Answer:
Step-by-step explanation:
Original equation:
7/2x - 3(5x - 1/2) = ?
Use distributive property for the parentheses
-3 · 5x = -15x
-3 · (-1/2) = 3/2 or 1.5
Plug these values into the equation
7/2x - 15x + 1.5 = ?
Combine like factors
-11.5x + 1.5 = a (a = answer)
The equation with fractions:
-11 1/2 + 1 1/2 = a
Hope this helps :)
If the endpoints of AB are located at (0,7) and (8,8) what is the length of AB?
Answer:
√65
Step-by-step explanation:
The distance formula can be represented as
\(\sqrt{(x_{2} -x_1)^2 + (y_2-y_1)^2}\)
Taking (8,8) as (x₂, y₂) and (0,7) as (x₁, y₁), we have
\(\sqrt{(8 -0)^2 + (8-7)^2}\\= \sqrt{8^2 + 1^2}\\= \sqrt{65}\)
as our answer
Use substitution to solve the system.
x = 3y +7
3x + 4y = 8
Answer:
x=4, y=-1
Step-by-step explanation:
x=3y +7. equation 1
3x+4y=8. equation 2
substitute equation 1 into equation 2
3 (3y +7)+4y =8
9y+21+4y=8
13y+ 21=8
13y=8-21
y=-13/13
y=-1
substitute the value of y into equation 1
x=3(-1)+7
x=-3+7
x=4
what is the product of 2 4/7 × 13/12
Answer:
2 11/14
Step-by-step explanation:
First make both of them improper fractions.
therefore,
2 4/7 = 18/7
now simplify.
18/7 × 13/12
18 and 12 get cancelled off as they're multiples of 3 and 6
therefore,
3/7 × 13/2
3× 13 = 39
7×2 = 14
39/14
now make it a proper fraction
2 11/14//
On the following composite figure, all angles are right angles. All short edges of the figure have a measure of 1.5 centimeters. All long edges have a measure of 3 centimeters. Find the area of the figure. Explain or show how you got your answer.
Answer:
27
Step-by-step explanation:
you have to break it down into 5 parts separating the middle part by itself being 3x3=9+ the 4 other parts that is 1.5x3=4.5x4=18 add them together and it's 27
someone help pleaseeeee
Answer: I think 1.2
Step-by-step explanation:
1.35
If the linear system −3x+6y−4z= −5
6x−5y+8z= −2
15x−2y+hz=k
has infinitely many solutions, then k__ and h__
The value for the linear system is k = -25 and h = -0.6.
The coefficient matrix for the given linear system of equations is:
[-3 6 -4]
[6 -5 8]
[15 -2 h]
The determinant of this matrix is:
(-3)(8) - (6)(-2) - (-4)(15h) = 24 + 12 + 60h
For the system to have infinitely many solutions, the determinant must be equal to 0.
Therefore, we have:
24 + 12 + 60h = 0
=> 60h = -36
=> h = -0.6
Also, the value of k must be such that the third equation in the system is a scalar multiple of the first two equations. In other words, we must have:
15x - 2y + hz = k
=> (5) * (-3x + 6y - 4z) = (5) * (-5)
=> -15x + 30y - 20z = -25
Comparing the coefficients of both sides, we have:
k = -25
Therefore, k = -25 and h = -0.6.
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Write the following statement in if-then form.
Happy people rarely correct their faults.
If people are happy, then they rarely correct their faults.
In if-then form, the statement "Happy people rarely correct their faults" can be expressed as an implication. The "if" part of the statement (the condition) is "people are happy," and the "then" part (the consequence) is "they rarely correct their faults."
This form indicates that when the condition is true (people being happy), the consequence tends to occur (they rarely correct their faults).
However, it does not necessarily mean that all happy people will never correct their faults or that correcting faults is solely dependent on happiness. It simply suggests a general tendency or pattern observed where happy individuals are less inclined to address their flaws compared to others.
