Anna is writing a computer game program. She needs to “move” a square 3 units to the left and 2 down by applying a translation rule to the coordinates of the vertices. One corner of the pre-image square is at the origin and the diagonally opposite corner is at (4,4). The sides of the square align with the coordinate axes. After the transformation what will be the coordinates of the image of each of the four vertices?

Answer:

  9 m

Step-by-step explanation:

  ∠CAB = 90° -∠ABC = 90° -30° = 60°

Since AL bisects angle A, we have ...

  ∠LAC = ∠LAB = 60°/2 = 30°

Then ∠BAL = ∠ABL = 30° and ΔABL is isosceles with AL = LB = 18 m.

The 30°-60°-90° triangle ALC has sides in the ratio ...

  CL : CA : AL = 1 : √3 : 2

so

  CL/AL = 1/2

  CL = AL/2 = (18 m)/2 = 9 m

_____

It can help to draw a diagram

In triangle BCL, since it is a 30-60-90 triangle, the side opposite the 60-degree angle is √3 times the side opposite the 30-degree angle. Thus, the length of side CL is 18√3 meters.

In triangle ABC, you're told that angle C is 90 degrees and the angle ABC is 30 degrees. Therefore angle ACB (or BAC) is 60 degrees because the sum of all angles in a triangle is 180 degrees.

You're also given that LB, a line that bisects angle B, is 18 meters.  The triangle BCL is a 30-60-90 triangle, a special type of triangle where the sides are in the ratio 1:√3:2.

In this case, LC (the side opposite the 60-degree angle) is √3 times the side opposite the 30-degree angle (LB), which is 18 meters. So, the length of CL = 18√3 meters.

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The average rate of change of a function is found with the formula (f(b) - f(a)) / (b - a). When applying this formula to the function p(x) = 6x + 7 over the interval [2, 2 + h], we find that the average rate of change is 6.

In Mathematics, the average rate of change of a function on the interval [a, b] is given by the formula (f(b) - f(a)) / (b - a). In this case, our function is p(x) = 6x + 7, and the interval is [2, 2 + h]. So, we can plug these values into the formula to get an expression for the average rate of change.

First, calculate p(2 + h) and p(2). Here they are:

Substitute these expressions into the average rate of change formula:

(P(2 + h) - P(2)) / (2 + h - 2) = (19 + 6h - 19) / (h) = 6h / h = 6.

So, the average rate of change of the function p(x) = 6x + 7 on the interval [2, 2 + h] is 6.

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Answer:

Suppose that you initially have $100 to spend on books or movie tickets.

The books start off costing $25 each and the movie tickets start off costing $10 each.

a. Your budget increases from $100 to $150 while the prices stay the same.

Increase

b. Your budget remains $100, the price of books remains $25, but the price of movie tickets rises to $20.

Decrease

c. Your budget remains $100, the price of movie tickets remains $10, but the price of a book falls to $15.

Increase

Answer:

  A)  The functions are not inverses of each other.

Step-by-step explanation:

[tex]f(g(x))=\sqrt{(x^2+3)-3}=\sqrt{x^2}=|x|\ne x[/tex]

The result of f(g(x)) is not always x, so the functions are not inverses of each other.

In general, a quadratic (or any even-degree polynomial) such as g(x) cannot have an inverse function because it does not pass the horizontal line test.

Check the picture below.

Answer: First, suppose that A is a knight. then when he says "i am a knave" he would be lying, so you have a logical failure because knights can't lie.

if A is a knave and says "I am a Knave, but B isn’t" then he would be telling a truth in the first part.

now you have two paths to tink itm as A said a truth, he can't be a knave. but if you consider the whole sentence can be splitted in two sentences.

I am a Knave ----- wealready know that will be a truth.

but B isn’t----- and now, as the first sentence is true, this must be false, so the sum of both sentences is false.

so A is a knave and B is a knave.

Final answer:

After analyzing the statements provided by A and the silence of B, the logical deduction reveals that both A and B are Knights, given the inherent contradictions in A's statement if he or B were Knaves.

Explanation:

The Island of Knights and Knaves presents a classic example of logical deduction. Given that A states he is a Knave but also says 'B isn’t a Knave', we can infer A's nature through contradiction. If A were a Knave, he would not tell the truth about himself or B, creating a paradox since a Knave can't tell the truth. If A is a Knight, his statement is also impossible since Knights cannot lie. Therefore, A must be a Knight, making the first part of his statement a lie (which is not possible for a Knight), but the second part true: B is not a Knave. Consequently, for the statement to uphold the rules of the island, B must be a Knight as well, which is consistent with the silent B offering no statements that could be lies.

Final answer:

The limit of f(x)/g(x) as x approaches 3 is negative infinity, since f(x) approaches 150 and g(x) approaches 0 with g(x) < 0.

Explanation:

We are given that as x approaches 3, f(x) approaches 150, and g(x) approaches 0 while being less than zero. The question is to determine the limit of f(x)/g(x) as x approaches 3.

To find this limit, we should consider the behavior of both f(x) and g(x) as x approaches 3.

Since f(x) approaches a finite number and g(x) approaches 0, the limit of the quotient could potentially be infinity or negative infinity, depending on the sign of g(x).

Since g(x) is less than 0 as x approaches 3, the quotient f(x)/g(x) will approach negative infinity.

Hence, the limit limx→3 f(x)/g(x) = -∞.

Answer:

The bus fair is 50% increases.

Step-by-step explanation:

The percentage is the proportion of the relation to the whole.

Percentage increase is calculate as ratio of difference of original and new value to the original value. i.e.

[tex]\frac{ Percentage\ increase\ \ =\ \ new\ value - original \ value}{original\ \ value}[/tex]

∴ [tex]\frac{ Percentage\ increase\ \ =\ \ 2.25 - 1.50 }{1.50}[/tex]

⇒ Percentage increase = 50%

By using percentage, the result obtained is-

Percentage increase in bus fare in Chicago  = 50%

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 2% means [tex]\frac{2}{100}[/tex]. Here 2 is expressed as a fraction of 100.

Here,

Bus fare in the year 1995  in Chicago= $1.50

Bus fare in the year 2008 in Chicago = $2.25

Increase in bus fare = $(2.25 - 1.50) = $0.75

Percentage increase in bus fare in Chicago = [tex]\frac{0.75}{1.50}\times 100[/tex]

                                                                         = 50%

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Answer: 3

Step-by-step explanation:

Given : Pooled variance : [tex]\sigma^2=18[/tex]

Sample sizes of each sample = [tex]n_1=n_2=4[/tex]

We know that the standard error for the sample mean difference is given by :-

[tex]S.E.=\sqrt{\sigma^2(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\\\=\sqrt{(18)(\dfrac{1}{4}+\dfrac{1}{4})}\\\\=\sqrt{(18)(\dfrac{1}{2})}=\sqrt{9}=3[/tex]

Hence, the estimated standard error for the sample mean difference =3

To find the percentage rate of growth, calculate the percentage change in enrollment from one year to the next using the graph. Perform these calculations for each pair of consecutive years to determine the overall percentage rate of growth.

To determine the percentage rate of growth, we need to analyze the graph showing the enrollment growth of the school. Exponential growth is represented by a curve that increases more and more steeply over time. To find the rate of growth, we can calculate the percentage change in enrollment from one year to the next.

For example, if the enrollment was 100 in Year 1 and 200 in Year 2, the percentage change would be (200-100)/100 * 100 = 100%. This means the enrollment doubled from Year 1 to Year 2.

By performing similar calculations for each pair of consecutive years, we can find the percentage rate of growth over the entire period represented by the graph.

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The percentage rate of growth for the school's enrollment is approximately 24% per year.

To determine the percentage rate of growth, we need to find the common ratio and the common difference in the exponential function that represents the school's enrollment. From the given graph, we can see that the enrollment doubles approximately every three years. This means that the common ratio is 2. The initial enrollment is 500, which is represented by the value "a" in the exponential function. The final enrollment, which is approximately 4000, is represented by "an". Using these values, we can write the exponential function as follows:

[tex]an = a * 2^(n-1)[/tex]

Substituting the initial enrollment and final enrollment in this equation, we get:

[tex]4000 = 500 * 2^(n-1)[/tex]

Dividing both sides by 500 and simplifying, we get:

[tex]8 = 2^(n-1)[/tex]

Taking the logarithm of both sides with base 2, we get:

(n-1) = log2(8)

(n-1) = 3

Adding 1 to both sides, we get:

n = 4

This means that it takes approximately four years for the school's enrollment to double. To find the percentage rate of growth per year, we need to find the common difference in the exponential function. The common difference is calculated as follows:

Common difference =[tex]ln(y2 / y1) / (x2 - x1)[/tex]

Here, x1 and x2 are two consecutive years, and y1 and y2 are their corresponding enrollments. Using this formula, we can calculate the common difference as follows:

Common difference = ln(4000 / 3200) / (7 - 4) = 0.263975 (approximately 24%) per year. This means that every year, the school's enrollment grows by approximately 24%.

answer is x is less than or equal to -13

hope this helps:-)

Answer:

x  ≤ -13.

Step-by-step explanation:

2(x + 1 ) - 3(x + 5) ≥ 0      Distribute the 2 and -3 over the parentheses:

2x + 2 - 3x - 15   ≥  0

-x  ≥  15 - 2

-x  ≥  13

x  ≤  -13      Note: when dividing by a negative the inequality sign is flipped .

Answer: 33%

Step-by-step explanation:

Given : The temperature dropped from 75 degrees to 50 degrees.

Decrease in temperature ( in degrees) = 75-50=25

The formula to find the percent decrease :-

[tex]\dfrac{\text{Decrease in temperature}}{\text{Initial temperature}}\times100\\\\=\dfrac{25}{75}\times100\\\\=33.3333333333\approx33\%\ \ \text{[Rounded to the nearest whole percent.]}[/tex]

Hence, the percent decrease in the temperature = 33%

Answer:

  your selection is correct

Step-by-step explanation:

You can divide by 9 to get ...

  | x+4 | ≥ 6

This resolves to two inequalities:

These are disjoint intervals, so the solution set is the union of them:

  x ≤ -10 or 2 ≤ x

Answer:

Step-by-step explanation: A is correct

Answer:

  segment EF over segment LM equals segment FG over segment MN

Step-by-step explanation:

The triangles are similar, not congruent, so any answer choice with the word "congruent" can be ignored.

The sequence of letters in the triangle name tells you the corresponding segments:

Corresponding segments have the same ratio, so ...

  EF/LM = FG/MN . . . . . . matches the first answer choice

  EF/LM = EG/LN . . . . does not match the 3rd answer choice

Answer:

segment EF over segment LM equals segment FG over segment MN

To determine the number of different eight-note melodies that alternate between black and white keys within a single octave, you calculate the permutations starting with either type of key and add them together, resulting in 141,120 possible melodies.

The question asks: How many different eight-note melodies within a single octave can be written if the black keys and white keys need to alternate? To solve this, we need to understand the structure of a piano octave, which consists of seven white keys and five black keys. Since melodies must alternate between black and white keys, starting with a white key will always result in a pattern of white-black-white-black, and so on, until eight notes are reached. Conversely, starting with a black key follows a black-white pattern.

If we start with a white key, we have 7 options for the first note. The next note (a black key) gives us 5 options. This alternating pattern continues, decreasing the number of options by 1 for each type of key used, until we have selected all eight notes. Mathematically, this calculates as 7 × 5 × 6 × 4 × 5 × 3 × 4 × 2. Similarly, starting with a black key would result in a calculation of 5 × 7 × 4 × 6 × 3 × 5 × 2 × 4.

However, since an eight-note melody can start with either a white or a black key, we calculate both scenarios and add them together for the total amount of possible melodies. The sum of the series for both starting options gives us 141,120 possible eight-note melodies that alternate between black and white keys within a single octave.

Answer:

x = 3+1/2 y -----Equation-1

-2x-y = 2 -------Equation-1

Multiplying equation 1 by 2  we get

2x = 2*(3+1/2y)

2x = 6+y

y = 2x-6

substituting the value of of y in equation2

-2x - (2x-6) = 2

-2x -2x +6 = 2

-4x = 2-6

-4x = -4

x = -4/-4 = 1

y = 2x-6 = 2-6 = -4

x = 1

y = -4

Step-by-step explanation:

Answer:

x=0.75 and Y=-4.5

Step-by-step explanation:

let x=3+1/2y.....(1)

-2x-y=3.......(2)

substitute (1) into (2)

-2(3+1/2y)-y=3

-6-y-y=3

-2y=9

y=-9/2

put y=-9/2 into (1)

x=3+(1/2)(-9/2)

x=-4.5

Answer:

Step-by-step explanation:

(a) You use the fact that the lengths RS and ST total the length RT.

