Problem 5
The missing interior angle of the triangle is also x because the base angles are congruent for any isosceles triangle. The triangle is isosceles because of the two tickmarks indicating those sides are the same length.
The angle 115 is supplementary to that angle x mentioned, so,
115+x = 180
x = 180-115
x = 65
Now to find y, we'll use the idea that adding the angles of any triangle always gets to 180
x+x+y = 180
65+65+y = 180
130+y = 180
y = 180-130
y = 50
--------------------
Answers: x = 65 and y = 50=======================================================
Problem 6
We use the same idea as the previous problem. The missing angle is x because it's a congruent base angle. This missing angle x is supplementary to the 135 degree angle
x+135 = 180
x = 180-135
x = 45
Now add up the interior angles of the triangle, set the sum equal to 180 and solve for x
x+x+y = 180
45+45+y = 180
90+y = 180
y = 180-90
y = 90
--------------------
Answers: x = 45 and y = 90=======================================================
Problem 8
This triangle is equilateral since all sides are the same length. Consequently, all angles are the same measure and equal to 180/3 = 60 degrees each.
Setting the bottom left angle equal to 60 and solving leads to
3y = 60
y = 60/3
y = 20
Do the same for the bottom right angle
2x = 60
x = 60/2
x = 30
--------------------
Answers: x = 30 and y = 20=======================================================
Problem 9
The x and 110 degree angles are supplementary. They form a straight angle of 180 degrees
x+110 = 180
x = 180-110
x = 70
Focusing on the smaller right triangle on the right side, we have the upper acute angle x = 70, and the bottom acute angle y, and a right angle of 90 degrees.
These three angles must add to 180
x+90+y = 180
70+90+y = 180
160+y = 180
y = 180-160
y = 20
--------------------
Answers: x = 70 and y = 20For 13 would you subtract because there's a negative and positive you always subtract and another question is would it be negative or positive
Answer:
20
Step-by-step explanation:
Whenever adding a positive to a negative, the answer will increase, it will be closer to zero and the positives than the original negative number.So, -10 + 30 = 30 - 1030 - 10 = 20I hope this helps!
thats the problem: 2x + 7 > 11
Answer:
x=3 or greater
Step-by-step explanation:
Answer: x > 2
Step-by-step explanation: so on a number line 2 should go right to ten ion really know how to eggsplain it lol
Determine the value of x for which r ∥ s if
m∠1 = 40 – 4x; and
m∠2 = 50 – 8x
The choices are
2.5
2
30
1.5
Answer:
2.5
Step-by-step explanation:
given this information, in order to use her 4 hours of time spent studying to get the highest possible test score, how many hours should she have spent solving multiple choice problems, and how many hours should she have spent reviewing lecture notes? 0 hours working on problems, 4 hours reading 2 hours working on problems, 2 hours reading 3 hours working on problems, 1 hour reading 4 hours working on problems, 0 hours reading
The most effective way to use her 4 hours of study time to get the highest possibility or probability of test scores would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
From the information given, it is clear that working on multiple-choice problems is the most effective way to improve her test score. Therefore, the highest possibility or probability of test scores would be achieved by spending the most time working on multiple-choice problems.
The available time for studying is 4 hours, so the maximum time that can be spent working on multiple-choice problems is 4 hours. If she spends 4 hours working on multiple-choice problems, she will not have any time left to review lecture notes.
So, the most effective way to use her 4 hours of study time to get the highest possible test score would be to spend 4 hours working on multiple-choice problems and 0 hours reviewing lecture notes.
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backtracking with conflict-directed back-jumping, where the variable order is (a1, h, a4, f1, a2, f2, a3, t), and the value order is (red, green, blue)
In backtracking with conflict-directed back-jumping, the search for a solution to a problem is performed using a depth-first search algorithm. The variable order you mentioned, (a1, h, a4, f1, a2, f2, a3, t), represents the sequence in which variables are assigned values during the search. The value order, (red, green, blue), indicates the order in which the algorithm will try assigning different values to the variables.
