A skydiver is planning her jump out of an airplane. Typically, she will jump at a height
of 13,500 feet and she will pull the cord when she is 5000 feet above the ground. If the
equation for distance traveled during freefall is given as d(t) = 16t², how long should
she wait before pulling the cord?

The slope of the function as a unit rate for the linear situation. y = [tex]-4\frac{4}{5}[/tex]x + [tex]13\frac{1}{2}[/tex] can be viewed as [tex]-4\frac{4}{5}[/tex] by taking the derivative of the first term of the equation.

The slope m=y/x of a straight-line y=mx+b quantifies the change in y for every unit change in x. This can also be interpreted as a kind of measure of "sensitivity''.

Finding the slope of a function is like finding the rate at which the value of y (the dependent variable) changes in relation to x is what this method entails (independent variable).

To find the slope of a line that is given with the equation of the line, first you have to write the equation of the line in a slope-intercept form.

Then use inverse operations in order to solve for y so that it is written as y=mx+b. Thereafter you can easily spot the slope since the slope is the coefficient of the x variable, or in other words, the number in front of x.

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g(x)×h(x) means we will have to multiply the two functions.

[tex]g(x) \times (h(x) = (3 {x}^{2} - 1)( {x}^{2} - x) \\ = 3 {x}^{2} ( {x}^{2} - x) - 1( {x}^{2} - x) \\ = 3 {x}^{4} - 3 {x}^{3} - {x}^{2} + x \\ g(x) \times h(x) = 3{x}^{4} - {x}^{3} - {x}^{2} + x[/tex]

ATTACHED IS THE SOLUTION

Answer:

3.375

3[tex]\frac{375}{1000}[/tex]

[tex]\frac{27}{8}[/tex]

Step-by-step explanation:

The first answer divide 81 by 24 and you will get the decimal answer of 3.375.

0.375 is [tex]\frac{375}{1000}[/tex]

[tex]\frac{81}{24}[/tex]  Divide the top and the bottom by 3 to get [tex]\frac{27}{8}[/tex]

Answer:

[tex]{ \tt{ - \frac{1}{6} = \frac{f - 3}{7 - 1} }} \\ \\ { \tt{6(f - 3) = - 6 }} \\ \\ { \tt{f - 3 = - 1}} \\ \\{ \tt{f = 2}}[/tex]

Answer:-2

Step-by-step explanation:

Mark receives a scale report and on the Math section, he earned a raw score of 39 which is at the 68th percentile, meaning that the total raw score on the Math section is 57

Find out the total score of the Math score, 100th percentile

     Given; raw score- 39 which is at the

                       68th- percentile

For someone to be at the 100th percentile, he or she must have scored all the questions right.

In Mark's case, he had a score of 68 percentile with a score of 39

Total raw score for the Math section;

    state;   If score of 39 = 68 percentile

                          ?                 100 percentile

Cross multiply to solve for the unknown

Thus;  39 * 100 / 68

         =  57

Therefore, total raw score on the Math section is 57, which is at the 100th percentile.

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Answer:

- 2, 7 , - 8

Step-by-step explanation:

substitute the given values of x into the expression

(a)

x = 0 : 3(0) - 2 = 0 - 2 = - 2

(b)

x = 3 : 3(3) - 2 = 9 - 2 = 7

(c)

x = - 2 : 3(- 2) - 2 = - 6 - 2 = - 8

100 keed lol keed lol keed

The composite result function of f( g(-2) ) in the given functions f( x ) = x² + 3x and g( x ) = 2x - 1 is 10.

A function is simply a relationship that maps one input to one output..

