Anthony shines a beam of light on the surface of a solution of glycerol at a certain angle. if the angle of refraction is 38°, what is the angle of incidence? the index of refraction of glycerol is 1.47, while that of air is 1.00. a. 38° b. 45° c. 55° d. 65° e. 70°

The given expression is [tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]. the option C [tex]\dfrac{ (r+2)}{(r-2)}[/tex]is correct.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

The given expression is

[tex]\dfrac{ r^2-r-6}{(r-2)(r-3)}[/tex]

By solving the numerator

[tex]r^2-r-6\\\\r^2 - (3-2)r- 6\\\\(r-3)(r+2)[/tex]

Put the solution in the above equation

[tex]\dfrac{ (r+2)(r-3)}{(r-2)(r-3)}[/tex]

[tex]\dfrac{ (r+2)}{(r-2)}[/tex]

Therefore, the option C is correct.

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The set that represents the same relation as the graph given is: B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).

A relation is defined as a relationship between the input and output, which can be displayed on a graph on a coordinate plane.

From the graph as shown in the image attached below,

The set that has the same coordinate points as indicated on the graph is:

B. (-5, 4), (-3, -2), (-1, -2), (2, 0), (3, 3), (4, 5), (6, -4).

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Step-by-step explanation:

the area of a triangle

baseline × height / 2

in our case

baseline × height / 2 = 60 in²

height = 6×baseline - 16

baseline × (6×baseline - 16) / 2 = 60

baseline × (3×baseline - 8) = 60

3×baseline² - 8×baseline = 60

baseline = x

3x² - 8x - 60 = 0

general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 3

b = -8

c = -60

x = (8 ± sqrt(64 - 4×3×-60))/(2×3) =

= (8 ± sqrt(64 + 720))/6 = (8 ± sqrt(784))/6 =

= (8 ± 28)/6

x1 = (8 + 28)/6 = 36/6 = 6

x2 = (8 - 28)/6 = -20/6 = -10/3

x2 as a negative number is not a valid solution for a length in a geometric shape.

so, x = 6 in is our solution for the baseline.

height = 6x - 16 = 6×6 - 16 = 36 - 16 = 20 in

base = 6 in

The answers to the three shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

Perimeter is the outside boundary of a plane shape.

Analysis:

for figure 7, perimeter = s + s + s = 3s = 3(5.4) = 16.2mm

                   Height of triangle = [tex]\sqrt{((5.4)^{2} - (2.7)^{2} }[/tex] = 4.68

            Area of triangle = 1/2 base x height = 1/2 x 5.4 x 4.68 = 12.64[tex]mm^{2}[/tex]

For figure 8, perimeter = b + b + a = 5.9 + 5.9 + 3.4 = 15.2 inches

                     Height of triangle = [tex]\sqrt{(5.9)^{2} - (1.7)^{2} }[/tex] = 5.65inches

           Area of triangle = 1/2 base x height = 1/2 x 3.4 x 5.65 = 9.61[tex]inches^{2}[/tex]

For figure 9, perimeter = b + a + c = 8.2 + 4.1 + 9.17 = 21.47yards

           Area of triangle = 1/2 x base x height = 1/2 x 8.2 x 4.1 = 16.81[tex]yards^{2}[/tex]

In conclusion, the perimeter and area of the given shapes are:

Figure 7; perimeter = 16.2mm, area = 12.64 square mm

Figure 8; perimeter = 15.2inches, area = 9.61 square inches

Figure 9; perimeter = 21.47yards,  area = 16.81 square yards

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The probability that Bridget makes all three free throws to win the game is; 42.2%

We are told that the probability of Bridget making her free throw correctly is 75%.

Now, if she has to get all three free throws correctly, then the probability for that is;

P(3 free throws correct) = 0.75 * 0.75 * 0.75

P(3 free throws correct) = 0.421875 ≈ 42.2%

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Answer:

The altitude to the hypotenuse of a right triangle forms two triangles that are similar to each other and to the original triangle

The Leg Rule (or Leg geometric mean theorem) relates the length of each leg of a right triangle with the segments projected by them on the hypotenuse.

Step-by-step explanation:

The altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse. Notice the triangle used with this rule. The leg of a right triangle is the mean proportional between the hypotenuse and the projection of the leg on the hypotenuse.

3) [tex]\angle B \cong \angle Y[/tex]

4) [tex]\triangle ABC \sim \triangle ZYX[/tex] by the SAS similarity theorem

ΔABC is similar ΔZYX by the SAS similarity theorem. Therefore, option B is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

1. AB/ZY = BC/YX = 2

2. ∠B and ∠Y are right angles

3. ∠B=∠Y

4. ΔABC is similar ΔZYX by the SAS similarity theorem.

Therefore, option B is the correct answer.

