Which expression is equivalent to 3x(-4x^2+5x-8)-6(x^2-5x+7)?

A. 12x^3-9x^2+6x-42
B.-12x^3-54x^2+6x-42
C.-12x^3+9x^2+6x-42
D.-27x^3-6x^2+6x-42

To calculate when the object would be at a particular height, we use the given equation, input the known height, and solve for the time (t), using the quadratic formula. The time when the object is at 1000ft is approximately 6.6 seconds and at 940ft it's approximately 6.9 seconds. The domain of the function is 0 <= t <= 10.3 and the range is 0 <= h <= 1700.

This question involves the application of the quadratic equation, in the context of Physics. You would use the given function h=-16t^2+1700 to solve for t when h is set to the desired height.

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The object will be at 1000ft and 940ft above the ground approximately 6.65 seconds and 6.87 seconds after being dropped, respectively.

The domain of the function representing this situation is t ≥ 0, and the range is 0 ≤ h ≤ 1700.

To find out when the object will be at certain heights, we can set h equal to those heights and solve for t.

a. When will the object be at 1000ft above the ground?

1000 = -16t^2 + 1700

16t^2 = 1700 - 1000

16t^2 = 700

t^2 = 700/16

t = √(700/16)

t ≈ 6.65 seconds

b. When will the object be 940ft above the ground?

940 = -16t^2 + 1700

16t^2 = 1700 - 940

16t^2 = 760

t^2 = 760/16

t = √(760/16)

t ≈ 6.87 seconds

c. What are a reasonable domain and range for the function h?

The domain of the function, which stands for time, would be t ≥ 0 as we do not consider negative time.

The range of the function, corresponding to the height, would be 0 ≤ h ≤ 1700 as we know the object's maximum height is 1700 ft and it can't go below ground level (0 ft).

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The sentence translates to the algebraic equation '53 + x - 10 = y,' which simplifies to 'x + 43 = y.' The closest matching option provided is d. 53 + x - 10 = y.

The sentence "the sum of fifty-three and x, minus ten, is y" translates to an algebraic equation that adds 53 to x and then subtracts 10 to equal y. This can be expressed mathematically as 53 + x - 10 = y. When simplified, this equation becomes x + 43 = y, which is not one of the provided options. Therefore, the correct option that most closely matches the sentence, after considering simplification, is d. 53 + x - 10 = y.

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Each of the three crew members received $132 for the job.

Total amount paid to Shannon = $560

Share received by Shannon = $164

So, money left for other 3 members = [tex]560-164=396[/tex] dollars

As Shannon shared the left money ($396) equally among the other three members of her crew, so each person got :

[tex]\frac{396}{3}[/tex] = $132

Therefore, each of the three crew members received $132 for the job.

By using proportions based on the concept of similar triangles, the height of the taller tree is calculated to be approximately 16.3 feet tall.

The question asks us to compare the heights and shadows of two trees to determine the height of the taller tree given the height and shadow length of the shorter tree and the shadow length of the taller tree. Since both trees will cast shadows in the same proportions if they're under the same conditions of light, we can use similar triangles to find the height of the taller tree.

The shorter tree is 10.5 ft tall and casts a shadow that is 11.25 feet long. If the taller tree casts a 17.5 ft shadow, we can set up a proportion as follows:

Height of the shorter tree / Shadow of the shorter tree = Height of the taller tree / Shadow of the taller tree

10.5 ft / 11.25 ft = Height of the taller tree / 17.5 ft

From the proportion, we can solve for the height of the taller tree:

Height of the taller tree = (10.5 ft / 11.25 ft) × 17.5 ft

Height of the taller tree = 16.333... ft

So, the taller tree is approximately 16.3 feet tall.

Answer:

The answer is 27

Step-by-step explanation:

The third term of the given geometric sequence is 27, calculated by using the geometric sequence formula with the first term of 3 and a common ratio of 3.

The third term of a sequence that has a first term of 3 and a common ratio of 3 is calculated using the formula for geometric sequences, which is a_n = a_1 \(\cdot\) r^{(n-1)}, where a_n is the nth term, a_1 is the first term, and r is the common ratio. To find the third term (when n=3), we substitute the given values into the formula to get: 3 \(\cdot\) 3^{(3-1)}.

Calculating that gives us 3 \(\cdot\) 3², which equals 3 \(\cdot\) 9, so the third term is 27.