  RS +ST = RT

  (6y+3) +(3y+5) = 80 . . . . . substitute the given values

  9y +8 = 80 . . . . . . . . . . . . .simplify

  9y = 72 . . . . . . . . . . . . . . . .subtract 8

  72/9 = y = 8 . . . . . . . . . . . .divide by the coefficient of y

___

(b) Now, the value of y can be substituted into the expressions for RS and ST to find their lengths.

  RS = 6y +3 = 6·8 +3

  RS = 51

  ST = 3y +5 = 3·8 +5

  ST = 29

___

Check

  RS +ST = 51 +29 = 80 = RT . . . . the numbers check OK

Answer:

x = 24

Step-by-step explanation:

Given that y varies directly with x the the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition y = 10 when x = 8, then

k = [tex]\frac{y}{x}[/tex] = [tex]\frac{10}{8}[/tex] = 1.25, thus

y = 1.25x ← equation of variation

When y = 30, then

30 = 1.25x ( divide both sides by 1.25 )

x = 24

Step-by-step explanation:

seriously i am not understanding your question

Answer: The shortest living man at that time had the height that was more​ extreme.

Step-by-step explanation:

We will z scores to solve this exercise. The formula we need is:

 [tex]z=\frac{x-\mu}{\sigma}[/tex]

Where [tex]x[/tex] is the raw score, [tex]\mu[/tex] is the mean and [tex]\sigma[/tex] is the standard deviation.

We know at that time heights of men had a mean of 170.53 centimeters and a standard deviation of 5.91 centimeters, then:

[tex]\u=170.53\\\\\sigma=5.91[/tex]

Knowing that the tallest living man at that time had a height of 230 centimeters, we get:

[tex]z=\frac{230-170.53}{5.91}\approx10.07[/tex]

And knowing that the shortest living man at that time had a height of 91.3 centimeters, we get:

[tex]z=\frac{91.3-170.53}{5.91}\approx-13.40[/tex]

Based on this, we can conclude that the shortest living man at that time had the height that was more​ extreme.

Answer:

Hello my friend! The answer is ZERO!

Step-by-step explanation:

If we substitue the values of "a" and "b" on the equation, will have:

3*(a*b)  + 5(b)  -6 =

3 * (-1 * 3)  +   5*(3)   - 6 =

-9 + 15 - 6 = 0

Final answer:

The terms in the expression 3 + 5 + 7b – 18a are the individual elements consisting of constants and variables with their coefficients: 3, 5, 7b, and -18a, with the correct response being option b.

Explanation:

The terms in the expression 3 + 5 + 7b – 18a are individual elements that are added or subtracted within the expression. These are individually known as terms. In an algebraic expression, coefficients and variables combined as a product (like 7b or -18a) are considered single terms. On the other hand, numbers without variables, such as 3 and 5, are also terms but are called constants because their values do not change. Consequently, each number or variable or product of a number and a variable that is separated by a plus or a minus sign is a separate term.

In this expression, we have four distinct terms which are 3, 5, 7b, and -18a. The correct answer is thus option b: The terms are 3, 5, 7b, and -18a.

Answer:

The answer to your question is: m∠LOM = 44°

Step-by-step explanation:

Data

m< LOM = 3x +38

m< MON= 9x+28

m< LOM = ?

Process

They are complementary angles

                    m∠LOM + m∠MON = 90°

                   3x + 38 + 9x + 28 = 90°

                   12x + 66 = 90°

                   12x = 90 - 66

                   12x = 24

                   x = 24/12

                   x = 2

m∠LOM = 3(2) + 38

             = 6 + 38

            = 44°

m∠ MON = 9(2) + 28

m∠MON = 18 + 28

m∠MON = 46°

Answer:

V = 9

Step-by-step explanation:

You can see it in the picture.

The side length of the square is found using the diagonal, which is the distance between the two parabolas. The area of each square cross section is then integrated from 0 to 3 to find the solid's volume, which is 9 cubic units.

