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liq [111]
2 years ago
8

Simplify this power raised to a power: (54)4 1. Expand using four factors of 54:         54 ∙ 54 ∙ 54 ∙ 54 2. Apply the product

of powers rule:         54+ 4+ 4+ 4 3. Simplify:                   5x What is the value of x in the simplified power? x =
Mathematics
2 answers:
Olegator [25]2 years ago
4 0

Answer:

X=16

Step-by-step explanation:

sasho [114]2 years ago
3 0

Answer:

x=16

Step-by-step explanation:

you add all the 4s from the second step and get a product of 16.

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On a coordinate plane, square P Q R S is shown. Point P is at (4, 2), point Q is at (8, 5), point R is at (5, 9), and point S is
sergey [27]

Answer:

(D)The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.

Step-by-step explanation:

  • Point P is at (4, 2),
  • Point Q is at (8, 5),
  • Point R is at (5, 9), and
  • Point S is at (1, 6)

Midpoint of SQ =\frac{1}{2}(1+8,5+6)=(4.5,5.5)

Midpoint of PR =\frac{1}{2}(4+5,2+9)=(4.5,5.5)

Now, we have established that the midpoints (point of bisection) are at the same point.

Two lines are perpendicular if the slope of one is the negative reciprocal of the other.

In option D

  • Slope of RP =7
  • Slope of SQ  =-\dfrac17

Therefore, lines RP and SQ are perpendicular.

Option D is the correct option.

6 0
2 years ago
The product of two consecutive, negative integers is 182. What equation represents the situation?
Sholpan [36]
-13 and -14

They both are consecutive negative integers that multiply to 182.
4 0
2 years ago
Read 2 more answers
Point H is the circumcenter of triangle DEF. Which must be true? Check all that apply. Point H is the center of the circle that
Dmitrij [34]
The circumcenter of a triangle is the intersection of the perpendicular bisectors.It is the center of the triangle's circumcircle. And a circumcircle is the circumscribed circle of the triangle. This unique circle passes through each of the triangle's three vertices. According to these definitions the following statement is true:
Point H is the center of the circle that passes through points D, E, and F. 


5 0
2 years ago
The sequence 6, 18, 54, 162, … shows the number of pushups Kendall did each week, starting
Andrei [34K]

a) The given sequence is geometric.

b) The next term in the sequence is 486

c) The rule is: a_n=6(3)^{n-1}

The 20th week will be: a_{20}=6973568802

Step-by-step explanation:

The sequence 6, 18, 54, 162, … shows the number of push ups Kendall did each week, starting  with her first week of exercising.

Part a) Is this an arithmetic or geometric sequence?

An arithmetic sequence is one, where difference between two consecutive terms is constant.

In the given sequence 6, 18, 54, 162,

18-6 = 12

54-18= 36

<u>The difference is not constant so, the sequence is not arithmetic.</u>

A geometric sequence is one, where ratio between two consecutive terms is constant.

In the given sequence 6, 18, 54, 162,

18/6 = 3

54/18 = 3

162/54 = 3

<u>The ratio is constant so, the sequence is geometric.</u>

The given sequence is geometric.

Part b) How can you find the next number in the sequence?

We can find next number in the sequence by using formula:

a_n=a(r)^{n-1}

where a_n= nth term

a= first term

r= common ratio

The next term will be 5th term of the sequence.

Finding 5th term:

a_n=a(r)^{n-1}\\a_5=6(3)^{5-1}\\a_5=6(3)^4\\a_5=6*81\\a_5=486

So, the next term in the sequence is 486

Part c) Give the rule you would use to find the 20th week. Find the 20th week

The rule used to find 20th week would be:

a_n=6(3)^{n-1}

Here n=20

Finding 20th week

a_n=6(3)^{n-1}\\a_{20}=6(3)^{20-1}\\a_(20)=6(3)^{19}\\a_{20}=6973568802

5 0
2 years ago
Out of six computer chips, two are defective. If two chips are randomly chosen for testing (without replacement), compute the pr
Ratling [72]

Answer:

The probability that of the two chips selected both are defective is 0.1089.

Step-by-step explanation:

Let <em>X</em> = number of defective chips.

It is provided that there are 2 defective chips among 6 chips.

The probability of selecting a defective chip is:

P(X)=p=\frac{2}{6}=0.33

A sample of <em>n</em> = 2 chips are selected.

The random variable <em>X</em> follows a Binomial distribution with parameter <em>n</em> = 2 and <em>p</em> = 0.33.

The probability function of a Binomial distribution is:

P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0, 1, 2, ...

Compute the probability that of the two chips selected both are defective as follows:

P(X=2)={2\choose 2}(0.33)^{2}(1-0.33)^{2-2}=1\times 0.1089\times 1=0.1089

Thus, the probability that of the two chips selected both are defective is 0.1089.

The sample space of selecting two chips is:

S = (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)

     (2, 1),  (2, 3), (2, 4), (2, 5), (2, 6)

     (3, 1), (3, 2), (3, 4), (3, 5), (3, 6)

     (4, 1), (4, 2), (4, 3), (4, 5), (4, 6)

     (5, 1), (5, 2), (5, 3), (5, 4), (5, 6)

     (6, 1), (6, 2), (6, 3), (6, 4), (6, 5)

3 0
2 years ago
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