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25. Use the relationship in the diagrams below to solve for the given variable.
Justify your solution with a definition or theorem.
Answers
Answer:
x = 110°
Step-by-step explanation:
The opposite angles are equal in a parallelogram
3x - 60 = 2x + 50
⇒ 3x - 2x = 60 + 50
⇒ x = 110°
Answer:
x = 110°
Step-by-step explanation:
As the top and bottom line segments of the given shape are the same length and parallel (indicated by the tick marks and arrows), the shape is a parallelogram.
As the opposite angles of a parallelogram are equal, to find the value of the variable x, equate the two angle expressions and solve for x:
[tex]\begin{aligned}3x-60^{\circ}&=2x+50^{\circ}\\3x-60^{\circ}-2x&=2x+50^{\circ}-2x\\x-60^{\circ}&=50^{\circ}\\x-60^{\circ}+60^{\circ}&=50^{\circ}+60^{\circ}\\x&=110^{\circ}\end{aligned}[/tex]
Therefore, the value of x is 110°.
Note: There must be an error in the question. If x = 110°, each angle measures 270°, which is impossible since the sum of the interior angles of a quadrilateral is 360°.
Related Questions
Use basic inference rules to establish the validity of the argument: p ⟹ ¬q ,q V r ,p V u ,¬r├ u
Answers
Using basic inference rules, we can establish the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
1. We are given the following premises:
- p ⟹ ¬q (Premise 1)
- q V r (Premise 2)
- p V u (Premise 3)
- ¬r (Premise 4)
2. To prove the conclusion, u, we need to use the premises and apply inference rules.
3. From Premise 4 (¬r) and the Disjunctive Syllogism rule, we can deduce ¬q: (¬r, q V r) ⟹ ¬q.
4. From Premise 1 (p ⟹ ¬q) and Modus Ponens, we can conclude ¬p: (p ⟹ ¬q, ¬q) ⟹ ¬p.
5. From Premise 3 (p V u) and Disjunctive Syllogism, we obtain ¬p V u.
6. Using Disjunctive Syllogism with ¬p V u and ¬p, we can derive u: (¬p V u, ¬p) ⟹ u.
7. From Premise 2 (q V r) and Disjunctive Syllogism, we have q.
8. Finally, using Modus Tollens with q and ¬q, we can deduce ¬p: (q, p ⟹ ¬q) ⟹ ¬p.
9. Therefore, combining ¬p and u, we can conclude the desired result: ¬p ∧ u.
10. Since ¬p ∧ u is logically equivalent to u, we have established the validity of the argument: p ⟹ ¬q, q V r, p V u, ¬r ├ u.
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If sin(x+y)= 1/2(sin x) + square root of 3/2(cos x), what is the value of y
Answers
Answer:
y = π/3
Step-by-step explanation:
To find the value of y, we can use the trigonometric identity for the sum of angles:
sin(x + y) = sin x * cos y + cos x * sin y
Comparing this with the given equation:
sin(x + y) = 1/2(sin x) + √3/2(cos x)
We can equate the corresponding terms:
sin x * cos y = 1/2(sin x) ----(1)
cos x * sin y = √3/2(cos x) ----(2)
From equation (1), we can see that cos y = 1/2.
From equation (2), we can see that sin y = √3/2.
To determine the values of y, we can use the trigonometric values of cosine and sine in the first quadrant of the unit circle.
In the first quadrant, cos y is positive, so cos y = 1/2 corresponds to y = π/3 (60 degrees).
Similarly, sin y is positive, so sin y = √3/2 corresponds to y = π/3 (60 degrees).
Therefore, the value of y is y = π/3 (or 60 degrees).
Please help me solve this
Answers
Answer:
Step-by-step explanation:
In order to compute a sample mean by hand, first the data values must be added up. Then the sum is divided by the
sample size.
x = xx
Given the data set below, compute the summation, identify the sample size, and calculate the sample mean.
