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3 years ago

Please help me solve the expression for “n”

Mathematics

1 answer:

Bingel [31]3 years ago

5 0

Answer:

n = 2

Step-by-step explanation:

In order for the ratio to have a value of 1, the sum of exponents in the numerator must equal the sum of exponents in the denominator:

n + 7 = 9

n = 9 -7 . . . . . . subtract 7 from both sides of the equation

n = 2

___

Alternatively, you can simplify the given expression:

$\dfrac{9^n(9^7)}{9^9}=1=\dfrac{9^n}{9^2}$

Hopefully, it is clear to you that the value of n must be 2 in order to make the numerator equal to the denominator.

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3 years ago

A rocket is launched from the top of a 55-foot cliff with an initial velocity of 138 ft/s.

melisa1 [442]

For this case we have that the equation that describes the height is:

$h = -16t ^ 2 + vt + c$

Where,

v: initial speed

c: initial height

Substituting values we have:

$h = -16t ^ 2 + 138t + 55$

Then, to find the time, we use the quadratic formula:

$t =\frac{-b +/-\sqrt{b^2 - 4ac} }{2a}$

Substituting values we have:

$t =\frac{-138 +/-\sqrt{138^2 - 4(-16)(55)} }{2(-16)}$

Rewriting:

$t =\frac{-138 +/-\sqrt{19044 + 3520} }{-32}$

$t =\frac{-138 +/-\sqrt{22564}}{-32}$

$t =\frac{-138 +/-150.21}{-32}$

We discard the negative root because we want to find the time.

We have then:

$t =\frac{-138 -150.21}{-32}$

$t =\frac{-288.21}{-32} \\t=9$

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3 years ago

Kari drew two parallel lines PQ and RS intersected by a transversal KL, as shown below:

Archy [21]

Answer: Same-Side Interior Angles Theorem

Step-by-step explanation:

Same-Side Interior Angles Theorem says that when two lines are parallel and a transversal intersects it , then the angles on the same interior side are supplementary.

We are given that Two parallel lines PQ and RS are drawn with KL as a transversal intersecting PQ at point M and RS at point N.

Angle QMN is shown congruent to angle LNS.

Also, angle QML and angle SNK are the angles lies on the same side of the transversal.

It means the measure of angle QML is supplementary to the measure of angle SNK [ By Same-Side Interior Angles Theorem ]

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3 years ago