Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
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The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
\(\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\\)
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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Related Questions
if you dont know pls dont give wrong answer
what is the measure of angle b
Answers
Need help ASAP! I’m very confused!
Answers
Answer:
4 would be your answer
Step-by-step explanation:
brainlesit pls
what is 67 divided by 9
Answers
Answer:
67 ÷ 9 = 7.444
Evaluate a2 when a=3/4
Answers
Answer:
1/4
Step-by-step explanation:
answer key lang sakalam
#carry learning
Graph y=15x+3.
Question 2
Identify the x-intercept.
x-intercept:
Answers
Answer:
y=19
Step-by-step explanation:
Anta's sister was born when he was exactly three years old. If the product of their ages is 1404, how old are they now?
Answer need to be.(36 and 39)
I need step by step
Thank you
Answers
Answer:
Below
Step-by-step explanation:
Anta = x sister = x+3 <======given in the question
x * x+3 = 1404
x^2 + 3x - 1404 = 0 Use quadratic formula with a = 1 b= 3 c = -1404
to find x = 36 and sister = 36 + 3 = 39 y/o
We assume that
G=0.108
Rewrite the equation by multiplying both sides
1000G = 108.108
the side
Subtract G from both sides
G=
HI
Answers
Answer:
G=.108108
Step-by-step explanation:
G=108.108/100
G=.108108
Which conclusion does the diagram support?
Answers
The answer to your question is c
The conclusion VY / WX = UZ / VY satisfies the diagram
What are angles in parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.
We can conclude three factors determining parallel lines ,
Alternate angles are equal
Corresponding angles are equal
Co-interior angles add up to 180°
Given data ,
Let the parallel lines be l , m and n
Now , the transversal line goes through the points W , V and U
The second transversal line goes through the points X , Y and Z
From the parallel lines , we can deduct that
VY / WX = UZ / VY
Hence , the conclusion is VY / WX = UZ / VY
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Suppose G is a connected graph on 100 vertices with 500 edges, every vertex of degree 10.
If you apply the randomized min cut algorithm to this graph, how many contractions are performed before the algorithm terminates?
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The number of contractions performed before the randomized min cut algorithm terminates in a connected graph G with 100 vertices, each of degree 10, and 500 edges is not deterministic and can vary.
The randomized min cut algorithm, also known as the Karger's algorithm, works by repeatedly contracting randomly chosen edges until two super vertices remain, representing the two merged components. The algorithm terminates when there are only two vertices left in the graph. In this case, the graph G has 100 vertices, each with degree 10, which means it has a total of 500 edges. During each contraction step, an edge is chosen uniformly at random and contracted. Since there are 500 edges in the graph, the algorithm will perform a maximum of 500 contractions before terminating. However, it's important to note that the actual number of contractions performed can be much lower than the maximum. The algorithm's termination depends on the random choices made during the contraction steps, and it is possible to find the min cut with significantly fewer contractions. The expected number of contractions required to find the min cut in a connected graph is typically much smaller than the number of edges.
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Imagine a consumer is interested in purchasing new professional cloths for their first job out of college and they want to figure out how many pants (x) and shirts ( y ) to buy, and they know their preferences are represented by the following utility function: + U(x,y)=x
0.4
y
0.6
a) Calculate Marshallian Demand for pants b) Calculate Marshallian Demand for shirts c) Calculate Hicksian Demand for pants d) Calculate Hicksian Demand for shirts
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The consumer's preferences are represented by the utility function \(U(x,y) = x^{0.4 }* y^{0.6}.\) We need to calculate the Marshallian demand for pants and shirts, as well as the Hicksian demand for pants and shirts.