For these types of volume problems, you'll need to integrate. However, first you have to find the area of the square formed by the diagonals. The distance between the parabolas y=-√x and y=√x forms the square's diagonal. This distance, or length of the diagonal, can be obtained by adding the y-values of the two parabolas which gives 2√x. Given the diagonal, the side length of the square (s) can be obtained from the diagonal using Pythagoras theorem: s=diagonal/√2 => s=2√x/√2 => s=√2* √x => s=√2x. The area of the square is the side length squared, A=s² => A= 2x. Now, integrate the area function from 0 to 3 to get the volume of the solid: Volume= ∫ from 0 to 3 [2x dx] = [x²] from 0 to 3 = 9 - 0 = 9 cubic units.

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Answer:

  $13

Step-by-step explanation:

Fill in the given values and solve for the unknown.

  110 = 10A -20

  130 = 10A . . . . . add 20

  13 = A . . . . . . . . divide by 10

You spent $13 on advertising.

Answer:

Step-by-step explanation:

g(x)= -2 x^2 + 3 x - 5

g(-2) = -2 . (-2)^2 + 3. (-2) - 5 = -2 . 4 - 6 - 5 = - 8 - 6 - 5 = - 19

g(0) = -2 . (0)^2 + 3 . 0 - 5 = -2 . 0 + 0 - 5 = 0 + 0 - 5 = - 5

g(3) = -2 . (3)^2 + 3 . (3) - 5 = -2 . 9 + 9 - 5 = -18 + 9 - 5 = - 14

The value of g(x) is the input values are  –2, 0, and 3 are -19, -5 and -14

Given the following function

g(x) =  –2x² + 3x – 5

For the input value of -2

g(-2) =  –2(-2)² + 3(-2) – 5

g(-2) = -8 - 6 - 5

g(-2) =-19

If the value of x is 0

g(0) =  –2(0)² + 3(0)– 5

g(0) = -5

If the vaue of x is 3

g(3) =  –2x² + 3x – 5

g(3) = -2(3)² + 3(3)– 5

g(3) =-18 + 9 - 5

g(3) = -14

Hence the value of g(x) is the input values are  –2, 0, and 3 are -19, -5 and -14

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Answer:

72 alligators, 128 turtles

Step-by-step explanation:

When you put the words into the form of an equation, with a being alligators, you get

3a-16=200

So you have to do 'letters left numbers right'. This gives you

3a=216

Now you have to divide. 216 divided by 3 equals 72. So there are 72 alligators. 200 minus 72 equals 128, so there are 128 turtles

Answer:

The number of alligators and number of turtles are 54 and 146 respectively.

Step-by-step explanation:

Given :

The number of turtles is 16 less than 3 times the number of alligators in the lake

There are 200 reptiles total.

To Find :  Find the numbers of alligators and turtles .

Solution:

Let the number of alligators be x

So, The number of turtles is 16 less than 3 times the number of alligators

Number of turtles = 3x-16

Now we are given that there are 200 reptiles in total .

[tex]x+3x-16=200[/tex]

[tex]4x-16=200[/tex]

[tex]4x=216[/tex]

[tex]x=54[/tex]

Number of alligators = 54

Number of turtles = 3(54)-16 = 146

Hence the number of alligators and number of turtles are 54 and 146 respectively .

Answer:

x = 2

Step-by-step explanation:

Since the parabola is opening vertically up then the equation of symmetry is vertical and of the form x = c

The axis of symmetry passes through the vertex (2, 0), thus

equation of axis of symmetry is x = 2

Answer:

SAS (side angle side)

Step-by-step explanation:

We have a pair of corresponding sides and the included angle. The angle is equal, but the sides are a fraction of the other triangle's side and has an equal rate.

2AC=DF

2AB=DE

The triangles are congruent

Answer:

SAS

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

You have to find a number that added with -6 equals -4, and multiplied equals -12.

Just have to do the opperations and that is all!

[tex](x-6)(x+2)=x^2+2x-6x-12=x^2-4x-12[/tex]

Hope you like it!

Answer:

Option C is the answer.

Step-by-step explanation:

Simon is factorizing the polynomial x² - 4x - 12 = (x - 6)( x + ......)

We will factorize the left hand side of the given expression

x² - 4x - 12

= x² - 6x + 2x - 12  

Now we will break 12 into the factors so that sum of the factors should equal to 4

{ 6 × 2 = 12 and 6 - 2 = 4]

= x(x - 6) + 2(x - 6)

= (x + 2)(x - 6)

Therefore, the blank space should be replaced by 2.

Option C is the answer.