Step-by-step explanation:
let's see.
first, let's deal with the asymptotes.
the vertical asymptote at x = -2.
it means that for x getting close to that value y is getting enormously larger and larger, so that for x = -2 we would get what we call y = infinity. we could even accept +infinity or -infinity. in both cases we get the same asymptote
I personally think using both +infinity and -infinity is easier to define. because coming from the left (negative direction) and from the right (positive direction) we can use the same expression and don't need to worry about the sign.
so, I go for something like
y = 1/(x + 2)
or even better considering we need a horizontal asymptote too :
y = x/(x + 2)
this will divide by 0 for x = -2 creating the asymptote.
now for the horizontal asymptote of y = 3.
it means that for x getting close to infinity (+infinity and/or -infinity) y has to get closer and closer to this finite value (3).
we achieve this by dividing a dimension of x by the same dimension of x.
so, for large values of x any additive parts of the terms become irrelevant for the limit.
as we had above
y = x/(x + 2)
the limit for x going to +infinity AND to -infinity would be
x/x = 1.
but we need the limit of 3.
so, all we need to do is to multiply the expression by 3 :
y = 3x/(x + 2)
now the limit for x going to +/- infinity is
3x/x = 3
and now for the y-intersect at (0, -4) :
we need to do something, so that y = -4 for x = 0.
let's look at what we have so far :
y = 3x/(x + 2)
-4 = 3×0/(0 + 2) = 0/2 = 0
clearly, that is wrong and therefore still not covered.
imagine, we keep the denominator of the fraction unchanged.
what do we need to do on the numerator side to create -4 as result ?
in other words, we need to find an n so that
-4 = (3x + n)/(x + 2)
for x = 0
-4 = n/2
n = -8
and we get as final result
y = (3x - 8)/(x + 2)
that includes the point (0, -4), and has the asymptotes at x = -2 and y = 3.
professor kelp decides to write a procedure that produces at random any permutation except the identity permutation, in which every element ends up where it started. he proposes the procedure permute-without-identity. does this procedure do what professor kelp intends?
The procedure permute-without-identity does what Professor Kelp intends.
As per the given question,
Professor Kelp wants to write a procedure that produces any permutation randomly except the identity permutation in which every element ends up where it started.
He has proposed the procedure permute-without-identity. We need to check whether this procedure does what Professor Kelp intends or not.
Procedure permute-without-identity:
Generate a permutation π ∈ Sn−1 uniformly at random. (Note that the identity permutation is not in Sn−1.)
Return the permutation obtained by shuffling the elements of π using a uniformly random shuffle.
Randomly shuffle the list using the Fisher-Yates shuffle, which creates a uniformly random permutation of the list.
Professor Kelp's procedure permute-without-identity chooses a permutation at random from the set of all permutations except the identity permutation.
So, there are n! - 1 possible choices of π.
Then, the elements of π are shuffled randomly using a uniformly random shuffle.
The identity permutation is excluded from π as it is not included in Sn-1.
Since the identity permutation is not included in Sn-1, it cannot be chosen by the procedure permute-without-identity.
Hence, the procedure does what Professor Kelp intends.
This procedure achieves the desired outcome by avoiding the case where all elements end up where they started.
For similar questions on identity:
https://brainly.in/question/22181989
#SPJ11
Two corners of the backyard are right angles. The third corner forms an obtuse angle measuring 127°. The fourth corner forms an acute angle measuring 53°. When transferring these angle measurements from the real world to the scale drawing, will their measures increase, decrease or stay the same?
Answer:
The angle measurement will stay the same.
Step-by-step explanation:
When you scale a figure the angle measurements stay the same.
Helping in the name of Jesus.
MAKE SURE TO SAY HOW TO GOT THE ANSWER SO I CAN HELP OTHERS AND SHOW MY MOM THIS!
1. By simplifying and comparing, the value of x is 4
2. By simplifying and comparing, the value of x is 6
3. By simplifying and comparing, the value of x is 0.53 and the value of y is 4
Simplifying an expressionFrom the question, we are to simplify the given expressions
1.
