Find a such that the line x = a divides the region bounded by the graphs of the equations into two regions of equal area. (Round your answer to three decimal places.)
y = x, y = 8, x = 0
a = _____.

Answer:

729

Step-by-step explanation:

The first term is 1 in the geometric sequence 1, −3, 9, −27, . .

First find out the nth term formula for the geometric sequence

[tex]a_n=a_1(r)^{n-1}[/tex]

where a_1 is the first term =1

r is the common ratio,

[tex]\frac{-3}{1}=-3[/tex]

[tex]\frac{9}{-3}=-3[/tex]

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

r=-3, a_1=1

[tex]a_n=a_1(r)^{n-1}[/tex]

[tex]a_n=1(-3)^{n-1}[/tex]

Now find out the seventh term, n=7

[tex]a_7=1(-3)^{7-1}=729[/tex]

To find the seventh term of the geometric sequence 1, −3, 9, −27, ..., we calculate the common ratio and use it in the formula for the n-th term. The common ratio is −3 and the seventh term turns out to be 729. So the correct option is  E.

Calculating the SEVENTH Term of a Geometric Sequence

The given geometric sequence is 1, −3, 9, −27, ... and we are asked to find the seventh term. In a geometric sequence, each term after the first is found by multiplying the previous term by a constant called the common ratio (r). To find the common ratio, we can divide the second term by the first term, or the third term by the second term, and so on.

Common ratio (r) calculation:
Divide the second term (−3) by the first term (1), which gives us r = −3.

To find the seventh term, we use the formula for the n-th term of a geometric sequence, which is:
a_n = a_1 × r^(n-1), where a_n is the n-th term, a_1 is the first term, and n is the term number.

Seventh term calculation:
a_7 = 1 × (−3)^(7-1) = 1 × (−3)^6. Since −3 to an even power is positive, the answer is 1 × 3^6 = 729.

Therefore, the seventh term of the geometric sequence is 729.

Answer:

2 fancy shirts and 5 plain shirts

Step-by-step explanation:

28x + 15x = 131

28(2) + 15(5) = 131

56 + 72 = 131

(there are no other equation i could find)

Answer:

y=4x

Step-by-step explanation:

Given : x represent the number of television show episodes that are taped in each seasons

To Find : write an expression for the number of episodes taped in 4 seasons

Solution:

Let number of episodes taped in 4 seasons be y

Number of the episodes taped in 1 season = x

So, number of episodes taped in 4 seasons :

y= 4x

Hence the required expression for the numder of episodes taped in 4 seasons :y= 4x

Answer:

9.6.

Step-by-step explanation:

Because DE || AC:

x/12 = 8/10

10x = 96

x = 9.6.

Answer:

B

Step-by-step explanation:

The discrete type of data contains observations that can be counted and consists of finite set of data. In the given problem the votes received by Derek consists of finite set of value and votes received by Derek are countable.

Hence the votes received by Derek  is discrete data set because there is finite number of values.

Answer:

Honestly, if you think about it, the answer is right in front of you!

Step-by-step explanation:

The y- intercept is 3, and the x-intercept is 1. This means that the curve should have coordinate plots of (0,3) and (1,0).

The other information is not really needed if you know the x-and-y-intercepts!

There is only 1 curve that has the included intercepts, and that is the curve on option A)'s graph.

I hope this helps and wasn't too confusing!

- sincerelynini

The distance between the harbor and the island is 20 nautical miles.

To find the distance between the harbor and the island, we need to calculate the average speed of the motorboat for the entire trip. Since the average speed on the outbound trip was 10 knots and the average speed on the return trip was also 10 knots, we can conclude that the boat traveled at a constant speed throughout the trip. Let's assume the distance between the harbor and the island is 'd'.

Since speed = distance / time, we can calculate the time taken for each leg of the trip using the average speeds and the total time of 4.0 hours:

Time taken for the outbound trip = d / 10 knots

Time taken for the return trip = d / 10 knots

Since the total time is 4.0 hours, we can write the equation: d / 10 + d / 10 = 4.0

Simplifying the equation, we get: 2d / 10 = 4.0

Multiplying both sides by 10, we get: 2d = 40

Dividing both sides by 2, we get: d = 20

Therefore, the distance between the harbor and the island is 20 nautical miles.