a) To calculate the Marshallian demand for pants, we need to maximize the utility function U(x, y) subject to the consumer's budget constraint and the prices of pants and shirts. The Marshallian demand for pants (x*) can be found by taking the partial derivative of U(x, y) with respect to x and setting it equal to the ratio of the prices of pants and shirts \((P_x / P_y)\):
∂U/∂x =\(0.4 \times x^{(-0.6)} \times y^{0.6}\) = \(P_x / P_y\)
By rearranging the equation, we can solve for x* in terms of y:
\(x^* = (0.4 \times y^{0.6} \times P_x / P_y)^{(1/0.6)}\)
b) Similarly, to calculate the Marshallian demand for shirts, we take the partial derivative of U(x, y) with respect to y and set it equal to the inverse of the price ratio:
∂U/∂y =\(0.6 \times x^{0.4} \times y^{(-0.4) }= P_y / P_x\)
Solving for y*, we have:
y* =\((0.6 \times x^{0.4}\times P_y / P_x)^{(1/0.4)}\)
c) The Hicksian demand for pants (\(x_{hicks}\)) can be obtained by minimizing the expenditure function E(p, u) subject to the utility level u and the prices of pants and shirts. Since the utility function is Cobb-Douglas, the Hicksian demand for pants is the same as the Marshallian demand:
\(x_{hicks} = x^*\)
d) Similarly, the Hicksian demand for shirts \((y_{hicks})\) is also equal to the Marshallian demand for shirts:
\(y_{hicks }= y^*\)
Therefore, both the Hicksian demand and the Marshallian demand for pants and shirts are the same in this case.
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ANSWER NEEDED QUICK!
Divide: 5/8 divided by 3/4
1/8
5/6
3/4
1 1/2
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find the standard form of the equation of the ellipse
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The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics.
Standard form of the equation of an ellipse is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
where (h,k) represents the center of the ellipse, 'a' is the length of the semi-major axis, and 'b' is the length of the semi-minor axis.
To find the standard form of the equation, you need the coordinates of the center and the lengths of the semi-major and semi-minor axes. Let's assume the center of the ellipse is (h,k), the length of the semi-major axis is 'a', and the length of the semi-minor axis is 'b'. Then the standard form equation becomes:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
The standard form of the equation of an ellipse is a useful representation that helps describe its shape and characteristics. By knowing the center and the lengths of the semi-major and semi-minor axes, you can easily write the equation in standard form, allowing for further analysis and calculations.
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A conjecture and the paragraph proof used to prove the conjecture are shown. Given: R S T U is a parallelogram. Angle 1 and angle 3 are complementary. Prove: angle 2 and angle 3 are complementary. Parallelogram J K L M. A diagonal segment U S is drawn across the parallelogram. Angle R U S is labeled 1. Angle U S T is labeled 2. A ray is extended diagonally up to the left of UT forming an interior angle labeled as 3. Drag an expression or phrase to each box to complete the proof. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse. It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 by the alternate interior angles theorem, and m∠1=m∠2 by the Response area. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the Response area. By substitution, m∠2+ Response area = 90°, and so ∠2 and Response area are complementary by the definition of complementary.
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Answer:
It is given that RSTU is a parallelogram, so RU¯¯¯¯¯∥ST¯¯¯¯¯ by the definition of parallelogram. Therefore, ∠1≅∠2 by the alternate interior angles theorem, and m∠1=m∠2 by the transitive property. It is also given that ∠1 and ∠3 are complementary, so m∠1+m∠3=90° by the definition of complementary angles. By substitution, m∠2+ m∠3 = 90°, and so ∠2 and ∠3 are complementary by the definition of complementary.
Let p(a) = 0.66, p(b | a) = 0.51, and p(b | ac) = 0.27. find the following probabilities:
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To find the probabilities, we will use the conditional probability formula:
P(A ∩ B) = 0.66 * 0.51
= 0.3366.
P(A' ∩ B) = P(A') * P(B | A')
= 0.34 * 0.27
= 0.0918.
P(B) = 0.3366 + 0.0918
= 0.4284.
P(A | B) = P(A ∩ B) / P(B). P(A | B)
= 0.7851.
1. P(A ∩ B): We need to find the probability of events A and B occurring together. Since we are given P(A) and P(B | A), we can calculate P(A ∩ B) using the formula P(A ∩ B) = P(A) * P(B | A).
P(A ∩ B) = 0.66 * 0.51 = 0.3366.
2. P(A' ∩ B): We need to find the probability of event A' (not A) and B occurring together. Since we are given P(B | A') and P(A'), we can calculate P(A' ∩ B) using the formula P(A' ∩ B) = P(A') * P(B | A').
To find P(A'), we subtract P(A) from 1: P(A') = 1 - P(A) = 1 - 0.66 = 0.34.
P(A' ∩ B) = P(A') * P(B | A') = 0.34 * 0.27 = 0.0918.
3. P(B): We need to find the probability of event B occurring. We can use the Law of Total Probability: P(B) = P(A ∩ B) + P(A' ∩ B).
