The area of the square is changing at 12√2 + 2√2t square inches/minute when the circle is increasing at 1 in/min.
Let us find the relationship between r and s using the Pythagorean theorem. Since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.
2r = s√2
Squaring both sides, we get:
4r² = 2s²or s² = 2r²
Dividing by 2 on both sides, we get:
s²/2 = r²
Differentiating both sides with respect to t, we get:
ds²/dt = 2r (dr/dt)
Dividing both sides by 2s, we get:
ds/dt = r (dr/dt) / s
Substituting r² = s²/2,
[tex]ds/dt = r (dr/dt) / √2s2s ds/dt = r (dr/dt)s ds/dt = (r/2) (dr/dt)2s ds/dt = r (dr/dt) or dA/dt = 2s ds/dt = 2r (dr/dt)[/tex]
Now, substituting r² = s²/2,
dA/dt = 2s ds/dt = 2(√2 s) (dr/dt) = 2(√2) r (dr/dt)
Now, substituting dr/dt = 1 in/min and r = 6 in (since the circle is increasing at 1 in/min, the radius after t minutes is 6 + t),
dA/dt = 2(√2) (6 + t) (1) = 12√2 + 2√2t square inches/minute
Therefore, the area of the square is changing at a rate of 12√2 + 2√2t square inches/minute.
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the sides of a square are growing at a rate of 3 inches per minute. how fast is the area increasing when each side is 5 inches long?
24 centimeters. Hope this helped!
Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.
A. h(-3) = -1
B. h(13) = 18
C. h(2) = 16
D. h(8) = 21
The statement that could be true for h for given function is Option C h(2) = 16 is correct.
What is Domain?The set of all potential values for the independent variable (typically designated as x) for which the function is specified is known as the domain of a function. In other terms, it refers to the entire set of input values for which a function returns a result.
We can state that for any value of x between -3 and 11, the corresponding value of h(x) will be between 1 and 25 because the function h has a domain of -3 x 11 and a range of 1 h(x) 25.
Indicates that the function h is not fixed and that its values change depending on the value of x.
Now, evaluate your options:
Option A h(-3) = -1 - This statement is false because the range of h(x) is stated to be between 1 and 25, so h(-3) cannot be less than 1.
OptionB h(13) = 18 - This statement cannot be true because h(x) is specified to have a range between -3 and 11, so h(13) is not defined.
OptionC h(2) = 16 - The statement may be accurate given that the value of h(x) for any x between -3 and 11 could range from 1 to 25, and there is no evidence to the contrary.
OptionD h(8) = 21 - Since we know that h(8) = 19, this assertion is false.
Therefore, the statement that could be true for h is: h(2) = 16
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eighteen more than 7 times a number is -12
The solution x = -30/7 is the value of the unknown number that satisfies the statement "eighteen more than 7 times a number is -12".
This question is incomplete, the complete question is:
Eighteen more than 7 times a number is -12, find the unknown number.
What is the value of the unknown number?Given that, eighteen more than 7 times a number is -12.
Let's use "x" to represent the unknown number.
From the given information, we can use algebra to translate this sentence into an equation.
We start by using "7x" to represent the product of 7 times "x", and adding 18 to it:
7x + 18
Then, we set this expression equal to -12, since that's what the sentence told us the expression is equal to:
7x + 18 = -12
To solve for "x", we can first subtract 18 from both sides:
7x + 18 - 18 = -12 - 18
7x = -30
Then, we can isolate "x" by dividing both sides by 7:
7x/7 = -30/7
x = -30/7
Therefore, the value of the unknown number is x = -30/7.
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How will the product of 7 x
Choose 1 answer:
64
5
compare to 7, and why?
It will be less because we are multiplying 7 by a fraction that is less
than 1.
It will be equal because we are multiplying 7 by a fraction that is
equal to 1.
It will be greater because we are multiplying 7 by a fraction that is
greater than 1.
According to the question the product of 7 x 5 will be greater than 7 from multiplication.
Explain Multiplication?Multiplication in mathematics is the addition of equal groups. As we proliferate, the quantity of items in the group increases. The product as well as the two elements are part of a multiplication issue. 6 and 9 are factors in the multiplication equation 6 9 = 54, and 54 is the result.
