What is the measure of ABC

The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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y = 5 - x. is the linear equation in point-slope form.

Points  (1,4) and (6,-1).

The formula for finding slope from two points (x₁, y₁) and (x₂, y₂) on a line is m = (y₂ - y₁) / (x₂ - x₁).

where , m = slope of the line. x₁ = the x-coordinate of the first point.

m = (-1 - 4) / (6 - 1 ).

m= -1

Substitute the values into the point-slope form,

y − y 1 = m ( x − x 1 ) .

y − 4 = -1 ( x − 1) .

y − 4 =  1 - x.

y = 5 - x.

complete question : Write the linear equation in point-slope form that passes through the given points. (1, 4) and (6, -1).

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The derivative of function y =eu is dy/dx = dy/du × du/dx

                                        Derivative refers to the rate of change of a variable with respect to any independent variables.

The function that has such a differentiable element which is also a function of other variable is termed as composite function. The method of differentiating composite function is called chain rule for differentiation.

In the above question, y is a composite function as y is a function of u and at the same time u is a function of x.

given, y =eu, where u is differentiable function of x, let u = g(x)

now, y =eu is differentiated using chain rule and we get dy/dx = dy/du×du/dx

hence, the derivative is dy/dx = dy/du×du/dx

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The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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The weighted arithmetic mean price per ton is $72.33

Given that, a purchasing agent placed the three orders for coal. tons of coal 1,200 3,000 500 price per ton $28.50, $87.25 and $88.00, we need to find the weighted arithmetic mean price per ton,

So, the mean = 28.50x1200+87.25x3000+88x500 / 1200+3000+500

= 339950 / 4700 = 72.33

Hence, the arithmetic mean price per ton is $72.33

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Polar form of complex numbers is z=a+bi is

z = r(cosθ + i sinθ) . So, first find the absolute value of r and then argument θ. Polar form of given expression are

a) 7(√3/2 + i/2 )

b) 7(√3/2 - i/2)

c) 14(√3/2 + i/2)

d) 14(√3/2 - i/2)

The polar form of complex numbers is a different way of representing complex numbers than the orthogonal form. Complex numbers are usually represented in the form z = x+iy. where "i" is an imaginary number. But in polar form, complex numbers are represented as a combination of modulus and argument.

Problems Algebra Convert to polar form

a) 7(cos(30°) + i sin(30°))

we simplify each term.

The exact value of cos(30°) = √3/2

=> 7((√3/2) + i sin(30°))

The exact value of sin(30°) = 1/2

=> 7(√3/2 + i/2 )

Combine all values we get, 7(√3/2 + i/2 )

7(cos(330°) + i sin(330°))

Using quadrant system

b) cos(330°) = cos(360°- 30°) = cos 30° = √3/2

sin(330°) = sin(360°- 30°) = - sin 30° = -1/2

so, 7 ((√3/2) + i(-1/2))

= 7√3/2 - 7i/2 = 7(√3/2 - i/2)

c) 14(cos(30°) + i sin(30°))

= 14 ((√3/2) + i (1/2)) = 14√3/2 + 14i/2=14(√3/2 - i/2)

d) 14(cos(330°) + i sin(330°))

= 14 (√3/2) + 14i(-1/2) = 14√3/2 - 14i/2

= 14(√3/2 - i/2)

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Answer:

14(cos(330o) + i sin(330o))

Step-by-step explanation:

The required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

Any matrix obtained by performing a single elementary row operation on the identity matrix is called an elementary matrix.

The elementary operations are as follows:

1. Interchange the two rows of a matrix

2. Multiply a row of a matrix by the non-zero scalar k.

3. Add k-times of a row into another row of the matrix.

Each type of elementary operation may be performed by matrix multiplication, using square matrices called elementary operators.To perform an elementary row operation on A, an n×m matrix, take the following steps:

1. To find E, the elementary row operator, apply the operation to an n×n identity matrix.

2. To carry out the elementary row operation, premultiply A by E.

We want to interchange the first and second rows of A, a 3×3 matrix to  get B. To create the elementary row operator E, we interchange the first and second rows of the identity matrix I3:

[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right][/tex] is changed to  [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex].

So, [tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex][tex]\left[\begin{array}{ccc}2&1&3\\-2&4&5\\3&1&4\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}2&1&3\\3&1&4\\-2&4&5\end{array}\right][/tex]

Thus, the required elementary matrix E such that EA = B is

[tex]\left[\begin{array}{ccc}1&0&0\\0&0&1\\0&1&0\end{array}\right][/tex]

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Answer:

-3.7%, 0.3%,7%,17%,70%

Step-by-step explanation:

The indicated angles in the parallel lines cut by the transversal are as follows:

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, linear angles, vertically opposite angles, alternate exterior angles etc.

Therefore, according to the diagram the two parallel lines are cut by a transversal. Let's use the angle relationships to find the m ∠1 and m∠3.

m ∠6 = 78 degrees.

m ∠1 = m ∠ 7 (alternate exterior angles)

Alternate exterior angles are congruent.

Hence,

m ∠7 = 180 - 78 = 102 degrees

m ∠ 1 = 102 degrees

m ∠ 1 = m ∠ 3 (vertically opposite angles)

vertically opposite angles are congruent.

m ∠ 3 = 102 degrees.

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Answer:

3. 44 root= between 6 and 7 (more on the 7 side)

The boat's distance and bearing from the port regions are as follows;

The boat is located around 157.15 kilometers from the harbor on a bearing of 150°.

In mathematics, a bearing is an angle measured clockwise from the north or y-axis direction.

The Coast Guard cutter travels at a speed of 30 kno

Angelica, a Coast Guard cutter, has a bearing of 95 degrees.

The coast guard goes for 2 hours in the first direction.

The shift in direction of the Coast Guard cutter = 185°

Travel time in the new direction = 2 hours

30 knots equals 55.56 km/hr

The distance traveled in the first direction = 55.56 km/hr = 111.12 km in 2 hours

Distance traveled in the other direction = 55.56 km/hr 2 hours = 111.12 km

According to the accompanying graphic, the figure produced by the Coast Guard cutter's course is an isosceles triangle.

The Pythagorean theorem gives the distance from the port to the position of the boat as l = √(111.122^2 + 111.122^2) ≈ 157.15.

The boat is roughly 157.15 kilometers away from the port.

An isosceles right triangle has 45° base angles.

As a result, the bearing is 95° + 45° = 150°.

The angle between the port and the boat is 150°.

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Answer:

£5.174

Step-by-step explanation:

Because you do 25.87 divided by 5

Answer:10

Rewriting input as fractions if necessary:

3/5, 1/2

For the denominators (5, 2) the least common multiple (LCM) is 10.

LCM(5, 2)

Therefore, the least common denominator (LCD) is 10.

Calculations to rewrite the original inputs as equivalent fractions with the LCD:

3/5 = 3/5 × 2/2 = 6/10

1/2 = 1/2 × 5/5 = 5/10

Answer:

Step-by-step explanation:

1/2 + 3/5 = 5/10 + 6/10 = (5+6)/10 = 11/10 or 1 1/10 Your pair of fractions is 5/10 and 6/10

Answer:

88 feet

Step-by-step explanation:

Use this formula

Circumference= 2*22/7*Radius

22/7 * 14=

2*44 =

88 feet

The amount of commission the agent receives if the bonus amount is Rs. 1,500, is Rs. 24,000.

To find the commission received by the agent, we first determine the excess sales using the bonus rate and bonus amount.

The excess sales are added to Rs. 900,000 to determine the total sales for the year.

The commission rate is applied to the total sales to ascertain the amount of the commission the agent received.

Commission on the total annual sales = 2%

Bonus on the excess of sales over Rs. 900,000 = 0.5%

Bonus amount = Rs. 1,500

Excess sales over Rs. 900,000 = Rs. 300,000 (Rs. 1,500/0.5%)

Total sales = Rs. 1,200,000 (Rs. 900,000 + Rs. 300,000)

Commission amount = Rs. 24,000 (Rs 1,200,000 x 2%)

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The solution to the inequality 4x + 10 < 6 is x < -1.

Given the inequality;

4x + 10 < 6

Solve for x.

Move all terms not containing x to the right side of the inequality by subtracting 10 from both sides of the inequality.

4x + 10 < 6

4x + 10 - 10 < 6 - 10

4x < 6 - 10

Subtract 10 from 6

4x < -4

Divide each term by 4 and simplify

4x < -4

4x/4 < -4/4

Simplify the left-hand side

x < -4/4

Simplify the right-hand side

x < -1

The result in inequality form is x < -1.

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The radius reduced to 57.3% of its normal value.

The expression of Poiseuille's law for flow in a tube is:

Q = Δpπr⁴/8ηl

where:

Q = is the flow rate

P₁ = is the pressure at first end of vain

P₂ = is the pressure at the other end

η = is the viscosity of the concrete

r - radius of pipe

l = is the length

Re arrange the expression for the radius of the pipe,

r = (8Qηl/πΔP)¹/⁴

the flow rate in an artery has been reduced to 10.0%and the difference in blood pressure is increased by 20%.

so,

Q' = 0.100Q and

ΔP' = 1.20ΔP

SUbstitute the above points.

r' = (8( 0.100Qηl/π(1.20ΔP))¹/⁴

= 0.537(8Qηl/πΔP)¹/⁴

Combine the expression of radius before the flow and pressure changes and the expression derived or the new radius,

r' = 0.537r

Hence the radius reduced to 57.3% of its normal value.

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The length of the sides of the special triangles, found using the relationship between the sides of the triangles are as follows;

(1) Length of the legs is 20 each

Length of the hypotenuse = 20·√2

(2) Length of the leg = 5

Length of the hypotenuse = 5·√2

5-50 a. Length of the leg is 10·√3

Length of the hypotenuse is 20

b. Length of the leg = 4

Length of the hypotenuse = 4·√2

c. Length of each leg = 8

d. Length of the leg = 9·√3

Length of the hypotenuse = 18

e. Length of the shorter leg = 4.5

Length of the longer leg = 4.5·√3

f. Length of the legs = 3·√2 each

5-51

What are triangles?

A triangle is a three sided polygon, that has a sum of interior angles of 180°

The lengths of the missing sides in the triangles found using the 30°–60°–90°, and 45°–45°–90°, triangle patterns are as follows;

In a 30°, 60°, 90° triangle, if the length of the shortest leg is x, the length of the hypotenuse is 2·x, and the length of the other leg is x·√3

In a 45°, 45°, 90° triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

(1) The length of the legs are the same and equivalent to 20

The length of the hypotenuse side is 20·√2

(2) The length of the legs are the same and equivalent to 5

The length of the hypotenuse 5·√2

5-50 a. In the 30°, 60°, 90° triangle, the length of the adjacent, longer leg is 10·√3

The length of the hypotenuse side is 2·x

b. The triangle is a 45°, 45°, 90°, triangle

The length of the legs are 4 unit each

The length of the hypotenuse is 4·√2

c. The length of the hypotenuse in the 45°, 45°, 90° is 8·√2, therefore, the length of the legs are;

8 units each

d. The length of the shortest leg in the 30°, 60°, 90°, right triangle is 9, therefore, the length of the hypotenuse side is 2 × 9 = 18

The length of the longest leg is 9·√3

e. The length of the hypotenuse in the 30°, 60°, 90°, right triangle is 9 units, therefore, the length of the shortest leg is 4.5 units

The length of the longest leg is 4.5·√3

f. The length of the hypotenuse side of the 45°, 45°, 90°, right triangle is 6, therefore;

The length of the legs are 6/√2 = 3·√2

5-51

The dimensions of the side length of the special right triangles are;

In a 30°-60°-90° triangle, if the length of the shortest leg is x, then;

The length of the hypotenuse is 2·x

The length of the longer leg is x·√3

In a 45°-45°-90° right triangle, the length of the legs are the same, and the length of the hypotenuse is √2 multiplied by the length of one leg.

Please attached diagrams of the 45°, 45°, 90°, and the 30°, 60°, 90° triangles created with MS Word

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The slope of the line of image 1 is 2

The slope of the line of image 2 is 5/2

The slope of the line of image 3 is 2/5.

The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.

The slope of the line of image 1 is:

The line is passing through the points (6, 10 and (2, 2)

So,

Slope=(y₂-y₁)/(x₂-x₁)

m=(2-10)/(2-6)

m=8/4

m=2

Therefore, the slope of the line for image 1 is 2.

Hence, option A is correct.

The slope of the line for image 2 is:

The line is passing through the points (3, 4) and (7, 14)

Slope=(y₂-y₁)/(x₂-x₁)

m=(14-4)/(7-3)

m=10/4

Therefore, the slope of the line for the image 2 is 5/2.

Hence, option F is correct.

The slope of the line for image 3 is:

The line is passing through the points (2, 1) and (7, 3)

Slope=(y₂-y₁)/(x₂-x₁)

m=(3-1)/(7-2)

m=2/5

Therefore, the slope of the line for the image 3 is 2/5

Therefore, option D is correct.

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Answer: 68 kilometers per hour

Step-by-step explanation:

Take 238 divided by 3.5 hours = 68 km per hour

Answer:

volume = 960π m³ ; surface area = 368π m²

Step-by-step explanation:

base area = 8²π = 64π m²

base perimeter = 8 x 2 x π = 16π m

lateral area = 16π x 15 = 240π m²

surface area = 2 x 64π + 240π = 128π + 240π = 368π m²

Volume = 64π x 15 = 960π m³

Answer:   The final balance is $9,013.73.

The total compound interest is $7,513.73.

Step-by-step explanation:

The numbers that are greater than -9 are 2.895, -8.92, 0.504, -2.9

What is a positive number?

A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, growing larger as you move to the right.

Given number is -9 which is a negative number.

All positive numbers are always greater a negative number

In the given number, the positive numbers are 2.895, 0.504.

Thus 2.895 and 0.504 are greater than -9.

The negative numbers whose absolute less than 9, they are also greater than -9.

The absolute value of -10.56, -8.92, -15.782, -2.9, -18.376 are

|-10.56| = 10.56 >9

|-8.92| = 8.92 <9

|-15.782| = 15.782 > 9

|-2.9| = 2.9 < 9

|-18.376| = 18.376 >9

Therefore -8.92 and -2.9 are also greater than -9.

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Applying the formula of the surface area of a box, the total amount of plastic wrapping needed to cover the box is: 697 cm².

The total surface area of a box is the sum of all the areas of the six faces of the box.

The area of each face can be found by multiplying the length by the width of that face.

The area of each face is given as:

Area = length * width.

To find the amount of plastic wrapping needed to cover the entire box, you first need to find the surface area of the box.

The surface area of the box is given by:

Surface area = 2(19 cm * 14 cm) + 2(19 cm * 1.5 cm) + 2(14 cm * 1.5 cm)

= 2(266 cm²) + 2(28.5 cm²) + 2(21 cm²)

= 532 cm² + 57 cm² + 42 cm²

= 631 cm²

To find the total amount of plastic wrapping needed to cover the box, you need to add the extra 66 cm² needed to allow for the overlapping at the edges.

This gives a total of 631 cm² + 66 cm² = 697 cm² of plastic wrapping needed to cover the box.

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The probability that out of 52 card the selected 3 cards are not a face card is 0.183.

There are 12 face cards in a deck of 52 cards.

The probability of selecting 3 cards which should not be a face card is ,

=30c3 / 52c3

= 4060 / 22,100

= 0.183

Combination is a means to choose items from a collection without worrying about their order. Let's say we have a trio of numbers: P, Q, and R. Then, combination determines how many ways we can choose two numbers from each group.

It is easy to count the number of combinations in smaller cases, but the likelihood of a set of combinations is also higher in cases with many groups of components or sets. As a result, a formula has been developed to determine the number of items that could be chosen, i.e., nCr .

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The correct statements regarding the linear function graphed are given as follows:

The correct statements are identified from the graph of the function.

The y-intercept of the function is of 18, which represents how much she has to pay when she does not pull any week, that is, the price of the book.

The x-intercept of the function is of 90, meaning that if she pulls 90 weeks, she earns $18 from her grandmother, which is the entire price of the book.

From the intercept, we get that when the input increases from 90, from 0 to 90, the output decays by 18, from 18 to 0, hence the slope of the function is given as follows:

m = -18/90 = -0.2.

Meaning that for each weed pulled, the amount her grandma pays is of $0.2, and thus for five weeds she is paid one dollar.

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Total Total revenues will exceed = 8782.01

What is Total Revenue?

Total revenue is the overall sum of money received by a business through the sale of its products and services. Based on demand and price, it measures how successfully a company is generating revenue from its main operations.

Let x - normal (101.15 ,12.15)

where µ = 101.15

σ = 12.15

Mean for 85 customers

µ = 85 * 101.15 =8597.75

standard deviation for 85 customers

σ = [tex]\sqrt{85}[/tex] * 12.15 = 112.017

P ( x >x₁ ) = 0.05

P ( x-µ/ σ > x₁-8597.75/112.017) = 0.05

P (Z >Z₁) = 0.05

Where

Z₁ = x- 8597.75/112.017

Z₁ = 1.645

Then x = 112.017 *1.645 +8597.75

x = 8782.01

Total total revenues will exceed = 8782.01

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If the discriminant, b² - 4ac is positive

From the question, we have the following equation of discriminant

The discriminant (d) is calculated as

d = b² - 4ac

The solutions of a quadratic equation are dependent on the following conditions

This means that "d > 0, the quadratic equation has 2 different real solutions" implies that the discriminant is positive

Hence, the complete statement is (b) positive

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Answer:

  2378 m

Step-by-step explanation:

You want the ground distance from the takeoff point to an airplane that has flown 2500 m in the air at a takeoff angle of 18°.

The cosine relation tells you ...

  Cos = Adjacent/Hypotenuse

  Adjacent = Hypotenuse · Cos

Here, the hypotenuse of the right triangle model is 2500 m, the angle is 18°, and we want to find the side of the triangle adjacent to the angle:

  AD = AP·cos(18°) = 2500·0.9510565 ≈ 2377.64 ≈ 2378 . . . . meters

The ground distance is about 2378 m.