If f(6)=7, find f−1(7)

A party-favor bag must have a volume of 140 cubic inches and the dimensions that are shown below. The equation x^3+6x^2-27x=140

KATRIN_1 [288]

For this case we have the following equation for the volume:

$x ^ 3 + 6x ^ 2-27x = 140$

Rewriting the equation we have:

$x ^ 3 + 6x ^ 2-27x-140 = 0$

We factor the equation to find the roots of the polynomial.

We have then:

$(x-5) (x + 4) (x + 7) = 0$

Then, we discard the negative roots, because the dimensions of the figure must be positive.

We have then that the length is:

$x = 5$

The height is:

$x + 9 = 5 + 9 = 14$

The width is:

$x-3 = 5-3 = 2$

Thus, the dimensions are:

$5 * 14 * 2$

Answer:

The length is 5 inches, the width is 2 inches, and the height is 14 inches.

3 0

2 years ago

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Evaluate: -1 2/5 ÷ 14/15

Sergio [31]

Answer:

Step-by-step explanation: Turn the mixed number into an improper fraction. -1 2/5 becomes -7/5. To divide fractions, you keep the first fraction, change the division sign to mulitplication and flip the second fraction. Then just multiply across the top and across the bottom. You will get 105/70. Reduce by dividing both numerator and denomination by 35 Result will be 3/2.

3 0

3 years ago

A jet plane is traveling at 840 km/h at 37,000 ft between NY and SF. What equation shows the relationship between total kilomete

fgiga [73]

What equation shows the relationship between total kilometers traveled (m), time spent traveling (t), and the plane's speed (s)?

m = t * s

7 0

3 years ago

Do these ratios form a proportion? 26 medium hats to 2 small hats 39 medium hats to 3 small hats

inessss [21]

$\bf \cfrac{\textit{medium hats}}{\textit{small hats}}\qquad \qquad \cfrac{26}{2}=\cfrac{39}{13}\implies \cfrac{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 13}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=\cfrac{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\cdot 13}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies 13= 13~~\textit{\Large \checkmark}$

7 0

2 years ago

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In triangle A B D , the measure of angle A is 10 degree less than the measure of angle B . The measure of angle D is 20 degree m

elixir [45]

Answer:

Measure of angle A is 27 7/9 degrees.

Step-by-step explanation:

Lets call measure of angle A is X-10

Lets call measure of angle B is X

Lets call measure of angle D is 2.5X+20

We know that the sum of triangles add up to 180 degrees

X+X-10+2.5X+20=180

X=37 7/9

So measure of angle A is 27 7/9 degrees.

I hope this is right. :)

8 0

2 years ago