got this rates of change equation. please list the 3 variables involved in the question
Answers
The area of the circle is decreasing at a rate of 0.2 cm³/s. We simply multiply dA/dr by dr/dt, giving us dA/dt.
What is radius?A line segment connecting the center of the circle to a point on the circle, and is equal in length to all other line segments connecting the center to points on the circle.
The three variables involved in the question are the area of a circle (A), the radius of a circle (r), and the rate of change of the radius (dr/dt). Using the chain rule, we can link all of these rates together with the equation dr/dt = dA/dr x dA/dt.
We know that the area of a circle is equal to r², so we can rewrite the equation as
dr/dt = 2r x dA/dt.
We are given the value of dr/dt, which = 0.4 cm/s, and so we can use this to calculate the value of dA/dr.
To do this, we first divide both sides of the equation by 2r, giving us dA/dr = dr/dt/2r.
Plugging in the values for dr/dt and r (which is 8 cm) gives us a value of dA/dr = 0.05 cm²/cm.
We can use this to calculate the rate at which the area of a circle is decreasing when its radius= 8 cm and decreasing at 0.4 cm/s.
To do this, we simply multiply dA/dr by dr/dt, giving us dA/dt = 0.2 cm³/s. This means that the area of the circle is decreasing at a rate of 0.2 cm³/s.
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Related Questions
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?
Answers
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.
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sketch the graph of each function in the interval from 0 to 2π y=cos θ
Answers
Answer:
The cosine curve is a type of periodic curve that is commonly used in mathematics and physics. It is defined by the equation y=cos(x). The cosine curve is a smooth wave-like curve that has the same shape as the sine wave, but shifted by a quarter of a period. The cosine curve is used to describe cyclical phenomena, such as sound waves and light waves. In addition, it is used in trigonometry and calculus to solve complex problems.
when estimating a task, what values are you likely to use? choose all that apply.group of answer choices2 days2 hours2 minutes2 sprints2 weeks
Answers
However, depending on the project, other units of time, such as minutes or sprints, may also be used.
When estimating a task, the values that are likely to be used include 2 hours, 2 days, and 2 weeks. These values are commonly used in project management for estimating the time required to complete a task.
An estimation is an approximate calculation of the time, effort, or resources required to complete a particular task or project.
It is a critical aspect of project planning, and a good estimate can help ensure that the project is completed on time and within budget. The most common time values used when estimating a task are hours, days, and weeks.
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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?
Answers
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%
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For what value(s) of x are the following Undefined
5x^2+x+1/x^2+4
Answers
Answer:
Undefined at x = 2 and x = -2
Step-by-step explanation:
(5x²+x+11)/(x²-4)
Function becomes undefined when the denominator goes to zero.
x² - 4 = 0
x = 2, -2
Answer:
In Real numbers: none (defined for all real numbers)
In Complex numbers: not defined for [tex]x = 2i, -2i[/tex]
Step-by-step explanation:
Fraction becomes undefined when the denominator = 0
[tex]x^2 + 4 = 0[/tex]
Has no real solutions
The fraction is defined for all real values of x
[tex]x^2 + 4 = 0[/tex]
[tex]x^2 = -4[/tex]
[tex]x = 2i, -2i[/tex]
The fraction is not defined for [tex]x = \dfrac{+}{-2i}[/tex] (in Complex Numbers)
events that occur in the extremes of the normal curve have a very small probability of occurring. group of answer choices true false
Answers
The statement, "Events which occur in extremes of normal-curve have a very small-probability of occurrence" is True because the normal distribution is a bell-shaped curve that is symmetrical around mean.
The Events which occur in extremes of normal curve have a very small probability of occurring because normal-distribution is a bell-shaped curve that is symmetrical around mean, with most values falling close to mean and fewer values occurring further away from mean.
So, as one moves further from the mean, the probability of occurrence decreases exponentially.
So, events that occur in the tails (extremes) of the normal curve have a very small probability of occurring.
Therefore, the statement is True.
