106. Find the inverse g for each function f. c.f(x) =23x+ 1

What is the length of the conjugate axis?

Lana71 [14]

ANSWER

The length of the conjugate axis is 6 units.

EXPLANATION

The given hyperbola has equation:

$\frac{(x - 1)^{2} }{25} - \frac{ {(y + 3)}^{2} }{9} = 1$

We can rewrite this equation in the form:

$\frac{(x - 1)^{2} }{ {5}^{2} } - \frac{ {(y + 3)}^{2} }{ {3}^{2} } = 1$

We compare this equation to:

$\frac{(x - h)^{2} }{ {a}^{2} } - \frac{ {(y - k)}^{2} }{ {b}^{2} } = 1$

This implies that;

$a = 5$

and

$b = 3$

The length of the conjugate axis of a hyperbola is

$= 2b$

Substitute b=3 to obtain;

$= 2 \times 3$

$= 6$

5 0

4 years ago

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8.Find the value of c that makes the expression be a perfect square trinomial p^2-30p+c

Darina [25.2K]

Hope this is the right one.

Problem 8
p^2 - 30p + c
Step One
Take 1/2 of - 30
1/2 * -30 = - 15

Step 2
Square -15
(-15)^2 = 225
c = 225

Problem Nine
$\text{x = }\dfrac{ -b \pm \sqrt{b^{2} - 4ac } }{2a} 
$
a = 1
b = 4
c = -15
$\text{x = }\dfrac{ -4 \pm \sqrt{4^{2} - 4*1*(-15) } }{2*1}$
$\text{x = }\dfrac{ -4 \pm \sqrt{\text{16} + \text{60} } }{2}$

x = [-4 +/- sqrt(76)] / 2
x = [-4 +/- 2*sqrt19]/2
x = [-4/2 +/- 2/2 sqrt[19]
x = - 2 +/- sqrt(19)

x1 = - 2 + sqrt(19)
x2 = -2 - sqrt(19)

These two can be broken down more by finding the square root. I will leave them the way they are. It's just a calculator question if you want it to go into decimal form.

Problem Ten

a = 1
b = 4
c = -32

The discriminate is sqrt(b^2 - 4ac)
D = sqrt(b^2 - 4ac)
D = sqrt(4^2 - 4(1)(-32)
D = sqrt(16 - - 128)
D = sqrt(16 + 128)
D = sqrt(144)
D = +/- 12

Since D can equal + or minus 12 there must be 2 possible (and different) roots. As a matter of fact, this quadratic can be factored.
(x + 8)(x - 4) = y
But that' s not what you were asked for.
The discriminate is > 0 so the roots are going to be real.
Answer; The discriminate is > 0 so there will be 2 real different roots.

4 0

3 years ago

PLease dont answer if you dont know... Use the Law of Sines to find side "b" of the triangle.

alexdok [17]

Using the law of sins:

side a / sin (angle A) = side b / sin(Angle B)

Side a is opposite angle A, so from the picture we know side a = 50, angle A is 58 degrees and angle B is 48 degrees.

replace those values in the formula we get:

50 / sin(58) = b/ sin(48)

so now we can cross multiply the 2 fractions to get:

50 * sin(48) = b*sin(58)

to get b by itself, divide both sides by sin(58) to get:

b = (50*sin(48)) / sin(58)

b = 43.82

You may need to round the answer as needed.

4 0

4 years ago

A liquid oral concentrate of morphine sulfate contains 2.4 g of morphine sulfate in a 120-mL bottle. Calculate the concentration

MrMuchimi

Answer:

20 mg/ml.

Step-by-step explanation:

We have been given that a liquid oral concentrate of morphine sulfate contains 2.4 g of morphine sulfate in a 120-mL bottle.

$\text{Concentration of morphine sulfate on g/mL basis}=\frac{\text{2.4 g}}{\text{120 ml}}$

To convert the concentration of morphine sulfate on a mg/mL basis, we need to convert 2.4 grams to milligrams.

1 gram equals 1000 milligrams.

$\text{Concentration of morphine sulfate on mg/mL basis}=\frac{\text{2.4 g}}{\text{120 ml}}\times\frac{\text{1,000 mg}}{\text{1 g}}$

$\text{Concentration of morphine sulfate on mg/mL basis}=\frac{2.4\times\text{1,000 mg}}{\text{120 ml}}$

$\text{Concentration of morphine sulfate on mg/mL basis}=\frac{2400\text{ mg}}{\text{120 ml}}$

$\text{Concentration of morphine sulfate on mg/mL basis}=\frac{20\text{ mg}}{\text{ml}}$

Therefore, the concentration of morphine sulfate would be 20 mg per ml.

5 0

3 years ago

Which transformation shows a translation of 3 units to the right?

Marina CMI [18]

It is the transformation shown in (B)

(look at one point of the letter P and how it moves precisely 3 units. Also there is only the move, no flipping of the figure)

4 0

4 years ago

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