(4.2 × 10⁷) / (2 × 10³)
This can be expressed
(4.2 / 2) × (10⁷ / 10³)
Simplifying and applying the division law of indices
= 2.1 × 10⁷⁻³
= 2.1 × 10⁴
By comparison, the value of x is 4
2.
(7.2 × 10⁻⁸) ÷ (1.2 × 10⁻³)
This can be expressed as
(7.2 ÷ 1.2) × (10⁻⁸ ÷ 10⁻³)
Simplifying and applying the division law of indices
6 × 10⁻⁸ ⁻ ⁻³
6 × 10⁻⁸ ⁺ ³
6 × 10⁻⁵
By comparison, the value of x is 6
3.
(4.24 × 10⁶) ÷ (8 × 10²)
This can be expressed as
(4.24 ÷ 8) × (10⁶ ÷ 10²)
Simplifying and applying the division law of indices
= 0.53 × 10⁶ ⁻ ²
= 0.53 × 10⁴
By comparison, the value of x is 0.53 and the value of y is 4
Learn more on Simplifying an expression here: https://brainly.com/question/28036586
#SPJ1
How could you correctly rewrite the equation 4(5+3)=2(22-6) using distribution property
Answer: 4(5+3) = 4(5) + 4(3) = 20 + 12 = 32
Step-by-step explanation:
Answer:
32=32 ?
Step-by-step explanation:
the surface area of a rectangular prism is 1300 square inches. find the surface area of a similar solid that is larger by a scale factor of 3.
The surface area after larger by scale factor is 11700 [tex]in^2[/tex].
What is surface area?The surface area οf an οbject refers tο the οverall space filled by its surfaces. Many 3D shapes in geοmetry have variοus surface areas, which may be quickly estimated using the fοrmulas we shall learn in this lessοn. Twο categοries are used tο classify the surface area:
Curved surface area οr Lateral surface areaSurface area in tοtalHere the given rectangular prism ,
Surface area = 1300 square inches
Here the given prism is larger by scale factor of 3 then,
=> surface area = 1300[tex]\times3^2[/tex] = 1300[tex]\times9[/tex] = 11700 [tex]in^2[/tex].
Hence the surface area after larger by scale factor is 11700 [tex]in^2[/tex].
To learn more about surface area refer the below link
https://brainly.com/question/16519513
#SPJ1
The possible range for the length of AC is greater than what but less than what .
Answer:10
Step-by-step explanation: one side of a triangle must be greater than the differnce and less than the sum of the lengths of the other two sides
Answer: 5.83095
explanation:
miss america winners from the 1920's and 1930's had a average bmi of 19.2. a sample of recent winners had reported bmis of 18.3, 19.6, 19.9, 18.8, 18.2, 18.1, 18.1, 18.3, 18.3, 18, and 19.8 . do recent winners appear to be significantly different from those in the 1920s and 1930s? (assume normality)
A one-sample t-test is conducted to determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s. The test results fail to reject the null hypothesis, indicating that recent winners do not appear to be significantly different from those in the 1920s and 1930s.
To determine if recent Miss America winners have a significantly different BMI compared to winners from the 1920s and 1930s, a one-sample t-test can be conducted. Using the given sample, the sample mean BMI is calculated to be 18.5.
The null hypothesis is that the population mean BMI of recent winners is equal to 19.2. The alternative hypothesis is that the population mean BMI of recent winners is different from 19.2.
Assuming a significance level of 0.05 and using a two-tailed test, the calculated t-value is -2.08 and the corresponding p-value is 0.057.
Since the p-value is greater than the significance level, we fail to reject the null hypothesis. This suggests that there is not enough evidence to conclude that recent Miss America winners have significantly different BMI compared to winners from the 1920s and 1930s.
Learn more about one-sample t-test here: brainly.com/question/29548761
#SPJ1
Haroldo, Xerxes, Regina, Shaindel, Murray, and Georgia are invited to a dinner party. They arrive in a random order and all arrive at different times. What is the probability that Xeres arrives first AND Regina arrives last?
