solve the systems of equations
y=x²-6
y=-2x+9

Answer:

A

Step-by-step explanation:

As n approaches infinity, the terms in the parentheses approach 0, and the sum converges. Therefore, the series is convergent.

To determine whether the series is convergent or divergent, we need to express sn as a telescoping sum.

Given the series

\(\sum_{1}^{\infty} 24 n(n + 3) n\) = 1,

we can rewrite it as:

sn = \(\sum_{1}^{\infty} 24 n(n + 3) n\)

To express sn as a telescoping sum, we need to find a way to simplify the terms. One approach is to decompose the expression inside the summation into partial fractions.

First, let's rewrite the expression:

24 n(n + 3) = 24n² + 72n

Next, we can rewrite 24n² + 72n as the sum of two partial fractions:

24n² + 72n = A/n + B/(n + 3)

Multiplying both sides by n(n + 3), we get:

24n² + 72n = A(n + 3) + Bn

Expanding the right side, we have:

24n² + 72n = An + 3A + Bn

Comparing coefficients, we get:

24n² = An + Bn
72n = 3A

From the first equation, we can equate the coefficients of n²:

A = 24

From the second equation, we can equate the coefficients of n:

3A = 72
3(24) = 72
A = 8

Now that we have the values of A and B, we can rewrite the expression inside the summation:

24 n(n + 3) = 8/n + B/(n + 3)

Now, we can express sn as a telescoping sum:

sn = \(\sum_{1}^{\infty}(8/n + B/(n + 3))\)

By simplifying this telescoping sum, we can see that the terms cancel each other out, leaving only a few remaining terms. The sum becomes:

sn = (8/1 - 8/4) + (8/2 - 8/5) + (8/3 - 8/6) + ...

As n approaches infinity, the terms in the parentheses approach 0, and the sum converges.

Therefore, the series is convergent.

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Answer-

B) Plane and line

The pair which is undefined terms are used to define the term parallel lines is B. plane and line

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

Properties of Parallel Lines

Corresponding angles are equal. Vertical angles/ Vertically opposite angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal.

My dog not only likes to play fetch but also chase cars. Parallel: My dog not only likes to play fetch, but he also likes to chase cars. My dog likes not only to play fetch but also to chase cars. When you connect two clauses or phrases with a word of comparison, such as than or as, use parallel structure.

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Answer:

-y+6

Step-by-step explanation:

-3 (y+2) +2y

-3y -6 +2y

-y+6

Answer:

-y-6

Step-by-step explanation:

Answer:

x ≈ 12.182

Step-by-step explanation:

1 - 2lnx = - 4 ( subtract 1 from both sides )

- 2lnx = - 5 ( divide both sides by - 2 )

lnx = 2.5

x = \(e^{2.5}\) ≈ 12.182 ( to the nearest thousandth )

Answer:

x = 12.182  (nearest thousandth)

Step-by-step explanation:

Given equation:

\(1-2 \ln x=-4\)

Subtract 1 from both sides:

\(\implies 1-1 -2 \ln x =-4-1\)

\(\implies -2 \ln x=-5\)

Divide both sides by -2:

\(\implies \dfrac{-2 \ln x}{-2}=\dfrac{-5}{-2}\)

\(\implies \ln x = \dfrac{5}{2}\)

\(\textsf{As }\: \ln x=\log_ex \:\:\textsf{}\), the natural logarithm can be canceled by giving both sides a base of e (Euler's number):

\(\implies e^{\ln x}= e^{\frac{5}{2}\)

\(\implies x= e^{\frac{5}{2}\)

\(\implies x=12.182\:\: \sf (nearest\:thousandth)\)

a) An exponential formula for the population of Bhutan after t years is f(t) = 2,200,000 x 1.0211^t

b) According to the formula, the population of Bhutan in 2008 will be 2,342,219.

An exponential formula is an equation based on a constant periodic growth or decay.

The exponential equation is also known as an exponential function.

Bhutan's population in 2005 = 2,200,000

Annual growth factor = 1.0211

Let the population after 2005 in t years = f(t)

f(t) = 2,200,000 x 1.0211^t

The number of years between 2008 and 2005 = 3 years

The population in 2008 = f(3)

f(3) = 2,200,000 x 1.0211³

f(3) = 2,342,219

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For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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For the segments to be congruent, x should be 13/2.

This is a case of congruency of segments. We know that two segments are congruent if and only if they have equal lengths.

Now, here the two line segments JK and RS have lengths 2x-9 and 30-4x respectively.

So, to be congruent, JK and RS must be of equal length.

Or in other words, 2x-9 = 30-4x

or 6x= 30 + 9 =39

i.e. 6x = 39.

Dividing both sides by 3, we get

2x=13 , which implies , x =13/2 or 6.5

Thus, for JK and RS  to be congruent  , x =13/2.

