Find the measure of angle DBC

The 5 most common Pythagorean triples are ( 3 , 4 , 5 ) , ( 5 , 12 , 13 ) ,

( 6 , 8 , 10 ) , ( 9 , 12 , 15 ) , and ( 15 , 20 , 25 ) .

Pythagorean triples:

Any three positive integers that completely satisfy the Pythagorean theorem is considered a Pythagorean triple number. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. A Pythagorean triple consists of the three sides of a right triangle. In this article, you will learn how to create multiple Pythagorean triples.

A Pythagorean triple consists of the three natural numbers a, b, c such that a² + b² = c². These triples are usually written as (a, b, c), examples

(3, 4, 5) are well known. If (a, b, c) is a Pythagorean triple, then (ka, kb, kc) is also a Pythagorean triple for all natural k. A primitive Pythagorean triplet is a triplet in which a, b, and c are coprime (i.e., have no common divisor greater than 1). For example, (3, 4, 5) is a basic Pythagorean triple, but (6, 8, 10) is not.

A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is necessarily a right triangle.

This name comes from the Pythagorean theorem, which states that the side lengths of each right triangle satisfy the formula a² + b² =c². A Pythagorean triple gives the length of three integers of the sides of a right triangle. However, right triangles whose sides are not integers do not form a Pythagorean triple. For example, a triangle with sides a = b = 1 and c = √2 but, (1,1,2) is not a Pythagorean triple because √2 is not an integer. Also, the numbers 1 and √2 do not have a common multiple because √2 is irrational.

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The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

Answer:

Step-by-step explanation:

m - 3.8 - 0

m = 3.8 + 0

m = 3.8

The first equation, y equals two thirds times x, shows a proportional relationship because the ratio of y to x is constant.

Ratio is a numerical comparison of two or more values. It is a mathematical expression that shows the relationship between two or more quantities. Ratios are used to compare the relative size of two or more values, to measure changes over time, to quantify proportions, and to evaluate relationships between sets of data. In some cases, ratios can also be used to compare absolute values. Ratios are often expressed in the form of fractions, although they can also be expressed as decimals or percentages. Ratios can be used to compare two or more items or groups of data, and can be expressed as a single number or in a range of numbers.

This means that as x increases, y will increase at the same rate. Similarly, as x decreases, y will decrease at the same rate.

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Answer:

\( y = 8 \)

Step-by-step explanation:

Equation of the line that passes through (-2, 8) with a slope of 0, can be written in point-slope form, \( y - y_1 = m(x - x_1) \) and also in slope-intercept form, \( y = mx + b \).

Using a point, (-2, 8) and the slope (m), 0, substitute x1 = -2, y1 = 8 and m = 0 in \( y - y_1 = m(x - x_1) \).

Thus:

\( y - 8 = 0(x - (-2)) \)

\( y - 8 = 0 \)

Rewrite in slope-intercept form

\( y - 8 + 8 = 0 + 8 \) (addition property of equality)

\( y = 8 \)

The solutions of the quadratic equation are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

For a general quadratic:

a*x^2 + b*x + c = 0

The solutions are given by the quadratic formula

\(x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}\)

Here we have the quadratic equation:

2x^2 + x + 3 = 0

\(x = \frac{-1 \pm \sqrt{1^2 - 4*2*3} }{2*2} \\\\x = \frac{-1 \pm \sqrt{-23} }{4}\)

So we will have two complex solutions, these are:

x = (-1 + i√23)/4

x = (-1  - i√23)/4

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Answer:

infinite number of solutions

Step-by-step explanation:

Given the 2 equations

4x + 6y = 12 → (1)

6x + 9y = 18 → (2)

Equation (2) is a multiple of (1)

Each term has been multiplied by 1.5

Thus the 2 equations are basically the same equation.

This indicates there are infinite solutions to the system

Answer: True, perpendicular lines intersect so if the lines didn’t they wouldn’t be perpendicular

Step-by-step explanation:

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

0 plus 0 is equals to 0 times 0.

The value of x when given the equation m∥n, and the angle measures (x-25)° and (6x-5)° is 4.

The angle measures given are (x-25)° and (6x-5)°. We can use the rules of parallel lines and transversals to find the value of x.

