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2 years ago

Determine if each relation is a function if not explain why

Mathematics

1 answer:

bekas [8.4K]2 years ago

8 0

Answer: a c d

Step-by-step explanation: they are functions because the line is intersecting points as well as being squared cubes and a is a absolute value function

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Find all solutions to each quadratic equation

romanna [79]

I hope this helps you

2x^2-4x+7=0 a=2 b=-4 c= 7

disctirminant =b^2-4ac

disctirminant =(-4)^2-4.2.7

disctirminant = 16-56= -40

x=-b+square root of disctirminant ÷2a

x=4+2square root of (-10)/4

x=2+square root of (-10)/2

x'=4 -2 square root of (-10)/4

x'=2 -square root of (-10)/2

6 0

3 years ago

A sleep time of 15.9 hours per day for a newborn baby is at the 10h percentile of the distribution of sleep times for all newbor

Nuetrik [128]

Answer:

option (D) 16.5

Step-by-step explanation:

Data provided:

Sleep time of , X = 15.9 is at the 10th percentile

Standard deviation, σ = 0.5 hour

also,

10th percentile of normal distribution is

Z = F⁻¹(0.10)

Z = - 1.28 (Using Standard Normal distribution)

Now,

$\\Z=\frac{X-\mu}{\sigma}$

X = μ + ( σ × Z )

μ = X - ( σ × Z )

on substituting the respective values, we get

μ = 15.9 - 0.5 × (-1.28)

μ = 16.5

Hence, the correct answer is option (D) 16.5

8 0

3 years ago

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream. Find the rate of the boat in still w

prohojiy [21]

Step-by-step explanation:

Given that,

A motor boat travels 60 miles down a river in 3 hours but takes 5 hours to return upstream,

We know that,

Speed = distance/time

The rate while moving downstream $=\dfrac{60}{3}=20\ mph$

The rate while moving upstream $=\dfrac{60}{5}=12\ mph$

The rate of the boat in still water is the average of these:

$v_s=\dfrac{20+12}{2}=16\ mph$

The rate of the current is the difference between the boat speed and actual speed = 16 mph - 12 mph = 4 mph

Hence, this is the required solution.

7 0

3 years ago

Aaron was offered a job that paid a salary of \$57,000$57,000 in its first year. The salary was set to increase by 1% per year e

Jobisdone [24]

Answer:

The total amount received is: $1906650

Step-by-step explanation:

Given

$a = \$57000$ --- initial

$b = 1\%$ --- rate

$n = 29$ --- time

Required

Determine the total amount at the end of 29 years

The given question is an illustration of geometric progression, and we are to solve for the sum of the first n terms

Where $n = 29$

$r = 1 + b$

$r = 1 + 1\%$

Express percentage as decimal

$r = 1 + 0.01$

$r = 1.01$

The required is the calculated using:

$S_n = \frac{a(r^n - 1)}{r - 1}$

So, we have:

$S_n = \frac{57000 * (1.01^{29} - 1)}{1.01 - 1}$

$S_n = \frac{57000 * (1.3345- 1)}{0.01}$

$S_n = \frac{57000 * 0.3345}{0.01}$

$S_n = \frac{19066.5}{0.01}$

$S_n = 1906650$

<em>The total amount received is: $1906650</em>

8 0

3 years ago

Find the range of the quadratic function. (y=2x^2-20x+53)

Anit [1.1K]

Answer: The range is y ≥ 3.

Step-by-step explanation:

When we have an equation:

y = f(x)

The range is the set of the possible values of y.

In this case, we have:

y = f(x) = 2*x^2 - 20*x + 53

This is a quadratic equation, and the leading coefficient is positive. This means that the arms of the graph will open upwards.

Then the minimum value of y will be the vale at the vertex.

We know that for a quadratic equation of the form:

a*x^2 + b*x + c

The vertex is at:

x = -b/2a

Then in this case, the vertex will be at:

x = -(-20)/(2*2) = 20/4 = 5

Then the smallest value of this function will be:

f(5) = 2*5^2 - 20*5 + 53 = 3

This is the smallest value that y can take, and y can take any value greater than 3.

Then the range can be written as:

y ≥ 3.

4 0

3 years ago