The sum of an infinite geometric sequence is seven times the value of its first term.
a) Find the common ratio of the sequence.
b) Find the least number of terms of the sequence that must be added in order for the sum to exceed half the value of
the infinite sum.

Answer: The total distance covered by the car is 331 9/16 km.

Step-by-step explanation:

We know that, speed= distance/time taken

Therefore, distance = speed x time taken

= 132 5/8 x 2 1/2

= 5/2 x 1061/8

= 5305/16

= 331 9/16 km

Therefore, total distance is 331 9/16 km.

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Answer:

1. a

2. d

3. c

4. b

Step-by-step explanation:

You're matching the formulas up with the sequences. Start with one of the formulas ("rules") and see if it matches up with any of the given sequences, that's what I would do.

So first, a little explanation:

A recursive formula tells you how to find a term of a sequence using the value of the previous term. another way to think of it is finding the next term of a sequence using a particular term.

aₙ refers to the nth term in a sequence. this means the position, such as first, second, third, etc.

So a₁ means the first term, and aₙ₋₁ refers to the term aₙ (aₙ will be the term we are talking about)

I'll explain as we go along.

1. aₙ=3+aₙ₋₁ ; a₁=2

The second part means that the sequence begins with 2, but all four sequences start with 2, so this doesn't help you narrow anything down.

The first part tells you that each term is derived by adding 3 to the previous term. how do you figure this out?

aₙ is the term in a given position. let's take n=2, for example. everywhere where there was n, substitute 2.

a₂=3+a₍₂₋₁₎=3+a₁

We already know that a₁=2, so a₂=3+2=5

You can try a few more examples, but by this point, it should be clear that recursive formula 1 matches up with sequence a.

2. The rule says that each term is the opposite of the term before it. Again, you can substitute values of n to see this for yourself. But the only sequence that satisfies this condition is d.

3.  This rule states that each term is given by 5 minus the previous term. Let's try to find a₂: a₂=5-a₁

a₁=2 for all of the sequences, so a₂=5-2=3

The only sequence with a₂=3 is c.

Again, you can try this with more values of n. and if the sequences didn't all happen to begin with the same number, you would just have to do a little more trial and error.

4. Of course, there is only one answer left. but let's try to work through the problem anyway.

for n=2

a₂=2-a₁=2-2=0

and this matches up with b. I think this formula is the most confusing out of the four, but with a little patience, you should be okay.

Hopefully this helped!

Answer:

4. x ≥ -1

Step-by-step explanation:

The graph shows a directed line that starts at -1 towards the your right. The full circle indicates that -1 is included among the possible values of x. This means that all possible values of x include -1 and above.

Therefore, we can say x is greater than or equal to -1.

This is represented as:

x ≥ -1

Hello!

\(slope = 2\\\\y-intercept = (0, 3)\\\\Equation: y = 2x + 3\)

We can find the slope using the slope formula:

\(slope = \frac{y_{2} - y_{1}}{x_{2}-x_{1}}\)

Plug in any two points from the table. We can use (0, 3) and (1, 5):

\(slope = \frac{5 - 3}{1-0}\)

\(slope = 2\)

Now, we can find the y-intercept by finding the y-value at which x = 0.

According to the table, when x = 0, y = 3. Thus, the y-intercept is:

\((0, 3)\)

We can write an equation using the slope and y-intercept in the format

y = mx + b where "m" is the slope and "b" is the y-intercept.

Plug in the solved values into the equation:

y = 2x + 3.

**Graphed below**

The value of x that makes the line containing (1,2) and (5,3) perpendicular to the line containing (x,4) and (3,0) is x = 2.

To determine the value of x such that the line containing (1,2) and (5,3) is perpendicular to the line containing (x,4) and (3,0), we need to find the slope of both lines and apply the concept of perpendicular lines.

The slope of a line can be found using the formula:

slope = (change in y) / (change in x)

For the line containing (1,2) and (5,3), the slope is:

slope1 = (3 - 2) / (5 - 1) = 1 / 4

To find the slope of the line containing (x,4) and (3,0), we use the same formula:

slope2 = (0 - 4) / (3 - x) = -4 / (3 - x)

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of a line perpendicular to it is -1/m.

