When you look at a pencil in water, it looks bent. This illusion is due to refraction, or the bending of light when it moves from one substance to the next.

c. Without measuring, determine how many degrees the path of the light changes after it enters the water. Explain your reasoning.

Answer:

3.1.1.  A(-4, 0)   B(0, -2)   E(4, 0)

3.1.2.  k = -16

3.1.3.  (-∞, ∞)

3.1.4.  [-16, ∞)

3.1.5.  [-6, 4]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=x^2+k\\g(x)=-2x+8\\h(x)=\dfrac{6}{x-2}+1\end{cases}[/tex]

Points A and B are the x-intercept and y-intercept of function h(x).

Point E is the x-intercept of function g(x).

The x-intercept of function h(x) is when h(x) = 0:

[tex]\begin{aligned}h(x) & = 0\\\implies \dfrac{6}{x-2}+1 & = 0\\\dfrac{6}{x-2} & = -1\\6 & = -1(x-2)\\6 & = -x+2\\4 & = -x\\x & = -4\end{aligned}[/tex]

Therefore, the coordinates of point A are (-4, 0).

The y-intercept of function h(x) is when x = 0:

[tex]\begin{aligned}h(x) & = \dfrac{6}{x-2}+1\\\implies h(0) & = \dfrac{6}{0-2}+1\\ & = -3+1\\& = -2\end{aligned}[/tex]

Therefore, the coordinates of point B are (0, -2).

The x-intercept of function g(x) is when g(x) = 0:

[tex]\begin{aligned}g(x) & = 0\\\implies -2x+8 & = 0\\-2x & = -8\\x & = 4\end{aligned}[/tex]

Therefore, the coordinates of point E are (4, 0).

As function f(x) passes through point C (-6, 20), substitute the point into the equation of the function to find the value of k:

[tex]\begin{aligned}f(-6) & = 20\\\implies (-6)^2 + k & = 20\\36 + k & = 20\\k & = 20 - 36\\k & = -16\end{aligned}[/tex]

Hence, proving that the value of k is -16.

The domain is the set of all possible input values (x-values).

The domain of function f(x) is unrestricted, therefore its domain is:

The range is the set of all possible output values (y-values).

The range of function f(x) is restricted, since the minimum point of the parabola is at (0, -16).  Therefore its range is:

[tex]\begin{aligned}g(x) - f(x) & \geq 0\\\implies g(x) &\geq 0+f(x)\\ \implies g(x) & \geq f(x)\end{aligned}[/tex]

Therefore, find the interval for which g(x) is greater than or equal to f(x).

From inspection of the given graph this is between points C and E:

Answer:

(x, y) --> (x, - y)

Step-by-step explanation:

.......

Answer:

14x

Step-by-step explanation:

2x*7=

2*7=14x

Step-by-step explanation:

this just means

q = k×p

and we need to find k.

the sum of both q values when p = 6 and p = 11 is then

k×6 + k×11 = 51

17k = 51

k = 51/17 = 3

so, our equation is

q = 3p

and when q = 72

72 = 3p

p = 72/3 = 24

The linear equation doesn't have a solution.

The linear equation given is illustrated as: 4x-(2x-1) = x+5+x-6

This will be solved thus:

4x - 2x + 1 = x+5+x-6

4x - 2x + 1 = 2x - 1.

2x + 1 = 2x - 1

Collect like terms

2x - 2x = -1 - 1

0 = -2

This illustrates that the equation doesn't have a solution.

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The probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

According to the given question.

Total number of cards in a deck is 52.

As we know that total number of red cards in a well shuffled deck is 26.

Since, Eric first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. Which means there is a replacement of cards.

So, the probability of drawing the first card is red = 26/52 = 1/2

And the probability of drawing the another card is red = 26/52 = 1/2

Therefore,

The probability of drawing a red card, placing it back in the deck, and drawing another red card

= 1/2  × 1/2

= 1/4

Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

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Answer:

Step-by-step explanation:

x < 0

Answer : x is less than or equal to 0

First, the direction of the number line in the graph is the negative number side, so it has to be 0 or less.