Conflict-directed back-jumping is an improvement over basic backtracking, as it helps reduce the search space by identifying and jumping over irrelevant parts of the search tree. When a conflict (i.e., an unsolvable assignment) is encountered, the algorithm doesn't simply backtrack to the previous variable but rather identifies the cause of the conflict and jumps back to the most recent variable responsible for the conflict. This allows the algorithm to skip parts of the search tree that are guaranteed not to yield a solution.
In summary, backtracking with conflict-directed back-jumping is an efficient search technique that uses a specific variable and value order to assign values during the search. It improves upon basic backtracking by identifying the cause of conflicts and jumping back to the most recent relevant variable, thus reducing the search space and time complexity.
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The equation of the line through (3, - 4) with slope 2/3
what is the probability that a player wins $100 by matching exactly three of the first five and the sixth numbers or four of the first five numbers but not the sixth number?
The probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018. The probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003.
To calculate the probability of winning $100 by matching exactly three of the first five and the sixth numbers, we first need to determine the total number of possible combinations for the first five numbers. Since each of the five numbers can be any number between 1 and 69, there are 69 choose 5 (written as 69C5) possible combinations, which is equal to 11,238,513. Out of these 11,238,513 possible combinations, we need to choose three numbers that will match the drawn numbers and two numbers that will not match. The probability of matching three numbers is calculated as 5C3/69C5, which is equal to 0.0018. The probability of not matching the remaining two numbers is 64C2/64C2, which is equal to 1.
Therefore, the probability of winning $100 by matching exactly three of the first five and the sixth numbers is 0.0018 x 1, which is equal to 0.0018. To calculate the probability of winning $100 by matching four of the first five numbers but not the sixth number, we need to determine the total number of possible combinations for four of the first five numbers. Since each of the four numbers can be any number between 1 and 69, there are 69 choose 4 (written as 69C4) possible combinations, which is equal to 4,782,487.
Out of these 4,782,487 possible combinations, we need to choose four numbers that will match with the drawn numbers and one number that will not match. The probability of matching four numbers is calculated as 5C4/69C4, which is equal to 0.0003. The probability of not matching the remaining number is 64/64, which is equal to 1. Therefore, the probability of winning $100 by matching four of the first five numbers but not the sixth number is 0.0003 x 1, which is equal to 0.0003.
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Write an equation of the line with the given slope that contains the piren point.
The equation of a line is written in the form,
\(\begin{gathered} y=mx+b \\ \text{The slope is m, and its given as 4} \\ x=1,y=-9 \\ \text{Therefore,} \\ y=mx+b\text{ becomes} \\ -9=4(1)+b \\ -9=4+b \\ \text{Collect like terms and you have} \\ -9-4=b \\ b=-13 \\ \text{Substitute the values of m and b into the equation and you'll have} \\ y=mx+b \\ y=4x+\lbrack-13\rbrack \\ y=4x-13 \end{gathered}\)The equation of the line therefore is
y = 4x - 13
The central claim of Passage 2 is that space mining
has positive potential but
A) it will end up encouraging humanity’s reckless
treatment of the environment.
B) its effects should be thoughtfully considered
before it becomes a reality.
C) such potential may not include replenishing key
resources that are disappearing on Earth.
D) experts disagree about the commercial viability
of the discoveries it could yield.
B, its effects should be thoughtfully considered before it becomes a reality.
According to Passage 2's author, "we all stand to gain: the mineral bounty and spin-off technologies could enrich us all," space mining may be beneficial to humanity (lines 50-52). which is a positive potential.
In addition, the author emphasizes numerous times that space mining must be properly examined before being put into action: "But before the miners start firing up their rockets, we should pause for thought" (lines 53–54); "But [space mining's] consequences—both here on Earth and in space—merit careful consideration" (lines 57-59).
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ST lie on the coordinate plane with S located at (3,2). the midpoint of ST is Z(3,5). Can the location of T be determined
Answer:
T(3, 8)
Step-by-step explanation:
Yes, it can.
Use the midpoint formula with points S and Z, and solve for point T.