The product of 7 x 5 by multiplying with each other we can get 35
The number being multiplied with 7 is greater than 1 so the product will also be greater than 7.
The product of 7 x 5 will be greater than 7 because we are multiplying 7 by a number greater than 1.
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Find the area of the following shapes. Please help
A=?cm2
The shape is an identical parallelogram and the area is equal to 30 square centimeters.
Area of parallelogramIn calculating for the area of parallelogram, the base is multiplied by the height, as the same way for calculating the area of a rectangle.
we shall calculate for the area of the shape by evaluating the area of the one parallelogram and then multiply the result by two as follows:
area of one identical parallelogram = 5 cm × 3 cm
area of one identical parallelogram = 15 cm²
area of identical parallelogram shape = 2 × 15 cm²
area of identical parallelogram shape = 30 cm²
Therefore, the area for the identical parallelogram shape is equal to 30 square centimetres.
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HELP 20 POINTS
NO WRONG ANSWERS OF LINKS THEY WILL GET REPORTED
Answer:
The second one, (x+1)(3x+2)
The answer is (x+1)(3x+2)
hope it helps
how could you lower the fat content of the following sandwich? 2 slices of white bread 2 ounces of sliced turkey 1 slice of provolone cheese 1 tablespoon of mayonnaise 1 leaf of lettuce 1 slice of tomato
1. Replace the white bread with whole grain bread
2. Replace the turkey with a leaner meat, such as chicken or turkey bacon
3. Replace the mayonnaise with low-fat Greek yogurt
4. Replace the provolone cheese with a lower-fat cheese such as mozzarella
5. Reduce the amount of lettuce used
6. Replace the tomato slice with tomato slices or tomato paste.
To lower the fat content of the sandwich, you can make these changes:
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Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Therefore, the correct answer is: The range is the best measure of variability, and it equals 78.
What is range?Range is a measure of variability that represents the difference between the maximum and minimum values in a dataset. It gives an indication of how spread out the data is. To find the range of a dataset, you simply subtract the minimum value from the maximum value. Range is often used as a quick and simple measure of variability, but it can be sensitive to outliers and extreme values.
Here,
1. For question 5, the appropriate measure of variability for the given data set is the range, which is the difference between the maximum value and the minimum value in the data set.
To find the maximum and minimum values from the given stem-and-leaf plot, we can look at the highest and lowest digits in each row. The highest value is 83 and the lowest value is 5, so the range is:
Range = 83 - 5 = 78
2. For question 6, the appropriate measure of center to represent the data in the given line plot is the median, because the data is skewed to the right and there are outliers present. The median is less sensitive to outliers than the mean.
Therefore, the correct answer is: The median is the best measure of center because there are outliers present.
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10. Which graph shows the solution to the inequality <-6?
When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because
When it comes to the sale of products such as pet food, the veterinary practice is at an advantage over feed stores and grocery stores because they have better knowledge and understanding about the pet food, and they have established trust with their customers.
What is pet food?
Pet food is a nutrient-rich food specially designed for domestic animals, like dogs, cats, and other pets. It is made from various animal and plant-based sources, such as beef, fish, and corn. Since pet food is designed to meet the nutritional needs of the pets, it must be balanced and complete to provide them with the necessary nutrients they need to be healthy and active.
Why veterinary practice is at an advantage over feed stores and grocery stores?Veterinarians are at an advantage over feed stores and grocery stores when it comes to the sale of pet food because they have the knowledge and expertise about the pet food. They are aware of the specific nutritional requirements of the pets and the various pet food brands available in the market. They can provide advice and recommendations to pet owners on what type of pet food is best suited for their pets based on their age, breed, and health conditions.
Moreover, veterinary practices have established trust with their customers. When customers know they can rely on a particular veterinary practice for quality products and trustworthy advice, they are more likely to shop there repeatedly.
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Franklin is an ecologist monitoring the catfish population in Athena Lake each year. When he first started monitoring the population one year ago, he estimated that there were 800 catfish in the lake. Today, Franklin estimates the population has decreased to 760 and it will continue decreasing each year.
Parker Paint has just created a new color, Sunset Orange, made by mixing 3 parts of Fire Red with 5 parts of Brilliant Yellow. A graph to help customers decide how much paint they need is hanging in the store. Use the point shown from the graph to help you decide how much Fire Red paint is needed to paint one 8 foot by 10 foot wall.