If it is less than 0, the dot that starts at the point 0 must have a hollowed out part in the middle. If it is 0 or less, the dot that starts at the point 0 is completely filled with no hollowed middle part.

Since the dot is completely blacked out, the answer is the second option.

The ratio of blue hats to red hats IS 3:2 , the ratio of the blue hats all hats is 3:5 and If the store purchased 45 hats, 27 hats were blue

The ratio of blue hats to red hats is 9:6, which can be simplified to 3:2

Therefore the ratio of blue hats to red hats is 3: 2

The total number of hats is the summation of blue hats and red hats = 9+6= 15

So, The ratio of blue hats to all hats is 9:15, which can be simplified to 3:5

Therefore the ratio of blue hats to red hats is 3: 5

If the store purchased 45 hats, and we need to find out the number of blue hats

We have to assume the number of blue hats be x

Then the ratio becomes x: 45::3:5

We can also write this as

X= 3a and 45= 5a

The value of a comes out to be 9

So the number of blue hats purchased in the lot is 3a= 3 9 = 27

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The missing points are listed below:

The picture attached aside shows us a right-angled parallelepiped and the Euclidean geometry indicates that a plane is generated by three non-colinear points, that is, three points that cannot be contained by a line.

Therefore, coplanar points are points that can be contained by one and same plane. Parallelepipeds are solids with eight vertices and twelve sides, each of them corresponding to a plane.

In this problem we must determine what fourth point is contained by the same plane that comprises the other three. Now we show the corresponding answers:

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Answer:

1:

Step-by-step explanation:

5 divided by 5 is 1, and 35 divided by 5 is

The sum of the measures of the interior angles of the chess board is equal to 720°.

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

Note: The number of sides (n) of a hexagon is 6.

In Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Sum of interior angles = 180 × (6 - 2)

Sum of interior angles = 180 × 4

Sum of interior angles = 720°.

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The circumference of the Canadian $1 coin is 83.21 mm

For given question,

We have been given the Canadian $1 coin has a diameter of 26.5 mm.

We need to find the circumference of the coin.

We know that circumference of a circle of radius r is,

c = 2πr

The Canadian $1 coin has a diameter of 26.5 mm.

So, the radius of the coin would be,

r = 26.5 /2

r = 13.25

Using the formula of circumference, the circumference of the coin would be,

⇒ c = 2πr

⇒ c = 2 × π × r

⇒ c = 2 × 3.14 × 13.25

⇒ c = 83.21 mm

Therefore, the circumference of the Canadian $1 coin is 83.21 mm

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Answer:

x2 + 8x + 15

Step-by-step explanation:

First - take the first terms of the brackets (so, x and x) and multiply them together: for this example that gives x2.

Outside - take the two outermost terms of the brackets (x and 5) and multiply them together: for this example that gives 5x.

Inside - take the two innermost terms of the brackets (3 and x) and multiply them together: for this example that gives 3x.

Some people may draw lines between terms when doing this (as seen in the diagram above) leaving you with a “crab claw” around the brackets.

Write down everything you have worked out as one long expression:

x2 + 5x + 3x + 15

Then, we will simplify this expression by grouping any “like” terms (this just means adding together any bits with x where they have the same power).

This leaves us with our final answer, which is:           

x2 + 8x + 15

Answer: K(8,6)

Step-by-step explanation:

M(8,3) - the midpoint of KL    L(8,0)    K(x,y)=?