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simplify the square root 0.2 squr 25y^2 if y<0
b) squr 1/16x^2 if x greater then or equal to 0
Answers
The simplified expression for expression √0.2 × √25y² will be √5|y| and for 1/16x² if x is greater than or equal to 0 simplified expressions will be (1/4)x.
a) Simplifying the expression √0.2 × √25y² using the properties of square roots, we get:
= √0.2 × √25y²
= √(0.2 × 25 × y²)
= √(5y²)
= √5 × √y²
= √5 × |y|
Since y<0, we need to take the absolute value of y to ensure that the result is positive. Therefore, the simplified expression is √5|y|.
b) Simplifying the expression √(1/16 x²), we get:
= √(1/16 x²)
= (1/4) √(x²)
= (1/4) |x|
Since x≥0, we do not need to take the absolute value of x. Therefore, the simplified expression is (1/4)x.
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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?
Answers
Answer:
1/9 ≅ 0.11
Step-by-step explanation:
Explanation:
To find the probability that both marbles drawn will be red, we need to find the probability of drawing a red marble on the first draw and then drawing another red marble on the second draw.
Total number of marbles in the bag = 3 red + 2 blue + 4 green = 9 marbles
Probability of drawing a red marble on the first draw:
P(Red₁) = (Number of red marbles) / (Total number of marbles) = 3/9 = 1/3
After drawing one red marble, there are now 2 red marbles left in the bag and 8 marbles total.
Probability of drawing a red marble on the second draw:
P(Red₂) = (Number of red marbles left) / (Total number of marbles left) = 2/8 = 1/4
Now, we need to find the probability of both events happening. We do this by multiplying the individual probabilities:
P(Red₁ and Red₂) = P(Red₁) × P(Red₂) = (1/3) × (1/4) = 1/12
Now let's convert this fraction to a percentage, rounded to the nearest 10th of a percent:
(1/12) × 100 ≈ 8.3%
So, the probability of drawing two red marbles consecutively is approximately 8.3%.
of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. how many of the students earned a c for the course?
Answers
Of the 180 students in a college course, of the 4 1 students earned an a for the course, of the students 3 earned a b for the course, and the rest of the students earned a c for the course. So, 136 students earned a C for the course.
To find the number of students who earned a C in the course, we'll follow these steps:
1. Determine the total number of students in the course.
2. Find out how many students earned an A and how many earned a B.
3. Subtract the number of A and B students from the total to find the number of C students.
We are given that there are 180 students in the course. It is also mentioned that 41 students earned an A and 3 students earned a B.
Now let's perform the calculations:
Step 1: We know that the total number of students is 180.
Step 2: We need to find the combined number of A and B students. We are given that 41 students earned an A, and 3 students earned a B. So, to find the total number of A and B students, we simply add these two numbers:
41 (A students) + 3 (B students) = 44 (A and B students)
Step 3: To find the number of C students, we subtract the total number of A and B students (44) from the total number of students (180):
180 (total students) - 44 (A and B students) = 136 (C students)
So, 136 students earned a C for the course.
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The possible range for the length of AC is greater than what but less than what .
Answers
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:
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
Answers
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".
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A sports store sells 92 pairs of swimming flippers per day for $50 each. The owner estimates that for each $3 increase in price, 3 fewer sales are made. What price should be charged to maximize profit?
Answers
Let's start by calculating the store's revenue at the current price of $50 per pair of swimming flippers:
Revenue = Price x Quantity Sold = $50 x 92 = $4,600 per day
Now, let's see how changes in the price affect the quantity sold. According to the problem, for each $3 increase in price, 3 fewer sales are made. This means that the demand function is:
Quantity Sold = 92 - 3/3 (Price - $50) = 92 - (Price - $50)
where Price is measured in dollars.
To calculate the store's profit, we need to subtract the cost of producing each pair of swimming flippers from the revenue:
Profit = (Price - Cost) x Quantity Sold
We don't have information about the cost of producing each pair of swimming flippers, so let's assume that it is a constant of $20 per pair. This means that the profit function is:
Profit = (Price - $20) x (92 - (Price - $50)) = (Price - $20) x (-Price + $142)
Expanding the brackets and simplifying, we get:
Profit = -$Price^2 + $122Price - $2840
To find the price that maximizes profit, we need to take the derivative of the profit function with respect to price, and set it equal to zero:
dProfit/dPrice = -$2Price + $122 = 0
Solving for Price, we get:
Price = $61
So, the store should charge $61 per pair of swimming flippers to maximize profit. To verify that this is indeed the maximum, we can take the second derivative of the profit function with respect to price:
d^2Profit/dPrice^2 = -$2
Since this is negative, we know that the profit function is concave down, which means that the critical point we found is indeed a maximum.