To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed.
Using the graph, we can calculate that for every 5 parts of Brilliant Yellow, 3 parts of Fire Red is needed. Since we need to paint an 8 foot by 10 foot wall, we need 80 square feet of paint. To calculate how much Fire Red is needed, we can use the equation: 3 parts of Fire Red = 5 parts of Brilliant Yellow. We can rearrange this equation to read: 5 parts of Brilliant Yellow = 3 parts of Fire Red. To get the amount of Fire Red required to paint the wall, we can multiply 80 (the square footage of the wall) by 3 and divide it by 5, giving us a total of 48 parts of Fire Red.
To paint an 8 foot by 10 foot wall with Sunset Orange, one needs 48 parts of Fire Red and 80 parts of Brilliant Yellow.
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use the properties of geometric series to find the sum of the series. for what values of the variable does the series converge to this sum?
7−14z+28z2−56z3+⋯
sum =
domain =
(Give your domain as an interval or comma separated list of intervals; for example, to enter the region x<−1 and 2
a) The sum of the given series is 7 / (1 + 2z)
b) The domain of convergence is (-∞, -1/2) U (1/2, ∞).
The given series can be expressed as
7 – 14z + 28z^2 - 56z^3 + ...
This is a geometric series with first term (a) = 7 and common ratio (r) = -2z. The formula for the sum of an infinite geometric series is
sum = a / (1 - r)
Substituting the values of a and r, we get
sum = 7 / (1 + 2z)
So, the sum of the given series is 7 / (1 + 2z).
For the series to converge, the absolute value of the common ratio must be less than 1. That is,
|r| = |−2z| < 1
Simplifying this inequality, we get
1/2 < |z|
So, the domain of convergence of the given series is (-∞, -1/2) U (1/2, ∞).
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How do I work this out
Therefore, the equation of the line is y = 6x + 1, in slope-intercept form.
What is equation?In mathematics, an equation is a statement that shows the equality of two expressions. An equation usually contains one or more variables, which represent unknown values that we are trying to solve for. Equations can also be more complex, involving multiple variables and operations such as exponents, logarithms, and trigonometric functions. Solving equations is an important part of mathematics, and has many practical applications in science, engineering, and everyday life.
Here,
The equation of a straight line in slope-intercept form is y = mx + b, where m is the gradient (or slope) of the line, and b is the y-intercept (where the line crosses the y-axis). We are given that the gradient of the line is 6, and that it passes through the point (3, 19). We can use this information to find the equation of the line. First, we can use the point-slope form of the equation of a line to find the equation of the line that passes through the point (3, 19) with a gradient of 6. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, and m is the slope of the line.
Substituting the values we know, we get:
y - 19 = 6(x - 3)
Expanding the brackets, we get:
y - 19 = 6x - 18
Adding 19 to both sides, we get:
y = 6x + 1
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the procedure used to obtain your sample (i.e., random or nonrandom sampling) is not the same as the procedure for assigning participants to conditions; distinguish between random sampling and random assignment.
Random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
Random sampling and random assignment are two distinct procedures that are often used in research studies, and it's important to understand the difference between them.
Random sampling refers to the process of selecting individuals or units from a larger population in such a way that every member of the population has an equal chance of being included in the sample. Random sampling is used to ensure that the sample is representative of the population and that the results can be generalized to the larger population.
Random assignment, on the other hand, refers to the process of assigning participants to different experimental conditions in a way that is completely random. This means that every participant has an equal chance of being assigned to any condition. Random assignment is used to control for extraneous variables that could influence the results of the study. By randomly assigning participants to conditions, researchers can be more confident that any differences observed between the groups are due to the manipulation of the independent variable, rather than pre-existing differences between the participants.
In summary, random sampling is used to ensure that the sample is representative of the population, while random assignment is used to control for extraneous variables and increase the internal validity of the study.
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you are placing 11 different pictures on separate pages of a photo album. how many different ways can you order the 11 pictures in the album?
The number of different ways to order 11 different pictures in a photo album is 39,916,800.
