pls help−4(3/2x−1/2)=−15

Given the lengths of the two sides and the angle between them, only one triangle can be created under the given circumstances.

1. Given that angle B is 32.5°, side AB is 37 cm, side AC is 26 cm, etc.

2. Calculate side BC using the Law of Cosines:

BC = (2(AB)(AC)cosB) + (AB)(AC)2

3. Input the values that are known: BC = (37 2 + 26 2 - 2(37)(26)cos32.5°)

4. Condense: BC = (1369 plus 676 minus 1848 cos 32.5 °)

5. Determine BC =. (2095 - 1539.07)

6. Condense: BC = 556.93

7. Determine BC as 23.701 cm.

8. Since the lengths of the two sides and the angle between them are specified, only one triangle can be formed under the current circumstances.

By applying the Law of Cosines, we can determine the length of the third side, BC, given that side AB is 37 cm, side AC is 26 cm, and angle B is 32.5°. In order to perform this, we must first determine the cosine of angle B, which comes out to be 32.5°. Then, we enter this value, together with the lengths of AB and AC, into the Law of Cosines equation to obtain BC.BC = (AB2 + AC2 - 2(AB)(AC)cosB) is the equation. BC is then calculated by plugging in the known variables to obtain (37 + 26 - 2(37)(26)cos32.5°). By condensing this formula, we arrive at BC = (1369 + 676 - 1848cos32.5°). Then, we calculate BC as BC = (2095 - 1539.07), and finally, we simplify to obtain BC = 556.93. Finally, we determine that BC is 23.701 cm. Given the lengths of the two sides and the angle between them.

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Answer:

-8(x+2.5)^2

This is the same function as if you were to graph h(g(f(x)))

I hope this helps

The general form of the equation of the given circle with center A is option A: \(x^2 + y^2 + 6x - 24y - 25 = 0.\)

To determine the general form of the equation of the given circle with center A, we need to complete the square for both the x and y terms.

The general form of a circle equation with center coordinates (h, k) is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is A, which is represented by (h, k) = (-3, 12) as given in the options.

Let's examine each option and determine which one matches the general form:

A. \(x^2 + y^2 + 6x - 24y - 25 = 0\)

Completing the square for x:\((x^2 + 6x) + (y^2 - 24y) = 25\)

\((x^2 + 6x + 9) + (y^2 - 24y) = 25 + 9\)

\((x + 3)^2 + (y - 12)^2 = 34\)

B. \(x^2 + y^2 - 6x + 24y + 128 = 0\)

Completing the square for x: \((x^2 - 6x) + (y^2 + 24y) = -128\)

\((x^2 - 6x + 9) + (y^2 + 24y) = -128 + 9\)

\((x - 3)^2 + (y + 12)^2 = -119\)  (Not a valid equation for a circle since the radius squared is negative)

C. \(x^2 + y^2 + 6x - 24y + 128 = 0\)

Completing the square for x: \((x^2 + 6x) + (y^2 - 24y) = -128\)

\((x^2 + 6x + 9) + (y^2 - 24y) = -128 + 9\)

\((x + 3)^2 + (y - 12)^2 = -119\) (Not a valid equation for a circle since the radius squared is negative)

D. \(x^2 + y^2 + 6x - 24y + 148 = 0\)

Completing the square for x: (\(x^2 + 6x) + (y^2 - 24y) = -148\)

\((x^2 + 6x + 9) + (y^2 - 24y) = -148 + 9\)

(\(x + 3)^2 + (y - 12)^2 = -139\) (Not a valid equation for a circle since the radius squared is negative)

From the options given, none of the equations represent a valid circle. Therefore, none of the options (A, B, C, D) correctly represent the general form of the equation of the given circle with center A.

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Answer: it’s. Q and w are similar but not congruent

Range: All real numbers greater than or equal to 3. The Option C.

To find the range of the function, we need to determine the set of all possible y-values that the function takes.

Since the line crosses the y-axis at (0, 2), we know that the function's range includes the value 2. Also, since the line turns at (-1, 3), the function takes values greater than or equal to 3.