19
10
15
17
16
a.) Ex =
b.) n =
c.) x =
Answers
a) The summation (Ex) of the given data set, we add up all the values
Ex = 77
b) n = 5
c) x = 15.4
a) To compute the summation (Ex) of the given data set, we add up all the values:
19 + 10 + 15 + 17 + 16 = 77
b) The sample size (n) is the total number of data points in the set. In this case, there are 5 data points, so:
n = 5
c) To calculate the sample mean (x), we divide the summation (Ex) by the sample size (n):
x = Ex / n
x = 77 / 5
x = 15.4
Therefore, the answers are:
a) Ex = 77
b) n = 5
c) x = 15.4
The summation is 77, the sample size is 5, and the sample mean is 15.4.
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Margie has a $50.00 budget to purchase a $45.00 pair of boots. If
there is an 8% sales tax rate, then how much under budget will
Margie be?
Answers
Answer:
She willl be $1.40 under budget
Step-by-step explanation:
8% = 8/100 = 0.08
Adding this to 100% of the price of the shoes, we get 108% = 108/100 = 1.08.
We multiply the price of the shoes by this:
45*1.08 = 48.60
Subtract this from 50:
50 - 48.60 = 1.40
Evaluate the expression. −3[−4(3−10)−12] over −2(−1) What is the value of the expression?
Answers
Answer: -24
Step-by-step explanation:
To evaluate the expression, I guess we need to break it down into steps:
Expression: -3[-4(3-10)-12] / -2(-1)
Step1: Simplify the innermost parentheses Inside the square brackets: 3 - 10 = -7 Expression becomes: -3[-4(-7) - 12] / -2(-1)
Step2: Simplify the multiplication in square brackets: -4 * (-7) = 28. Expression becomes: -3[28 - 12] / -2(-1)
Step3: Simplify the subtraction inside the square brackets: 28 - 12 = 16. Expression becomes: -3[16] / -2(-1)
Step4: Simplify the multiplication outside the square brackets: -3 * 16 = -48. Expression becomes: -48 / -2(-1)
Step5: Simplify the multiplication inside the denominator: -2 * (-1) = 2 Expression becomes: -48 / 2
Step 6: Perform the division -48 divided by 2 is equal to -24
Therefore, the value of the expression -3[-4(3-10)-12] / -2(-1) is -24.
What's the area of the following triangle?
A. 24 ft.²
B. 128 ft.²
C. 12 ft.²
D. 64 ft.²
Answers
Answer:
D
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
here b = 16 and h = 8 , then
A = [tex]\frac{1}{2}[/tex] × 16 × 8 = 8 × 8 = 64 ft²
a spinner with 10 equally sized slices 4 yellow, 4 red, 2 blue. probability that the dial stops on yellow?
Answers
The probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
To find the probability that the spinner stops on yellow, we need to determine the number of favorable outcomes (yellow) and the total number of possible outcomes.
The spinner has 10 equally sized slices, with 4 yellow, 4 red, and 2 blue.
The number of favorable outcomes (yellow) is 4 because there are 4 yellow slices.
The total number of possible outcomes is 10 because there are 10 slices in total.
Therefore, the probability of the spinner stopping on yellow can be calculated as:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 4 / 10
Simplifying this fraction, we get:
Probability = 2 / 5
So, the probability that the dial stops on yellow is 2/5 or 0.4 (or 40%).
Therefore, there is a 40% chance that the spinner will stop on yellow.
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
Answers
Answer:
Third option
Step-by-step explanation:
-3(2x - 5) < 5(2 - x)
-6x + 15 < 10 - 5x <-- Third option
15 < 10 + x
5 < x
x > 5
There only appears to be one option. The solution to the inequality is x>5, not x<5.
Use a Calculator to evaluate The following. Round the answer to the nearest hundredths
1. Cos 10
2. Sin 30
3. Sin 20
4. Tan 25
5. Tan 48.5
Answers
1. Using a calculator, we find that cos 10 ≈ 0.98.
2. Using a calculator, we find that sin 30 ≈ 0.50.
3. Using a calculator, we find that sin 20 ≈ 0.34.
4. Using a calculator, we find that tan 25 ≈ 0.47.
5. Using a calculator, we find that tan 48.5 ≈ 1.14.
Using a calculator to evaluate the given trigonometric functions, rounded to the nearest hundredth, we have:
Cos 10:
Using a calculator, we find that cos 10 ≈ 0.98.
