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Mandarinka [93]
3 years ago
11

The first three steps for solving the quadratic equation by completing the square are shown. Fill in the missing number in the l

ast step.
9x2 +54x = 7

9(x2 + 6x) = 7

9(x2 + 6x + 9) = 7 +.?
Mathematics
2 answers:
gulaghasi [49]3 years ago
5 0
Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left. 
<span>9x2 +54x = 7
</span>
2. Make sure that the coefficient of the x^2 term is 1.
<span>9(x2 + 6x) = 7
</span>
3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.
<span>9(x2 + 6x + 9) = 7 + 81

9(x+3)^2 = 88
</span>
Westkost [7]3 years ago
4 0

Answer:

? = 81

Step-by-step explanation:

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A solid lies between planes perpendicular to the x-axis at x tox=. The cross sections perpendicular to the x-axis are circular d
cluponka [151]

It's unclear what the planes are supposed to be, so I'll take x=a and x=b with 0\le a.

The cross sections are disks with diameter \csc x-\cot x, so each disk of thickness \Delta x has a volume of

\dfrac{\pi(\csc x-\cot x)^2}4\Delta x

Then taking infinitesimally thin disks, we find the solid has a volume of

\displaystyle\frac\pi4\int_a^b(\csc x-\cot x)^2\,\mathrm dx

Since

(\csc x-\cot x)^2=2\csc^2x-2\csc x\cot x-1

and

\dfrac{\mathrm d(\csc x)}{\mathrm dx}=-\csc x\cot x

\dfrac{\mathrm d(\cot x)}{\mathrm dx}=-\csc^2x

it follows that the volume is

\displaystyle\frac\pi4\left(-2\cot x+2\csc x-x\right)\bigg|_a^b

=\dfrac\pi4(2(\cot a-\cot b)+2(\csc b-\csc a)+a-b)

=\dfrac\pi4\left(2\tan\dfrac b2-2\tan\dfrac a2+a-b\right)

3 0
3 years ago
Pls help!!!! Match all of the angle and arc measures with the appropriate letter ? A through H
Charra [1.4K]

Answer:

Step-by-step explanation:

a = 180 - 2(19) = 142°

b = 90° Triangle in a circle with one side as a diameter makes right triangle

c = 2(19) = 38°

d = 38°

e = 38°

f = 19° alternate angle

g = 19° equilateral triangle

h = 90 - 19 = 71°

8 0
2 years ago
Solve for a <br> -3= 5a/7+4/7
Nastasia [14]

Answer:

a = -5

Step-by-step explanation:

4 0
3 years ago
Write an expression for each sentence
Nitella [24]

Answer:

  1. x^2+y
  2. 3(n-7)
  3. 37x-9.85

Step-by-step explanation:

1. If x represents a number, then x^2 represents its square. If y represents a second number, then the sum of that square and the second number is ...

  x^2 + y

__

2. The difference of a number (n) and 7 is (n-7). Three times that difference is ...

  3(n - 7)

__

3. If x represents a number, then the product of 37 and a number is 37x. 9.85 less than that is ...

  37x - 9.85

7 0
3 years ago
What the slope of a line
swat32

Answer:

The slope of a line is a number that measures its "steepness", usually denoted by the letter m. It is the change in y for a unit change in x along the line.

Hope it helps.

5 0
3 years ago
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