Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Given conditions:

6th term (T6) = -2

first term (a) = 18

n = 6, r = ?

Formula for finding the nth term of a GP:

[tex]tn = a {r}^{n - 1} [/tex]

Where:

T = the given value for the number of term(s)

n = the given number of term

a = The first term

r = The common ratio

Replacing for the values:

[tex] - 2 = 18 {r}^{6 - 1} \\ - 2 = 18 {r}^{5} [/tex]

Dividing both sides by 18, we have:

[tex] {r}^{5} = \frac{ - 2}{18} [/tex]

Now, we have to fifth root both sides to find the value of r.

[tex] \sqrt[5]{ {r}^{5} } = \sqrt[5]{ \frac{ - 2}{18} } [/tex]

Therefore:

Common ratio, [tex]r = -0.0638165752[/tex] [tex]≈ -0.064[/tex] to 3 decimal places.

The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.

Herein we have a rational function, of which we must derive the equation of the line tangent to the curve at a given point. First, find the first derivative of the function by derivative rules:

f'(x) = [(6 · x + 6) - 6 · (x - 9)] / (6 · x + 6)²

f'(x) = 60 / (6 · x + 6)²

Second, evaluate the first derivative of the function:

f'(11) = 60 / (6 · 11 + 6)²

f'(11) = 5 / 432

This value represents the slope of the tangent line.

Third, calculate the y-value of the curve:

f(11) = (11 - 9) / (6 · 11 + 6)

f(11) = 1 / 36

Fourth, determine the intercept of the tangent line:

b = 1 / 36 - (5 / 432) · (11)

b = - 43 / 432

The equation of the line tangent to the curve at x = 11 is y = (5 / 432) · x - 43 / 432.

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The standard deviation of the fitness center is larger than the standard deviation of the last shipment

The given parameters are:

Distribution: Normal distribution

The last shipment

Mean weight = 2.7 grams

Standard deviation = 0.1 gram.

Fitness center

Mean weight = 100.2 pounds

Standard deviation = 0.1 pound

In the above parameters, we can see that the fitness center has a larger mean weight than the last shipment, while they both have the same standard deviation

This means that the standard deviation of the fitness center is larger than the standard deviation of the last shipment

And so, the distribution of the fitness center is more dispersed

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Answer:

The function f defined by the formula f(x) = 2x +1 can be expressed as: f(4) = 9; f(-5) = - 9, f(0) = 1,

The function of a function defines and explains the relationship between two different variables. From the given information, we are meant to replace x with the following given options and solve for the value of x.

f(4) = 2(4) + 1

f(4) = 8 + 1

f(4) = 9

f(-5) = 2(-5) + 1

f(-5) = -10 + 1

f(-5) = - 9

f(0) = 2(0) + 1

f(0) = 0 + 1

f(0) = 1

Step-by-step explanation:

Basically first you have to check what the f(x) fits into what category.

The picture shows different equations based on what the f(x) is.

In this case, f(x) is 7. So first check is 7 greater than 5, YES. But check with the next one too. Is 7 less than or equal to 5, NOPE

So your equation your going to be substituting with is x squared-x

Little bit stuck still? Here:

What is 7 to the power of 2 is 7x7=49

Then, 49-7=42

42 is your answer. If this is for RSM ENTER ONLY 42 INTO THE PORTAL.

I'm a student too and had this question too.

Step-by-step explanation:

[tex]{ \tt{3x - 8 \leq 4}} \\ \\ { \tt{3x \leq4 + 8}} \\ \\ { \tt{3x \leq12}} \\ \\ { \tt{x \leq4}}[/tex]

Answer:72 bracelets

Step-by-step explanation:

24*3

72 bracelets

If she can make 4 bracelets with 12 beads, you divide to get three. Three times 24 is 72 bracelets

The new coordinates after translating 2 units right and 1 unit down are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

Given, triangle DHS has the coordinates D(-5, 1), H(-4, 5) and S(-1, 2). Now, we have to find the coordinates of D'H'S' if DHS is translated 2 units right and 1 unit down.

A translation is a transformation that occurs when a figure is moved from one location to another location without changing its size, shape or orientation. In the coordinate plane we can draw the translation if we know the direction and how far the figure should be moved.

