which statement best describes the roots of f(x)=x^2-6x+25?

Answers

Answer 1

Answer:

permiteme veré en álgebra baldor

Answer 2

The roots of the equation f(x) = x² - 6x + 25 will be 3 - 4i and 3 + 4i.

What are the roots of the equation?

Let the equation be ax² + bx + c = 0. Then the roots of the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4 a c }}{2a}[/tex]

The quadratic equation is given below.

f(x) = x² - 6x + 25

Compare both the equations, then the value of a, b, and c will be 1, -6, and 25, respectively.

Then the roots of the equation are given as,

[tex]\rm x = \dfrac{-(-6) \pm \sqrt{(-6)^2 - 4 \times 1 \times 25 }}{2 \times 1}\\x = \dfrac{6 \pm \sqrt{-64}}{2}[/tex]

Simplify the equation further, then we have

x = 3 ± 4i

The roots of the equation f(x) = x² - 6x + 25 will be 3 - 4i and 3 + 4i.

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Related Questions

Given m ∥ n, find the value of x.

Answers

The value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

What are angles formed by a pair of parallel lines cut by a transversal line?

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, alternate angles, complementary and supplementary angles.

(2x - 13) + 123 = 180° {supplementary angles}

2x - 13 + 123 = 180°

2x + 110 = 180

2x = 180 - 110 {collect like terms}

2x = 70

x = 70/2 {divide through by 2}

x = 35

Therefore, the value of x for the angle (3x + 43)° on the pair of parallel lines cut by a transversal line is equal to 3

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

In a rectangle, the value of x is,

⇒ x = 5

We have to given that;

ABCD is a rectangle.

And, AC = 5x + 2

BD = x + 22

Since, We know that;

Diagonal of a rectangle are equal in length.

Hence, We get;

AC = BD

(5x + 2) = (x + 22)

5x - x = 22 - 2

4x = 20

x = 20/4

x = 5

Thus, the value of x is,

⇒ x = 5

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a triangle is shown below, find the m

Answers

The value of angle L is 61°

What is exterior angle theorem?

Exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

If angle A and B are interior angles and angle C is the exterior angle, what this theorem is saying is that;

A+B = C

Similarly,

angle L and angle E are the interior angles and 113 is the exterior angle, therefore;

113 = L + 52

L = 113 -52

L = 61°

Therefore angle L is 61°

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The coordinates of vertex D in the parallelogram are (-7, -10).

We have,

To find the coordinates of vertex D of the parallelogram, we need to use the properties of a parallelogram.

One of these properties states that opposite sides of a parallelogram are parallel and have equal lengths.

Given that A = (8, 2), B = (6, -4), and C = (-5, -4), we can find the coordinates of D as follows:

Find the vector representing one of the sides of the parallelogram.

We can use the vector AB.

Vector AB = (x-coordinate of B - x-coordinate of A, y-coordinate of B - y-coordinate of A)

= (6 - 8, -4 - 2)

= (-2, -6)

Add this vector to point C to find the coordinates of D.

Coordinates of D = (x-coordinate of C + x-coordinate of AB, y-coordinate of C + y-coordinate of AB)

= (-5 - 2, -4 - 6)

= (-7, -10)

Therefore,

The coordinates of vertex D are (-7, -10).

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A ferris wheel has a radius of 10 inches and is 2 inches off the ground. It makes a complete revolution every 10 seconds.

If a rider is directly horizontal to the center of the wheel and moving downward, find an equation that gives his height above the ground as a function of time .

Answers

Answer:

  y = -10·sin(πt/5) +12

Step-by-step explanation:

You want the equation of the height of a rider of a Ferris wheel that has a radius of 10 and is 2 off the ground, with a period of 10 seconds, moving downward, starting from even with the center.

Equation

The general form of the equation will be ...

  y = A·sin(2πt/T) + B

where A is a scale factor that is based on the radius and initial direction, and B is the height of the center of the wheel above the ground.

Height

We assume that 2 [units] off the ground means the low point of the travel is at that height. Then the middle of the wheel is those 2 [units] plus the radius of the wheel:

  B = 2 + 10 = 12

Scale factor

The scale factor A will be the radius of the wheel, made negative because the initial direction is downward from the initial height. That is, ...