Sin 30:
Using a calculator, we find that sin 30 ≈ 0.50.
Sin 20:
Using a calculator, we find that sin 20 ≈ 0.34.
Tan 25:
Using a calculator, we find that tan 25 ≈ 0.47.
Tan 48.5:
Using a calculator, we find that tan 48.5 ≈ 1.14.
These values represent the approximate decimal values of the trigonometric functions at the given angles, rounded to the nearest hundredth.
Just a reminder, when using a calculator, make sure it is set to the correct angle mode (degrees or radians) as per the given problem.
It's important to note that these values are approximate since they are rounded to the nearest hundredth. If you need more precise values, you can use a calculator that allows for a greater number of decimal places or use trigonometric tables.
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true or false euclidean geometry is geometry on a sphere
Answers
Answer: False
Step-by-step explanation:
Spherical geometry, on the other hand, is a type of non-Euclidean geometry that is specifically concerned with studying the properties of curved surfaces, such as spheres.
Hope this help! Have a good day!
Please answer ASAP I will brainlist
Answers
The resulting matrix after the rows are interchanged is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
How to obtain the resulting matrix?The matrix for this problem is defined as follows:
[tex]\left[\begin{array}{cccc}8&-2&1&7\\2&9&4&5\\1&4&-4&9\end{array}\right][/tex]
The row 1 is given as follows:
[8 -2 1 7].
The row 2 is given as follows:
[2 9 4 5].
Interchanging the rows means that the elements of the row 1 in the matrix is exchanged with the elements of row 2, hence the resulting matrix is given as follows:
[tex]\left[\begin{array}{cccc}2&9&4&5\\8&-2&1&7\\1&4&-4&9\end{array}\right][/tex]
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What 2 numbers can multiply to -40 and add up to 6
Answers
Answer: 10 and -4
Step-by-step explanation: 10 + - 4 = 6 and 10 x -4 = -40
If the mean of a negatively skewed distribution is 122, which of these values could be the median of the distribution
Answers
118 be the median of a positively skewed distribution with a mean of 122. Option D.
To determine which of the given values could be the median of a positively skewed distribution with a mean of 122, we need to consider the relationship between the mean, median, and skewness of a distribution.
In a positively skewed distribution, the tail of the distribution is stretched towards higher values, meaning that there are more extreme values on the right side. Consequently, the median, which represents the value that divides the distribution into two equal halves, will typically be less than the mean in a positively skewed distribution.
Let's examine the given values in relation to the mean:
A. 122: This value could be the median if the distribution is perfectly symmetrical, but since the distribution is positively skewed, the median is expected to be less than the mean. Thus, 122 is less likely to be the median.
B. 126: This value is higher than the mean, and since the distribution is positively skewed, it is unlikely to be the median. The median is expected to be lower than the mean.
C. 130: Similar to option B, this value is higher than the mean and is unlikely to be the median. The median is expected to be lower than the mean.
D. 118: This value is lower than the mean, which is consistent with a positively skewed distribution. In such a distribution, the median is expected to be less than the mean, so 118 is a plausible value for the median.
In summary, among the given options, (118) is the most likely value to be the median of a positively skewed distribution with a mean of 122. So Option D is correct.
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Note the complete question is
If the mean of a positively skewed distribution is 122, which of these values could be the median of the distribution?
A. 122
B. 126
C. 130
D. 118
(08.01 MC)
A function is shown: f(x) = 4x² - 1.
Choose the equivalent function that best shows the x-intercepts on the graph.
Of(x) = (4x + 1)(4x - 1)
Of(x) = (2x + 1)(2x - 1)
f(x) = 4(x²+1)
f(x) = 2(x²-1)
Answers
The equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b): Of(x) = (4x + 1)(4x - 1).
The correct answer to the given question is option a or b.
The given function is f(x) = 4x² - 1. We need to choose the equivalent function that best shows the x-intercepts on the graph.The x-intercepts are the points where the graph of a function intersects the x-axis. At the x-intercepts, the value of y is zero.
