The correct statement regarding the congruence of the triangles in this problem is given as follows:
Yes, they are congruent by either ASA or AAS.
What is the Angle-Side-Angle congruence theorem?The Angle-Side-Angle (ASA) congruence theorem states that if any of the two angles on a triangle are the same, along with the side between them, then the two triangles are congruent.
The sum of the internal angles of a triangle is of 180º, hence the missing angle measure on the triangle to the right is given as follows:
180 - (85 + 42) = 53º.
Hence we have a congruent side between angles of 53º and 42º on each triangle, thus the ASA congruence theorem can be used for this problem.
As the three angle measures are equal for both triangles, and there is a congruent side, the AAS congruence theorem can also be used.
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consider the function f(x) =xlnx.
let Tn be the nth degree Taylor approximation of f(2) about x=1. Find T1= T2= T3=
use 3 decimal places in your answer but make sure you carry all decimals when performing calculations
T3 is an over/under estimate of f(2)
If R3 is the remainder given by the Lagrange Remainder formula
R3<=
The first degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T1(x) = f(1) + f'(1)(x-1) = 0 + 1(x-1) = x-1. Therefore, T1(2) = 2-1 = 1.
The second degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T2(x) = T1(x) + f''(1)/2(x-1)^2. We have f''(x) = -1/x^2, so f''(1) = -1. Thus, T2(x) = x-1 - (1/2)(x-1)^2. Therefore, T2(2) = 2-1 - (1/2)(2-1)^2 = 1/2.
The third degree Taylor polynomial of f(x) = xlnx about x = 1 is given by T3(x) = T2(x) + f'''(c)/3!(x-1)^3, where c is some number between 1 and x. We have f'''(x) = 2/x^3, so f'''(c) = 2/c^3.
Thus, T3(x) = x-1 - (1/2)(x-1)^2 + (2/3!c^3)(x-1)^3. To find an upper bound for the error R3 = f(2) - T3(2), we need to find the maximum value of |f'''(x)| on the interval [1,2].
We have |f'''(x)| = 2/x^3, which is decreasing on the interval. Therefore, the maximum value occurs at x = 1, and we have R3 <= (2/3!)(2-1)^3/1^3 = 2/3.
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A line is perpendicular to y = -x-2
and intersects the point (-5, 10).
What is the equation of this
perpendicular line?
y = x + [?]
The equation of the perpendicular line is y = x + 15.
How to determine the equation of the perpendicular line
In this problem we need to determine the equation of the line perpendicular to another line, that intersects at the point (x, y) = (- 5, 10). The explicit form of the equation of the line is defined by the following first order polynomial:
y = m · x + b
Where:
m - Slopeb - y-Interceptx - Independent variabley - Dependent variableThe first line has a slope - 1 and the slope of the second line is:
m' = - 1 / m
m' = 1
Then, the intercept of the second line is:
b = y - m · x
b = 10 - (- 5)
b = 15
The equation of the perpendicular line is y = x + 15.
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mr. sosa, mrs. perepelitsa, and mr. dougmay wanted to compute the area under the curve f(x)=x−4 2x−6x2 cos(x) over the interval [2,10]. to do this, each one used a different anti-derivative.
To find the area under the curve, you can evaluate the anti-derivative of the function and then apply the definite integral over the interval [2, 10].
To compute the area under the curve of the function f(x) = (x - 4)/(2x - 6x^2) cos(x) over the interval [2, 10], three different anti-derivatives were used by Mr. Sosa, Mrs. Perepelitsa, and Mr. Dougmay.
Since the specific anti-derivatives used by each person are not provided, it is not possible to determine the exact values they obtained for the area under the curve. However, if the anti-derivatives were calculated correctly, their results should be equal due to the Fundamental Theorem of Calculus.
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What is the slope of a line which makes an angle of 45 degree with x-axis? *
Answer:
First we have to find slope m=Tan45°=1
so slope is 1.
Answer:
slope = 1
Step-by-step explanation:
The relationship between slope and the positive angle it makes with the x- axis is
slope = tanθ ( θ is the angle measured from the x- axis ), then
slope = tan45° = 1
Find the slope of the line through the given points.
(-2,7) and (2,-5)
Answer:
y = -3x + 1
Step-by-step explanation:
hope this is right!
the length of a rectangle is 5 times the width. if the perimeter is to be greater than 120 meters. what are the possible values for the width? (use w as the width)
The possible value for the width is 10.
