Robbie received a gift card for $20. He bought a cookie for $2.39 and 4 coffees. He still has some money left on the gift card. Which inequality could help you solve for c, the cost of each coffee in dollars?

Answer: First point 6x -2y and second point 3x 4y

Step-by-step explanation:

The equation of the plane through the origin and the points (2, –4, 6) and (5, 1, 3) is - 9x + 12y + 11 x = 0.

The general equation of a plane through (0, 0, 0) is a(x - 0) + b(y - 0) + c(z - 0) = 0

Since the plane passes though the origin, the equation of the plane is given by ( x, y, z ) = 0. Simplify it so that you write the equation of the plane in the form a x + b y + c z = 0

ax + by + cx = 0...(1)

It will pass through B(2, -4, 6) and C(5, 1, 3) if

a(2) + b(-4) + c(6) = 0

2a - 4b + 6c = 0

a - 2b + 3c = 0 ...(2)

a(5) + b(1) + c(3) = 0

5a + b + 3c = 0 ... (3)

Solving (2) and (3) by cross-multiplication, we have

[tex]& \frac{a}{-6-3}=\frac{b}{15-3}=\frac{c}{1+10} \\[/tex]

[tex]& \Rightarrow \frac{a}{-9}=\frac{b}{12}=\frac{c}{11}=\lambda[/tex] (say) }

[tex]& \Rightarrow[/tex] a = - 9 [tex]\lambda[/tex], b = 12 [tex]\lambda[/tex]  and c = 11 [tex]\lambda[/tex]

Substituting the values of a, b and c in (1), we get

- 9 [tex]\lambda[/tex] x + 12 [tex]\lambda[/tex] y + 11 [tex]\lambda[/tex] x = 0

- 9x + 12y + 11 x = 0

which is the required equation of the plane.

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The confidence interval in the form of ^p-E < p < ^p+E is 0.013 < p < 0.089.

A confidence interval is a range of values that is likely to contain the true population parameter with a certain level of confidence. In this case, the population parameter is the true proportion or probability of success, represented by the symbol "p". The interval is defined by a lower bound and an upper bound, represented by "^p-E" and "^p+E" respectively.

E is the margin of error.

In this case, the lower bound of the interval is 0.013, and the upper bound is 0.089. So, we can say that there is a certain level of confidence that the true proportion of success falls between 0.013 and 0.089.

It is important to note that confidence intervals are not a measure of how well a model or estimate predicts future observations. It is only a measure of how uncertain we are about the true population parameter.

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The standard form of the given polynomial is x⁶ + 53x⁵ + 2x⁴ - 2 which has a highest degree of 6 while the leading coefficient is 1. This polynomial is called a quadrinomial because it has 4 terms

A polynomial is an equation that only uses addition, subtraction, multiplication, and non-negative integer exponents of variables and consists of variables (also known as indeterminates) and coefficients. Algebra, calculus, and numerical analysis are just a few of the mathematics and scientific disciplines that use polynomials.

In the presented problem, we must determine the terms, variables, coefficients, and other properties of the polynomial f(x).

f(x) = 2x⁴ + 53x⁵ - 2 + x⁶

The standard form of this polynomial is x⁶ + 53x⁵ + 2x⁴ - 2

The degree of the polynomial is 6

The leading coefficient is 1 which is the coefficient of the degree of the polynomial

This is called a Quadrinomial because it has 4 terms

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The equation of the hyperbola in standard form is y²/8² - (x-5)²/6² = 1

Given that the center of the hyperbola is (5,0) and the vertex is (5,6), we can see that the center is on the x-axis, so the y-coordinate of the center, k, is 0. The x-coordinate of the center, h, is 5.

We know that equation of Hyperbola is

(y-k)²/a² - (x-h)²/b² = 1

Where (h,k) is the center and given (h, k) = (5, 0) and b is the transverse axis and a is the conjugate axis.

