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3 years ago

Which equation is the universe of y=9x^2-4

Mathematics

2 answers:

user100 [1]3 years ago

8 0

Answer:

$y = \frac{\sqrt{x+4} }{3}, \ y = -\frac{\sqrt{x+4} }{3}$

Step-by-step explanation:

To find inverse we replace and y first.

$y = 9x^2 - 4 \ becomes \ x = 9y^2 -4$

$Then \ solve \ for \ y\\\\9y^2 = x+ 4\\\\y^2 = \frac{x+4}{9}\\\\y = \pm \sqrt{\frac{x+4}{9}} \\\\y = \pm {\frac{\sqrt{x+4}}{3}$

Sladkaya [172]3 years ago

5 0

Step-by-step explanation:

keep in mind that, to get the inverse expression of any relation, we start off by doing a quick switcheroo on the variables, and then solve for "y", so let's do so,

You might be interested in

2x+y=-6<br><br>what are the x and y intercepts

Deffense [45]

Answer:

Step-by-step explanation:

y intercept

To find the y intercept, make x = 0

2(0) + y = - 6 zero times anything is 0

0 + y = -6

The y intercept is (0,-6)

x intercept

The x intercept happens when y = 0

2x + 0 = -6 zero added to anything = whatever you started with.

2x = - 6 Divide by 2

2x/2 = -6/2 Do the division

x = - 3

The x intercept = (-3,0)

5 0

4 years ago

Please show work for it.

Komok [63]

Answer:

7over9 or -7over9

Step-by-step explanation:

81x power 2 - 8 = 41

(left side) (right side)

first we let the 8 from left side go to the right side,so it will be +8:

81x power 2 = 41+ 8

=49

so now we let the 81 from left side go to right side, so it will be ÷81:

x power 2= 49 over 81

and now we let the power 2 (square) go to the other side so it will become square root:

x = + - √49 over 81

at the end, you will get 2 answers which is 7 over 9 and - 7 over 9

8 0

3 years ago

4÷25times4÷100times4÷4

notsponge [240]

Answer:

0.0064 is your answer

Step-by-step explanation:

because 4÷25 = 0.16 and 4÷100=0.04 and of course 4÷4=1

When the 0.16 and 0.04 that gets 0.0064

3 0

3 years ago

I now have another question to ask.

marissa [1.9K]

Answer:

23.6 ft

Step-by-step explanation:

Sketch a right triangle representing this situation. The length of the hypotenuse is 26 ft and the angle of elevation from ground to top of ladder is 65°. The "opposite side" is the reach of the ladder, which we'll call x.

Then:

opp

sin 65° = ----------
26 ft

or (26 ft)(sin 65°) = opp side = height off the ground of top of ladder.

Evaluating this, we get:

(26 ft)(0.906) = 23.56 ft, or, rounded off, 23.6 ft

The ladder reaches 23.6 ft up the side of the building.

8 0

3 years ago

A random sample of 20 students yielded a mean of ¯x = 72 and a variance of s2 = 16 for scores on a college placement test in mat

Helen [10]

Answer:

The 98% confidence interval for the variance in the pounds of impurities would be $8.400 \leq \sigma^2 \leq 39.827$ .

Step-by-step explanation:

1) Data given and notation

$s^2 =16$ represent the sample variance

s=4 represent the sample standard deviation

$\bar x$ represent the sample mean

n=20 the sample size

Confidence=98% or 0.98

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population mean or variance lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The Chi square distribution is the distribution of the sum of squared standard normal deviates .

2) Calculating the confidence interval

The confidence interval for the population variance is given by the following formula:

$\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}$

On this case the sample variance is given and for the sample deviation is just the square root of the sample variance.

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

$df=n-1=20-1=19$

Since the Confidence is 0.98 or 98%, the value of $\alpha=0.02$ and $\alpha/2 =0.01$ , and we can use excel, a calculator or a table to find the critical values.