Given the data in the question;

First, set up the composite result function f( g(x) )

f( x ) = x² + 3x

f( g(x) ) = f( 2x - 1 ) = ( 2x - 1 )² + 3( 2x - 1 )

f( g(x) ) = ( 2x - 1 )² + 3( 2x - 1 )

Simplify

f( g(x) ) = ( 2x - 1 )( 2x - 1 ) + 3( 2x - 1  )

f( g(x) ) = 2x( 2x - 1 ) -1(2x - 1 ) + 3( 2x - 1 )

f( g(x) ) = ( 4x² - 2x  - 2x + 1 ) + 3( 2x - 1 )

f( g(x) ) = ( 4x² - 4x + 1 ) + 6x - 3

f( g(x) ) = 4x² - 4x + 1 - 6x - 3

f( g(x) ) = 4x² - 4x + 6x + 1 - 3

f( g(x) ) = 4x² + 2x - 2

Now,  replace all the occurrence of x with -2 in the function and simplify.

f( g(-2) ) = 4(-2)² + 2(-2) - 2

f( g(-2) ) = 4×4 - 4 - 2

f( g(-2) ) = 16 - 4 - 2

f( g(-2) ) = 10

The composite result function of f( g(-2) ) in the given functions is 10.

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Answer:

44.77

Step-by-step explanation:

13.1x3.70=13.1x3.7

37x131=4477

get back the decmial point 44.77

Given the coordinates above, the area of the trapezoid is approximately 41. See the explanation below.

A trapezoid is a quadrilateral with at least one set of parallel sides in American and Canadian English. A trapezoid is known as a trapezium in British and other varieties of English.

For the calculation showing the above solution:

Step 1 - Given:

A = (-3,2)

B = (1, 5)  = ⊥

C = (-7, -3)

D = (0.-2)

Step 2 - To get the distance between the points we need to use the formula for Distance between two points which is given as:

d=√((x2 – x1)² + (y2 – y1)²).

Distance of Line AB =

√((1 – (-3))² + (5 – 2)²).

= √[(4)² + (3)²]

= √( 16 + 9)
= √25

AB= 5

Repeat this for  BC, CD, DA and we'd get the following

BC =  11.313708498985
CD = 7.0710678118655

DA = 5

Step 3  - From the above structure, [see attached] we then apply the formula for the area of a Trapezoid (Trapezium) which is given as:

A = [(a+b)/2] h

Where a = 5

b = 11.313708498985

h = 5

=  [(5+11.313708498985)/2] 5

= 40.7842712475

[tex]\approx[/tex] 41

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Answer: Yes, because 4 + 5 > 8

Step-by-step explanation: The sum of 4 + 5 must be more than 8 to be a triangle

Answer:

The answer is A) Yes, because 4 + 5 > 8

Step-by-step explanation:

I got it right loves <3

x=102°(Corresponding angles are equal m || n)

HOPE THIS HELPS

Answer:

A

Step-by-step explanation:

Do long division. See the attached image for work.

Answer:

B

Step-by-step explanation:

[tex]\frac{56}{90}[/tex]

= 56 ÷ 90

= 0.6222222..

= 0.62 ( with a bar above the 2 , indicating the 2 is repeating )

The percentage of money spent on books to that of cost for last semester is 16%

The cost for last semester was 2000.

The cost books was 320.

The percentage formula = part/whole × 100

Part = 320

Whole = 2000

Equation = 320/2000× 100

               = 32/20

               = 16%

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For the given parallel lines AB and CD, the measure of the angle of the triangle ∠FAB = 25°.

For the given question;

Line AB || Line CD

From the given diagram,

∠CFD = ∠AFB = 110 (corresponding angles)

Now, in triangle ABF

By the property of triangle; sum of all interior angles of triangle is 180.

Thus,

∠AFB + ∠ABF + ∠FAB = 180°

Put the values;

110° + 45° + ∠FAB = 180°

∠FAB = 180° - 155°

∠FAB = 25

Thus, the measure of the angle ∠FAB = 25° in triangle FAB.

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Answer:

17 : 420

Step-by-step explanation:

  When finding the ratio of two quantities, both quantities should be in same type.

Convert 7 minutes to seconds.

     7minutes = 7 * 60

                     = 420 seconds

17 seconds : 7 minutes = 17 : 420

Answer:

G= (8,9)

Step-by-step explanation:

Answer:

1. 4

2. 2

3. 35

4. 96

Step-by-step explanation:

1. (6-2)÷4=4

2. 18÷(2+7)=2

3. (11-4)×5= 35

4.(4+2+6)×8= 96

Answer:

1. 1

2. 2

3. 35

4. 96

Answer:

166,460 doctors registered.