Therefore, to find the x-intercepts, we need to solve the equation f(x) = 0 for x. The function f(x) = 4x² - 1 can be factored as:(2x + 1)(2x - 1)
To find the x-intercepts, we set f(x) = 0:4x² - 1 = 0(2x + 1)(2x - 1) = 0So, either 2x + 1 = 0 or 2x - 1 = 0. Solving these equations, we get:
x = -1/2 or x = 1/2
These are the x-intercepts of the graph of f(x) = 4x² - 1.Now, let's look at the given options and determine which one shows the x-intercepts on the graph:
Option (a):
Of(x) = (4x + 1)(4x - 1)
This is the factored form of f(x) = 4x² - 1. It correctly shows the x-intercepts.
Option (b):
Of(x) = (2x + 1)(2x - 1)
This is the same as option (a) and correctly shows the x-intercepts.
Option (c): f(x) = 4(x² + 1)
This function does not have any x-intercepts. It has a minimum value of 4 at x = 0.
Option (d): f(x) = 2(x² - 1)
This function has x-intercepts at x = -1 and x = 1. It does not show the x-intercepts of the given function.
Therefore, the equivalent function that best shows the x-intercepts on the graph of f(x) = 4x² - 1 is option (a) or (b):
Of(x) = (4x + 1)(4x - 1).
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Which is equivalent to 4/9 1/2x*?
92x
9 1/8x
Answers
Answer:
B. [tex] 9^{\frac{1}{8}x} [/tex]
Step-by-step explanation:
[tex] \sqrt[4]{9}^{\frac{1}{2}x} = [/tex]
[tex] = ({9}^{\frac{1}{4}})^{\frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{4} \times \frac{1}{2}x} [/tex]
[tex] = 9^{\frac{1}{8}x} [/tex]
Select the correct answer.
Mr. Miller owns two hotels and is ordering towels for the rooms. He ordered 27 hand towels and 48 bath towels for a bill of $540 for the first hotel. He
ordered 50 hand towels and 24 bath towels for a bill of $416 for the other hotel.
What is the cost of one hand towel and one bath towel?
O A.
OB.
OC.
O D.
The cost of one hand towel is $4 and the cost of one bath towel is $9.
The cost of one hand towel is $9 and the cost of one bath towel is $4.
The cost of one hand towel is $5 and the cost of one bath towel is $8.
The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answers
Answer: D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Step-by-step explanation:
Let's assume the cost of one hand towel is 'x' dollars and the cost of one bath towel is 'y' dollars.
For the first hotel, Mr. Miller ordered 27 hand towels and 48 bath towels, resulting in a bill of $540. This can be expressed as the equation:
27x + 48y = 540 ...(equation 1)
For the second hotel, Mr. Miller ordered 50 hand towels and 24 bath towels, resulting in a bill of $416. This can be expressed as the equation:
50x + 24y = 416 ...(equation 2)
To solve this system of equations, we can use any suitable method such as substitution or elimination. Let's use the elimination method:
Multiplying equation 1 by 2 and equation 2 by 3, we get:
54x + 96y = 1080 ...(equation 3)
150x + 72y = 1248 ...(equation 4)
Now, subtracting equation 4 from equation 3, we have:
(54x + 96y) - (150x + 72y) = 1080 - 1248
-96x + 24y = -168
Dividing both sides of the equation by -24, we get:
4x - y = 7 ...(equation 5)
Now, we have a system of equations:
4x - y = 7 ...(equation 5)
50x + 24y = 416 ...(equation 2)
Solving this system of equations, we find that x = 8 and y = 5.
Therefore, the cost of one hand towel is $8 and the cost of one bath towel is $5.
So, the correct answer is option D: The cost of one hand towel is $8 and the cost of one bath towel is $5.
Answer:
Step-by-step explanation:
Total cost of hand towels for first hotel = 27 * $5 = $135
Total cost of bath towels for first hotel = 48 * $8 = $384
Total cost of hand towels for second hotel = 50 * $5 = $250
Total cost of bath towels for second hotel = 24 * $8 = $192
Total cost of all hand towels = $135 + $250 = $385
Total cost of all bath towels = $384 + $192 = $576
Total number of hand towels = 27 + 50 = 77
Total number of bath towels = 48 + 24 = 72
Average cost of one hand towel = $385 / 77 = $5
Average cost of one bath towel = $576 / 72 = $8
Choose the justification for each step of the given equation. -6=-2/3(x+12)+1/3x
Answers
The steps used in the solution of the equation -6 = -2/3(x + 12) + 1/3x are based on the principles of the Distributive Property, combining like terms, addition property of equality, symmetric property, subtraction property of equality, and multiplication property of equality.
