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3 years ago

If (9 to the 2nd power)p = 9 to the 8th power , what is the value of p?

Mathematics

2 answers:

scoray [572]3 years ago

7 0

Answer:

p = 9^6

Step-by-step explanation:

(9^2)p = 9^8 may be solved for p as follows:

9^8

p = --------- = 9^(8-2) = 9^6

9^2

Novay_Z [31]3 years ago

3 0

$(9^2)^p=9^8\\\\9^{2p}=9^8\\\\2p=8\\\\p=4$

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A particular sound wave can be graphed using the function y = 1 sin 2x y = 1 sin 2 x . Find the amplitude of the function.

alexira [117]

Answer

Explanation

The general equation of a wave is ;

y = a sin(kX+Ф)

Where a represent the amplitude, 360/k represent the period of the wave and Ф represent the phase angle.

∴ In the equation y = 1 sin 2x,

Amplitude = 1

4 0

3 years ago

What is -x+3>2x+1 Help please!

scoray [572]

x<2/3

Is the answer of x

3 0

3 years ago

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A circle has a radius of \sqrt{13}√ 13 square root of, 13, end square root units and is centered at (-9.3,4.1)(−9.3,4.1)le

timofeeve [1]

Answer: The equation of the circle is

$x^2+y^2+18.6x-8.2y+90.3=0.$

Step-by-step explanation: We are given to write the equation of the circle with radius √13 units and center at the point (-9.3, 4.1).

We know that

the standard equation of a circle with radius r units and center at the point (h, k) is given by

$(x-h)^2+(y-k)^2=r^2.$

In the given circle,

radius, r = √13 units and center, (h, k) = (-9.3, 4.1).

Therefore, the equation of the circle will be

$(x-(-9.3))^2+(y-4.1)^2=(\sqrt{13})^2\\\\\Rightarrow (x+9.3)^2+(y-4.1)^2=13\\\\\Rightarrow x^2+18.6y+86.49+y^2-8.2y+16.81=13\\\\\Rightarrow x^2+y^2+18.6x-8.2y+103.3=13\\\\\Rightarrow x^2+y^2+18.6x-8.2y+90.3=0.$

Thus, the equation of the circle is

$x^2+y^2+18.6x-8.2y+90.3=0.$

7 0

3 years ago

In two or more complete sentences, describe the transformation(s) that take place on the parent function, f(x) = log(x), to achi

lubasha [3.4K]

Answer:

Shift 2 unit left

Flip the graph about y-axis

Stretch horizontally by factor 2

Shift vertically up by 2 units

Step-by-step explanation:

Given:

Parent function: $f(x)=\log x$

Transformation function: $f(x)=\log(-2x-4)+2$

Take -2 common from transform function f(x)

$f(x)=\log[-2(x+2)]+2$

Now we see the step-by-step translation

$f(x)=\log x$

Shift 2 unit left ( x → x+2 )

$f(x)=\log(x+2)$

Flip the graph about y-axis ( (x+2) → - (x+2) )

$f(x)=\log[-(x+2)]$

Stretch horizontally by factor 2 [ -x(x+2) → -2(x+2) ]

$f(x)=\log[-2(x+2)]$

Shift vertically up by 2 units [ f(x) → f(x) + 2 ]

$f(x)=\log[-2(x+2)]+2$

Simplify the function:

$f(x)=\log(-2x-4)+2$

Hence, Using four step of transformation to get new function $f(x)=\log(-2x-4)+2$

3 0

3 years ago

Read 2 more answers

Brent claims that more students at his school prefer hot dogs over hamburgers. His friend Shaun doesn’t agree. To settle their a

photoshop1234 [79]

Answer:

Using conditional probabilities it can be shown that the results are influenced by the gender.

Explanation:

To prove that the results are influenced by gender you can calculate both the probability of preferring hot dogs and the conditional probability of preferring a hot dog given that is a female.

If the two results are different the probability of preferring hot dog is dependent on whether the person is a female or a male.

The probability of preferring hot dogs given that is a female is stated by the problem: 34.2%.

The probability of preferring hot dogs by the whole sample is:

Number of males that prefer hot dogs: 184 (stated by the problem)
Number of females that prefer hot dogs:

100% - 34.2% = 65.8%

65.8% of 635 = 0.658 × 635 = 417.83 ≈ 418

Samples size: 542 males + 635 females = 1177

Probability of preferring hot dogs =

number of students that preffer hot dogs / number of students =

(184 + 418) / 1177 = 602 / 1177 = 0.5115 ≈ 51.2%

Thus, the probability of preferring hot dogs given that the student is a female (34.2%) is different from the probability of preferring hot dog for the whole sample, making the results dependent of the gender.

3 0

4 years ago