[tex]\displaystyle\\Mx=\frac{Kx+Lx}{2}[/tex]

Multiply both parts of the equation by 2:

[tex]2Mx=Kx+Lx\\2Mx-Lx=Kx+Lx-Lx\\2Mx-Lx=Kx\\Mx=8\ \ \ \ Lx=8\\Hence,\\2(8)-8=Kx\\16-8=Kx\\8=Kx\\\\2My-Ly=Ky\\My=3\ \ \ \ Ly=0\\Hence,\\2*(3)-0=Ky\\6-0=Ky\\6=Ky\\Thus,\\K(8,6)[/tex]

Answer:

What is the amount (to the nearest cent) in the account at the end of three years if the interest rate is 2%? $1,350.68

Step-by-step explanation:

DATA:

Deposits (at beginning of year):

Year 1 = $500

Year 2 = $200

Year 3 = $600

growth factor: z = 1 + r

interest rate is 2% so replace r with 2%. Growth factor equation is now:

z = 1 + 2%

z = 1.02

Year 1 account balance end of year = account balance + growth factor

= $500 + 1.02

= $ 510 account balance at end year 1

Year 2 account balance end of year = (previous year ending balance + current year deposit) * growth factor

= ($510 + $200) * 1.02

= $724.20

Year 3 account balance end of year = (previous year ending balance + current year deposit) * growth factor

= ($724.20 + $600) * 1.02

=$1,350.684

rounded: = $1,350.68 (This answer assumes no money has been withdrawn at any time.)

Answer: 48

Step-by-step explanation: 48 is the highest mileages

Answer:

3/10

Step-by-step explanation:

4/5 * 3/8

We can rewrite the fractions as

4/8 * 3/5

4/8 simplifies to 1/2

1/2 * 3/5

Multiply the numerators

1*3 = 3

Multiply the denominators

2*5 = 10

Numerator over denominator

3/10

The equivalent expression to the given expressions after using distributive property is [tex]6(13+7)[/tex]

As per the question statement, we are supposed to find the expression equivalent to the given expression [tex]6*13 + 6*7[/tex] after using the distributive property. Before solving this problem, we should know about the distributive property, which states that [tex]a(b+c) = a*b + a*c[/tex].

Therefore, [tex]6*13 + 6*7[/tex]

[tex]=6(13+7)[/tex], as per the definition of the distributive property.

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The graph can be viewed at the conclusion of the response. We want to graph a number line and certain points on it.

Let A denote the truck stop and then it is 0 miles away from the truck stop.

Let us take the north side of the truck stop as the negative side.

Then the south side of the truck stop is the positive side.

We are asked to represent the following positions on the number line:

a. The truck stop

b. 5 miles to the north of the truck stop

c. 3.5 miles to the south of the truck stop

Point A refers to the truck stop.

Let B denote the point 5 miles away from A towards the north side of the truck stop.

And let C denote the point 3.5 miles away from A towards the south side of the truck stop.

Refer to the attached image for the required number line.

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John is playing a game with a standard deck of playing cards - this statement is true.

playing a card game, set of cards that are numbered or outlined (or both) and are utilized for messing around, for schooling, for divination, and for conjuring. Generally, Western playing a card game are made of rectangular layers of paper or slight cardboard stuck together to frame a level, semirigid material. Some have proposed that the playing a card game previously worked as "play cash" and addressed the stakes utilized for other betting games, and later turned out to be essential for the actual games. Others have proposed associations between playing a card game and chess or dice games, yet this is again theoretical. Different games, for example, a 25-card variation of Euchre which involves the Joker as the most elevated trump, make it one of the main in the game. Frequently, the Joker is a special case, and subsequently permitted to address other existing cards.

