Find the sum of the first 9 terms of the following sequence. Round to the nearest hundredth if necessary.

3,-15,75

Sum of a finite geometric series:
Sn=a1-a1r^n/1-r

awnser

12

Step-by-step explanation:

Answer:

x^2 – 4 = 0   AND   4x^2 = 16

Step-by-step explanation:

a) x^2 – 4 = 0 --> (x + 2)(x - 2)=0 --> x= -2 AND x= +2

b) x^2 = -4 doesn't have any solution in the real numbers.

c) 3x^2 +12 = 0 -->(divide by 3)-->  x^2 +4 =0 ---> x^2 = -4  as b)

d) 4x^2 = 16 -->(divide by 4)--> x^2 = 4  --> x^2 -4 = 0 as a)

e) 2(x -2)^2 =0 -->(divide by 2)--> (x-2)^2 =0 --> one solution that is x=+2

Answer:

34

Step-by-step explanation:

The angles of a triangle add to 180

56+ F + 90 = 180   ( the box means 90 degrees)

Combine like terms

146+F = 180

Subtract 146 from each side

F = 180-146

F = 34

Answer:

Step-by-step explanation:

The tractor-trailer rig is a fixed input under the circumstances described because it is necessary for the business to service this profitable market and it cannot be replaced with any other type of capital equipment. The tractor-trailer is a quasi-fixed input because it has a five-year contract that requires monthly lease payments, so it is not completely fixed in the sense that the business can replace it with another piece of capital equipment at any time.

Option A. c - 0 = b - a is the missing statement in Step 4 of the proof.

To determine the missing statement in Step 4 of the proof, let's examine the given table and image related to the relationship between the slopes of two parallel lines.

Step 1: Given the slopes of two parallel lines, m₁ and m₂.

Step 2: Assume two points on each line: (0, a) and (c, b).

Step 3: Calculate the slopes using the slope formula: m₁ = (b - a) / (c - 0) and m₂ = (d - a) / (0 - c).

Step 4: ??? (Missing Statement)

Step 5: Since the lines are parallel, the slopes are equal, so m₁ = m₂.

By analyzing the given information, we can identify the missing statement by comparing the calculated slopes:

From Step 3, we have:

m₁ = (b - a) / (c - 0)

m₂ = (d - a) / (0 - c)

Comparing the two slopes, we can see that (b - a) / (c - 0) = (d - a) / (0 - c).

To express this relationship, the missing statement in Step 4 should be:

A. c - 0 = b - a

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First, write the coefficients of the polynomial in order of decreasing degree and include a placeholder for missing terms:

2 -8 -27 14 24

6

Bring down the leading coefficient:

2 -8 -27 14 24

6

2

Multiply the divisor by the result of the previous step and subtract from the corresponding coefficients:

2 -8 -27 14 24

6

2 -12

48

2 -12 21

-42

2 -12 21 -28

168

2 -12 21 -28 192

The result of the division is 2x³ - 12x² + 21x - 28 with a remainder of 192.

Answer: 2x2 + 1000 x 1000 = 1000004

Step-by-step explanation: you add on 5 0's to the one and 2x2 = 4 so add on the 4 also

Answer:

1000004

Step-by-step explanation:

First we do can separate it into the parentheses: (2*2) + (1000*1000)

= 4 + 1000000

= 1000004

Answer:

0.2

Step-by-step explanation:

Answer:

1.66666666667

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

The equation to use for CONTINUOUS compounding is :

FV = PV e^(it)

18532.08 = 8327 * e^( i*10)        where i is the interest in decimal form

18532.08/8327  = e^(10i)

2.225541 = e^(10i)             now take natural log  (ln) of both sides to get

.8000 = 10i

i = .08     or 8% interest

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

\(\displaystyle\bf\\3x+2y=4\\-2x+2y=24~\Big|\cdot(-1)\\-----\\3x+2y=4\\2x-2y=-24\\-----------~We~add~up~the~equations\\\\5x~~~~\backslash~~=-20\\\\x=\frac{-20}{5} \\\\\boxed{\bf x=-4}\\\\3x+2y=4\\\\3\cdot(-4)+2y=4\\\\-12+2y=4\\\\2y=4+12\\\\2y= 16\\\\y=\frac{16}{2} \\\\\boxed{\bf y=8}\)

Correct answer:   c) (-4, 8)  

Answer:

The answer is 269 in.

hope this helps!

