Answers
To solve the for x the equation will be 3x° = 80° - x° and the value of x is 20°.
When two or more lines meet at a common point it is known as intersecting lines.
According to the question we have been given that there are two lines who are intersection at a point. And we have been given measure of two angles.
Let the first angle be given as ∠A and the second angle be given as ∠B.
The measure of angles given to us are :
∠A = 3x° and ∠B = (80 - x)°
We know that when two lines intersect then the vertically opposite angles are equal, that is
∠A = ∠B
Putting the required values we get
3x° = 80° - x°
4x° = 80°
x = 20°
Hence the value of x = 20°. Thus the measure of ∠A = 60° and ∠B = 60°
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Related Questions
The optimal amount of x1, x2, P1, P2 and income are given by the
following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I
=4189 The new price of P1 is the foll
Answers
The total change in the consumed quantity of x₁ as per given price and income is equal to 213.
x₁ = (21/7)P₁
x₂ = (51/7)P₂
P₁ = 10
P₂ = 5
P₁' = 81
To calculate the total change in the quantity consumed of x₁ when the price of P₁ changes from P₁ to P₁',
The difference between the quantities consumed at the original price and the new price.
Let's calculate the quantity consumed at the original price,
x₁ orig
= (21/7)P₁
= (21/7) × 10
= 30
x₂ orig
= (51/7)P₂
= (51/7) × 5
= 36.4286 (approximated to 4 decimal places)
Now, let's calculate the quantity consumed at the new price,
x₁ new
= (21/7)P1'
= (21/7) × 81
= 243
x₂ new
= (51/7)P2
= (51/7) × 5
= 36.4286
The total change in the quantity consumed of x₁ can be calculated as the difference between the new quantity and the original quantity,
Change in x₁
= x₁ new - x₁ original
= 243 - 30
= 213
Therefore, the total change in the quantity consumed of x₁ is 213.
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The above question is incomplete, the complete question is:
The optimal amount of x1, x2, P1, P2 and income are given by the following:
x1= 21/ 7p1 x2= 51 / 7p2
The original prices are: P1=10 P2=5 The original income is: I =4189 The new price of P1 is the following: P1'=81 Assume that the price of x1 has changed from P1 to P1'. What is the total change in the quantity consumed of x1?
Please answer step by step
m∠1 =?
m∠2 = ?
m∠3 = ?
Answers
2 would be 121
3 would be 47
Answer:
1= 31 degrees
2= 121 degrees
3= 47 degrees
Step-by-step explanation:
IMPORTANT: SUM OF ALL THREE ANGLES OF A TRIANGLE EQUAL 180
For angle 1 we add 59+90 since those are the 2 known angles
90+59=149
Now subtract by 180
180-149=31
Angle 1 is equal to 31
Now for angle 2 we subtract 59 from 180 since it is on a flat surface the sum of those angles will equal 180 degrees
180-59=121
Angle 2 is 121 degrees
Now for angle 3 we add 121 and 12 since we know those 2 angles
121+12=133
Now subtract from 180
180-133= 47
Angles 3 is 47 degrees
Hopes this helps please mark brainliest
What information would you need to use the Side-Angle-Side Similarity Theorem to prove that the triangles are similar
Answers
With these three pieces of information, you can apply the SAS Similarity Theorem to conclude that the triangles are similar.
To use the Side-Angle-Side (SAS) Similarity Theorem to prove that two triangles are similar, you would need the following information:
1. Side-Side Ratio: You need to know that the ratio of the lengths of corresponding sides of the triangles is equal.
2. Angle: You need to know that the included angle between the corresponding sides of the triangles is equal.
3. Side: You need to know that one pair of corresponding sides of the triangles is proportional.
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Reggie wants to join a gym and spend no more than $250 per year. There is a $40 registration fee, and then he will be charged a fee each month for 12 months. Which inequality shows the relationship between the monthly fee (x), the registration fee, and Reggie’s $250 limit?
I REALLY NEED HELP!!!
Answers
Monthly fee for 12 months will be represented as 12x
Therefore
250>40+12x
Use the Secant method with p0=−0.5,p1=−0.8 to find the solution of m(x)=2sin(x) accurate within 10^−1
a. 0.7032 b. 1.5211
c. 1.8012 d. −0.7032
e. 1.7502
Answers
Using the Secant method with initial guesses p0 = -0.5 and p1 = -0.8, the solution of the equation m(x) = 2sin(x) accurate within 10^-1 is approximately 1.5211.
This method was chosen because it is an iterative numerical method that provides a good approximation of the root without requiring the derivative of the function.
The Secant method is an iterative numerical method used to find roots of equations. It is similar to the Newton-Raphson method but does not require the computation of the derivative.
To apply the Secant method, we start with two initial guesses, p0 and p1, which are -0.5 and -0.8 in this case. We then iterate using the formula:
p_{n+1} = p_n - f(p_n) * (p_n - p_{n-1}) / (f(p_n) - f(p_{n-1})),
where p_n and p_{n-1} are the current and previous approximations, and f(p_n) is the function value at p_n.
In this case, the function m(x) = 2sin(x) is given, and we need to find a solution accurate within 10^-1. We start with initial guesses p0 = -0.5 and p1 = -0.8.
We then evaluate the function at p0 and p1 to get f(p0) = 2sin(-0.5) and f(p1) = 2sin(-0.8).
Next, we substitute the values into the Secant formula to compute p2:
p2 = p1 - f(p1) * (p1 - p0) / (f(p1) - f(p0)).
We repeat this process until we reach a desired level of accuracy or convergence.
Using this method, we find that the solution accurate within 10^-1 is approximately 1.5211.
The Secant method is chosen in this case because it does not require the derivative of the function, making it suitable when the derivative is difficult to compute. Additionally, it provides a good approximation of the root even with initial guesses that are not as close to the actual root. Therefore, it is a suitable choice for finding the solution of the given equation accurate within 10^-1.
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Maricella solves for x in the equation 4 x minus 2 (3 x minus 4) + 4 = negative x + 3 (x + 1) + 1. She begins by adding –4 + 4 on the left side of the equation and 1 + 1 on the right side of the equation. Which best explains why Maricella’s strategy is incorrect?
The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
In order to combine like terms on one side of the equation, the inverse operation must be used.
When the problem is worked in the correct order, the numbers that Maricella added are not actually like terms.
Maricella did not combine all three constants on both sides of the equation; she combined only two.
Answers
Answer:
The multiplication that takes place while distributing comes before addition and subtraction in order of operations.
Step-by-step explanation:
edge 2020
Answer:
A
Step-by-step explanation:
please helpppppppppppppppppppppppppppppppppppppppp
Convert the following fractions into percent and decimals.
1/4, 1/25 , 1/6 , 1/3
Answers
Answer:
1/4 is 0.25
1/25 is .04
1/6 is 0.16
1/3 is 0.3
A boy wants to carve a figure of Robert E. Lee. If Robert E. Lee was 5 ft. 10 in. tall, what should the scale be if the boy wants his figure to be 10 in. tall? a. 1 in. : 5 in. b. 1 in.: 1 ft. c. 1 in. : 5.83 in. d. 1 in.: 10 in. e. 1 in. : 7 in.
Answers
Given data:
The given height of Robert E.Lee is H=5 feet 10 inches.
The given height in inches.
\(\begin{gathered} H=5(12\text{ in) +10 in} \\ =70\text{ in} \end{gathered}\)The given height must be 10 in according to the scale.
\(\begin{gathered} 10\text{ in = 70 in} \\ 1\text{ in =7 in} \end{gathered}\)Thus, the scale represents 1 in :7 in, so the last
6 9/10
Round the mixed number to the nearest whole number
Answers
Answer:
7Step-by-step explanation:
it says round to the "nearest WHOLE NUMBER", not nearest ten, or nearest 10th, but whole number (like 1, 2, 3, 4, 5, 78) therefore, 6 and 9/10 rounds to 7 because 9/10 is more than half (it must be 5/10 or more), it rounds 6 up one number, making it 7.
What is the complementary angle of an angle that measures 30 degrees?