To calculate this number, we can use the formula for permutations, which is:
n! / (n - r)!
where n is the total number of items to choose from (in this case, 11 pictures) and r is the number of items to be selected (also 11, since we want to order all the pictures).
Plugging in the values, we get:
11! / (11 - 11)! = 11! / 0! = 11!
We can simplify 11! as:
11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
Using a calculator or by hand, we can find that 11! equals 39,916,800.
Therefore, there are 39,916,800 different ways to order 11 different pictures in a photo album.
Hence, the number of ways to order 11 pictures in a photo album can be calculated using the permutation formula, which gives a total of 39,916,800 possible arrangements.
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What is the volume of a sphere with a radius of 60.5ft
Answer: V ≈ 927,587
Step-by-step explanation:
Formula for volume of a sphere:
V = [tex]\frac{4}{3}[/tex]πr³
Substitute the known value for radius:
V = [tex]\frac{4}{3}[/tex]π(60.5ft)³
Simplify:
V ≈ 927,587
Pls just say a b c or d
The prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.
What is PrοbabiIity?PrοbabiIity is a measure οf the IikeIihοοd οf an event οccurring, expressed as a number between 0 and 1. It is caIcuIated as the number οf favοrabIe οutcοmes divided by the tοtaI number οf pοssibIe οutcοmes.
The prοbabiIity οf the spinner stοpping at green is 1/3 since there are three equaI parts.
The prοbabiIity οf seIecting a yeIIοw card frοm the six cards is 1/6 since there is οne yeIIοw card οut οf six cards in tοtaI.
Tο find the prοbabiIity οf bοth events happening, we muItipIy the individuaI prοbabiIities:
P(green and yeIIοw) = P(green) * P(yeIIοw)
= (1/3) * (1/6)
= 1/18
Therefοre, the prοbabiIity οf the spinner stοpping at green and a yeIIοw card being seIected is 1/18.
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Help please hurry
Maria spins a penny 100 times and it lands head side up 62 times. Explain why Maria's experimental probability may be different from the theoretical probability of spinning a coin. (10 points)
Answer:
To solve the question we shall proceed as follows:
Theoretical probabilities generally deals with the nature of the experiment and events, this differs from the experimental probabilities relies on the fact of actual occurrence of the experiment and the events. In other words, experimental probability is an estimate simply based on the probabilities that cannot at all be determined by simple logic. It is the ratio of the number of times an event is occurring to the total number of times or trials that an activity has been repeated for.
From the question, the experimental probability will be:
62/100
=0.62
this differs with theoretical probability which states that at any occasion the probability of the coin coming up heads when tossed is 1/2
Step-by-step explanation: I really hope this helps!! :))). Mark me brainliest!! :))
Kevin is hiking on a trail that is 4. 9 miles long. So far, he has hiked 90% of the total distance. How many more miles does Kevin have to hike in order to complete the trail? Complete the explanation on how you found your answer. Part 1 out of 2 Kevin has to hike more miles in order to complete the trail
Kevin has 0.49 miles, or approximately 0.5 miles, left to hike in order to complete the trail.
Kevin has hiked 90% of the trail, which means he still has to hike 10% of the trail to complete it. To find out how many miles he has left to hike, we can use the proportion:
10/100 = x/4.9
where x represents the number of miles Kevin has left to hike.
To solve for x, we can cross-multiply and simplify:
10 * 4.9 = 100x
49 = 100x
x = 49/100
x = 0.49
Therefore, Kevin has 0.49 miles, or approximately 0.5 miles, left to hike in order to complete the trail.
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Complete Question:
Kevin is hiking on a trail that is 4. 9 miles long. So far, he has hiked 90% of the total distance. How many more miles does Kevin have to hike in order to complete the trail?
Use the rational zeros theorem to find all the real zeros of the polynomial function. use the zeros to factor f over the real numbers. f(x)=x^3-5x^2-61x-55???
The polynomial function f(x) = x³ - 5x² - 61x - 55 has the following
Real zeros: x = -5, x = -1, and x = 11.
To find the rational zeros of a polynomial, we use the rational zeros theorem. We look at the factors of the leading coefficient and the factors of the constant coefficient.
The states that if a polynomial function is defined as P(x) = anxn + an-1xn-1 + ... + a1x + a0 with integers, then each rational zero of the polynomial can be expressed in the form p/q where p is a factor of a0 and q is a factor of an.
For example, if P(x) = 2x³ - 5x² + 3x + 6 then p can be any factor of 6 and q can be any factor of 2.
The factors of the leading coefficient, 1, and the factors of the constant coefficient, -55, are: ±1, ±5, ±11, ±55. So the possible rational zeros are: ±1, ±5, ±11, ±55, ±1/1, ±5/1, ±11/1, ±55/1, ±1/1, ±5/1, ±11/1, ±55/1.
Simplifying the results, we have that the potential rational zeros are: ±1, ±5, ±11, ±55, ±1, ±5, ±11, and ±55.
By testing each possible rational zero, we find that x = -5, x = -1, and x = 11 are the real zeros of f(x).
Hence, using synthetic division, we get:
(x + 5)(x + 1)(x - 11) = x³ - 5x² - 61x - 55
Thus, the function can be factored over the real numbers as
f(x) = (x + 5)(x + 1)(x - 11).
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If g(x) = 1 – 2x + 3x2, find the average rate of change of the function as x varies from 2 to 5
The average rate of change of the function as x varies from 2 to 5 is 22.
Given function: g(x) = 1 – 2x + [tex]3x^2[/tex]
To find the average rate of change of the function as x varies from 2 to 5.
Solution: We are given a function: g(x) = 1 – 2x + [tex]3x^2[/tex]
The average rate of change of the function as x varies from a to b is given by:
Average rate of change = f(b) - f(a) / b - a
Let a = 2 and b = 5
We have to find the average rate of change of g(x) as x varies from 2 to 5.
So, the average rate of change of g(x) is given by:
Average rate of change = g(5) - g(2) / 5 - 2
= [1 - 2(5) + 3([tex]5^2[/tex])] - [1 - 2(2) + 3([tex]2^2[/tex])] / 3
= [1 - 10 + 75] - [1 - 4 + 12] / 3= 66 / 3= 22
Therefore, the average rate of change of the function as x varies from 2 to 5 is 22.
An average rate of change is the amount that the function changes on average over a specified interval.
The formula for average rate of change is given as the change in the function value divided by the change in x value for two distinct points on the function.
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two cyclists, 48 mi apart, start riding towards each other at the same time. one cycles twice as fast as the other. if they meet 1 hr later, at what average speed is each cyclist traveling?
The slower cyclist travels at a speed of 16 miles per hour, while the faster cyclist travels at twice the speed, which is 32 miles per hour.
Let's assume that the slower cyclist's speed is x mi/h, then the faster cyclist's speed is 2x mi/h.
Since they are riding towards each other, their relative speed is the sum of their speeds, which is 3x mi/h.
They travel a total distance of 48 mi in 1 hour, so we can use the formula:
distance = rate x time
48 = 3x x 1
Solving for x, we get:
x = 16
Therefore, the slower cyclist's speed is 16 mi/h and the faster cyclist's speed is 32 mi/h.
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how do u sovle Find x .
Two non-congruent parallelograms. The width and length of one parallelogram are marked 4 centimeters and 6 centimeters respectively. The width and length of the other parallelogram are marked 6 centimeters and x respectively.
The length of the second parallelogram is 2 cm.
What are parallelograms ?
A parallelogram is a quadrilateral with opposite sides parallel and equal in length. It has two pairs of parallel sides and opposite angles are equal. Some common properties of parallelograms include:
According to the question:
To solve for x, we need to use the fact that opposite sides of a parallelogram are equal in length.
For the first parallelogram, we know that the width is 4 cm and the length is 6 cm. Therefore, the opposite side lengths are also 4 cm and 6 cm.
For the second parallelogram, we know that the width is 6 cm. Since the opposite sides are equal in length, the length of the parallelogram must be x cm.
So, we have:
Width of first parallelogram = Width of second parallelogram
4 cm = 6 cm
Length of first parallelogram = Length of second parallelogram
6 cm = x cm
Simplifying the first equation, we get:
2 cm = x
Therefore, the length of the second parallelogram is 2 cm.
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Please help me I need this
There are 35 counters in a bag the ratio of red to blue counters is 2:5 there are 9 more blue counters the rest are green how many green counters are there?
there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information. The given information provides us with the ratio of red to blue counters in a bag, which is 2:5. This means that for every 2 red counters in the bag, there are 5 blue counters.