Let's analyze the steps of the solution for the given equation -6 = -2/3(x + 12) + 1/3x:
Step 1: Distributive Property
The equation begins with the Distributive Property, which states that you can distribute a factor to each term inside parentheses. In this case, we distribute -2/3 to (x + 12), resulting in -2/3 * x and -2/3 * 12.
Step 2: Simplification
We simplify the expression -2/3 * 12 to -8, as multiplying -2/3 by 12 gives us -24, and simplifying the fraction -24/3 yields -8.
Step 3: Combine Like Terms
We combine the like terms -2/3x and -8. The equation becomes -2/3x - 8 + 1/3x.
Step 4: Combine Like Terms
We combine the like terms -2/3x and 1/3x by adding their coefficients. The sum of -2/3x and 1/3x is -1/3x.
Step 5: Addition Property of Equality
We add -1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 - 1/3x = -1/3x.
Step 6: Symmetric Property
Since the equation has a form of -1/3x = -6 - 1/3x, we can rearrange the terms using the Symmetric Property.
Step 7: Addition Property of Equality
We add 1/3x to both sides of the equation to isolate the constant term. The equation becomes -6 = 0.
Step 8: Subtraction Property of Equality
We subtract 0 from both sides of the equation to simplify it further. The equation remains -6 = 0.
Step 9: Multiplication Property of Equality
We multiply both sides of the equation by any non-zero number to check for consistency. In this case, there is no need for multiplication as the equation is already in its simplified form.
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Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
Answers
Given the information in the diagram, the theorem that best justifies why lines j and k must be parallel include the following: D. converse alternate exterior angles theorem.
What are parallel lines?In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.
In Mathematics and Geometry, the alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
Since the alternate exterior angles are congruent, we can logically deduce the following based on the converse alternate exterior angles theorem;
93° ≅ 93° (lines j and k are parallel lines).
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Complete Question:
Given the information in the diagram, which theorem best justifies why lines j and k must be parallel?
alternate interior angles theorem
alternate exterior angles theorem
converse alternate interior angles theorem
converse alternate exterior angles theorem
Which point could not be part of a function that includes (3, -1), (4, 2), (5, 4), (-2, 0), and (8, -3)?
(6, -7)
(2,2)
(3, -2)
(7, 4)
Answers
Answer:
(3, -2) is the correct choice.
I WILL GIVE BRAINLIEST
Answers
Step-by-step explanation:
In a randomized block design blocked by gender, treatments should be assigned randomly within each gender block. The correct assignment maintains a distribution of one treatment for each gender. Looking at the given options, only one meets this criterion:
OA: (1f, 2f), B: (1m, 2m). C: (3f, 3m). D: (4f, 4m)
Each treatment group A, B, C, and D contains one male and one female, making the distribution of treatments blocked by gender.
what is the value of m
Answers
Answer:
114°--------------------------
Angle G is central angle and angle E is inscribed angle, both with same endpoints.
According to the inscribed angle theorem the inscribed angle is half of the central angle.
Hence the central angle G measures:
m∠G = 2(m∠E)m∠G = 2(57°)m∠G = 114°Two models R1 and R2 are given for revenue (in millions of dollars) for a corporation. Both models are estimates of revenues from 2030 through 2035, with t = 0 corresponding to 2030.
R1 = 7.23 + 0.25t + 0.03t^2
R2 = 7.23 + 0.1t + 0.01t^2
How much more total revenue (in millions of dollars) does that model project over the six-year period ending at t = 5? (Round your answer to three decimal places.)
Answers
Step-by-step explanation:
To find the difference in total revenue projected by the two models over the six-year period ending at t = 5, we need to calculate the revenue for each model from t = 0 to t = 5 and subtract the results.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5:
R1(5) = 7.23 + 0.25(5) + 0.03(5^2)
R1(5) = 7.23 + 1.25 + 0.75
R1(5) = 9.23 + 0.75
R1(5) = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5:
R2(5) = 7.23 + 0.1(5) + 0.01(5^2)
R2(5) = 7.23 + 0.5 + 0.25
R2(5) = 7.73 + 0.25
R2(5) = 7.98 million dollars
To find the difference, we subtract R2(5) from R1(5):
Difference = R1(5) - R2(5)
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects 2 million dollars more in total revenue than R2 over the six-year period ending at t = 5.
For R1:
R1 = 7.23 + 0.25t + 0.03t^2
Substituting t = 5 into the equation:
R1 = 7.23 + 0.25(5) + 0.03(5^2)
R1 = 7.23 + 1.25 + 0.75
R1 = 9.23 + 0.75
R1 = 9.98 million dollars
For R2:
R2 = 7.23 + 0.1t + 0.01t^2
Substituting t = 5 into the equation:
R2 = 7.23 + 0.1(5) + 0.01(5^2)
R2 = 7.23 + 0.5 + 0.25
R2 = 7.73 + 0.25
R2 = 7.98 million dollars
To find the difference in total revenue, we subtract R2 from R1:
Difference = R1 - R2
Difference = 9.98 - 7.98
Difference = 2 million dollars
Therefore, the model R1 projects $2 million more in total revenue over the six-year period ending at t = 5 compared to model R2.
Sarah has 12 cents. If she adds 1 dime and 1 quarter, how much money will she have?
Answers
Answer:
47 cents or $0.47
Step-by-step explanation:
1 dime = 10 cents (or $0.1)
1 quarter = 25 cents or ($0.25)
12 cents + 1 dime + 1 quarter = 12 + 10 + 25 = 47 cents
PLSPLSS PLSSMSL HELP ME
Answers
Answer:
1. x = 18
2. x = 31
Step-by-step explanation:
1. Angles in a quadrilateral sum to 360°.
360 -(60 +130 +70) = 360 -260 = 100
So, x +82 = 100. x = 100 -82 = 18
2. Angles in a triangle sum to 180°. 180 -(29 +75) = 180 -104 = 76.
So, -17 +3x = 76. 3x = 93. x = 93/3 = 31
Christine has 1 blue sock, 3 purple socks and 1 green sock in a box.
Christine takes one sock at random from the box, puts it back, and takes another sock from the box. Find the probability that Christine takes at least one blue sock.
Answers
The total number of socks in the box is 1 (blue) + 3 (purple) + 1 (green) = 5 socks.
The probability of not getting a blue sock on the first draw is (4 socks that are not blue) / (5 total socks) = 4/5.
Since Christine puts the first sock back before the second draw, the probabilities are independent. Thus, the probability of not getting a blue sock on the second draw is also 4/5.
To find the probability of not getting a blue sock in both draws, we multiply the probabilities: (4/5) * (4/5) = 16/25.
Finally, to find the probability of getting at least one blue sock, we subtract the probability of not getting any blue sock from 1: 1 - 16/25 = 9/25.
Therefore, the probability that Christine takes at least one blue sock is 9/25.
Does anybody know the answer i need. It quick!!!!!
Answers
The area of the obtuse triangle is 34 square feet with a base of 10 ft and height of 6.8 ft.
To find the area of the obtuse triangle, we can use the formula A = (1/2) * base * height. Let's denote the unknown part of the base as x.
In the given triangle, we have the width of the obtuse angle triangle as 10 ft, the height (perpendicular) as 6.8 ft, and the unknown part of the base as x.
Using the formula, we can calculate the area as:
A = (1/2) * (10 + x) * 6.8
Simplifying this expression, we get:
A = 3.4(10 + x)
Now, we need to determine the value of x. From the given information, we know that the width of the obtuse angle triangle is 10 ft. This means the sum of the two parts of the base is 10 ft. Therefore, we can write the equation:
x + 10 = 10
Solving for x, we find:
x = 0
Since x = 0, it means that one part of the base has a length of 0 ft. Therefore, the entire base is formed by the width of the obtuse angle triangle, which is 10 ft.