The probability that Xeres arrives first AND Regina arrives last is 3.33%.
What is probability?Prοbability is a way οf calculating hοw likely sοmething is tο happen. It is difficult tο prοvide a cοmplete predictiοn fοr many events. Using it, we can οnly fοrecast the prοbability, οr likelihοοd, οf an event οccurring. The prοbability might be between 0 and 1, where 0 denοtes an impοssibility and 1 denοtes a certainty.
Here The number of possible arrangements of n elements is given by:
[tex]A_n=n![/tex]
In this problem:
6 people are invited, so the number of ways they can arrive is T = [tex]6![/tex]
Xeres first and Regina last, for the middle 4 there are way D= 4! ways
Then the probability is P = [tex]\frac{D}{T}=\frac{4!}{6!}[/tex] = 0.0333 = 3.33%
To learn more about probability refer the below link
https://brainly.com/question/13604758
#SPJ1
]
D
5²
25
2) A two-dimensional preimage is dilated by a scale factor to result in a new image. Fill in the
blanks with the number needed to calculate the area of the new image compared to the area
of the preimage.
25
1
If the scale factor is , then the area of the preimage is multiplied by or to calcu-
late the area of the new image.
()'
Answer:
Let’s start by defining the variables:
Let A be the area of the preimage.
Let k be the scale factor.
If the scale factor is k, then the area of the preimage is multiplied by k² to calculate the area of the new image. Therefore, we have:
Area of new image = k²A
We are given that:
k = 1/5
Therefore, we have:
k² = (1/5)² = 1/25
The area of the preimage is not given. Therefore, we cannot calculate the area of the new image
find the length of SU is S is -15 and U is 10
The requried length of the line segment on number line SU is 25 units.
To find the length of the line segment SU, we need to subtract the coordinates of S from the coordinates of U and take the absolute value. So we have:
|SU| = |U - S| = |10 - (-15)| = |25| = 25
Therefore, the length of the line segment on number line SU is 25 units.
Learn more about number line here:
https://brainly.com/question/16191404
#SPJ1
Please show working out.
A line has the equation y = 3x + k. What is the gradient of the line?
3
when the line is at the y=ax+b form the gradient is equal to a
Josiah is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 12 in and the height of the pyramid is 14in. To get the wax for the candle, Josiah melts cubes of wax that are each 6 in by 6 in by 6 in. How many of the wax cubes will Josiah need in order to make the candle? Show your work.
Answer:
13
Step-by-step explanation:
The volume of the pyramid can be calculated using the formula:
Volume = (1/3) * base area * height
The base area of the pyramid is equal to the area of one of the square sides, which is:
Base area = 12 in * 12 in = 144 in^2
Therefore, the volume of the pyramid is:
Volume = (1/3) * 144 in^2 * 14 in = 2,688 in^3
Each wax cube has a volume of:
Volume of a wax cube = 6 in * 6 in * 6 in = 216 in^3
To find out how many wax cubes Josiah needs, we can divide the volume of the pyramid by the volume of each wax cube:
Number of wax cubes = Volume of pyramid / Volume of each wax cube
Number of wax cubes = 2,688 in^3 / 216 in^3 = 12.4444...
Since we can't use a fraction of a wax cube, Josiah will need to use 13 wax cubes to make the candle.
Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.25 hours and charged him $116 for parts. The total was $719.75. Which equation could be used to determine cc, the cost of labor per hour?
One way to approach this problem is to use the formula:
total cost = cost of parts + cost of labor
We can plug in the given values:
719.75 = 116 + cost of labor x 5.25
Simplifying:
603.75 = cost of labor x 5.25
To solve for the cost of labor per hour (cc), we can divide both sides by 5.25:
cc = 603.75 / 5.25
Simplifying:
cc ≈ 114.76
Therefore, the equation that could be used to determine the cost of labor per hour is:
cc = (total cost - cost of parts) / hours of labor
or:
cc = (719.75 - 116) / 5.25
4. Use the spinner to decide where soch event would be located on the scale
below. Write the letter for each event in the appropriate place on the
probability scale.
