Create a table of values to show that the exponential expression 2^x eventually overtakes the quadratic expression 8x^2

The equation of the circle with radius 9 and center ( -1,-8 ) is( x + 1 )² + ( y + 8  )² = 81.

The standard form equation of a circle with center (h, k) and radius r is:

( x - h )² + ( y - k )² = r²

Given that the circle has a center of (-1, -8) and the radius is 9.

Hence; from the standard form of the equation of the circle:

Center ( h , k ) = ( -1, -8 )

h = -1

k = -8

And radius r = 9

Plug these values into the above formula and simplify.

( x - h )² + ( y - k )² = r²

( x - ( -1 ) )² + ( y - ( -8 ) )² = 9²

Simplify

( x + 1 )² + ( y + 8  )² = 81

Therefore, the equation of the circle is ( x + 1 )² + ( y + 8  )² = 81.

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Answer:

11/66, or 11 times

Answer: 3. Prism

explanation: An apex is basically, the point where all lines meet at one point, and a prism is the one shape that doesn't have a apex. Hope this helps!

There are more than one solution for the given system.

Hence the correct option is C.

The given system of equations is,

y=-x-3

2y + 2x = -6

Write the equation in the form of ax + by = c,

Therefore, the system be

x  +  y  = -3

2x + 2y = -6

We know that,

The system of equations  a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If  [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]

Then the system has more than one solution.

Therefore,

1/2 = 1/2 = -3/-6

              =  1/2

Hence, this has more than one solution or roots.

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12.50

Parallel lines are lines that will never intersect.

Parallel Lines

Parallel lines run opposite of each other without intersecting. For lines to be parallel, they must have the same slope. The equation given to us is written in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. So, the slope from the equation is 12.50.

Finding Parallel Lines

In order to find other lines that are parallel to the line given, all we need to do is write another equation with the same slope. However, 2 lines that are the same are not considered to be parallel. This means that for 2 lines to be parallel they must have the same slope but different y-intercepts. For example, a parallel line could be y = 12.50x + 6.

a. The z-score for a value of 25 is -0.57, to the nearest hundredth.

b. The percent of the data is greater than 34 is about 2%.

To find the z-score for a value of 25, we can use the following formula;

z = (x - μ) /σ

where;

z = (25 - 27) / 3.5

z = -0.57

Rounding to the nearest hundredth, we get the z-score of -0.57.

The z-score for x = 34 is calculated as follows;

z = (x - μ) / σ

z = (34 - 27) / 3.5

z = 2

Using a standard normal distribution table, we find that the percentage of data that is greater than 34 = 2.28%.

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Answer: Most Data takes 10 seconds to download. (sorry if this answer is very vague its hard to explain)

Answer:

Step-by-step explanation:

This is a triangle with sides 15.2 cm, 6.6 cm, and 15.6 cm. To solve for the angles, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where a = 6.6 cm, b = 15.6 cm, c = 15.2 cm, and C is the angle opposite side c.

Using this formula, we can solve for the cosine of angle C:

cos(C) = (a^2 + b^2 - c^2) / 2ab

cos(C) = (6.6^2 + 15.6^2 - 15.2^2) / (2 * 6.6 * 15.6)

cos(C) = 0.748

Taking the inverse cosine of 0.748, we get:

C = 41.5 degrees

To find the other angles, we can use the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle B:

sin(B) = (b/sin(C)) * sin(A)

sin(B) = (15.6/sin(41.5)) * sin(A)

sin(B) = 0.614 * sin(A)

Using the fact that sin(A) + sin(B) + sin(C) = 1, we can solve for sin(A) and sin(B):

sin(A) = (sin(C) - sin(B)) / (1 + cos(C))

sin(A) = (sin(41.5) - 0.614 * sin(A)) / (1 + cos(41.5))

Solving for sin(A), we get:

sin(A) = 0.266

Using this value of sin(A), we can solve for sin(B):

sin(B) = 0.614 * sin(A)

sin(B) = 0.157

Taking the inverse sine of these values, we get:

A = 15.4 degrees

B = 123.1 degrees

Therefore, the triangle has angles of approximately 15.4 degrees, 123.1 degrees, and 41.5 degrees.

We can see here that the 90% confidence interval will be: 420.2 to 585.8.

An interval of values known as a confidence interval is one that is likely to include the real value of a population parameter. A confidence interval of 95%, for instance, indicates that there is a 95% likelihood that the population parameter's real value falls inside the interval.

We will find the sample mean first:

Sample mean = sum of data points / number of data points

Sample mean = 8551 / 17 = 503

Then the standard error will be:

Standard error = population standard deviation / square root of number of data points

Standard error = 190 / √(17) = 41.7

Confidence interval = Sample mean ± 1.645 × standard error.

where 1.645 is the z-score for a 90% confidence interval.

Confidence interval = 503 ± 1.645 * 41.7 = 420.2 to 585.8

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It is true that the functions f(x) and h(x) share a common x-intercept.

On the definition of a function, the x-intercept is given by the value/values of x for which the function assumes a value of zero.