Learn more about Calculating distance and speed here:

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The truck, experiencing a force of 1500 N, skids a distance of 25 meters, resulting in a change in kinetic energy of 37,500 J. Now, let's break down the concept of kinetic energy and the given data:

Definition of Kinetic Energy:

Kinetic energy, in physics, is the energy possessed by a moving object.

It represents the effort required to accelerate an object of a specific mass from rest to a particular velocity.

The body retains its kinetic energy even with slight speed variations, maintaining the energy acquired during acceleration.

Kinetic Energy Conservation:

When the body decelerates from its current velocity to a state of rest, the same amount of energy is expended.

Formal Definition:

Kinetic energy is formally described as any quantity exhibiting a gradient with respect to time in the Lagrangian of a system.

Given Data:

Force (F) = 1500 N

Distance (d) = 25 m

Calculation of Change in Kinetic Energy:

Utilize the formula for change in kinetic energy: ΔK.E = F × d

Substitute the values: ΔK.E = 1500 × 25

This results in ΔK.E = 37,500 J.

Therefore, the observed change in kinetic energy for the truck, moving a distance of 25 meters with a force of 1500 N, is precisely 37,500 J.

Complete questions

A truck skids for a distance of 25 m with the road pushing on its tires with force of 1500 N as its brakes are applied. What is the change in kinetic energy for the truck? Round the answer to two significant digits.J

Answer:

  £375

Step-by-step explanation:

The tax changed from 17.5% of the car's price to 20% of the car's price, an increase of 2.5% of the car's price.

The increased tax amount is ...

  0.025 × £15000 = £375

The price of the car went up by £375 due to the increase in VAT.

Answer:

So such system with fewer equations than unknowns can never have a unique solution.

Step-by-step explanation:

Linear equations are equations which contain variable with degree 1.

The variables can be 1 or 2 or any other number

say there are n varaibles

Then to solve this we must have n independent equations.

If number of equations are less than number of variables we can have parametric solutions only with infinite points lying on it.

There is no chance for this to have a unique solution.

For unique solutions, there must be equal number of equations with the variables and the determinant formed by the coefficients should not be 0.

So such system with fewer equations than unknowns can never have a unique solution.

Answer:

i say its c or b

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

Answer:the point slope form is

y + 1 = - 1/2(x - 6)

Step-by-step explanation:

The point slope form of a line is expressed as

y - y1 = m(x - x1)

Where

m represents the slope of the line.

Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

From the information given,

slope, m = - 1/2

y1 = - 1

x1 = 6

Therefore, the point slope eqy would be

y - - 1 = - 1/2(x - 6)

y + 1 = - 1/2(x - 6)

Answer:

y - - 1 = - 1/2(x - 6)

y + 1 = - 1/2(x - 6)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of a rectangle is 48 in. It means that

48 = 2(L + W)

L + W = 48/2

L + W = 24 - - - - - - - - - 1

the length of the rectangle is 6 in greater than the width. It means that

L = W + 6

Substituting L = W + 6 into equation 1, it becomes

W + 6 + W = 24

2W + 6 = 24

2W = 24 - 6 = 18

W = 18/2 = 9

L = W + 6 = 9 + 6 = 15

Final answer:

The student's problem involves finding the length and width of a rectangle given its perimeter and the fact that the length is 6 inches greater than the width. To solve it, we defined the width as a variable, set up an equation based on the perimeter, and used substitution to find that the width is 9 inches and the length is 15 inches.

Explanation:

The perimeter of a rectangle is given by the formula 2(length + width). In the stated problem, we are given the total perimeter (48 inches) and told that the length is 6 inches greater than the width. We can define the width as w and the length as w + 6. So, the perimeter equation is:

2(w + (w + 6)) = 48

Now that we have the width, we can find the length using substitution:

w + 6 = 9 + 6 = 15

Therefore, the width is 9 inches and the length is 15 inches.

Answer:

The diameters of circles that could fit completely inside circle O are 25, 36, 42, 48 and 54.