M( (x_1 + x_2)/2 , (y_1 + y_2)/2 )
Z(3, 5) = ( (3 + x)/2 , (2 + y)/2 )
(3 + x)/2 = 3
3 + x = 6
x = 3
(2 + y)/2 = 5
2 + y = 10
y = 8
T(3, 8)
Which of the following equations have no solutions?
Choose all answers that apply:
Choose all answers that apply:
(Choice A)
A
29x+29=29x-1129x+29=29x−1129, x, plus, 29, equals, 29, x, minus, 11
(Choice B)
B
29x+92=29x-1129x+92=29x−1129, x, plus, 92, equals, 29, x, minus, 11
(Choice C)
C
29x+11=29x-1129x+11=29x−1129, x, plus, 11, equals, 29, x, minus, 11
(Choice D)
D
29x-29=29x-1129x−29=29x−11
Answer:
All of the options
Step-by-step explanation:
Did it KA
Simplify the given polynomial expressions as much as possible.
(3x - 6)(8x + 2)
Answer:
Step-by-step explanation:
Remark
All you can really do is remove the brackets. Use FOIL
Solution
First: 3x*8x = 24^2
Outside: 2* 3x = 6x
Inside: -6*8x = - 48x
Last: -6*2 = - 12
Answer
24x^2 + 6x - 48x - 12
24x^2 - 42x - 12
If r - 5y = 6, what is the value of y when:=-4?
Answer:
r=26
Step-by-step explanation:
Answer:
-2/5 or in decimal form, -0.4
Step-by-step explanation:
Please help me with this question ASAP.
How many planes of symmetry are there in a regular hexagonal prism?
Answer:
we have 6 planes of symmetry
I need help, please. PLEASE, I NEED IT FAST.
Answer:
Hint: x is a negative number.
Step-by-step explanation:
The equation is x + 12 = -6 and you are trying to find x. The easiest way to solve this equation is by first subtracting 12 from both sides. It would look like x + 12 - 12 = -6 - 12. Since positive 12 and negative 12 are opposite and equal, they cancel each other out. This can be drawn as well into circles and crossed out for every positive circle with a negative circle. As for -6 and -12, you can use the same method of drawing circles, (trust me they can be very helpful, especially for people like me who need to see it visually before getting a hang of it). Since both are negatives, you would have to add them together and that would give you x.
(Please reply if you still have questions. :) Have a wonderful day)
Triangle SAM is congruent to Triangle REN. Find x and y.
\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)
I don’t even get the question but plz help lol
Answer:
2nd choice: constructing a line perpendicular to a given line
Step-by-step explanation:
a. Place your compass on the given point (point P)
b. From each arc on the line, draw another arc on the opposite side of the line
from the given point (P)
c. Use your ruler to join the given point (P) to the point where the arcs
intersect (Q)
Stan, Greg, and Seth were cleaning the school gym in shifts. Stan
cleaned first, then Greg, then Seth. If they each cleaned the same
amount of time for a total of 11 hours, how many minutes did each one
clean?
CAN YOU PLEASE HELP ME I AM IN GRADE 12 I NEED SOLVE THIS QUESTION
WHATS 1+1=
Answer:
2
Step-by-step explanation:
1 + 1 = 2
I hope my answer helps you :)
Answer:
2 or Window
Step-by-step explanation:
1 + 1 = 2
OR
1 + 1 = WINDOW!
HELP PLEASE!! THIS IS DUE IN A BIT
Answer:
my bestie john is correct!!
everything was correct
The coordinates of the vertices of quadrilateral HIJK are H (-2, -1), I (2, 1), J (5, 0), and K (-1, -3). Isabella states that quadrilateral HIJK is a parallelogram. Is Isabella correct? Support your answer and show all work.
Answer: No
Step-by-step explanation:
Which of the following is least likely to be a warning sign that one's debt is at a critical point? a. all credit cards are at their limits b. having several credit cards c. making only minmum payments on credit cards d. using cash advances to pay bills please select the best answer from the choices provided. a b c d
The option which is least likely to be a warning sign that one's debt is at a critical point is having several credit cards.