Since line is parallel to line m, we know that corresponding angles are equal. This means that (x-25)° is equal to some other angle that is also (x-25)°.

Similarly, since line m is parallel to line n, we know that corresponding angles are equal. This means that the angle that is equal to (x-25)° is also equal to some other angle in line n.

Using the same logic, we can find the measure of the other angle in line n that is equal to (6x-5)°.

Now, we have two angles in line n that are equal in measure: one is (x-25)° and the other is (6x-5)°.

We can set up an equation to solve for x:

(x-25)° = (6x-5)°

Simplifying this equation, we get:

x - 25 = 6x - 5

Solving for x, we get:

x = 4

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Complete Question:

Given m ∥ n, find the value of x. when m = (x-25)° and n = (6x-5)°

Answer: n - 6

Step-by-step explanation:

Multiply -3 and 2.

-3 x 2 = -6

n -6

sorry if this is incorrect

Answer:

24

Step-by-step explanation:

-3N^2=24

Move all terms to the left:

-3N^2-(24)=0

a = -3; b = 0; c = -24;

Δ = b2-4ac

Δ = 02-4·(-3)·(-24)

Δ = -288

Delta is less than zero, so there is no solution for the equation!Q

Hope this helps You! :D

The equivalent units for the Compounding Department for August 2019 is 57,000 pounds.

Here is the explanation -

To calculate the equivalent units for the Compounding Department in August 2019 using the weighted average method, we need to consider the units that were started and completed, as well as the ending work-in-process.

Step 1: Calculate the equivalent units for units started and completed:
- 36,000 pounds were started.
- 34,000 pounds were transferred out.
Equivalent units for units started and completed = 34,000 pounds.

Step 2: Calculate the equivalent units for ending work-in-process:
- Ending work-in-process was 70% processed.
- Beginning work-in-process was 2,000 pounds (60% processed).
Equivalent units for ending work-in-process = (70% x Ending work-in-process) + (60% x Beginning work-in-process)
Equivalent units for ending work-in-process = (70% x 2,000 pounds) + (60% x 36,000 pounds)
Equivalent units for ending work-in-process = 1,400 pounds + 21,600 pounds
Equivalent units for ending work-in-process = 23,000 pounds.

Step 3: Calculate the total equivalent units:
Total equivalent units = Equivalent units for units started and completed + Equivalent units for ending work-in-process
Total equivalent units = 34,000 pounds + 23,000 pounds
Total equivalent units = 57,000 pounds.

Therefore, the equivalent units for the Compounding Department for August 2019 is 57,000 pounds.

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The factored form of the quadratic equation is given as follows:

y = 3(x + 0.6667)(x - 6).

The quadratic equation for this problem is defined as follows:

3x² - 16x - 7 = 5.

3x² - 16x - 12 = 0.

The coefficients are given as follows:

a = 3, b = -16, c = -12.

Hence the discriminant is of:

D = (-16)² - 4(3)(-12)

D = 400.

Then the roots are of:

Considering the leading coefficient of 3 and the roots, the factored form of the equation is given as follows:

y = 3(x + 0.6667)(x - 6).

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Answer:

w=13

Step-by-step explanation:

Answer:

w =13

Step-by-step explanation:

\(15+w=3w-11\)

Collect like terms

\(15+11 =3w-w\\\)

Simplify

\(26 = 2w\)

Divide both sides of the equation by 2

\(\frac{26}{2} = \frac{2w}{2}\)

Simplify

\(13 = w\)

Switch sides

\(w =13\)

Answer:

Step-by-step explanation: for you to get the answer you have to understand that 3 to 1 means to multiply by 3 so 45x3=135

Answer:

135

Step-by-step explanation:

1x = 45

3x (boys) = 45 ×3

= 135

Range: lowest possible y-value to the highest possible y-value

In this case, the graph spans from -4 to 1, taking on all of the y-values between those two points. But, the graph also has a straight line at y=3.

Range: -4 < y <= 1 or {3}

Hope this helps!

