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2 years ago

Write the equation -4x^2+9y^2+32x+36y-64=0 in standard form. Show each step of the process.

Mathematics

1 answer:

Blizzard [7]2 years ago

3 0

Answer:

The answer to your question is below

Step-by-step explanation:

-4x² + 9y² + 32x + 36y - 64 = 0

-4x² + 32x + 9y² + 36y = 64

-4(x² + 8x ) + 9(y² + 4x ) = 64 Factor coefficients

-4(x² + 8x + 4²) + 9(y² + 4x + 2²) = 64 - 64 + 36 Complete trinomials

-4(x + 4)² + 9(y + 2)² = 36 Factor trinomials

$\frac{-4(x+4)^{2} }{36} + \frac{9(y + 2)^{2} }{36} = \frac{36}{36}$

Divide by 36

$- \frac{(x+ 4)^{2} }{9} + \frac{(y + 2)^{2} }{4} = 1$ Simplify

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Suppose the mean height for adult males in the U.S. is about 70 inches and the standard deviation is about 3 inches. Assume men’

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Question options :

a. They should be between 64 and 76 inches tall.

b. They should be close to the height that is 95% of the mean. That is, 66.5 inches, plus or minus 2 standard deviations.

c. They should be at or below the 95th percentile, which is 74.92 inches.

d. None of the above.

Answer: a. They should be between 64 and 76 inches tall.

Step-by-step explanation:

Given the following :

Assume men's height follow a normal curve ; and :

Mean height = 70 inches

Standard deviation= 3 inches

According to the empirical rule ;

Assuming a normal distribution with x being random variables ;

About 68% of x-values lie between -1 to 1 standard deviation of the mean. With about 95% of the x values lying between - 2 and +2 standard deviation of mean. With 99.7% falling between - 3 to 3 standard deviations from the mean.

Using the empirical rule :

95% will fall between + or - 2 standard deviation of the mean.

Lower limit = - 2(3) = - 6

Upper limit = 2(3) = 6

(-6+mean) and (+6+ mean)

(-6 + 70) and (6+70)

64 and 76

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2 years ago

What is the opsilute value for 27/90 and 100/99

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Answer:

3 /10

Decimal Form:

0.3

Step-by-step explanation:

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2 years ago

The graph shows the relationship between the number of apples and their cost. For the point (1, r), what is the value of r?

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Answer:

Step-by-step explanation:

When you check the point that is on X, it is a little over halfway to the point 1,2. It would be like 1,1.5 or 1,1.6.

5/3 is the equivalent to 1.6 so that answer would make the most sense.

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2 years ago

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The table represents an exponential function. A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4

scoray [572]

Answer:

The multiplicative rate of change of the function is $\dfrac{2}{3}$

Step-by-step explanation:

You are given the table

$\begin{array}{cc}x&y\\ \\1&6\\2&4\\ \\3&\dfrac{8}{3}\\ \\4&\dfrac{16}{9}\end{array}$

An exponential function can be written as

$y=a\cdot b^x,$

where b is the multiplicative rate of change of the function.

Find a and b. Substitute first two corresponding values of x and y into the function expression:

$6=a\cdot b^1\\ \\4=a\cdot b^2$

Divide the second equality by the first equality:

$\dfrac{4}{6}=\dfrac{a\cdot b^2}{a\cdot b^1}\Rightarrow b=\dfrac{2}{3}$

Substitute it into the first equality:

$6=a\cdot \dfrac{2}{3}\Rightarrow a=\dfrac{6\cdot 3}{2}=9$

So, the function expression is

$y=9\cdot \left(\dfrac{2}{3}\right)^x$

Check whether remaining two values of x and y suit this expression:

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So, the multiplicative rate of change of the function is $\dfrac{2}{3}$

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2 years ago

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