9 to the third power

Answer:  The correct option is (B) [tex]a_n=3n+9.[/tex]

Step-by-step explanation:  We are given to select the equation that represents the nth term of the following sequence :

12,   15,   18,   21,  .    .   .

We see that

the given sequence is an arithmetic one with first term a = 12  and common difference d given by

d = 15 - 12 = 18 - 15 = 21 - 18 =  .   .   .   =3.

We know that

the nth term of an arithmetic sequence with first term a and common difference d is given by

[tex]a_n=a+(n-1)d.[/tex]

Therefore, the nth term of the given sequence is

[tex]a_n=a+(n-1)d=12+(n-1)\times3=12+3n-3=3n+9.[/tex]

Thus, the required nth term of the given sequence is [tex]a_n=3n+9.[/tex]

Option (B) is CORRECT.

Answer:

x^3 - x^2 - 17x + 12

Step-by-step explanation:

To multiply two polynomials together, first multiply each term of one polynomial by each term of the other polynomial. Then, collect like terms.

(x + 4)(x^2 - 5x + 3) =

Multiply x by each term of x^2 - 5x + 3. Multiply 4 by each term of x^2 - 5x + 3.

= x^3 - 5x^2 + 3x + 4x^2 - 20x + 12

Now collect like terms and write them in descending order of degree.

= x^3 - x^2 - 17x + 12

Answer:

x^3-x^2-17x+12

Step-by-step explanation:

Answer:

1 2/3 pages per minute

Step-by-step explanation:

1) 10/6 = 1.6666666666666 = 1 2/3

Final answer:

To calculate the printing time per page for a color printer, divide the total printing time by the number of pages. In this case, it takes 0.6 minutes to print one page.

Explanation:

To find out how many minutes it takes to print one page on a color printer that prints 10 pages in 6 minutes, we can use time quantification. We divide the total time taken to print the pages by the number of pages printed. So, performing the calculation:

Identify the total time taken for a known number of pages: 6 minutes for 10 pages.

Divide the total time by the number of pages to find the time per page: 6 minutes \/ 10 pages = 0.6 minutes per page.

Hence, the printer takes 0.6 minutes to print one page.

The measure of the congruent angle of the triangle MNO will be 28.7°.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

Triangle MNO is an isosceles triangle in which only one angle measures 122.6°.

Let the measure of the congruent angle be 'x'. Then the equation is given as,

x + x + 122.6° = 180°

2x = 180° - 122.6°

2x = 57.4°

x = 28.7°

The measure of the congruent angle of the triangle MNO will be 28.7°.

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Answer:

(x + 9, y - 12)

Step-by-step explanation:

It's just telling the change from the pre image to the post image. Sorry for the lame explanation lol

Answer:

D (x.y) right arrow (x + 9, y - 12)

Step-by-step explanation:

hello this is the answer yw have a wonderful day!! :)

Answer:

Option A. Angle RNQ is equal in measure to arc PR.

Step-by-step explanation:

we know that

The triangle NOR is an equilateral triangle, because has three equal sides

NO=OR=RN ----> radius of the circle O

therefore

The interior angles of the triangle NOR measures 60 degrees each

so

∠RNO=60°

Find the measure of angle RNQ

we have that

∠RNO+∠RNQ=180° ------> by supplementary angles (linear pair)

substitute

60°+∠RNQ=180°

∠RNQ=180°-60°=120°

we know that

arc PR= 120° ----> see the graph

therefore

∠RNQ=arc PR

Angle RNQ is equal in measure to arc PR.

Answer:

it’s a

Step-by-step explanation:

Answer:

B.  The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee

Step-by-step explanation:

Lets define correlation first:

Correlation is the connection or link between two things. We have to remember that both things or events being correlated doesn't mean that one is caused by the other.

By observing the given question we can conclude that the the increase in sale of hot chocolate is correlated to the sale of coffee but none of them is caused by each other.

