QuestionFind the unit rate.$9.60 for 4 poundsThe unit rate is $per pound

The next two terms in the sequence are -216 and -343. The formula for the nth term is given by f(n) = -n^3. This is an explicit formula because each term can be directly calculated using the value of n. By substituting different values of n into the formula, we obtain the corresponding terms in the sequence.

To find the next terms in the sequence, we need to observe the pattern. Looking at the sequence, we can see that each term is obtained by taking the cube of the negative of the corresponding natural number. For example, the first term is -1, which is obtained by taking -1^3 = -1. The second term is -8, which is obtained by taking -2^3 = -8.

Therefore, we can see that the formula for the nth term is given by f(n) = -n^3, where n represents the corresponding natural number. By substituting different values of n into this formula, we can calculate the corresponding terms in the sequence.

For example, when n = 3, we have f(3) = -(3^3) = -27, which matches the third term in the sequence. Similarly, when n = 4, we have f(4) = -(4^3) = -64, which matches the fourth term in the sequence.

This formula is explicit because each term can be directly calculated using the value of n. We do not need to rely on previous terms to determine the current term. Each term can be independently calculated using the given formula.

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Answer:

x = 20

Step-by-step explanation:

2x + 7x = 180

9x = 180

x = 20

Answer:

chatGPT

Step-by-step explanation:

Let's denote the speed of each car as v, and the distance that Car A travels as d. Then we can set up two equations based on the information given:

d = v * (12/60) (since Car A reaches its destination in 12 minutes)

d + 4 = v * (18/60) (since Car B travels 4 miles farther than Car A and reaches its destination in 18 minutes)

Simplifying the equations by multiplying both sides by 60 (to convert the minutes to hours) and canceling out v, we get:

12v = 60d

18v = 60d + 240

Subtracting the first equation from the second, we get:

6v = 240

Therefore:

v = 240/6 = 40

So the cars travel at a speed of 40 miles per hour.

The mean goals scored by the soccer players this season is 18.3 goals

Mean is the ratio of the sum of data to the total sample of data.

If three soccer players are scored 25 goals this season., five soccer players  scored 19 goals this season and ten soccer players scored 16 goals this season, the mean goal scored is expressed as:

Mean goal scored = 3(25)+5(19)+10(16)/3+5+10

Mean goal scored = 75 + 95+160/18

Mean goal scored = 330/18

Hence the mean goals scored by the soccer players this season is 18.3 goals

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The value of expanding (2x -3)^4 is 16x^4  + 96x^3  +216x^2 -216x + 81

The expression is given as:

(2x -3)^4

Using the binomial expansion, we have:

\((2x -3)^4 = ^4C_0 * (2x)^4 * (-3)^0 +^4C_1 * (2x)^3 * (-3)^1 + ^4C_2 * (2x)^2 * (-3)^2 + ^4C_3 * (2x)^1 * (-3)^3 + ^4C_4 * (2x)^0 * (-3)^4\)

Evaluate the combination factors.

So, we have:

\((2x -3)^4 = 1 * (2x)^4 * (-3)^0 + 4 * (2x)^3 * (-3)^1 + 6 * (2x)^2 * (-3)^2 + 4 * (2x)^1 * (-3)^3 + 1 * (2x)^0 * (-3)^4\)

Evaluate the exponents and the products

\((2x -3)^4 = 16x^4 + 96x^3 +216x^2 -216x + 81\)

Hence, the value of expanding (2x -3)^4 is 16x^4  + 96x^3  +216x^2 -216x + 81

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Answer: Slope is 1 and the intercept is 4

Answer:

$25

Step-by-step explanation:

If it was $25.59 then we would round up

But it isn't

So the answer is $25

Answer:

$26

Step-by-step explanation:

25.49,

then 9 will turn to plus 1

making 4 turn into 5

ten making 25 turn into 26

Answer:

10^2*10^2

Step-by-step explanation:

1) Write 100*100 in as powers of 10: 10^2 * 10^2

The volume of the solid generated by revolving the shaded region about the y-axis is given by the formula V = π∫ab (y2) dy, where a and b are the limits of integration.