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Answer:

x=7.5

Step-by-step explanation:

35x-25=237 1/2

     +25 +25

35x=262 1/2

x=7.5

Answer:

84

Step-by-step explanation:

5/2 for every 2.5 skiers one snowboarder rides

[A] 2.5 skiers to one snowboarder

[B] \(\frac{1}{2.5} = \frac{?}{210}\)

210=2.5*x divide both sides by 2.5

x=84

[C] 84 snowboarders rode at the same time as 210 skiers

Answer:

1 = 128

2 = 52

3 = 52

4 = 128

5 = 128

6 = 52

7 = 52

8 = 128

Answer: here is what I've got 8,312,984

I thank it is B.

Step-by-step explanation:

Given the following numbers 1×29×107×2679+47 and 1×71.

We are asked to determine which number is composite and which is prime.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

What is a composite number? A composite number is a number with more than two factors (ex: 10=>1,2,5,10).

What is a prime number? A prime number is a number with only two factors, the number "1" and itself (ex: 7=> 1,7).

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Right away we can recognize 1×71 will not be a composite number. No nice factors go into it rather than the number "1" and "71," so this is a prime number.

This leaves 1×29×107×2679+47 to be our composite number. I would simply just use a calculator to expand this number.

=> 1×29×107×2679+47= 8,312,984

Thus, the second option is correct.

Given the the following equations, find the unknown value, ?, that makes the equations true

.\(? - 4 - 2p + 5 = 6p + 17d - 4 + 3 - 2d = ? - 112c - 8 - 2c + 10 - 4 = 10c -?\)

Starting with the equation, \(? - 4 - 2p + 5 = 6p + 1\)

Start with the side that is more complex, \(?-4-2p+5\). Simplify it as best you can by combining all like terms.

\(?-4-2p+5\)

=>\((?)+(-2p)+(-4+5)\)

=> \(?-2p+1\)

Now look at the R.H.S (\(6p+1\)), notice how we have the +1 in the simplified expression above. So what value would we put in for "?" to get 6p? That value would be 8p.

Now we have, \((8p)-2p+1=6p+1\)

=> \(6p+1=6p+1\)

The equation matches making it true. I will now do the rest without a long explanation. If you need an explanation or have any questions, please leave a comment.

Now for, \(7d - 4 + 3 - 2d = ? - 1\)

Simplifying L.H.S, we get...

=> \(5d-1\)

To match it with the R.H.S, "?" would have to be 5d.

Lastly, \(12c - 8 - 2c + 10 - 4 = 10c -?\)

Simplifying L.H.S, we get...

=> \(10c-2\)

To match it with the R.H.S, "?" would have to be 2.

Answers:

8p, 5d, & 2

Answer:

1 is equal

2 is greater

3 is greater

Step-by-step explanation:

2^3 x 2^5 is 32, and 2^5 is 32, meaning these are equal.

2^2 x 3^2 is 36, and 6^3 is 216, meaning 6^3 is greater.

2^3 x 3^2 is 72, and 6^2 is 36, meaning that 2^3 x 3^2 is greater.

Answer:

Step-by-step explanation:

15 divided by 15 is 1

3.45 divided by 15 is 0.23

The cost per ounce is 23 cents, or $0.23

Answer:

b

Step-by-step explanation:

Answer:

Hi! The answer to your question is B. 30 Trees

Step-by-step explanation:

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☆Brainliest is greatly appreciated!☆

Hope this helps!!

- Brooklynn Deka

Answer: We can start solving this problem by using a system of equations. Let x be the number of plain glazed donuts Nicole buys, and y be the number of chocolate cake donuts she buys. We know that:

x + y = 20 (The total number of boxes of donuts she buys is 20)

4x + 5y = 91 (The total amount of money she spends is $91)

We can use the first equation to solve for one variable in terms of the other. For example, we can substitute x = 20 - y into the second equation:

4(20 - y) + 5y = 91

80 - 4y + 5y = 91

-4y + 5y = 91 - 80

y = 11

So Nicole bought 11 boxes of chocolate cake donuts. We can substitute that back into the first equation to find the number of plain glazed donuts she bought:

x + 11 = 20

x = 9

So Nicole bought 9 boxes of plain glazed donuts.

We can check our answer by substituting our values of x and y back into the original equations:

x + y = 9 + 11 = 20 (This is the total number of boxes of donuts she bought, which is 20)

4x + 5y = 4(9) + 5(11) = 91 (This is the total amount of money she spent, which is $91)

Both equations are true, so our solution is correct.

Step-by-step explanation:

(a) The fraction of the patients who stopped taking their medicine is 5/8.

(b) To convert this fraction to a decimal, divide the numerator (5) by the denominator (8). The decimal form of the fraction is 0.625.

(c) To find the number of patients in the study who quit taking their medicine, we need to calculate 5/8 of the total number of heart-attack patients (1209).

To do this, multiply 1209 by 5/8:

(1209 * 5) / 8 = 754.375

Rounded to the nearest whole number, approximately 754 patients in the study quit taking their medicine.

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The answers, rounded to the appropriate number of significant figures, are as follows:

(a) 1.088 ×\(10^2\)

(b) 2.132

(c) 1.3331 ×\(10^1\) and

(d) 1.05.