Now b is the y-coordinate of vertex (5,6) ⇒b=±6

and c is the y-coordinate of focus (5,10)c=±10

And also c² = a²+b²

(±10)²=a²+(±6)²

⇒a²=100−36=64

Hence a=±8

Thus, the equation of the hyperbola is y²/8² - (x-5)²/6² = 1

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Answer:

Step-by-step explanation:

Given ∆PQR with ∠P = (4x-9)°, ∠Q = (6x+2)°, and ∠R = x°, you want an equation to find x, and the measures of the angles.

The equation expresses the fact that the sum of angles in a triangle is 180°.

  ∠P +∠Q +∠R = 180°

  (4x -9)° +(6x +2)° +x° = 180°

  11x -7 = 180 . . . . . . . . . . . . divide by °, collect terms

  11x = 187 . . . . . . . . . add 7

  x = 17 . . . . . . . . divide by 11

The angle measures are found by substituting for x in the angle expressions:

  ∠P = (4·17 -9)° = 59°

  ∠Q = (6·17 +2)° = 104°

  ∠R = 17°

The volumes of right prisms are listed below:

Case A: 150 cm³

Case B: 525 m³

Case C: 429 m³

The volume of right prism (V), in cubic length units, is always equal to the product of the base area (A), in square length units, and height (h), in length units:

V = A · h

There are three right prisms, whose areas are combinations of right triangles and rectangles. The area formulas are shown below:

Rectangle

A = w · l

Right triangle

A = 0.5 · w · l

Where:

The complete procedure is listed below:

Case A

A = 0.5 · (4 cm) · (5 cm) + (3 cm) · (5 cm)

A = 25 cm²

V = (25 cm²) · (6 cm)

V = 150 cm³

Case B

A = (5 m) · (8 m) + (5 m) · (7 m)

A = 75 m²

V = (75 m²) · (7 m)

V = 525 m³

Case C

A = (8 m) · (4 m) + (3 m) · (9 m) + 0.5 · (5 m) · (5 m)

A = 71.5 m²

V = (71.5 m²) · (6 m)

V = 429 m³

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Answer:

[tex]-\infty \: < x < \infty[/tex]

or, in interval notation as

[tex]\left(-\infty \:,\:\infty \:\right)[/tex]

Step-by-step explanation:

The domain of a function [tex]f(x)[/tex] is the set of all values of [tex]x[/tex] for which [tex]f(x)[/tex] is real and defined

The given function is f(x) = x³ + 6x² + 5

There are no undefined points. So the domain is the set of all real numbers that can be expresses as

[tex]-\infty \: < x < \infty[/tex]

or, in interval notation

[tex]\left(-\infty \:,\:\infty \:\right)[/tex]

The integral evaluates the area under a curve by taking the antiderivative of the given function and evaluating the limits of the integral. The final result is (1/3) ax3 - (1/2) b2 ax + c.

∫ (ax)2 − b2 3/2 dx = (1/3) ax3 - (1/2)b2 ax + c

The integral evaluates the area under a curve. It is calculated by taking the antiderivative of the given function and then evaluating the limits of the integral. To find the antiderivative, we use the power rule to calculate the derivative of the function and then integrate the result. In this case, the function is (ax)2 - b2 3/2. Using the power rule, we find that the derivative of this function is (3/2) ax2 - (1/2) b2 ax. We then integrate this result and add the constant of integration (c) to obtain the integral. The final result for this integral is (1/3) ax3 - (1/2) b2 ax + c.

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The number of union workers is 42

A ratio can be defined in mathematics as an ordered pair of numbers, like  y and z, that is written in the form y / z such that the values of  z is not equal  to zero.

It also shows how many the times a number contains another number in a given proportion.