So, we can set up the equation:

-1 / (1/4) = -4 / (3 - x)

Simplifying this equation:

-4 = -4 / (3 - x)

To remove the fraction, we can multiply both sides by (3 - x):

-4(3 - x) = -4

Expanding and simplifying:

-12 + 4x = -4

Adding 12 to both sides:

4x = 8

Dividing both sides by 4:

x = 2

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Answer:

I can't understand anything

Answer:

11

Step-by-step explanation:

Rewrite expression using given information:

20 - 3a + 2b = 20 - 3*7 + 2*6

20 - 21 + 12 = 11

Answer:

A. 54 miles B. 27 miles for the bikeathon

Answer:

solid photo

Step-by-step explanation:

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

175 units cubed

Step-by-step explanation:

I think 7, 5, and 5 are the length, width, and height. multiply to find the volume and you have 175 units cubed.

have a great day and thx for your inquiry :)

Using a calculator, the value of  csc (203°) is -1.086

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since csc (203°) = 1/[sin (203°)]

Press 1/ [sin (203°)] and then the equal to button on your calculator. We have:

1/[sin (203°)] = -1.086

Note: If you calculator have "cosec" or "csc" button, you can simply press cosec (203°) or csc (203°) to get the answer.

Thus, the value of  csc (203°) is -1.086

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The number of miles that Jose will have left after resting will be 1 1/8 miles.

Total distance to be covered = 2 3/4 miles

Distance traveled = 1 5/8 miles

Therefore, in order to get the distance that's left for Jose to complete his journey, we've to subtract the distance traveled from the total distance and this will be:

= 2 3/4 - 1 5/8

= 2 6/8 - 1 5/8

= 1 1/8

Therefore, he has 1 1/8 miles left to travel.

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Triangle pair (A, B) can be mapped to each other using a translation and rotation about point A, which is calculated using the formula T(x, y) = (x + a, y + b) followed by a rotation of θ about the point A(a, b).

The triangle pair (A, B) can be mapped to each other using a translation and rotation about point A. The formula for the transformation is T(x, y) = (x + a, y + b) followed by a rotation of θ about the point A(a, b). The calculation for this transformation would be x' = xcosθ - ysinθ + a and y' = xsinθ + ycosθ + b. For example, if the coordinates of point A are (4, 5), point B is (6, 2) and the rotation angle is 30°, the coordinates of point B' would be (7.9, 5.4) after the transformation.

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Answer:

1700 meters / hour

Step-by-step explanation:

160x20 = 3200

3200/ 2 = 1700

Answer:

☑ 3 is a constant.

☑ 5 is a coefficient

Step-by-step explanation:

It is a sum of two terms.

It a product of different terms

5 and 4 are coefficients.

Answer:

y = -7x - 5

Step-by-step explanation:

y-intercept= 16 - (-7) (-3) = - 5

Answer: yes

Step-by-step explanation:

\(\frac{7}{8} -\frac{1}{5} \\\\frac{35}{40}-\frac{8}{40} \\\frac{27}{40}\)

The value(s) for which the rational expression −5u+12−2u+2 is undefined is u = 1.

The expression or an equation which can be undefined at some point is a celled the radial expression.

f(u) = -5u +12 / -2u +2

For the function to be undefined, denominator must be equal to zero.

-2u +2 =0

-2u =-2

u = 1

Thus, the value for which the given expression is undefined is 1.

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Answer: 4:00 pm

Step-by-step explanation:

I think its just 6.60 divided by six, thats how many each one costs, then multiply it by 3

Hope this helps :)

Answer:

3.3

Step-by-step explanation:

because you can divide 6.60 by 6 which is 1.1 then multiply it by 3

Answer:

\(x > -1\) or

\(x > 2\) or

\(x > 3\)

Step-by-step explanation:

Given

\((x + 1)(x - 2) (x - 3) > 0\)

Required

Solve; with steps

\((x + 1)(x - 2) (x - 3) > 0\)

Start by splitting the inequality as follows

\(x + 1 > 0\) or \(x - 2 > 0\) or  \(x - 3 > 0\)

Solve the inequalities one after the other

Solving: \(x + 1 > 0\)

Subtract 1 from both sides

\(x + 1 - 1 > 0 - 1\)

\(x > -1\)

Solving: \(x - 2 > 0\)

Add 2 to both sides

\(x - 2 +2 > 0 +2\)

\(x > 2\)

Solving: \(x - 3 > 0\)

Add 3 to both sides

\(x - 3 +3> 0+3\)

\(x > 3\)

Hence, the solution to the inequality is

\(x > -1\) or

\(x > 2\) or

\(x > 3\)

Answer:

9

Step-by-step explanation:

You don't need to pass through each edge once.

