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guajiro [1.7K]
3 years ago
9

What is the range of the absolute value function below?

Mathematics
2 answers:
Rashid [163]3 years ago
6 0

answer: f(x)<4

I really hope that heped

satela [25.4K]3 years ago
5 0

Answer:

D The bottom choice.

Step-by-step explanation:

The range is the y value of (in this case) an absolute value. The maximum value of this is 4. Everything else is less than 4. The answer would be written as

4≥f(x) which is the same thing as D

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Suppose `h\left(t\right)=-5t^{2}+10t+3`is an expression giving the height of a diver above the water (in meters), t seconds afte
prisoha [69]

Answer:

Step-by-step explanation:

a) The height of the springboard above the water should be h(0) : Read, the height at t = 0

h(0) = -5(0) + 10(0) + 3

h(0) = 0 + 0 + 3

h(0) = 3

a) 3 meters

b)  The time it takes the diver to hit water should be, the positive 0 solution for t.  Remember, in a quadratic equation,  there are two values for t where a parabola crosses the horizontal axis, which in this case would be t.  Just by looking at the function, h(t) = -5t2 + 10t + 3 , one should be able to see that it cannot be factored easily, so it requires the Quadratic Formula to find the zeros ; x = -b ±√(b2-4ac)  / 2a

Substitute t for x, and use the coefficients for a, b, c:

t  =  (-10 ± √((102 - 4(-5)(3)))/2(-5)

t = (-10 ±√(100 + 60))/-10

t = (-10 ±√160)/-10) ; Now factor the 160 to simplify:

t = (-10 ±√(10*16))/-10

t = (-10 ±4√10)/-10 ; Factor out leading coefficient of -2 from the numerator:

t = -2(5 ± 2√10)/-10

t = (5 ± 2√10)/5

Using a calculator to find the zeros, and disregarding the negative zero (because t starts at 0):

t ≈ 2.265

b) approx. 2.265 seconds for diver to hit water.

c) To find this, set the function equal to 3 to find what other value for t would be equal to 3 (we know one is 0).

-5tt + 10t + 3 = 3

-5t2 + 10t = 0 ; factor out t

t(-5t + 10) = 0

We know t = 0:

We also know that -5t + 10 = 0

-5t = -10

t = 2

c) 2 seconds. This is the time that diver would equal height of t=0 which is where he started, and where he equals the height of the springboard.

d and e) The peak of the dive (parabola), is determined using the formula h = -b/2a (Derived from the Quadratic Formula) to find the y value (in this case, the h value, answering e) and then using that result in the function to find the x value (in this case, the t value answering d) of the point where the parabola (dive path) reaches a maximum(height), or minimum(in upward opening parabolas).

h = -10/2(-5)

h = -10/-10

h = 1

h(1) = -5(1)2 + 10(1) + 3

h(1) = -5 + 10 + 3

h(1) = 8

d) At t = 1 second, diver will have reached peak of dive.

e) At t = 1 second, diver will have reached a maximum height of 8 meters.

5 0
2 years ago
Please help, its so simple
antoniya [11.8K]

Answer:

117

Step-by-step explanation:

Subtract from 180 to get interior and exterior angles.

180 - 101 = 79

79 + 38 = 117

180 - 117 = 63

180 - 63 = 117

5 0
3 years ago
Read 2 more answers
If 5r + 6 &lt; 36, then <br> a) r&lt;6<br> b) r&lt;8<br> c) r&lt;12<br> d) r&lt;30<br> e) not given
Irina18 [472]
The answer is r<6

yycjj. hgxs tfdg
4 0
3 years ago
A pair of ordinary dice is rolled. What is the probability that each die will show a number higher than 4. 1. (1/36) 2. (1/12) 3
mihalych1998 [28]

Answer:

the answer is 1/12

Step-by-step explanation:

it is 1/12 because if there are only a pair you would have 2 dice. and since each die has numbers all the way up to 6 all you have to do is add them. and don't count all the numbers. like add 1+2+3+4+5+6. that's just plain wrong just do add the highest number on each die (6+6)

8 0
3 years ago
340% of what is 88.8
Gala2k [10]
Since 340 % van be written to 3.4, just use 88.8 to divide it by 3.4, so the answer should be 26.1176470588, if ur question needs you to round up to a number of decimals, do it
7 0
3 years ago
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