P(B) = 0.3366 + 0.0918 = 0.4284.
4. P(A | B): We need to find the probability of event A occurring given that B has occurred. Using the conditional probability formula, P(A | B) = P(A ∩ B) / P(B).
P(A | B) = 0.3366 / 0.4284 = 0.7851.
To summarize:
- P(A ∩ B) = 0.3366
- P(A' ∩ B) = 0.0918
- P(B) = 0.4284
- P(A | B) = 0.7851.
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The probabilities are as follows, P(B) = 0.5032 and P(A | B) = 0.6686. To find the requested probabilities, we can use the conditional probability formula: P(A | B) = P(A and B) / P(B)
Let's calculate each probability step by step:
1. P(B and A): This represents the probability of both events B and A happening simultaneously. Since P(B | A) = 0.51, we can use this value along with P(A) = 0.66 to calculate P(B and A):
P(B and A) = P(B | A) * P(A) = 0.51 * 0.66 = 0.3366
2. P(B and A complement): This represents the probability of event B happening while A does not happen. We can use P(B | A complement) = 1 - P(B | A) = 1 - 0.51 = 0.49 to calculate P(B and A complement):
P(B and A complement) = P(B | A complement) * (1 - P(A)) = 0.49 * (1 - 0.66) = 0.1666
3. P(B): This represents the probability of event B happening. We can calculate this using the law of total probability:
P(B) = P(B and A) + P(B and A complement) = 0.3366 + 0.1666 = 0.5032
4. P(A complement): This represents the probability of event A not happening. We can calculate this by subtracting P(A) from 1:
P(A complement) = 1 - P(A) = 1 - 0.66 = 0.34
5. P(B | A complement): This represents the probability of event B happening given that event A does not happen. We are given that P(B | A complement) = 0.27, so no further calculation is needed.
Now, we can find the remaining probability:
6. P(A | B): This represents the probability of event A happening given that event B happens. We can calculate this using the conditional probability formula:
P(A | B) = P(A and B) / P(B) = 0.3366 / 0.5032 = 0.6686
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Consider the following numerical example of the IS-LM model: C=233+0.47Y D I=143+0.22Y−1,094i G=299 T=239 i=0.06 Derive the IS relation. (Hint: You want an equation with Yon the left side of the equation and everything eise on the right.) Y= ( (Round your calculations of the intercept and slope terms to two decimal places.)
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The IS relation is given by: Y = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places) in the numerical example of the IS-LM model.
To derive the IS relation, we need to equate aggregate demand (AD) to aggregate supply (AS). Aggregate demand consists of consumption (C), investment (I), government spending (G), and net exports (NX). In this case, we assume net exports to be zero.
Given:
C = 233 + 0.47YD
I = 143 + 0.22Y - 1,094i
G = 299
T = 239
Aggregate demand (AD) = C + I + G
Substituting the given equations into AD:
AD = (233 + 0.47YD) + (143 + 0.22Y - 1,094i) + 299
Simplifying:
AD = 233 + 143 + 299 + 0.47YD + 0.22Y - 1,094i
Combining like terms:
AD = 675 + 0.47YD + 0.22Y - 1,094i
Since we want an equation with Y on the left side, we need to express YD in terms of Y by substituting YD = Y - T.
AD = 675 + 0.47(Y - T) + 0.22Y - 1,094i
AD = 675 + 0.47Y - 0.47T + 0.22Y - 1,094i
Combining like terms again:
AD = (0.47Y + 0.22Y) + (675 - 0.47T - 1,094i)
AD = 0.69Y - 0.47T - 1,094i + 675
Comparing with the IS relation Y = a + bAD, we have:
Y = 0.69Y - 0.47T - 1,094i + 675
Rearranging terms to have Y on the left side:
Y - 0.69Y = -0.47T - 1,094i + 675
0.31Y = -0.47T - 1,094i + 675
Dividing both sides by 0.31:
Y = (-0.47T - 1,094i + 675) / 0.31
Now, we can calculate the intercept and slope terms:
Intercept term = (-0.47T - 1,094i + 675) / 0.31
Slope term = 1 / 0.31
Rounding these values to two decimal places, the IS relation is:
Y = Intercept term + Slope term = (intercept value rounded to two decimal places) + (slope value rounded to two decimal places).
