At what point do the curves r₁(t) = ⟨t, 1 − t, 3 + t ²⟩ and r2(s) = ⟨3 − s, s − 2, s²⟩ intersect? Find their angle of intersection correct to the nearest degree.
Answers
We need to equate the corresponding components of the two curves and solve for the common parameter values, the point of intersection between the curves is (2, -1, 7), and the angle of intersection is approximately 135 degrees.
Equating the x-components gives us t = 3 - s.
Equating the y-components gives us 1 - t = s - 2.
Solving these two equations simultaneously, we find t = 2 and s = 1.
Substituting these parameter values back into one of the original curves, we find the point of intersection: r₁(2) = ⟨2, -1, 7⟩.
To find the angle of intersection, we can calculate the dot product of the tangent vectors of the curves at the point of intersection and then use the dot product formula: cosθ = (v₁ · v₂) / (|v₁| |v₂|).
The tangent vectors of the curves at the point of intersection are r₁'(2) = ⟨1, -1, 4⟩ and r₂'(1) = ⟨-1, -1, 2⟩. Calculating their dot product gives us -5.
Using the magnitudes of the tangent vectors, we have |r₁'(2)| = √18 and |r₂'(1)| = √6.
Plugging these values into the formula, we get cosθ = -5 / (√18 √6).
Using a calculator, we find the value of cosθ to be approximately -0.631.
To find the angle θ, we take the inverse cosine (arccos) of -0.631, which is approximately 135 degrees.
Therefore, the point of intersection between the curves is (2, -1, 7), and the angle of intersection is approximately 135 degrees.
To learn more about angle of intersection click here: brainly.com/question/15892963
#SPJ11
Related Questions
Consider two variable linear regression model : Y = a + Bx+u The following results are given below: EX= 228, EY; = 3121, EX;Y₁ = 38297, EX² = 3204 and Exy = 3347-60, Ex? = 604-80 and Ey? = 19837 and n = 20 Using this data, estimate the variances of your estimates.
Answers
The estimated variance of B is 0.000014 and the estimated variance of a is 26.792.
To estimate the variances of the parameter estimates in the linear regression model, we can use the following formulas:
Var(B) = (1 / [n * EX² - (EX)²]) * (EY² - 2B * EXY₁ + B² * EX²)
Var(a) = (1 / n) * (Ey? - a * EY - B * EXY₁)
Given the following values:
EX = 228
EY = 3121
EXY₁ = 38297
EX² = 3204
Exy = 3347-60
Ex? = 604-80
Ey? = 19837
n = 20
We can substitute these values into the formulas to estimate the variances.
First, let's calculate the estimate for B:
B = (n * EXY₁ - EX * EY) / (n * EX² - (EX)²)
= (20 * 38297 - 228 * 3121) / (20 * 3204 - (228)²)
= 1.331
Next, let's calculate the variance of B:
Var(B) = (1 / [n * EX² - (EX)²]) * (EY² - 2B * EXY₁ + B² * EX²)
= (1 / [20 * 3204 - (228)²]) * (3121² - 2 * 1.331 * 38297 + 1.331² * 3204)
= 0.000014
Now, let's calculate the estimate for a:
a = (EY - B * EX) / n
= (3121 - 1.331 * 228) / 20
= 56.857
Next, let's calculate the variance of a:
Var(a) = (1 / n) * (Ey? - a * EY - B * EXY₁)
= (1 / 20) * (19837 - 56.857 * 3121 - 1.331 * 38297)
= 26.792
To know more about variance,
brainly.com/question/28426562
#SPJ11
when the consumption schedule lies below the 45-degree reference line, saving:
Answers
When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.
How to explain the informationThe consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.
In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.
Learn.more about consumption
https://brainly.com/question/30623688
#SPJ4
When the consumption schedule lies below the 45-degree reference line, saving what does it means?
The annual per capita consumption of bottled water was 30.9 gallons. Assume that the per capita consumption of bottled water is approximately normally distributed with a mean of 30.9 and a standard deviation of 10 gallons.
a. What is the probability that someone consumed more than 36 gallons of bottled water?
b. What is the probability that someone consumed between 30 and 40 gallons of bottled water?
c. What is the probability that someone consumed less than 30 gallons of bottled water?
d.90% of people consumed less than how many gallons of bottled water?
Answers
The probability that someone consumed > 36 gallons of bottled water is 27.09%. The probability that someone consumed between 30 and 40 gallons of bottled water is 63.72%.
The per capita consumption of bottled water is normally distributed with a mean of 30.9 gallons and a standard deviation of 10 gallons.
The formula to find the probability that someone consumed more than 36 gallons of bottled water is:
P(X > 36) = 1 - P(X ≤ 36)
By plugging in the values, we have:
P(X > 36) = 1 - P(Z ≤ (36 - 30.9) / 10) = 1 - P(Z ≤ 0.61)
From the z-table, we find that the probability of Z ≤ 0.61 is 0.7291.
Therefore, P(X > 36) = 1 - 0.7291 = 0.2709 or 27.09%.
The formula to find the probability that someone consumed between 30 and 40 gallons of bottled water is:
P(30 ≤ X ≤ 40) = P(Z ≤ (40 - 30.9) / 10) - P(Z ≤ (30 - 30.9) / 10)
By plugging in the values, we have:
P(30 ≤ X ≤ 40) = P(Z ≤ 0.91) - P(Z ≤ -0.91)
From the z-table, we find that the probability of Z ≤ 0.91 is 0.8186 and the probability of Z ≤ -0.91 is 0.1814.
Therefore, P(30 ≤ X ≤ 40) = 0.8186 - 0.1814 = 0.6372 or 63.72%.
The formula to find the probability that someone consumed less than 30 gallons of bottled water is:
P(X < 30) = P(Z ≤ (30 - 30.9) / 10)
By plugging in the values, we have:
P(X < 30) = P(Z ≤ -0.09)
From the z-table, we find that the probability of Z ≤ -0.09 is 0.4641.
Therefore, P(X < 30) = 0.4641 or 46.41%.
We need to find the z-score for the 90th percentile. From the z-table, we find that the z-score for the 90th percentile is 1.28. Therefore, we can find the corresponding value of X by using the formula:
X = μ + zσ
By plugging in the values, we have:
X = 30.9 + 1.28(10) = 44.88
Therefore, 90% of people consumed less than 44.88 gallons of bottled water.
In conclusion, the probability that someone consumed more than 36 gallons of bottled water is 27.09%. The probability that someone consumed between 30 and 40 gallons of bottled water is 63.72%. The probability that someone consumed less than 30 gallons of bottled water is 46.41%. Finally, 90% of people consumed less than 44.88 gallons of bottled water.
Learn more about probability visit:
brainly.com/question/11461187
#SPJ11
HElLP me PLZ 20 points but give the answer
Answers
Answer:
YOU GOT THIS!
Answer:
m = 5g
g = 1/5m
Step-by-step explanation:
The areas of two similar triangles are 144 cm² and 81 cm. If one side of the first triangle is 6 cm, what is the length of the corresponding side of the second?
Answers
Answer:
4.5 centimeters
Step-by-step explanation:
For the triangle with area 144 square cm:
144 = (1/2)(6)x
144 = 3x, so x = 48 cm
So for the triangle with area 81 square cm:
(1/2)(x)(8x) = 81
4x^2 = 81
x^2 = 81/4 so x = 9/2 = 4.5 cm and
8x = 36 cm
Answer:
4.5
Step-by-step explanation:
use ratio method to form the equation (X/6)^2=81/144solvethe principal of a high school wants to gather opinions from the parents of students at his school. he starts with the 2nd name in the parents teacher association (pta) phone handbook and then selects every 5th name in the directory. the 2nd, 7th, 12th, … names in the directory are chosen for his sample. this is an example of a/an sample.
Answers
This example is an part of systematic sampling.
What are the advantages and disadvantages of systematic sampling ?Simple to Use and Understand.A sense of process and control.Clustered Selection is no longer used.Low risk componentassumes it is possible to estimate the population size.Natural Degree of Randomness is required.Data Manipulation Risk is Greater.