To translate the point P(x,y), 'a' units right and 'b' units down, use P′(x+a,y-b).

Now, let's proceed to solve the question according to above listed points accordingly.

D(-5, 1), H(-4, 5) and S(-1, 2), these coordinates are translated 2 units right and 1 unit down. So, we will simply add 2 to the x-coordinate of the points and will subtract 1 from the y-coordinate.

Let's translate D, H and S accordingly into D', H' and S'.

D(-5,1)⇒ D(-5+2, 1-1)⇒ D'(-3,0)

H(-4,5)⇒ H(-4+2, 5-1)⇒ H'(-2,4)

S(-1,2)⇒ S(-1+2, 2-1)⇒ S'(1,1)

Therefore, the new coordinates after translation are D'(-3,0), H'(-2,4) and S'(1,1) respectively.

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Answer:

(7/8 - 4/5)^2 = 9/

1600

= 0.005625

Answer:

b, c, a

Step-by-step explanation:

The answer would be 4/21 if divided 2/7 by 1.5 which is the correct option (C).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We have to determine the divide 2/7 by 1.5

⇒ 2/7 ÷ 1.5

Here 1.5 = 3/2

⇒ 2/7 ÷ 3/2

Apply the division operation between both term

⇒ (2/7)/(3/2)

Reciprocal the terms, we get

⇒ (2/7)×(2/3)

⇒ (2×2)/(7×3)

⇒ 4/21

Therefore, the answer would be 4/21

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Answer: Question: 306 × 673 = 205,938  Estimate: 300 × 700 = 210,000

See more below

Step-by-step explanation:

306 round to the nearest hundred is 300 because 306 ≥ 300

And 673 rounds to 700 because its to the nearest hundred. Here is the problem.    

    306

  × 673

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

  205,938

So, 205, 938 is underestimate to 210,000

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The estimated the product of 306×673 by first rounding each number to the nearest hundred is: the estimated product of 306 and 673 is 210000.

Given: 306 × 673 = 205,938  

Estimate: 300 × 700 = 210,000

306 round to the nearest hundred is 300 because 306 ≥ 300

And 673 rounds to 700 because its to the nearest hundred.

Now, we have,

   306

 × 673

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

 205,938

Now, multiply the rounded numbers:

300 * 700 = 210000

So, the estimated product of 306 and 673 is 210000.

So, We have,

205, 938 is underestimate to 210,000.

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The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8) is 2y - 5x = 0.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

Let's suppose the equation of that line as the slope-intercept form is

y = mx + c

Where m is the slope while c is the y-intercept.

Now this line is parallel to a line that passes through points  (8, 3) and

(10, 8) thus meaning the slope of both lines must be the same.

So,

Slope associated with points  (8, 3) and (10, 8) ⇒

m = difference in y's coordinate / difference in x's coordinate

m = (8 - 3)/(10 - 3)

m = 5/7

So our equation will be y = (5/7)x + c

Since it is passing through the origin or (0,0) so it will satisfy the coordinate.

Therefore,

0 = (5/7)0 + c ⇒ c = 0

It means y = (5/7)x ⇒ 7y - 5x = 0 will be the equation.

Hence "The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8) is 2y - 5x = 0".

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The given question is an incomplete complete question as follows;

The equation of a line passing through the origin and parallel to the line passing through the points (8, 3) and (10, 8).

The value of m<DEC is given as 35 degrees

In the given figure, to find the missing value of angle DEC, we can easily relate this to angle on a straight line.

The law states that the sum of all angles on a straight line are equal to 180 degrees.

[tex]m < CEF + m < DEC = 180^0\\145^0 + m < DEC = 180^0\\m < DEC = 180^0 - 145^0\\m < DEC = 35^0[/tex]

The value of the angle m<DEC is equal to 35 degrees.

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Answer: (5,2)

Step-by-step explanation:

5 + 2 = 7

5 = 2 + 3

The length of each equal side of the isosceles right triangle will be 11 cm.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The hypotenuse of an isosceles right triangle is √242 cm.

In an isosceles right triangle, the two legs of the isosceles right triangle are congruent.

