)A bicyclist rides 14 miles in 112 minutes. If she continues at this speed, how long will it take her to travel 35 miles?

What is the domain of the function y = l n (x + 2)

SashulF [63]

Answer: x > -2

Step-by-step explanation:

The domain of the natural language function (ln) is greater than 0.

A such, x + 2 > 0

x > -2

Thus the domain of the function are values of x greater than -2.

6 0

3 years ago

What is the equation of this line? y=12x−3 y=−12x−3 y=−2x−3 y=2x−3 Number graph ranging from negative 5 to 5 on both the x and y

Tems11 [23]

We are given that

A line passes through two points as

(0,-3) and (4,-1)

$(x_1,y_1)=(0,-3)$

$x_1=0,y_1=-3$

$(x_2,y_2)=(4,-1)$

$x_2=4,y_2=-1$

Firstly, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{-1+3}{4-0}$

$m=\frac{2}{4}$

$m=\frac{1}{2}$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

we can plug values

$y+3=\frac{1}{2} (x-0)$

$y+3=\frac{1}{2}x$

$y=\frac{1}{2}x-3$

so, the equation of line is

$y=\frac{1}{2}x-3$ ...............Answer

5 0

3 years ago

Read 2 more answers

What 4.1555 rounded to the nearest tenth

Shkiper50 [21]

The answer is 4.2 because if the next digit is 5 or more it will round up

7 0

2 years ago

Read 2 more answers

$650 is invested in an account earning 8.6% interest (APR), compounded monthly. Write a function showing the value of the accoun

IRISSAK [1]

Answer:

The value of the acount after t years is of $A(t) = 650(1.0072)^{12t}$

The annual growth rate is of 0.72%.

Step-by-step explanation:

Compound interest:

The compound interest formula is given by:

$A(t) = P(1 + \frac{r}{n})^{nt}$

Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.

$650 is invested in an account earning 8.6% interest (APR), compounded monthly.

This means that $P = 650, r = 0.086, n = 12$ . So

$A(t) = P(1 + \frac{r}{n})^{nt}$

$A(t) = 650(1 + \frac{0.086}{12})^{12t}$

$A(t) = 650(1.0072)^{12t}$

The value of the acount after t years is of $A(t) = 650(1.0072)^{12t}$

Annual growth rate

1.0072 - 1 = 0.0072 = 0.72%

The annual growth rate is of 0.72%.

5 0

3 years ago

If a polynomial function f(x) has roots 1+square root of 2 and-3, what must be a factor of f(x)?

nevsk [136]

To find the factor a a polynomial from its roots, we are going to seat each one of the roots equal to $x$ , and then we are going to factor backwards.

We know for our problem that one of the roots of our polynomial is -3, so lets set -3 equal to $x$ and factor backwards:
$x=-3$
$x+3=0$
$(x+3)$ is a factor of our polynomial.

We also know that another root of our polynomial is $1+ \sqrt{2}$ , so lets set $1+ \sqrt{2}$ equal to $x$ and factor backwards:
$x=1+ \sqrt{2}$
$x-1= \sqrt{2}$
$x-1- \sqrt{2}=0$
$(x-(1+ \sqrt{2})=0$
( $(x-(1+ \sqrt{2} ))$ is a factor of our polynomial.

We can conclude that there is no correct answer in your given choices.

8 0

3 years ago