Consider the system of equations

Jana ran the first 3 and a half miles of a 5 mile race in 1 3rd of an hour. what was her average rate, in mph, for the first par

Lisa [10]

Answer:

always try to draw a diagram first

Step-by-step explanation:

Jana ran The first 3.5 miles in 1/3 of an hour. remember the problem tells us that we want our answer in miles per hour or mph. so we have to set up our problem so that our units match in the end. The diagram above shows 3.5 mi over 1/3 hour. so we must divide 3.5 miles by 1/3 hour

note:

$3 \frac{1}{2} mi = \frac{7mi}{2}$

therefore

$\frac{7mi}{2} \: \div \: \frac{1hr}{3} =$

$\frac{7mi}{2} \times \frac{3}{1hr} = \frac{21mi}{2hr} = 10 \frac{1}{2} \frac{mi}{hr}$

7 0

2 years ago

Which of the following is equivalent to log50^7 rounded to three decimal places

Vitek1552 [10]

Answer:

11.886

Step-by-step explanation:

Given :

$log 50^7$

Applying formula

$log a^m=m log a$

So,

$7 log 50\\=7(1.698)\\=11.886$

Answer will be 11.886

3 0

3 years ago

What value of b makes the trinomial below a perfect square x^2-bx+100

Aloiza [94]

1. Perfect square trinomials, are 2nd degree polynomials, of the form $a x^{2} +bx+c$ so that $a \neq 0, b \neq 0, c \neq 0$ , which can be written as perfect squares.

2. For example $(x+1) ^{2} = x^{2} +2x+1
 
(3x-1)^{2}= (3x)^{2}-2(3x)+(-1) ^{2}= 9x^{2}-6x+1 
$

3. Thus $x^{2} +2x+1, 9x^{2}-6x+1$ are perfect square trinomials.

4. $x^{2} -bx+100= x^{2} -bx+ 10^{2}= (x+10)^{2} or (x-10)^{2}$

5. In the first case -b=20, so b=-20. In the second case, -b=-20, so b=20.

6. b∈{-20, 20}

6 0

2 years ago

The antibiotic clarithromycin is eliminated from the body according to the formula A(t) = 500e−0.1386t, where A is the amount re

PolarNik [594]

Answer:

Time(t) = 11.61 hours (Rounded to two decimal place)

Step-by-step explanation:

Given: The antibiotic clarithromycin is eliminated from the body according to the formula:

$A(t) = 500e^{-0.1386t}$ ......[1]