The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or
4
1
2
0
Impossible
4
2
3
2
a. The spinner landing on 1
b. The spinner landing on an even number
c. The spinner landing on the number 8
3
d. The spinner landing on a number
e. The spinner landing on the left side of the circle
Unlikely
Probability Scale
125
1
2
Equally Likely to
Occur or Not Occur
1
Likety
1
Certain
The spinner has 8 equal-sized sections, each labeled 1, 2, 3, or 4 and correct options are:
a. The spinner landing on 1 - 1 (Likely)
b. The spinner landing on an even number - 2 and 4 (Equally likely to occur or not occur)
c. The spinner landing on the number 8 - Impossible (0)
d. The spinner landing on a number - 1, 2, 3, and 4 (Equally likely to occur or not occur)
e. The spinner landing on the left side of the circle - Unlikely (2)
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain to occur.
Here,
a. The spinner landing on 1 - There is only one section labeled 1 on the spinner, out of a total of 8 sections. Therefore, the probability of the spinner landing on 1 is 1/8. On the probability scale provided, this probability would be located closer to "Likely" than to "Equally Likely to Occur or Not Occur", but not as close to "Certain".
b. The spinner landing on an even number - There are 4 sections labeled with even numbers (2 and 4), out of a total of 8 sections. Therefore, the probability of the spinner landing on an even number is 4/8 or 1/2. On the probability scale provided, this probability would be located exactly halfway between "Equally Likely to Occur or Not Occur" and "Certain".
c. The spinner landing on the number 8 - There is no section labeled 8 on the spinner, so this event is impossible. On the probability scale provided, this probability would be located at the very bottom of the scale, labeled "Impossible".
d. The spinner landing on a number - Every section of the spinner is labeled with a number, so this event is certain to occur. On the probability scale provided, this probability would be located at the very top of the scale, labeled "Certain".
e. The spinner landing on the left side of the circle - There are 2 sections labeled with numbers that are on the left side of the circle (1 and 2), out of a total of 8 sections. Therefore, the probability of the spinner landing on the left side of the circle is 2/8 or 1/4. On the probability scale provided, this probability would be located closer to "Unlikely" than to "Equally Likely to Occur or Not Occur", but not as close to "Impossible".
To know more about probability,
https://brainly.com/question/30034780
#SPJ1
After a blizzard the amount of snow on the ground melted by 3 inches one day and then another 8 inches the next day. write an expression that represents the total change in the amount of snow on the ground over the two days.
The expression that represents the total change in the amount of snow on the ground over the two days is -3 + (-8) = -11
The problem asks for the total change in the amount of snow on the ground over two days after a blizzard. The problem states that the snow melted by 3 inches one day and 8 inches the next day. The expression that represents the total change can be found by adding the two changes together. However, since the snow is melting, we need to use negative values to represent the change. Therefore, we can write the expression as:
-3 + (-8)
Simplifying this expression, we get:
-3 - 8 = -11
Therefore, the total change in the amount of snow on the ground over the two days is -11 inches.
To learn more about expression follow the link: https://brainly.com/question/14083225
#SPJ1
The bishop family brought a case of water containing 24 bottles. During one week,Lydia drank 1/8 of the bottles,Mitchell drank 33 1/3% of the bottles,Alexa drank 0.25 of the bottles, and Todd drank the rest.What % did todd drink.
Todd drank 29.17% of the bottles. First, we need to calculate the total number of bottles drank by Lydia, Mitchell, and Alexa.
Lydia = (1/8) x 24 = 3 bottles
Mitchell = (33 1/3%) x 24 = (1/3) x 24 = 8 bottles
Alexa = 0.25 x 24 = 6 bottles
The total number of bottles drank by Lydia, Mitchell, and Alexa is 3 + 8 + 6 = 17 bottles.
Therefore, the number of bottles Todd drank is 24 - 17 = 7 bottles.
To find the percentage of bottles Todd drank, we can use the following formula:
Percentage = (Part/Whole) x 100%
Where the Part is 7 and the Whole is 24.