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Final answer:

The cross product a~ × b~, where a~ points south and b~ points west, is directed downwards. This direction is determined using the right-hand rule and is perpendicular to the original plane formed by a~ and b~.

Explanation:

If vector a~ points south and vector b~ points west, their cross product a~ × b~ can be determined using the right-hand rule. By pointing the fingers of your right hand towards the direction of a~ (south) and then rotating your wrist to point your fingers towards b~ (west), your thumb will point downwards. Therefore, the direction of a~ × b~ is downwards, which is into the ground if you are standing in the Northern Hemisphere.

The cross product of two vectors is always perpendicular to the plane that contains the original vectors. So in this case, since a~ and b~ are orthogonal and lie in the horizontal plane, their cross product a~ × b~ will be orthogonal to this horizontal plane. As the vectors move from a~ to b~ in an anticlockwise direction, the resultant vector points downward, opposite to the upward direction that would be indicated by b~ × a~.

The probability that the office doors were unlocked when the delivery van arrived is 5/6. The correct option is A. 5/6.

To determine the probability that the office doors were unlocked when the delivery van arrived, we first need to understand the time intervals:

The total available time for the delivery van to arrive is 120 minutes, out of which the doors were locked for 20 minutes.

18 is the answer folks.

0.08 is already a decimal.

To make 0.08 into a fraction, look at the image attached.

Answer:

The value of [tex]f^{-1}(f(3))[/tex] is 3.

Step-by-step explanation:

Here, the given function is,

[tex]f(x)=9x+1-----(1)[/tex]

For finding [tex]f^{-1}(f(3))[/tex] we have to find out the inverse of f(x),

The steps are as follows,

Step 1 : Replace f(x) by y,

[tex]y=9x+1[/tex]

Step 2 : Switch x and y,

[tex]x=9y+1[/tex]

Step 3 : Isolate y in the left side,

[tex]-9y=1-x[/tex]

[tex]\implies y = \frac{x-1}{9}[/tex]

Step 4 : replace y by [tex]f^{-1}(x)[/tex],

[tex]f^{-1}(x)=\frac{x-1}{9}------(2)[/tex]

Now,

[tex]f^{-1}(f(3))=f^{-1}(9\times 3+1)[/tex]   ( From equation (1) )

[tex]=f^{-1}(28)[/tex]

[tex]=\frac{28-1}{9}[/tex]     ( From equation (2) )

[tex]=\frac{27}{9}[/tex]

[tex]=3[/tex]

Answer:

The answer is (k-9)(k+9)  

Step-by-step explanation:

After deducting the monthly membership fee of $4.95 from Shanti's budget, $37.05 remains for DVD rentals. At $1.95 per DVD rental, Shanti can rent 19 DVDs while staying within her budget.

To calculate how many DVDs Shanti can rent without going over her monthly budget of $42, we first need to deduct her monthly membership fee from her total budget. This leaves us with the amount she can spend on renting DVDs.

The monthly membership fee is $4.95. After subtracting this fee from her total budget, we have:

$42 - $4.95 = $37.05 available for DVD rentals.

Each DVD rental costs $1.95. To find out how many DVDs Shanti can rent, we divide the amount available for rentals by the cost per DVD rental:

$37.05 / $1.95 = 19 DVDs (rounded down since you cannot rent a fraction of a DVD)

Therefore, Shanti can rent 19 DVDs in her first month and stay within her budget of $42.

Answer:

In 3 hour 45 minutes Both working together do all of yard work.

Step-by-step explanation:

Time taken by Steve to do yard work = 6 hours

Work Done by Steve in a hour = [tex]\frac{1}{6}[/tex]

Time taken by Bill to do yard work = 10 hours

Work Done by Steve in a hour = [tex]\frac{1}{10}[/tex]

Work done by both in a hour = [tex]\frac{1}{6}+\frac{1}{10}=\frac{5+3}{30}=\frac{8}{30}=\frac{4}{15}[/tex]

Time taken by by both working together = [tex]\frac{1}{\frac{4}{15}}=\frac{15}{4}=3.75=3\,hour\,45\,minutes[/tex]

Therefore, In 3 hour 45 minutes Both working together do all of yard work.

Let q = quarter

Let d = dime

Here is your system:

q + d = 23

0.25q + 0.10d = 3.80

Take it from here.

Answer:

The Answer is 20

Step-by-step explanation:

if ya know ya know