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Answer:

5, 10, 15

Step-by-step explanation:

the increase in the sequence is 5 so since it starts from 0 which you can find out because 25 is the 5th sequence and that means that +2*5 =25 . x=0

0+ 5 = sequence 1

0+ 5+5 = seq 2

0+5+5+5= seq 3

Answer:

  ay = 39 -6(n -1)

Step-by-step explanation:

The explicit formula for an arithmetic sequence can be written by using the first-term value and the common difference in the generic formula.

__

The generic formula for the n-th term of an arithmetic sequence is ...

  [tex]a_n=a_1+d(n-1)[/tex]

where a₁ is the first term of the sequence (39), and d is the difference between sequential terms (33-39 = -6).

Using the values for this sequence in the generic formula, we have ...

  ay = 39 -6(n -1)

Answer:

Ans = A: 57

Step-by-step explanation:

Because

sum of the angke of opposite side of quardilateral triangle is 180°

x°+30°+93°=180°

x°+123°=180°

x°=180°-123°

x°=57°

Hence proved.

The value of x is option A. 57.

A cyclic quadrilateral is a polygon with four sides where all of it's four vertices lie on a circle.

The circle thus formed is called circumcircle or circumscribed circle.

We have a property for the cyclic quadrilateral that the opposite angles formed on the quadrilateral is supplementary.

That is, sum of the opposite angles is 180°.

Here B and D are opposite angles.

So,

∠B + ∠D = 180

9x + x + 30 = 180

Solving,

x = 57

Hence the value of x is 57.

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Using it's concept, it is found that there is a 0.3043 = 30.43% probability of at least one O-ring failing.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, of the 23 flights, 7 had at least one failure, hence the probability is given by:

p = 7/23 = 0.3043.

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The operation that should be completed first to find the value of the expression is 6 - 3

The expression is given as:

12 + 30/(6 - 3) + 1

When solving an expression;

All expressions in the bracket must be first evaluated

This means that the operation that should be completed first is 6 - 3

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Considering the definition of equation, the equation that represents the statement "Two times a number x increased by 8 is 20" is: 2x + 8= 20

An equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values, called unknowns, appear in addition to certain known data.

The unknown values represents the number (or numbers), if any, that make the equality true. This unknown number is the solution of the equation.

Considering that:

the equation that represents the statement "Two times a number x increased by 8 is 20" is:

2x + 8= 20

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The equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

The given statement is two times a number x increased by 8 is 20.

We need to write the equation to represent this statement.

What is an equation?

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, two times a number x=2x

Increased by 8 is 20=2x+8=20

Hence, the equation for the statement "two times a number x increased by 8 is 20" is 2x+8=20.

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Answer:

3

Step-by-step explanation:

Put both expressions equal to each other.

2x+4=3x+1

Solve:

2x+4=3x+1

4-1=3x-2x

3=1x

x=3

Given the steps used to calculate the interquartile range, Bryan did not make any mistake.

The interquartile range is the difference between the third quartile and the first quartile.

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Answer:

-12X^7-27X^6

Step-by-step explanation:

-3x^6(-4X+9)=(-3X^6*)(4X^1)+-27X^6=-12X^7+-27X^6

I assume you know that there are n total n-th roots for any non-zero complex number.

(If you're looking for "the" principal root, you'll have to specify which branch you're calling the principal branch of the n-th root function.)

Start by writing [tex]1 - i\sqrt3[/tex] in exponential form. We have modulus/magnitude

[tex]|1 - i\sqrt3| = \sqrt{1^2 + (-\sqrt3)^2} = \sqrt4 = 2[/tex]

and [tex]1-i\sqrt3[/tex] lies in the fourth quadrant of the complex plane, so its argument is

[tex]\arg(1-i\sqrt3) = \tan^{-1}\left(-\sqrt3\right) = -\dfrac\pi3[/tex]

Then the exponential form is

[tex]1 - i \sqrt3 = 2 \exp\left(-i\dfrac\pi3\right)[/tex]

(where [tex]\exp(x) = e^x[/tex], if you're not familiar with the notation)

By de Moivre's theorem, we have the fourth roots

[tex]\sqrt[4]{1 - i\sqrt3} = \sqrt[4]{2} \exp\left(i \dfrac{-\frac\pi3+2k\pi}4\right)[/tex]

where [tex]k\in\{0,1,2,3\}[/tex], so that we have a choice of

[tex]\sqrt[4]{1 - i\sqrt3} = \begin{cases} \sqrt[4]{2} \exp\left(-i\dfrac\pi{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{5\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{11\pi}{12}\right) \\\\ \sqrt[4]{2} \exp\left(i\dfrac{17\pi}{12}\right) = \sqrt[4]{2} \exp\left(-i\dfrac{7\pi}{12}\right) \end{cases}[/tex]

(I rewrote the exponent to the last root just to be consistent about having each argument between -π and π radians)

If you want these in rectangular form (a + bi), sorry, that's where I draw the line; it can be done with simple trigonometry and algebra, but it's rather tedious, and the exponential forms are far more compact.