What is the length of a rectangle?
Since its sides are coupled, it essentially only has two distinct dimensions. The length of the rectangle is traditionally thought of as being the longer of these two dimensions, however, when the rectangle is depicted standing on the ground, the vertical side is typically referred to as the length.
Here, we have
The length of a rectangle is 5 times the width
L = 5w
120 < Perimeter = 2L + 2w
= 2(5w) + 2w
= 10w+2w = 12w
10 > w
w < 10
Hence, the possible value for the width is 10.
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Multiply: (6a³3b³) (5a² + 46²)
O 11a³ + 10a³b² + 2a²b³ + b³
O 30a5 +24a³b² - 15a²b³ - 1265
O 30a5 +9a5b5 - 1265
O30a6 +24a³ b² - 15a² b3 - 1266
please help me with these three questions, i'll give brainliest
Answer:
The result would be 0 (zero)
Step-by-step explanation:
Okay so it is kind of difficult to explain with words but I will try to make it simple, so you could start with each number first.
What I mean by that is graph it like it says first, starting with -9 and then go four spaces to the right and then five more spaces to the right.
Next, Start four spaces to the right then go five more spaces right and then go nine spaces to the left.
And lastly, start five spaces to the right and go nine spaces to the left and then go four spaces to the right. H
Hopefully this is what you were looking for!
if a graph gets arbitrarily close to a line (without necessarily reaching it) in some direction, then the line is a(n) _____ of the graph.
If a graph moves arbitrarily near to a line in one direction (without necessarily crossing it), then the line is a(n) asymptote of the graph.
What is an asymptote?An object that serves as the limit of another line or curve in mathematics. Asymptotic to an axis, or the asymptote of a curve, refers to a falling curve that approaches but does not reach the horizontal axis.
An asymptote is a value that you approach steadily but never quite achieve. An asymptote is a line that a graph skirts but never touches in mathematics. It can be horizontal, vertical, or slanted. A graph that approaches a line but does not cross it is said to be an asymptote.
An asymptote of a curve in analytical geometry is a line along which the angle between the curve and the line decreases when one or both of the x or y coordinates tend to infinity. A line that is tangent to a curve at a point at infinity is said to be the asymptote of the curve in projective geometry and similar contexts.
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WRITE A PIECE WISE FUNCTION FOR EACH GRAPH!! I need this answer ASAP !!
Answer:
y = -1/2 x - 2 for x <= -2
y = x + 4 for x > -2
Step-by-step explanation:
The lower left line has equation
y = -1/2 x - 2
The upper right line has equation
y = x + 4
Answer:
y = -1/2 x - 2 for x <= -2
y = x + 4 for x > -2
find the volume of 2 and 1/2 1 and 1/2 and 3
To find the volume multiply all 3 numbers together.
2 1/2 x 1 1/2 = 3 3/4
3 3/4 x 3 = 11 1/4
The volume is 11 and 1/4 cubic units
A restaurant offers pizzas with 2 types of crust, 7 different toppings, and in 5 different sizes. how many different pizzas could be ordered?
There are 70 different types of pizzas could be ordered
A permutation is an act of arranging the objects or numbers in order.
Combinations are the way of selecting the objects or numbers from a group of objects or collection, in such a way that the order of the objects does not matter
Given,
Number of options on crust=2
Number of options on topping= 7
Number of options on size= 5
Therefore for each type of crust there are 7 different topping, for each toppings there are 5 different sizes
The total number ways of ordering pizza=2×7×5=70
Hence, there are 70 different types of pizzas could be ordered
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A single-phase feeder (or branch circuit) conductor will have a total resistance ____ that of one conductor.
A single-phase feeder or branch circuit conductor will have a total resistance equal to twice that of one conductor.
When referring to a single-phase circuit, we typically have two conductors: a hot (phase) conductor and a neutral conductor. These conductors carry the electrical current. Each conductor has its own resistance, but when considering the total resistance of the circuit, we need to take into account both conductors.
The resistance of a conductor is typically measured per unit length. Assuming that the two conductors in the circuit are of the same material and cross-sectional area, their individual resistances will be equal. When we calculate the total resistance of the circuit, we add the resistances of both conductors together.
Since we have two conductors in a single-phase circuit, the total resistance will be equal to twice the resistance of one conductor. This is because the resistances of both conductors are added together to determine the total resistance of the circuit.
