Determine whether the sequence is arithmetic or geometric.sequence 1: 32, 16, 0, –16, ...
sequence 2: 32, 16, 8, 4, ...
which of the following statements are true regarding sequence 1 and sequence 2.

sequence 1 is arithmetic and sequence 2 is geometric.
both sequences are arithmetic.
both sequences are geometric.
sequence 2 is arithmetic and sequence 1 is geometric.

Answers

Answer 1

Answer: S1.
32, 16, 0, -16, ...
It's an arithmetic sequence:
$a_1=32;\ d=16-32=-16\n\na_n=a_1+(n-1)d\n\na_n=32+(n-1)\cdot(-16)=32-16n+16=48-16n$

S2.
32, 16, 8, 4, ...
It's a geometric sequence:
$a_1=32;\ r=16:32=(1)/(2)\n\na_n=a_1r^(n-1)\n\na_n=32\cdot\left((1)/(2)\right)^(n-1)$

Answer: sequence 1 is arithmetic and sequence 2 is geometric.

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What multiplies to 42 and adds to -27

Answers

Consider ways to multiply to get 42. Then see if the numbers can be used to make -27.

42 = 21 × 2...not going to work.
42 = 14 × 3...not going to work. (Though -14 and -3 add to -17)
42 = 7 × 6...not going to work.

There are no whole number solutions to this question.

Which expression is a difference of cubes?
X^6-6
X^6-8
x^8-6
X^8-8

Answers

Answer: The correct expression is, $x^6-8$

Step-by-step explanation:

$x^6$ is represented in cube form as, $(x^2)^3$

'8' is represented in cube form as, $2^3$

$x^8$ and '6' will not show cube form of integer power.

The expanded form of the given expression, $x^6-8$ is represented as,

$x^6-8=(x^2)^3-2^3$

This expression will showing the difference of cubes.

And the other options, $x^6-6,x^8-6,x^8-8$ will not show the difference of cubes.

Therefore, the correct answer is, $x^6-8$

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Further Explanation:

The cubic formula can be expressed as follows,

$\boxed{{a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)}$

Given:

The options are as follows,

(a). ${x^6} - 6$

(b). ${x^6} - 8$

(c). ${x^8} - 6$

(d). ${x^8} - 8$

Calculation:

8 is a cube of 2 and can be written as follows,

$8 = {2^3}$

${x^6}$ can be written as a cube of ${x^2}.$

${x^6} = {\left( {{x^2}} \right)^3}$

Use the identity ${a^3} + {b^3} = \left( {a + b} \right)\left( {{a^2} - ab + {b^2}} \right)$ in above expression.

$\begin{aligned}{x^6} - 8&= {\left( {{x^2}} \right)^3}- {\left( 2 \right)^3} \n&= \left( {{x^2} - 2} \right)\left( {{x^4} + 2{x^2} + 4} \right)\n\end{aligned}$

The expression $\boxed{{x^6} - 8}$ is a difference of cubes. Option (b) is correct.

Option (a) is not correct.

Option (b) is correct.

Option (c) is not correct.

Option (d) is not correct.

Learn more:

1. Learn more about unit conversion brainly.com/question/4837736

2. Learn more about non-collinear brainly.com/question/4165000

3. Learn more aboutbinomial and trinomial brainly.com/question/1394854

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Exponents and Powers

Keywords: Solution, factorized form, $x^12y^18+1$ , exponents, power, equation, power rule, exponent rule.

A piling for a high-rise building is pushed by two bulldozers at exactly the same time. One bulldozer exerts a force of 1250 pounds in a westerly direction. The other bulldozer pushes the piling with a force of 2650 pounds in a northerly direction. What is the magnitude of the resultant force upon the piling, to the nearest ten pounds?

Answers

The forces result in a right triangle. To obtain the resultant force, one can simply use the Pythagorean theorem. 1250 lbf and 2650 lbf both act as the legs of the triangle. Obtaining the hypotenuse via the theorem would yield the resultant force. This is done below:

c^2 = a^2 + b^2
c^2 = (1250)^2 + (2650)^2
c = 2930.017 lbf

Therefore, the magnitude of the resultant force is approximately equal to 2930 lbf.

The magnitude of the resultant force is 2930 pounds.

What is the resultant force?

The resultant force is the single force that has the same effect as two or more forces acting together. Two forces that act in the same direction produce a resultant force that is larger than either individual force.

If one bulldozer exerts force in west direction of magnitude 1250 pounds and the other exerts a force in north direction of magnitude 2650 pounds .

let F $_1$ = 1250 pounds and F $_2$ = 2650 pounds

Using magnitude,

|F|=√F $_1$ ²+ F $_2$ ²

|F|= √1250²+2650²

= √1562500+7022500

=√2*2*5*5*5*5*5*5*5*5+2*2*5*5*5*5*53*53

=√2*2*5*5*5*5(5*5*5*5+53*53)

=50√3434

= 2930.017 pounds.

Hence, the magnitude of the resultant force is approximately equal to 2930 pounds.

Learn more about of Resultant force here:

brainly.com/question/16380983

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Bc reflects about a line such that N is the reflection of B and O is the reflection of C. Point N is shown on the coordinate plane, but point O is not. What will the coordinates of point O be?

Answers

From my research, the coordinate points can be found on image below. Since N is the reflection of B and O is the reflection of C, if we were to draw a line to the right of N and a vertical line below C, the point of intersection of these two lines should give us the location of point O. Doing just that, point O is found at (5,5).

The coordinates of point O of the given Reflection is; 5, 5

How to find the point coordinates?

The coordinates point is missing and so I have attached it.

Now, from the question, we are told that N is the reflection of B and O is the reflection of C. Thus, from the attached image, drawing a line to the right of N and a vertical line below C, the point of intersection of these two lines would give us the location of point O.

Drawing a line to the right of N and a vertical line below C, the point of intersection of these two lines which is point O has coordinates at (5,5).

Read more about Point Coordinates at; brainly.com/question/17206319

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Write a compound inequality that represents the evelation range for each type of plant life

Answers

Let E=elevation range
Low elevation=1700≤E≤2500
Mid elevation= 2500≤E≤4000
Sulbarine=4000≤E≤6500
Alpine=6500≤E≤14,410

Final answer:

To represent the elevation range for each type of plant life, write a compound inequality for each type using the minimum and maximum elevations.

Explanation:

To write a compound inequality to represent the elevation range for each type of plant life, we need to consider the minimum and maximum elevations for each type. Let's say Type A has a minimum elevation of 1000 ft and a maximum elevation of 3000 ft, and Type B has a minimum elevation of 2000 ft and a maximum elevation of 4000 ft. We can represent the elevation range for Type A as: 1000 ≤ x ≤ 3000, and for Type B as: 2000 ≤ x ≤ 4000.

Learn more about Compound inequality representation here:

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Write an algebraic expression that models the word phrase. the sum of the product of a number x and 22, and 11Choose the correct answer below
A. (2+11)x
B. 22+x
C. 11x+2
D. 2x+11

Answers

my math teacher said it was c

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