Step-by-step explanation:

The actual diameter of the circle:

[tex]\pi r^{2} = 16 x \\2\pi r = x\\\\16(2\pi r)=16x\\\\32\pi r= \pi r^{2} \\\\\frac{32\pi r}{\pi r} = \frac{\pi r^{2} \\}{\pi r} \\\\r = 32[/tex]

Since the radius is equal to 32 units, the diameter is equal to 64 units.

Therefore, the diameters of circles that could fit completely inside circle O must be smaller than or equal to 64.

Answer:

J < T - 5

Step-by-step explanation:

T =  The number of juice boxes Thomas had

J =  The number of juice boxes Thomas gave to his sisters

Thomas had 12 juice boxes

T = 12

He gave some to his sisters he now has more than 5 left.

T - J > 5

-J > 5 - T

J < -5 + T

J < T - 5

To determine the number of juice boxes Thomas gave to his sisters, the inequality 12 - j > 5 is used, which simplifies to j < 7, indicating that he gave away fewer than 7 juice boxes.

To find j, the number of juice boxes Thomas gave to his sisters, we start with the total number he had initially, which is 12. We know that he gave away some juice boxes and still has more than 5 left. If we let j represent the number of juice boxes given to his sisters, then 12 - j > 5 would be the inequality that can be used to determine j.

Since Thomas has more than 5 left, but we don't know the exact number, we use the inequality to represent the situation. Therefore, if we solve the inequality, subtracting 5 from both sides, we get j < 7. This means that Thomas gave away fewer than 7 juice boxes to his sisters because he had more than 5 remaining.

Answer:

After evaluating the given expression we get the value as 4.

Step-by-step explanation:

Given:

[tex]\frac{j}{k}-0.2k[/tex]

We need to evaluate the expression when j =25 and k =5

Solution:

On substituting the values of k and j in the expression we get;

[tex]\frac{25}{5}-0.2\times5[/tex]

We will use PEDMAS which means first operation performed will be division.

So we can say that;

[tex]5-0.2\times5[/tex]

Now next Operation to be performed is multiplication.

So we can say that;

[tex]5-1[/tex]

Finally we will use subtraction operation and then we will get;

[tex]4[/tex]

Hence After evaluating the given expression we get the value as 4.

Answer:

$828

Step-by-step explanation:

15% = 0.15

0.15 x 720 = 108

total cost = $720 + $108 = $828

Final answer:

To find the total cost of an iPad that is on sale at 15% off with a 6% sales tax, calculate the discount, subtract it from the original price, determine the sales tax, and add it to the discounted price.

Explanation:

To find the total cost of the iPad:

Calculate the discount: $720 * 15% = $108 discount

Subtract the discount from the original price: $720 - $108 = $612

Calculate the sales tax: $612 * 6% = $36.72

Add the sales tax to the discounted price: $612 + $36.72 = $648.72

Answer:

Part 1) The slopes are negative reciprocals of one another.

Part 2) There is no relationship.

Step-by-step explanation:

Part 1)

we know that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

[tex]m_1*m_2=-1[/tex]

Part 2)

The y-intercept is the value of y when the value of x is equal to zero

Two linear functions that are perpendicular, could have the same y-intercept (the y-intercept would be the point of intersection between both lines)

so

There is no relationship

Answer:

The answer is C

Step-by-step explanation:

The rule for reflecting over the X axis is to negate the value of the y-coordinate of each point, but leave the x-value the same. Example, when point P with coordinates (5,4) is reflecting across the X axis and mapped onto point P', the coordinates of P' are (5,-4)

Final answer:

A person can talk for at most 19 minutes on a long-distance call without exceeding a $2 limit, accounting for the initial charge and the cost of additional minutes.

Explanation:

To find out at most how many minutes a person can talk on a phone without exceeding $2, considering the initial charge is 40 cents for the first three minutes, and 10 cents for each additional minute, we need to calculate the total cost based on the number of minutes.

The problem can be broken down as follows:

The cost for the first 3 minutes is 40 cents.

After the initial 3 minutes, each additional minute costs 10 cents.

We have a budget of $2 (or 200 cents) to not exceed.

