Let x be a positive number such that the distance between x and -3.8 on a number line is exactly two times the distance between x and 1.7. What is the value of x? Express your answer as a decimal to the nearest tenth.

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.

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:

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:

Which day was the weather forecast most accurate? Forecast vs Actual Temperature Day Degrees above (+) or below (–) forecast Monday +4 Tuesday –6 Wednesday +7 Thursday –2

(i) Monday

(ii) Tuesday

(iii) Wednesday

(iv) Thursday

Ans

(iv)Thursday

Step-by-step explanation:

Forecast for

Monday +4 Abs |+4| = 4

Tuesday –6 Abs |-6| = 6

Wednesday +7 Abs |+7| = 7

Thursday –2 Abs |-2| = 2

The most accurate is the day closest the temperature forecast is closest to observed temperature, which is

Thursday (-2)

Answer:

it is thursday

Step-by-step explanation:

hope it helps

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:

[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.

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 combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Step-by-step explanation:

We have to add the fractional weight of both boxes to find the combined weight of both boxes.

Given

Weight of Box 1: [tex]8\frac{2}{9}[/tex] kilograms

Weight of Box 2: [tex]3\frac{2}{10}[/tex] kilograms

So the total weight will be:

[tex]= 8\frac{2}{9} + 3\frac{2}{10}[/tex]

Simplifying the fractions

[tex]=\frac{74}{9} + \frac{32}{10}\\\\= \frac{74(10)+32(9)}{90}\\\\=\frac{740+288}{90}\\\\=\frac{1028}{90}\\\\=11\frac{38}{90}\\\\=11\frac{19}{45}\\[/tex]

Hence,

The combined weight of both boxes is: [tex]11\frac{19}{45}\ kilograms[/tex]

Keywords: Fractions, addition

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Answer:

[tex]\sqrt{29}[/tex]

Step-by-step explanation:

The complex number x + yi can be expressed in coordinate form as

x + yi → (x, y ), thus

4 + 3i → (4, 3 )

6 - 2i → (6, - 2 )

Calculate the distance d using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (4, 3) and (x₂, y₂ ) = (6, - 2)

d = [tex]\sqrt{(6-4)^2+(-2-3)^2}[/tex]

   = [tex]\sqrt{2^2+(-5)^2}[/tex]

   = [tex]\sqrt{4+25}[/tex]

   = [tex]\sqrt{29}[/tex]

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)

Answer:

6

Step-by-step explanation:

Answer:

Smallville is growing at a greater rate

Step-by-step explanation:

use the formula for percentage increase to find what percentage the population of Bigville increased.

(Increase ÷ original number) * 100 = % of increase

increase = 571,533 - 387,480 = 184,053

(184,053 ÷ 387,480) * 100 = 47.5

Bigville percent of increase is 47.5%

Smallville percent of increase is 53.67%

since, smallville has a bigger percentage, it is growing at the greater rate  

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: 38

Step-by-step explanation:

14 - 2xy

(substitute x and y)

14 - 2 (-6) (2)

14 + 24

38

Answer:

its 38

Step-by-step explanation:

Do xy first and you get -24 and 14-(-28) would be a double negative so you add them together.

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:

Answer:

i say its c or b

Step-by-step explanation:

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

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.

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Answer:

Area of each tile = 19.5 inches^2

Step-by-step explanation:

Rhombus:-

A rhombus is a type of quadrilateral whose opposite sides are parallel and equal.Also, the opposite angles of a rhombus are equal and the diagonal intersect each other perpendicularly.

To find the area of a rhombus when the measures of its height and side length are given, use the formula

A = Base X height

Area of a rhombus = 6.5 X  3

                          A      = 19.5 inches^2

The area of each rhombus-shaped tile is 19.5 square inches for the given dimensions. Thus, each tile has an area of 19.5 square inches.

To find the area of a rhombus, you can use the formula

⇒ Area = base × height

In this case, the height is given as 3 inches and the length of each side is 6.5 inches, but the length of the sides is not needed, as we are working with the base and height directly.

So, the area can be calculated as follows:

⇒ Base = 6.5 inches

⇒ Height = 3 inches.

⇒ Area = base × height.

⇒ Area = 6.5 inches × 3 inches

= 19.5 square inches.

Therefore, the area of each rhombus-shaped tile is 19.5 square inches.

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:

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:

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:the equation relating E to H is

E = 20H

Step-by-step explanation:

Let E represent her earnings (in dollars) after tutoring for H hours.

For each hour that she tutors, she earns 20 dollars. This means that in H hours, her total earnings would be

E = 20H

To find Mai's earnings after tutoring for 17 hours, we would substitute H = 17 into the equation. It becomes

E = 20 × 17

E = $340

Mai's earnings [tex](\(E\))[/tex] after tutoring for 17 hours would be $340, calculated as [tex]\(E = 20 \times 17\).[/tex]

To relate Mai's earnings [tex](\(E\))[/tex] to the number of hours she tutors [tex](\(H\))[/tex], we can use the following equation:

[tex]\[E = 20H\][/tex]

This equation represents that Mai earns $20 for each hour she tutors. By multiplying the number of hours [tex](\(H\))[/tex] by the rate of $20 per hour, we get her total earnings [tex](\(E\))[/tex].

Now, to find Mai's earnings after tutoring for 17 hours, we can plug in [tex]\(H = 17\)[/tex] into the equation:

[tex]\[E = 20 \times 17\][/tex]

[tex]\[E = 340\][/tex]

So, Mai's earnings after tutoring for 17 hours would be $340.

The equations that are true according to the exponent rules for powers of 10 include: [tex]10^5 / 10^3 = 10^5-3, 10^5 * 10^3 = 10^5+3,[/tex] and [tex]10^5 / 10^3 = 10^5-3.[/tex]

The subject in question deals with exponent rules for powers of 10. Here, we'll identify which equations are true based on these rules:

a. (10^5)^3 = 10^5×3. This is not correct. According to the power of a power rule, we should multiply the exponents, so the answer should be 10^15.

b. [tex]10^5 / 10^3 = 10^5-3.[/tex] This is correct. When dividing bases that are the same, we subtract the exponent of the denominator from the exponent of the numerator, hence 10^(5-3) = 10^2.

c. 10^5 × 10^3 = 10^5+3. This is correct. When multiplying bases that are the same, we add the exponents, hence 10^(5+3) = 10^8.

d. [tex]10^5 / 10^3 = 10^5-3[/tex]. This is correct, as explained in point b. The answer is 10^2.

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Final answer:

Equation c [tex](10^5*10^3 = 10^{(5+3)})[/tex] and equations b and d [tex](10^5/10^3 = 10^{(5-3)})[/tex] are correct. To multiply or divide numbers in scientific notation, multiply or divide the coefficients and add or subtract the exponents, respectively. This method can be used to calculate without converting to standard form.

Explanation:

The equations that are true out of the ones provided are as follows:

To evaluate (8.552 × 10^6) ÷ (3.129 × 10^3) without entering scientific notation into your calculator, first divide the coefficients (8.552 ÷ 3.129) and then subtract the exponents for the powers of 10 (10^6 ÷ 10^3 = 10^(6-3) or 10^3). The result is approximately 2.73189 × 10^3.

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

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:

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 answer to your question is A coordinate plane with a line passing through (0, -3) and (2,0)

Step-by-step explanation:

Line

                             3x - 2y = 6

Solve for y

                              -2y = -3x + 6

                                 y = 3/2 x - 3

Find "y" when x = 0

                                 y = 3/2(0) - 3

                                 y = -3                      Point (0, -3)

Find "x" when y = 0

                                0 = 3/2x - 3

                                 3 = 3/2 x

                                x = 6/3

                                x = 2                       Point (2, 0)

The graph of the equation 3x - 2y = 6 passes through the points (0, -3) and (2, 0). This conclusion is reached after rearranging the equation into the slope-intercept form and comparing the slope and the y-intercept with coordinates of the given lines.

To find the correct graph for the equation 3x - 2y = 6, we first need to rearrange the equation in the slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.

We rearrange our equation as follows: 3x - 6 = 2y. Simplifying, we get y = 1.5x - 3.

This equation tells us that the y-intercept (where the line crosses y-axis) is -3, and the slope is 1.5, in other words, for each step in positive x-direction, y increases by 1.5 steps.

Now looking at our coordinate plane options, the graph that fits this description is the one with a line passing through the points (0, -3) and (2, 0). Hence, this is the graph of the given equation.

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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