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a) What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL;
Based on the given data, we can calculate the control limits using 3-sigma for the diameter of the auto pistons.
a) The value of x is 155.56 mm (rounded to two decimal places).
b) The value of R is 4.44 mm (rounded to two decimal places).
c) Using 3-sigma, the Upper Control Limit (UCL) for the diameter is calculated as:
UCL = x + 3R = 155.56 + 34.44 = 156.93 mm (rounded to two decimal places)
The Lower Control Limit (LCL) for the diameter is calculated as:
LCL = x - 3R = 155.56 - 34.44 = 154.19 mm (rounded to two decimal places)
d) Using 3-sigma, the Upper Control Limit for the Range (UCLR) is calculated as:
UCLR = D4 * R = 2.115 * 4.44 = 7.89 mm (rounded to two decimal places)
The Lower Control Limit for the Range (LCLR) is always 0 in this case since negative ranges are not possible.
e) If the true diameter mean should be 155 mm, the new centerline (nominal line) would be 155 mm. In this case, the UCL and LCL would be calculated using 3-sigma as follows:
UCL = Nominal + 3R = 155 + 34.44 = 156.37 mm (rounded to two decimal places)
LCL = Nominal - 3R = 155 - 34.44 = 153.63 mm (rounded to two decimal places)
Please note that the control limits calculated using 3-sigma assume a normal distribution and the data follows the same pattern in the future.
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The complete question is:
What is the value of x? = x= 155.56 mm (round your response to two decimal places). b) What is the value of R? R= 4.44 mm (round your response to two decimal places). c) What are the UCL, and LCL; using 3-sigma? Upper Control Limit (UCL) = 156.93 mm (round your response to two decimal places). Lower Control Limit (LCL) = 154.19 mm (round your response to two decimal places). d) What are the UCLR and LCLR using 3-sigma? Upper Control Limit (UCLR)= 7.89 mm (round your response to two decimal places). Lower Control Limit (LCLR)= 0.99 mm (round your response to two decimal places). e) If the true diameter mean should be 155 mm and you want this as your center (nominal) line, what are the new UCL and LCL? Upper Control Limit (UCL)= 156.37 mm (round your response to two decimal places). Lower Control Limit (LCL;)= 153.63 mm (round your response to two decimal places). Refer to Table 56.1-Factors for Computing Control Chart Limits (3 sigma) for this problem Auto pistons at Wemming Chung's plant in Shanghai are produced in a forging process, and the diameter is a critical factor that must be controlled. From sample sizes of 10 pistons produced each day, the mean and the range of this diameter have been as follows: Day 1 2 3 4 5 Mean x (mm) 150.9 153.2 153.6 153.5 154.6 Range R (mm) 4.0 4.8 4.1 4.8 4.5
How many times will 1/5 go into 37
A. 7 2/5
B. 2 1/5
C. 185
D. 1/185
Answer:
A
Step-by-step explanation:
Using the inverse operation of division which is multiplication I can do 37×1/5 to get 7.4 or 7 2/5.
MARK ME AS BRAINLIEST
Answer:
C 185
Step-by-step explanation:
Well you need 5 1/5th to make on whole, so all we need to do is 5×37 is 185
Find the value of x that makes the quadrilateral a parallelogram.
The value of x that makes the quadrilateral a parallelogram is
31How to fine the value of xConsecutive Interior Angles: These are the angles that are on the same side of the transversal and inside the parallelogram.
They are supplementary, which means their sum is 180 degrees.
hence we have that
(5x - 7) + (x + 1) = 180
5x + x = 180 - 1 + 7
6x = 186
x = 186 / 6
x = 31
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When we are computing a simple linear regression line, there are certain conditions that must be met for this model to be valid. One of these conditions is the equal spread condition. Which of these answers best explains how we check to make sure that this condition is met? a. Make sure there is similar spread around the sample mean of x. b. Make sure there is similar spread around the line at each value of x.
c. Make sure that there is similar spread around the sample mean of y. d. Make sure all outliers are only below the line.