Let x be the other leg.

(√242)² = x² + x²

242 = 2x²

x² = 121

x = 11 cm

The length of each equal side of the isosceles right triangle will be 11 cm.

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0 is correct, though...

[tex]\dfrac{\frac1x - \frac13}{x + 3}[/tex]

is continuous at [tex]x=3[/tex], so

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x + 3} = \frac{\frac13 - \frac13}{\frac13 + 3} = \frac0{\frac{10}3} = 0[/tex]

What was probably intended was the limit

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x - \frac13}{x - 3}[/tex]

which requires a little more finesse because the function is not continuous at [tex]x=3[/tex].

Rewrite it as

[tex]\dfrac{\frac1x - \frac13}{x - 3} = \dfrac{3 - x}{3x(x-3)} = -\dfrac{x-3}{3x(x-3)}[/tex]

When [tex]x\neq3[/tex], we can cancel [tex]x-3[/tex] so that

[tex]\displaystyle \lim_{x\to3} \frac{\frac1x-\frac13}{x-3} = \lim_{x\to3} -\frac1{3x} = -\frac1{3\times3} = -\frac19[/tex]

Answer:

B

Step-by-step explanation:

x - y = 0 ( add y to both sides )

x = y → (1)

6x + 5y = - 22 → (2)

substitute x = y into (2)

6y + 5y = - 22

11y = - 22 ( divide both sides by 11 (

y = - 2

since x = y then x = - 2

the lines intersect at (- 2, - 2 )

Answer:

The answer would be 250.

Step-by-step explanation:

Cindy started off with 250 lollipops, gave away 30 (which is 12% of 250) and stayed with 220.

250-30=220

The best estimate of the product of 8 and 629 is 5600

The statement is given as

The best estimate of the product of 8 and 629

Express as a product

So, we have

8 x 629

Round 629 to the smallest hundred greater than 629

So, we have

8 x 629 = 8 x 700

Evaluate the product

8 x 629 = 5600

Hence, the best estimate of the product of 8 and 629 is 5600

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Step-by-step explanation:

try this option (see the attachment), if it is possible, check the yellow text.

Answer:6,7,8,9x4

Step-by-step explanation:

the purpose is to solve th equation5789x4

Part (b)

[tex]f(3)=-3^3 + 4(3)^2-2(3)+2 \\ \\ =-27+36-6+2 \\ \\ =9-4 \\ \\ =\boxed{5}[/tex]

Part (c)

[tex]f(-2)=-(-2)^3+4(-2)^2-2(-2)+2 \\ \\ =16+16+4+2 \\ \\ =\boxed{38}[/tex]

Answer: second quadrant

Step-by-step explanation:

The current assets total of  Adventure Travel. at December 31, 20XX is $44,300

What are current assets?

Current assets are short-term resources owned by Adventure Travel which are used in its daily operations such as the cash, accounts receivable as well the office supplies which are current assets until consumed

In other words, in a bid to determine current assets total, we sum up the cash, accounts receivable and the office supplies of the company since there are no other current assets aside the aforementioned ones.

Current assets total=cash+ accounts receivable+ office supplies

cash=$25,000

accounts receivable=$ 15,000

office supplies=$4,300

current assets total=$25,000+$15,000+$4,300

current assets total=$44,300

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The domain of the quadratic equation is all non-negative real numbers.

The picture indicates the case of the launch of an object from the top of a building. The height of the object (f(x)), in feet, as a function of time, (x), in seconds. Both height and time are represented by non-negative real numbers and hence the following solutions do not make sense in the context of problem:

Now we proceed to fill the blanks in the four paragraphs:

f(- 2) = 0, meaning that - 2 second after the object was launched, the object was 0 feet above the ground. This interpretation does NOT make sense in the context of the problem.

f(0.5) = 100, meaning that 0.5 seconds after the object was launched, the object was 100 feet above the ground. This interpretation make sense in the context of the problem.

f(6) = - 224, meaning that 6 seconds after the object was launched, the object was - 224 feet above the ground. This interpretation does NOT make sense in the context of the problem.

Based on the observation above, it is clear that an approximate domain for the function is all non-negative real numbers.

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