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Evgen [1.6K]
3 years ago
10

The 2 in the middle is the one that I needed help Please

Mathematics
1 answer:
r-ruslan [8.4K]3 years ago
4 0

Answer:

The equation is p=34a+12, and a=7

Step-by-step explanation:

Perimeter is all of the sides added together

p=12a+6a+8+6a+8+10a-4

Combine like-terms

p=34a+12

Solve for a by making p equal to 250

250=34a+12

Subtract 12 from both sides

238=34a

Divide both sides by 34

7=a

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The quotient of a number and 3, less 8, is 16. What is the number?
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The way I am reading this is 16=(x/3)-8. In that case, x=72. I hope that's the right way of interpreting this :)
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3 years ago
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An 8-car Ferris wheel is shaped like a regular octagon. Does the Ferris wheel have rotational symmetry?
sleet_krkn [62]

Answer:

Yes, it does.

Step-by-step explanation:

Every regular shaped figure will have rotational symmetry, since they are built with identical segments all around.

To find the answer, ask yourself « If I rotate the shape, is there a time where I’ll find the exact same shape again with a different angle? »

So, a square has rotational symmetry, but not a rectangle.

A equilateral triangle has rotational symmetry, but not any other type of triangle.

8 0
3 years ago
Consider the following function. f(x) = 2x3 + 9x2 − 24x (a) Find the critical numbers of f. (Enter your answers as a comma-separ
viktelen [127]

Answer:

(a) The critical number of f(x) are x=-4, 1

(b)

  • Increasing for (-\infty, -4)
  • Decreasing for (-4, 1)
  • Increasing for  (1, \infty)

(c)

  • relative maximum (-4, 112)
  • relative minimum (1, -13)

Step-by-step explanation:

(a) The critical numbers of a function are given by finding the roots of the first derivative of the function or the values where the first derivative does not exist. Since the function is a polynomial, its domain and the domain of its derivatives is (-\infty, \infty). Thus:

\frac{df(x)}{dx}  = \frac{d(2x^3+9x^2-24x)}{dx} =6 x^2+18x -24\\6 x^2+18x -24=0\\\boxed{x=-4, x=1}

(b)

  • A function f(x) defined on an interval is monotone increasing on (a, b) if for every x_1, x_2 \in (a, b): x_1 implies f(x_1)
  • A function f(x) defined on an interval is monotone decreasing on (a, b) if for every x_1, x_2 \in (a, b): x_1 implies f(x_1)>f(x_2)

Combining  the domain (-\infty, \infty) with the critical numbers we have the intervals (-\infty, -4), (-4, 1) and (1, \infty). Note that any of the points are included, in the case of the infinity it is by definition and the critical number are never included because the function monotony is not defined in the critical points, i.e. it is not monotone increasing or decreasing. Now, let's check for the monotony in each interval, for this, we check for the sign of the first derivative in each interval. Evaluating in each interval the first derivative (one point is enough), we obtain the monotony of the function to be:

  • Increasing for (-\infty, -4)
  • Decreasing for (-4, 1)
  • Increasing for  (1, \infty)

(c) From the values obtained in (a) so the relative extremum are the points (-4, 112) and (1, -13). The y-values are found by evaluating the critical numbers in the original function. Since the first derivative decreases after passing through  x=-4 and increases after passing through the point x=1 we have:

  • relative maximum (-4, 112)
  • relative minimum (1, -13)

3 0
3 years ago
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tatiyna
F(x) = 3x - 16x - x + 4
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lyudmila [28]

Answer:

The answer is below

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The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

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z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.8/\sqrt{45} }= -1.68

Therefore from the normal distribution table, P(x < 10) = P(z < -1.68) =  0.0465

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