the germination rate is the rate at which plants begin to grow after the seed is planted. a seed company claims that the germination rate for their seeds is 90 percent. concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. what are the
Answers
The correct hypothesis for a one-sample z-test for a population proportion p for germination is p <0.9
A hypothesis is an informed estimate about the solution to a scientific issue that is supported by sound reasoning. It is the expected result of the trial, though it is not evidence in an experiment. Depending on the information collected, it might be supported or might not be allowed at all.
The material provided indicates that the following is the appropriate theories for a one-sample z-test for a population proportion where H0 is p = 0.9 and H1 <0.9. Thus, at the null hypothesis, it is tested if the germination rate is actually of 90%, that is H = 0.9 and at the alternative hypothesis, it is tested if the germination rate is of less than 90%, that is H1 <0.9.
Complete Question:
The germination rate is the rate at which plants begin to grow after the seed is planted. A seed company claims that the germination rate for their seeds is 90 percent. Concerned that the germination rate is actually less than 90 percent, a botanist obtained a random sample of seeds, of which only 80 percent germinated. What are the correct hypotheses for a one-sample z-test for a population proportion p ?.
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Please help me, only 20 points if answered !!
Answers
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ s=\pi \end{cases}\implies \pi =\cfrac{\theta \pi (4)}{180}\implies \cfrac{180}{4\pi }\cdot \pi =\theta\implies 45=\theta[/tex]
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
Answers
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.
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?
Answers
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.
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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.
Answers
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.
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Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?
WRONG ANSWER = REPORTED
Answers
Answer:
47/60
Step-by-step explanation:
You want to know the probability of a randomly selected student is on the honor roll or varsity team when 176 of 240 students are on the honor roll, 48 are on the varsity team, and 36 are on both.
One or the otherThe probability of A or B is ...
P(A+B) = P(A) +P(B) - P(A·B)
The probability of interest is ...
P(honor roll + varsity) = P(honor roll) + P(varsity) - P(honor roll & varsity)
P(honor roll + varsity) = 176/240 +48/240 -36/240 = (176 +48 -36)/240
= 188/240 = 47/60
The probability of interest is 47/60.
[tex]\blue{\huge {\mathrm{PROBABILITY}}}[/tex]
[tex]\\[/tex]
[tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{Q} {\large \mathrm {UESTION : }}}}[/tex]
Of 240 students, 176 are on the honor roll, 48 are members of the varsity team, and 36 are in the honor roll and are also members of the varsity team. What is the probability that a randomly selected student is on the honor roll or is a member of the varsity team?[tex]{===========================================}[/tex]
[tex] {\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} [/tex]
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex][tex]{===========================================}[/tex]
[tex]{\underline{\huge \mathbb{S} {\large \mathrm {OLUTION : }}}}[/tex]
We can use the inclusion-exclusion principle to find the number of students who are on the honor roll or are members of the varsity team.
This principle states that:
[tex]\sf |A\cup B| = |A| + |B| − |A\cap B|[/tex]where:
A and B are sets,|A| is the cardinality (number of elements) of set A, andA∩B is the intersection of sets A and B.Using this principle, we can find that:
[tex]\begin{aligned}\sf |Honors\cup Varsity|& =\sf |Honors| + |Varsity| − |Honors\cap Varsity|\\& =\sf 176 + 48 - 36\\& =\sf\red{188}\end{aligned}[/tex]
Therefore, there are 188 students who are on the honor roll or are members of the varsity team.
The probability that a randomly selected student is on the honor roll or is a member of the varsity team is then:
[tex]\begin{aligned}\sf P(Honors\cup Varsity)& =\sf \dfrac{|Honors\cup Varsity|}{|Total|} \\ &=\sf \dfrac{188}{240} \\&=\boxed{\bold{\: \dfrac{47}{60}\:}}\end{aligned}[/tex]
Therefore, the probability that a randomly selected student is on the honor roll or is a member of the varsity team is [tex]\boxed{\bold{\:\dfrac{47}{60}\:}}[/tex]
[tex]{===========================================}[/tex]
[tex]- \large\sf\copyright \: \large\tt{AriesLaveau}\large\qquad\qquad\qquad\qquad\qquad\qquad\tt 04/02/2023[/tex]
Given: m∠KAL=100°, m∠L=25°, and OA=25
Find: AK, AL, and KL
Answers
AK = AL ≈ 28.77, KL < 57.54. In summary, the values of AK = AL ≈ 28.77 and KL < 57.54 .
