Solve for |x + 4|= -8
If anyone helps thank u
Answer:
no solution!
Step-by-step explanation:
The absolute value of a quantity is always non-negative, meaning it cannot be negative. However, in this equation, we have the absolute value of x + 4 equaling -8, which is a negative value. Therefore, there is no solution to this equation.
The test scores for a local DMV had an average of 20 and a standard deviation of 5. Hank scored a 23.
What is the z-score for Hank?
We need to find the z-score for Hank using the above formula.z = (x - μ) / σ= (23 - 20) / 5= 0.6So, the z-score for Hank is 0.6.
The z-score measures the number of standard deviations a particular value is away from the mean. A positive z-score indicates that Hank's score is above the mean, while a negative z-score would indicate a score below the mean. In this case, a z-score of 0.6 suggests that Hank's score is 0.6 standard deviations above the average.
The z-score is a measure of the number of standard deviations that a value is above or below the mean of a distribution. It is calculated using the formula z = (x - μ) / σ, where x is the value being evaluated, μ is the mean of the distribution, and σ is the standard deviation.
The given problem states that the test scores of a local DMV had an average of 20 and a standard deviation of 5.
So, the mean μ = 20 and the standard deviation σ = 5.Hank scored a 23. This means that his score is 0.6 standard deviations above the mean of the distribution.
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The venn Diagram represents the result of survey that asked participants wether they would want a bird or fish as a pet .
Match the box with the value that goes into the box to Conroe the way table
41. 1. Box 1
22. 2. Box . 2
3 . Box 3
32. Box 4
10. Box 5
19. Box 6
57. Box 7
16. Box 8
25. Box 9
6
The venn diagram has been created and solved in the table below
How to sdolve the venn diagramAs we can see the venn diagram:
number of bird+fish=6
number of bird+not fish= 10
number of fish+not bird=19
and number of not fish and not bird=22
Hence, we get the following table
Fish Not Fish Total
Bird 6 10 16
Not Bird 19 22 41
Total 25 32 57
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Can someone help me please
Denis's and Dasha's methods use different operations to simplify the expressions in different orders.
Denis's method uses addition, subtraction, and multiplication operations, but Dasha's method does not.
What are multiplication operations?Multiplication operations are described as using mathematical operation that indicates how many times a number is added to itself.
Denis's Assignment
2* 6+2w-54
12+2w = 54
12-12+2w= 54-12
2w=42
w= 21
Dasha's Assignment
54-2* 6
54-12= 42
The two widths add to 42 cm
42/ 2-21
We can see that Dasha's method also uses addition and subtraction operations, but she simplifies the expression by performing the operations in a different order.
She subtracts the product of 2 and 6 from 54.
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A train travels 70 feet in 1/10th of a second. At this same speed, how many feet will it travel in 3 and 1/2 ( three and one half) seconds?
Answer:
the train will travel 245 feet in 3 and 1/2 seconds
Step-by-step explanation:
To determine the distance the train will travel in 3 and 1/2 seconds, we can use a proportion based on the given information.
Let's set up the proportion:
70 feet / (1/10 second) = x feet / (3 1/2 seconds)
To solve this proportion, we can first convert the mixed number 3 1/2 to an improper fraction.
3 1/2 = 7/2
Now we can rewrite the proportion:
70 / (1/10) = x / (7/2)
To simplify the proportion, we can multiply the numerator and denominator of the right side by 10/1:
70 / (1/10) = (x * 10) / (7/2)
Simplifying further, we get:
70 * (10/1) = x * (10/7/2)
700 = x * (20/7)
To find x, we can divide both sides of the equation by (20/7):
x = 700 / (20/7)
x = 700 * (7/20)
x = 245 feet
Therefore, at the same speed, the train will travel 245 feet in 3 and 1/2 seconds.
NO LINKS!! URGENT HELP PLEASE!!
Solve each problem involving direct or inverse variation.