Therefore, the range of the function is all real numbers greater than or equal to 3.

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Explanation:

5 & 1/3 = 5 + 1/3 = 15/3 + 1/3 = 16/3

The mixed number 5 & 1/3 converts to 16/3

The fraction 16/3 means we have 16 copies of 1/3 added together, while 2/3 means we have 2 copies of 1/3. Note that 16/2 = 8 which tells us how many bags Taylor needs.

In other words, the solution to (2/3)*x = 16/3 is x = 8. This is the same as solving 2x = 16 after multiplying both sides by 3. Then we divide both sides by 2 to isolate x fully.

Answer is attached

Which grade you in btw?

Answer:

its D. (3,0)

Step-by-step explanation:

The ordered pair makes both inequalities true is (3,0) if the inequalities are y > –2x + 3, and y < x – 2.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

It is given that:

The inequalities are:

y > –2x + 3

y < x – 2

Plug the point in the above inequality:

(3,0)

The above point satisfy the inequality.

Thus, the ordered pair makes both inequalities true is (3,0) if the inequalities are y > –2x + 3, and y < x – 2.

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The simplified form of the given equation is \(=\frac{6}{5x^{10}}\)

We have given that,

\(\sqrt{\frac{72x^{16}}{50x^{36} }\)

Apparently, you want to simplify the given equation,

\(\sqrt{\frac{72x^{16}}{50x^{36} }\)

The applicable rules of exponents are,

 (a^b)(a^c) = a^(b+c)

 1/a^b = a^(-b)

 (a^b)^c = a^(bc)

So the expression simplifies as

 \(=\sqrt{\frac{72x^{16}}{50x^{36} }}\\\\=\frac{6}{5x^{10}}\)

Therefore the simplified form of the given equation is \(=\frac{6}{5x^{10}}\)

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a. x is an eigenvector of B belonging to an eigenvalue µ = (1 - 2α + α²) of B. b. x is an eigenvector of B belonging to an eigenvalue µ = 0 of B. Since B has a zero eigenvalue, it is singular.

a) Let x be an eigenvector of A belonging to an eigenvalue α of A, then we have:

Ax = αx

Multiplying both sides by A and rearranging, we get:

A²x = αAx = α²x

Now, substituting (I - 2A + A²) for B, we have:

Bx = (I - 2A + A²)x = Ix - 2Ax + A²x

 = x - 2αx + α²x (using Ax = αx and A²x = α²x)

 = (1 - 2α + α²)x

So, x is an eigenvector of B belonging to an eigenvalue µ = (1 - 2α + α²) of B.

b) If α = 1 is an eigenvalue of A, then we have:

Ax = αx = x

Multiplying both sides by A and rearranging, we get:

A²x = A(x) = α(x) = x

Now, substituting (I - 2A + A²) for B, we have:

Bx = (I - 2A + A²)x = Ix - 2Ax + A²x

= x - 2x + x (using Ax = x and A²x = x)

 = 0

So, x is an eigenvector of B belonging to an eigenvalue µ = 0 of B. Since B has a zero eigenvalue, it is singular.

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Answer:

BC = 17.1

m<B = 6.7 deg

m<C = 83.3 deg

Step-by-step explanation:

Find BC

a^2 + b^2 = c^2

AC^2 + AB^2 = BC^2

2^2 + 17^2 = BC^2

4 + 289 = BC^2

BC^2 = 293

BC = sqrt(293)

BC = 17.1

Find <B

tan B = opp/adj

tan B = 2/17

B = tan^-1 2/17

B = 6.7 deg

Find <C

m<A + m<B + m<C = 180

90 + 6.7 + m<C = 180

m<C = 180 - 90 - 6.7

m<C = 83.3

The measure of angle A in the isosceles triangle ABC is 62.5 degrees.

In an isosceles triangle ABC, where AB = AC, we are given that angle B (denoted as ∠B) measures 55 degrees. We need to calculate the measure of angle A (denoted as ∠A).