To solve this problem, we will need to determine the limits of integration and integrate the function to find the volume.

The lower limit of integration, a, is given by the x-intercept of the region, which is (1, 0). Therefore, a = 1.

The upper limit of integration, b, is given by the y-intercept of the region, which is (0, 2). Therefore, b = 2.

Plugging these values into the equation, we get: V = π∫12 (y2) dy = π∫12 y2 dy

Integrating the function yields: V = π [y3/3]12 = π (23/3 - 13/3) = 8π/3

Therefore, the volume of the solid generated by revolving the shaded region about the y-axis is V = 8π/3.

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Answer:

3

Step-by-step explanation:

Answer:

I don't really understand the question but the absolute values of everything is

7.5

10

9

6

4

2

0

2

5

6

8

10

7.5

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

72/6=12

48/4=12

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.

To determine the distance from Fresno where the cars meet, we need to consider the relative speeds and the time it takes for each car to travel. Car A starts in Sacramento and travels at a speed of 30 mph, while Car B starts in Los Angeles and travels at a speed of 75 mph.

Car A starts one hour earlier than Car B, so it has a head start. In that one hour, Car A would have traveled 30 miles (30 mph x 1 hour). The remaining distance between Car A and Fresno would be 400 miles - 30 miles = 370 miles.

Now, we need to calculate the time it takes for Car B to travel from Los Angeles to Fresno, which is 150 miles. Using the formula Time = Distance / Speed, the time taken by Car B would be 150 miles / 75 mph = 2 hours.

Since Car B starts at noon, it will take 2 hours to reach Fresno, which means it will arrive at Fresno at 2pm. At that time, Car A would have been traveling for 3 hours (11am to 2pm). Given that Car A's speed is 30 mph, it would have covered a distance of 30 mph x 3 hours = 90 miles.

Therefore, the distance between Car A and Car B when they meet is 150 miles (distance from Fresno to Los Angeles) - 90 miles (distance covered by Car A) = 60 miles. Thus, they meet 60 miles away from Fresno, which is 200 miles away from Fresno along the entire route.

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Answer:

\(m=\frac{y2-y1}{x2-x1}\)

Step-by-step explanation:

Answer:

\(\huge\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\)

Step-by-step explanation:

The equation for slope is \(m=\frac{y_2-y_1}{x_2-x_1}\), when given two points,

\((x_1,y_1), and (x_2,y_2)\).

Hope it helps :) and let me know if you want me to elaborate.

answer:

∠B = 70°

step-by-step explanation:

∠A = ∠B

8x + 6 = 4x + 38

4x + 6 = 38

4x = 32

x = 8

4(8) + 38

32 + 38

= 70

Answer:

8 1/3

Step-by-step explanation:

4 1/2 + 3 5/6

First, we must convert the fraction to a common denominator.

1/2 = 3/6

4 3/6 + 3 5/6

3/6 + 5/6 = 8/6 = 1 2/6 = 1 1/3

1 1/3 + 4 + 3 = 8 1/3

The answer is 8 1/3.

Answer: 8 1/3

Step-by-step explanation:

4 1/2 + 3 5/6

So what we do is we make them have the same denominator

1/2 = 3/6

Now... 3/6 + 5/6 = 8/6

8/6 will have to be converted into a mixed number so...

that will be 1 2/6

now we add the two whole numbers 4 and 3 which is 7

7+1=8

8 + 2/6 = 8 2/6

now simplify that and you get 8 1/3

By definition, the distance between two points is always positive, so the correct option is D.

Let's say that our plane has rectangular coordinates, so it would be something like a xy-plane.

Each point has 2 coordinates, so we can write:

A = (x₁, y₁)

B = (x₂, y₂)

The distance between the points is given by:

\(D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

As you can see, the distance is defined as positive (indifferent of the coordinates of the points).

So the correct option is D, the distance is always positive.

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Hello! :)

To solve you equation, we will first Distribute

(-3) (w) + (-3) (3) + 4w

= -3w + -9 +4w

Now, we will combine like terms

-3w + -9 + 4w

= (-3w + 4w) + (-9)

= w + 9

Hope this helped you!