Understanding the total resistance is important for determining voltage drop and power losses in electrical circuits, as well as for proper sizing of conductors to meet safety and electrical code requirements.
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pls help me 10 points
Answer:
the answer is one fourth 1/4
can u mark me as brainliest
What is the conversion of 24 mm into inches ?
The conversion of 24 mm into inches is 0.94488 inches.
Millimeter (mm) and inch are both units of length or distance, but they are used in different parts of the world.
A millimeter is a metric unit of length used in most countries outside the United States. It is equal to one-thousandth of a meter (1/1000 of a meter), or approximately 0.03937 inches.
To convert millimeters (mm) to inches, you can use the conversion factor of 1 mm = 0.03937 inches.
So, to convert 24 mm to inches, you can multiply 24 by 0.03937:
24 mm * 0.03937 inches/mm = 0.94488 inches
Therefore, 24 millimeters is approximately equal to 0.94488 inches.
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find the percentage of 0 ratio 7
Step-by-step explanation:
ratio - 0:7
in percentage=0÷7×100
Joey built a skateboarding ramp. The base of the ramp along the ground is 13 feet, and the top of the ramp is 7 feet off the ground. What is the length of the ramp's incline?
Answer:
14.77 feet
Step-by-step explanation:
Using the pythagoras theorem to get the length of the ramp
l² = 13² + 7²
l is the length of the ramp
l² = 169 + 49
l² = 218
l = √218
l = 14.77 feet
Hence the length of the ram is 14.77 feet
In the diagram below, BD is parallel to XY. What is the value of x? 76 y
Answer:
x = 76°
Step-by-step explanation:
Corresponding angles are formed when a transversal line cuts across two parallel lines. The angles formed are in corresponding position close to the transversal. Corresponding angles formed like this are congruent.
In the diagram given above, BD and XY are parallel lines cut across by a transversal line.
Angle labelled x corresponds with the angle measuring 76°. Therefore they are both congruent. Thus: x = 76°.
please help, i will give brainliest!
....i cant even read it
⊂∫⊃
The equation $f\left(x\right)=2x-9$ translated 6 units up is $g\left(x\right)=$ .
The equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
The equation is
f(x) = 2x - 9
Then it is translated 6 units up
The translation is the process of moving the shape to left/right of up or down. During the translation process the shape and size of the graph will not change. In translation we are only changing the coordinates of the points of the shape.
Here it is translated 6 units up.
During the upward motion it will be positive
g(x) = f(x) + 6
Substitute the value of f(x)
g(x) = 2x-9 + 6
g(x) = 2x-3
Hence, the equation f(x) = 2x - 9 translated 6 units up, then the equation g(x) = 2x-3
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What is the perimeter of triangle ABC?
5
A
B.
0 20 units
4
o 22 units
3
0 24 units
2
o 26 units
1
-5 4
-2 -1
4
2 3
5
-2
-4
с
-5
Answer: 24 Units
Step-by-step explanation:
Got it right on edge!
The graphs below have the same shape. What is the equation of the red
graph?
g(x) = ?
f(x)=5-x²
The equation of the blue graph is y = -x² + 5. We can determine the general form of the equation for the red graph
To determine the equation of the red graph, let's analyze the given equation for the blue graph, f(x) = 5 - x². The equation represents a downward-facing parabola with its vertex at the point (0, 5). The general form of a quadratic equation is y = ax² + bx + c, where a, b, and c are constants.
Comparing f(x) = 5 - x² with the general form, we can see that a = -1, b = 0, and c = 5. Therefore, the equation of the blue graph is y = -x² + 5.
Given that the red graph has the same shape as the blue graph, it will also have a downward-facing parabola. However, the vertex might be at a different position.
To determine the equation of the red graph, we need to find the equation that represents the same parabolic shape but with a different vertex. Let's assume the vertex of the red graph is at the point (h, k), where h and k are constants.
Using the standard vertex form of a quadratic equation, the equation of the red graph can be written as:
g(x) = a(x - h)² + k
To find the equation, we need to determine the values of a, h, and k. Since the shape of the red graph is the same as the blue graph, we know that a = -1.
The vertex of the red graph is not given explicitly in the problem, so we cannot determine the exact equation. However, we can conclude that the equation of the red graph will have the form:
g(x) = -(x - h)² + k
where h and k represent the coordinates of the vertex of the red graph.