Answers
Answer:
60
Step-by-step explanation:
Complementary angles means that the angles add up to 90 degrees
So the complementary of 30 is 60
30+60=90
Let the other Complementary Angle be x,
We know that, Sum of Complementary Angles = 90°
therefore,
\(x + 30\degree = 90\degree\)\(x = 90\degree - 30\degree\)\(x = 60\degree\)Thirty more than one half of the students at at canyon middle school are in band.Five less than three fifths of the students are in athletics.If the number of students who are in band is equal to the number of students in athletics how many students are enrolled in canyon middle school
Answers
Answer:
Students at canyon middle school = 350
Step-by-step explanation:
Students at canyon middle school = x
Band = 1/2x + 30
Athletics = 3/5x - 5
athletics.If the number of students who are in band is equal to the number of students in athletics
1/2x + 30 = 3/5x - 5
1/2x - 3/5x = -5 - 30
5x-6x/10 = -35
-x/10 = -35
= -x(1/10)= -35
x = -35 ÷ -1/10
= -35 × -10/1
= 350
x = 350
Students at canyon middle school = 350
what is meant by each additive term must have the same units
Answers
The each additive term must have the same units means that the units of measurement used for each term must be the same
In mathematics and physics, an additive term refers to a term that is added to another quantity to obtain a sum
When we say that each additive term must have the same units, we mean that the units of measurement used for each term must be the same. This is because when we add or subtract quantities, they must be expressed in the same units.
Similarly, when we have an expression with multiple additive terms, such as "5 kg + 2.5 g + 7 lbs", we need to convert each term to the same unit before adding them together. In this example, we could convert the grams to kilograms or the pounds to kilograms, so that all terms are in the same unit of measurement.
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Simplify the expression 3x•(7•x) explain
Answers
Steps to solve:
3x * (7 * x)
~Simplify
3x * 7x
~Combine like terms
21x
Best of Luck!
Multiply x and to get x^2
3x^2*7
Multiply 3 and 7
21x^2
using the clausius‐clapeyron equation determine what variables related to the measured values would be graphed on the x and y axes, along with what m and b would represent.
Answers
In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.
Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.
The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.
The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.
By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.
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81 + 7x² +8yt-sx
if x = 2 what is the answer
Answers
ANSWER:
109 + 8yt - 2s
WORKING:
81 + 7x² + 8yt - sx
81 + 7(2)² + 8yt - s(2)
81 + 7(4) + 8yt - 2s
81 + 28 + 8yt - 2s
81 + 28 + 8yt - 2s
109 + 8yt - 2s
Freemont Run Club surveyed a random sample of 303030 of their members about their running habits. Of the members surveyed, 999 said that they run more than 555 days a week. There are 848484 Freemont Run Club members.
Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 555 days a week?
Answers
Answer:
the answer is 25 according to Khan
Step-by-step explanation:
Please Help! 60 points for a rapid reply- please look at the question below= The Figure of circle A shown has a diameter of PR which intersects with QS at point B and the measurements shown, Calculate the following measures-
Answers
The measures in the circle given in the image above are calculated as:
1. m<PSQ = 130°; 2. m<AQS = 30°; 3. m(QR) = 100°; 4. m(PS) = 110°; 5. (RS) = 70°.
How to Find the Measures in the Circle?In order to find the measures in the circle shown, recall that according to the inscribed angle theorem, the measure of intercepted arc is equal to the central angle, but is twice the measure of the inscribed angle.
1. m<PSQ = m<PAQ
Substitute:
m<PSQ = 130°
2. Find m<PBQ:
m<PBQ = 1/2(m(PQ) + m(RS)) [based on the angles of intersecting chords theorem]
Substitute:
m<PBQ = 1/2(130 + 2(35))
m<PBQ = 100°
m<AQS = 180 - [m<BAQ + m<PBQ]
Substitute:
m<AQS = 180 - [(180 - 130) + 100]
m<AQS = 30°
3. m(QR) = m<QAR
Substitute:
m(QR) = 100°
4. m(PS) = 180 - m(RS)
Substitute:
m(PS) = 180 - 2(35)
m(PS) = 110°
5. m(RS) = 2(35)
m(RS) = 70°
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Management at Kelsh is pondering the elimination of the North Division. If the North Division were eliminated, its traceable fixed expenses could be avoided. The total common corporate expenses would be unaffected. Given this data, you will advise:
Answers
Based on the given data, it is advisable for management at Kelsh to eliminate the North Division in order to avoid the traceable fixed expenses associated with it, while keeping the total common corporate expenses unaffected.
When considering the elimination of a division, it is crucial to analyze the impact on expenses and overall profitability. In this case, the information states that if the North Division is eliminated, its traceable fixed expenses can be avoided. Traceable fixed expenses refer to the costs that are directly associated with a specific division or segment of a company. By eliminating the North Division, Kelsh can avoid incurring these interests, potentially improving the company's financial performance.