26. If y varies directly as x, and y = 15/4 when x = 15, find y when x = 11
27. If y varies inversely as x, and y = 4 when x = 9, find when x = 7
Answer:
see explanation
Step-by-step explanation:
26
given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
to find k use the condition y = [tex]\frac{15}{4}[/tex] when x = 15
[tex]\frac{15}{4}[/tex] = 15k ( divide both sides by 15 )
[tex]\frac{\frac{15}{4} }{15}[/tex] = k , then
k = [tex]\frac{15}{4}[/tex] × [tex]\frac{1}{15}[/tex] = [tex]\frac{1}{4}[/tex]
y = [tex]\frac{1}{4}[/tex] x ← equation of variation
when x = 11 , then
y = [tex]\frac{1}{4}[/tex] × 11 = [tex]\frac{11}{4}[/tex]
27
given y varies inversely as x then the equation relating them is
y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation
to find k use the condition y = 4 when x = 9
4 = [tex]\frac{k}{9}[/tex] ( multiply both sides by 9 )
36 = k
y = [tex]\frac{36}{x}[/tex] ← equation of variation
when x = 7 , then
y = [tex]\frac{36}{7}[/tex]
Answer:
26) y = 11/4
27) y = 36/7
Step-by-step explanation:
Question 26Direct variation is a mathematical relationship between two variables where a change in one variable directly corresponds to a change in the other variable. It is represented by the equation y = kx, where y and x are the variables and k is the constant of variation.
To find the constant of variation, k, substitute the given values of y = 15/4 when x = 15 into the direct variation equation and solve for k:
[tex]\begin{aligned}y&=kx\\\\\dfrac{15}{4}&=15k\\\\k&=\dfrac{1}{4}\end{aligned}[/tex]
To find the value of y when x = 11, substitute the found value of k and x = 11 into the direct variation equation, and solve for y:
[tex]\begin{aligned}y&=kx\\\\y&=\dfrac{1}{4} \cdot 11\\\\y&=\dfrac{11}{4}\end{aligned}[/tex]
Therefore, if y varies directly as x, then y = 11/4 when x = 11.
[tex]\hrulefill[/tex]
Inverse variation is a mathematical relationship between two variables where an increase in one variable results in a corresponding decrease in the other variable, and vice versa, while their product remains constant. It is represented by the equation y = k/x, where y and x are the variables and k is the constant of variation.
To find the constant of variation, k, substitute the given values of y = 4 when x = 9 into the inverse variation equation and solve for k:
[tex]\begin{aligned}y&=\dfrac{k}{x}\\\\4&=\dfrac{k}{9}\\\\k&=36\end{aligned}[/tex]
To find the value of y when x = 7, substitute the found value of k and x = 7 into the inverse variation equation, and solve for y:
[tex]\begin{aligned}y&=\dfrac{k}{x}\\\\y&=\dfrac{36}{7}\end{aligned}[/tex]
Therefore, if y varies inversely as x, then y = 36/7 when x = 7.
write inequality shown y=-11/7x-4
Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:
y ≤ -11/7x - 4
This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.
Step-by-step explanation: .
(12sin(pi/2x)*lnx)/((x³+5)(x-1))
lim as x approaches 1
The limit of the given function as x approaches 1 is 0.