Sorry I’m late oops

Step-by-step explanation:

Answer/Step-by-step explanation:

7. The graph is a proportional relationship because the line passes through the point of origin, (0, 0). To find the equation the proportional relationship the graph represents, we need to find the unit rate of red paint (y) to white paint (x). The unit rate will represent the constant of proportionality, k. Then substitute the value of k in \( y = kx \).

Unit rate or k = y/x

Using the point, (4, 1),

k = \( \frac{1}{4} \)

Substitute k = ¼ in \( y = kx \)

✅The equation would be:

\( y = \frac{1}{4}x \)

8. The graph Franco made is incorrect.

The equation, \( y = -x \), shows a negative constant of proportionality of -1. Therefore, the slope of the line descend downwards, from the left to the right. So, the graph Franco made to represent the equation, \( y = -x \) is not correct.

9. a. Proportional relationship can be represented as \( y = kx \). To derive an equation that represents the graph, find k, the constant of proportionality between variable y and x.

Using the point, (2, 24), therefore:

k = y/x = 24/2 = 12.

Substitute k = 12 in \( y = kx \)

✅The equation would be:

\( y = 12x \)

b. We know an equation is represents a proportional relationship, when it is tales the form, \( y = kx \). Where k is the constant of proportionality. Thus, for if you substitute the pair of values given (x, y) into the equation, you would get the same value of k for any pair of value you substitute in the given set of values.

Also, we know a graph represents a proportional relationship when a straight line passes through the point of origin, (0, 0), and has a constant of proportionality or unit rate all through.

Answer:

Step-by-step explanation

Answer:

$13.47 per hour

Step-by-step explanation:

Total earnings = 9.25 (h) + 8 (t/20)

Where h is the number of hours and t is the number of transformers.

Since he worked for 36 hours and assembled 380 transformers:

Total earnings = 9.25 (36) + 8 (380/20)

Total earnings = 333+152 = $485

Finally, to find how much he earned per hours, we simply have to divide the result by the number of hours worked (36):

485/36 = $13.47 per hour.

The equation of a line in point slope form is expressed according to the formula;

y-y0 = m(x-x0)

Given the following parameters

m = -3

(x0, y0) = (-4, 1)

Substitute into the formula above will givee;

y - 1 = -4(x+4)

y -1 = -4x - 16

y = -4x - 15

Next is to plot the graph of the line y = -4x - 15 on the coordinate plane as shown:

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The solution by substituting 15 for b in the Original equation. The answer is true.

The steps needed to solve the equation b + 6 = 21 are:

Subtract 6 from both sides of the equation: b + 6 - 6 = 21 - 6, which simplifies to b = 15.

Check the solution by substituting 15 for b in the original equation: 15 + 6 = 21, which is true.

Therefore, the correct steps to solve the equation are:

Subtract 6 from both sides of the equation. The answer is b = 15

the solution by substituting 15 for b in the original equation. The answer is true.

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Answer:

120

Step-by-step explanation:

Because its a circle and 360-240 =120

The product of the given expression will be -49 + 13√7.

Product of two entities may be used to increase the amount of those entities. A radical expression may be defined as an expression which along with numbers and variables contain square root symbol. Instead of square root there can be cube root, fourth root or of root with any power. For example, 1 + √4, 1 + ∛4 etc. We have the expression (7 - √7) (-6 + √7). The product of this expression will be

Product = (7 - √7) (-6 + √7)

Product = -42 + 7√7 + 6√7 - 7

Product = -49 + 13√7 which is the required expression.

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Answer:

\(-49 + 13\sqrt{7}\)

Step-by-step explanation:

\((7 - \sqrt{7} )(-6 + \sqrt{7})\\) Distribute.

\(7 * -6 + 7 * \sqrt{7} - \sqrt{7} * -6 - \sqrt{7} * \sqrt{7}\) Multiply. Keep in mind \(- \sqrt{7} * \sqrt{7} = (-\sqrt{7})^{2} = - 7\).

\(-42 +13\sqrt{7} - 7\) Combine like radicals/terms.

\(-49 +13\sqrt{7}\)

They will be when they pass each other at 44 4/9 mins.

This is a classic question on Speed, time, & distance.

1. When time traveled in each segment is constant, then average speed is simple mean of speeds.

2. When distance traveled in each segment is constant, then average speed is reciprocal of simple mean of reciprocal of speeds. It is basically called Harmonic mean.

So this question falls in the category of 2.

=> So, average speed = Reciprocal of mean of reciprocals of 40 & 50.

=> Average speed = Reciprocal of mean of 1/40 & 1/50.

=> Average speed = Reciprocal of (1/40 + 1/50)/2

= Reciprocal of (5+4)/400

= 44 4/9 mins

Hence, they will be when they pass each other at 44 4/9 mins.

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Answer:

\(y=\frac{1}{6}x+6\)

Step-by-step explanation:

Let \((x_1,y_1)\rightarrow(-6,5)\) and \((x_2,y_2)\rightarrow(6,7)\)

Determine slope

\(m=\frac{y_2-y_1}{x_2-x_1}\\ \\m=\frac{7-5}{6-(-6)}\\ \\m=\frac{2}{6+6}\\ \\m=\frac{2}{12}\\ \\m=\frac{1}{6}\)

Use either ordered pair to find the y-intercept

\(y=mx+b\\\\7=\frac{1}{6}(6)+b\\\\7=1+b\\\\6=b\)

Final equation

\(y=\frac{1}{6}x+6\)

Step-by-step explanation:

the answer is 16.8 :)hope this helps

Answer: 30 :) have a nice day!!!

Answer:

The number is 8

Step-by-step explanation:

Let n = number

n+9 = 17

Subtract 9 from each side

n+9-9 = 17-9

n = 8

Answer:

-1 is not in the domain of (f o g)(x)

Step-by-step explanation:

f(x) = sqrt(x - 9)

g(x) = -6x - 3

(f o g)(x) = f(g(x)) = sqrt(g(x) - 9)

(f o g)(x) = sqrt(-6x - 3 - 9)

(f o g)(x) = sqrt(-6x - 12)

Let x = -1:

(f o g)(-1) = sqrt(-6(-1) - 12)

(f o g)(-1) = sqrt(6 - 12)

(f o g)(-1) = sqrt(-6)

Since sqrt(-6) is not a real number, -1 is not in the domain of (f o g)(x).

Answer:   \(\frac{3}{4}\)c

Step-by-step explanation:

       If one pound of chicken costs c dollars, and we are writing an expression for 3/4 a pound of chicken, our expression will be the price (c) multiplied by how much chicken there is (3/4):

               3/4c

- In mathematics, an expression is a combination of numbers, variables (represented by letters), symbols, and operators, arranged in a way that represents some meaningful mathematical relationship or calculation.

- Expressions can be simple, like 3x or 4 + 5, or complex, like (3x + 4y) / (2x - 5y). Expressions are not equations or inequalities, as they do not contain an equal sign, but they can be used to build equations or inequalities.

The price of 1 pound of chicken is c dollars. To find the price of 3/4 pound of chicken, we can multiply the price of 1 pound by 3/4:

\(\begin{aligned}\sf Price\: of\: \dfrac{3}{4}\: pound\: of\: chicken& =\sf \dfrac{3}{4} \times c \\&=\boxed{\bold{\:\dfrac{3}{4}c\:}}\end{aligned}\)

Therefore, the expression for the price of 3/4 pound of chicken is 3/4c.

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We know the sum of the interior angles of a triangle is 180°. Knowing this, we can consider and solve the following equation:

Thus x=6 and the missing angle is 50°

To determine the area of the remaining piece of cardboard expressed in terms of x when a square of side length x inches is cut out from a rectangular piece of cardboard having a length of 6x+2 inches and a width of 2x-4 inches, use the following steps.

Draw and label a diagram of the problem. The rectangle should be labeled as 6x+2 inches by 2x-4 inches, and the square cut out should be labeled as x inches by x inches. This is how the diagram looks like: Determine the area of the rectangle, Arect.

The area of the rectangle is given by the product of its length and width. Thus, Arect = (6x + 2)(2x - 4) Determine the area of the square, Asq. The area of the square is given by the square of its side length. Thus, Asq = x²Step 4: Determine the area of the remaining cardboard after the square is cut out, Ar.

This is the difference between the area of the rectangle and the area of the square. Thus, Ar = Arect - Asq= (6x + 2)(2x - 4) - x²= 12x² - 20x - 16

Simplify the expression. The final answer is given in terms of x. Thus, Ar = 12x² - 20x - 16.The area of the remaining piece of cardboard is expressed in terms of x as 12x² - 20x - 16.

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Answer:

below

Step-by-step explanation:

When y = 0    the negative x value of the vertex needs to be a negative number ....the second equation will do this...the first will not

Answer:

the answer is

Step-by-step explanation:

So 12 more than N would be 12 + N.

Answer:

b) 12 + n

Step-by-step explanation:

The statement is,

→ 12 more than a number.

Now equation will be,

→ 12 + n

≈ (or) n + 12

So, option (b) is correct.