  A = 10

Period

The period (T) is given as 10 seconds.

Height function

Putting these parameters together gives ...

  y = -10·sin(2πt/10) +12

  y = -10·sin(πt/5) +12

__

Additional comment

We wonder if this wheel is really only 20 inches (20 in) in diameter, as that dimension seems suitable only for a model. We suspect it is probably 20 meters (20 m) in diameter.

Sometimes "m" is confused with "in" when it is written in Roman font and reproduced with poor resolution.

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Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15. (A reading above 140 is considered to be high blood pressure). Find the percentage of people with blood pressure below 133.

Answers

The percentage of people with blood pressure below 133 is 78.81%.

First, we need to calculate the Z-score for the value 133 using the formula:

Z = (X - μ) / σ

where X is the value (133), μ is the mean (121), and σ is the standard deviation (15).

Z = (133 - 121) / 15

Z = 12 / 15

Z = 0.8

Next, we can use a standard normal distribution table or a calculator to find the area under the curve to the left of the Z-score 0.8.

Looking up the Z-score of 0.8 in the standard normal distribution table, we find that the area to the left of 0.8 is 0.7881.

Therefore, the percentage of people with blood pressure below 133 is 78.81%.

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Five males with an​ X-linked genetic disorder have one child each. The random variable x is the number of children among the five who inherit the​ X-linked genetic disorder. Determine whether a probability distribution is given. If a probability distribution is​ given, find its mean and standard deviation. If a probability distribution is not​ given, identify the requirements that are not satisfied.

Does the table show a probability​ distribution? Select all that apply.

Find the mean of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Find the standard deviation of the random variable x. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

Answers

The standard deviation of the random variable x is 1.1145

Since the Probability distribution of a random variable is the collection of value and its probability pair for values of that considered random variable.

The probability of a value of x is never neg.

The sum of the probabilities is always 1.

The sum of all values of P(X = x) equals 1, which is, considering n values

There are no negative values of P(X = x).

Since we are given the probability distribution as below, we will go and calculate the mean and standard deviation using the formula:

E(X)= ∑xP(X=x)

Standard deviation = √Variance(x)

Var(x) = E(x²) - [E(x)]²

X           0          1            2        3        4          5

p(x=x)   0.032   0.152   0.316  0.316  0.152  0.032

First we have to find E(x)

E(x) = (0x0.032) + (1x0.152) + (2x0.316) + (3x0.316) + (0.152) + (5x0.032)

The mean E(x) = 2.5

To find variance, we use Var(x) = E(x²) - [E(x)]²

But we have to calculate E(x²) first, since we already have found E(x)

So,

E(x²) = (0²x0.032) + (1²x0.152) + (2²x0.316) + (3²x0.316) + (4²x0.152) + (5²x0.032)

therefore, E(x²) = 7.492

Now we have all the values we can find the variance:

Var(x) = E(x²) - [E(x)]²

=7.492 - [2.5]²

= 1.242

With variance now we can find the standard deviation;

S.D = √Var(x)

= √1.242

= 1.1145

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The graph shows the distribution of the amount of chicken (in ounces) that adults eat in one sitting. The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

A graph titled Chicken Consumption has amount (ounces) on the x-axis, going from 3.2 to 12.8 in increments of 1.2. The highest point of the curve is at 8.

What percentage of adults eat between 5.6 and 8 ounces of chicken in one sitting?

2.5%
34%
47.5%
95%

Answers

Using concepts of the normal and of the uniform distribution, it is found that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

In an uniform distribution, all outcomes are equally as likely, thus they have the same height.

In the normal distribution,

The outcomes with the highest likelihood are those closest to the mean, thus they have the highest height.

This means that the mean of this distribution is 8.

The standard deviation cannot be a negative value,

So in this problem, it is 1.2,

Which means that the correct option is:

The distribution is approximately Normal, with a mean of 8 ounces and a standard deviation of 1.2 ounces.

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Make selections to complete the proof.

