Use inductive reasoning to make a conjecture about the given quantity

Which of the following equations best represents the graph of a function f(m)?

Inessa [10]

Answer: y = f(m)

Justification:

By definition, the graph of a function in the cartesian coordinate plane is the plot of the curve that join all the points that satisfy the equation of the function.

In the cartesian coordinate plane, each point is represented by a pair of coordinates (y, x). y is the value of the function f(x), and x is any input value of the function.

In this case, the function is given as f(m), which means that the input value is represented by m.

Hence, the graph is the plot of y = f(m).

The choice of the letter used for the variable is completely arbitrary and does not change either the math or the graph. It could have been said that the function is f(x) in which case the graph would be y = f(x). Nothing changes but the name that you use.

4 0

2 years ago

A laptop has a listed price of $537.95 before tax. If the sales tax rate is 7.5%, find the total cost of the laptop with sales t

nexus9112 [7]

Answer:

$578.30

Step-by-step explanation:

537.95(.075)= 40.35

$40.35 + $537.95 = $578.30

6 0

3 years ago

"The sum of the abscissa and the ordinate is six"?

Alenkinab [10]

The answer will be <span>x + y = 6 </span>

3 0

3 years ago

Alexander deposited money into his retirement account that is compounded annually at an interest rate of 7%.

anzhelika [568]

Tow rates are equivalent if tow initial investments over a the same time, produce the same final value using different interest rates.

For the annually rate we have that:
$V_{0} =(1+ i_{a} ) ^{1}$
Where
$V_{0}$ = initial investment.
$i_{a}$ = annually interest rate in decimal form.
And the exponent (1) represents the full year.

For the quarterly interest rate we have that:
$V_{0} =(1+ i_{q} ) ^{4}$
Where
$V_{0}$ = initial investment.
$i_{q}$ = quarterly interest rate in decimal form.
And the exponent (4) the 4 quarters in the full year.

Since the rates are equivalent if tow initial investments over a the same time, produce the same final value, then
$(1+ i_{a} )=(1+ i_{q} ) ^{4}$
Notice that we are not using the initial investment $V_{0}$ since they are the same.

The first thin we are going to to calculate the equivalent quarterly rate of the 7% annually rate is converting 7% to decimal form
7%/100 = 0.07
Now, we can replace the value in our equation to get:
$(1+0.07)=(1+ i_{q} ) ^{4}$
$1.07=(1+ i_{q} ) ^{4}$
$\sqrt[4]{1.07} =1+ i_{q}$
$i_{q} = \sqrt[4]{1.07} -1$
$i_{q} =0.017$
Finally, we multiply the quarterly interest rate in decimal form by 100% to get:
(0.017)(100%) = 1.7%
We can conclude that Alexander is wrong, the equivalent quarterly rate of an annually rate of 7% is 1.7% and not 2%.

6 0

3 years ago

f(x) is a quadratic function with x-intercepts at (−1, 0) and (−3, 0). If the range of f(x) is [−4, [infinity]) and g(x) = 2x^2

iren2701 [21]

Answer with Step-by-step explanation:

We are given that function f(x) which is quadratic function.

x -intercept of function f(x) at (-1,0) and (-3,0)

x-Intercept of f means zeroes of f

x=-1 and x=-3

Range of f =[-4, $\infty$ )