Disadvantage
A population must be closely approximated for this procedure to work.Some populations are able to recognize the sample pattern.A little likelihood of selection is produced.There is a significant risk of data manipulation.In comparison to random sample, systematic sampling is less random.To learn more about systematic sampling, visit
brainly.com/question/13600657
#SPJ4
List the domain and range of the inverse trig functions using interval notation and radians for angles. sin^(-1)(x) Domain: Range: cos^(-1)(x) Domain: Range: tan^(-1)(x) Domain: Range:
Answers
For the \(sin^{-1}x\), domain is [-1, 1], and range is [\(-\pi /2, \pi /2\)] .
For the \(cos^{-1}x\), domain is [-1, 1], and range is [\(0, \pi\)] .
For the \(tan^{-1}x\), domain is [-∞, ∞], and range is [\(-\pi /2, \pi /2\)] .
A function has its inverse only if it is a bijective function.
Sine function is always restricted in its domain [\(-\pi /2, \pi /2\)] and range [-1, 1], thus \(sin^{-1}x\) will have domain is [-1, 1], and range is [\(-\pi /2, \pi /2\)] .
Cosine function is always restricted in its domain [\(0, \pi\)] and range [-1, 1], thus \(cos^{-1}x\) , will have domain is [-1, 1], and range is [\(0, \pi\)] .
Tangent function is always restricted in its domain [\(-\pi /2, \pi /2\)] and range [-∞, ∞]. Thus \(tan^{-1}x\), will have domain is [-∞, ∞], and range is [\(-\pi /2, \pi /2\)] .
To know more about Tangent refer the link https://brainly.com/question/19064965
#SPJ4
2. Gamma Tail BoundLetXhave the gamma(r, λ)distribution.a)Show thatP(X≥2E(X))≤(2/e)r.[Remember that ifhis a positive function ofx, then the value ofxthat minimizeshis the sameas the value ofxthat minimizes log(h).]b) [CODE]Fixλ= 1. Display overlaid plots of the following three graphs as functions ofr, forrin the interval (0.5, 15)$ :•P(X≥2E(X))•(2/e)r• Markov’s bound onP(X≥2E(X))The code usesplt.plotwhich is also used in Lab 9.The expressionstats.gamma.cdf(x, r,scale=1)evaluates to the cdf of the gamma(r,1)distribution at the pointx
Answers
P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r=> Minimum value of g(x) = g(r) = -1 - r log(r/e) => Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.
a) Let h(x) = e^(-x/r) (x/r)^r P(X≥2E(X)) = P(X/2E(X)≥1) ≥ h(X/2E(X)) = e^(-X/2E(X)) (X/2E(X))^r {By Markov's inequality, for any positive r.v. Y and any positive constant c, P(Y≥c)≤E(Y)/c}
So, P(X≥2E(X)) ≤ E(X)/2E(X) = 1/2
For minimizing log(h), consider g(x) = log(h(x)) = -x/r + r log(x/r)g'(x) = -1/r + r/x = 0 => x = r
=> Minimum value of g(x) = g(r) = -1 - r log(r/e)
=> Maximum value of h(x) = e^-1 [r/e]^r=> P(X≥2E(X)) ≤ [e^(1/e)/2]^r = (2/e)^r b) import matplotlib.pyplot as pltimport numpy as npfrom scipy import statsdef markov(r): return (2/e)**rdef gamma(r): return stats.gamma.cdf(2*stats.gamma.mean(r, scale=1), r, scale=1)def main(): lmbda = 1 r = np.linspace(0.5, 15, 1000) plt.plot(r, gamma(r), label='P(X>=2E(X))') plt.plot(r, [(2/e)**i for i in r], label='(2/e)^r') plt.plot(r, [markov(i) for i in r], label="Markov's bound on P(X>=2E(X))") plt.legend(loc="upper left") plt.show()if __name__ == '__main__': main()The overlaid plots are as follows:
To know more about function,
https://brainly.com/question/30056459
#SPJ11
triangle MNO has vertices at (-3,-8), (2,-8) and (0,-15). translate it up 8 units.
Answers
Answer:
(-3,0) (2,0) (0,-7)
Step-by-step explanation:
Up and Right are addition and Left and Down are subtraction. add 8 to the y coordinates.
Integrate the ODE
dy/dx = x² √y, 0 < x < 2, y(0) = 1
using Euler's method (Δx = 0, 2) to compute y(2). Obtain analytical solution to the ODE and compare y(2) obtained using Euler's method with that obtained analytically.
Answers
we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.
Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:
Step 1: For x = 0, y = 1 (initial condition).
Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.
Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.
Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.
Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.
Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.
Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.
Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.
Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.
Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.
Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.
Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.
To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:
∫(1/√y) dy = ∫x² dx
Integrating both sides gives:
2√y = (1/3)x³ + C
Solving for y:
y = (1/4)(x³ + C)²
Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:
1 = (1/4)(0³ + C)²
1 = (1/4)C²
4 = C²
C = ±2
Since C can be either 2 or -2, the general solution to the ODE is:
y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²
Now, let's evaluate y(2) using the analytical solution:
y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5
Learn more about Integrate here : brainly.com/question/31744185
#SPJ11
Need answer ASAP!! Im really bad at fractions. There were 12 cookies at the bake sale. 4 were sold. The fraction of the cookies left is 8/12 . Reduce the fraction.
Answers
The reduced fraction of 8/12 is 2/3. This means that out of the initial 12 cookies, 8 cookies are left.
To reduce the fraction 8/12, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is the largest number that divides both numbers evenly. In this case, the GCD of 8 and 12 is 4.
Dividing both the numerator and denominator by the GCD, we get:
8 ÷ 4 / 12 ÷ 4 = 2/3
Therefore, the fraction 8/12 is equivalent to 2/3 when reduced.
In conclusion, after reducing the fraction, the fraction of cookies left is 2/3. This means that out of the initial 12 cookies, 4 were sold and there are now 8 cookies remaining.
To learn more about Fractions, visit:
https://brainly.com/question/1622425
#SPJ11
An item sells for $75 and is on sale for 35% off. The sales tax is 9.8%. What is the final cost of the item?
Answers
The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.
The given problem is related to percentage discounts and sales tax and can be solved using the following steps:
Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25
Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75
Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79
Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.
Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54
Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!
For more such questions on final cost
https://brainly.com/question/29509552
#SPJ8
Tell whether w = 16 is a solution of w-12<4.
Answers
Answer:
No, this is not a solution.
Step-by-step explanation:
To solve this you have to substitute 16 into the inequality w - 12 < 4.
Subtracting 12 from 16 gives you 4 which is equal to 4 not less than. So 16 is not a solution to this problem.
NGEROUS MANEUVERS
Somewhere in the Mojave Desert, the army set up training camps
named Arachnid, Feline, Canine, Lupine, Bovine, and Thirty-Nine.
Several camps are connected by roads:
Arachnid is 15 miles from Canine, Bovine is 12 miles from Lupine,
Feline is 6 miles from Thirty-Nine, Lupine is 3 miles from Canine,
Bovine is 9 miles from Thirty-Nine, Bovine is 7 miles from Canine,
Thirty-Nine is 1 mile from Arachnid, and Feline is 11 miles from Lupine.
No other pairs of training camps are connected by roads.
Answer each of the following questions (in each answer, indicate
both the mileage and the route): What is the shortest route from
Feline to Bovine?
Canine to Thirty-Nine?
Lupine to Bovine?
Arachnid to Feline?
Lupine to Thirty-Nine
Canine to Feline?
Arachnid to Lupine?
Answers
Answer:
can I get a brainlesst
Step-by-step explanation:
A machine produces 312 bolts in 30 minutes at the same rate many minutes would it take to produce 260 bolts
Answers
Answer:
The answer is 25 I am a great person for math
Step-by-step explanation:
The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ______ variables.
a.
nominal
b.
interval
c.
ordinal
d.
ratio
Answers
The Spearman rank-order correlation coefficient is a measure of the direction and strength of the linear relationship between two ordinal variables.
Spearman's rank-order correlation is used when two variables are measured on an ordinal scale.
What is the Spearman Rank-Order Correlation Coefficient?
The Spearman Rank-Order Correlation Coefficient is a non-parametric statistical measure that estimates the relationship between two variables using ordinal data.