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The equation is 8x + 4.79= 60.39 and the value is x is $6.95

Nabhitha pays a total of $60.39 for the cookies and onions

She pays a total of $4.79 for the cookies

She buys 8 bags of onions that each costs the same amount of money

The equation used to find the value of x is written as

8x + 4.79= 60.39

Collect the like terms

8x= 60.39 - 4.79

8x= 55.6

Divide both sides by the coefficient of x which is 8

8x/8 = 55.6/8

x= 6.95

Hence the price of each bag of onions is $6.95

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Answer:non terminating

Step-by-step explanation:

The value of ∠ F L H  is 3x-6°

∠FLG and ∠FLH are adjacent angles with L being the common vertex  and both the angles form the ∠HLG

As ∠FLG is given as 14x + 5° and  ∠ H L G is given as 17 x − 1 °

We need to find the value of ∠ F L H

We can write that ∠FLG +∠FLH = ∠ H L G

by putting the values given

14 x + 5 ° + ∠ F L H  = 17 x − 1 °

∠ F L H = 17x-1 - (14x + 50

Here we got a linear equation in one variable and by solving the equation we will get the value of ∠ F L H

∠ F L H = 17x - 1 - 14x -5

∠ F L H  = 3x-6

Hence, the value of ∠ F L H  is 3x-6°

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The second vector that's perpendicular to the line we want (call it L) is missing; I'll denote it by ⟨a, b, c⟩.

The cross product of ⟨1, 1, 0⟩ and ⟨a, b, c⟩ is perpendicular to both of these vectors. The direction vector of L will be parallel to this cross product.

Compute the cross product.

⟨1, 1, 0⟩ × ⟨a, b, c⟩ = ⟨1•c - 0•b, 0•a - 1•c, 1•b - 1•a⟩ = ⟨c, -c, b - a⟩

Then the vector equation of L is

L(t) = ⟨c, -c, b - a⟩ t + ⟨-3, 3, -1⟩

As parametric equations, we write

x(t) = ct - 3

y(t) = -ct + 3

z(t) = (b - a) t - 1

Eliminating the parameter above, we get

x + y = (ct - 3) + (-ct + 3) = 0   ⇒   x = -y

and substituting

x = ct - 3   ⇒   t = (x + 3)/c

into z(t), we get

z = (b - a) (x + 3)/c - 1   ⇒   x = c (z + 1)/(b - a) - 3

As symmetric equations, then, we write

x = -y = c (z + 1)/(b - a) - 3

Answer:

a. 3 units

Step-by-step explanation:

The length of BC can be found in 3 main steps, namely the formation of equations, solving for x and substitution.

Let's rewrite the given lengths:

AB= 4x +1 -----(1)

BC= 2x -7 -----(2)

AC= 24 -----(3)

Form an equation which relates the 3 lengths:

Given that B is between A and C,

AC= AB +BC -----(4)

Substituting equations (1) to (3) to equation (4):

24= 4x +1 +2x -7

Simplify:

24= 6x -6

Add 6 to both sides:

6x= 24 +6

6x= 30

Divide both sides by 6:

x= 5

Substitute x= 5 into (2):

BC

= 2x -7

= 2(5) -7

= 10 -7

= 3 units

Thus, option a is correct.

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The given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.

Notice that the given conjecture does not necessarily be always true.

To be precise, there are no reasons as to why A, B and C must be noncollinear.

They could lie on the same line.

Therefore, the given conjecture "If you have three points A, B , and C , then A, B, C are noncollinear" is false.

A Counterexample of the given statement is; A, B, C are three points that lie on the same line and so they are collinear.

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Answer:

8x - 4y

Step-by-step explanation:

First: solve the parentheses

8x - 7y - (3-6y)

Second: combine like terms (terms that both have y or x, or other variable)

8x - 7y - (-3y)

Third: there are no more like terms, so you are left with this as your answer

8x - 4y

Cost of pen = 20x  when x< 10

                              and

                      =10x when x>10

Let the number of pens bought be x.

So the total pen cost is 20x when the number of the pen is less than 10.

Now let's take that the number of pens bought is more than 10

So the pen will cost a 50% discount  

    50% of 20x

  = 20/100 × 20x

  = 10x

So the cost of the pen will be 10x when the number of the pen is greater than 10.

From this, we get to know that

Cost of pen = 20x when x<10

                              and

                       = 10x when x>10

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