The answers that best explains how we check to make sure that this condition is met is: c. Make sure there is similar spread around the sample mean of y.
How we check to make sure that this condition is met?The equal spread condition states that the residuals (differences between the actual and predicted values of y) should have roughly equal variance at each value of x.
To check if this condition is met, we examine the residual plot, which is a scatterplot of the residuals versus the independent variable x. If the spread of residuals around the mean is roughly equal for all x, then the equal spread condition is satisfied.
Therefore the correct option is C.
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Geometric proofs 2.0 i need help on this plz
Opcions:
According to the midpoints formula, the price elasticity of demand between points A and B on the initial graph is approximately (0.01, 0.45, 1, 2.2, 22)
Suppose the price of bippitybops is currently $50 per bippitybop, shown as point B on the initial graph. Because the price elasticity of demand between points A and B is (elastic, inelastic, unitary elastic) , a $10-per-bippitybop increase in price will lead to (a decrease, an increase, no change) in total revenue per day.
In general, in order for a price decrease to cause an increase in total revenue, demand must be (elastic, inelastic, unitary elastic) .
If the price elasticity of demand between points A and B is elastic, a $10-per-bippitybop increase in price will lead to a decrease in total revenue per day, and for a price decrease to cause an increase in total revenue, demand must be elastic.
What is the relationship between the price elasticity of demand and its impact on total revenue?According to the midpoints formula, the price elasticity of demand between points A and B on the initial graph can be determined using the following formula:
Price Elasticity of Demand = [(Q2 - Q1) / ((Q1 + Q2) / 2)] / [(P2 - P1) / ((P1 + P2) / 2)]
Since the options provided for the price elasticity are 0.01, 0.45, 1, 2.2, and 22, we need to calculate the price elasticity using the given points A and B on the graph. Unfortunately, without specific numerical values for the quantities demanded at points A and B, as well as their corresponding prices, we cannot determine the exact price elasticity of demand between those points.
Moving on to the second part of the question, if the price of bippitybops is currently $50 per bippitybop at point B on the graph, and the price elasticity of demand between points A and B is elastic, then a $10-per-bippitybop increase in price will lead to a decrease in total revenue per day.
This is because elastic demand implies that a price increase will cause a proportionally larger decrease in quantity demanded, resulting in a decrease in total revenue.
Finally, in general, for a price decrease to cause an increase in total revenue, demand must be elastic. Elastic demand means that a change in price will result in a proportionally larger change in quantity demanded, thus increasing total revenue when the price decreases.
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Jair orders a chicken burrito bowl for $6.84, a side of guacamole for $1.89, and a large fountain drink for $2.59. he wants to tip the server 20%. how much money will jair's tip be?
Answer:
2.264
Step-by-step explanation:
6.84+1.89+2.59 = 11.32
20 percent of 11.32 is 2.264
Money for Jair's tip to server = $2.26
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100.
Hence, the percentage means, a part per hundred. The word per cent means per 100.
Given,
Price of chicken burrito bowl = $6.84
Price of guacamole = $1.89
Price of drink = $2.59
Total price = $6.84 + $1.89 + $2.59
= $11.32
Tip to server = 20% of total price
= (20 × 11.32)/100
= 226.4/100
= $2.264
Hence, amount $2.26 will be Jair's tip to the server.
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a student has a class that is supposed to end at 9:00am and another that is supposed to begin at 9:15am. suppose the actual ending time of the 9am class is normally distributed random variable (x1) with a mean of 9:02 and a standard deviation of 2.5 minutes and that the starting time of the next class is also a normally distributed random variable (x2) with a mean of 9:15 and a standard deviation of 3 minutes. suppose also that the time necessary to get from one class to another is also a normally distributed random variable (x3) with a mean of 10 minutes and a standard deviation of 2.5 minutes. what is the probability that the student makes it to the second class before the second lecture starts? (hint: assume x1, x2 and x3 are independent also think linear combinations)
The probability that the student makes it to the second class before it starts is very close to 0.
To find the probability that the student makes it to the second class before it starts, we can use the concept of linear combinations of random variables and the properties of normal distributions.
Let's define the random variable X as the total time it takes for the student to transition from the end of the first class to the start of the second class. Since X is a linear combination of independent normally distributed random variables (X1, X2, X3), we can use their means and variances to calculate the mean and variance of X.
The mean of X is the sum of the means of X1, X2, and X3:
μX = μ1 + μ2 + μ3 = 9:02 + 9:15 + 10 = 28:17 minutes.
The variance of X is the sum of the variances of X1, X2, and X3:
σX^2 = σ1^2 + σ2^2 + σ3^2 = (2.5)^2 + (3)^2 + (2.5)^2 = 15.25 minutes^2.
Now, we need to calculate the probability that X is less than or equal to 0, meaning the student arrives before the second lecture starts. Since X follows a normal distribution, we can standardize the variable and calculate the probability using the standard normal distribution table.
Z = (0 - μX) / σX = (0 - 28:17) / √15.25 ≈ -9.43.
Using the standard normal distribution table or a calculator, we can find the probability corresponding to Z = -9.43. The probability is essentially 0, as the value is significantly far in the left tail of the standard normal distribution.
Therefore, the probability that the student makes it to the second class before it starts is very close to 0.
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Find the common ratio for the geometric sequence: 4, 20, 100, 500.
Answer:
common ratio r = 5
Step-by-step explanation:
the common ratio r is the ratio of consecutive terms, that is
r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{20}{4}\) = 5
If you deposit $1,000 every year in 20 years in a savings account that earns 7% compounded yearly. What is the future value of this series at year 20 if payments are made at the beginning of the period? $60,648.57 $43,865.18 $65,500,45 $40,995.49 If you deposit $3,000 every year for 15 years at an APR of 9% compounded monthly, what would be the future value at the end of this series? $90,757,36 $39,360.46 549,360,46 598,393,95 At what interest rate should you invest $1000 today in order to have $2000 dollars in 10 years? 7.2% 14.9% 6.2% 10%
The future value of depositing $1,000 every year for 20 years, with payments made at the beginning of each period, at an interest rate of 7% compounded yearly, is approximately $43,865.18.
To calculate the future value of a series of deposits, we can use the formula for the future value of an ordinary annuity:
FV = P * [(1 + r)^n - 1] / r
Where:
FV is the future value
P is the periodic payment
r is the interest rate per period
n is the number of periods
In this case, the periodic payment is $1,000, the interest rate is 7% (or 0.07), and the number of periods is 20.
Plugging these values into the formula, we get:
FV = 1000 * [(1 + 0.07)^20 - 1] / 0.07
= 1000 * [1.07^20 - 1] / 0.07
≈ 1000 * [2.6532976 - 1] / 0.07
≈ 1000 * 1.6532976 / 0.07
≈ 43,865.18
Therefore, the future value of this series after 20 years would be approximately $43,865.18.
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Declaring variables - Declare two integer variables x and y, - Assign them any values. - Print addition/subtraction/multiplication and division of these two variables on to the screen
Submission Task (- Grade 1%) Follow the same steps asin Exercise 2, but change the step 2 to ask the user for input forthese values by using Scanner class.