What is a warning sign for credit cards?The most likely warning sign for credit cards is not paying or clearing the debt of the credit card in full each month.
The options given in the problem are,
a. All credit cards are at their limits. b. Having several credit cards. c. Making only minimum payments on credit cards. d. Using cash advances to pay bills.In these options, least likely to be a warning sign is having several credit cards as having multiple cards and well management of them required the carefulness and awareness.
Thus, the option which is least likely to be a warning sign that one's debt is at a critical point is having several credit cards.
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solve for brainliest please
Answer:
136 = 9x+10 (alternate interior angles for parallel lines m and n)
9x = 126
x = 14
Step-by-step explanation:
Stop by my you tube channel "Sciency Sergei". You may suggest a topic to discuss or problem to solve.
The sum of two numbers is 18. The difference between the two numbers
is 12. What is the two numbers?
a+b in terms of a and evaluated these expressions when a = 3
Answer:
a+b=a
or, 3+b=3 (a=3)
or, b= 3-3
or, b=0
u=e^xy cos(x^2/2-y^2/2)
show that it’s harmonic and
get conjugate harmonic function
The function u(x, y) = e^(xy) * cos(x^2/2 - y^2/2) is harmonic. The conjugate harmonic function v(x, y) is given by v(x, y) = -e^(xy) * sin(x^2/2 - y^2/2) * (x + y) + g(y), where g(y) is an arbitrary function of y.
To show that the function u(x, y) = e^(xy) * cos(x^2/2 - y^2/2) is harmonic, we need to verify that it satisfies Laplace's equation:
∇^2u = 0,
where ∇^2u represents the Laplacian operator. The Laplacian operator in two dimensions is given by:
∇^2u = (∂^2u/∂x^2) + (∂^2u/∂y^2),
where (∂^2u/∂x^2) and (∂^2u/∂y^2) are the second partial derivatives of u with respect to x and y, respectively.
Let's calculate these partial derivatives:
(∂^2u/∂x^2) = e^(xy) * (y^2 - 1) * cos(x^2/2 - y^2/2) - x^2 * e^(xy) * sin(x^2/2 - y^2/2),
(∂^2u/∂y^2) = e^(xy) * (x^2 - 1) * cos(x^2/2 - y^2/2) + y^2 * e^(xy) * sin(x^2/2 - y^2/2).
Now, let's substitute these derivatives into Laplace's equation:
∇^2u = (∂^2u/∂x^2) + (∂^2u/∂y^2)
= e^(xy) * (y^2 - 1) * cos(x^2/2 - y^2/2) - x^2 * e^(xy) * sin(x^2/2 - y^2/2)
+ e^(xy) * (x^2 - 1) * cos(x^2/2 - y^2/2) + y^2 * e^(xy) * sin(x^2/2 - y^2/2)
= 0.
Therefore, we have shown that u(x, y) = e^(xy) * cos(x^2/2 - y^2/2) is a harmonic function.
To obtain the conjugate harmonic function v(x, y), we need to find a function v(x, y) such that the Cauchy-Riemann equations are satisfied:
(∂v/∂x) = (∂u/∂y),
(∂v/∂y) = - (∂u/∂x).
Let's solve these equations:
(∂v/∂x) = (∂u/∂y) = -e^(xy) * sin(x^2/2 - y^2/2) * (x + y),
(∂v/∂y) = - (∂u/∂x) = -e^(xy) * sin(x^2/2 - y^2/2) * (x + y).
Integrating (∂v/∂x) with respect to x, we get:
v(x, y) = -e^(xy) * sin(x^2/2 - y^2/2) * (x + y) * dx + g(y),
where g(y) is an arbitrary function of y.
To find g(y), we differentiate v(x, y) with respect to y and equate it to (∂v/∂y):
(∂v/∂y) = -e^(xy) * sin(x^2/2 - y^2/2)
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Chase and Simon (1973) studied the memory of chess novices and experts for positions of chess pieces on a chessboard. Although experts generally have a far better memory for chess positions than do novices, they found that the novices performed as well or better than the experts when asked to recall random arrangements of chess pieces on the chessboard. The random arrangements included arrangements that could not possibly occur in a real game of chess. Why did novices do as well as experts when the pieces were arranged at random
Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.
