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3 years ago

what is the inverse of h(x)=12e^2x. based on your answer write an expression write an expression equivalent to where x is h of 1

1 answer:

3 0

Let y = 12 e^2x

e^2x = y/12
Taking [email protected]
ln e^2x = ln (y/12)

2x = ln (y/12)

x = (1/2) ln (y / 12)

so the inverse h-1(x) = (1/2) ln ( x / 12)

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1.) You are the crew chief of the Algebra 2 formula racing team. Your current task is to

s344n2d4d5 [400]

Answer:

a). Mileage for carA= $\frac{2}{x}$ , and mileage for carB= $\frac{ 3x+2}{x(x+1)}$

b).total mileage for both is similar to average of them= $\frac{(mileageA + mileageB)}{2}$

= $\frac{5x+4}{2x(x+1)}[tex]mil/gal$

Step-by-step explanation:

It is given that the distance traveled by car $A=2x+2=2(x+1)$

And distance traveled by car $B= 3x+2$

We know the mileage is mile/gallon,

a).So mileage of car $A= \frac{distance traveled by car A}{gallos of fuel used}$

$=\frac{2x+2}{x^2 +x}\\ =\frac{2(x+1)}{x(x+1)} \\=\frac{2}{x}mil/gal$

Similarly , the mileage for car $B= \frac{distance traveled by car A}{gallons of fuel used}$

$=\frac{3x+2}{x^2+x} \\=\frac{3x+2}{x(x+1)}$ $mil/gal$

b).total mileage for both is similar to average of them= $\frac{(mileageA + mileageB)}{2}$

$=\frac{2x+2}{x(x+1)}+\frac{3x+2}{x(x+1)}\\ =\frac{2x+2+3x+2}{x(x+1)}\\=\frac{5x+4}{x(x+1)}mil/gal$

Now divide by 2 for total(average) mileage.

$\frac{\frac{5x+4}{x(x+1)} }{2}\\ =\frac{5x+4}{2x(x+1)} mil/gal$ .

Thus those are the answers.

4 0

3 years ago

4 pairs of pants for 22.60. what is the unit rate?

Alona [7]

Answer:

$5.65

Step-by-step explanation:

Divide 22.6 / 4.

5.65

Best of Luck!

8 0

3 years ago

Gabriel wants to paint the model. How

enyata [817]

Answer:

<h2>The area of the base is 144 square inches.</h2><h2>The area of each triangular face is 66 square inches.</h2><h2>Grabiel needs 408 square inches of paint.</h2>

Step-by-step explanation:

The complete problem is attached.

Notice that the figure is a square pyramid, where its base dimensions are 12 inches by 12 inches, which represents an area of

$B=12 \times 12 = 144 \ in^{2}$

The slant height of the pyramid is 11 inches, which allow us to find the area of each triangle face

$A=\frac{1}{2}bh =\frac{1}{2}(12)(11)= 66 \ in^{2}$

But there are four triangle faces, so $A_{faces} =4(66)=264 \ in^{2}$ .

Therefore, the area of each triangular face is 66 square inches.

So, the total surface area would be the sum

$S=144+264=408 \ in^{2}$

Therefore, Gabriel needs 408 square inches to paint the whole model.

4 0

3 years ago

Which of the following graphs shows the solution set for the inequality below? 3|x + 1| < 9

Bas_tet [7]

Step-by-step explanation:

The absolute value function is a well known piecewise function (a function defined by multiple subfunctions) that is described mathematically as

$f(x) \ = \ |x| \ = \ \left\{\left\begin{array}{ccc}x, \ \text{if} \ x \ \geq \ 0 \\ \\ -x, \ \text{if} \ x \ < \ 0\end{array}\right\}$ .

This definition of the absolute function can be explained geometrically to be similar to the straight line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ , however, when the value of x is negative, the range of the function remains positive. In other words, the segment of the line $\textbf{\textit{y}} \ = \ \textbf{\textit{x}}$ where $\textbf{\textit{x}} \ < \ 0$ (shown as the orange dotted line), the segment of the line is reflected across the <em>x</em>-axis.

First, we simplify the expression.

$3\left|x \ + \ 1 \right| \ < \ 9 \\ \\ \\\-\hspace{0.2cm} \left|x \ + \ 1 \right| \ < \ 3$ .

We, now, can simply visualise the straight line, $y \ = \ x \ + \ 1$ , as a line having its y-intercept at the point $(0, \ 1)$ and its <em>x</em>-intercept at the point $(-1, \ 0)$ . Then, imagine that the segment of the line where $x \ < \ 0$ to be reflected along the <em>x</em>-axis, and you get the graph of the absolute function $y \ = \ \left|x \ + \ 1 \right|$ .

Consider the inequality

$\left|x \ + \ 1 \right| \ < \ 3$ ,

this statement can actually be conceptualise as the question

$``\text{For what \textbf{values of \textit{x}} will the absolute function \textbf{be less than 3}}"$ .

Algebraically, we can solve this inequality by breaking the function into two different subfunctions (according to the definition above).

Case 1 (when $x \ \geq \ 0$ )

$x \ + \ 1 \ < \ 3 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 3 \ - \ 1 \\ \\ \\ \-\hspace{0.9cm} x \ < \ 2$

Case 2 (when $x \ < \ 0$ )

$-(x \ + \ 1) \ < \ 3 \\ \\ \\ \-\hspace{0.15cm} -x \ - \ 1 \ < \ 3 \\ \\ \\ \-\hspace{1cm} -x \ < \ 3 \ + \ 1 \\ \\ \\ \-\hspace{1cm} -x \ < \ 4 \\ \\ \\ \-\hspace{1.5cm} x \ > \ -4$

*remember to flip the inequality sign when multiplying or dividing by

negative numbers on both sides of the statement.

Therefore, the values of <em>x</em> that satisfy this inequality lie within the interval

$-4 \ < \ x \ < \ 2$ .

Similarly, on the real number line, the interval is shown below.

The use of open circles (as in the graph) indicates that the interval highlighted on the number line does not include its boundary value (-4 and 2) since the inequality is expressed as "less than", but not "less than or equal to". Contrastingly, close circles (circles that are coloured) show the inclusivity of the boundary values of the inequality.

3 0

3 years ago

If a teacher brings 3 gallons of juce on a feild trip for 36 students how many fluid ounces did she bring

Elza [17]

If there are 128 fluid ounces per US gallon, and there are 3 gallons, 3x128=384. The teacher brought 384 fluid ounces of juice on the feild trip.

6 0

4 years ago

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