From the information given, we have that;

Then,

If 3 = 18 workers

Then 7 = x workers

cross multiply

3x = 18(7)

Multiply the values

3x = 126

x = 42 workers

Hence, the number is 42

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If the lease factor is given as 0. 00045 then the interest rate is that equivalent to 4.5%

The lease factor of 0.00045 is equivalent to an interest rate of 4.5%. This is because the lease factor is a measure of the interest rate a lessee pays on a lease.

It is calculated by dividing the interest rate by 2400. This means that the higher the lease factor, the higher the interest rate that the lessee pays.

For example, if the interest rate is 12%, then the lease factor would be 0.005.

In this case, the lessee would be paying an interest rate of 12%, or 0.005 as a lease factor.

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the centroid of the region bounded by the given curves is (x, y) = (15, 225).

To show that f is continuous on (−∞,∞), we need to show that the limit of f(x) as x approaches any point from the left and from the right is equal.

First, let's consider the limit of f(x) as x approaches 1 from the left.

As x approaches 1 from the left, f(x) = 1-x^2, so the limit of f(x) as x approaches 1 from the left is 1.

Now, let's consider the limit of f(x) as x approaches 1 from the right.

As x approaches 1 from the right, f(x) = ln x, so the limit of f(x) as x approaches 1 from the right is 0.

Since the limit of f(x) as x approaches 1 from the left is 1 and the limit of f(x) as x approaches 1 from the right is 0, we can conclude that f is continuous on (−∞,∞).

To find the centroid of the region bounded by the given curves, we need to calculate the area of the region and the area-weighted centroid of the region.

The area of the region is given by the integral of x3 from 0 to 10, which is equal to 1125/4.

The area-weighted centroid of the region is given by the integral of (x3*x)/(1125/4) from 0 to 10, which is equal to 15.

Therefore, the centroid of the region bounded by the given curves is (x, y) = (15, 225).

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A polynomial of the form ax^n + bx^(n-1) + cx^(n-2) + ... + z is called an nth-degree polynomial, where n is a positive integer. The highest exponent in the polynomial is n.

The term "nth-degree polynomial" refers to the highest exponent in the polynomial. In other words, a polynomial is an nth-degree polynomial if the highest exponent in the polynomial is n.

For example, the polynomial x^2 + 3x + 5 is a 2nd-degree polynomial because the highest exponent is 2. Similarly, the polynomial 3x^4 + 2x^3 - 5x^2 - 6x + 9 is a 4th-degree polynomial because the highest exponent is 4.

The degree of a polynomial can be helpful in determining the number of roots that the polynomial has. For example, a 2nd-degree polynomial will have at most 2 roots, while a 4th-degree polynomial can have up to 4 roots.

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Answer:

c ≤ -36

Step-by-step explanation:

c/9 ≤ −4

Multiply both sides by 9.

c ≤ -36

Answer: c ≤ −36

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

1/9c ≤ −4

Step 2: Multiply both sides by 9.

9*(1/9c) ≤ (9)*(−4)

Answer:

c ≤ − 36

The function that correctly depicts the scenario is represented as; f(x) = 18.50 (1.06)^x

The cost of the buffet in 10 years is; $33.13

The cost of the buffet 15 years ago is ; $7.71

Function is a type of relation, or rule, that maps one input to specific single output.

Here we have the following parameters that can be used in our computation:

Value of buffet = $18.50

Rate of increment = 6%

The function that correctly depicts the scenario is;

f(x) = Value of buffet  (1 + Rate of increment)^x

Substitute the values in the above equation, so;

f(x) = 18.50 (1 + 6%)^x

So, we have;

f(x) = 18.50 (1.06)^x

The buffet cost 10 years from now means that

x = 10

Substitute the values in the above equation,

f(10) = 18.50 (1.06)^10

Evaluate;

f(10) = 33.13

x = -15

Substitute the values in the above equation, so, we have

f(-15) = 18.50 (1.06)^(-15)

Evaluate;

f(-15) = 7.71

Hence, the amount 15 years ago is $7.71

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The value of x in the expression is 10