To find the limit of the given function as x approaches 1, we need to evaluate the expression by substituting x = 1. Let's break it down step by step:
1. Begin by substituting x = 1 into the numerator:
[tex]\[12\sin\left(\frac{\pi}{2}\cdot 1\right)\ln(1) = 12\sin\left(\frac{\pi}{2}\right)\ln(1) = 12(1)\cdot 0 = 0\][/tex]
2. Now, substitute x = 1 into the denominator:
(1³ + 5)(1 - 1) = 6(0) = 0
3. Finally, divide the numerator by the denominator:
0/0
The result is an indeterminate form of 0/0, which means further analysis is required to determine the limit. To evaluate this limit, we can apply L'Hôpital's rule, which states that if we have an indeterminate form 0/0, we can take the derivative of the numerator and denominator and then evaluate the limit again. Applying L'Hôpital's rule:
4. Take the derivative of the numerator:
[tex]\[\frac{d}{dx}\left(12\sin\left(\frac{\pi}{2}x\right)\ln(x)\right) = 12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{x} + \frac{\sin\left(\frac{\pi}{2}x\right)\ln(x)}{x}\right)\][/tex]
5. Take the derivative of the denominator:
[tex]\[\frac{d}{dx}\left((x^3 + 5)(x - 1)\right) = \frac{d}{dx}\left(x^4 - x^3 + 5x - 5\right) = 4x^3 - 3x^2 + 5\][/tex]
6. Substitute x = 1 into the derivatives:
Numerator: [tex]\[12\left(\cos\left(\frac{\pi}{2}\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{-1}{1} + \sin\left(\frac{\pi}{2}\right) \cdot \frac{\ln(1)}{1}\right) = 0\][/tex]
Denominator: 4(1)³ - 3(1)² + 5 = 4 - 3 + 5 = 6
7. Now, reevaluate the limit using the derivatives:
lim as x approaches 1 of [tex]\[\frac{{12\left(\cos\left(\frac{\pi}{2}x\right) \cdot \left(\frac{\pi}{2}\right) \cdot \frac{{-1}}{{x}} + \sin\left(\frac{\pi}{2}x\right) \cdot \frac{{\ln(x)}}{{x}}\right)}}{{4x^3 - 3x^2 + 5}}\][/tex]
= 0 / 6
= 0
Therefore, the limit of the given function as x approaches 1 is 0.
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find by a digit to make the number divisible by 3 1234?
A digit to make the number divisible by 3 is by adding the digit 2 to the number 1234.
To make the number 1234 divisible by 3, we can find the sum of its digits and determine if it is divisible by 3. If the sum of the digits is divisible by 3, then the original number is also divisible by 3.
Let's calculate the sum of the digits in 1234:
1 + 2 + 3 + 4 = 10
The sum of the digits is 10. Since 10 is not divisible by 3, we need to add or subtract a digit to make the sum divisible by 3.
To find the digit we need to add or subtract, we can use the fact that the difference between the original sum and the next multiple of 3 is the required digit.
The next multiple of 3 greater than 10 is 12 (12 - 10 = 2). Therefore, we need to add 2 to the number 1234 to make it divisible by 3.
1234 + 2 = 1236
we obtain the number 1236, which is divisible by 3.
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Please help me w this
The solution of the given algebraic expression is: ⁷/₁₂ + ⁴/₆q
How to solve Algebraic Expressions?We are given the algebraic expression as:
¹¹/₁₂ - ¹/₆q + ⁵/₆q - ¹/₃
Combining Like terms gives us:
(¹¹/₁₂ - ¹/₃) + (⁵/₆q - ¹/₆q)
Solving both brackets individually gives us:
((11 - 4)/12) + ⁴/₆q
= ⁷/₁₂ + ⁴/₆q
Thus, we conclude that is the solution of the given algebraic expression problem
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pls help and draw it so it's more easier
In this rectangle, there are two lines of symmetry.
A line of symmetry is a line that divides a shape into two equal halves, such that each half is a mirror image of the other. The lines of symmetry in a rectangle are vertical and horizontal.
Vertical Line of Symmetry:
A vertical line of symmetry runs from the top to the bottom of the rectangle, dividing it into two equal halves. Each half is a mirror image of the other. To identify the vertical line of symmetry in a rectangle, you can visualize folding the rectangle along a line from top to bottom. The left and right sides of the folded rectangle will match perfectly.
Horizontal Line of Symmetry:
A horizontal line of symmetry runs from one side of the rectangle to the other, dividing it into two equal halves. Each half is a mirror image of the other. To identify the horizontal line of symmetry in a rectangle, imagine folding the rectangle along a line from left to right. The top and bottom sides of the folded rectangle will align perfectly.
I find the lines of symmetry in a rectangle, you can also observe its properties. In a rectangle, opposite sides are parallel and equal in length, and all interior angles are right angles (90 degrees). By considering these characteristics, you can determine that the vertical and horizontal lines passing through the center of the rectangle will be the lines of symmetry.
Understanding the lines of symmetry in a rectangle is essential in various applications, such as geometry, design, and architecture. These lines allow for balanced and symmetrical arrangements, providing aesthetic appeal and structural stability.
Final answer:
In following rectangle, there are two lines of symmetry.