Furthermore, the data states that the total common corporate expenses would be unaffected by the elimination of the North Division. Common corporate expenses are costs incurred at the corporate level that are not directly attributable to any specific division or segment.
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The square footage and monthly rental of 10 similar one-bedroom apartments yield the linear regression
equation y 0.7752 +950.25 where x represents the square footage of the apartment and y represents the
monthly rental price.
Joey can afford $1,500 per month for rent. Using the given equation, what size apartment should he expect
to be able to rent for that price?
Round to the nearest square foot
Answers
The footage of the room with a rental price of $1500 is 709 square foot
Linear equationA linear equation is given by:
y = mx + bwhere m is the rate of change, b is the initial value of y, y, x are variables.
Let y represent the monthly rental price and x represent the square footage. Given the equation:
y = 0.7752x + 950.25
For a rent of $1500:
1500 = 0.7752x + 950.25
x = 709 square foot.The footage of the room with a rental price of $1500 is 709 square foot
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Find the perimeter of ABC with vertices A (-4, 4) , B(2,- 2) , and C(-4, - 2)
Round your answer to the nearest hundredth. The perimeter of ABC is about what Units ?
Answers
Answer:
20.49 units
Step-by-step explanation:
Apply the distributive property to create an equivalent expression.
(6e - 3f - 4)\cdot 2 =(6e−3f−4)⋅2=? #algebra
Answers
Answer:
12e - 6f -8
Step-by-step explanation:
(6e−3f−4)⋅2
Multiply the 2 by each term inside the parentheses
2*6e -2*3f -4*2
12e - 6f -8
miss austin gives her class 6 sets of data and asks them to identify which data set can most accurately be summarized by the mean. what topic is she covering?
Answers
Miss Austin is covering the topic of central tendency in statistics, specifically the mean. By giving her class 6 sets of data and asking them to identify which one can be most accurately summarized by the mean, she is testing their understanding of how the mean represents the average value of a set of data.
This also involves understanding how to calculate the mean and interpret its value in relation to the other values in the dataset. Therefore, Miss Austin is helping her class develop skills in data analysis and statistical reasoning. The use of the term "set" is not clear, but assuming it means "sets of data," it is relevant to the topic being covered.
Miss Austin is covering the topic of "Descriptive Statistics" in her class. Specifically, she is focusing on the concept of "mean" as a measure of central tendency to summarize data sets. By asking her students to identify which data set can most accurately be summarized by the mean, she is teaching them how to understand the appropriateness of using the mean for different sets of data.
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What is the median of the data set?
A. 49
B. 86
C. 87
D. 85
Answers
The value of the median of the data set is,
⇒ 86
We have to given that;
Math test score are shown in figure.
Here Number of values are 21
Hence, The value of the median of the data set is,
⇒ (21 + 1)/2
⇒ 22/2
⇒ 11th term
⇒ 8 | 6
⇒ 86
Hence, The value of the median of the data set is,
⇒ 86
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If A and B are any two events defined on a sample space S of an experiment, then p(A ∩ B) = p(A).p(B)
True or False
Answers
The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.
This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).
If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).
Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.
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x2 +16x – 36/x2 + 6x-16
Answers
Answer:
x^4+23x^3-16x^2-36/x^2
Step-by-step explanation:
Answer:
\(\frac{x+18}{x+8}\)
Step-by-step explanation:
Assuming you require the simplification.
Given
\(\frac{x^2+16x-36}{x^2+6x-16}\) ← factorise numerator and denominator
= \(\frac{(x+18)(x-2)}{(x+8)(x-2)}\) ← cancel the common factor (x - 2)
= \(\frac{x+18}{x+8}\)
In \triangle LMN,△LMN, \angle N \cong \angle M,∠N≅∠M, LM = 14LM=14 and MN = 8MN=8. Find the length of NL.NL.
Answers
Answer:
11.5
Step-by-step explanation:
We solve using :
Pythagoras Theorem
LM² = MN² + NL²
NL² = LM² - MN²
NL = √LM² - MN²
NL = √14² - 8²
NL = √(132)
NL = 11.489125293
NL = 11.5
Therefore, the length of NL = 11.5
For the following set of data, find the percentage of data within 2 population standard
deviations of the mean, to the nearest 10th of a percent.
103, 57, 55, 61, 58, 58, 57, 54, 54
copy values for calculator
open statistics calculator
Answers
Approximately 66.7% of the data falls within 2 population standard deviations of the mean.
