If f(x)=x²-1, and
g(x)=x+2, then

Answer:

Step-by-step explanation:

Well since the questions are related to geometric series I'm assuming the reasoning for 0.99999.... = 1, is going to be a geometric series in this instance. All though there are other ways to prove this.

1.

 a. So if you think about it, 0.999 can be represented as: [tex]\frac{9}{10} + \frac{9}{100} + \frac{9}{1000}....[/tex] and so on. This is a geometric series. The geometric sequence explicit equation can be determined by realizing each term is the previous term multiplied by 1/10, since the numerator is staying the same, but the denominator is being multiplied by 1/10. So the explicit equation for the sequence is: [tex]a_n=\frac{9}{10}*(\frac{1}{10})^{n-1}[/tex]. The sum of an infinite series can be defined as: [tex]S_\infty=\frac{a_1}{1-r}[/tex] when |r| <1 , which in this case it is. So plugging the values into the equation you get: [tex]S_\infty=\frac{\frac{9}{10}}{1-0.10}=\frac{\frac{9}{10}}{\frac{9}{10}} = 1[/tex]. So the sum of this infinite series that represents [tex]0.\overline{9}[/tex] is equal to 1.

 b. Another repeating decimal can easily be determined using the repeating decimal 0.9. If you multiply both sides by 10, you'll get: [tex]9.\overline9 = 10[/tex].

2.

 a. So this is an arithmetic sequence and it appears to be increasing by 5, with the first term being 3. So an explicit formula can be written using these two values: [tex]a_n=3+5(n-1)[/tex] which can also be simplified by distributing the 5, to get: [tex]a_n=3+5n-5=5n-2[/tex]. A recursive rule can also be easily defined using these two values, it's simply: [tex]a_n=a_{n-1}+5\\a_1=3[/tex]

 b. The 1000th term can be evaluated using the explicit formula by plugging in 1000 in as n: [tex]a_{1000} =5(1000)-2=5000-2=4998[/tex]

 c. The explicit formula, since it's much easier to evaluate values, by simply plugging in 1000 as n

 d. The issue with a recursive rule, is you need to know all previous values, to determine [tex]a_n[/tex], because it's doing some operation on the previous value, except to know that previous value, you need the previous previous value, and so on. This is an issue with much larger numbers, which is why the explicit formula is generally more better.

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

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Answer:

Step-by-step explanation:

The true statement about right-angle triangle ABC is that: A. sin(A) = cos(C) and cos(A) = sin(C).

How to apply basic trigonometry?

In order to determine the angles, we would apply basic trigonometry. From the diagram of the right-angled triangle shown below, we can deduce the following parameters:

Angle (θ) = 45°.

Opposite (Opp) side = a.

Hypotenuse (Hyp) = c.

Adjacent (Adj) side = b.

By applying the basic trigonometry functions, we have:

sin(A) = Opp/Hyp = a/c.

sin(C) = Opp/Hyp = c/b.

cos(A) = Adj/Hyp = c/b.

cos(C) = Adj/Hyp = a/c.

From the above, we can logically deduce that sin(A) is equal to cos(C) and cos(A) is equal to sin(C).

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The solution to the inequality: [tex]1.29m\leq 25[/tex]  is m=19.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Value of gift card=$25

Cost of each song=$1.29

Let m be the number of songs purchased.

Then, the required inequality is as follows:

[tex]1.29m\leq 25\\m\leq \frac{25}{1.29}\\ m\leq 19.38[/tex]

The value of m rounded to the nearest whole number is 19.

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Answer:

22

Step-by-step explanation:

BD bisects <ABC, this means the half-line divided the angle into two equal parts.

If m<ABC is equal to 44 then m<ABD is

44/2 = 22

Answer:

Find the derivative using the chain and power rules.

-6csc^(2 )(x^(3)-2x^(2))(3x^(2)-4x)

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

first you need to memorize

SOH CAH TOA

IT means

Sine =opposite/hipotenuse

Cosine = adjecent/hipotenuse

tangent = opposite/adjecent

in this case, we need to find sine

so it's SOH

opposite of theta Θ is 15

and it's hipotenuse , we don't know yet. so need to find it by using Pythagorean theorem

let it be x

x =√ 15²+ 8²

=√ 225+ 64

=√289

= 17

so the answer is 15/17

Answer:

12.198

hope it helps

12.198

To round over 7 into 8, the ten-thousandth place needs to be 5 or over, and as we can see the ten-thousandth place is 5.

The length of the other leg to the nearest tenth of a foot is 5.7 feet.

What is Pythagorean theorem?

We can use the Pythagorean Theorem to find the length of the other leg

[tex]a^{2} + b^{2} = c^{2}[/tex]

"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.

So,

      [tex]b^{2} = c^{2} - a^{2}[/tex]

        =  7² - 4²

  b = [tex]\sqrt{49 - 16}[/tex]

  [tex]b = \sqrt{33}[/tex] ⇒ 5.7 feet

Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.

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Answer:

E represents a number, for this question we need to keep in mind that the product of 1E and E must end in E.

E must be 6.

E = 6

Step-by-step explanation:

16 * 6 = 96

The line having the equation, y = -2x + 5, has a slope = -2, and y-intercept = (0, 5). Thus, option A is the best choice.

The slope of a line is the tangent of the angle that the line makes with the positive side of the x-axis.

The y-intercept of a line is the point at which the line intersects the y-axis.

The standard form of a line is y = mx + b, where m represents the slope of the line, and b represents its y-intercept.

In the question, we are asked to identify the slope and the y-intercept of the line whose equation is y = -2x + 5.

Comparing the given equation of the line, y = -2x + 5, with the standard equation of a line, y = mx + b, we can say that,

m = -2, and b = 5.

Representing b as an ordered pair, we get (0, 5), as b represents the y-intercept which is a point on the y-axis, where the x-coordinate is always equal to zero.

Thus, we get the slope = -2, and the y-intercept = (0, 5).

The option representing the answer is option A.

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The closest surface area of the container is: 1,696 ft².

Curved surface area of a cone = πrl

Surface of a cylinder = 2πr(h + r)

Surface area of the container = Curved surface area of a cone + Surface of a cylinder - area of circular base

= πrl + 2πr(h + r) - πr²

r = 24/2 = 12 ft

l = 13 ft

h = 10 ft

Plug in the values

Surface area of the container = π(12)(13) + 2π×12(10 + 12) - π(12²) = 1,696.5 ft².

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Answer:

10

Step-by-step explanation:

2 legs because you walked into the room and 4 legs of the bed and 4 legs of the chair.

The total number of legs in the room would be 10.

From the given information, it can be inferred that none of the legs of the animals is on the floor of the room.

It is given that 2 dogs, 4 horses, 1 giraffe, and a duck are lying on the bed. 3 chickens are flying over a chair.

The legs of the bed and the chair do.

So we can say that the chair and the bed each have four legs.

so that would be two more legs.

In total we have:

4 + 4 + 2 = 10.

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The number line that shows that x ≥ -4 is; Option B

We want to find the number line that represents x ≥ -4

Now, for greater than sign, the number line would point to the right while  for less than sign the number line would point to the left.

Now, for greater than or equal to sign the dot would be shaded and as such looking at the correct number line would be that in Option B.

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Step-by-step explanation:

so you have the equation: [tex]\sqrt{32x^3y^2z^7}[/tex] which I'm assuming is what you meant to input. and the next step I'm assuming you wrote: [tex]\sqrt{8} * \sqrt{4} * \sqrt{x^2} * \sqrt{y^2} * \sqrt{x} * \sqrt{z^6} * \sqrt{z}[/tex], although I'm not 100% sure, I'm basing this assumption off of step 3. Anyways this will simplify to [tex]2xyz^3\sqrt{8xz}[/tex] which is correct kind of, but since they were asked to FULLY SIMPLIFY, then it's not completely done. This is because 8 has a factor of 4 which is a perfect square. This is because in step 1, the student rewrote 32 as sqrt(8) * sqrt(4) instead of writing it as sqrt(2) * sqrt(16) which is the greatest factor of 32 that is a perfect square. So they could've either done that in step 1, or they could've realized in step 2, that they can further simplify sqrt(8) and then have a step 3 showing that.

The linear function which represents the line given by the point slope equation y+1=-3(x-5) is f(x) =-3x+14 which is option D.

Given the equation y+1=-3(x-5) and we have to find the equation of line that represents this equation.

An equation is a relationship between two or more variables which are expressed in equal to form. Equation of two variables looks like ax+ by=c. It is solved in order to get the values of variables. Linear function is like equation whose graph shows a straight line.

We have to just find out the value of y in terms of x to find the linear function which can be done as under:

y+1=-3x(x-5)

y+1=-3x+15

y=-3x-1+15

y=-3x+14

Hence y=-3x+14 is the linear equation which represents the point slope equation y+1=-3(x-5).

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Answer:

So the shorter version of what the guy above me is saying is that it is:

[tex]f(x) = -3x + 14[/tex]  or

D

Step-by-step explanation:

I got it right on the test.

71% is the required probability here.

What is a probability simple definition?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

                                        The probability serves as a gauge for the possibility that an event will occur. and a The probability equation is stated by the following notation: P(E) = Number of Favorable Outcomes/Number of Total Outcomes.

The number of customers out of 5 who agree to take the survey here could be modelled as a binomial distribution given as

 x ` Bin (n = 5 , p = 0.22 )

Thus the probability here is computed as

P(X≥ 1) = 1 - P(X = 0) = 1 - (1 - 0.22)⁵

           = 0.71 %

Therefore 71% is the required probability here.

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When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

     Distances                     Time

            0                              0

            1                               3

            2                              6

            3                               9

            4                               12

            5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

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Answer:

Step-by-step explanation:

Let the first number be x.

Then, given:

Since their sum is 131, we get the following equation:

or

This is matching the answer choice C.

Answer:

Brand A

Step-by-step explanation:

If you divide both brands to find how much one can costs, brand B costs more per can.

79 ÷ 3 = 26.34

87 ÷ 4 = 21.75

That being said, if brand B were to sell 4 cans instead of 3 it would be more than brand A's 4 cans. Brand A is cheaper than brand B would be.

Answer:

-8 and 1

Step-by-step explanation:

-8 x 1 is -8

-8+1 is -7

Since

[tex]17^a = 16 = 4^2 \implies 17^{a/2} = 4[/tex]

it follows that

[tex]17^b = 4 \implies 17^{a/2} = 17^b \implies \dfrac a2 = b \implies a = 2b[/tex]

Then

[tex]2^{a - b} = 2^{2b - b} = 2^b[/tex]

so that

[tex]\dfrac1{2^{a-b}} = 2^{-b}[/tex]

We also have

[tex]17^b = 4 \implies b = \log_{17}(4)[/tex]

so we can go on to say

[tex]\dfrac1{2^{a-b}} = \boxed{2^{-\log_{17}(4)}}[/tex]

Answer:

1:4

2:8

7:28

Step-by-step explanation:

The correct option is last one  77 degrees.

Therefore the measure angle W is 77 degrees.

Step-by-step explanation:

Given:

Exterior angle = 122°

∠W = (2x-13)°

∠Y= x°

To Find:

∠W = (2x-13)° = ?

Solution:

Exterior Angle Property:

An exterior angle of a triangle is equal to the sum of the opposite interior angles.

Angle W and Angle Y are the interior angles of Exterior angle 122°.

∴

Substituting the values we get

Now Substitute 'x' in angle W we get

Therefore the measure angle W is 77 degrees.

Step-by-step explanation:

Answer:

-1 <= x <= 1

Step-by-step explanation:

√((1-2x+x^2)+2-2x^2)

= √((1-x)^2 + 2*(1-x)(1+x) )

điều kiện là 1 - x > =0 và 1+x >=0

giải 2 bất phương trình trên ta thu đc kết ququả

The equation that is true and one that matches the set of ordered pairs of functions is option C. f (0) = 6

Note that a function can be made to be a given set of ordered pairs such as the ordered pairs (2,4), (3,5), (4,6)  can have  input functions of ​​(as domain) 2,3,4 and output functions of ​​(as range) of 4,5,6.

So when you see the ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)} one can see that the option that matches to the set of ordered pairs of functions above is f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

See full question below

The function f (x) is given by the set of ordered pairs. {(1,0), (–10,2), (0,6), (3,17), (–2, –1)}:Which equation is true?

f(-10)=1

f(2)=-10

f(0)=6

f(1)=-10

The answer choices are :

f (-10) = 1 values ​​x = -10, f (x) = y = 1, ordered pairs (-10,1)

f (2) = - 10 values ​​x = 2, f (x) = y = -10, ordered pairs (2, -10)

f (0) = 6 value x = 0, f (x) = y = 6, ordered pairs (0.6)

f (1) = - 10 values ​​x = 1, f (x) = y = -10, ordered pairs (1, -10)

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The perimeter of the shaded part is: 25.1 cm.

The area of the shaded part is: 36.6 cm².

Area = Area of square - 2(area of square - area of quarter circle) = s² - 2(s² - 1/4πr²).

Parameters given are:

Plug in the values into the equation

Area = 8² - 2(8² - 1/4π(8²)).

Area = 64 - 2(64 - 50.3)

Area = 36.6 cm²

Perimeter = 2(perimeter of quarter circle) = 2(1/4(2πr)) = 2(1/4(2π8)) = 25.1 cm

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Answer:

y-intercept: (0,2)

x-intercepts: (-4,0), (2,0)

Step-by-step explanation:

y-intercepts are found where the graph intersects the y-axis

same with x-intercepts, are found where the graph intersects the x-axis

The y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Where the line segment crosses the y-axis is the y-intercept,

And where the line segment crosses the x-axis is the x-intercept,

From the graph,

y-intercept is at (0,2)

x-intercepts is at (-4,0), (2,0)

Thus, the y-intercept is 2, and the x-intercept is -4 and 2 where the line segment crosses the y-axis and x-axis.

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Reason:

These angles are both in the same corresponding direction. Both are in the same western corner, or point to the west. If the lines were parallel, then the corresponding angles would be congruent.

Answer:

The length of one side is 12ft

Step-by-step explanation:

The triangle is equilateral so all the sides are the same length.

So you are simply going to divide 36ft by the 3 sides.

36ft/3 = 12ft

The difference is 2003.

The formula for the sum of the first n even numbers is SE = n^{2} + n, (E standing for even).

The sum of the first n odd numbers is SO = n^{2}, (O standing for odd).

Knowing this, plug 2003 for n,

SE - SO= (2003^{2} + 2003) - (2003^{2}) = 2003

The difference is 2003.

A number that can be divided into two halves, i.e. into two equal parts is called an even number. Even numbers are exactly divisible by 2 which means the remainder will be 0.

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