Is 16.5 the same thing as 16 or is it greater than 16?

ValentinkaMS [17]

Answer:

FALSE

Step-by-step explanation:

4 0

4 years ago

What is the base of the natural logarithm function f(x) = ln(x)? Explain how you know.

Zarrin [17]

Answer:

base = e

Step-by-step explanation:

The general log function is defined as

$f(x)=\log_a x$ .... (1)

where, a is the base of the log function.

The natural logarithm function is

$f(x)=\ln x$

It can be rewritten as

$f(x)=\log_e x$ .... (2)

where, e is a constant or Euler's number is:

e ≈ 2.71828183

On comparing (1) and (2) we get

$a=e$

Therefore, the base of the natural logarithm function is e.

4 0

3 years ago

Find the area of the trapezoid by decomposing it into other shapes

lakkis [162]

Answer:

60 cm ( squared )

Step-by-step explanation:

you can find the area of the trapezoid ( by decomposing it into other shapes ) by separating two triangles, and using the formula to find the area of triangles, which is A= 1/2 ( b x h ) and add the answer to those together ( 16 cm squared and 4 cm squared ), and after that, you can find the area to the rectangle by multiplying the l x w, which is 10 x 4 ( after separating the triangles.). That equals 40, and when you add them all together ( 16 + 4 + 40 ) it equals 60 cm (squared).

4 0

3 years ago

Dave deposits $400.00 each month into an annuity with a 3.25% interest rate compounded quarterly. What is the account balance af

noname [10]

I think it’s 4,003.25 sorry if I got it wrong

7 0

4 years ago

Read 2 more answers

Please help, fast‍♀️‍♀️

kramer

Inequalities are used to express unequal expressions.

The inequalities from the word problems are:

$\mathbf{m - 3.5 \le -2}$ .
$\mathbf{0 \ge 2x + 1}$ .
$\mathbf{-\frac 12 \ge 2k - 4}$

The statements from the inequalities are:

-4 is not a solution to $\mathbf{x + 8 < -3}$
-6 is not a solution to $\mathbf{10 \le 3 - m}$
-1 is not a solution to $\mathbf{-3x \le -12.5}$

Graph b represents $\mathbf{x > -7}$

<h3>The word problems</h3>

<u>1. A number minus 3.5 is less than or equal to -2</u>

The statement can be broken down into the following expressions

$\mathbf{A\ number\ minus\ 3.5 \to m - 3.5}$

$\mathbf{less\ than\ or\ equal\ to\ -2 \to \le -2}$

So, when the expressions are brought together, we have:

$\mathbf{m - 3.5 \le -2}$

<u>2. Zero is greater than or equal to twice a number x plus 1</u>

The statement can be broken down into the following expressions

$\mathbf{Zero\ is\ greater\ than\ or\ equal\ to \to 0 \ge }$

$\mathbf{twice\ a\ number\ x\ plus\ 1\ \to 2x + 1}$

So, when the expressions are brought together, we have:

$\mathbf{0 \ge 2x + 1}$

<u />

<u>3. -1/2 is at least twice a number k minus 4</u>

The statement can be broken down into the following expressions

$\mathbf{-\frac 12\ is\ at\ least \to -\frac 12 \ge }$

$\mathbf{twice\ a\ number\ k\ minus\ 4\ \to 2k - 4}$

So, when the expressions are brought together, we have:

$\mathbf{-\frac12 \ge 2k - 4}$

None of the options is correct

<h3>The solutions</h3>

<u>4. Tell whether -4 is a solution to x + 8 < -3</u>

We have:

$\mathbf{x + 8$

Subtract 8 from both sides

$\mathbf{x + 8 - 8$

$\mathbf{x$

The above inequality means that:

-4 is not a solution, because -4 is greater than -11

<u>5. Tell whether -6 is a solution to 10 <= 3 - m</u>

We have:

$\mathbf{10 \le 3 - m}$

Subtract 3 from both sides

$\mathbf{10 -3\le 3 - 3 - m}$

$\mathbf{7 \le - m}$

Multiply both sides by -1 (the inequality sign changes)

$\mathbf{-7 \ge m}$

Make m the subject

$\mathbf{m \le -7}$

The above inequality means that:

-6 is not a solution, because -6 is greater than -7

<u>6. Tell whether -1 is a solution to -3x <= -12.5</u>

We have:

$\mathbf{-3x \le -12.5}$

Divide both sides by -3 (the inequality sign changes)

$\mathbf{x \ge 4\frac16}$

The above inequality means that:

<em>x is greater than or equal to </em> $\mathbf{4\frac16}$ <em />

-1 is not a solution, because -1 is less than $\mathbf{4\frac16}$ <em />

<h3>The graph</h3>

The inequality is given as: $\mathbf{x > -7}$

The less than sign (>) means that:

The graph would use an open circle
The arrow must point to the right

Only graph b satisfies this condition

Hence, the graph of $\mathbf{x > -7}$ is graph b