use the formula for the sum of a geometric series to find the sum or state that the series diverges 3^n/12^n

Answer:

I think your answer is  [tex]\frac{2}{5} x-3[/tex]

Step-by-step explanation:

Answer:

P/mh

Step-by-step explanation:

P = mgh  to solve for g  Divide both sides by mh

[tex]\frac{P}{mh}[/tex] = [tex]\frac{mgh}{mh}[/tex]    On the right side of the equation the m and h cancel out and you are left with

[tex]\frac{P}{mh }[/tex] = g

Answer:

true 6=hepti

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We have f(x) = 10x^3 and g(x) = 4x^(8/3) given. We need to find f/g, evaluating at x = 8. So how do we do this?

First, let's put our x value into the function f. f(8) = 10*8^3 = 5120.

Next, let's put our x value into the function g. g(8) = 4*8^(8/3) = 1024.

Now we just need to find f/g, which is just the result from our function f divided by our result from function g. This is f(8) / g(8). Substituting our solutions in, we have 5120/1024 = 5.

Answer:

5120/1024 = 5

Step-by-step explanation:

5120/1024 = 5

Answer:

20.69 m

Step-by-step explanation:

36/360 * 2πr = 13

r = 130/2π = 20.69 m

Answer:

Step-by-step explanation:

Yes, the lines are parallel.

so its d. trust me :)

if you solve the equation you get k=-1

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

Complementary angles are two angles whose total is 90 degrees in geometry. In other terms, complimentary angles are two angles whose sum is 90 degrees. 60° and 30°, for instance.

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

60° + 30° in the figure below equals 90°. These two angles are therefore complimentary according to the "Definition of Complementary Angles." The term "complement" refers to each angle that is one of the complimentary angles. Here,

The opposite of 30° is 60°.

The opposite of 60° is 30°.

Given;

24,(7d-4) are complementary angles

So, 24°+7d-4 =90°;

⇒7d-4=90-24;

⇒7d-4=66;

⇒7d=70;

⇒d=10.

As two angles are Complementary Angles they sum up to 90.

So value of d is 10.

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Answer:

0 muffins and 8 cookies

6 muffins and 4 cookies

Explain:

These are the only two combinations of muffins and cookies that Jordan could have sold to earn $24. If Jordan sold 0 muffins and 8 cookies, they would have earned $24 because 0 x $3 + 8 x $2 = $24. If Jordan sold 6 muffins and 4 cookies, they would have earned $24 because 6 x $3 + 4 x $2 = $24.

The approximate measures of the angles of ΔABC and the images formed by translation, reflection, and rotation of ΔABC, which are rigid transformations are;

   ΔABC [tex]{}[/tex]                 ΔA'B'C'                 ΔA''B''C''                     ΔA'''B'''C'''

∠A    =  [tex]{}[/tex]  22°           ∠A'  =  22°              ∠A'' = 22°                  ∠A'''  = 22°

∠B    = [tex]{}[/tex]   120°          ∠B'  =  120°            ∠B   = 120°                 ∠B'''  = 120°

∠C [tex]{}[/tex]   =    38°            ∠C'  = 38°              ∠C  =  38°                   ∠C'''  = 38°

A rigid transformation, also known as congruence transformation, in geometry, is one in which the length of the pre-image is preserved, such that the image and the pre-image have the same side lengths, and are therefore congruent.

The coordinates of the vertices of triangle ΔABC, obtained from a similar question online are;

A(-6, -1), B(-3, -3), C(-1, -2)

The lengths of the sides of triangle ΔABC are;

AB = √((-3 - (-6))² + (-3 - (-1))²) = √(13)

BC = √((-1 - (-3))² + (-2 - (-3))²) = √5

AC = √((-1 - (-6))² + (-2 - (-1))²) = √(26)

The law of cosines can be used to fined the measure of an angle of the triangle as follows;

Let a represent the side BC, let b represent the side AC, and let c represent the side AB, the formula for the law of cosines is presented as follows;

a² = b² + c² - 2·b·c·cos(A)

Where;

∠A = The angle at the vertex A

Therefore;

(√5)² = (√(26))² + (√(13))² - 2 × √(26) × √(13) × cos(A)

5 = 26 + 13 - 2 × √(26) × √(13) × cos(A)

cos(A) = (5 - (26 + 13))÷ (-2 × √(26) × √(13))

∠A = arccos((5 - (26 + 13))÷ (-2 × √(26) × √(13))) ≈ 22°

Similarly, we get:

cos(B) = (26 - (5 + 13))÷ (-2 × √(5) × √(13))

∠B = arccos((26 - (5 + 13))÷ (-2 × √(5) × √(13))) ≈ 120°

cos(C) = (13 - (26 + 5))÷ (-2 × √(5) × √(26))

∠C = arccos((13 - (26 + 5))÷ (-2 × √(5) × √(26))) ≈ 38°

The transformation from  ΔABC to ΔA'B'C', obtained from a similar question online, is a translation 5 units to the right and 2 units up

The transformation from ΔA'B'C' to ΔA''B''C'' is a reflection across the line y = -x

The transformation from ΔA''B''C'' to ΔA'''B'''C''' is a counterclockwise rotation by 270° about the origin

The translation, reflection, and rotation transformations are rigid transformations, such that the shape and sizes of the pre-images are preserved, and we get;

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle ABC & 120^{\circ} & \angle A'B'C' & 120^{\circ} &\angle A''B''C'' &120^{\circ} &\angle A'''B'''C''' &120^{\circ} \\\angle ACB &38^{\circ} & \angle A'C'B' & 38^{\circ} &\angle A''C''B'' &38^{\circ} &\angle A'''C'''B''' &38^{\circ} \\\\end{bmatrix}[/tex]

[tex]\begin{array}{|c|c|c|c|c|c|c|c|}\Delta ABC &Measure & \Delta A'B'C' &Measure & \Delta A''B''C'' & Measure & \Delta A'''B'''C''' & Measure \\\angle CAB & 22^{\circ} &\angle C'A'B' & 22^{\circ} &\angle C''A''B'' &22^{\circ} &\angle C'''A'''B''' &22^{\circ} \end{bmatrix}[/tex]

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solving for m

distribute into parentheses

3m + 15 + 18 -2m = 29

simplify

m + 33 = 29

subtract

m = -4

verify

3(-4+5) -2(-9-4) = 29

3 + 26 = 29

29 = 29

true

m = -4

hope this helps :)

jeron

Answer: for the first one, the one that says 7 x 5 = 5 x 7, as the blank is 7.

for the second one, 10 x 11 = 11 x 10, the blank is 10

for the third one, which is Julia's candy, draw 6 pieces of candy in each box and do 4 x 6, which is 24 pieces of candy [4 being the amount of bags].

for the fourth one, draw 5 pieces of candy in each box, then do 5 x 6 = 30.

for the fifth one, it is 4 x 6 = 6 x 4

for the final box, it is 5 x 6 = 6 x 5

Step-by-step explanation:

math

Answer: Hope this helps..

Step-by-step explanation:

7 * 5 - 5 = 30

10 * 11 - 11 = 99

For the candy questions the answers are:

Julia has 24 pieces of candy.

Tommy has 30 pieces of candy.

The equation for Julia is: 4 * 6 = 24

The equation for Tommy is: 5 * 6 = 30

Answer:

  0.63 or 5.37 seconds

Step-by-step explanation:

You want to know how long a ball was in the air when its height is 54 feet, and its height is described by -16s^2 +96s, for time (s) in seconds.

A graph shows the value of the height function is 54 when s = 0.63 or 5.37.

These solutions mean the ball was in the air 0.63 seconds when it passed 54 feet going up, and it was in the air 5.37 seconds when it was 54 feet in the air on the way down.

Answer:

(4,-10)

Step-by-step explanation:

Graphing calculator

The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

The primary indicator of an object's position and speed is its velocity. It is the distance that an object travels in one unit of time. The displacement of the item in one unit of time is the definition of velocity. Velocity can be defined as the rate at which something moves in a specific direction. as the speed of a car driving north on a highway or the pace at which a rocket takes off. The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. As the rate at which velocity changes, acceleration is likewise a vector quantity.

Given

A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

Velocity,

v = √(1.65)² + (10.7)²

v = √2.722 + 114.49

v = √117.212

v = 10.82

The velocity of the boat relative to shore is 10.82. When A river flows due east at 1.65 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10.7 m/s due north relative to the water.

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Answer:

$162

Step-by-step explanation:

8% of 150 = 12 + 150

The evaluation of the table, equations, and graphs in the question are as follows;

First question;

Part A; The table does not represent a function

Part B; The value of f(300) is $123 represents the total cost for driving 300 miles

Second question;

Part A; The equation is; y = -2·x + 8

Part B; The graph can be obtained by finding the ordered pair of values for the first five hours and plotting the result on a graph, to form a straight line graph.

Third question;

Part A; The solution is; (2, -1)

Part B; Two solutions for f(x) are; (1.5, 0) and (0, 3)

Part C; The solution for the equation, g(x) = f(x) is the point (0, 3)

A function is rule, law or expression that maps the elements of one set A unto the elements of another set B such that each element of the set A maps unto exactly one element of the set B.

First question;

Part A: The value of x = 4 has two values of y = 2, and -2

The value of x = 9 has to values of output, y = 3 and -3

The function therefore is; y = f(x) = ±√x

The above function indicates that a value of x returns two values of y, which indicates that a vertical line drawn through the graph of the function f(x) = ±√x intersects the graph twice for values of x > 0, therefore, the equation, f(x) = ±√x, represented by the values in the table is not a function

Part B: The function for the total cost of driving a car is f(x) = 90 + 0.11·x

Where; f(x) = The total cost in dollars

x = The distance the car is driven in miles

Therefore, f(300) is obtained by plugging in x = 300 as follows;

f(300) = 90 + 0.11 × 300 = 123

The value of f(300) = $123

f(300) represents the total cost of driving the car for 300 miles

Second question set;

The velocity of the runner after one hour = 6 km/h

The velocity of the runner after three hours = 2 km/h

Part A:  The ordered pair of points of the function are; (1, 6) and (3, 2)

Making use of a linear model, we get;

Slope of the equation of the model, m = (2 - 6)/(3 - 1) = -2

The equation of the model is therefore; y - 6 = (-2) × (x - 1) = -2·x + 2

y = -2·x + 2 + 6

y = -2·x + 8

Where: y = The speed of the runner

x = The number of hours the runner has been running

Part B:

The graph of the equation can be plotted from the values of y obtained from the corresponding values of x for the first 5 hours as follows;

[tex]\begin{array}{|c|c|}x & y \\1 & 6 \\2 & 4\\3 & 2 \\4 & 0 \\5 & -2\\\end{bmatrix}[/tex]

Please find attached the graph of the velocity of the runner with time created using the above table of values found with MS Excel

Third Question;

Part A; The solution to pair of equation can be found from the point of intersection of their graphs

Therefore, the solution of the pair of equations represented by p(x) and f(x) is the point of intersection of the graph of f(x) and p(x), which is the point (2, -1)

Part B; Two solutions for the function f(x) can be obtained by the point of intersection of the x- and y-axis as follows;

The x-intercept of f(x) = (1.5, 0)

The y-intercept of f(x) = (0, 3)

Part C; The solution for g(x) = f(x), is the point of intersection of g(x) and f(x), which is the point (0, 3)

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Using mathematical operations, we know that the all-star players of Claremont are 2.

Calculating a value using operands and a math operator is referred to as performing a mathematical "operation."

The math operator's symbol has predetermined rules that must be applied to the supplied operands or numbers.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, we know that 25 players in 3 cities.

1 city has 12 players.

Another city has 11 players.

So, the number of players that the 3rd city will have:

12 + 11 + x = 25

23 + x = 25

x = 25 - 23

x = 2

Therefore, using mathematical operations, we know that the all-star players of Claremont are 2.

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The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

Suppose that you have ​$4000 to invest.

The total amount of the investment after 10 years in each case will be given as,

At = r = 7.83% compounded daily, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.0783}{365} \right)^{10\times 365}[/tex]

A = $4,000 × (1.000214521)³⁶⁵⁰

A = $4,000 × 2.1878

A = $8,751.37

At = r = 7.9% compounded quarterly, then we have

[tex]\rm A = \ \$4,000 \times \left (1 + \dfrac{0.079}{4} \right)^{10\times 4}[/tex]

A = $4,000 × (1.01975)⁴⁰

A = $4,000 × 2.186

A = $8,745.98

The investment yields a greater return over a 10-year​ period if he invested 7.83​% compounded daily.

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The area of the circle is obtained as 78.50 square feet. The correct option is (A).

A circle is a geometric shape, all of which points are equidistant from a fixed point called as the Centre.

The Centre of the circle does not lie on it.

Given that,

The radius of the circle is 5 feet.

The expression for the area of the circle is given as πr².

Substitute the value of r and take π = 3.14 to obtain,

Area = πr²

        = 3.14 × 5²

        = 3.14 × 25

        = 78.50

Hence, the area of the circle with given radius is obtained as 78.50 square feet.