Function f(x) is defined as follows:

x² + 4x.

Hence the x-intercepts are obtained as follows:

x² + 4x = 0

x(x + 4) = 0

x = 0 and x + 4 = 0 -> x = -4.

On a graph, the x-intercept of a function is the value of x at which the graph of the function crosses the x-axis.

Hence the x-intercept of function h(x) is given as follows:

x = -4.

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Answer:

-------------------------

Use the formula for the sum of n terms of a GP:

And use the nth term formula:

We can rearrange the sum formula to solve for the first term:

Plugging in the given values, we get:

Therefore, the first term of the GP is 121.5.

The ratio which represents the ratio of paperback books to hardcover books is 6 : 5.

Given that,

Michelle had 6 paperback books and 5 hardcover books on the shelf by her bed.

We have to find the ratio of the paperback books to hardcover books.

We have,

Number of paperback books = 6

Number of hardcover books = 5

We need to find the ratio of the paperback books to hardcover books.

Ratio = Number of paperback books / Number of hardcover books

         = 6/5

Hence the ratio is 6/5.

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The water level in the aquarium will rise by 18 cm.

The volume of water in the aquarium before adding the sand is given by:

Volume = (1/2) x 23 cm x 15 cm = 172.5 cm³

When the sand is added, its volume is 2350 cm³. Therefore, the new volume of water and sand in the aquarium is:

 = 172.5 cm³ + 2350 cm³

 = 2522.5 cm³

Let h be the height of the water level after adding the sand. The new volume of water in the aquarium is given by:

Volume = (1/2) x 23 cm x 15 cm x h

Setting this equal to the new total volume, we can solve for h:

(1/2) x 23 cm x 15 cm x h = 2522.5 cm³

h = 2522.5 cm³ / (1/2 x 23 cm x 15 cm) = 18 cm

Therefore, the water level in the aquarium will rise by 18 cm.

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Answer:

6 small baskets

Step-by-step explanation:

Ms smith has decided to split 45 apples among 5 learners. So, 45/5=9 apples.

However, she realizes only 8 apples can be held in a small basket, She will need to use at least two baskets to give 9 apples to each learner.

So, the number of baskets required can be calculated as:

45 apples ÷ 8 apples per basket = 5.625 baskets

Since we can't use a fraction of a basket, 5.625 is approximately equal to 6.

Therefore, Ms. Smith will need 6 small baskets to divide the apples equally among her learners

The measures of the arcs are: 16. m(MN) = 72°;  17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°; 24. m(PRN) = 265°; 25. m(MQN) = 288°

To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.

16. m(MN) = m<QRN

Substitute:

m(MN) = 72°

17. m(NQR) = 180° [semicircle is equal to 180 degrees]

18. m(NQ) = 180 - 72

m(NQ) = 108°

19. m(MRP) = 180 + (180 - 95)

m(MRP) = 180 + 85

m(MRP) = 265°

20. m(QR) = 72° [central angle is equal to intercepted arc measure)

21. m(MR) = 180 - 72

m(MR) = 108°

22. m(QMR) = 360 - 72 = 288°

23. m(PQ) = 180 - 95 - 72 = 13°

24. m(PRN) = 360 - 95

m(PRN) = 265°

25. m(MQN) = 360 - 72

m(MQN) = 288°

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The proportion is solved and value of a = 9 and constant is k =45

Given data ,

If a is inversely proportional to b, it means that their product remains constant

a * b = k

where "k" is the constant of proportionality.

Given that a = 1.5 when b = 30, we can substitute these values into the equation:

1.5 * 30 = k

k = 45

Now, we can use the value of k to determine the value of "a" when b = 5:

a * 5 = 45

Dividing both sides by 5:

a = 45 / 5

a = 9

Hence , proportionality constant is k = 45 and when b = 5, the value of "a" is 9

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A reading that is not possible is given as follows:

A. 0.102cal/g*f

The possible readings are obtained applying the proportions in the context of the problem.

The percent error is of 20%, hence the minimum reading is given as follows:

0.8 x 0.174 = 0.1392 cal/gf

The maximum reading is given as follows:

1.2 x 0.174 = 0.2088 cal/gf.

The reading from option A is the only reading that is not between the minimum and the maximum values.

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The probability of rolling a number other than 1 on a standard number cube is 5/6.

When rolling a standard number cube, there are six equally likely outcomes, one for each face of the cube. To find the probability of rolling a number other than 1, we need to determine the number of              favorable outcomes and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are rolling any number from 2 to 6, which gives us five possibilities. Therefore, the probability of rolling a number other than 1 is 5 out of 6.

Expressing this as a fraction, the probability can be written as 5/6. This means that out of all the possible outcomes, there is a 5/6 chance of rolling a number that is not 1.