Since AB = AC, we know that angles A and C are congruent (denoted as ∠A ≅ ∠C). In an isosceles triangle, the base angles (the angles opposite the equal sides) are congruent.

Therefore, we have:

∠A ≅ ∠C

Also, the sum of the angles in a triangle is always 180 degrees. Hence, we can write:

∠A + ∠B + ∠C = 180

Substituting the given values:

∠A + 55 + ∠A = 180

Combining like terms:

2∠A + 55 = 180

Subtracting 55 from both sides:

2∠A = 180 - 55

2∠A = 125

Dividing by 2:

∠A = 125 / 2

∠A = 62.5

Therefore, the measure of angle A in the isosceles triangle ABC is 62.5 degrees.

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Answer:

12960

Step-by-step explanation:

(30+2)*405

405*30 + 405*2

12150+810

12960

Hope this helps plz hit the crown :D

According to the question Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

To calculate the probability of obtaining a straight flush in a five-card poker hand, we need to determine the number of possible straight flush hands and divide it by the total number of possible five-card hands.

A straight flush consists of five consecutive cards of the same suit. There are four suits in a standard deck of cards (hearts, diamonds, clubs, and spades), and for each suit, there are nine possible consecutive sequences (Ace, 2, 3, 4, 5, 6, 7, 8, 9; 2, 3, 4, 5, 6, 7, 8, 9, 10; etc.). Therefore, there are \(\(4 \times 9 = 36\)\) possible straight flush hands.

The total number of possible five-card hands can be calculated using the concept of combinations. In a standard deck of 52 cards, there are \(\({52 \choose 5}\)\) different ways to choose five cards. The formula for combinations is \(\({n \choose k} = \frac{n!}{k!(n-k)!}\), where \(n\)\) is the total number of items and \(\(k\)\) is the number of items being chosen.

Using the formula, we have \(\({52 \choose 5} = \frac{52!}{5!(52-5)!} = 2,598,960\).\)

Therefore, the probability of obtaining a straight flush in a five-card poker hand is:

\(\[\frac{\text{{number of straight flush hands}}}{\text{{total number of five-card hands}}} = \frac{36}{2,598,960} \approx 0.00001385\]\)

Rounded to four decimal places, the probability is approximately 0.00001385, or approximately 0.0014%.

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Answer:

9a + 27

Step-by-step explanation:

=> 3(a+3) + 6(a+3)

Expand the brackets

=> 3a+9 + 6a+18

Combining like terms

=> 3a+6a+9+18

=> 9a + 27

Answer:

9a+24

Step-by-step explanation:

3a+6+6a+18

Simplify:

9a+24

Answer:

The semi-circles form an entire circle with a diameter of 74.

The radius is 37

The area of the rectangle is 95 x 74 = 7030

The area of the circle is 3.142 x 37*37 = 4298.66

The total area is 11328.66

The rate of decay in this equation is 1, which means that the value is decreasing by 100% per unit of time. In other words, the value is decreasing to zero and there is no growth or stabilization happening

Rate of decay refers to the speed at which a quantity or substance is decreasing over time. It is often used in the context of radioactive decay, where a radioactive substance is decreasing in concentration or activity over time due to the decay of its unstable nuclei.

The rate of decay (r) in the equation y = a(r)^t can be found by using the formula:

r = 1 - (y2/y1)^(1/t2-t1)

where y1 is the initial value, y2 is the final value, t1 is the initial time, and t2 is the final time.

In this case, we have the equation y = 575(1-0.6)^t, which means that y1 = 575, y2 = 0 (since the value is decaying to zero), t1 = 0 (since we are starting at time zero), and t2 is unknown. We want to find the rate of decay (r).

(1-0.6)^t = y/575

t = log(1-0.6)^-1 * log(y/575)

We can substitute this value of t into the formula for r:

r = 1 - (y2/y1)^(1/t2-t1)

r = 1 - (0/575)^(1/t-0)

r = 1 - 0

r = 1

Therefore, the rate of decay in this equation is 1, which means that the value is decreasing by 100% per unit of time. In other words, the value is decreasing to zero and there is no growth or stabilization happening.