It evaluates the strength and direction of a relationship between two variables by rank-ordering the data.
The Spearman correlation coefficient, named after Charles Spearman, calculates the association between two variables' rankings.
The correlation coefficient ranges from -1 to +1. A value of +1 indicates that there is a perfect positive relationship between the variables, whereas a value of -1 indicates that there is a perfect negative relationship between the variables.
In contrast, a value of 0 indicates that there is no correlation between the variables.
To learn more about Spearman rank-order correlation coefficient :
https://brainly.com/question/31502090
#SPJ11
for the following scenario, would you utilize a wilcoxon sign rank or friedman's rank test? a researcher wanted to test the ratings of three different brands of paper towels. each brand had 7 reviewers. group of answer choices wilcoxon sign rank test friedman rank test
Answers
For the following scenario where a researcher wanted to test the ratings of three different brands of paper towels with 7 reviewers each, you would utilize Friedman's rank test.
For the given scenario, the appropriate test to use would be the Friedman's rank test. This is because we have three different brands of paper towels, and each brand is rated by 7 reviewers.
The Friedman's test is used to determine if there are significant differences among the groups in a repeated measures design, where the same individuals are rated on multiple occasions. Therefore, it is the appropriate test for this scenario where the ratings are collected from multiple reviewers for each brand.
This test is also appropriate because there are more than two related groups being compared (three brands of paper towels), and the data is likely ordinal (ratings). The Wilcoxon sign rank test is typically used when comparing only two related groups.
Know more about Friedman's rank test here:
https://brainly.com/question/29772048
#SPJ11
(Trig word problems)
From a hot-air balloon, Enola measures a 22° angle of depression to a landmark that’s 310 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest hundredth of a foot if necessary.
Answers
Step-by-step explanation:
See image
The graph of y = 5x4 - x5 has an inflection point (or points) at
A. x = 3 only
B. x = 0, 3
C. x = -3 only
D. x = 0, -3
Answers
The inflection points of the given function are at x = 0 only. The answer is D.
How to find the inflection points of the given function?To find the inflection points of the given function, we need to find the second derivative of the function and set it equal to zero.
y = 5x^4 - x^5
y' = 20x^3 - 5x^4
y'' = 60x^2 - 20x^3
Setting y'' = 0, we get:
60x^2 - 20x^3 = 0
20x^2(3 - x) = 0
x = 0 or x = 3
Now, we need to determine whether these values of x correspond to inflection points. To do this, we can examine the sign of the second derivative in the intervals around each value of x.
For x < 0, y'' is positive (since both terms are positive), so there is a local minimum at x = -3.
For 0 < x < 3, y'' is negative (since 60x^2 < 20x^3), so there is a point of inflection at x = 0.
For x > 3, y'' is positive (since both terms are positive), so there is a local minimum at x = 3.
Therefore, the inflection points of the given function are at x = 0 only. The answer is D.
Learn more about inflection
brainly.com/question/1289846
#SPJ11
suppose that the miles-per-gallon (mpg) rating of passenger cars is normally distributed with a mean and a standard deviation of 31.2 mpg and 4.5 mpg, respectively. [you may find it useful to reference the z table.] a. what is the probability that a randomly selected passenger car gets more than 32 mpg? (round final answer to 4 decimal places.) b. what is the probability that the average mpg of three randomly selected passenger cars is more than 32 mpg? (round final answer to 4 decimal places.) c. if three passenger cars are randomly selected, what is the probability that all of the passenger cars get more than 32 mpg? (round final answer to 4 decimal places.)
Answers
The standard normal distribution that represents the variable in the question indicates that we get;
a. The probability is about 0.42858
b. The probability that the average mpg of 3 randomly selected passenger cars is more than 32 mpg is 0.35197
c. The probability that all the three cars get more than 32 mpg is about0.0788
What is a standard normal distribution?A standard normal distribution, also known as the Gaussian distribution, and the z-distribution, has a mean of 0, and a standard deviation of one.
a. The standard score (z-score) of 32 mpg can be obtained as follows;
z = (32 - 31.2)/4.5 ≈ 0.178
The probability that a standard normal variable has a z-score, larger than 0.178, obtained from the z-score table is therefore;
P(Z > 0.178) ≈ 1 - 0.57142 = 0.42858
The probability that a random selected car gets more than 32 mpg, therefore is about 0.42858b. The of the sample is μ = 31.2
The standard deviation of the sample is, σ = 4.5/√(3)
z = (x - μ)/(σ/√n)
Therefore;
z = (32 - 31.2)/(4.5/√(3)) ≈ 0.308
The probability that a standard normal variable has a z-score larger than 0.308, from the z-score table, therefore is; p(z > 0.308) = 1 - 0.64803 = 0.35197
The probability that average mpg of three (randomly) selected passenger cars is more than 32 mpgs is 0.35197 (35.197%)c. The mpg ratings are independent, therefore, we get;
P(the three cars get more than 32 mpg) = P(car 1 gets more than 32 mpg) × P(car 2 gets more than 32 mpg) × P(car 3 gets more than 32 mpg)
The probability that a car gets more than 32 mpg is about 0.42858
Therefore;
P(the three cars get more than 32 mpg) = 0.42858 × 0.42858 × 0.4288 ≈ 0.0788
The probability that all three cars get more than 32 mpg ≈ 0.0788 = 7.88%Learn more on the normally probability distribution here: https://brainly.com/question/30236866
#SPJ1
What is the measure of lmn in kite klmn? 49° 99° 106° 155°
Answers
The measure of ∠ LMN in kite KLMN be 49°.
What is meant by internal angles?In geometry, a polygon's angle is made up of two of its sides that have a common terminal. If a point within the angle is inside the polygon's interior, the angle is referred to as an interior angle for a simple polygon, whether it is convex or not.
Interior angles are those that are located inside a shape, or they can also be described as the angles that are located in the region enclosed by two parallel lines and a transversal.
The total of a triangle's three interior angles will always be 180 degrees. A triangle cannot have a single angle with a measure of 180° since the other two angles (180° + 0° + 0°) would not be present.
If the measure
LM = MN
LK = KN
∠ MNK = ∠ MLK
we have
∠ MNK = 106°
∠ LKN = 99°
∠ MLK = 106°
The sum of the internal angles in the kite exists equivalent to
∠ MNK + ∠ LKN + ∠ MLK + ∠ LMN = 360°
substitute values and solve for ∠ LMN
∠ LMN = 360° - 106° - 106° - 99°
∠ LMN = 49°
Therefore, the measure of ∠ LMN in kite KLMN be 49°.
The complete question is:
What is the measure of ∠LMN in kite KLMN?
To learn more about internal angles refer to:
https://brainly.com/question/29122096
#SPJ1
find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points (-6,-1) and (1.7)
Answers
Answer:
Step-by-step explanation:
1. Calculate the slope for the line with points (-6,-1) and (1,7). Rise/Run, so take the difference between the two points for both x and y:
Change in x (the run) is 1 - (-6) = 7
Change in y (the rise) is 7 - (-1) = 8
The slope is rise/run so 8/7.
Any line of the form y=mx+b, where m is the slope, will be parallel to this line if it has the same slope: y = (8/7)x + whatever.
Any line in the same format with be perpendicular if the slope is the negative inverse of the reference line. In this case the perpendicular slope would be (-7/8). y = (-7/8)x + whomever.
Jennifer made these measurements on ABC,BC must be-?
Answers
Answer:
between 10 and 12
Step-by-step explanation:
Given the measure of angles:
m∠B = 70°
m∠C = 60°
m∠A = 50°
We know m∠B = 70° because the sum of interior angles in a triangle is equal to 180°.Following this information, since the side lengths are directly proportional to the angle measure they see:
Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.
Angle C is the smallest angle, so the side AB is the shortest side.
Therefore, side BC must be between 10 and 12 inches.
Need this for my homework! Please help! Image attached!