Percentage = (7/24) x 100% = 29.17%
Therefore, Todd drank 29.17% of the bottles.
To know more about percentage of bottles click here:
brainly.com/question/15731128
#SPJ1
What is the axis of symmetry of the graph of the function f(x) = 2x^2 + 8x − 5?
Answer:
The axis of symmetry is at x = -2.
Step-by-step explanation:
To find the axis of symmetry of a quadratic function in the form of f(x) = ax^2 + bx + c, you can use the formula x = -b / (2a).
In the function f(x) = 2x^2 + 8x − 5, a = 2 and b = 8, so we can plug those values into the formula and get:
x = -b / (2a) = -8 / (2 * 2) = -2
Therefore, the axis of symmetry of the function f(x) = 2x^2 + 8x − 5 is located at x = -2.
This means that the graph of the function is symmetric with respect to the vertical line x = -2. Any point on the graph that is a distance of t from the line x = -2 will have a corresponding point on the graph that is also a distance of t from the line.
suppose that you and a friend are playing cards and you decide to make a friendly wager. the bet is that you will draw two cards without replacement from a standard deck. if both cards are hearts, your friend will pay you $16 . otherwise, you have to pay your friend $3 . step 2 of 2 : if this same bet is made 762 times, how much would you expect to win or lose? round your answer to two decimal places. losses must be expressed as negative values.
It means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.
To calculate the expected value of this bet, we first need to determine the probability of drawing two hearts and the probability of not drawing two hearts.
There are 52 cards in a standard deck, with 13 cards of each suit (hearts, diamonds, clubs, and spades). To calculate the probability of drawing two hearts without replacement, we consider the following:
1st card: The probability of drawing a heart is 13/52, as there are 13 hearts in the deck and 52 cards total.
2nd card: After drawing one heart, there are 12 hearts left and 51 cards total. The probability of drawing another heart is 12/51.
Thus, the probability of drawing two hearts is (13/52) * (12/51).
Next, we need to find the probability of not drawing two hearts. This can be calculated by subtracting the probability of drawing two hearts from 1.
Probability of not drawing two hearts = 1 - [(13/52) * (12/51)]
Now, we can calculate the expected value of the bet:
Expected value = (probability of winning * winnings) + (probability of losing * losses)
In this case, the winnings are $16, and the losses are $3.
Expected value = [(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)
Now, let's calculate the expected value for 762 bets.
Expected value for 762 bets = 762 * {[(13/52) * (12/51) * $16] + {1 - [(13/52) * (12/51)]} * (-$3)}
Round the final expected value to two decimal places. If it's a positive value, it means you would expect to win that amount, and if it's negative, it means you would expect to lose that amount.
Know more about Probability here:
https://brainly.com/question/24756209
#SPJ11
A Dress, is discounted at 75% off. The original price is $185.
What is the sales price?
O $46.25
O $42.50
O $36.25
$32.75
The discount is 75% off the original price of $185.
To find the amount of the discount, we can multiply the original price by 0.75:
$185 x 0.75 = $138.75
Therefore, the dress has been discounted by $138.75.
To find the sales price, we can subtract the discount from the original price:
$185 - $138.75 = $46.25
Therefore, the sale price of the dress is $46.25.
a swimming pool can hold 2,376 m3 of water. its length is 33 meters and its width is 9 meters. calculate the height of the pool. what is the answer
Answer: 8 meters
Step-by-step explanation:
33x9=297
2376 divided by 297= 8
The height of the swimming pool is approximately 2.6 meters. This can be answered by the concept of Surface Area.
To calculate the height of the swimming pool, we can use the formula for the volume of a rectangular prism, which is V = lwh, where V is the volume, l is the length, w is the width, and h is the height. We know that the volume of the pool is 2,376 m3, the length is 33 meters, and the width is 9 meters.
Plugging these values into the formula, we get 2,376 = 33 x 9 x h. Solving for h, we get h = 2.6 meters.
Therefore, the height of the swimming pool is approximately 2.6 meters, which can be calculated by using the formula for the volume of a rectangular prism and plugging in the known values of length, width, and volume.
To learn more about Surface Area here:
brainly.com/question/29298005#
#SPJ11
A bag contains 3 red marbles, 2 blue marbles and 4 green marbles. If two marbles are drawn out of the bag, what is the probability, to the nearest 10th of a percent, that both marbles drawn will be red?
Answer:
1/9 ≅ 0.11
Step-by-step explanation:
Which transformation maps quadrilateral ABCD onto quadrilateral HGFE?
The correct answer to the given question about mapping quadrilateral ABCD onto quadrilateral HGEF is option D Translation 6 units left and 2 units down
To determine the transformation that maps quadrilateral ABCD onto quadrilateral HGFE, we need to compare the corresponding sides and angles of the two quadrilaterals.
Option 1: Rotation of 180° about the origin
A rotation of 180° about the origin would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side AB of ABCD would not match side HG of HGFE after the rotation. Therefore, option 1 is incorrect.
Option 2: Reflection across the y-axis
A reflection across the y-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, angle A of ABCD would not match angle H of HGFE after the reflection. Therefore, option 2 is incorrect.
Option 3: Reflection across the x-axis
A reflection across the x-axis would not map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are not congruent. For example, side BC of ABCD would not match side GF of HGFE after the reflection. Therefore, option 3 is incorrect.
Option 4: Translation 6 units left and 2 units down
A translation 6 units left and 2 units down would map quadrilateral ABCD onto quadrilateral HGFE because the corresponding sides and angles are congruent. Each point of ABCD would move left by 6 units and down by 2 units to reach its corresponding point in HGFE. Therefore, option 4 is the correct transformation that maps quadrilateral ABCD onto quadrilateral HGFE.
To learn more about quadrilateral click here
brainly.com/question/29934440
#SPJ1
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 12 N acts on a certain object, the acceleration
of the object is 4 m/s². If the acceleration of the object becomes 10 m/s², what is the force?
ON
Answer: [tex]F=30N[/tex]
Step-by-step explanation:
1. You know that the force acting on the object varies directly with the object's acceleration. Then, by definition, you have:
[tex]F=ka[/tex]
Where [tex]F[/tex] is the force acting on the object, [tex]a[/tex] is the object's acceleration and [tex]k[/tex] is the constant of proportionality.
2. Keeping this on mind, you can calculate the constant of proportionality by substituting [tex]F=12[/tex] and [tex]a=4[/tex] into the equation and solving for [tex]k[/tex]:
[tex]12=k4[/tex]
[tex]k=\dfrac{12}{4}[/tex]
[tex]k=3[/tex]
3. Now, you can calculate the force when the acceleration of the object becomes 10 m/s², as following:
[tex]F=3(10)[/tex]
[tex]F=30[/tex]
3. The result is:
[tex]F=30N[/tex]
solve for y
A)115º
B)108º
C)90º
D)130º
Answer:
[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to find the measure of} \ \tt \angle Y.[/tex]
[tex]\textsf{We are given a shape, but we aren't given what shape it is.}[/tex]
[tex]\large\underline{\textsf{What is a Shape?}}[/tex]
[tex]\textsf{A Shape is a specific outline sometimes dependent of how many sides it has.}[/tex]
[tex]\underline{\textsf{Shapes that depend on outlines;}}[/tex]
[tex]\textsf{Non-Polygons,}[/tex][tex]\textsf{Shapes that aren't quadrilaterals,}[/tex][tex]\textsf{Any shapes that are not classified under something.}[/tex][tex]\underline{\textsf{Shapes that depend on the number of sides;}}[/tex]
[tex]\textsf{Mainly the opposite.}[/tex]
[tex]\textsf{Polygons,}[/tex][tex]\textsf{Quadrilaterals,}[/tex][tex]\textsf{Any shapes that are classified under something.}[/tex][tex]\textsf{Because our shape has 5 sides, it's dependent on the amount of sides it has, which}[/tex]
[tex]\textsf{makes the shape a Polygon.}[/tex]
[tex]\large\underline{\textsf{What is a Polygon?}}[/tex]
[tex]\textsf{A Polygon is a closed shape that classifies as a;}[/tex]
[tex]\textsf{Triangle, or any shape with 3 sides,}[/tex][tex]\textsf{Square/Rectangle, or any shape with 4 sides,}[/tex][tex]\textsf{Pentagon, or any shape with 5 sides,}[/tex][tex]\textsf{Hexagon, or any shape with 6 sides,}[/tex][tex]\textsf{Heptagon, or any shape with 7 sides,}[/tex][tex]\textsf{Octagon, or any shape with 8 sides,}[/tex][tex]\textsf{Nonagon, or any shape with 9 sides,}[/tex][tex]\textsf{Decagon, or any shape with 10 sides.}[/tex][tex]\textsf{The list goes on forever.}[/tex]
[tex]\textsf{Our shape is a Pentagon, due to the shape having 5 sides.}[/tex]
[tex]\large\underline{\textsf{What is a Pentagon made up of?}}[/tex]
[tex]\textsf{A Pentagon is a polygon that has 5 sides, meaning that it has 5 angles.}[/tex]
[tex]\textsf{The total of the angles is what we should find out with a pattern.}[/tex]
[tex]\underline{\textsf{What is the total of all the angles' measures of a Pentagon?}}[/tex]
[tex]\textsf{A Triangle has 3 sides with 3 angles, which add up to 180}^{\circ}.[/tex]
[tex]\textsf{A Quadrilateral has 4 sides with 4 angles, which add up to 360}^{\circ}.[/tex]
[tex]\textsf{The Pattern is that when an extra side is added, the total measure of the angles}[/tex]
[tex]\textsf{increase by 180}^{\circ}.[/tex]
[tex]\textsf{A Pentagon has 5 sides with 5 angles, which add up to} \ \boxed{\tt 540^{\circ}.}[/tex]
[tex]\textsf{Now that we know the total, we can form an equation.}[/tex]
[tex]\tt 540^{\circ} = 135^{\circ} + 112^{\circ} + 88^{\circ} + y^{\circ} + 90^{\circ}[/tex]
[tex]\textsf{Remember that Right Angles are 90}^{\circ} \ \textsf{angles that are represented with a box}[/tex]
[tex]\textsf{symbol.}[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Now that we have our equation, we should \underline{combine like terms}, then use the}[/tex]
[tex]\textsf{\underline{subtraction rule of equality} to find the measure of y.}[/tex]
[tex]\underline{\textsf{Combine Like Terms;}}[/tex]
[tex]\tt 540^{\circ} = \boxed{135^{\circ}} + \boxed{112^{\circ}} + \boxed{88^{\circ}} + y^{\circ} + \boxed{90^{\circ}}[/tex]
[tex]\tt 540^{\circ} = 425^{\circ} + y^{\circ}[/tex]
[tex]\underline{\textsf{Use the Subtraction Rule of Equality;}}[/tex]
[tex]\tt 540^{\circ} - 425^{\circ} = 425^{\circ} - 425^{\circ}+ y^{\circ}[/tex]
[tex]\large\boxed{\tt y = 115^{\circ}.}[/tex]
A number gives a remainder of 5 when divided by 10. Another number gives a remainder of 4 when divided by 10. The sum of these two numbers is multiplied by 3 to give the third number. What is the remainder when this third number is divided by 10?
Answer:
The remainder is 7.
Step-by-step explanation:
Let's pick 15 and 14. The sum of these two numbers is 29. Multiplying 29 by 3, we have 87. 87 divided by 10 is 8 with a remainder of 7.
Help me solve e this question?
The correct statement regarding the transformations is given as follows:
g(x) is stretched vertically by a factor of 5 and translated 3 units to the right.
What is a translation?A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.
The four translation rules for functions are defined as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.The transformations to the parent function in this problem are given as follows:
Multiplication by 5 -> vertical stretch by a factor of 5.x -> x - 3: translation right 3 units.More can be learned about translations at brainly.com/question/28174785
#SPJ1
Your station charges $6.50 for a lubrication job. As a promotion you sell six coupons for lubrication jobs for $32.50 What percentage discount are you offering for customers who purchase the 6-coupon lube booke (to the nearest tenth)
Answer:
16.7%
Step-by-step explanation:
The regular price for a lubrication job is $6.50. With the promotion, customers can purchase 6 coupons for $32.50.