Answer:

See below ~

Step-by-step explanation:

We need to prove that the figures are similar by applying the various kinds of transformations.

===============================================================

Question A :

⇒ Compare the side lengths of A and B

⇒ 2 : 5 (for all sides)

⇒ 1 : 2.5

⇒ Hence, Shape A has been dilated with a scale factor of 2.5 to form Shape B

=============================================================

Question B :

⇒ Compare the side lengths of A and B

⇒ A : B = 2 : 6

⇒ A : B = 1 : 3

⇒ Shape A has been dilated with a scale factor of 1/3 to form Shape B

D) Caitlin should take the position in her preferred location because the annual salary is $45,400 after rent and utilities.

To calculate your annual salary, multiply your gross income (before taxes) by the number of pay periods in a year. If an employee earns $1,500 each week, his or her annual income is $1,500 x 52 = $78,000.

Job 1 and Job 2 both generate the same or similar amount of income of $45,400 per year after additional expenses.

This means that Caitilin should choose her career based on the preferences of her neighboring neighborhood so that she can travel easily.

This is because moving to a more distant job location would result in no increase in her income, making it nonsensical to do so.

So, the correct answer is option D.

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Answer: D. edge 2023

The jobs have equal annual incomes of $45,400 after rent and utilities so Caitlin should take the job in her favorite locale.

Answer:

40 Rs per kg.

Step-by-step explanation:

solution

Let the rate of tea be x Rs per kg and that of sugar be y Rs per kg.

When Kantabai bought the items by going to the shop,

3/2x+5y+50=700

⇒3x+10y=1300....(I)

When Kantabai bought the items online then

2x+7y=880......(II)

Multiplying (I) with 2 and (II) with 3 we get

6x+20y=2600......(III)

6x+21y=2640.......(IV)

eq.(IV)−(III)

y=40

Putting the value of y =40 in (II)

2x+7(40)=880

⇒2x=880−280=600

⇒x=300

Thus, tea is at 300 Rs per kg and sugar is 40 Rs per kg.

The phrase "in spite of" refers to a scenario where regardless of what happened, there is always a yearning desire and ability to remain positive.

The meaning of the phrase "in spite of" mean notwithstanding or whatever the circumstances, there is no room for complaining and thinking negatively.

This phrase is used to rejuvenate the positive and optimism of a man's thoughts and desires during dark moments. Hence, "in spite of" what happened, there is always an ability to remain positive.

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Step-by-step explanation:

[tex]12y^{2} + 4y \\4y( \frac{12y^{2} }{4y} + \frac{4y}{4y} ) \\ 4y(3y + 1)[/tex]

Step-by-step explanation:

12y²+4y

divide both sides by 4

therefore,

3y²+y

y(3y+1)

Using the permutation formula, it is found that these offices can be filled in 336 ways.

There are different roles, hence the order in which the people are chosen is important, hence the permutation formula is used.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

3 people will be chosen from a set of 8, hence the number of ways is given by:

[tex]P_{8,3} = \frac{8!}{5!} = 336[/tex]

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The number of each type Mika bought =x = 6.8 rolls; y= 2.2 rolls.

The number of rolls of film Mika  bought =  9 rolls

The number of rolls that had 36 exposures = x

The number of rolls that had 12 exposures = y

The total number of exposures = 36 + 12 = 48

To find the exposure by one roll = 48/9 = 5.3

If one roll = 5.3 exposure

    x roll    = 36 exposure

Make x roll the subject of formula,

x roll = 36/5.3 = 6.8 rolls

    y roll    = 12 exposure

Make y roll the subject of formula,

y = 12/5.3 = 2.2 rolls

Therefore, the number of each type Mika bought = x = 6.8 rolls; y= 2.2 rolls.

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Three points must be removed from this graph so that it will be a function

The points are given as:

(-3, 2), (-3, 3), (1, 4), (1, -4), (2, -4), (2, -2).

For a set of point to represent a function;

Each x coordinate must point to only one y coordinate

From the given points, we have the following highlights:

In the above highlights, one point each must be removed.

This means we have a total of 3 points

Hence, three points must be removed from this graph so that it will be a function

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Answer:

C. 3 points

Step-by-step explanation:

Answer:

Laila assumed that the lines that formed the angles x and 18° added up to 90. This is in fact false because of the lack of the square marking to signify it as a right or 90 degree angle.

Answer:

34 degrees

Step-by-step explanation:

Just reverse the cos function   ( you will need a calculator)

arc cos (.8290) = 34 degrees

this is sometimes written as   cos^-1 (.8290)   <====it is the same thing

Answer:

Image included:

Step-by-step explanation:

Answer:

8x+120 is the answer

Step-by-step explanation:

8(x+15)

=8x + 8×15

=8x+120