THEDIPER

Answer:

(6 – √25)/4

=(6 – 5)/4

= 1/4

Answer:

-2X=O

X=0

THE ANSWER IS X=0

Step-by-step explanation:

Hopes it helps

Answer:

the worm line would be 4 inches long

We are asked to find the equation (in vertex form) of the given parabolla, by using the information from its graph.

We know that the vertex is located at the top of the graph (-2, 9), and that it is a parabolla with branches pointing down (so the leading coefficient must be a negative value.

We use the vertex form of the parabola , using the coordinates of the vertex we see:

and proceed to determine the value of "a" by using the point we know the function is going through: (0, 5):

Therefore, we found the vertex form of the quadratic represented by the given graph to be:

f(x) = - (x+2)^2 + 9

Answer:

Similar to the question: They figure that they will drive 792 miles round trip. If their car gets 25 miles per gallon and the current cost of gasoline is $2.35, what will the gas for their trip cost? $74.45 George is taking the same trip to San Antonio (792 miles)

Step-by-step explanation:

Hope it helps :)

To solve the inequalities -2x + 4 < 8 and 3x + 4 ≤ -5, we will solve them individually and then represent the solutions on a number line.

For the first inequality, -2x + 4 < 8, we will isolate x:

-2x + 4 - 4 < 8 - 4

-2x < 4

Dividing both sides by -2 (remembering to reverse the inequality when multiplying/dividing by a negative number):

x > -2

For the second inequality, 3x + 4 ≤ -5, we isolate x:

3x + 4 - 4 ≤ -5 - 4

3x ≤ -9

Dividing both sides by 3:

x ≤ -3

Now we represent the solutions on a number line. We mark -2 with an open circle (since x > -2), and -3 with a closed circle (since x can be equal to -3). Then we shade the region to the right of -2 and include -3 to represent the solutions.

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Answer:

see image...

start with Graphing Form: y = a(x-h)²+ k

knowing that h is the x value (negative of it)  of the vertex , and k is the y value of the vertex

Graphing Form Equation: y =  a(x+3)²+32

you are also given that when the x value is 5 the y value has to be 0

0 = a(4)^2 + 32

a has to be - 1/2    

Step-by-step explanation:

Range of the value of the game played:To get the range of the value of the game played, we have to find the minimum and maximum possible scores. Minimum score of the game: The minimum score is when both teams play their strongest defense strategy.

For Letran, their strongest defense strategy is the Man-to-man defense and for Mapua, their strongest defense strategy is the Half-court Press defense.Using these defense strategies, Letran can get a score of 45 and Mapua can get a score of 30.Thus, the minimum possible score is 45 + 30 = 75.Maximum score of the game: The maximum score is when both teams play their weakest defense strategy.

For Letran, their weakest defense strategy is the Press defense and for Mapua, their weakest defense strategy is the Man-to-man defense.Using these defense strategies, Letran can get a score of 55 and Mapua can get a score of 40.Thus, the maximum possible score is 55 + 40 = 95.Therefore, the range of the value of the game played is 75 to 95.b) To find the defense strategy in which Letran is weak, we have to see which defense strategy allows Mapua to get the highest score.

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Answer:

it is C when I calculate

Answer:

The code is 571113

Step-by-step explanation:

The problem requires that we find the prime factors of 5005

1. 5005 is a multiple of 5 since it ends with a number 5

5 is one of the numbers

Dividing 5005/5 = 1001

the next prime number after 5 is 7

so 1001/7= 143

7 is one of the numbers

the next prime number after 7 is 11

so 143/11= 13

13 is one of the numbers

In all the prime factorization of 5005 is found as follows

5,7 11,13

Combining these numbers gives the 6 digit code

571113

Answer:

Step-by-step explanation:

The two square roots of 12.25 are:

(1) 3.5: 3.5 x 3.5 = 12.25

(2) -3.5: -3.5 x -3.5 = 12.25

Both of these numbers squared give a result of 12.25. However, -3.5 is the negative of 3.5, so it's important to specify which root is meant, depending on the context of the problem.