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26. The length FE in the circle is 6 units

27. The arc AE has a measure of 64 degrees

From the question, we have the following parameters that can be used in our computation:

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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The trigonometric value equation is solved and sin θ = 24/25

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

And , sin² θ + cos² θ = 1

where the measure of cos θ = 7/25

On simplifying the equation , we get

sin θ = √ ( 1 - cos² θ )

sin θ = √ ( 1 - 49/625 )

sin θ = √576/625

sin θ = 24/25

Hence , the trigonometric relation is sin θ = 24/25

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Answer:

How could the intersection of the graphs of the two equations be located on a coordinate grid?

-From the origin, move three units right and nine units up

What does the solution to a system of two linear equations mean on a graph?

-The point of intersection of the two lines

Can you have more than one solution to a system of linear equations?

-Yes, if both lines are the same exact line

Can you have exactly two solutions to a system of linear equations?

-No, because lines are straight

Can you have no solutions to a system of linear equations?

-Yes, if the lines are parallel

Step-by-step explanation:

Please look at the images attached. Sorry for the bad handwriting, I'm on a computer.

Basically, a linear system of equations has one solution if the equations yield two lines that intersect exactly once.

A linear system of equations has no solutions if the lines are parallel, because they will never intersect.

A linear system of equations has infinite solutions if the system of equations yields two lines that are the same, because they will forever intersect.

If you have any questions about these answers, please tell me in the comments below my answer. I'll be happy to answer them :)

The value of x is 12.82, the value of z is 40.25.

Using Pythagorean theorem

50²= 39² + y²

y²= 2500- 1521

y= 32.28

Again Using Pythagorean theorem

z²= y²+ x²

z²- x²= 979

and, (39 + x)² = 50² + z²

(39 + x)² = 50² + (x² + 979)

1521 + 78x + x² = 2500 + x² + 979

78x = 1000

x ≈ 12.82

Substituting this value of x back into the first equation, we get:

z² - x² = 979

z² - (12.82)² = 979

z² ≈ 1620.12

Taking the square root of both sides, we get:

z ≈ 40.25

Therefore, the value of x is 12.82, the value of z is 40.25.

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The population of the patch land in 50 years is given as follows:

13,547.

An exponential function has the definition presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters are given as follows:

The parameter values in this problem are given as follows:

a = 42, b = 2, n = 6.

Hence the function for the population after x years is given as follows:

[tex]y = 42(2)^\frac{x}{6}[/tex]

The population in 50 years is given as follows:

[tex]y = 42(2)^\frac{50}{6}[/tex]

y = 13,547.

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The cosine of the angle's complement is 20/29

Let's start by using the fact that the sum of the measures of an angle and its complement is 90 degrees.

Let's call the angle A, and its complement B. Then we have:

cos A = 21/29

We want to find cos B. We know that cos B = sin A, because the sine of an angle is equal to the cosine of its complement.

So we need to find sin A.

We can use the Pythagorean identity:

sin²A + cos²A = 1

Substituting in cos A = 21/29, we get:

sin²A + (21/29)² = 1

Solving for sin A, we get:

sin A = ± 20/29

Therefore, we have:

cos B = sin A = 20/29

Hence, the cosine of the angle's complement is 20/29

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The nearest Whole percent, the percent increase of women students is approximately 21%.

The percent increase of women students, we need to compare the number of women students in 2005 and 2006.

In 2005, the number of women students was 123.

In 2006, the number of women students was 149.

To find the increase, we subtract the initial value (2005) from the final value (2006):

Increase = Final Value - Initial Value

Increase = 149 - 123

Increase = 26

Next, we need to calculate the percent increase. The percent increase is given by the formula:

Percent Increase = (Increase / Initial Value) * 100

Plugging in the values:

Percent Increase = (26 / 123) * 100

Calculating the percent increase:

Percent Increase ≈ 21.14%

Rounding to the nearest whole percent, the percent increase of women students is approximately 21%.

Therefore, the answer is 21%.

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Answer:

5

Hope this helps!

Step-by-step explanation:

Plug in m = 1 into the equation.

m = 1  :  [tex]\frac{4}{m} +1[/tex]  =>  [tex]\frac{4}{(1)} +1[/tex] = 4 + 1 = 5

Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90.

The wage rates for a junior employee are based on a percentage of the adult rate, but the exact percentage is not provided. Therefore, it is impossible to determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee without knowing the specific percentage and calculating the wages accordingly  Based on the Supermarkets Agreement 2012, the normal weekly pay for an adult aged 21 and over is $565.90. To determine how many people aged 16 and under 17 years can be employed for the same cost as one adult employee, we need to know the percentage of the adult rate for junior employees. Once we have that information, we can calculate the number of junior employees that can be employed for the same cost as one adult employee.

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The length of segment WK is given as follows:

B. [tex]2\sqrt{5}[/tex]

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

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

The endpoints of the segment in this problem are given as follows:

K(-2,0) and W(-6,-2).

Hence the length of the segment is given as follows:

[tex]\sqrt{(2 - (-6))^2 + (0 - (-2))^2} = \sqrt{20} = \sqrt{4 \times 5} = 2\sqrt{5}[/tex]

Meaning that option B is the correct option in the context of this problem.

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