if x equals 3= xequals 4 then use the equation 2x y -6 x equals 18 Z to find the value of y

divide the two

40.8 / 8 = 5.1 gallons per container

Answer:

109

Step-by-step explanation:

Given that there is a sequence of numbers as

4,11,25,53,...

We have to find the next number.

To find the next number, let us see the pattern from the given four numbers

We have

I number = 4

II number = 4+7

III number = II number + 2(7)

Iv number = III number +4(7)

So if we guess this pattern continues the next number namely v number would be

V number = IV number +8(7)

=53+56

109

i.e. I number is added by 7, II number by 2(7), III number by 2^2(7)

hence next number 2^3(7)

Answer is 109

The next number in the sequence is:

As can be seen, the first number is a selected number, which in this case is four, to which seven are added to obtain:

Then double 7 is added to that number, that is 14, with which you get:

And to get the next number, double 28 must be added, which is 56, therefore:

By this reason, the next number in the sequence is 109.

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A sequence can be both arithmetic and geometric, and this is illustrated where terms follow both an arithmetic and geometric progression.

Yes, a sequence can be both arithmetic and geometric. An example of such a sequence is when the terms of the sequence follow both an arithmetic progression, where the difference between consecutive terms is constant, and a geometric progression, where each term after the first is found by multiplying the previous term by a fixed, non-zero number.

Final answer:

The scale factors for the points given are 1.5 for A to A', indicating an enlargement, and 0.5 for B to B', indicating a reduction. G to G' also indicates a reduction with a factor of 0.5.

Explanation:

To determine the scale factor given the point and its image, you can find the ratio between the coordinates of the image and the original coordinates. Let's analyze the pairs of points you've provided:

A (3, 6) and A' (4.5, 9)

G (1.5, 3) and G' (3, 6)

B (2, 5) and B' (1, 2.5)

We can find the scale factor by dividing the x-coordinates of the image by the original x-coordinate and doing the same for the y-coordinates. For point A:

Scale factor for x: 4.5 / 3 = 1.5

Scale factor for y: 9 / 6 = 1.5

For point G, we see that it's actually the reverse (original to image), but you can still calculate:

Scale factor for x: 3 / 1.5 = 2

Scale factor for y: 6 / 3 = 2

Lastly, for point B:

Scale factor for x: 1 / 2 = 0.5

Scale factor for y: 2.5 / 5 = 0.5

So, the scale factors for A to A' and for B to B' are 1.5 and 0.5, respectively, showing that A to A' is an enlargement while B to B' is a reduction. For G to G', the reverse is a reduction with a factor of 0.5.

To convert the distance from the Earth to the Moon from miles to feet, multiply 250,000 miles by the number of feet in a mile, which is 5,280. This calculation yields a result of approximately 1.32 billion feet.

The distance from the Earth to the Moon is given as 250,000 miles. To convert this distance from miles to feet, we use the fact that there are 5,280 feet in a mile. Thus, we multiply the distance in miles by the number of feet per mile.

To find the distance in feet, perform the following calculation:

Multiply the distance in miles by the number of feet per mile: 250,000 miles × 5,280 feet/mile.

This equals 1,320,000,000 feet.

Therefore, the Moon is approximately 1.32 billion feet away from Earth.

The solution to the inequality -1.3 ≥ 2.9 -0.6r, is r ≤ 7. This is represented on a graph by placing a closed circle on 7 and drawing a line to the left, to represent all numbers less than 7.

To solve this inequality, -1.3 ≥ 2.9 -0.6r, first, we isolate the variable r (which represents solving for 'r'). Start by subtracting 2.9 from both sides of the inequality.

This gives us -4.2 ≥ -0.6r. Then divide both sides by -0.6. However, remember when dividing or multiplying an inequality by a negative number, the direction of the inequality changes. So, it becomes r ≤ 7.

When graphing this inequality, you will place a closed circle at 7 (showing that point is included) and draw a line to the left from 7, extending to infinity (since all numbers less than 7 satisfy the inequality).

The graph represents the mathematical solution to the inequality.

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In this composition, we first apply the function h, which is simply the identity function, to the input 4, resulting in 4. Then, we apply the function g to this result. As g(x) = 5x - 3, g(4) equals 17. Hence, (g◦h)(4) = 17.

To find (g◦h)(4), which represents the composition of functions g and h evaluated at x = 4, we first need to find h(4), then substitute the result into g(x).

Given h(x) = x, h(4) = 4.

Now, we substitute h(4) into g(x).

So, g(h(4)) becomes g(4).

Given g(x) = 5x - 3, substituting x = 4 into g(x), we get g(4) = 5(4) - 3 = 20 - 3 = 17.

Therefore, (g◦h)(4) = 17.

For the round trip of 930 miles each way, you will need to purchase about 62 gallons of gas, given a car's gas mileage of 30 miles per gallon.

To calculate the gallons of gas needed for the round trip, follow these steps:

Calculate the total distance for the round trip.

The round trip distance is twice the one-way distance.

Round trip distance = 2 * 930 miles = 1860 miles.

Find the number of gallons required for the round trip.

Divide the total distance by the car's gas mileage (miles per gallon).

Gallons required = Round trip distance / Gas mileage

Gallons required = 1860 miles / 30 miles per gallon

Perform the division.

Gallons required = 62 gallons.

Round the answer.

Since you cannot purchase a fraction of a gallon, round the answer to the nearest gallon.

You will need to purchase approximately 62 gallons of gas for the round trip.

So, to make the trip to see your friends and return home, you will need to purchase about 62 gallons of gas.

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An example of one possible outcome in the sample space:

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