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Four equal-sized equilateral triangles form a larger equilateral triangle, as shown
below.
EF-2a
ED=3b
a) Express FB in terms of b
b) Express FD in terms of a and b
c) Express CB in terms of a and b
Give each answer in its simplest form
a) To express FB in terms of b, we need to consider the relationship between FB and EF. Since EF is equal to 2a, we can substitute this value into the expression for FB:
FB = EF - FB
= (2a) - (2a)
= 0
Therefore, FB is equal to 0 in terms of b.
b) To express FD in terms of a and b, we can use the given relationship between ED and FD. ED is equal to 3b, so we can substitute this value into the expression for FD:
FD = ED - FB
= (3b) - (0)
= 3b
Therefore, FD is equal to 3b in terms of a and b.
c) To express CB in terms of a and b, we need to consider the relationship between CB and EF. Since EF is equal to 2a, we can substitute this value into the expression for CB:
CB = EF - EB
= (2a) - (FB + FD)
= (2a) - (0 + 3b)
= 2a - 3b
Therefore, CB is equal to 2a - 3b in terms of a and b.
PLEASE ANSWER NOW I NEED THIS ASAP FOR 100 POINTS!!!!
[tex]1\frac{3}{4}[/tex] feet as a multiplication expression using the unit, 1 foot, as a factor is [tex]1\frac{3}{4}[/tex]×1.
The given fraction is [tex]1\frac{3}{4}[/tex].
[tex]1\frac{3}{4}[/tex] feet can be written as a multiplication expression as follows: 1 foot × 1 3/4. This is because [tex]1\frac{3}{4}[/tex] is the same as 1 + 3/4.
Furthermore, 3/4 can be written as 0.75, which is the same as 0.75 × 1 foot.
Therefore, the multiplication expression is 1 foot × [tex]1\frac{3}{4}[/tex] = 1 foot × (1 + 0.75) = 1 foot × 1 + 1 foot × 0.75 = 1 foot + 1.75 feet.
Therefore, [tex]1\frac{3}{4}[/tex] feet as a multiplication expression using the unit, 1 foot, as a factor is [tex]1\frac{3}{4}[/tex]×1.
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Step-by-step explanation:
1ft=12in
1¾ft=x
x=12×7/4=21in
1¾ft=1¾×1 ft
Compare the graph of Car A to the table of Car B to determine:
a. The rate of each car,
b.
Which has the greatest speed,
C. How many times faster is the fastest car. (example: 2, 3 or 4 times faster)
Car A is 2 times Faster than Car B during the first hour.
The graph of Car A is a straight line, indicating that it is traveling at a constant speed.
The graph shows that Car A is traveling 100 miles in 2 hour .The table of Car B shows that it travels 50 miles in 1 hour, 100 miles in 2 hours, and 150 miles in 3 hours. Thus, the rate of Car B is increasing, as it travels at a faster speed during each hour compared to the previous hour.To find the rate of each car, we need to divide the distance by the time. For Car A, rate = distance ÷ time = 100 miles ÷ 2 hours = 50 miles per hour.
For Car B, we can find the average rate for each hour by dividing the distance traveled during that hour by the time. Thus, the rates are: First hour: 50 miles per hour Second hour: 50 miles ÷ 1 hour = 50 miles per hour Third hour: 50 miles ÷ 1 hour = 50 miles per hour By comparing the rates, we see that both cars are traveling at the same speed during the second and third hours. However, during the first hour, Car A is traveling faster than Car B.
Thus, Car A has the greatest speed.To determine how many times faster Car A is compared to Car B during the first hour, we can divide their rates. The rate of Car A is 50 miles per hour, while the rate of Car B is 50 miles per hour. Therefore, Car A is traveling at the same speed as Car B during the second and third hours. During the first hour, Car A is traveling twice as fast as Car B. Thus, Car A is 2 times faster than Car B during the first hour.
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grade 11 2022 June common test mathematics memorandum?
Note that the roots of the equation Unequal and rational (Option D)
How is this so ?The roots of the equation (x - 3)² = 4 can be found by taking the square root of both sidesof the equation.
x - 3 = ±√4
⇒ x - 3 = ±2
Solve for x
For the positive square root.
x - 3 = 2
x = 2 + 3
x = 5
For the negative square root.
x - 3 = -2
x = -2 + 3
x = 1
Since the equation has two roots, x = 5 and x = 1. These roots are unequal and rational. (Option D)
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Full Question:
Although part of your question is missing, you might be referring to this full question:
The roots of the equation (x - 3)² = 4 are
A.Unequal and irrational.
B.Equal and rational.
C. Equal and irrational.
D. Unequal and rational.
Determine the equation of a straight line that is parallel to the line 2x + 4y =1 and which passes through the point (1, 1).
The equation of the straight line parallel to 2x + 4y = 1 and passing through the point (1, 1) is y = (-1/2)x + 3/2.
To determine the equation of a straight line that is parallel to the line 2x + 4y = 1 and passes through the point (1, 1), we can use the fact that parallel lines have the same slope.
First, let's rearrange the given equation 2x + 4y = 1 into slope-intercept form, y = mx + b,
where m is the slope and b is the y-intercept.
2x + 4y = 1
4y = -2x + 1
y = (-2/4)x + 1/4
y = (-1/2)x + 1/4
From this equation, we can see that the slope of the given line is -1/2.
Since the parallel line we want to find has the same slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1),
where (x1, y1) is the given point.
Plugging in the values (1, 1) and the slope -1/2 into the equation, we have:
y - 1 = (-1/2)(x - 1)
To simplify, we distribute the -1/2:
y - 1 = (-1/2)x + 1/2
Next, we isolate y by adding 1 to both sides of the equation:
y = (-1/2)x + 1/2 + 1
y = (-1/2)x + 3/2.
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What is the total weight of the bags that weighed /8 pound each?
The total weight of Rice that Mark buys is given as follows:
2.5 pounds.
How to obtain the total weight?The total weight of Rice that Mark buys is obtained applying the proportions in the context of the problem.
The weight of each bag is given as follows:
5/8 pounds = 0.625 pounds.
The number of bags is given as follows:
4 bags.
Hence the total weight of Rice that Mark buys is given as follows:
4 x 0.625 = 2.5 pounds.
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a system of equations is shown below
y = 3x - 1
y = - 2x + 4
what is the sum of X and Y in the solution to the system
Answer:
3
Step-by-step explanation:
You want the value of (x+y) as determined by the system of equations ...
y = 3x -1y = -2x +4SolutionWe can subtract the second equation from the first to get ...
(y) -(y) = (3x -1) -(-2x +4)
0 = 5x -5
0 = x -1
1 = x
Using the first equation to find y, we have ...
y = 3(1) -1 = 2
The sum of x and y is (x +y) = (1 +2) = 3.
Alternate solutionLet t = x+y. This means y = t -x.
Now, the equations become ...
t -x = 3x -1t -x = -2x +4Adding 4 times the second equation to the first gives ...
(t -x) +4(t -x) = (3x -1) +4(-2x +4)
5t -5x = -5x +15
Adding 5x and dividing by 5 gives ...
t = 3
The sum of x and y is 3.
__
Additional comment
Sometimes you can find the value of the objective function directly, as in the second solution here.
The reason we chose 4 as a multiplier in the alternate solution is that we observed the equations could be written as ...
t -4x = -1
t +x = 4
where the variable x has coefficients with a ratio of -4. Using 4 as the multiplier eliminates the x-variable, leaving t — the variable whose value we want.
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find the slope of 1,5 and 0,4
A portion of the Quadratic Formula proof is shown. Fill in the missing statement.