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1. For the given line segment if PQ = RS then it is proved that PR = QS .

2. From the given angles  if ∠1 is complement to ∠2 (∠1 + ∠2 = 90° )  then angle 1 is complement to angle 3.

As given in the question,

1. Given : PQ = RS

To prove : PR = QS

Proof:

PQ = RS ( given )

Add both the side QR we get,

PQ + QR = QR + RS

From the diagram, it is given P - Q - R - S are collinear points

PR = QS  ( PQ + QR = PR and QR + RS = QS)

Hence, PQ = RS implies that PR = QS.

2. Given: ∠1 is a complement of ∠2

∠2 ≅ ∠3

To prove : ∠1 is a complement of ∠3

proof: ∠1 is a complement of ∠2

⇒∠1 + ∠2 = 90°

⇒∠1 + ∠3 = 90° ( given ∠2 = ∠3 )

⇒∠1 is a complement of ∠3.

Hence, it is proved that ∠1 is a complement of ∠2 implies that ∠1 is a complement of ∠3.

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By solving a linear equation, it can be calculated that

x = [tex]\frac{-3y + 5}{2}[/tex]

Option A is correct

What is a linear equation?

At first, it is important to know about algebraic expression.

Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.

Now we need to know about equation

Equation shows the equality between two algebraic expressions by connecting the two algebraic expressions by an equal to sign.

A one degree equation is known as linear equation.

Linear equation is a very important tool in mathematics

The given linear equation is

2x + 3y = 5

Now,

2x + 3y = 5

2x = -3y + 5

x = [tex]\frac{-3y + 5}{2}[/tex]

Option A is correct

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Elyse has the option of combination of 960 cities, or another to choose from. If Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.

Given,

Elyse is going to buy an around-the-world plane ticket. She will get to see just one city from each continent she will visit. The following table below shows the continents on her trip and how many cities she can choose from for each continent.

To determine how many options Elyse will have, we use permutations and combinations.

We can say that she has a choice of any of the eight cities in Asia for every ten cities in Europe. Similar to how she can select any of the 4 cities in Africa for every 8 cities in Asia. The same is true for Australia and Africa.

Elyse has a choice of a total:

10×8×4×3

960

Elyse has the option of combination of 960 cities, or another.

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Answer:

Below

Step-by-step explanation:

Assuming a circular track

Outside track is 3 m 'thicker ' so the diameter is (44 + 3 + 3) = 50 m

Outside track circumference = pi * d =  pi * 50 = 50 pi m

  Inside track circumference = 44 pi

Outside 10 laps = .500 pi   KM     time = .5 pi  km / 4.5 km/hr = .3490658 hr

Inside 10 laps = .444 pi KM            time = .444 pi km / 4.5 km/hr = .309974

Difference = .039095 hr =2.35 minutes

The values of x and are 28° and 58° respectively

It is important to note the properties of a trapezium;

We then have that;

2y + (y + 6) = 180

4x + 2x + 12 = 180

From equation (1), we have;

3y + 6 = 180

collect like terms

3y = 180 -6

3y = 174

y = 58°

From equation (2), we have;

6x = 180 -12

6x = 168

x = 28°

Hence, the values are 28° and 58°

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For isosceles trapezoid PQRS the coordinates for point R are;; (a - b, c).

We are told that the following figure is an isosceles trapezoid. This tells us that the two non - parallel sides of the given trapezoid are equal.

A parallel side of the trapezoid lies on the x-axis, which tells us that the opposite side is a horizontal line parallel to the x-axis and that the y-coordinate remains the same for all point lie on that side.

Since the opposite side has vertex (b, c), therefore the y-coordinate for point R is c.

The non-vertical sides are equal. Since the horizontal distance between (0,0) and (b, c) is b, then it means that the horizontal distance between point R and (a, 0) is b. So, the x-coordinate of R is (a - b).

Therefore we conclude that the coordinates for point R are (a - b, c).

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The approximate height of the kite from the ground will be 159 feet

The best angle to fly the kite = 45 degrees

Th length of the string = 225 feet

To find the height above the ground to the kite, we have to use the trigonometric function

sin θ = Opposite side / Hypotenuse

The angle θ = 45 degrees

The length of the hypotenuse = 225 feet

Substitute the values in the equation of sin θ

sin 45 = Opposite side / 225

Opposite side = 225 × sin 45

= 159 feet

Therefore, the height of the kite from the ground is 159 feet

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