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Answer:

Step-by-step explanation:

98.8

Answer:

99

Step-by-step explanation:

The angle of depression looking from the tower is the same as the angle of elevation looking at the top of the tower from the spot of the fire.  So, tan (12 degrees) = 21 / distance between the tower and fire.  Thus, the distance = 21 / tan(12).  

tan (12) = 0.2126

Distance = 21 / 0.2126 = 98.78

The question asks about the distance from the base to the fire (to the nearest foot.)  Thus, it is 99 feet.  

Answer:

its 0.8

Step-by-step explanation:

Answer:

the answer to your question is 9 miles

Answer:

387,420,489

Step-by-step explanation:

Use the product rule that says (x^a)(x^b)=x^a+b

\(\frac{3^{12}}{(3^{2})^{-3}}\)

Then the negative power rule:

\(\frac{3^{12}}{3^{-6}}\)

Then simplify:

\(\frac{531441}{\frac{1}{729} }\)

387,420,489

haha simple work, but the answer is not that simple :)

The function f(x) = x/(x-1) is neither surjective nor injective.

To determine whether the function f(x) = x/(x-1) is surjective, injective, or neither, let's analyze each property separately:

1. Surjective (Onto):

A function is surjective (onto) if every element in the codomain has at least one preimage in the domain. In other words, for every y in the codomain, there exists an x in the domain such that f(x) = y.

Let's consider the function f(x) = x/(x-1):

For f(x) to be surjective, every real number y in the codomain (R) should have a preimage x such that f(x) = y. However, there is an exception in this case. The function has a vertical asymptote at x = 1 since f(1) is undefined (division by zero). As a result, the function cannot attain the value y = 1.

Therefore, the function f(x) = x/(x-1) is not surjective (onto).

2. Injective (One-to-One):

A function is injective (one-to-one) if distinct elements in the domain map to distinct elements in the codomain. In other words, for any two different values x1 and x2 in the domain, f(x1) will not be equal to f(x2).

Let's consider the function f(x) = x/(x-1):

Suppose we have two distinct values x1 and x2 in the domain such that x1 ≠ x2. We need to determine if f(x1) = f(x2) or f(x1) ≠ f(x2).

If f(x1) = f(x2), then we have:

x1/(x1-1) = x2/(x2-1)

Cross-multiplying:

x1(x2-1) = x2(x1-1)

Expanding and simplifying:

x1x2 - x1 = x2x1 - x2

x1x2 - x1 = x1x2 - x2

x1 = x2

This shows that if x1 ≠ x2, then f(x1) ≠ f(x2). Therefore, the function f(x) = x/(x-1) is injective (one-to-one).

In summary:

- The function f(x) = x/(x-1) is not surjective (onto) because it cannot attain the value y = 1 due to the vertical asymptote at x = 1.

- The function f(x) = x/(x-1) is injective (one-to-one) as distinct values in the domain map to distinct values in the codomain, except for the undefined point at x = 1.

Thus, the function f(x) = x/(x-1) is neither surjective nor injective.

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In trigonometry, it should be noted that the value of sin(-5pi/6) is -0.5.

In order to find the value, we can use the following steps:

Draw a unit circle and mark an angle of -5pi/6 radians.

The sine of an angle is represented by the ratio of the opposite side to the hypotenuse of the triangle formed by the angle and the x-axis.

In this case, the opposite side is 1/2 and the hypotenuse is 1.

Therefore, sin(-5pi/6) will be:

= 1/2 / 1

= -0.5.

We can also use the following identity to find the value of sin(-5pi/6):

sin(-x) = -sin(x)

Therefore, sin(-5pi/6)

= -sin(5pi/6)

= -0.5.

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Answer:

(b)

Step-by-step explanation:

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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1. the solutions to the equation are x = π/3 and x = 2π/3.