You should understand that an equation is a mathematical statement showing the equality of two things

The given equation is 1250=1/2×50×(2x+3x)

To find the value of x, we have to simplify the right hand side of the equation

This is = 1250 = 50(5x)/2

This will give us 2500 250x after cross multiplication

Then make x the subject of the relation by dividing by 250

This implies that x = 10

The expression leaves the value of x at 10

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Answer:

To solve the equation 2(4x - 1) = -10(x - 3) + 4, we can follow these steps:

Step 1: Distribute the 2 on the left side of the equation:

8x - 2 = -10x + 6 + 4

Explanation: When we distribute the 2, we get 2 * 4x - 2 * 1, which simplifies to 8x - 2.

Step 2: Combine like terms on both sides of the equation:

8x - 10x = 6 + 4 - 2

-2x = 8

Explanation: On the left side of the equation, we have 8x - 10x, which simplifies to -2x. On the right side of the equation, we have 6 + 4 - 2, which simplifies to 8.

Step 3: Divide both sides of the equation by -2 to solve for x:

x = -4

Explanation: When we divide both sides of the equation by -2, we get -2x / -2 = 8 / -2, which simplifies to x = -4.

Therefore, the solution to the equation is x = -4.

To solve the equation 2(4x - 1) = -10(x - 3) + 4,we can follow these steps:

Distribute the 2 on the left side of the equation:

8x - 2 = -10x + 6 + 4

When we distribute the 2, we get 2 * 4x - 2 * 1, which simplifies to 8x - 2.

Combine like terms on both sides of the equation:

8x - 10x = 6 + 4 - 2

-2x = 8

On the left side of the equation, we have 8x - 10x, which simplifies to -2x. On the right side of the equation, we have 6 + 4 - 2, which simplifies to 8.

Divide both sides of the equation by -2 to solve for x:

x = -4

When we divide both sides of the equation by -2, we get -2x / -2 = 8 / -2, which simplifies to x = -4.

Therefore, the solution to the equation is x = -4.

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The Probability of receiving 7 three times is 0.0025566, but the likelihood of getting 7 just once is 3.7528.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or probability of several outcomes. Statistics is the study of events that follow a probability distribution.

The given question is related to the binomial distribution.

Given n = 10 trials. The probability of one successful trial is p = 1/8. You want k=3 successes and n − k = 7 failures. The probability is:

[tex](\frac{n}{k}) p^k (1-p)^{n-k}[/tex]

One way to understand this formula: You want k successes (probability: pk) and n−k failures (probability: (1−p)n−k). The successes can occur anywhere in the trials, and there are (n/k) to arrange k successes in n trials.

substituting the values in the given formula.

[tex](\frac{10}{3}) 1/8^3 (1-1/8)^{10-3}[/tex]

Probability of getting 7, 3 times = [tex](\frac{10}{3}) 1/8^3 (7/8)^7[/tex]

Probability of getting 7, 3 times = [tex](\frac{10}{3}) 1/216 (7/8)^7[/tex]

Probability of getting 7, 3 times = 0.0025566

The Same goes for the probability of getting 7 only one times

the probability of getting 7 only one time = [tex](\frac{10}{1}) 1/8^1 (1-1/8)^{10-1}[/tex]

the probability of getting 7 only one time = 3.7528

Therefore, The Probability of getting 7, 3 times is 0.0025566 and the probability of getting 7 only one time is 3.7528.

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Answer: 15

Step-by-step explanation:

Area = bh

Area = 120

Height = 8

Since you have the area and the height you need to divide:

120/8

=

15

__________________________________________________________

You can also check your answer by doing bh

15 x 8

=

120

The measure of angle are:

m∠1 = 35°; m∠2= 125°; m∠3= 55°; m∠4 =125° ; m∠5 =55°.

What are similar triangles?