In summary, we can determine the general form of the equation for the red graph, but without additional information about the specific vertex, we cannot determine the exact equation.
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please help and I will give brainest
Answer:
-7
0
0.999
-4
0.9
-2
0.99
Step-by-step explanation:
Can you help me solve this!
Hello!
surface area
= 2(6*2) + 2(4*2) + 4*6
= 2*12 + 2*8 + 24
= 24 + 16 + 24
= 64 square inches
Can anyone help with this? I'm having some trouble.
let γ1, γ2, . . . , γp be cycles of generalized eigenvectors of a linear operator t corresponding to an eigenvalue λ. prove that if the initial eigenvectors are distinct, then the cycles are disjoint.
If the initial eigenvectors corresponding to distinct eigenvalues are different, then the cycles of generalized eigenvectors for each eigenvalue will be disjoint.
Let's assume that γi and γj are cycles of generalized eigenvectors corresponding to eigenvalues λi and λj, respectively. Since the initial eigenvectors are distinct, λi ≠ λj.
Now, let's suppose there exists a vector v that belongs to both cycles γi and γj. Then, by definition, we have t(v) = λi(v) and t(v) = λj(v). Since λi ≠ λj, this implies that v is a common eigenvector for two distinct eigenvalues, which contradicts the assumption that the initial eigenvectors are distinct.
Therefore, our assumption that there exists a vector v belonging to both γi and γj is false. Thus, the cycles γi and γj are disjoint.
By extension, we can apply the same reasoning to any pair of cycles γi and γj where i ≠ j, ensuring that all cycles corresponding to distinct eigenvalues will be disjoint.
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Anyone know this answer? Please
Answer:
1/24
Step-by-step explanation:
multiply all the values
What is the equation of a plane that passes through a point and is parallel to the YZ plane?
The equation of a plane that passes through a point and is parallel to the YZ plane can be written as:
x = constant
When a plane is parallel to the YZ plane, it means that its normal vector is perpendicular to the X-axis. Since the normal vector is perpendicular to the X-axis, the X-coordinate of any point on the plane remains constant.
To find the equation of the plane, we need a point that lies on the plane. Let's assume the point (a, b, c) lies on the plane.
Since the plane is parallel to the YZ plane, the X-coordinate of any point on the plane will remain constant. Therefore, we can say that x = a.
The equation of the plane becomes:
x = a
The equation of a plane that passes through a point and is parallel to the YZ plane is given by the equation x = a, where a is the constant X-coordinate of any point on the plane. This equation represents all points where the X-coordinate remains constant, while the Y and Z coordinates can vary freely.
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How does SAS work in math?
In mathematics, SAS stands for 'Side-Angle-Side' which is a criterion used to determine congruence (equality in size and shape) between two triangles.
The SAS criterion states that if two triangles have two sides that are proportional in length
and the included angles between those sides are congruent, then the two triangles are congruent.
To understand how SAS works,
Side,
This refers to a specific side of a triangle.
In the SAS criterion, we compare the lengths of the sides of two triangles to determine if they are proportional.
Angle
This refers to a specific angle within a triangle.
In the SAS criterion, compare the angles formed by the corresponding sides of the two triangles to determine if they are congruent.
Side-Angle-Side
This combination of a side, an angle, and another side is what we compare between two triangles.
If the two triangles have the same proportions for the corresponding sides and the same measures for the included angles,
they are considered congruent.
To illustrate this, let's consider an example
Suppose we have two triangles, triangle ABC and triangle DEF.
If side AB is proportional in length to side DE, angle BAC is congruent to angle EDF, and side BC is proportional in length to side EF,
then conclude that triangle ABC is congruent to triangle DEF using the SAS criterion.
By applying the SAS criterion,
mathematicians can determine whether two triangles are congruent without relying on other criteria such as Side-Side-Side (SSS),
Angle-Angle-Side (AAS), or Side-Angle-Angle (SAA).
Congruence is a fundamental concept in geometry and plays a significant role in various geometric proofs and constructions.
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Need help! much appreciated
Answer:
C-D = 6
A-B = 3.25
D = 118
Step-by-step explanation:
C-D = 6 because the line is the same as B-C
A-B = 3.25 because the line is the same as A-D
D = 118 because the angle of B is vertically opposite to D