First, subtract the initial 40 cents from the total budget:

200 cents - 40 cents = 160 cents

With 160 cents left and each additional minute costing 10 cents:

160 cents[tex]\(\div\)[/tex] 10 cents = 16 additional minutes

Therefore, adding the initial 3 minutes:

3 + 16 = 19 minutes

A person can talk for at most 19 minutes without exceeding a $2 limit.

Answer:

Step-by-step explanation:

Let x represent the number of miles with either company A or company B.

Company A charges ​$70.50 and 18 cents per mile. Converting 18 cents to dollars, it becomes

18/100 = $0.18

Total cost of x miles with company A would be

0.18x + 70.50

Company B charges $30.50 and 11 cents per mile. Converting 11 cents to dollars, it becomes

11/100 = $0.11

Total cost of x miles with company B would be

0.11x + 30.50

For the amount that company A charges more than company B, it becomes

0.18x + 70.50 - 0.11x + 30.50

0.18x - 0.11x + 70.5 - 30.5

0.07x + 40

Company A charges 0.07x + 40 more than company B

Answer:

51.2

Step-by-step explanation:

To divide 2560 by 50, you can use long division. The answer is 51.

To divide 2560 by 50, you can use long division. Here's how:

Therefore, 2560 divided by 50 equals 51.

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Answer:

2x^2.

Step-by-step explanation:

2x^2 / x^3y^2

= 2/xy^2

Answer:

I'm pretty sure if there's two answers you can mark them brainliest.

Step-by-step explanation:

When y = 3, the value of z is 2.

Since x is directly proportional to y and inversely proportional to z, we can write this relationship as:
[tex]x = k \frac{y}{z}[/tex]
where k is a constant of proportionality.

We are given the values x = 3, y = 6, and z = 4. Let's use these values to find k.

[tex]3 = k \frac{6}{4}[/tex]

Simplifying this, we get:

[tex]3 = k \cdot 1.5[/tex]

Solving for k:

[tex]k = \frac{3}{1.5} = 2[/tex]

Now we know the constant k. We can use it to find z when y = 3.

We know the relationship:

[tex]x = 2 \frac{y}{z}[/tex]

We need to find z when x = 3 and y = 3.

[tex]3 = 2 \frac{3}{z}[/tex]

Rearranging to solve for z:

[tex]3 = 6 \div z[/tex]

[tex]z = 2[/tex]

Answer:

A

Step-by-step explanation:

p = 25 + 5s

s = amount of shoes sold

Rich sold 7 shoes. Plug in 7 for s

p = 25 + 5(7)

p = 25 + 35

p = 60

Answer: the correct answer is a. $60

Step-by-step explanation:

Using the formula that states Rich's weekly salary

P= 25 + 5s , where p is the salary and s the number of pairs sold, then

P= $25 + $5*7

P=$25 + $ 35

P= $ 60

Answer:

The expression that represents the number of hits he got in the rest of the​ games is [tex]t=52-h[/tex].

Step-by-step explanation:

Given:

Number of hits in one season = 52 hits

Number of hits in one game = 'h'

We need to write expression that represents the number of hits he got in the rest of the​ games.

Solution:

Let the number of hits he got in the rest of the​ games be 't'.

Now we can say that;

The number of hits he got in the rest of the​ games is equal to Number of hits in one season minus Number of hits in one game.

framing in equation form we get;

[tex]t=52-h[/tex]

Hence expression that represents the number of hits he got in the rest of the​ games is [tex]t=52-h[/tex].

Answer:

52 - h

Step-by-step explanation:

Simplify: 52 - h

Answer:

[tex]\displaystyle -5 = f(5)[/tex]

Step-by-step explanation:

[tex]\displaystyle -2[5] + 5 = -10 + 5 = -5[/tex]

I am joyous to assist you anytime.

Answer: -5

Explanation: In this problem, we're given the function f(x) = -2x + 5 and we are asked to find f(5).

To find f(5) or the value of the function when x = 5, we simply substitute 5 in for x in our function.

So we have f(x) = -2(5) + 5 or -10 + 5 which equals -5.

So f(5) or the value of the function when x = 5 is -5.