Hence, the correct answer is:

B.  The increase in the sale of hot chocolate is correlated to, but not caused by, the sale of coffee..

Answer:

The correct answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\left(\dfrac{1}{7}\right)^{3a+3}=343^{a-1}\qquad\text{use}\ a^{-n}=\left(\dfrac{1}{a}\right)^n\\\\7^{-(3a+3)}=(7^3)^{a-1}\qquad\text{use the distributive property}\\\\7^{-3a-3}=7^{3a-3}\iff-3a-3=3a-3\qquad\text{add 3 to both sides}\\\\-3a=3a\qquad\text{subtract}\ 3a\ \text{from both sides}\\\\-6a=0\qquad\text{divide both sides by (-6)}\\\\a=0[/tex]

the greatest common factor of 270 and 360 is 90.

because 2 x 3 x 3 x 5 = 90

the factors of each number is:

270: 1, 270, 2, 135, 3, 90, 5, 54, 6, 45, 9, 30, 10, 27, 15, 18

360: 1, 360, 2, 180, 3, 120, 4, 90, 5, 72, 6, 60, 8, 45, 9, 40, 10, 36, 12, 30, 15, 24, 18, 20

Answer:

The answer is x^2-4x+1

Step-by-step explanation:

For this case, we must build a quotient that, when multiplied by the divisor, eliminates the terms of the dividend, until reaching the remainder.

It must be fulfilled that:

Dividend = Quotient * Divider + Remainder

Answer:

Option C

See attached image

Answer:

36

Step-by-step explanation:

(-6)^ 2

-6*-6 = 36

Answer:

The value of F(5) + G(6) is 63.

Step-by-step explanation:

[tex]F(x)=x^2+5x[/tex]

[tex]G(x)=2x+1[/tex]

Value of F(x) , x = 5

[tex]F(5)=5^2+5\times 5=50[/tex]

Value of G(x) , x = 6

[tex]G(6)=2\times 6+1=13[/tex]

F(5) + G(6) :

= 50 + 13 = 63

The value of F(5) + G(6) is 63.

Answer:

A; [tex]\frac{-5}{-3}[/tex]

Step-by-step explanation:

[tex]-(-\frac{5}{3}) = \frac{5}{3}[/tex]

[tex]\frac{-5}{-3} = \frac{5}{3}[/tex]

[tex]\frac{5}{3} = \frac{5}{3}[/tex]

The mathematical expression -(-5/3) translates to positive 5/3 due to the fact that two negative signs cancel each other out. The expressions equivalent to this is -5/-3, while 5-(-3) is not equivalent.

In mathematics, negative signs can change the sign of the operand they are applied to. Essentially, the expression -(-5/3) means the negative of negative 5/3. In mathematics, multiplying or dividing two negative numbers yields a positive result, hence two negative signs cancel each other out. So, -(-5/3) becomes positive (5/3).

Now, let's look at the options provided:

a. -5/-3: As stated before, two negative signs cancel each other, so the result is positive 5/3 which is the same as -(-5/3).

b. 5-(-3): According to the order of operation rules (PEMDAS/BODMAS), subtraction and division operations aren't equivalent. Therefore, this expression is not equivalent to -(-5/3).

So, the answer is a. -5/-3.

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The solution to the inequality is [tex]\(x > -9\)[/tex]. Therefore, the option b is correct.

To solve the inequality [tex]\(-3x - 7 < 20\)[/tex], we'll isolate the variable [tex]\(x\)[/tex] step by step.

Given inequality:

[tex]\[ -3x - 7 < 20 \][/tex]

Add 7 to both sides of the inequality:

[tex]\[ -3x < 20 + 7 \ \\\\\\[ -3x < 27 \][/tex]

Now, divide both sides by [tex]\(-3\)[/tex]. Remember, when dividing or multiplying by a negative number, we need to reverse the inequality sign:

[tex]\[ x > \frac{27}{-3} \ \\\\\\[ x > -9 \][/tex]

The solution to the inequality is [tex]\(x > -9\)[/tex]. This means that any value of [tex]\(x\)[/tex] that is greater than -9 satisfies the inequality [tex]\(-3x - 7 < 20\)[/tex].

Answer:

B and D

Step-by-step explanation:

Given a line with slope m = - [tex]\frac{3}{5}[/tex]

Since the lines are parallel we require the points with the same slope

Using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = 8, 8) and (x₂, y₂ ) = (2, 2)

m = [tex]\frac{2-8}{2-8}[/tex] = 1 ← not parallel

Repeat with (x₁, y₁ ) = (5, - 1) and (x₂, y₂ ) = (0, 2)

m = [tex]\frac{2+1}{0-5}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel

with (x₁, y₁ ) = (- 3, 6) and (x₂, y₂ ) = (6, - 9)

m = [tex]\frac{-9-6}{6+3}[/tex] = - [tex]\frac{5}{3}[/tex] ← not parallel

with (x₁, y₁ ) = (- 2, 1) and (x₂, y₂ ) = (3, - 2)

m = [tex]\frac{-2-1}{3+2}[/tex] = - [tex]\frac{3}{5}[/tex] ← Parallel

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (5, 5)

m = [tex]\frac{5-2}{5-0}[/tex] = [tex]\frac{3}{5}[/tex] ← not parallel

The ordered pairs (-5, -1) and (0, 2); (0,2) and (5,5) could be points on a parallel line because they have the same slope according to the slope formula.

