Find the 53rd term of the following arithmetic sequence.

3, 12, 21, 30, ...

Answer: El índice de refracción del vidrio flint es mayor que el del aire. Cuando la luz pasa de un medio con un índice de refracción menor (como el aire) a un medio con un índice de refracción mayor (como el vidrio), experimenta un cambio de dirección. Este fenómeno se conoce como refracción.

Cuando observamos el bloque de vidrio flint desde arriba, la luz que proviene del bloque sufre refracción al pasar del vidrio al aire. Debido a la refracción, los rayos de luz se desvían y parecen venir de una posición más alta dentro del vidrio de lo que realmente están. Esto crea una ilusión óptica que hace que el espesor aparente del bloque de vidrio se vea más delgado de lo que realmente es.

La cantidad exacta de adelgazamiento aparente depende del ángulo de incidencia de la luz y de los índices de refracción del vidrio y el aire. Sin más información, no es posible determinar el espesor aparente específico del bloque de vidrio flint cuando se ve desde arriba.

Step-by-step explanation:

The area of triangle EFG is given as follows:

A = 18.63 square units.

The area of a rectangle of base b and height h is given by half the multiplication of dimensions, according to the formula presented as follows:

A = 0.5bh

The base is given by segment EF as follows:

\(EF = \sqrt{(9 - 4)^2 + (-7 -(-9))^2}\)

EF = 5.4.

The midpoint of EF is given as follows:

M(6.5, -8).

The height is given by the segment MG as follows:

\(MG = \sqrt{(6.5 - 3)^2 + (-2 - (-8))^2}\)

MG = 6.9.

Hence the area is given as follows:

A = 0.5bh

A = 0.5 x 5.4 x 6.9

A = 18.63 square units.

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theseSOLUTION

To get the coordinates of D

First: We get the coordinates of A and B. From the graph, this are A(5, -2) and B(8, 3)

Secondly: We subtract coordinate A from B, that is B - A

B - A = (8 - 5, 3 - (-2)

B - A = (3, 5)

Lastly; subtract (B - A) from C to get coordinate D. Coordinate C is C(3, 8)

C - (B - A) = (3 - 3, 8 - 5)

C - (B - A) = (0, 3)

Therefore Coordinate D = (0, 3)

Answer:

7z + 17

Step-by-step explanation:

Like terms

All the numbers without letters are like terms

All the numbers with letters are like terms

Since we have 2 numbers without letters, we'll combine those.

15 + 2 = 17

Since there's only one number with letters, we can keep it the same since there's no others to combine it with

7z + 17

Answer:

13.25

Step-by-step explanation:

1. you have to subract the cost of the drink:

94.25-1.50=92.75

2.you have to divide to get the individual cost of pizzas by doing

92.75÷7=13.25

so therefore your answer is 13.25 per pizza

Answer:

1/4 lol

Step-by-step explanation:

1/2=2/4

2/4-1/4=1/4

or in decimal form

.50-.25 =.25

Answer:

3/35

Step-by-step explanation:

3*1=3

5*7=35

3/35

1.) Probability of getting 1: 0.12 or 12%.

2.) Probability of getting 2: 0.16 or 16%.

3.) Probability of getting 3: 0.25 or 25%.

4.) Probability of getting 4: 0.18 or 18%.

5.) Probability of getting 5: 0.15 or 15%.

6.) Probability of getting 6: 0.14 or 14%.

To calculate the probability of getting a specific number on a fair die, we divide the number of times that number appears by the total number of rolls. In this case, the die was rolled 100 times, and the results are given as follows:

Number: 1 2 3 4 5 6

Times: 12 16 25 18 15 14

To find the probability of getting each number, we divide the corresponding number of times by the total number of rolls (100):

Probability of getting 1 = 12 / 100 = 0.12.

Probability of getting 2 = 16 / 100 = 0.16.

Probability of getting 3 = 25 / 100 = 0.25.

Probability of getting 4 = 18 / 100 = 0.18.

Probability of getting 5 = 15 / 100 = 0.15.

Probability of getting 6 = 14 / 100 = 0.14.

Therefore, the probabilities of getting each number on a fair die, based on the given results of 100 rolls, are approximately:

1: 0.12 or 12%,

2: 0.16 or 16%,

3: 0.25 or 25%,

4: 0.18 or 18%,

5: 0.15 or 15%,

6: 0.14 or 14%.