Two integer variables x and y, prompts the user to enter values for them using the Scanner class, and performs addition, subtraction, multiplication, and division operations on those variables:
import java.util.Scanner;
public class VariableOperations {
public static void main(String[] args) {
Scanner scanner = new Scanner(System.in);
System.out.print("Enter the value for x: ");
int x = scanner.nextInt();
System.out.print("Enter the value for y: ");
int y = scanner.nextInt();
// Addition
int addition = x + y;
System.out.println("Addition: " + addition);
// Subtraction
int subtraction = x - y;
System.out.println("Subtraction: " + subtraction);
// Multiplication
int multiplication = x * y;
System.out.println("Multiplication: " + multiplication);
// Division
if (y != 0) {
double division = (double) x / y;
System.out.println("Division: " + division);
} else {
System.out.println("Cannot divide by zero.");
}
}
}
This code prompts the user to enter values for x and y, performs the four basic arithmetic operations, and displays the results on the screen.
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How many positive integers x satisfy the inequality ?\(100 \leqslant {x}^{2} \leqslant 200\)
ANSWER:
5 positive integers
STEP-BY-STEP EXPLANATION:
We have the following inequality:
\(100\le x^2\le200\)Solving for x:
\(\begin{gathered} \sqrt[]{100}\le\sqrt[]{x^2}\le\sqrt[]{200} \\ \pm10\le x\le\pm10\sqrt[]{2} \end{gathered}\)Being only positive numbers, it would then remain:
\(10\le x\le10\sqrt[]{2}\)Being only integers, it would then remain:
\(\begin{gathered} 10\le x\le10\sqrt[]{2} \\ 10\sqrt[]{2}=14.14\cong14 \\ \text{therefore:} \\ 10\le x\le14 \\ x=10,11,12,13,14 \end{gathered}\)Which means that 5 positive integers satisfy the inequality (10, 11, 12, 13, 14)
if f(x) = 3 - x^2, find f(-2)
Based on the function f(x) = 3 - x², the value of f(-2) include the following: f(-2) = -1.
What is a function?In Mathematics and Geometry, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair in tables or relations.
What is a domain?In Mathematics and Geometry, a domain is sometimes referred to as input value and it can be defined as the set of all real numbers for which a particular function is defined.
When the domain (input value) of the given function f(x) is -2, the output value (range) is given by;
f(x) = 3 - x²
f(x) = 3 - (-2)²
f(x) = 3 - 4
f(x) = -1
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HELP ASAP.
A biologist is studying the growth of a particular species of algae. She writes the following equation to show the radius of the algae, f(d), in mm, after d days:
f(d) = 7(1.06)d
Part A: When the biologist concluded her study, the radius of the algae was approximately 13.29 mm. What is a reasonable domain to plot the growth function? (4 points)
Part B: What does the y-intercept of the graph of the function f(d) represent? (2 points)
Part C: What is the average rate of change of the function f(d) from d = 4 to d = 11, and what does it represent?
Part A: The reasonable domain for the growth function is d ≥ 0, allowing for positive days and future growth.
Part B: The y-intercept is 7, indicating the initial radius of the algae when the study began.
Part C: The average rate of change from d = 4 to d = 11 is approximately 0.55 mm/day, representing the daily increase in radius during that period.
Part A: To determine a reasonable domain to plot the growth function, we need to consider the context of the problem. The biologist's equation for the radius of the algae is given by f(d) = 7(1.06)^d, where d represents the number of days.
Since time (d) cannot be negative or non-existent, the domain for the growth function should be restricted to positive values.
Additionally, we can assume that the growth function is applicable within a reasonable range of days that align with the biologist's study. It's important to note that the given equation does not impose any upper limit on the number of days.
Based on the information given, a reasonable domain for the growth function would be d ≥ 0, meaning the number of days should be greater than or equal to zero.
This allows us to include the starting point of the study and extends the domain indefinitely into the future, accommodating any potential growth beyond the conclusion of the study.
Part B: The y-intercept of a function represents the value of the dependent variable (in this case, the radius of the algae) when the independent variable (days, d) is zero. In the given equation, f(d) = 7(1.06)^d, when d = 0, the equation becomes:
f(0) = 7(1.06)^0
f(0) = 7(1)
f(0) = 7
Therefore, the y-intercept of the graph of the function f(d) is 7. In the context of the problem, this means that when the biologist started her study (at d = 0), the radius of the algae was approximately 7 mm.