Statements Reasons
x squared plus b over a times x plus the quantity b over 2 times a squared equals negative 4 times a times c all over 4 times a squared plus b squared over 4 a squared Find a common denominator on the right side of the equation
x squared plus b over a times x plus the quantity b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Add the fractions together on the right side of the equation
the quantity x plus b over 2 times a squared equals b squared minus 4 times a times c all over 4 times a squared Rewrite the perfect square trinomial on the left side of the equation as a binomial squared
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared Take the square root of both sides of the equation
? Simplify the right side of the equation
The missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
The missing statement in the proof of the Quadratic Formula, we need to simplify the right side of the equation:
x plus b over 2 times a equals plus or minus the square root of b squared minus 4 times a times c, all over 4 times a squared
To simplify the right side, we can take the square root of the numerator and denominator separately:
√(b squared minus 4 times a times c) = √((b^2 - 4ac))
Now, substituting the simplified expression into the equation, we have:
x plus b over 2 times a equals plus or minus √((b^2 - 4ac)) all over 4 times a squared
This completes the missing statement in the proof of the Quadratic Formula.
In conclusion, the missing statement in the proof of the Quadratic Formula involves simplifying the right side of the equation by taking the square root of the numerator, resulting in x plus b over 2a equals plus or minus √((b^2 - 4ac)) all over 4a squared.
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List all the 4-tuples in the relation {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}
We have a total of seven 4-tuples that satisfy the given relation.The given relation is {(a,b,c,d) | a,b,c,d∈!+ , a+b+c+d = 6}. It can be understood as the set of 4-tuples (a, b, c, d) such that a, b, c, and d are positive integers and their sum is equal to 6.
Let's now list all the possible 4-tuples that satisfy the given relation. The possible combinations are as follows: (1, 1, 1, 3), (1, 1, 2, 2), (1, 2, 1, 2), (2, 1, 1, 2), (1, 2, 2, 1), (2, 1, 2, 1), and (2, 2, 1, 1).
Here's a brief explanation on how these 4-tuples were obtained. Let a, b, c, and d be positive integers such that a+b+c+d = 6. The least possible value that each variable can take is 1.
So, we start with a=1 and find all possible values of (b, c, d) that satisfy the given equation. Then, we move to a=2 and repeat the process. Finally, we list all the possible 4-tuples that we obtained.
Thus, we have a total of seven 4-tuples that satisfy the given relation.
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No do I solve this problem?
Using law of sine, the value of A is 54°, b is 4.4 units and c is 6.1 units
What is sine rule?The sine rule, also known as the law of sines, is a mathematical principle used in trigonometry to relate the sides and angles of a triangle. It states that the ratio of the length of a side of a triangle to the sine of the opposite angle is constant for all sides and angles of the triangle.
The formula is given as;
a / sin A = b / sin B = c / sin C
To find the value of angle A
A + B + C = 180°
Reason: The sum of angles in a triangle is equal to 180°
46° + A + 80° = 180°
126° + A = 180°
A = 180° - 126°
A = 54°
Using this, we can apply sine rule;
a / sin A = b / sin B
5/ sin 54 = b / sin 46
b = 5sin46 / sin 54
b = 4.4 units
Using sine rule again;
a/ sin A = c / sin C
5/ sin 54 = c / sin80
c = 5sin80 / sin 54
c = 6.1 units
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Cómo despejar an
Sn= (a1 + an)/2 n
Step-by-step explanation:
The formula:
�
�
=
�
2
(
�
1
+
�
�
)
S
n
=
2
n
(a
1
+a
n
)
is used to solve for the sum of the arithmetic sequence given the first term a₁, the number of terms n, and the last term in an.
Example:
3, 6, 9, 12, 15,...,123
The first term, a₁ = 3
The last term an = 123
Common difference, d = 3 (because the sequence are multiples of 3)
Number of terms, n= ?
Find the number of terms, n:
an = a₁ + (n-1) (d)
123 = 3 + (n-1) (3)
123 = 3 - 3 + 3n
123/3 = 3n/3
n = 41
To find the sum of the given sequence without adding 3 + 6 + 9, ... + 123, we use the formula:
S₄₁ = (41/2) (3 + 123)
S₄₁ = (41/2) (126)
S₄₁ = (41)(63)
S₄₁ = 2,583 ⇒ the sum of the given sequence
Prove the following?
X is an inductive set, then {X [tex]\in[/tex] x is transitive} is also an inductive set. Consequently, every n [tex]\in[/tex] N is transitive.
To prove the statement, we need to demonstrate that if X is an inductive set, then the set {[tex]X \in x[/tex]is transitive} is also an inductive set.
Let's break down the proof into two parts:
If X is an inductive set, then {[tex]X \in x[/tex] is transitive} is a subset of X:
To show that {[tex]X \in x[/tex]is transitive} is a subset of X, we need to prove that every element in {[tex]X \in x[/tex] is transitive} is also an element of X.
If X is an inductive set, it means that X contains the empty set (∅) and for every element x in X, the successor of x (denoted as S(x)) is also in X. Now, consider an arbitrary element y in {[tex]X \in x[/tex] is transitive}. By definition, y is a transitive set.
Since X is inductive, it contains the empty set and for every element in X, its successor is also in X. Thus, y must also be in X, and {[tex]X \in x[/tex] is transitive} is a subset of X.
{[tex]X \in x[/tex] is transitive} is an inductive set:
To show that {[tex]X \in x[/tex] is transitive} is an inductive set, we need to demonstrate that it satisfies the properties of an inductive set.
First, we prove that the empty set (∅) is an element of {EX: x is transitive}. Since the empty set is transitive (it vacuously satisfies the definition of transitivity), it belongs to {[tex]X \in x[/tex] is transitive}.
Second, we prove that for every element y in {[tex]X \in x[/tex] is transitive}, its successor S(y) is also in {[tex]X \in x[/tex] is transitive}. Let y be an arbitrary element in {[tex]X \in x[/tex] is transitive}.
By definition, y is a transitive set. We need to show that S(y) is also a transitive set. Since X is inductive, it means that for every element x in X, its successor S(x) is also in X. Applying this property to y, we conclude that S(y) is in X. Since S(y) is in X, it is also in [tex]X \in x[/tex] is transitive}. Hence, {[tex]X \in x[/tex] is transitive} satisfies the property of an inductive set.
By proving both parts, we have shown that if X is an inductive set, then {[tex]X \in x[/tex] is transitive} is also an inductive set. Consequently, every [tex]n \in N[/tex] is transitive.
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Name two pairs of congruent angles
The two pairs of congruent angles are determined as angle XWY and angle YZX.
What are congruent angles?Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.
So congruent angles are two or more angles that are identical or equal to each other.
From the given diagram , the pair of angles are congruent to each other.
Angle XWY is congruent to angle YZX, this is because vertical opposite angles in a cyclic quadrilateral are equal in measure.
Thus, the two pairs of congruent angles are determined as angle XWY and angle YZX.
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In APQR, m2 P = 60°, mz Q = 30°, and m2 R = 90°. Which of the following
statements about APQR are true?
Check all that apply.
A. PQ=2. PR
B. QR=
PQ
C. QR= 2 • PR
☐ D. PR = = 4. PQ
•
□E. QR=√√√3 PR
F. PQ=√√3 PR
The statements that are true about triangle PQR are QR = (sqrt(3))/2 * PQ and PR = (sqrt(3))/2 * PQ.The correct answer is option B and D.
Let's analyze the statements one by one:
A. PQ = 2PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.
Therefore, PQ = x, and PR = x√3. Since √3 is not equal to 2, this statement is false.
B. QR = (sqrt(3))/2 * PQ:
This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x.
Therefore, QR = x√3/2 = (sqrt(3))/2 * x = (sqrt(3))/2 * PQ. This statement holds true.
C. OR = 2PR:
We don't have any information regarding the length of OR, so we cannot determine if this statement is true or false based on the given information.
D. PR = (sqrt(3))/2 * PQ:
This statement is true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PR = x√3 = (sqrt(3))/2 * 2x = (sqrt(3))/2 * PQ. This statement is correct.
E. QR = sqrt(3) * PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, QR = x√3, and PR = x√3. So, QR = PR, but not QR = sqrt(3) * PR.
F. PQ = sqrt(3) * PR:
This statement is not true. In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows: opposite the 30-degree angle is x, opposite the 60-degree angle is x√3, and the hypotenuse (opposite the 90-degree angle) is 2x. Therefore, PQ = x, and PR = x√3. So, PQ = PR/√3, but not PQ = sqrt(3) * PR.
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The probable question may be:
In triangle PQR , m angle P = 60 deg , m angle Q = 30 deg and m angle R = 90 deg Which of the following statements about triangle PQR are true?
