Answers
The question seems to be written incorrectly, because m(3) = 4 and that is not an option.
If instead we wanted to find m(2) (where the function has the jump) we can see that m(2) = 2, and in this case the third option is the correct one.
How to find the value of m(3)?Here we have the graph of a piecewise function m(x), we can see that this function has a jump at x = 2 (where you can see the jump from the line with negative slope to a line with positive slope).
We want to use this graph to find the value m(3)
Notice that x = 3 belongs in the second line, just find x = 3 in the horizontal axis and then go up until you meet the graph.
At that point move to the left until you meet the y-axis at the correspondent value of m(3).
Doing that, we can see that:
m(3) = 4
That is not an option, and I think that your teacher actually should have asked to find the value of m(2), where we have the jump.
To identify the value just need to locate which of the segments has the closed circle, that is the correct option.
With that in mind we can se that m(2) = 2, so in this case the third option is the correct.
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Related Questions
Consider a pair of integers, (a, b). The following operations can be performed on (a, b) in any order, zero or more times: • (a, b)(a + b, b) • (a, b) → (a, a + b) Return a string that denotes whether or not (a, b) can be converted to to (c,d) by by performing zero or more of the operations specified above. Example (a, b) = (1, 1) (c,d) = (5,2) Perform the operation (1,1 + 1) to get (1, 2), perform the operation (1 + 2, 2) to get (3, 2), and perform the operation (3+2, 2) to get (5,2). Alternatively, the first operation could be (1+1, 1) to get (2, 1) and so on. The diagram below demonstrates the example representing the pairs as Cartesian coordinates: 5 4 3 2 (1,1+1) (3+2,2) (1+2,2) Goal 1 a Start(1,1) b 1 2 3 4 5 Function Description Complete the function is possible in the editor below. isPossible has the following parameter(s): int a: first value in (a, b) int b: second value in (a, b) int c: first value in (c,d) int d: second value in (c,d) Returns: str: Return 'Yes' if (a, b) can be converted to (c,d) by performing zero or more of the operations specified above, or 'No' if not Constraints • 1 sa,b,c,ds 1000
Answers
We return "Yes"; otherwise, we return "No".
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.
To solve this problem, we can work backward from (c,d) to (a,b) and check if each step is valid. Specifically, we can use the following observations:
If c < a or d < b, it is impossible to reach (c,d) from (a,b) using the given operations.
If c - a = d - b, we can reach (c,d) from (a,b) using only the second operation. Specifically, we can perform the operation (a, a+b) repeatedly until we reach (c,d).
If c - a != d - b, we can reach (c,d) from (a,b) using a combination of the two operations. Specifically, we can perform the first operation (a,b) -> (a+b,b) repeatedly until we get to a point where c - a = d - b, and then use the second operation to get to (c,d).
Here, we first check if it is impossible to reach (c,d) from (a,b) using the observations above. If not, we perform the second operation as many times as possible to reduce the difference between c and a, and d and b. Once this is done, we check if we have arrived at (a,b).
Therefore, we return "Yes"; otherwise, we return "No".
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PLSSS HELP IF YOU TURLY KNOW THISSSS
Answers
Also an easier way to put it a constant is a number in next to a variable
20. Which of these do NBA players attempt much more now than players in the 1990s did?
O A. Slam dunks
O B. Mid-range shots
C. Free throws
O D. Three-point shots
Answers
D. Three-point shots are attempted much more now by NBA players than players in the 1990s did.
Which of these do NBA players attempt much more now than players in the 1990s did?Three-point shooting has become more prevalent in the NBA over the past few decades.
In the 1990s, teams averaged around 11 three-point attempts per game. By the 2020-2021 season, that number had increased to over 34 three-point attempts per game.
The NBA has also made changes to its rules and regulations over the years to encourage and facilitate more three-point shooting.
In contrast, slam dunks, mid-range shots, and free throws have not seen as significant a shift in attempt rates over the years.
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Does positive selection increases the frequency of an allele until it goes to fixation?
Answers
positive selection can increase the frequency of an allele within a population, but whether it reaches fixation depends on a range of factors, including the initial frequency of the allele, the strength and duration of the selection, and the effects of genetic drift.
Positive selection refers to the process where a particular allele or trait is favored by natural selection and consequently increases in frequency within a population. The selective advantage can arise due to factors such as enhanced survival, reproduction, or immunity to diseases. As a result, the frequency of the advantageous allele in the population increases over time.
However, whether the allele eventually reaches fixation, meaning it becomes the only allele present in the population, depends on several factors. One of the key factors is the initial frequency of the allele in the population. If the allele is rare, positive selection can increase its frequency, but it may not necessarily reach fixation due to genetic drift or other factors.
In contrast, if the allele is initially common, it is more likely to reach fixation through positive selection as it has a higher chance of being passed on to future generations. Additionally, the strength and duration of positive selection also play a role in determining whether an allele reaches fixation or not. Strong and long-lasting positive selection increases the likelihood of an allele reaching fixation, whereas weak or short-lived selection may not lead to fixation.
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NEED HELP DUE TOMORROW!!!
Solve n + 6 < 10. Please Graph the solution.
Solution:
Answers
Therefore , the solution of the given problem of inequality comes out to be inequality n + 6 < 10 is satisfied by all numbers to the left of 4.
What is an inequality?In algebra, a disparity can be represented by an association or collection of numbers, even without the equal symbol. Equity always comes after equilibrium. When standards are still incompatible, inequality results. Fairness and disparity are not the same. Because parts are variable frequently not similar in any way or close to one another, we selected the most common symbol ().
Here,
The inequality n Plus 6 10 can be resolved by taking 6 away from both sides:
=> n + 6 - 6 < 10 - 6
Simplifying:
=> n < 4
Therefore, n > 4 is the answer to the contradiction. By shading the area to the left of number 4, we can graph this answer as a number line:
Because n is strictly less than 4, the shaded circle at 4 shows that 4 is not part of the solution. The inequality n + 6 10 is satisfied by all numbers to the left of 4.
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Fill in the blanks to complete the table.
一/7
0.392 X 1
0.392 × 10
0.392 × 102
0.392 × 103
0.392 X 104
Answers
Answer:
一/7
0.392 X 1 = 0.392
0.392 × 10 = 3.92
0.392 × 102 = 39.2
0.392 × 103 = 392
0.392 X 104 = 3,920
If f(x) = { (x^2, x !=2), (2, x=2) :} then evaluate lim_(x rarr 2) f(x)?
Answers
If f(x) = { (x^2, x !=2), (2, x=2) :} then evaluate lim_(x rarr 2) f(x) =2
The limit as x approaches 2 of f(x) is equal to 2.
To evaluate this limit, we can substitute x = 2 into f(x) to get f(2) = 2.
In mathematics, a limit is a value that a function or sequence approaches as the input or index approaches a certain value or infinity. The concept of limit is used to describe the behavior of a function or sequence around a certain point or as the input or index goes to infinity.
More formally, we say that a function f(x) approaches a limit L as x approaches a if, for every ε > 0, there exists a δ > 0 such that if 0 < |x - a| < δ, then |f(x) - L| < ε. This means that as x gets arbitrarily close to a (but not equal to a), the values of f(x) get arbitrarily close to L.
Similarly, we say that a sequence {an} approaches a limit L as n approaches infinity if, for every ε > 0, there exists a natural number N such that if n > N, then |an - L| < ε. This means that as the index n gets arbitrarily large, the values of the sequence {an} get arbitrarily close to L.
There are several techniques for finding limits, including algebraic manipulation, direct substitution, L'Hopital's rule, and series expansions. The behavior of functions and sequences at their limits is important in many areas of mathematics, including calculus, analysis, and differential equations.
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use interval notation to indicate where on the interval [0,π2] the function f(x)=9x 5cos2x, is continuous.
Answers
"use interval notation to indicate where on the interval [0,π2] the function f(x)=9x 5cos2x, is continuous" is [0,π2].
The function f(x)=9x 5cos2x is continuous on the interval [0,π2] because it is a combination of two continuous functions, 9x and 5cos2x. The product of two continuous functions is also continuous, so f(x) is continuous on the entire interval [0,π2].
In interval notation, we can indicate this by writing [0,π2]. This means that f(x) is continuous on the interval from 0 to π2, inclusive.
So, "use interval notation to indicate where on the interval [0,π2] the function f(x)=9x 5cos2x, is continuous" is [0,π2].
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The model (1) can be written in a sample version as follows: yi = β1 + β2xi2 = x 0 iβ + ui , (2) where i = 1, . . . , N, β = (β1, β2) 0 , xi = (xi1, xi2) 0 = (1, SFLAi) 0 , and the definition of yi should be obvious. Further define X = (x1, . . . , xN ) 0 in case one may need this notation to answer the following questions
(a). To obtain the OLS estimate of β of (2), we need to minimize an objective function. Please write down the correct function form of the objective function.
(b). Describe the basic assumptions of the classic linear regression models using the notations of (2).
(c). Provided that these assumptions hold, what conclusions can you make about the OLS estimator?
Answers
a. $$ \min_{\beta} \sum_{i=1}^{N} (y_i - \beta_1 - \beta_2 x_{i2})^2$$
b.
$y_i = \beta_1 + \beta_2 x_{i2} + \epsilon_i$, where $\epsilon_i$ is the random error term$\sigma^2$non-stochastic and fixed in repeated samplesc.
Unbiased: the expected value of the estimator is equal to the true parameterConsistent: as the sample size increases, the OLS estimator converges to the true parameterEfficient: among all unbiased estimators, it has the smallest variancea. The objective function to obtain the OLS estimate of β of (2) can be written as: $$ \min_{\beta} \sum_{i=1}^{N} (y_i - \beta_1 - \beta_2 x_{i2})^2$$
b. The basic assumptions of the classic linear regression models are:
c. Provided that these assumptions hold, the OLS estimator is:
Unbiased: the expected value of the estimator is equal to the true parameter
Consistent: as the sample size increases, the OLS estimator converges to the true parameter
Efficient: among all unbiased estimators, it has the smallest variance
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PLEASE HELP EASY POINTS UP FOR GRABS
Answers
Answer: 6x + 9
Step-by-step explanation:
you would multiply 2 by 5x and 3 giving you 10x + 3. You would do the same thing to the other equation giving you -4x +6. After this you would subtract 4x from 10x and add 6 and 3 giving you 6x + 9
Answer:
it would be 6x + 12
Step-by-step explanation:
Subtract 4x from 10x.
6x+6+6
add 6 and 6.
6x+12
I hope this helps!!
What is the center of a circle whose equation is x2 + y2 – 12x – 2y + 12 = 0?
A.) (–12, –2)
B.) (–6, –1)
C.) (6, 1)
D.) (12, 2)
Answers
forty samples of 100 are taken, with the total number of defective units being 150. what is the upper control limit of the three sigma (z
Answers
The upper control limit of the three-sigma process is approximately 3.807 defective units per sample.
To calculate the upper control limit (UCL) of the three-sigma (z) process, we first need to find the average number of defective units per sample and the standard deviation.
1. Calculate the average number of defective units per sample (p-bar):
Divide the total number of defective units (150) by the number of samples (40).
p-bar = 150 / 40 = 3.75 defective units per sample
2. Calculate the proportion of defective units (p) in each sample:
Divide the average number of defective units (3.75) by the sample size (100).
p = 3.75 / 100 = 0.0375
3. Calculate the standard deviation (σ) of the process using the formula:
σ = √(p * (1 - p) / n),
where n is the sample size.
σ = √(0.0375 * (1 - 0.0375) / 100)
= √(0.03609375 / 100) ≈ 0.0190
4. Calculate the three-sigma upper control limit (UCL) using the formula:
UCL = p-bar + 3 * σ
UCL = 3.75 + 3 * 0.0190 ≈ 3.75 + 0.057 ≈ 3.807.
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For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. B. exactly 1.96 C. a large negative number. D. close to E. close to 1.
Answers
A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is a large positive number.
Hence option A is correct.
X2 (chi-squared) statistic is utilized to evaluate the relationship between two categorical variables.
The null hypothesis is evaluated using this statistic, and it is used to determine whether the observed values deviate significantly from the expected values.
The chi-squared statistic is used to compute a p-value,
which is then used to determine whether to reject or fail to reject the null hypothesis.
A p-value of less than or equal to 0.05 indicates that the null hypothesis should be rejected, and the alternative hypothesis should be accepted.
A large positive chi-squared value, in particular, indicates a strong relationship between the two categorical variables, which supports the alternative hypothesis.
A large negative chi-squared value, on the other hand, is an indication of no correlation, and a chi-squared value that is close to 1 indicates a weak relationship between the two variables.
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In statistics, a chi-squared test is a hypothesis test that compares observed frequencies to expected frequencies in one or more categories.
It is frequently used in goodness-of-fit tests to determine if an observed frequency distribution fits a theoretical distribution. The chi-squared test statistic, denoted χ2, is calculated as the sum of the squared differences between observed and expected frequencies, divided by the expected frequency, for all categories.To assess the goodness of fit of a chi-square distribution, we use a chi-square test statistic. The chi-square test statistic is a quantity that compares the observed frequencies in a contingency table to the expected frequencies. It follows the chi-square distribution, with degrees of freedom equal to the number of categories minus one. A large chi-square test statistic value indicates that the observed frequencies are significantly different from the expected frequencies, resulting in the null hypothesis being rejected. Conversely, a small chi-square test statistic value indicates that the observed frequencies are similar to the expected frequencies, resulting in the null hypothesis being retained.Chisquared test statistic value indicates the probability of rejecting the null hypothesis in favor of the alternative hypothesis. If the chi-squared test statistic value is small, then the null hypothesis cannot be rejected in favor of the alternative hypothesis, but if the chi-squared test statistic value is large, then the null hypothesis can be rejected in favor of the alternative hypothesis. So, the answer is a large positive number. Therefore, the correct option is (a).
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Umm I kinda need some help
Answers
Answer: 8.25$ + 2.25$m
hope this helped =)
The distance of the satellite from the top of Nanda Devi is
Answers
If the angle of elevation from the top of Nanda devi to the satellite is 30°, then the distance between the satellite and top of Nanda devi is 200m.
We use trigonometry ratio to find the distance between Satellite and Nanda Devi.
In particular, we can use the Sine function:
⇒ Sin(θ) = opposite/hypotnuse,
In this case, the opposite side is 100m , and we have to find the hypotnuse(h) which is the required distance,
The angle of elevation(θ) = 30°,
⇒ Sin(30°) = 100/h
Solving for h, we get:
⇒ h = 100/Sin(30°) = 200m.
Therefore, the distance of the satellite from the top of Nanda Devi is 200meters.
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The given question is incomplete, the complete question is
The angle of elevation from the top of Nanda devi to the satellite is 30°, and the perpendicular distance from the satellite is 100m. Find The distance of the satellite from the top of Nanda Devi.
Melanie and her friends bought lunch for $15 and three admission tickets to Adventure Land. Write an expression that could be used to represent the total amount of money they spent if t represent the total cost of tickets. Then find the total if the tickets cost $7 each
Answers
The total amount of money Melanie and her friends spent if each ticket costs $7 would be $26.
Let's call the total amount of money Melanie and her friends spent "M". We know that they spent $5 on lunch, and they also bought three admission tickets to Adventure Land. Let's call the cost of each ticket "t".
So the equation that represents the total amount of money they spent would be
M = 5 + 3t
If we know that each ticket costs $7, we can substitute that value for "t" in the equation
M = 5 + 3(7)
M = 5 + 21
M = $26
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Which values are solutions to the inequality below? Check all that apply. √x < 12 A. -144 B. 100 C. 144 D. 4 E 148 F. 32
Answers
Answer:
b and d
Step-by-step explanation:
To solve the inequality, we can square both sides:
√x < 12
(√x)^2 < 12^2
x < 144
Therefore, any value of x that is less than 144 is a solution to the inequality.
Checking each option:
A. -144 is not a solution because the square root of a negative number is not a real number.
B. 100 is a solution because √100 = 10 < 12.
C. 144 is not a solution because the inequality is strict, meaning that x must be less than 144.
D. 4 is a solution because √4 = 2 < 12.
E. 148 is not a solution because 148 is greater than 144.
F. 32 is a solution because √32 < 12.
Therefore, the solutions are B and D.
Answer: B, D
you want to develop a three-sigma x bar-chart. you know the mean of the means is 30 and the average range is 5 based on several samples of size 10. what is the lcl of the x bar-chart? round your answer to two decimal places.
Answers
The lower control limit (LCL) for a 3-sigma X-bar chart is 17.50. This is calculated by subtracting 3 times the average range (5) from the mean of the means (30). Therefore, LCL = 30 - (3 x 5) = 17.50.
To construct the 3-sigma X-bar chart, the mean and average range must be calculated from a sample size of 10. The mean of the means is calculated by summing up all the sample means and then dividing it by the total number of samples. The average range is calculated by summing up the individual range values for all the samples and then dividing it by the total number of samples.
Finally, the LCL is calculated by subtracting 3 times the average range from the mean of the means. Once all these values have been calculated, the 3-sigma X-bar chart can be created with the LCL, mean of means, and average range as the three points.
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Consider the following hypothesis test: H0: U=100 Ha: u = 100 A sample of 65 is used. Identify and state your conclusion for each of the following sample results. Use level of significance = .05. a. mean = 103 and s= 11.5 b. mean =102 and 5= 10.5
Answers
The population mean (U) is equal to 100.
In this hypothesis test, the null hypothesis (H0) is that the population mean (U) is equal to 100, and the alternative hypothesis (Ha) is that the population mean (U) is not equal to 100.
We can use the given level of significance, α = 0.05, to determine our decision rule.
For the given sample results, we will first consider a. mean = 103 and s = 11.5.
We can use the Z-test to calculate the Z-score which is: Z = (103 - 100)/(11.5/√65) = 2.16. Since the Z-score is greater than the critical value (1.96), we can reject the null hypothesis and conclude that the population mean (U) is not equal to 100.
Next, for the sample result b. mean = 102 and s = 10.5,
we will again use the Z-test to calculate the Z-score which is: Z = (102 - 100)/(10.5/√65) = 1.85.
Since the Z-score is less than the critical value (1.96), we fail to reject the null hypothesis and conclude that the population mean (U) is equal to 100.
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The perimeter of a rectangular swimming pool is 70 yards. Its length is 24 yards. Which of the following can be used to find the width?
Answers
Perimeter is the total distance around the edge of a two-dimensional shape. It is calculated by adding up the lengths of all sides of the shape.
Calculations:
Let the width of the swimming pool be represented by 'w'.
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + width)
In this case, we are given the perimeter and the length, so we can substitute those values into the formula and solve for the width:
70 = 2(24 + w)
Dividing both sides by 2, we get:
35 = 24 + w
Subtracting 24 from both sides, we get:
w = 11
Therefore, the width of the swimming pool is 11 yards.
So the equation that can be used to find the width is:
w = (Perimeter - 2×length)/2
or
w = (70 - 2×24)/2 = 11.
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3,2
Find the error and explain why the polynomial is factored incorrectly. Work the problems
yourself, if needed. 10x²+49x-5=(10x-5)(x+1)
Answers
The given factorization is incorrect. The correct factorization of the polynomial is (10x-1)(x+5).
To check this, let's multiply the factors (10x-5)(x+1) using the distributive property:
(10x-5)(x+1) = 10x(x+1) - 5(x+1) = 10x² + 10x - 5x - 5 = 10x² + 5x - 5
As we can see, the result is not equal to the original polynomial 10x² + 49x - 5.
To factor the polynomial correctly, we can use either factoring by grouping, completing the square, or the quadratic formula. Factoring by grouping can be done as follows:
10x² + 49x - 5
= 10x² + 50x - x - 5
= 10x(x+5) - 1(x+5)
= (10x-1)(x+5)
Therefore, the correct factorization of the polynomial is (10x-1)(x+5).
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A circular loop of wire carries a constant current. If the loop is
placed in a region of uniform magnetic
field, the net magnetic
force on the loop is
A. perpendicular to the plane of the loop, in a direction given by the right-hand rule.
B. perpendicular to the plane of the loop, in a direction given by the left-hand rule.
C. in the same plane as the loop.
D. zero.
E. The answer depends on the magnitude and direction of the current and on the magnitude and direction of the magnetic field.
Answers
(D) is the correct answer. The net force on a current loop in a uniform magnetic field is zero. With a homogeneous magnetization, the net force on any plane-shaped current-carrying loop is zero.
The net torque on something like a previous loop of any shape in a constant magnetic field is computed using =B = B, where B is the magnetic field strength.
Why is there no net magnetic force in a closed loop?
Assumption: Under a uniform magnetic field, the net force on a closed circular conductive loop is zero. Reason: When ever a conducting spherical ring is put in a homogeneous magnetic field such that the magnetism is parallel to the surface of the loops, the torque is produced is zero.
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If f(a) = 3a – a2, which of the following are not true statements? Select all that apply. f(-5) = -40 f(4) = -4 f(-1) = 2 f(0) = 3 f(3) = 0
Answers
If the function, f(a) = 3a – a2, then, The statement which are not true are:
1. f(-1) = 2
2. f(0) = 3
Function:
Functions, in mathematics, expression, rule or law that defines the relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and essential for establishing physical relationships in science.
According to the Question:
Given that:
f(a) = 3a - a²
The statements which are correct are as follow:
f(4)= 3*4-4²= -4
f(3)= 3*3-3²= 0
f(-5) = 3*(-5)-(-5)²= -15-25= -40
Now,
The statements which are not correct are as follow:
f(-1) = 3*(-1)-(-1)²=-3+1= -2
f(0) = 3*0-0²= 0
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Tanya bought five adult tickets and one children's ticket to a movie for $27. 70. Li bought four adult tickets and five children's tickets for $33. 0. Find the cost of one adult ticket and the cost of one children's ticket
Answers
Answer:
1 Adult ticket is 5.0.
1 Child ticket is 2.7.
Step-by-step explanation:
I think this is it! I tried so many different solutions! =)
Find the distance around a pizza if its diameter is 16 inches. Round to the nearest inch.
Answers
An image of a rhombus is shown.
A rhombus with a base of 17 inches and a height of 14 inches.
What is the area of the rhombus?
62 in2
119 in2
124 in2
238 in2
Answers
The area of a rhombus is given by the formula A = (base x height)/2. Plugging in the values, we get A = (17 x 14)/2 = 119 [tex]in^2[/tex]. Therefore, the area of the rhombus is 119 square inches.
The area of a rhombus can be calculated as the product of its diagonals divided by 2, or as the product of its base and height.
In this case, we have the height and need to find the length of one diagonal. Since the opposite angles of a rhombus are congruent, we know that the diagonals bisect each other, and the base forms a right angle with the diagonals.
Using the Pythagorean theorem, we can find the length of one diagonal:
[tex](diagonal/2)^2 + (base/2)^2 = height^2[/tex]
[tex](diagonal/2)^2 + (8.5)^2 = (14)^2[/tex]
[tex](diagonal/2)^2 = (14)^2 - (8.5)^2[/tex]
[tex](diagonal/2)^2 = 119.75[/tex]
[tex]diagonal/2 = \sqrt{(119.75)[/tex]
[tex]diagonal = 2*\sqrt{(119.75)[/tex]
diagonal ≈ 19.48 inches
Now we can calculate the area:
Area = (base * height)/2
Area = (17 * 14)/2
Area = 119 in²
Therefore, the area of the rhombus is approximately 119 square inches, which is option B.
A rhombus is a quadrilateral (a polygon with four sides) in which all sides are of equal length. It is a special case of a parallelogram, which means that opposite sides are parallel to each other. In addition to having sides of equal length, a rhombus also has opposite angles that are equal to each other, and its diagonals bisect each other at a right angle. A rhombus can also be thought of as a diamond shape, with two acute angles and two obtuse angles. Some examples of real-world objects that have a rhombus shape include playing cards, road signs, and some types of jewelry.
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solve for x, y, and z
[5 -8] + [x 7] = [-2 z]
[2 y] [11 4] [13 13]
Answers
So, the solution is: x = -49, y = 429/4, z = 22.
What is matrix?A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. The elements in a matrix can be real or complex numbers, or other mathematical objects such as polynomials, vectors, or functions. Matrices are often used in mathematics, physics, engineering, computer science, and many other fields to represent and manipulate data and equations.
The size of a matrix is determined by the number of rows and columns it contains. For example, a matrix with m rows and n columns is called an m-by-n matrix. Matrices can be added, subtracted, multiplied, and transformed using various operations, such as matrix addition, matrix multiplication, and matrix inversion. These operations are useful for solving systems of linear equations, finding eigenvalues and eigenvectors, and many other applications.
by the question.
This is an equation of matrices, so we need to perform matrix addition and multiplication.
Starting with the left-hand side of the equation:
[tex][5 -8] + [x 7] = [5+x -1][/tex]
[tex][2 y] [11 4] [2y+11 4y][/tex]
Now, setting this equal to the right-hand side of the equation:
[tex][5+x -1] = [-2z][/tex]
[2y+11 4y] [13 13]
We can separate this into two equations:
[tex]5 + x = -2z[/tex]
[tex]2y + 11 = 13z[/tex]
[tex]4y = 13z[/tex]
From the third equation, we can solve for y:
[tex]4y = 13z[/tex]
[tex]y = 13z/4[/tex]
Substituting this into the second equation:
[tex]2y + 11 = 13z[/tex]
[tex]2(13z/4) + 11 = 13z[/tex]
[tex]26z/4 + 44/4 = 13z[/tex]
[tex]13z/2 + 11 = 13z[/tex]
[tex]z/2 = 11[/tex]
[tex]z = 22[/tex]
Now, substituting z = 22 into the first equation:
[tex]5 + x = -2z[/tex]
[tex]5 + x = -44[/tex]
[tex]x = -49[/tex]
So, the solution is:
[tex]x = -49[/tex]
[tex]y = 429/4[/tex]
[tex]z = 22[/tex]
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whats the most logical first step in solving this quadratic equation x^2+2x-11x=4
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Answer:
Move 4 to the left side of the equation so the equation is equal to 0
tan(-20°) = -tan20° True or False
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Answer:
True
Step-by-step explanation:
Angles in the Cartesian plane move from x-axis to an anticlockwise direction to give positive angles
When angles are formed through clockwise movement they fall on the Fourth quadrant ....in the fourth quadrant only Cosine is positive meaning Sin and Tan are negative hence
tan(-20°) = -tan 20°
In a summary
cos(-a)= cosa
tan(-a) = -tana
sin(-a) =-sina
find a unit vector that has the same direction as the given vector. −9i 3j − k
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The unit vector that has the same direction as the given vector is: unit vector = (−9/√91)i + (3/√91)j − (1/√91)k
To find a unit vector that has the same direction as the given vector, we need to divide the given vector by its magnitude.
The magnitude of a vector is given by the formula:
magnitude = √(x² + y² + z²)
For the given vector, −9i + 3j − k, the magnitude is:
magnitude = √((-9)² + (3)² + (-1)²) = √(81 + 9 + 1) = √91
Now, to find the unit vector, we divide the given vector by its magnitude:
unit vector = (−9i + 3j − k) / √91
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