A more clear view of the graph.

Answer:

D)  8 + 4 + 2 + 1 + 1/2 + ...

Step-by-step explanation:

The sum of an infinite geometric series can be found when the absolute value of the common ratio, r, is less than 1.

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\quad $|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

To determine which of the given infinite geometric series can be summed using the formula, calculate the value of r for each series.  To do this, divide a term by the previous term.

Given infinite geometric series:

[tex]\implies r=\dfrac{6}{-2}=-3[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{12}{3}=4[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{2}{1}=2[/tex]

As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.

Given infinite geometric series:

[tex]\implies r=\dfrac{4}{8}=\dfrac{1}{2}[/tex]

As |r| < 1 the sum of the infinite series can be found using the formula.

Therefore, the infinite series for which the sum can be found by using the formula is:

Answer:

Let's call the distance between Cape Town and East London "d".

We know that the average speed on the outward trip was 108 km/h, so the time it took to travel from Cape Town to East London can be calculated using the formula:

time = distance / speed

So the time it took on the outward trip can be expressed as:

time = d / 108

We also know that the average speed on the return trip was 72 km/h, and we're told that this trip took 12 hours. So we can use the same formula to find the distance between Cape Town and East London:

d = speed * time

d = 72 * 12

d = 864 km

Now we can use the formula for time again to find how long the outward trip took:

time = d / 108

time = 864 / 108

time = 8 hours

Therefore, the outward trip took 8 hours.

Step-by-step explanation:

Answer:

To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:

6 ÷ 2 = 3

18 ÷ 6 = 3

54 ÷ 18 = 3

162 ÷ 54 = 3

So the common ratio is 3.

Next, we can use the general form of a geometric sequence to find the explicit formula:

a(n) = a(1) * r^(n-1)

where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.

In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:

a(n) = 2 * 3^(n-1)

For example, if we want to find the 6th term, we can plug in n = 6:

a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486

Therefore, the 6th term of the sequence is 486.

The simplified form of csc²t/ [csc²(t) - 1] is sec²t  

Trigonometric identities are mathematical relationships between trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant. These identities are used to simplify trigonometric expressions and solve trigonometric equations.

To solve the given expression we used the following trigonometric identities  

Here we have

csc²t/ [csc²(t) - 1]  

As we know csc θ = 1/sin θ  

=> sinθ = 1/cscθ

Take csc² t as common from numerator and denominator

=> csc²t [1]/ csc²t [ 1 - (1/csc²t)]

=> 1/ 1 - (1/csc²t)     [ csc²t will be canceled ]

=> 1/ 1 - sin²t  

From trigonometric identities  1 - sin²t  = cos²t

=> 1/ cos²t

= sec²t

Therefore,

The simplified form of csc²t/ [csc²(t) - 1] is sec²t

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Answer:

We can start by using the given information to find the initial value of the gift card, which is the value before Alexander started using it:

Initial value of gift card = $9 + 4 x $1.50 = $15

Let's use A to represent the amount of money remaining on the card after buying x cups of coffee. Each cup of coffee costs $1.50, so the amount spent on coffee after buying x cups is 1.5x. The remaining balance on the card can be found by subtracting the amount spent on coffee from the initial value of the card:

A = $15 - 1.5x

Therefore, the equation for A in terms of x is:

A = $15 - 1.5x

Step-by-step explanation:

Answer:

27.5

Step-by-step explanation:

Joe wants to hang a flag weighing 800 N because Cable A, tied to the store, forms a 30.0° angle, and Cable B, attached to a neighboring building, is horizontal. Cable B is thus under 461 N of stress.

First, a [+ object] measuring the weight of something or someone in order to determine its size (someone or something) Every day she weighs herself. To weigh the bananas, he used a scale.

Let's refer to the tensile stress in cables A or B, respectively, as T A and T B. With an 800 N magnitude, the sign's weight is acting downward. The weight must be balanced by the vertical tension force components because the sign also isn't moving vertically:

800 N when T A is cos 30°

T A = 800 N/cos (30°)

T A = 922 N

Without any horizontal acceleration, a horizontal component of the tensile stress must also be balanced. T A's horizontal component is T A sin 30°, while T B's horizontal component is 0 (since cable B is horizontal). Therefore:

A sin (30°) = T b

T A = T B sin (30°)

T B ≈ 922 N x 0.5, or 461 N.

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Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex]  simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]

To find the equation of a line that is parallel to   [tex]y = (-5/9)x - 2,[/tex]  we need to note that parallel lines have the same slope. The slope of   [tex]y = (-5/9)x - 2[/tex] is -5/9, so the slope of the parallel line will also be -5/9.

We can use this information and the given point (-9, -4) to find the equation of the parallel line using the point-slope form of the equation of a line:

[tex]y - y1 = m(x - x1)[/tex]

where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get:

[tex]y - (-4) = (-5/9)(x - (-9))[/tex]

Simplifying and rearranging, we get the equation of the parallel line:

[tex]y = (-5/9)x + (34/9)[/tex]

To find the equation of a line that is perpendicular to y = (-5/9)x - 2, we need to note that perpendicular lines have opposite reciprocal slopes. The slope of y = (-5/9)x - 2 is -5/9, so the slope of the perpendicular line will be 9/5 (the opposite reciprocal).

We can use this information and the given point (-9, -4) to find the equation of the perpendicular line using the point-slope form of the equation of a line:

[tex]y - y1 = m(x - x1)[/tex]

Therefore, where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex]  simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]

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The expressiοn a² + b² = a + b is true when a = 1 and b = 1.

An expressiοn is a cοmbinatiοn οf variables, numbers, and mathematical οperatiοns that represents a quantity οr value. Expressiοns can be simple οr cοmplex, and they can invοlve a variety οf οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and radicals.

a. It is impοssible tο cοmbine the expressiοn √√3x + 2√3x intο a single term because the twο terms have different radical expressiοns. The first term has a dοuble square rοοt, while the secοnd term has a single square rοοt. These cannοt be cοmbined unless simplified first.

b. Ratiοnalizing the denοminatοr means tο eliminate any radical expressiοns frοm the denοminatοr οf a fractiοn by multiplying bοth the numeratοr and denοminatοr by a suitable expressiοn that will result in an integer οr ratiοnal denοminatοr.

c. Let a = 1 and b = 1, then a² + b² = 1² + 1² = 2, and a + b = 1 + 1 = 2. Therefοre, a² + b² = a + b is true when a = 1 and b = 1.

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Answer: To compare the rates of change of the line y = -2x + 6 at the points (2, 2) and (1, 6), we need to find the slope (rate of change) of the line at each point.

The slope of a line is given by the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

where (x₁, y₁) and (x₂, y₂) are two points on the line.

Using the points (2, 2) and (1, 6), we can find the slopes of the line at these points:

At point (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - 6) / (2 - 1)

= -4

So the slope of the line at point (2, 2) is -4.

At point (1, 6):

slope = (y₂ - y₁) / (x₂ - x₁)

= (6 - 2) / (1 - 2)

= 4

So the slope of the line at point (1, 6) is 4.

Since the slope at (1,6) is positive and greater than the slope at (2,2), we can conclude that the rate of change of y with respect to x is increasing as we move from point (2,2) to (1,6). In other words, the line is getting steeper as we move from right to left along the line.

Step-by-step explanation:

Answer:

the answer to ur question is: 1.4

Solving the quadratic equation we can see that the object will be 6.5 seconds falling down.

We know that the height is modeled by the quadratic equation

h=-16t²+676

The object will reach the ground when the height is zero, so we need to solve:

-16t²+676 = 0

Solving this for t we will get:

16t² = 676

t² = 676/16

t = √(676/16)

t = 6.5

The object will be 6.5 seconds falling down.

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Answer:

k = 16.806404 and k = 95.174404

Step-by-step explanation:

To determine the value of k in which the graph touches, you set both equations equal to each other

4x + k = -x^2 +8x + 20

k = -x^2+4x+20

You can use the quadratic formula -b^2+-(sqrt(b^2-4(a)(c))) / 2a

You will get the values of x = -2.898 and 6.898 for your answers

My bad, I forgot to add also input the values of x in your equation and get k = 16.806404 and k = 95.174404

Elvira's walking speed is 5 miles per hour, and Aletheia's walking speed is approximately 4.17 miles per hour.

Let's denote Elvira's walking speed as x (in miles per hour).

Then, Aletheia's walking speed is x - 0.6 (since she walks 0.6 miles per hour slower than Elvira).

We know that Elvira walked to the coffee shop in half an hour, covering a distance of 2.5 miles.

This means her speed can be calculated as:

x = distance / time = 2.5 miles / 0.5 hours = 5 miles per hour

Now, we can find Aletheia's speed using the equation we found earlier:

x - 0.6 = Aletheia's speed

We also know that Aletheia walked to the coffee shop in three-fifths of an hour (which is 0.6 hours), covering the same distance of 2.5 miles.

This means her speed can be calculated as:

x - 0.6 = distance / time = 2.5 miles / 0.6 hours ≈ 4.17 miles per hour

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The volume of the cylinder with a diameter of 8cm and height of 2m is 100.48 cubic meters.

This question is incomplete, the complete question is:

Find the volumes of each of the following;

7) A cylinder with a diameter of 8cm and height of 2m?

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

The volume of a cylinder is expressed as;

V = π × r² × h

Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )

Given that;

Plug the given values into the above formula and solve for V.

V = π × r² × h

V = 3.14 × ( 4m )² × 2m

V = 3.14 × 16m² × 2m

V = 100.48 m³

Therefore, the volume is 100.48 cubic meters.

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Answer:

14 is 45

Step-by-step explanation:

To create the cylindrical travel case, we need approximately 588.75 square inches of leather.

What is a cylinder?

A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The curved surface is formed by connecting every point on the edge of one circular base to the corresponding point on the other circular base with straight lines that are perpendicular to the bases. The distance between the two circular bases is the height of the cylinder.

Now,

The surface area of a cylinder is given by the formula:

A = 2πr² + 2πrh

where r is the radius of the circular base, h is the height of the cylinder, and π is the mathematical constant pi, which is approximately equal to 3.14.

In this case, we are given that the cylinder has a diameter of 15 inches, so the radius is 7.5 inches (half of the diameter). We are also given that the height of the cylinder is 5 inches. Using these values in the formula, we can calculate the surface area of the cylinder as:

A = 2π(7.5)² + 2π(7.5)(5)

= 2π(56.25) + 2π(37.5)

= 2(π)(93.75)

= 187.5π

≈588.75

Therefore,

                  we need approximately 588.75 square inches of leather to create the travel case.

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Answer:

This statement is false as it suggests a negative correlation between average annual income and the record time to run 1 mile. A negative correlation means that as one variable increases, the other decreases. However, it is unlikely that there is any correlation between these two variables as they are not directly related. One's ability to run a mile does not necessarily depend on their income, and vice versa. It is possible that both variables have been changing over time, but it does not necessarily mean that there is a correlation between them.

Step-by-step explanation:

Answer and Step-by-step explanation:

We can see that because Line K is acting as an Angle Bisector (a line that divides an angle into two angles of equal measures) on angle ∠LMJ, the angles ∠LMK and ∠JMK are equal to each other.

This allows us to solve for angle ∠LMK.

We do this by first setting the angles equal to each other.

10x - 22 = 2x + 66

Now, we want to isolate x by itself. We will subtract 2x from both sides of the equation, and then add 22 to both sides of the equation.

10x - 22 - 2x = 2x + 66 - 2x

8x - 22 = 66

8x - 22 + 22 = 66 + 22

8x = 88

Finally, we will divide both sides of the equation by 8.

8x ÷ 8 = 88 ÷ 8

x = 11

We aren't finished yet, as the question asks to find ∠LMK.

Plug 11 in for x into the equation 10x - 22.

10(11) - 22 =

110 - 22 =

= 88°

So, the measure of angle ∠LMK is 88°.

Have a good day!

Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.

Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.

Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.

Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.

Step-by-step explanation:

Option A. To translate a figure 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex.

The original vertices are:

(4, 4), (4, 2), and (6, 3)

Subtracting 4 from the x-coordinates, we get the new vertices:

(0, 4), (0, 2), and (2, 3)

To understand how to translate a figure, it is helpful to visualize the original and new positions of the figure in a coordinate plane. In this case, the original triangle has vertices (4, 4), (4, 2), and (6, 3) as shown below:

   (4,4)

     / \

    /   \

(4,2)----- (6,3)

To translate this triangle 4 units to the left, we need to subtract 4 from the x-coordinates of each vertex. This will shift the entire triangle to the left by 4 units.

So, the new x-coordinates of the vertices become:

x-coordinate of (4, 4) - 4 = 0

x-coordinate of (4, 2) - 4 = 0

x-coordinate of (6, 3) - 4 = 2

The y-coordinates of the vertices remain the same.

Therefore, the new vertices of the triangle are:

(0, 4), (0, 2), and (2, 3)

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A triangle with vertices (4, 4), (4, 2), and (6, 3) is translated a distance of 4 units to the left. What are the new coordinates?

A. (0, 4), (0, 2), (2, 3)

B. (4, 0), (4, -2), (6, -1)

C. (4, 8), (4, 6), (6, 7)

D. (8, 4), (8, 2), (10, 3)

Part A: The intersection of these two lines is (-1,-4).  Since x=-1, this is also the solution to 4x=2x-2 as per the graph.

Part B: Table attached.

Part C: Graph attached.

Graphing a function involves tracing the curve on a coordinate plane that corresponds to the function. If the curve represents the function for the curve, then each point on the curve will satisfy the function equation. The graph below shows the linear function f(x) = -x+ 2 as an illustration.

In the question,

The expression 4x = 2x - 2 reduces to x = -1.  This is true for all values of y, since y is not a factor in this expression.

The two other equations intersect at point (-1, -4).  See the attached graph (Solutions2)

y = 4x

y = 2x−2

Mathematically, we can substitute the value of y from the first equation into the second:

y = 2x−2

(4x) = 2x−2

2x = -2

x = -1

The intersection of these two lines is (-1,-4).  Since x=-1, this is also the solution to 4x=2x-2.

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Therefore, the solutions to the equation [tex]p^{2} -4=21[/tex]are p = 3, -3, 7, and -7. Neither 1/4 nor 21 are solutions to this equation.

In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers can all divide 12 evenly.

by the question.

We can solve this equation by first moving all the terms to one side of the equation:

[tex]p^{2}[/tex] - 4 = 21

[tex]p^{2}[/tex] = 25

Now, we can factor the left-hand side of the equation by using the difference of squares formula:

(p + 2) (p - 2) = 25

We can now solve for p by setting each factor equal to a possible value of the square root of 25:

p + 2 = 5 or p + 2 = -5

p - 2 = 5 or p - 2 = -5

Solving each of these equations, we get:

p = 3 or p = -7, p = 7 or p = -3

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The answer of tan B can be calculated only by knowing all the sides of triangle by using Pythagorean theorem and the answer is 8/15.

What is Pythagorean theorem?

The pythagorean theorem says In a right angle triangle if any of the two sides is known then the third side can be calculated.

                                      c²= a²+ b²

Now in the following to calculate 3rd side, let us say x

                                                 => 8²+x² = 17²

                                                     x= 15

                              Tan B= opposite /adjacent

                                          = 8/15

                     So the tan B value will be 8/15

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Answer: D 11.9

Step-by-step explanation:

To find the height of the flower pot 3 seconds after it falls, we need to substitute t=3 in the given function H(t) and calculate the value.

H(3) = 56 - 4.9(3)^2

H(3) = 56 - 4.9(9)

H(3) = 56 - 44.1

H(3) = 11.9

Therefore, the height of the flower pot, in meters, 3 seconds after it falls is 11.9 meters.

The answer is option D, 11.9.

Answer:

To find the x-intercept, we set y = 0 and solve for x:

r(x) = 2x^2 + 10x - 12 / x^2 + x - 6

0 = (2x^2 + 10x - 12) / (x^2 + x - 6)

0 = 2(x-1)(x+6) / (x-2)(x+3)

This gives us x-intercepts of x = 1 and x = -6.

To find the y-intercept, we set x = 0 and solve for y:

r(0) = 2(0)^2 + 10(0) - 12 / (0)^2 + (0) - 6

r(0) = -12/-6 = 2

So the y-intercept is y = 2.

To find the vertical asymptotes, we set the denominator of the function equal to zero and solve for x:

x^2 + x - 6 = 0

(x+3)(x-2) = 0

This gives us vertical asymptotes at x = -3 and x = 2.

To find the horizontal asymptote, we look at the degrees of the numerator and denominator. Since the degree of the numerator is 2 and the degree of the denominator is also 2, we divide the leading coefficient of the numerator by the leading coefficient of the denominator:

2 / 1 = 2

So the horizontal asymptote is y = 2.

Therefore, the x-intercepts are x = 1 and x = -6, the y-intercept is y = 2, the vertical asymptotes are x = -3 and x = 2, and the horizontal asymptote is y = 2.

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