One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.
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The partial sum −3+(−6)+(−12)+⋯+(−192) equals
The partial sum of the given series -3 + (-6) + (-12) + ... + (-192) can be calculated using the formula for the sum of an arithmetic series. The sum is -2016.
To find the partial sum of the series -3 + (-6) + (-12) + ... + (-192), we can use the formula for the sum of an arithmetic series.
The given series is an arithmetic series where each term is obtained by multiplying the previous term by -2. We can observe that each term is obtained by multiplying the previous term by -2. Therefore, the common ratio of this series is -2.
To find the partial sum of an arithmetic series, we can use the formula:
Sn = (n/2)(a + L),
where Sn is the sum of the first n terms, a is the first term, and L is the last term.
In this series, the first term a = -3, and we need to find the last term L. We can use the formula for the nth term of an arithmetic series:
Ln = a * r^(n-1),
where r is the common ratio.
We need to find the value of n that corresponds to the last term L = -192. Setting up the equation:
-192 = -3 * (-2)^(n-1).
Dividing both sides by -3, we get:
64 = (-2)^(n-1).
Taking the logarithm base 2 of both sides:
log2(64) = n - 1,
6 = n - 1,
n = 7.
Now we can substitute the values into the formula for the partial sum:
Sn = (n/2)(a + L) = (7/2)(-3 + (-192)) = (7/2)(-195) = -1365/2 = -682.5.
Therefore, the partial sum -3 + (-6) + (-12) + ... + (-192) equals -682.5.
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find the equations of the tangents to the curve x = 6t2 2, y = 4t3 2 that pass through the point (8, 6). y = (smaller slope) y = (larger slope)
The equations of the tangents to the curve are y = 3x - 6 and y = -3x + 30.
To find the equations of the tangents to the curve, we need to determine the slope of the tangent line at the given point of tangency.
The given curve is defined by the parametric equations x = 6t^2 - 2 and y = 4t^3 - 2.
We can eliminate the parameter t by expressing t in terms of x.
Rearranging the first equation, we have t^2 = (x + 2) / 6, and taking the square root of both sides, we get t = ±√((x + 2) / 6).
Substituting this value of t into the equation for y, we have y = 4(±√((x + 2) / 6))^3 - 2.
Simplifying this expression, we obtain y = ±(4/3)√((x + 2)^3 / 6) - 2.
Now, let's find the slopes of the tangents at the point (8, 6). We take the derivative of y with respect to x and evaluate it at x = 8.
Differentiating y with respect to x, we get dy/dx = ±(4/3)√(2(x + 2)^3 / 3)(1 / 2) = ±(2/3)√((x + 2)^3 / 3).
Evaluating the derivative at x = 8, we have dy/dx = ±(2/3)√((8 + 2)^3 / 3) = ±(2/3)√(10^3 / 3) = ±(2/3)√(1000/3) = ±20√10/3.
Since the slopes of the tangents are given by the derivative, the two possible slopes are ±20√10/3.
Now we can find the equations of the tangents using the point-slope form. Using the point (8, 6), we have:
y - 6 = (±20√10/3)(x - 8).
Simplifying these equations, we get:
y = 3x - 6 and y = -3x + 30.
Therefore, the equations of the tangents to the curve that pass through the point (8, 6) are y = 3x - 6 (the smaller slope) and y = -3x + 30 (the larger slope).
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Bryce has heard that gas appliances are cheaper to use and can lower utility costs. He is interested in purchasing a new gas stove for his kitchen to replace his electric stove. Assuming that the
stove gets used one hour per day, use the following chart to determine how much Bryce will save each month in utility costs by purchasing the gas appliance. (Assume 30 days per month.)
Electric Stove 13 cents per hour
Gas Stove
5 cents per hour
A $3.90
B. $1.50
c. $2.40
D$4.30