In Mathematics, to find whether two points could be on a parallel line, we first need to understand the concept of slope. The slope of a line is determined by the ratio of the vertical change (delta y) to the horizontal change (delta x) between any two points on a line. It is often expressed as 'rise over run'.

If two lines are parallel, they have the same slope. Now, let's check the given ordered pairs. Using the slope formula (slope = (y₂-y₁) / (x₂-x₁)), you find the slope between each set of points:

From the calculation, (-5, -1) and (0, 2) have the same slope with (0,2) and (5,5). Therefore, the lines passing through these pairs of points are parallel to each other.

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Answer:

127

Step-by-step explanation:

As we know that the sum of all angles of a triangle is 180°.

So, here we will apply this knowledge.

[tex]115\°+12\°+x\°=180\°[/tex]

[tex]127\°+x\°=180\°[/tex]

Now, we will subtract 127° from both sides of the equation, and we get;

[tex]x\°=180\°-127\°[/tex]

[tex]x\°=53\°[/tex]

Therefore,[tex]x=53.[/tex]

The value of x° is 53°.

Hence, the third angle in the given triangle is 53°.

A triangle is a 3-sided polygon sometimes (but not very commonly) called the trigon. Every triangle has three sides and three angles, some of which may be the same.

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon. The above figure is a triangle denoted as △ABC. Examples of Triangles. Some real-life examples of triangles include sandwiches, traffic signs, cloth hangers, and a rack in billiards.

All triangles have three sides and three corners (angles). The point where two sides of a triangle meet is called a vertex. The base of a triangle can be any one of its three sides, but it is usually the bottom one.

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Answer:

Option 2

Step-by-step explanation:

As we can see, the old graph was:

y=x^2

And the new graph is:

y = -x^2 + 3

We can determine from the new graph that the minus sign with x^2 means the graph is reflected upon x-axis.

Now, there is 3 with the new graph. As 3 is separate from the function, this means there is vertical shift. Since the sign of the constant defines the direction of shift, the positive or plus sign means the shifting is upwards while the negative sign means downward shifting.

The given new function is obtained from reflecting the old function over the x-axis and shifting up 3.

So, option 2 is correct ..

Answer:

b less than or equal to -2.

Step-by-step explanation:

- 2/3 (9+12b) ≥ 10

-6 - 8b ≥ 10

-8b ≥ 16

b ≤ -2.    ( Note the inequality sign flips as we are dividing by a negative).

Answer:18542

Step-by-step explanation:simplemath

The diameter of the circular DVD is d = 12 cm

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the diameter of the circular DVD be d

The total number of ridges = 73,000

The total number of valleys = 73,000

The width of each ridge = 0.000032 cm

The width of each valley = 0.000074 cm

The length of center portion c = 4.26 cm

And , the diameter of circular DVD = total width of ridges + total width of valleys + center portion

The total width of ridges = ( 0.000032 cm ) x 73,000

The total width of valleys = ( 0.000074 cm ) x 73,000

So , the total width of ridges and valleys  = 73,000 ( 0.000106 ) = 7.738 cm

On simplifying , we get

The diameter of circular DVD d = 7.738 cm + 4.26 cm

The diameter of circular DVD d = 11.998 cm

The diameter of circular DVD d ≈ 12 cm

Hence , the diameter of the circular DVD is 12 cm

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Answer:

$2,830.09

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 5.8/100

r = 0.058 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,000.00(1 + 0.058/12)(12)(6)

A = 2,000.00(1 + 0.004833333)(72)

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $2,000.00 at a rate of 5.8% per year compounded 12 times per year over 6 years is $2,830.09.

The question asks about the amount of money Haley would have after 6 years, saving $2000 in an account earning 5.8% interest compounded monthly. Using the compound interest formula, she would have approximately $2780.73.

This question deals with a financial concept known as compound interest. The formula for compound interest is A = P(1+r/n)^(nt), where A is the amount that the principal P has grown to after n number of times compounded over t periods at an interest rate of r. To calculate how much money Haley has, plug in the values: P=$2000, r=5.8/100=0.058, n=12 (since interest is compounded monthly), and t=6 years.