Now, substituting this value of x back into the area formula, we have:
A = 3.4(10 + 0)
A = 3.4 * 10
A = 34 square feet
Hence, the area of the obtuse triangle is 34 square feet.
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MLMS4 Day 3 (1 hour) SBA Task: Project November 2023 Which sides of the rectangle (that formed the sides of the cylinder) has the same length as the circumference of the circles? Which sides of the rectangle has the same length of the height of the cylinder. What do you notice between your model and the practical calculation.
Answers
The sides of the rectangle that have the same length as the circumference of the circles are the sides parallel to the bases of the cylinder. The sides of the rectangle that have the same length as the height of the cylinder are the sides perpendicular to the bases. While the model provides a simplified representation, practical calculations might have slight differences due to real-world factors.
In a cylinder, the two circular bases are connected by a curved surface, forming a three-dimensional shape. The rectangular shape that wraps around the curved surface of the cylinder is called the lateral surface or the lateral area.
To determine which sides of the rectangle have the same length as the circumference of the circles, we need to understand the geometry of a cylinder. The circumference of a circle is calculated using the formula:
Circumference = 2πr,
where r is the radius of the circle. In a cylinder, the bases are identical circles, so the circumference of each base is equal. Therefore, the sides of the rectangle that are parallel to the bases have the same length as the circumference of the circles.
Now, let's consider the height of the cylinder. The height is the distance between the two bases and is perpendicular to the bases. In the rectangular representation of the cylinder, the sides that are perpendicular to the bases represent the height. Hence, the sides of the rectangle that are perpendicular to the bases have the same length as the height of the cylinder.
When comparing the model (rectangular representation) with practical calculations, we may notice some differences. The model provides a simplified representation of the cylinder, assuming that the lateral surface is perfectly wrapped around the curved surface. However, in practical calculations, there might be slight variations due to factors like material thickness, manufacturing processes, or measuring precision. These variations can result in minor deviations between the model and the practical calculations.
It's important to consider that the model is an approximation and serves as a visual aid to understand the basic properties of the cylinder. In real-life applications or engineering calculations, precise measurements and considerations of tolerances are crucial.
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For the sequence -27,-12, 3, 18,..., the expression that defines the nth term where a, = -27 is
Answers
Answer:
-27+15 (N-1)
Step-by-step explanation:
-27, -12, 3, 18
Take the second term and subtract the first term to find the common difference
-12 - (-27)
-12+27 = 15
The common difference is +15
We are adding 15 each time
The formula for an arithmetic sequence is
an = a1+d(n-1)
an = -27 +15(n-1)
The expression
28 (78-14)9-13(78-49)9
can be
rewritten as
(X-y)" (262 + y? + gxy). Whatis the value of p?
Answers
Answer:
p =1 0
Step-by-step explanation:
x³(x - y)⁹ - y³(x - y)⁹ = (x - y)⁹[x³ - y³]
= (x - y)⁹(x - y)(x² + y² + xy)
= (x - y)¹⁰(x² + y² + xy)
where p = 10 and q = 1
Answer:
p = 10
Step-by-step explanation:
Given expression:
[tex]x^3(x-y)^9 - y^3(x-y)^9[/tex]
Factor out the common term (x - y)⁹:
[tex](x-y)^9(x^3- y^3)[/tex]
[tex]\boxed{\begin{minipage}{5cm}\underline{Difference of two cubes}\\\\$x^3-y^3=(x-y)(x^2+y^2+xy)$\\\end{minipage}}[/tex]
Rewrite the second parentheses as the difference of two cubes.
[tex](x-y)^9(x-y)(x^2+y^2+xy)[/tex]
[tex]\textsf{Apply\:the\:exponent\:rule:} \quad a^b\cdot \:a^c=a^{b+c}[/tex]
[tex](x-y)^{9+1}(x^2+y^2+xy)[/tex]
[tex](x-y)^{10}(x^2+y^2+xy)[/tex]
Comparing the rewritten original expression with the given expression:
[tex](x-y)^{10}(x^2+y^2+xy)=(x-y)^p(x^2+y^2+qxy)[/tex]
We can see that [tex](x-y)^p[/tex] corresponds to [tex](x-y)^{10}[/tex] in the given expression.
Therefore, we can conclude that p = 10.