If we name the top vertex 1 and the bottom vertex 2 then here are the possible combinations:

A-1-B

A-B

A-2-B

A-1-B-A-2-B

A-2-B-A-1-B

A-B-1-A-2-B

A-B-2-A-1-B

A-1-B-2-A-B

A-2-B-1-A-B

Some people say 6 because they think you need to pass through all the edges. But the only restriction with travelling on the edges is you can't pass one twice. The point is read the wording and it becomes easy.

Hope this helps!

Answer:

C. \(F(x) = -x^2 - 3\)

Step-by-step explanation:

The function, F(x), has flipped over the x-axis (as seen) meaning that the function has to have a negative sign in front. The function has also shifted downwards 3 units, meaning that 3 has to have been subtracted from the function.

This makes "C," the correct answer, as it fulfills these requirements.

Square Area = side x side = 3x3 = 9

Rectangle Area = side x side= 7x3= 21

9 + 21 = 30 square inches

Answer:

30 square inches

Step-by-step explanation:

   \(\boxed{\text{\bf Area of rectangle = length *width}}\)

Rectangle1:

     Area = 6 * 3

              = 18 square inches

Rectangle2:

Area = 4 * 3

          = 12 square inches

Area of the figure = area of rectangle1 + area of rectangle2

                             = 18 + 12

                             = 30 square inches

Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Answer:

Since f(-1) = 0 and f(-2) = 0, we can set up two equations:

(-1)³ + p(-1)² - q(-1) - 4 = 0

(-2)³ + p(-2)² - q(-2) - 4 = 0

Simplifying each equation, we get:

-1 + p - q - 4 = 0

-8 + 4p - 2q - 4 = 0

Simplifying further, we get:

p - q = 5

2p - q = 6

Solving for p and q, we can add the two equations together to eliminate q:

p - q + 2p - q = 5 + 6

3p - 2q = 11

Then, we can substitute the value of q from the first equation into this equation to solve for p:

3p - 2(q + 5) = 11

3p - 2q - 10 = 11

3p - 2q = 21

3p - 2(5 + p) = 21

p - 10 = 7

p = 17

Substituting this value of p into either equation for q, we get:

q = p - 5 = 12

Therefore, the coefficients are p = 17 and q = 12. To factor the expression, we can use synthetic division or long division. Using synthetic division, we get:

-1 | 1 17 -12 -4

|__ -1 -16 28

1 1 12

This gives us the factorization:

f(x) = (x + 1)(x² + x + 12)

To find the solutions, we can use the quadratic formula on the quadratic factor:

x = (-1 ± sqrt(1 - 4(1)(12))) / 2(1)

x = (-1 ± sqrt(1 - 48)) / 2

x = (-1 ± sqrt(-47)) / 2

x1 = (-1 + i(sqrt(47))) / 2

x2 = (-1 - i(sqrt(47))) / 2

Therefore, the solutions are x1 = (-1 + i(sqrt(47))) / 2, x2 = (-1 - i(sqrt(47))) / 2, and x3 = -1.

Step-by-step explanation:

give me thanks for more! your welcome bud!

Answer: 72.36

Step-by-step explanation:

To find the total amount of salt in the bowl after Omar poured 13.2 grams, we need to add the initial amount of salt in the bowl to the amount of salt Omar added.

The initial amount of salt in the bowl was 59.16 grams.

Omar added 13.2 grams of salt to the bowl.

To find the total amount of salt in the bowl now, we add these two amounts: 59.16 + 13.2 = 72.36

Therefore, the bowl contains 72.36 grams of salt now.