To find the percentage discount offered, we need to compare the regular price with the discounted price.
The regular price for 6 lubrication jobs would be:
$6.50 x 6 = $39
With the coupon book, the customer pays $32.50 for 6 lubrication jobs.
The amount of discount is:
$39 - $32.50 = $6.50
Therefore, the percentage discount offered is:
($6.50 / $39) x 100% = 16.7%
So the station is offering a discount of 16.7% to customers who purchase the 6-coupon lube book.
Scott filled his gas tank up with 19 5/9 gallons of gas. If he uses 1 5/6 gallons of gas each day, after how many days will he need to refill his tank?
Answer:
Using division the answer to the equation is 10 2/3 but the correct answer to the question would most likely be he needs to refill his tank after 10 days.
Step-by-step explanation:
19 5/9 ÷ 1 5/6 = 10 2/3
Ignore the graph it’s for a different question
Answer:
35. Radius= 12 cm
36. (B) 50 cm
Step-by-step explanation:
35.
TSA = 2πr(h+r)
Expanding the brackets, we get:
TSA = 2πrh + 2πr^2
Rearranging the equation, we get:
TSA - 2πrh = 2πr^2
Dividing both sides by 2π, we get:
r^2 = (TSA - 2πrh) / 2π
Taking the square root of both sides, we get:
r = √[(TSA - 2πrh) / 2π]
We need to simplify the given equation to solve for r.
r = √[(905.143) - 2(22/7)r(14)) / 2(22/7)]
r = √[(905.143) - (88/7)r] / (44/7)
Squaring both sides, we get:
r^2 = [(905.143) - (88/7)r] / (44/7)
Multiplying both sides by (44/7) and simplifying:
7r^2 - 88r - 905.143 = 0
Using the quadratic formula:
r = [88 ± √(88^2 - 4(7)(-905.143))] / (2(7))
r ≈ 12.009 or r ≈ -12.892
Since r represents the radius of a circle, which cannot be negative, we ignore the negative solution.
Therefore, the solution is r ≈ 12.009.
36.
We can use the formula for the volume of a cylinder:
volume = πr^2h
where r is the radius and h is the height of the cylinder.
First, we need to find the radius of the drum. The diameter is given as 56 cm, so the radius is half of that, or 28 cm.
Next, we can use the given volume of 123.2 liters. However, we need to convert liters to cubic centimeters (cm^3) since the dimensions are in centimeters.
1 liter = 1000 cm^3
So, 123.2 liters = 123,200 cm^3.
Now we can plug in the values:
123,200 cm^3 = π(28 cm)^2h
Simplifying:
123,200 cm^3 = 2464π cm^2h
Dividing both sides by 2464π cm^2:
50 cm = h
Therefore, the height of the drum is 50 cm.
deena has pairs of white socks, pairs of black socks, pair of red socks, and pairs of navy socks in her sock drawer. each pair of socks is folded together. if she pulls a pair of socks out of her drawer in the morning without looking, what is the probability that she will choose a pair of navy socks?
The final answer is 1 / 11
Deena has a total of 11 pairs of socks in her sock drawer. One pair of those 11 pairs is navy socks. Therefore, the probability that she will choose a pair of navy socks is 1/11.What is probability? Probability is the numerical measure of the possibility of an event taking place. Probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes.The probability of Deena picking navy socks is calculated as:Probability of selecting navy socks = Number of pairs of navy socks/ Total number of pairs of socks in the drawerNumber of pairs of navy socks = 1Total number of pairs of socks in the drawer = 1 /11Probability of selecting navy socks = 1/11Therefore, the probability that Deena will select a pair of navy socks is 1/11.
Therefore, the answer is 1 / 11.
To know more about probability visit : https://brainly.com/question/30034780
#SPJ11