To find the percentage of data within 2 population standard deviations of the mean for the given set of data, we need to calculate the mean and standard deviation of the data set and then determine the percentage of data within the specified range. The final answer will provide the percentage to the nearest tenth of a percent.
To calculate the percentage of data within 2 population standard deviations of the mean, we follow these steps:
1. Calculate the mean (average) of the data set.
2. Calculate the standard deviation of the data set.
3. Determine the lower and upper limits of the range by subtracting and adding twice the standard deviation to the mean, respectively.
4. Count the number of data points that fall within the range.
5. Divide the number of data points within the range by the total number of data points.
6. Multiply the result by 100 to obtain the percentage.
Let's calculate the values:
1. Mean:
Sum of data = 103 + 57 + 55 + 61 + 58 + 58 + 57 + 54 + 54 = 557
Mean = Sum of data / Number of data points = 557 / 9 = 61.89 (rounded to two decimal places)
2. Standard Deviation:
Calculate the differences between each data point and the mean, square them, sum the squares, divide by the number of data points, and take the square root.
Standard Deviation = √((∑(xi - x)^2) / n) = √((165.56 + 18.36 + 40.96 + 0.04 + 5.76 + 5.76 + 18.36 + 45.76 + 45.76) / 9) ≈ 12.43
3. Lower Limit: Mean - (2 * Standard Deviation) ≈ 61.89 - (2 * 12.43) ≈ 36.03
Upper Limit: Mean + (2 * Standard Deviation) ≈ 61.89 + (2 * 12.43) ≈ 87.75
4. Count the number of data points within the range: 6 (57, 55, 58, 58, 57, 54)
5. Percentage within the range: (6 / 9) * 100 ≈ 66.7%
Therefore, approximately 66.7% of the data falls within 2 population standard deviations of the mean.
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Which function has a domain of x 25 and a range of y s3?
Answers
Answer:
Step-by-step explanation:
The function has a domain x ≥ 5.
This is because the function remains real for (x - 5) ≥ 0 as negative within the square root is imaginary.
Hence, (x - 5) ≥ 0
⇒ x ≥ 5
Now, for all x values that are greater than equal to 5 the value of will be negative.
So,
⇒
⇒ y ≤ 3
Therefore, the range of the function is y ≤ 3. (Answer)
Note: Thanks rani
ASAP find both x and y please!!
Answers
Answer:
y = 4√6
x = 12√2
Step-by-step explanation:
See the attached image for a graphical representation of the rule regarding 30-60-90 triangles:
If the triangle's short leg is x, then the long leg is x√3, and the hypotenuse is 2x.
In the given triangle, we can see that the hypotenuse is 8√6, y is the short leg, and x is the long leg.
To solve for x and y, we can work backwards.
y is half the hypotenuse (8√6)
2y = 8√6
y = (8/2) · √6
y = 4√6
x is y times root 3
x = y√3
x = (4√6)(√3)
x = 4 · √18
x = 4 · 3√2
x = 12√2
A survey found that 37 of 77 randomly selected women and 44 of 85 randomly selected men follow a regular exercise program. Find a 95% confidence interval for the difference between the proportions of women and men who follow a regular exercise program. Please check assumptions and interpret the interval.
Answers
To proceed with this analysis, we assume that the individuals in the sample were randomly selected and that the samples are independent.
Additionally, the sample sizes are large enough to apply the normal approximation to the sampling distribution of the difference in proportions.Using these assumptions, we can calculate the confidence in is 37/77 ≈ 0.481. The proportion of men who follow a regular exercise program is 44/85 ≈ 0.518. The difference between these proportions is 0.518 - 0.481 ≈ 0.037.
The 95% confidence interval for the difference in proportions can be calculated using the formula: difference ± (critical value) * sqrt[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)] where p1 and p2 are the proportions of women and men, n1 and n2 are the respective sample sizes, and the critical value corresponds to a 95% confidence level. Performing the calculations, the 95% confidence interval for the difference in proportions is approximately 0.037 ± 0.129, which gives us a range from -0.092 to 0.166.
Interpreting this interval, we can say that with 95% confidence, the true difference between the proportions of women and men who follow a regular exercise program lies within the range of -0.092 to 0.166. This means that there is insufficient evidence to conclude that there is a significant difference in the proportions of women and men who follow a regular exercise program. The interval includes zero, indicating that the difference could be negligible or non-existent.
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