Part C: To calculate the average rate of change of the function f(d) from d = 4 to d = 11, we need to find the slope of the line connecting the two points on the graph.
Let's evaluate the function at d = 4 and d = 11:
f(4) = 7(1.06)^4
f(4) ≈ 7(1.26)
f(4) ≈ 8.82 mm
f(11) = 7(1.06)^11
f(11) ≈ 7(1.81)
f(11) ≈ 12.67 mm
The average rate of change (slope) between these two points is given by the difference in y-values divided by the difference in x-values:
Average rate of change = (change in y) / (change in x)
= (12.67 - 8.82) / (11 - 4)
= 3.85 / 7
≈ 0.55 mm/day
The average rate of change of the function f(d) from d = 4 to d = 11 is approximately 0.55 mm/day. This represents the average daily increase in the radius of the algae during the period from day 4 to day 11.
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The following set of data is for the measurement of the mass of Ca in g in a solid sample with an average total mass of 4.3382 ± 0.0054 g.
0.3775, 0.3795, 0.3788, 0.3762, 0.3802
a. Calculate the mean, standard deviation, and relative standard deviation for the mass of Ca in g.
b. Using the average total mass and standard deviation is given, calculate the average percent weight of Ca and standard deviation in the percent weight? You will need to use propagation of error to get the standard deviation of the percent weight Ca. From the average and standard deviation, calculate the RSD and 95% confidence interval of the percent weight Ca also.
a. The mean mass of Ca in the solid sample is 0.3784 g with a standard deviation of 0.0014 g and a relative standard deviation of 0.37%.
b. The average percent weight of Ca in the solid sample is 8.73% with a standard deviation of 0.32%. The 95% confidence interval for the percent weight of Ca is 8.09% to 9.37%.
To calculate the mean mass of Ca in the solid sample, we sum up the individual measurements and divide by the total number of measurements. Adding the given values, we get a sum of 1.8912 g. Dividing this sum by 5 (the number of measurements) gives us the mean mass of Ca as 0.3784 g.
To calculate the standard deviation, we subtract the mean from each individual measurement, square the differences, sum up the squared differences, divide by the total number of measurements minus 1 (in this case, 4), and take the square root of the result. This gives us a standard deviation of 0.0014 g.
The relative standard deviation (RSD) is calculated by dividing the standard deviation by the mean and multiplying by 100 to express it as a percentage. In this case, the RSD for the mass of Ca is 0.37%.
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Factor -1.75 out of -14m - 5.25n
Answer:
Step-by-step explanation:
-14m - 5.25n = (-1.75*8)m + (-1.75 * 3)n
= (-1.75) [ 8m + 3n)
help plsss!!!
For which interval is the function constant?
(2, 6)
(6, ∞)
(−∞, 0)
(0, 2)
9514 1404 393
Answer:
(a) (2, 6)
Step-by-step explanation:
The function is constant where its graph is horizontal. That portion of the graph lies between x=2 and x=6. In interval notation, the function is constant in the interval (2, 6).
Jim makes $5 an hour at the surf shop. His boss gives him a one-time bonus of $50. Sarah makes $8 an hour at the clothes store. Her boss givers her a one-time bonus of $14. If they both work 15 hours, who will have a bigger paycheck?
Answer:
Sarah had the bigger paycheck of $134
Step-by-step explanation:
First we would need to find the total amount of money each one of them made in those 15 hours. We do this by multiplying their hourly rate by the hours worked and then adding the bonus
Jim: (5*15) + 50 = x
75 + 50 = x
125 = x
Sarah: (8 * 15) + 14 = x
120 + 14 = x
134 = x
Finally, we can say that Sarah had the bigger paycheck of $134 which is $9 more than Jim's
wilson bought a painting for x dollars. after 1 year, the value of the painting increased by 5%. which expression best represents the new value of the painting?