Similar triangles are triangles that have the same shape but differ in size. Similar objects include all equilateral triangles and squares with any side length. In other words, if two triangles are similar, their corresponding angles and sides are congruent and in equal proportion.

The △ABC is a right triangle.

Given that, 2AE = AC, 2CD = BD

AE/AC = 1/2; CD/BD = 1/2

∠ACD = ∠ECD = right angle

According to SAS rule, △ABC ≅ △ECD.

Thus the corresponding angles of △ABC and △ECD are congruent.

∠A = ∠E; ∠B = ∠D; ∠C = ∠C

Consider  △ABC:

∠A = 35°, ∠C =90°

The sum of all interior angles of a triangle is 180°.

∠A + ∠B + ∠C = 180°

35° +  ∠B + 90° = 180°

∠B + 125° = 180°

∠B  = 180° -  125°

∠B  = 55°

Therefore ∠1 = 55°; ∠5 = 55°; ∠3 = 55°.

The sum of the exterior angle and corresponding to the interior angle is 180°.

∠1  + ∠2 = 180°

55° + ∠2 = 180°

∠2 = 125°

Again:

∠5  + ∠4 = 180°

55° + ∠4 = 180°

∠4 = 125°

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Answer:

3

Step-by-step explanation:

Pothagorean theorem:

a² + b² = c²

c = 8

b = √55

a² + 55 = 64

a² = 9

a = 3

The Intermediate Value Theorem there must be a time t0: 0 < t0 < 12, where (x1 − x2)(t0) = 0 =⇒ x1(t0) = x2(t0).

What is the intermediate value theorem ?

Intermediate value theorem states that if “f” be a continuous function over a closed interval [a, b] with its domain having values f(a) and f(b) at the endpoints of the interval, then the function takes any value between the values f(a) and f(b) at a point inside the interval.

Let d be the distance between the monastery and the top of the hill.

Define x1(t) to be the distance traveled by the monk in t hours on day one and similarly

define x2(t) to be the distance traveled by the monk in t hours on day two.

In the above setup x1(0) = 0, x1(12) = d, x2(0) = d and x2(12) = 0.

Next consider the function (x1 − x2)(t), which is continuous on [−d, d]. Also, note that

(x1 − x2)(0) = −d and (x1 − x2)(12) = d.

The Intermediate Value Theorem there must be a time t0: 0 < t0 < 12, where (x1 − x2)(t0) = 0 =⇒ x1(t0) = x2(t0).

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A quadratic equation is an equation of degree 2 and has the standard form: ax² + bx + c = 0,  with a ≠ 0. Example: 2x² - 3x - 2 = 0, the solution is {-1/2, 2}.

A quadratic equation is an equation of degree 2. The standard form of a quadratic equation is:

ax² + bx + c = 0,  with a ≠ 0

The quadratic equations can be solved using:

- factorization

- completing the square

- abc formula

Example 1:

2x² - 3x - 2 = 0

Using factorization:

2x² - 3x - 2 = (2x +1) (x-2)

Hence,

(2x +1) (x-2) = 0

Solution:

x = -1/2  and x = 2

x = {-1/2, 2}

Example 2:

x² - 6x + 4 = 0

By completing the square:

x² - 6x + 5 = (x - 3)² - 4

Hence,

x² - 6x + 5 = 0

(x - 3)² - 4 = 0

(x - 3)² = 4

x - 3 = ± 2

The solutions are

x = 3 - 2 = 1  or

x = 3 + 2 = 5

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The exact length of the curve y=ln[(e^x+1)/(e^x-1)], a ≤ x ≤ b, is equals to the ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

The exact length of curves implies the length of arc of curve. Arc length is the distance between two points along a section of a curve, formula

Arc length = ₕ∫ᵏ√( 1 + ( y')² dx , h≤x≤k

We have a curve , y = ln[ (eˣ + 1) /(eˣ - 1) ] , a≤x≤b , a> 0

firstly, determine the first derivative of y with respect to x ..