2. the solutions to the equation are: x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

3. Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

1. Solving the equation 16cos^2(x) - 4 = 0:

Let's rewrite the equation in terms of the double-angle formula for cosine:

16(1 - sin^2(x)) - 4 = 0

Simplifying the equation:

16 - 16sin^2(x) - 4 = 0

12 - 16sin^2(x) = 0

16sin^2(x) = 12

sin^2(x) = 12/16

sin^2(x) = 3/4

Taking the square root of both sides:

sin(x) = ±√(3/4)

sin(x) = ±√3/2

Now, we can find the values of x by considering the unit circle and the quadrants where sin(x) is positive or negative.

In the first quadrant (0 < x < π/2):

sin(x) = √3/2

x = π/3

In the second quadrant (π/2 < x < π):

sin(x) = √3/2

x = π - π/3 = 2π/3

Note: Since we're using radians, we don't need to consider the angles in the third and fourth quadrants.

Therefore, the solutions to the equation are x = π/3 and x = 2π/3.

Answer: π/3, 2π/3

2. Solving the equation cos(6x)(2cos(x) + 1) = 0:

We have two possibilities for this equation to be true:

1) cos(6x) = 0

2) 2cos(x) + 1 = 0

For the first possibility, cos(6x) = 0, we know that cosine is equal to zero at odd multiples of π/2.

6x = π/2 + nπ        (n is an integer)

Solving for x:

x = (π/2 + nπ)/6        (n is an integer)

For the second possibility, 2cos(x) + 1 = 0, we can solve for cos(x):

2cos(x) + 1 = 0

2cos(x) = -1

cos(x) = -1/2

We know that cosine is equal to -1/2 at 2π/3 and 4π/3.

Therefore, the solutions to the equation are:

x = (π/2 + nπ)/6, 2π/3, 4π/3        (n is an integer)

Answer: (π/2 + nπ)/6, 2π/3, 4π/3

3. Solving the multiple-angle equation sec(3x) - 2 = 0:

To solve this equation, we need to isolate the secant function.

sec(3x) - 2 = 0

sec(3x) = 2

Taking the reciprocal of both sides:

1/cos(3x) = 2

Now, we can solve for cos(3x):

cos(3x) = 1/2

We know that cosine is equal to 1/2 at π/3 and 5π/3.

Now, we can solve for x:

3x = π/3 + 2nπ, 5π/3 + 2nπ        (n is an integer)

Dividing both sides by 3:

x = π/9 + (2nπ)/3, 5π/9 + (2nπ)/3        (n is an integer)

Answer: π/9 +(2nπ)/3, 5π/9 + (2nπ)/3 (n is an integer)

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The price per share if its equity cost of capital is 17.8% per year is $3.31.

What does the equity cost of capital represent?

The rate of return a business must offer equity investors is known as the cost of equity. It stands for the compensation that the market demands in return for taking on the risk of ownership of an asset.

When experts wish to value stocks, the cost of equity is crucial. The equity investment's worth can be determined in part by the cost of equity. So, if someone is investing in a business or project, they might desire to see at least the cost of equity return on their investment.

According to the given information:

As per the Dividend growth model,

Price of the stock

= Dividend / Cost of capital

= 0.79 / 0.178

= $3.31

So, the price per share, if its equity cost of capital is 17.8% per year, is $3.31.

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$90m + $500 is the correct expression for the given data.

Troy's grandpa gave him a one-time gift of $700, so let's start there.

Next, let's think about Troy's monthly salary. He receives $40 a month from his grandfather, so in m months he would have gotten 40 million dollars.

He gets $50 a month from his mother, but she just started doing so 4 months after his grandfather, so he would have gotten that amount for (m-4) months. The entire sum he received from his mother would be as follows:

50(m-4)

We can add up the three sums to make the statement for Troy's overall payment after m months simpler:

Total amount = $700 + $40m + $50(m-4)

Condensing the phrase:

Total amount = $700 + $40m + $50m - $200

Total amount = $90m + $500

Therefore, the simplified expression for the amount of money Troy received m months after his mother started giving him money is $90m + $500.

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Answer:

2x+3y

Step-by-step explanation:

you add up the known sides: (x-y)+(x+y) = 2x

Then you subtract the answer from the perimiter: 4x+3y-2x=2x+3y