Check all that apply
A. PQ = 2PR
B.QR = (sqrt(3))/2 * PQ
C. OR = 2PR
D.PR = (sqrt(3))/2 * PQ
E. QR = sqrt(3) * PR
F. PQ = sqrt(3) * PR
Find the smallest whole number by which 16087 should be multiplied or divided to get a perfect square
There is no whole number by which you can multiply or divide 16087 to make it a perfect square.
To determine by which number you should multiply or divide 16087 to make it a perfect square, we can analyze its prime factorization. The prime factorization of 16087 is 13 × 1237.
In order to make 16087 a perfect square, we need each prime factor to have an even exponent. However, when we examine the prime factors of 16087, we find that both 13 and 1237 have an exponent of 1.
To make the exponents even, we need to multiply or divide 16087 by additional prime factors and their respective exponents. However, since 16087 is a product of two prime numbers (13 and 1237), we cannot introduce any additional prime factors to make the exponents even.
A perfect square is a number that can be expressed as the product of two equal factors. In the case of 16087, it cannot be transformed into a perfect square by multiplying or dividing by any whole number. The prime factors 13 and 1237 remain with an exponent of 1 each, indicating that there is no integer that can be applied to make them equal and convert 16087 into a perfect square.
Therefore, there is no whole number by which you can multiply or divide 16087 to make it a perfect square.
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the slope of the line is below -3. Which of the following is the point slope form if the line?
Answer: y=-3x+b
Step-by-step explanation:
You didn't give the answers, but it would look something like this:
y=-3x+b
Marianna finds an annuity that pays 8% annual interest, compounded quarterly. She invests in this annuity and contributes $10,000 each quarter for 6 years. How much money will be in her annuity after 6 years? Enter your answer rounded to the nearest hundred dollars.
The amount of money in Marianna's annuity after 6 years will be approximately $300,516.
To calculate the amount of money in Marianna's annuity after 6 years, we can use the formula for compound interest on an annuity:
A = P * ((1 + r/n)^(n*t) - 1) / (r/n)
Where:
A = the final amount in the annuity
P = the regular contribution (each quarter) = $10,000
r = annual interest rate = 8% = 0.08
n = number of compounding periods per year = 4 (since it's compounded quarterly)
t = number of years = 6
Plugging in the values:
A = 10000 * ((1 + 0.08/4)^(4*6) - 1) / (0.08/4)
Calculating this expression:
A ≈ 10000 * ((1.02)^24 - 1) / 0.02
A ≈ 10000 * (1.601032449136241 - 1) / 0.02
A ≈ 10000 * 0.601032449136241 / 0.02
A ≈ 10000 * 30.05162245681205
A ≈ 300,516.22
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Answer:
304200
Step-by-step explanation:
To find the value of P6, use the savings annuity formula
PN=d((1+r/k)N k−1)r/k.
From the question, we know that r=0.08, d=$10,000, k=4 compounding periods per year, and N=6 years. Substitute these values into the formula gives
P6=$10,000 ((1+0.08/4)6⋅4−1)/(0.08/4).
Simplifying further gives P6=$10,000 ((1.02)24−1)/(0.02) and thus P6=$304,218.62.
Rounding as requested, our answer is 304200.
Hi, I just needed some help with the question that is attached.
a. The total impedance, z is 6 Ohms
b. The modulus of the total impedance is 6 Ohms, which represents its magnitude or absolute value. The angle is not provided for the principal argument.
How to determine the impedanceFrom the information given, we have that;
z₁ = R₁ + Xₐ
z₂ = R₂ - Xₙ
We have that the values are;
R₁ = 3 OhmsXₐ = 3 OhmsR₂ = 4 OhmsXₙ = 4 OhmsNow, substitute the values, we have;
z₁ = 3 + 3
Add the values
z₁ = 6 Ohms
z₂ = 4 - 4
z₂ = 0 Ohms
To determine the total impedance, we have;
1/z = 1/z₁ + 1/z₂
Substitute the values
1/z = 1/6 + 1/0
1/z = 1/6
z = 6 Ohms
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