What is triangles?A closed triangle is a polygon with three sides and three angles in two dimensions.
We know that the radius of the circle, OA, is 25. Since OA is a radius of the circle and bisects triangle ΔKAL, we can conclude that AK = AL.
Let's call AK = AL = x.
Now we use the fact that the sum of the angles in a triangle is 180 degrees to find the measure of angle K.
We know that angle L is 25 degrees, and since angle KAL is 100 degrees, angle K must be:
K = 180 - L - KAL
K = 180 - 25 - 100
K = 55 degrees
Now, we can use the law of sines to find x, which is the length of both AK and AL:
sin(K) / x = sin(L) / OA
sin(55) / x = sin(25) / 25
x = sin(55) * 25 / sin(25)
x ≈ 28.77
Therefore, AK = AL ≈ 28.77.
To find KL, we can use the fact that AK = AL = x and OA = 25 to find OK and OL:
OK = OA - AK
OK = 25 - 28.77
OK ≈ -3.77
OL = OA - AL
OL = 25 - 28.77
OL ≈ -3.77
Since OK and OL are both negative, we know that O must be located inside triangle ΔKAL. Therefore, we can use the triangle inequality to find KL:
KL < AK + AL
KL < 2x
KL < 2(28.77)
KL < 57.54
Therefore, KL < 57.54.
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Find the inverse of the following function: f(x)=[tex]\sqrt[3]{4x+7}[/tex]
Answers
All functions have an inverse function, and for a function to have an inverse. The inverse of [tex]f(x) = 3\sqrt(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex]
What is the inverse function?The inverse function, often known as the "inverse mapping," is a function that "undoes" another function's operation. If a function f(x) translates an input x to an output y, the inverse function f(-1)(y) transfers the result y back to the input x.
To find the inverse of the function f(x) = 3√(4x + 7), we need to solve for x in terms of y.
Step 1: Replace f(x) with y
[tex]y = 3√(4x + 7)[/tex]
Step 2: Cube both sides to eliminate the cube root
[tex]y^3 = 27(4x + 7)[/tex]
Step 3: Simplify and solve for x
[tex]y^3 = 108x + 189[/tex]
[tex]x = (y^3 - 189)/108[/tex]
Step 4: Replace x with [tex]f^-1(x)[/tex]
[tex]f^-1(x) = (x^3 - 189)/108[/tex]
Therefore, the inverse of [tex]f(x) = 3√(4x + 7) is f^-1(x) = (x^3 - 189)/108[/tex] .
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]
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.
()'
Answers
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
solve for y
A)115º
B)108º
C)90º
D)130º
Answers
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]
Multiply polynomials
HELP I NEED THIS ASAP
Answers
Answer:
6x^3-5x^2+9x+10
Step-by-step explanation:
Use the distributive property and multiply like terms.
How could you correctly rewrite the equation 4(5+3)=2(22-6) using distribution property
Answers
Answer: 4(5+3) = 4(5) + 4(3) = 20 + 12 = 32
Step-by-step explanation:
Answer:
32=32 ?
Step-by-step explanation:
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?
Answers
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
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.
Answers
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
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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)
Answers
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.
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?
Answers
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
Look at the pattern below.
step 1 with 1 square
step 2 with 3 squares
step 3 with 6 squares
step 4 with 10 squares
How does the pattern grow at each step?
Choose 1 answer:
Answers
Answer: The pattern grows by adding the consecutive counting numbers starting from 1.
For example:
Step 1: 1 square
Step 2: 1 + 2 = 3 squares
Step 3: 1 + 2 + 3 = 6 squares
Step 4: 1 + 2 + 3 + 4 = 10 squares
So at each step, the number of squares increases by adding the next consecutive counting number.
Step-by-step explanation:
Help me solve e this question?
Answers
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
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