Step-by-step explanation:

32.2% -------- 53,600 female doctors

100% --------          X

X * 32.2% = 100% * 53,600

X = (100% * 53,600) / 32.2%

X = 166,460 doctors

The water level drop each​ hour by 0.0384 inch

Firstly, the deacrease in water level is takes as per the question

Decrease = 3/8 inches

Decrease=0.375 inches

Then the time interval is calculated

From 10 pm to  7:45 hours will be 9.45 hours

Time interval= (9 + 45/60) hours

Time interval=9.75 hours

Now, the drop in water level per hour is determined, to do so, total water level decreased is divided by the time taken to decrease that water level

that is 0.375/9.75 inches/hour

= 0.03846 inches/hour

Therefore, if between 10 P.M. and 7:45 A.M.​, the water level in a swimming pool decreased by 3/8 inches and the water level decreased at a constant​ rate, the water level drop each​ hour is 0.03846

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Answer:

62.5

Step-by-step explanation:

Answer: One seventh of the sum of 19: 2.714

Product of 4 and 11: 44

Step-by-step explanation:

4x11=44

One seventh times 19 equal 2.714.

1/7 x 19/1 = 19/7

Simpified 2 5/7

2 5/2 as decimals is 2.714

Answer: 3/4 of a gallon

Step-by-step explanation:

1/4 times 1/3 is 3/4 so she would need to buy a gallon of paint

Answer:

X>-99/4

Step-by-step explanation:

Let's solve your inequality step-by-step.

−2/5x−9<9/10

Step 1: Add 9 to both sides.

−2/5x−9+9<9/10+9

−2/5x<99/10

Step 2: Multiply both sides by 5/(-2).

(5/−2)*(−2/5x)<(5/−2)*(99/10)

x>−99/4

Answer:

x>−99/4

Step-by-step explanation:

we sadly need to do all the multiplications for the whole polynomial in standard form.

the other 3 things we get out of the given form :

we multiply 3 terms, each in x. the result will be x³.

so, we have the 3rd degree.

the leading coefficient is 1, as for the x³ term we get x×x×x = x³. no other number is involved.

the constant term is the extreme on the other end. it is 4×2×1 = 8.

so, now for the full multiplications, that should also show you, why I could make the conclusions above.

(x+4)(x-2)(x+1)

we do this by multiplying first 2 terms with each other, and then we multiply that result by the third term.

remember, we need to multiply every item of one term with every item in the other term.

(x+4)(x-2) = x² -2x + 4x - 8 = x² + 2x - 8

now

(x² + 2x - 8)(x+1) = x³ + x² + 2x² + 2x - 8x - 8 =

= x³ + 3x² - 6x - 8

so, that is already the standard form

f(x) = x³ + 3x² - 6x - 8

The value of x is 10

The perimeter of the triangle is 30 units

An equilateral triangle can be defined as a triangle which has all its sides equal or congruent to each other.
The properties of an equilateral triangle includes;

From the information given, we have the sides as;

Since all of its sides are equal, we have to  equate two side, we have;

x + 5 = 2x - 5

collect like terms

x - 2x = -5 - 5

subtract the like terms

-x = -10

make 'x' the subject

x = 10

But the perimeter of an equilateral triangle = 3a = 3(10) = 30 units

Thus, the value is 10

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Answer:

Explanation:

Here, we want to rewrite the given expression

What we have to do is to start by opening up the bracket

To do this, we have to multiply the term on the left with each term inside the bracket

Then we collect the like terms and perform the necessary arithmetic operation

We have this as follows:

Answer:

68y-42

Step-by-step explanation:

7(9y+2y-6)-9y

Find the expression in simplest terms

Combine like terms

7(11y-6)-9y

Distribute

77y -42-9y

Combine like terms

68y-42

When we try to convert the value of one kilo meter to feet, the value that we obtain is 3280.8 ft.

We know that there are several units that we could use for calculations. t is often common that we need to convert the units from one unit to the other so that we can be able to carry out calculations. The number that allows us to be able to carry out such a a conversion is what we call the conversion factor for that particular operation.

Given that;

1 foot = 0.0003048 kilo meter

We can see that if we seek to convert a value of One km to feet we would have 3280.8 ft

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Answer: The coordinates W' after a rotation 270° counterclockwise about the origin is (3,-1)