Therefore, the money Haley has is A=$2000 (1+0.058/12)^(12×6) ≈ $2780.73. Thus, after 6 years, Haley has approximately $2780.73, due to the monthly compounded interest of her savings.

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Answer:

31 / 12

Step-by-step explanation:

To get the perimeter, just add up all the sides of the parallelogram, so 5/8 + 5/8 + 2/3 + 2/3 = 31/12

In order to add the numbers 9.73 and 21.6 correctly, follow the steps below:

Step 1: Write the numbers so that the decimal points are aligned. If the numbers have a different number of decimal places, you can add zeros to the end of one of the numbers so that they both have the same number of decimal places. This doesn't change the value of the number, but it makes them easier to add.

```
 9.73
+21.60
```

Step 2: You begin adding from the rightmost digit and move to the left, regrouping (carrying over) as necessary.

Starting with the rightmost decimal digits, you have:

```
 3 (from 9.73)
+ 0 (from 21.60 because we added a zero to match the number of decimal places)
```

Adding these together, you simply get 3 since 3 + 0 = 3.

Step 3: Now add the second rightmost decimal digits:

```
 7 (from 9.73)
+ 6 (from 21.60)
```

Adding these together, 7 + 6 = 13, so you write down the 3 and carry over the 1 to the next higher place value.

Step 4: Add the digits to the left of the decimal point next, remembering to add any carried over value:

```
 1 (carried over from the previous step)
+ 9 (from 9.73)
+ 1 (from 21.60, there's no decimal here but we align based on the decimal point)
```

This gives us 1 + 9 + 1 = 11. So we place the 1 right to the left of the decimal point and carry over the other 1.

Step 5: Continue to the next highest place value:

Since there is no other digit in 9.73 at this place value, we can simply add what we have:

```
 1 (carried over from the previous step)
+ 0 (since there is no other digit in 9.73)
+ 2 (from 21.60)
```

This gives us 1 + 0 + 2 = 3.

Now, combine all of the numbers we've placed:

```
 31.33
```

So, the correct way to add 9.73 and 21.6 is to align the digits on the decimal point and add from right to left, regrouping as necessary. This corresponds to answer choice D.

Answer:

g = 8.  (Answer C)

Step-by-step explanation:

We are given 8/3 = g/3.

If we multiply both sides by 3, this will eliminate the fractions, and we will be left with g = 8.  (Answer C).

The solution to the proportion 8/3 = g/3 is g = 8, corresponding to option C.

In this proportion, the value of g can be found by solving the equation 8/3 = g/3. Because both sides of the equation are divided by 3, the 3's essentially cancel each other out, leaving you with g = 8.

Therefore, the solution to the proportion 8/3 = g/3 is g = 8. So, the correct answer is C. 8.

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Let's first find the slope

To find the slope you can use any two points in the table. The following are the two I picked:

(-3, 18) and (0, 12)

The formula for slope is

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

In this case...

[tex]y_{2} =12\\y_{1} =18\\x_{2} =0\\x_{1} =-3[/tex]

^^^Plug these numbers into the formula for slope...

[tex]\frac{12 - 18}{0 - (-3)}[/tex]

[tex]\frac{-6}{3}[/tex]

Simplify to...

-2

^^^This is your slope

Y-intercept is where the graph intersect with the y axis, which makes the x value 0. This means that the coordinate should look like so...

(0, y)

In this case the y-intercept is:

(0, 12)

Your answer is B!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

B. The slope is -2, and the y-intercept is 12.

Step-by-step explanation:

Slope formula:

       ↓

[tex]\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]

Slope-intercept formula:

       ↓

[tex]Y=MX+B[/tex]

[tex]\frac{12-18=-6}{0-(-3)=3}=\frac{-6\div3}{3\div3}=\frac{-2}{1}=-2[/tex]

Therefore, the answer is B.

Answer:

Step-by-step explanation:

5 * 5 * 5 * 5

= 625

ANSWER

[tex] {5}^{4} = 625[/tex]

EXPLANATION

We want to simplify the exponential expression 5⁴ by writing and simplifying a multiplication expression that represents it.

This implies that

[tex] {5}^{4} = 5 \times 5 \times 5 \times 5[/tex]

This simplifies to

[tex]{5}^{4} = 25 \times 2 5[/tex]

We finally obtain:

[tex] {5}^{4} = 625[/tex]

Answer:  7.2

Step-by-step explanation:

Use pythag. here: a(a)+b(b)=c(c)

4(4)=16

6(6)=36

16+36= 52

The square root of 52 is your answer: 7.21110255093. You can round this to 7.2