dy/dx = y' = [ 1/(eˣ +1) /(eˣ -1)] d/dx (( eˣ + 1) /(eˣ -1) )

( apply chain rule )

= (eˣ -1 )/(eˣ +1 )[{(eˣ -1) eˣ - ( eˣ +1)eˣ}/(eˣ - 1)²]

( using quotient rule)

= (eˣ -1 )/(eˣ +1 )[(e²ˣ - eˣ - e²ˣ - eˣ)/(eˣ - 1)²]

= (eˣ -1 )/(eˣ +1 )[(- 2eˣ)/(eˣ - 1)²]

= -2eˣ /(eˣ -1 )(eˣ +1 )

dy/dx = - 2eˣ /e²ˣ -1

so, (dy/dx)² = (- 2eˣ /(e²ˣ -1) )²

= 4e²ˣ /(e²ˣ -1 )²

and 1 + (dy/dx)² = 1 + {4e²ˣ /(e²ˣ -1 )² }

= {(e²ˣ -1 )² + 4e²ˣ}/(e²ˣ -1 )²

= (e⁴ˣ + 1 - 2e²ˣ + 4e²ˣ)/(e²ˣ -1 )²

= ( e⁴ˣ + 1 + 2e²ˣ )/(e²ˣ -1 )²

1 + (dy/dx)² = (e²ˣ + 1)²/(e²ˣ -1 )²

Now plugging the value in arc length formula,

Arc length = ₐ∫ᵇ √{1 + (dy/dx)²} dx

= ₐ∫ᵇ √{(e²ˣ + 1)²/(e²ˣ -1 )²} dx

= ₐ∫ᵇ√{(e²ˣ + 1)/(e²ˣ -1 )}² dx

= ₐ∫ᵇ {(e²ˣ + 1)/(e²ˣ -1 )} dx

= ₐ∫ᵇ[eˣ(eˣ + e⁻ˣ)/eˣ(eˣ - e⁻ˣ )] dx

= ₐ∫ᵇ[(eˣ + e⁻ˣ)/(eˣ - e⁻ˣ )] dx

Arc length= ₐ∫ᵇ(cosh x)/(sinh x)dx ( using hyperbolic functions formulas )

let sinh x = t => cosh xdx = dt

and when x = a => t = sinh a

when x = b => t = sinh b

so, arc length = ₛᵢₙₕ ₐ∫ˢᶦⁿʰ ᵇ (1/t) dt

= [ ln( sinh b ) - ln(sinh a) ]

= ln( sinh b/ sinh a)

Arc length= [( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)]

Hence, length of curve is ln[( eᵇ - e⁻ᵇ )/ ( eᵃ - e⁻ᵃ)].

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Linear regression is a statistical tool used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables.

Linear regression is a statistical technique used in predictive analytics to identify the relationship between a dependent variable and one or more independent variables. It is used to predict future outcomes by analyzing data from the past. It works by fitting a linear equation to the data, which is then used to estimate the value of the dependent variable for any given combination of values of the independent variables. The linear equation is constructed by finding the line of best fit through the data points. Linear regression can be used to identify trends and patterns in the data, and to make predictions about future outcomes. It is a powerful tool for predicting the future, and can be used to make informed decisions about how to best use resources.

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Inequality compares two variables, to show if one is less than, equal to or greater than the other variable being compared.

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Answer: 10

scince x is equal to -4 the equation becomes g(-4)=6- -4

The proof of <BED = <BAC  is shown below.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

AE ⊥ BC

and, CD ⊥ AB

As, AE is perpendicular to BC then BE = EC = 1/2 BC

and, BD = AD = 1/2 AB

Now, In ΔBED and ΔBCA

<EBD = <ABC {common}

BD/AB = BE/ BC = 1/2

By ASA similarity Criteria ΔBED ~ ΔBCA

So, <BED = <BAC

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