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which graph best represents the following inequality y<_ -5/6 +2/3
Answers
The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
The inequality is,
⇒ y ≤ - 5/6x + 2/3
Now, We can draw the graph of inequality y ≤ - 5/6x + 2/3.
Hence, The best representation of the inequality y ≤ - 5/6x + 2/3 is shown in figure by red shade region.
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which of the following quadrilaterals have four congruent sides?
A. parallelogram B. rectangle C. rhombus D. square
Answers
The quadrilateral that has four congruent sides is option D. square. A square is a special type of rectangle and rhombus, characterized by having all four sides of equal length.
A parallelogram (option A) is a quadrilateral with opposite sides that are parallel. While the opposite sides of a parallelogram are congruent, it does not guarantee that all four sides are equal.
A rectangle (option B) is a quadrilateral with four right angles. While opposite sides of a rectangle are congruent, it does not necessarily have four congruent sides unless it is also a square.
A rhombus (option C) is a quadrilateral with all sides of equal length. While a rhombus does have four congruent sides, it is not the only quadrilateral with this property.
Therefore, among the given options, the quadrilateral that has four congruent sides is the square (option D).
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Whats a decimal in tenths that is less than 2.4 but greater than 2.0
Answers
Answer:
If your looking for 2.4 - 2.0 just see what numbers are between them 2.1 2.2 and 2.3
Step-by-step explanation:
Answer:
2.3 or 2.2 or 2.1
Step-by-step explanation:
point) We say a definite integral is improper if one is infinite, or if the is infinite.
Answers
A definite integral is said to be improper if one or both of the limits of integration are infinite, or if the integrand function has a vertical asymptote within the interval of integration.
In other words, an improper integral is one that cannot be evaluated using the usual techniques of integration, such as the fundamental theorem of calculus, because it involves infinite limits or a function that is not integrable over the interval.
For example, the definite integral of f(x) = 1/x from 1 to infinity is an improper integral because the upper limit of integration is infinity, which is not a finite number. Similarly, the definite integral of f(x) = ln(x) from 0 to 1 is an improper integral because the lower limit of integration is 0, and the function has a vertical asymptote at x=0.
To evaluate improper integrals, we use limit processes to determine whether the integral converges (has a finite value) or diverges (has an infinite value). If the integral converges, we can find its value by taking the limit of a related integral as one or both of the limits of integration approach infinity or zero.
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Why is. 10 *. 10-8 is NOT a correct representation of scientific notation?
Answers
The correct representation of the expression 10 * 10^-8 in scientific notation would be 1.0 x 10^-7
The expression 10 * 10^-8 is not a correct representation of scientific notation because it is not in the proper form. Scientific notation is a way of writing very large or very small numbers in a more compact and convenient form. It consists of two parts: a coefficient (which is always greater than or equal to 1 and less than 10) and a power of 10.
The correct representation of the expression 10 * 10^-8 in scientific notation would be:
1.0 x 10^-7
To put a number in scientific notation, we need to move the decimal point to the left or right until we have a number between 1 and 10. In this case, we can move the decimal point one place to the left to get 1.0, and we need to increase the power of 10 by one to compensate for the decimal point movement. Therefore, the correct exponent is -7.
In summary, the expression 10 * 10^-8 is not a correct representation of scientific notation because it does not have the proper coefficient (which should be between 1 and 10) and exponent (which should be a power of 10). The correct scientific notation representation for this expression is 1.0 x 10^-7.
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Find the inverse of the following function: f(x) = 8√x for x ≥ 0
Answers
Answer:
B
Step-by-step explanation:
y = 8√x (square both of side)
y² = 64x
x = y²/64
f-¹(x) = x²/64
The inverse is B.) f-¹(x) = x²/64 for, x≥0
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Here, given that, f(x) = 8√x for x ≥ 0
Let, f(x)=y
Then, we get,
y = 8√x (square both of side)
y² = 64x
x = y²/64
i.e. f-¹(x) = x²/64
Hence, The inverse is B.) f-¹(x) = x²/64 for, x≥0
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Assuming a three-variable model Yt = α1 + α2x2+ a3x3 where α2,and α3 are partial regression coefficients. You have been asked in a job interview to briefly describe the meaning of the two parameters in this context.
Answers
the partial regression coefficients in a multiple regression model represent the expected change in the dependent variable associated with a unit change in the corresponding independent variable, holding other variables constant.