A. 0.05x
B. 1.05x
C. 1.5x
D. 5x
Thus, the expression that best represents the new value of the painting is 1.05x (option B).
Wilson bought a painting for x dollars. After one year, the value of the painting increased by 5%. The expression that best represents the new value of the painting is option B, 1.05x.
What is an expression?
An expression is a mathematical phrase made up of numbers, operations, and/or variables. It doesn't include any equals sign and cannot be solved since it doesn't provide a specific value.The given expression represents the new value of the painting after an increase of 5% in its original price. Therefore, the new price of the painting is 1.05 times the original price.Wilson bought a painting for x dollars, so the new value of the painting will be given by:
New value = original value + 5% of the original value
New value = x + (5/100)xNew value = x + 0.05xNew value = 1.05x.
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The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
Answer:
The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
Step-by-step explanation:
The volume of a triangular pyramid is 24 cubic inches. The base is a right triangle with a length
of 4 inches and height of 3 inches. What is the height of the pyramid, in inches?
three circles of radius are drawn in the first quadrant of the -plane. the first circle is tangent to both axes, the second is tangent to the first circle and the -axis, and the third is tangent to the first circle and the -axis. a circle of radius is tangent to both axes and to the second and third circles. what is ?
The value of r/s is equal to 9.
There exists a theorem that states that the square of a hypotenuse in a right-angled triangle is equal to the sum of squares of the perpendicular side and the base side. This theorem is known as Pythagoras theorem. By applying Pythagoras' theorem in this right-angled triangle formed in our image, we obtain the given formula
\(H^2 = P^2 + B^2\)
\((r + s)^2 = (r - s)^2 + (r - 3s)^2\)
\(r^2 + 2r.s + s^2 = 2r^2 - 8r.s + 10.s^2\)
\(r^2 - 10.r.s + 9s^2 = 0\)
(r - 9s) (r - s) = 0
Now we will equate these two factors to 0.
By equating, we get r/s = 9 and r/s = 1.
r/s = 1 does not apply to the geometry in this question.
So, r/s = 9 is the solution for the given equation.
Therefore, our answer is 9.
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The complete question is -
"Three circles of radius s are drawn in the first quadrant of the xy-plane. The first circle is tangent to both axes, the second is tangent to the first circle and the x-axis, and the third is tangent to the first circle and the y-axis. A circle of radius r>s is tangent to both axes and to the second and third circles. What is r/s? "
A florist has 72 red roses and 40 white roses. If the florist creates the greatest number of identical bouquets possible with a combination of red and white roses without any roses leftover, how many white roses are in each bouquet?.
The number of white roses left in each bouquet is 5.
Explain the term Greatest Common Factor?A group of numbers' greatest common factor (GCF) is the biggest factor that almost all numbers have in common. The biggest number it is a factor for two or more integers is known as the GCF.You must identify the most prevalent common factor for this task (GCF).
The actions are:
1. Divide the supplied numbers into prime factors.2. Select the usual ones, then multiply them.The florist's stock of 72 red roses with 40 white roses reveals what the most common factor is, which is:
72 = 2×2×2×3×3 = 2³×3²
40 = 2×2×2×5 = 2³×5
GCF = 2³
Divide this number of white roses in the first bouquet (40 roses) first by Greatest Common Factor to get how many white roses are in each arrangement.
The result is:
= 40 white roses / 8
= 5 white roses
Thus, number of white roses left in each bouquet is 5.
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How many triangles exist with the given angle measures?
60°, 60°, 60°
A. Exactly one unique triangle exists with the given angle measures.
B. No triangle exists with the given angle measures.
C. More than one unique triangle exists with the given angle measures.
Answer:
The sum of the angles in a triangle is 180°, so the angles do form a triangle. Since two of the three angles are congruent, the triangle is an isosceles triangle. An infinite number of isosceles triangles exist with different side lengths. Therefore, more than one triangle exists with the given angle measures.