The expected value is 0.8, variance is 0.48, and standard deviation is 0.693 with the given probability.

a. The probability of getting one success in two trials with p=0.4 is given by the binomial probability formula:

f(1) = 2C1 * (0.4)^1 * (0.6)^1 = 0.48

b. The probability of getting zero successes is:

f(0) = 2C0 * (0.4)^0 * (0.6)^2 = 0.36

c. The probability of getting two successes is:

f(2) = 2C2 * (0.4)^2 * (0.6)^0 = 0.16

d. The probability of at least one success is:

P(at least one success) = 1 - P(no success)

= 1 - f(0)

= 1 - 0.36

= 0.64

e. The expected value of a binomial distribution with n trials and probability of success p is given by:

E(X) = np

In this case, n = 2 and p = 0.4, so:

E(X) = 2 * 0.4 = 0.8

The variance of a binomial distribution is given by:

Var(X) = np(1-p)

So:

Var(X) = 2 * 0.4 * 0.6 = 0.48

The standard deviation is the square root of the variance:

SD(X) = sqrt(Var(X)) = sqrt(0.48) = 0.693.

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The area that will be taken up is 183.75 square feet, the volume of water is 131.25 cubic feet, and the cost of filling the pool is.

To calculate the total area follow this procedure:

Area:  2 (lh +wh + lw )

Area: 2 (8.75x 3.5 + 5 x 3.5 + 8.75 x 5)

Area: 2 ( 30.625 + 17.5 +43.75)

Area: 2 x 91.875 = 183.75 square feet

The volume follow this procedure:

Volume: length x width x height - 6 inches or 0.5 feet

Volume: 8.75 feet x 5 feet x 3 feet = 131.25 cubic feet

To do this, just multiply the volume by the cost:

131.25 cubic feet x $0.29 = $38.06

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Answer:

x=2

Step-by-step explanation:

x= 4/2

x =2

You divide X by Y

If you have a ratio of X:Y then to find the slope you simply divide the Y axis by the X axis to get a constant rate (unit rate, etc).

Hope this helps and have a nice day.

-R3TR0 Z3R0

Answer: negative 2 minus radical 3

Step-by-step explanation:

We can use the tangent half-angle formula to find the exact value of tangent of 7π/12:

tan(θ/2) = ±√[(1-cosθ)/1+cosθ)]

Here, θ = 7π/6, and cos(7π/6) = -sqrt(3)/2.

Substituting these values, we get:

tan(7π/12) = ±√[(1-(-sqrt(3)/2))/(1+(-sqrt(3)/2))]

= ±√[(2+sqrt(3))/(2-sqrt(3))]

Multiplying the numerator and denominator by (2+sqrt(3)), we get:

= ±√[(2+sqrt(3))^2/(4-3)]

= ±√[(2+sqrt(3))^2]

= ±(2+sqrt(3))

Since 7π/12 lies in the second quadrant, and tangent is negative in the second quadrant, the exact value of tangent of 7π/12 is - (2+√3)

Answer:24-25a

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

-5 x 15 = -75

This is according to the rule -a ÷ a = -a and -a x a = -a. Where a negative divided/multiplied by a positive number equals a negative number.

-75 ÷ -5 = 15

-75 ÷ 15 = -5

Answer:

You would write it like -

y = 7 + 4x

or y = 4x + 7

A number line showing the solution of -8 - (-6) is :  A number line from negative 10 to 10 is shown with numbers labeled at intervals of 2. An arrow is shown from point 0 to negative 8. Another arrow points from negative 8 to negative 2.

A number line is a straight line drawn horizontally where the numbers are placed at an equal intervals.

Given expression is -8 - (-6).

That is the number -6 is subtracted from the number -8.

So we have to first draw an arrow to the number -8.

Then we have to draw an arrow of length -6 units from the number -8.

Then the arrow will stop at -2, which is the solution.

Hence the solution of the expression is -2.

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The additional set of values which could be included in the table is; (10,2).

As evident in the task content, it follows that for a 15 unit increase in x, depth, there is a 3 unit increase in y, pressure.

On this note, it follows that with each 5 unit increase in x corresponds to 1 unit increase in y.

And ultimately, at x = 10, y = 2 × 1 = 2.

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Answer:

Step-by-step explanation:

Answer:

independent

Step-by-step explanation: