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sattari [20]
3 years ago
12

In a certain function, an output is 4 more than half its input.

Mathematics
1 answer:
patriot [66]3 years ago
7 0

Answer:

x          y

-10      -1

0         4

4          6

6          8

Step-by-step explanation:

an output is 4 more than half its input.

Input of a function is x and the output of a function is y

output y is 4 + half of input x

y= \frac{1}{2} x + 4

Now we complete the below table, plug in the value of x  and find out y

x = -10 , y= \frac{1}{2}(-10) + 4=-5+4 = -1

x = 0 , y= \frac{1}{2}(0) + 4=0+4 = 4

x = 4 , y= \frac{1}{2}(4) + 4=2+4 = 6

x = 8, y= \frac{1}{2}(8) + 4=4+4 = 8


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Factorise: a squared +8a -20
Vaselesa [24]
Factor out the 4 in both equations
8a^2-20^2=(2^2 times a^2 times 2)-(2^2 times 5)
therefor it is also equal to
(2a)^2 times 2-(2^2 times 5)
we can force it into a difference of 2 perfect squares which is a^2-b^2=(a-b)(a+b)
(2a√2)^2-(2√5)^2=((2a√2)-(2√5))((2a√2)+(2√5))


8 0
3 years ago
The Wind Mountain excavation site in New Mexico is an important archaeological location of the ancient Native American Anasazi c
timurjin [86]

Answer:

a) 28

b)

Class Limits  Class Boundaries   Midpoint    f      Rf         Cf

10 - 37            9.5-37.5                   23.5            7     0.096     7      

38 - 65           37.5-65.5                 51.5           25    0.342     32    

66 - 93           65.5-93.5                 79.5          26    0.356     58    

94 -  121        93.5-121.5                   107.5         9     0.123       67    

122 - 149      121.5-149.5                  135.5         5      0.068     72  

150 - 177       149.5-177.5                  163.5        0         0.0      72    

178 - 205       177.5-20.5                  191.5         1       0.014      73  

Total                                                                  73          1.0    

c)

The histogram is in attached file.

Step-by-step explanation:

a)

The width of class interval=range/desired number of classes

The width of class interval=(maximum-minimum)/7

The width of class interval=(200-10)/7

The width of class interval=190/7

The width of class interval=27.14=28 (rounded to next whole number)

Part(b) and part (c) is explained in attached word document.

Download docx
5 0
3 years ago
Select the BEST classification for sq. root 25 . A) irrational B) rational C) imaginary Eliminate D) complex
tatuchka [14]

Answer:

B. Rational

Step-by-step explanation:

the square root of 25 is 5. 5 best fits the classification of rational

4 0
3 years ago
A piston rises to 5 cm and falls to 3 cm in such a way that it returns to the maximal height three times every two seconds. If w
sveticcg [70]

Answer:

(1 cm)cos3πt

Step-by-step explanation:

Since the piston starts at its maximal height and returns to its maximal height three times evert 2 seconds, it is modelled by a cosine functions, since a cosine function starts at its maximum point. So, its height h = Acos2πft

where A = amplitude of the oscillation and f = frequency of oscillation and t = time of propagation of oscillation.

Now, since the piston rises in such a way that it returns to the maximal height three times every two seconds, its frequency, f = number of oscillations/time taken for oscillation where number of oscillations = 3 and time taken for oscillations  = 2 s

So, f = 3/2 s =1.5 /s = 1.5 Hz

Also, since the the piston moves between 3 cm and 5 cm, the distance between its maximum displacement(crest) of 5 cm and minimum displacement(trough) of 3 cm is H = 5 cm - 3 cm = 2 cm. So its amplitude, A = H/2 = 2 cm/2 = 1 cm

h = Acos2πft

= (1 cm)cos2π(1.5Hz)t

= (1 cm)cos3πt

7 0
3 years ago
Jada purchases movie tickets online. She buys 2 tickets for adults and 4 tickets for children. The cost of a ticket for a child
grandymaker [24]

Answer:

Step-by-step explanation:

58 is the answer without tax

so the cost of an adult ticket is 13 dollars

and the kids ticket is 8 dollars

use system of equations to solve this.

58=2x+4y

y=x-4

8 0
3 years ago
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