In the context of the three-variable model Yt = α1 + α2x2+ a3x3 where α2 and α3 are partial regression coefficients, the coefficients represent the changes in Y associated with a unit change in x2 and x3, respectively. The partial regression coefficient represents the expected change in Y when x2 or x3 increases by one unit, while keeping other variables constant.
The partial regression coefficient for α2, α2, measures the effect of the variable x2 on Y. It tells us how much Y is expected to change for every unit increase in x2, holding the other variables constant. Similarly, the partial regression coefficient for α3, α3, measures the effect of the variable x3 on Y, and tells us how much Y is expected to change for every unit increase in x3, holding the other variables constant.
It is important to note that the regression coefficients are estimates obtained from sample data, and are subject to sampling variability. Therefore, it is important to consider the uncertainty associated with the estimates when interpreting the results.
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if you have 3 apples and you take away 2 how many apples do you have now
Answers
Answer:
1 apple
Step-by-step explanation:
3-2=1
But if you want to be Technical You still have 3. Because you took them away so you still have what you started with.
but the answer is 1 apple. 193 IQ
HELPP FIRST ANSWER IS BRAINLIEST SHOW WORK PLEASE!!!!!!!!
Answers
Explanation: (click attached photos to see)
18.
If a - b = 12 and b/2 = 10, what is the value
of a +b ?
A) 2
B) 12
C) 32
D) 52
Answers
A line passes through the points (-4,4) and (-9,2)
Answers
Answer:
y=2/5x+28/5
Step-by-step explanation:
what is 9x187647x27489x638927
Answers
Answer:
2.9661582
Step-by-step explanation:
2.9661582e+16 this is the answer
The triangle on the right is a scaled copy of the triangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
First triangle
15
15
second triangle
45/2
45/2
Answers
Answer: 3
Step-by-step explanation:
The scale factor is the ratio of corresponding side lengths of the two triangles.
In the given triangles, the length of the corresponding sides of the triangles are:
For the first triangle:
Side A = 15 units
Side B = 15 units
For the second triangle:
Side A = 45/2 units
Side B = 45/2 units
To find the scale factor, we can divide the length of one side of the second triangle by the corresponding length of the first triangle.
For example, we can use Side A:
Scale factor = (length of Side A of the second triangle) / (length of Side A of the first triangle)
Scale factor = (45/2) / 15
Scale factor = (45/2) * (1/15)
Scale factor = 3/2
Since the two triangles are scaled copies of each other, the scale factor should be the same for all corresponding sides.
Thus, the scale factor is 3 (in simplest form).
3) Find the equation of the line that passes through the points (1,2,3) and (−2,1,0)
Answers
The equation of the line passing through the points (1, 2, 3) and (-2, 1, 0) using direction vector is (x - 1) / -3 = (y - 2) / -1 = (z - 3) / -3
To find the equation of the line passing through the points (1, 2, 3) and (-2, 1, 0), we can use the point-slope form of a linear equation.
First, let's find the direction vector of the line by taking the difference between the two points:
Direction vector = (-2, 1, 0) - (1, 2, 3) = (-2 - 1, 1 - 2, 0 - 3) = (-3, -1, -3)
Now, we have a direction vector (-3, -1, -3) that represents the slope of the line.
Next, we can choose either of the given points, let's use (1, 2, 3), and plug it into the point-slope form:
(x - x₁) / a = (y - y₁) / b = (z - z₁) / c
where (x₁, y₁, z₁) is a point on the line, and (a, b, c) are the components of the direction vector.
Using the point (1, 2, 3) and the direction vector (-3, -1, -3), we have:
(x - 1) / -3 = (y - 2) / -1 = (z - 3) / -3
Simplifying, we can also write the equation of the line in symmetric form:
x - 1 = -3(y - 2) = -3(z - 3)
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If BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6. What is AC?
Answers
Answer:
AC=44
Step-by-step explanation:
The value of AC is 12 unit.
What is parallelogram?A special form of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.
Given:
ABCD is a parallelogram.
And BE = 2x + 2, BD = 5x – 3, and AE = 4x – 6.
The two diagonals bisect each other.
AC = AE + EC
AC = 2AE
AC = 8x-12
The diagonals of a parallelogram are equal.
So,
BD = AC
5x+3 = 8x-12
x = 3
So, AC = 12
Therefore, the AC is 12 unit.
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