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The value of the missing length to the nearest tenth are;

a. x = 7.5

b. x = 7.8

Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Therefore ;

c² = a²+b²

a. x² = 9²-5²

x² = 81-25

x² = 56

x = √56

x = 7.5 ( nearest tenth)

b. using Pythagoras theorem also!

x² = 6²+5²

x² = 36+25

x² = 61

x = √61

x = 7.8( nearest tenth).

Therefore the value of the missing values are 7.5 and 7.8

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Answer: B (−5 < x < 3)

Steps

−19 < 3x − 4 < 5

−19 < 3x − 4 and 3x − 4 < 5

x > −5 and x < 3

−5 < x < 3

Number Line

−19 < 3x − 4 < 5 : Solution: − 5 < x < 3

[ Interval Notation: (−5, 3)]

If a < u < b then a < u and u < b

−19 < 3x − 4 : x > −5

3x − 4 < 5 : x < 3

Combine the intervals

Merge Overlapping Intervals

And that equals=

−5 < x < 3

Answer:

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

\(0.455\)

Step-by-step explanation:

Divide the number of round blue blocks in the box from the total number of round blocks in the box. Remember that only the round blocks are in the box.

\(\dfrac{\# \textrm{ of blue blocks}}{\textrm{total }\# \textrm{ of blocks}} = \dfrac{5}{5 + 2 + 4}\)

\(= \dfrac{5}{11}\)

\(\approx 0.455\)

Answer:you have 2 lines that cross.

the left angle formed is equal to 3x + 8

the right angle formed is equal to 5x - 20.

the bottom angle formed is equal to 5x + 4y

since the lines are crossed, the opposite angles to each other are equal.

this means that:

3x + 8 = 5x - 20

solve for x to get x = 14 degrees.

the angle on the left side will be equal to 3(14) + 8 = 50 degrees.

the angle on the right side will be equal to 5(14) - 20 = 50 degrees.

this is at it should be since the angles are equal to each other.

since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.

since those 2 angles are equal, then each one must be equal to 130 degrees.

one of those angles is equal to 5x + 4y.

you get 5x + 4y = 130

since x was already found to be 14, replace x with 14 to get:

5(14) + 4y = 130

solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.

when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.

your answers are:

x = 14 degrees

y = 15 degrees

2 of the angles measure 50 degrees each.

2 of the angles measure 130 degrees each.

The value of x in chords is 25.857 and this is a isosceles triangle.

In geometry, a chord is a line segment that connects two points on the circumference of a circle. A chord is the longest distance between two points on a circle, and it passes through the center of the circle. The endpoints of a chord are referred to as its "endpoints." A chord that passes through the center of a circle is called the "diameter" of the circle. The length of a chord can be calculated using the Pythagorean theorem, given the radius and the distance between the center and the chord. Chords are used in various geometric calculations involving circles, such as finding the area of a sector or segment of a circle.

The sum of the angles of a triangle is 180 degrees. In a circle, the angle subtended by an arc at the center of the circle is twice the angle subtended by the same arc at any point on the circumference. Using these facts, we can set up the following equation to find x:

(1/2)(14x - 7) + (1/2)(12x + 4) + (1/2)(4x) = 180

Simplifying and solving for x, we get:

7x - 1 = 180

7x = 181

x = 25.857

Therefore, x is approximately equal to 25.857.

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

Answer:

(0, 1)

Step-by-step explanation:

you have to put the equation in the slope point form

y=mx+b and here b is the y-intercept (where it crosses the y axis)

y-4x=1 add 4x to both sides

y=4x+1 so the coordinats are (x=0, y=1)

The derivative of the function \(-4^x\) is \(-4^{x}log4\).

The definition of a derivative in mathematics is a technique for displaying the simultaneous rate of change. The amount by which the given function is changing at a particular point is thus represented by it.

The derivative of the function will be calculated as:-

\(y = -4^x\)

Take logs on both sides,

logy = -xlog4

Differentiate both sides with respect to x.

(dy / dx)logy = dy / dx [ -xlog4 ]

(dy/dx) x ( 1 / y) = -x (0) + log(4) x -1

dy /dx = y x -log(4)

dy / dx = \(-4^x\)logx

Therefore, the solution will be  \(-4^{x}log4\).

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Answer:

x-variable

5x-term

5-coefficient

12-constant

Answer:

Dababy A baby. (=

The required solution to the given equation  (7h + 1) = (3h - 7) is h = -2.

A solution to an equation is a number that can be replaced for the variable to equip a true number statement.

The equation is given in the question, as follows:

7h + 1 = 3h - 7

We need to isolate the variable h on one side of the equation by performing inverse operations. First, we can simplify the equation by combining like terms on both sides:

7h - 3h = -7 - 1

4h = -8

Next, we can solve for h by dividing both sides by 4:

h = -2

Therefore, the solution to the given equation is h = -2.

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The complete question would be as:

Find the solution to the below equation.

(7h + 1) = (3h - 7)

Answer:

Below

Step-by-step explanation:

a) they won 120 games out of 369 played  = 40/23=.325

b) they lost 248 out of 369 played = 248/369 = .672

c) Home games are 185 out of 369 = .501

d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389

Answer:

13

Step-by-step explanation:

Using the triangle midsegment theorem, \(UV=4, TU=5, VT=4\).

So, the perimeter of \(\triangle TUV\) is \(4+4+5=13\).

The two roots of the quadratic equation x² - 5x + 3 = 0 are (5 + √13) / 2 and (5 - √13) / 2.

To find the roots of the quadratic equation x² - 5x + 3 = 0, we can use the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a, b, and c are the coefficients of the quadratic equation.

Substituting the values of a, b, and c from the given equation, we have:

x = (-(-5) ± √((-5)² - 4(1)(3))) / 2(1)

x = (5 ± √(25 - 12)) / 2

x = (5 ± √13) / 2

Therefore, the roots of the equation are (5 + √13) / 2 and (5 - √13) / 2.

To verify that these are indeed the roots of the equation, we can substitute each of these values for x in the original equation and check if the equation is satisfied. For example, if we substitute (5 + √13) / 2 for x, we get:

(5 + √13)² - 5(5 + √13) + 3 = 0

Simplifying this equation, we get:

13 - 5√13 + 8 + 13 - 5√13 + 3 = 0

This equation is true, which means that (5 + √13) / 2 is a root of the equation x² - 5x + 3 = 0. Similarly, we can verify that (5 - √13) / 2 is also a root of the equation.

These roots can be found using the quadratic formula, which is a useful tool for solving quadratic equations.

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Answer: I’m not for sure but I think it is the third one

Step-by-step explanation:

Answer:

  731 square feet

Step-by-step explanation:

The surface area can be found using the given formula, along with the formula for the area of a trapezoid. (The bases have the shape of a trapezoid.)

We are given "h", so we need to find "p" and "B" for the formula.

__

The perimeter is the sum of the side lengths:

  p = 13 ft + 7 ft + 10 ft + 8 ft = 38 ft . . . perimeter

The height is shown as 15 ft.

__

The base area is the area of a trapezoid with base lengths 13 ft and 10 ft and height 7 ft. (The height is the perpendicular distance between the parallel bases. The two right angle corners show you the bases are parallel, and that 7 ft is the distance between them.)

  A = 1/2(b1 +b2)h

  A = 1/2(13 ft +10 ft)(7 ft) = 80.5 ft²

__

Using your formula for the surface area, we find ...

  SA = hp +2(B)

  SA = (15 ft)(38 ft) +2(80.5 ft²) = 570 ft² +161 ft²

  SA = 731 ft²

The area of the trapezoidal prism is 731 square feet.

Answer:

R23 470

because 3 is below 5 so =0

A formula without free variables is a formula that does not contain any variables that are not quantified.

Sentences are commonly referred to as formulas devoid of any unrestricted variables. These statements hold a truth value independent of the variable values, hence the reason.

Open formulas are frequently referred to as formulas with free variables. These are not actually declarations; instead, they are arrangements that can transform into declarations by allotting definite values to the independent variables.

Formulas without free variables are often easier to work with than formulas with free variables.

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The length of time that it will take for each of the workout sessions would be: Plan A = 1.5 hours, and Plan B =  0.5 hours.

The length of the sessions can be obtained by first obtaining drawing a system of equations for the two cases. On Wednesday, we can represent the sessions as follows:

2A + 12B = 9 hours

On Thursday, we would have

5A + 3B = 9 hours

2A + 12B = 9  Eqn 1

5A + 3B = 9   Eqn 2

Multiply equation 2 by -4

2A + 12B = 9

-20A - 12B = -36

2A - 20A = 9 -36

-18A = -27

Divide both sides by -18

A = 1.5 hours

For B, substitute A in the first equation

2(1.5) + 12B = 9

3 + 12B = 9

12B = 9 - 3

12B = 6

Divide both sides by 12

B = 0.5

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Complete Question:

Ann the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 2 clients who did Plan A and 12 who did Plan B. On Thursday there were 5 clients who did Plan A and 3 who did Plan B. Ann trained her Wednesday clients for a total of 9 hours and her Thursday clients for a total of 9 hours. How long does each of the workout plans last?