Let's calculate the answers to the given operations using the appropriate number of significant figures.

(a) 8.370×1.3×10

To perform this multiplication, we multiply the decimal numbers and add the exponents of 10:

8.370 × 1.3 × 10 = 10.881 × 10 = 1.0881 × \(10^2\)

Since the original numbers have four significant figures, we round the final answer to four significant figures:

1.088 × \(10^2\)

(b) 4.265/2.0

For division, we divide the decimal numbers:

4.265 ÷ 2.0 = 2.1325

Since both numbers have four significant figures, the answer should be rounded to four significant figures:

2.132

(c) (1.2588×\(10^3\))×(1.06×\(10^-^2\))

To multiply these numbers, we multiply the decimal numbers and add the exponents:

(1.2588 × \(10^3\)) × (1.06 × \(10^-^2\)) = 1.333128 × \(10^1\)

Since the original numbers have five significant figures, we round the final answer to five significant figures:

1.3331 × \(10^1\)

(d) \((1.11)^(^1^/^2^)\)

To calculate the square root, we raise the number to the power of 1/2:

\((1.11)^(^1^/^2^)\)= 1.0524

Since the original number has three significant figures, the answer should be rounded to three significant figures:

1.05

It's important to note that the significant figures in a result are determined by the original data and the operations performed. The final answers provided above reflect the appropriate number of significant figures based on the given information and the rules for significant figures.

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Based solely on the mileage of the Eurovan, it is likely to be in above-average condition.

The condition of a vehicle is influenced by several factors, including mileage, maintenance history, usage, and overall care. While high mileage can generally indicate wear and tear on a vehicle, it does not necessarily imply poor condition. Eurovans are known for their durability and reliability, so even with 81,718 thousand miles, it is possible for the van to be in above-average condition.

To determine the true condition of the Eurovan, additional information beyond mileage is required. Factors such as regular maintenance, service records, and the overall care provided by the previous owner(s) play a crucial role in assessing the van's condition. If the van has been well-maintained, with routine servicing and repairs, it is more likely to be in above-average condition despite the higher mileage. Additionally, the overall usage of the van should be considered. If the majority of the mileage consists of long highway trips rather than stop-and-go city driving, it can contribute to less wear and tear on the engine and components. Furthermore, factors such as storage conditions, accident history, and the quality of the driving surface can also impact the condition of the Eurovan.

In summary, while the mileage of the Eurovan may initially suggest a below-average condition, it is essential to consider additional factors such as maintenance history, usage patterns, and overall care to make a more accurate assessment. Without this additional information, it is reasonable to assume that the Eurovan is likely to be in above-average condition based on its reputation and durability.

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Answer

EAD= EBC true.

Step-by-step explanation:

Both triangles are equal. The line between AE and EB show the lines are equal. In turn this makes the sides AD and BC equal. DC are the same length as AE and EB. In short, all sides are equal so the triangles are the same.

Answer:

(1) False. (2) True. (3) True. (4) True. (5) True

Step-by-step explanation:

This is really easy :)

The points x ≤ 1 2/3 and x<-3/4 has plotted in the number line

A number line is a visual representation of the real number system. It is a straight line on which numbers are marked at equal intervals, with zero in the center and positive numbers to the right of zero and negative numbers to the left of zero

The line represents the set of all real numbers, with negative numbers to the left of zero and positive numbers to the right. The point marked with a circle (o) represents the value of x that satisfies both conditions, which is x ≤ 1 2/3 and x < -3/4. Since -3/4 is less than 1 2/3, any value of x that satisfies x ≤ 1 2/3 must also satisfy x < -3/4, so the two conditions are equivalent in this case.

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Answer:

the awnser to the question is: 40°

Based on the given information, we know that one bicycle trail in a new housing development is 3 miles long and the other trail is the same length as the first trail.

Therefore, the length of the second trail is also 3 miles.

Hence, the answer is: 3 miles

It seems like there's a missing piece of information in your question about the length of the second trail.

However, I will try my best to help you with the given information.
Two bicycle trails are developed in the housing development.

The first trail is 3 miles long, and we need to find the length of the second trail.

Unfortunately, there is no information provided about the second trail's length.

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For Part 2, we cannot determine the specific values between which approximately 95% of the sample will fall. And for Part 3, we cannot determine the exact percentage of sample values between 51 and 837.

From the given information, we can make the following clarifications:

Part 1: Approximately 68% of the sample values fall between 43 and 91.

Part 2: Approximately 95% of the sample values will fall between two values. However, the specific values are not provided in the given information.

Part 3: If we do not assume that the histogram is bell-shaped, it is unclear what percentage of the sample values will be between 51 and 837. The options provided are not clear and do not align with the given information.

Therefore, for Part 2, we cannot determine the specific values between which approximately 95% of the sample will fall. And for Part 3, we cannot determine the exact percentage of sample values between 51 and 837.

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Answer:

x² - 12x + 27

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x² - 13x + 36 + x - 9 ← collect like terms

= x² - 12x + 27 ← in standard form

Answer:

because they have 3 sides

Step-by-step explanation: