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Dennis_Churaev [7]
3 years ago
9

The graph of a linear function f passes through the point (-1,9) and has a slope of -3. what is the zero of f?

Mathematics
1 answer:
klio [65]3 years ago
5 0

Answer:

<em>Answer: x=2 (third option)</em>

Step-by-step explanation:

<u>Equation of a line</u>

Being m is the slope and (h,k) is a point through which the line passes, the point-slope form of the equation of a line is:

y - k = m ( x - h )

We have the function f passes through the point (-1,9) and has a slope of m=-3. The point-slope equation of the line is:

y - 9 = -3 ( x - (-1) )

Operating:

y - 9 = -3 ( x + 1 )

y - 9 = -3x - 3

Adding 9:

y = -3x + 6

To calculate the zero of the function we set y=0 and solve for x:

-3x + 6 = 0

Subtracting 6:

-3x = - 6

Dividing by -3

x = - 6 / ( - 3 )

x = 2

Answer: x=2 (third option)

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The measures of the angles of a triangle are shown in the figure below. Solve for x.
mote1985 [20]

Answer:

X=22

Step-by-step explanation:

In a triangle all the angles add up to 180 so you add them all up and get      6x-21+69=180

                  +21

                 -69

  6x=132 132/6= 22

4 0
3 years ago
The amount y (in grams) of the radioactive isotope fermium-253 remaining after t hours is y=a(0.5)t/72, where a is the initial a
almond37 [142]

Answer:

Per hour decay of the isotope is 0.96%.

Step-by-step explanation:

Amount of radioactive element remaining after t hours is represented by

y=a(0.5)^{\frac{t}{72}}

where a = initial amount

t = duration of decay (in hours)

Amount remaining after 1 hour will be,

y=a(0.5)^{\frac{1}{72} }

y = 0.9904a

So amount of decay in one hour = a - 0.9904a

                                                      = 0.0096a gms

Percentage decay every hour = \frac{\text{Amount of decay}}{\text{Initial amount}}\times 100

                                                  = \frac{0.0096a}{a}\times 100

                                                  = 0.958 %

                                                  ≈ 0.96 %

Therefore, per hour decay of the radioactive isotope is 0.96%.

7 0
3 years ago
Please help asap !!!
denpristay [2]

Answer:

B. x=3/7   y=22/7

C. because it is not precise

D. you need to replace these values in the above equation

<u>Check Understanding</u>

to find the intersection point:

y=y

-3x-2=x-10

solve, x=2

B. by graphing the 2 lines (equations)

Step-by-step explanation:

3 0
3 years ago
Which one is the greater fraction 1/2 or 19/56
vazorg [7]

1/2 is the greater fraction

5 0
3 years ago
Read 2 more answers
What are the domain and range of f (x) = log (x minus 1) 2?.
statuscvo [17]

You can use the definition of logarithm and the fact that a positive number raised to any power will always stay bigger than 0.

The domain of the given function is  {x | x > 1 and a real number }

The range of the given function is \mathbb R (set of real numbers)

<h3>What is the definition of logarithm?</h3>

If a is raised to power b is resulted as c, then we can rewrite it that b equals to the logarithm of c with base a.

Or, symbolically:

a^b =  c \implies b = log_a(c)

Since c was the result of a raised to power b, thus, if a was a positive number, then a raised to any power won't go less or equal to zero, thus making c > 0

<h3>How to use this definition to find the domain and range of given function?</h3>

Since log(x-1) is with base 10 (when base of log isn't specified, it is assumed to be with base 10) (when log is written ln, it is log with base e =2.71828.... ) thus, we have a = 10 > 0 thus the input x-1 > 0 too.

Or we have:

x > 1 as the restriction.

Thus domain of the given function is {x | x > 1 and a real number }

Now from domain, we have:

x >  1\\&#10;x-1 > 0\\&#10;log(x-1) > -\infty\\&#10;log(x-1) + 2 > -\infty\\&#10;f(x) > -\infty (log(x-1) > -infinity since log(0) on right side have arbitrary negatively large value which is denoted by -infinity)

Thus, range of given function  is whole real number set \mathbb R (since all finite real numbers are bigger than negative infinity)

Thus, the domain of the given function is  {x | x > 1 and a real number }

The range of the given function is \mathbb R (set of real numbers

Learn more about domain and range here:

brainly.com/question/12208715

8 0
3 years ago
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