Let the number of red counters in the bag be 2x, where x is a constant. Then, the number of blue counters in the bag is 5x. We are also given that there are 9 more blue counters than before, so the new number of blue counters is 5x + 9.
We know that there are 35 counters in total, so we can write an equation based on this information:
2x + 5x + 5x + 9 = 35
Simplifying this equation, we get:
12x + 9 = 35
Subtracting 9 from both sides, we get:
12x = 26
Dividing both sides by 12, we get:
x = 2.1667
Since we cannot have a fraction of a counter, we can round x up to 3.
Therefore, the number of red counters in the bag is 2x = 2(3) = 6, and the number of blue counters in the bag is 5x + 9 = 5(3) + 9 = 24.
Finally, we can find the number of green counters in the bag by subtracting the number of red and blue counters from the total number of counters:
35 - 6 - 24 = 5
So there are 5 green counters in the bag.
In summary, there are 6 red counters, 24 blue counters, and 5 green counters in the bag, based on the given information.
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WILL GIVE BRIANLIST TO BEST ASNWWR
Richard buys a new car for $28,000. The car depreciates in value by 9% each year. Which of the following uses the variable y to represent the value of the car after t years in an exponential model to represent the situation?
y=28,000(1.09)
y=28,000(91)
y-28,000(-9)
y=28,000(0.09)
The variable y is used to represent the worth of the car after t years like an exponential model to reflect the scenario, and the third option, y=28,000(0.91)t, is the correct response.
The formula for the exponential model is what?A = A0(b)t/c is the formula for an exponential model, where A0 denotes the starting quantity of the thing being modeled. t stands for passing time. The quantity at time t is equal to A.
The exponentially decaying formula for an asset's value over time with such a consistent rate of depreciation is: y = a(1-r)t
Where:
Y is equal to the car's value after t years.
In this scenario, the car's original value is $28,000, and its rate of depreciation is 9%, or 0.09 in decimal notation.
t equals the amount of years
The exponential model can be expressed using the following formula: y = 28,000(1-0.09)t
By condensing the formula, we obtain the following result: y = 28,000(0.91)t
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The value of y varies directly with x
The calculated value of y when x is -4 is -10 given that the variation is a direct variation
Calculating the value of y when x is -4Direct variation is a mathematical concept that describes the relationship between two variables that change in proportion to each other.
More formally, two variables x and y are said to vary directly if their ratio is constant. This can be expressed mathematically as:
y = kx
So, we have
20 = -8k
This gives
k = -2.5
This means that
y = -2.5x
When the value of x is -4 we have
y = -2.5 * -4
Evaluate
y = 10
Hence, the value of y when x is -4 is -10
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Solve:
6n-5=-35
R=12=25
9x+3=21
Answer:
6n - 5 = -35
Adding 5 on both sides, we get
6n = -30
Dividing by 6 on both sides, we get
n = -5
R/12 = 25
Multiplying both sides by 12, we get
R = 300
9x + 3 = 21
Subtracting 3 from both sides, we get
9x = 18
Dividing by 9 on both sides, we get
x = 2
HELP NOW!
Without graphing, identify the key features of the given function.
-vertex
-axis of symmetry
-direction of opening
-number of x-intercepts
-compression/expansion
[tex]f(x)=2(x-3)^2+5[/tex]
Explain your answers on how you found each answer.
The key features of the given function include the following:
Vertex = (3, 5)
Axis of symmetry = 3.
Direction of opening: upward.
Number of x-intercepts = 0.
Expansion.
What is the vertex form of a quadratic equation?In this exercise, you are required to determine the vertex form of a quadratic function h(x) that is written in standard form. Mathematically, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided about this quadratic function, we can reasonably infer and logically deduce that its vertex can be determined as follows:
y = a(x - h)² + k
f(x) = 2(x - 3)² + 5
Vertex, (h, k) = (3, 5)
Axis of symmetry, Xmax = -b/2a = -(-6)/2(1) = 6/2 = 3.
In conclusion, the function does not have an x-intercept and it represents an expansion because the scale factor is greater than one (1) i.e k = 2.
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