Answers
The relationship between the variables x, y and z is an illustration of similar triangles
The values of x, y and z are 6, \(\sqrt{117}\) and \(\sqrt{52\)
How to determine the values of x, y and zRight triangles are triangles with an angle measure of 90 degrees, and we have the following equivalent ratio from the triangle
\(x : 9 = 4 : x\)
Express as fraction
\(\frac x9 = \frac 4x\)
Cross multiply
\(x^2 = 36\)
Take the square root of both sides
\(x = 6\)
The value of y is then calculated using the following Pythagoras theorem
\(y = \sqrt{9^2 + x^2\)
This gives
\(y = \sqrt{9^2 + 6^2\)
\(y = \sqrt{117\)
The value of z is then calculated using the following Pythagoras theorem
\(z = \sqrt{4^2 + x^2\)
This gives
\(z = \sqrt{4^2 + 6^2\)
\(z = \sqrt{52\)
Hence, the values of x, y and z are 6, \(\sqrt{117}\) and \(\sqrt{52\)
Read more about triangles at:
https://brainly.com/question/17972372
Solve 2(x + 1) + 4 = 8
Answers
Answer: X=1
Step-by-step explanation:
2( x+1) +4=8
2x+2+4=8
2x+6=8
2x=8-6
2x=2
Divide both sides by 2
x=1
~~~~Inuola1234
lmk if you need me to explain further
Answer:
x=1
Step-by-step explanation:
An integer is chosen at Random from the first 100 positive integers. What is the probability that the integer chosen is exactly divisible by 7?
Answers
The probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.
The probability of choosing an integer from the first 100 positive integers that is exactly divisible by 7 can be calculated by determining the number of integers in the range that are divisible by 7 and dividing it by the total number of integers in the range.
To find the number of integers between 1 and 100 that are divisible by 7, we need to find the largest multiple of 7 that is less than or equal to 100.
By dividing 100 by 7, we get 14 with a remainder of 2. This means that the largest multiple of 7 less than or equal to 100 is 14 * 7 = 98.
So, there are 14 integers between 1 and 100 that are divisible by 7 (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98).
Now, we can calculate the probability by dividing the number of integers divisible by 7 (14) by the total number of integers in the range (100).
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 14 / 100
Simplifying the fraction, we get:
Probability = 7 / 50
Therefore, the probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.
To know more about probability, visit:
https://brainly.com/question/31828911
#SPJ11
If point P is 4 over 7 of the distance from M to N white ratio does the point P partioned the directed line segments from M to N into
Answers
Answer:
4 : 3
Step-by-step explanation:
The first segment is 4/7 of the whole, so the second segment is 1 - 4/7 = 3/7 of the whole. Then the ratio of the two segments is ...
(4/7) : (3/7) = 4 : 3
what’s the answer to this problem , figure out the area and perimeter of this triangle
Answers
Answer:
Area: 16.65m^2 (^2 means to the power of 2 exponent, or squared)
Perimeter: 26.3 m
Step-by-step explanation:
Triangle Area formula: bh/2
Plug it in: (7.4)(4.5)/2=16.65
Perimeter: Add the sides
12.6+7.4+6.3=26.3
Answer:
Step-by-step explanation:
Remark
Here are the formulas for what you are asking for.
P = s1 + s2 + s3
Area = height * base / 2
Givens
s1 = 12.6
s2 = 6.3
s3 = 7.4
height = 4.5
base = 7.4
The area is just slightly different than it normally is. The reason is the height. It is not directly connected to the base. The construction is called the base extended. See the givens for what that is.
Solution
Perimeter
P = s1 + s2 + s3 Substitute givens into the formula
P = 12.6+6.3 + 7.4
p = 26.3
Area
Area = (B * H)/ 2
Area = 7.4 *4.5 / 2
Area = 16.65
The diameter of a circle is 19 meters. Complete the description for how you would find the circumference.
Answers
Answer:
The circumference of a circle is 2*pi*r or pi*diameter. The circumference is 19pi
Prove that 3a + 3b is equivalent to 3(a + b) when a = 4 and b = 3.
Answers
Step-by-step explanation:
= 3a+3b
or, 3×4+3×3
or, 12+9
or, 21
again,
= 3(a+b)
or, 3×(4+3)
or, 3×7
or, 21
hence 3a+3b is equivalent to 3(a+b) is proven