimal places).

Therefore, the  weight of the lunch box is equal to 0.92 pounds (rounded to two decimal places).

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Analyn and John ate a total of 1/8 + 3/8 = 4/8 = 1/2 of the bibingka. So they ate half of the bibingka, or in other words, they ate 50% of the bibingka.

Analyn sliced the bibingka into 8 equal pieces. She ate 1/8 of the bibingka, which means that there are 7/8 left. John ate 3/8 of the remaining bibingka, which means that there are 4/8 or 1/2 of the bibingka left after they both ate. Therefore, the total amount of bibingka that they ate is 1/2 of the whole bibingka.

In terms of percentage, 1/2 can be written as 50%, so they ate 50% of the bibingka.

In this scenario, Analyn sliced the bibingka into 8 equal pieces. She ate 1/8 of the bibingka, which means she ate one of the eight equal pieces. John ate 3/8 of the bibingka, which means he ate three of the eight equal pieces.

To find the total part of the bibingka they ate together, we can add the fractions 1/8 and 3/8. After adding these fractions, we get:

1/8 + 3/8 = 4/8

Simplifying the fraction 4/8, we get:

4/8 = 1/2

Therefore, Analyn and John ate 1/2 of the bibingka together, which means they ate 4 of the 8 equal pieces.

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(A) The equation for the population p in terms of time t in minutes is:

                  \(P = 250 * 3^{t/16}\)

(B) The population after one hour is 267.5

According to the Question,

Given that,

(B) Tyrell is working in a lab testing bacteria populations. After starting out with a population of 250 bacteria, he observes the change in population and notices that the population triples every 15 minutes.

Therefore, the equation for the population P in terms of time t in minutes is

   \(P = 250 * 3^{t/16}\)

(B) The population after one hour.

   \(P = 250 * 3^{t/16}\\P = 250* 3^{1/16} \\P = 250*3^{0.0625}\)    P

Or, P = 250 × 1.07

Or, P = 267.5

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Answer:

n × 2

Step-by-step explanation:

Or 2n

a. The fraction of the cup of juice that remained in the jug is 0

b. the total amount of juice in the 3 glasses is 1 cup of juice

c. The total amount of juice in the four glasses is 2 cups of juice

d. no juice was left in the jug after the 4 glasses have been poured

The total amount of juice is deduced from the problem to be 2 cups of juice

Total amount of juice poured out

= 1 cup was shared among three glasses + 1cup of juice in the fourth glass

= 1 cup + 1cup

= 2 cups of juice hence nothing is left in the jug

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