Given: ∠WXZ≅∠YXZ, ∠XZW≅∠XZY, WX⎯⎯⎯⎯⎯⎯≅YX⎯⎯⎯⎯⎯, WZ⎯⎯⎯⎯⎯⎯≅YZ⎯⎯⎯⎯⎯


Prove: ∆WXZ≅∆YXZ

Answers

The required angles are,

∠BAC = 73 degree

∠BCA = 17 degree

∠DCF = 17 degree

∠CDF = 80 degree

∠CFD = 95 degree

Since we can see that,

In triangle ABC

The angle B is right angled

Since we know that,

Sum of interior angles of triangle = 180 degree

Therefore, in triangle ABC

⇒ (9x -8 ) + (2x-1) + 90 = 180

⇒ 11x  = 99

⇒    x  = 9

Thus,

Angle BAC =  9x - 8

                   = 9x9 - 8

                   = 73 degree

Angle BCA = 2x - 1

                   = 2x9 - 1

                    =  17 degree

Now in triangle, CDF,

Angle C is alternate angle for both the triangles,

Therefore,

Interior angle C of triangle CDF = angle DCF = 17 degree

Angle CDF = 9y  - 1

                   = 9x9 - 1

                   = 80 degree

Angle CFD = 11y + 4

                   = 11x9 - 4

                   = 95 degree

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Which statement accurately describes the relationship between JKL and MNP?

Answers

The triangles are not similar

Given data ,

Let the first triangle be ΔJKL

Let the second triangle be ΔMNP

Now , the corresponding sides are

JK / JL ≠ NM / MP

where the corresponding sides of similar triangles are not in the same ratio

And , the common angle to both the triangles is ∠J = ∠M

So , ∠J = ∠M and JK / JL ≠ NM / MP

Hence , the triangles are not similar

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make t the subject of the formula k=2(t+3)/t-3

Answers

t = (6 + 3k)/(k - 2) is the formula for t in the equation k=2(t+3)/t-3.

The given equation is k=2(t+3)/t-3.

We need to isolate t on one side of the equation.

Let's start by cross-multiplying:

k(t - 3) = 2(t + 3)

Expanding the brackets:

kt - 3k = 2t + 6

Now, let's gather all the terms with t on one side and all the constant

terms on the other side:

kt - 2t = 6 + 3k

Factoring out t on the left side:

t(k - 2) = 6 + 3k

Finally, we can solve for t by dividing both sides of the equation by (k - 2):

t = (6 + 3k)/(k - 2)

Therefore, t is the subject of the formula, and it is given by t = (6 + 3k)/(k - 2).

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The grid shown below is in the shapr of a rectangle. What is the area innsquare units, of the shaded part of the rectangle? It have 48

Answers

Based on the information provided, it seems that you have a rectangular grid with a shaded area, and the grid contains  option D.  48 square units.

To calculate the area of the shaded part, we would need to know the dimensions of the rectangle as well as the specific location and size of the shaded region within it.

If you can provide more details about the dimensions of the rectangular grid and the shaded region, I would be happy to help you calculate the area of the shaded part. Once we have that information, we can apply the formula for calculating the area of a rectangle,

which is Area = length × width. The result will give us the area of the shaded part in square units.

The area in square units, of the shaded part of the rectangle It has 48. Therefore the correct option  D

The Question was Incomplete, Find the full content below :

The grid shown below is in the shape of a rectangle. What is the area, in square units, of the shaded part of the rectangle? a 14 b 24 c 28 d 48

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The equation of line, L is given by r=3i+3j-k+t 2i-j+3k Find an Cartesian equation for the plane pi which contains L and the origin.​

Answers

The equation of the plane pi is: -6x-7y-9z=0.

To find the equation of the plane that contains the given line L and the origin as well, we first need to find two vectors that lie on the plane. One vector can be the direction vector of the line L, which is (2i - j + 3k). Now to find the second vector, we can take the vector from the origin to any point on the line L, and this vector will lie on the plane.

Let us now take t=0, and find the point on the line L:

r = 3i + 3j - k + 0(2i - j + 3k)

= 3i + 3j - k

So, the vector from the origin to this point is simply (3i + 3j - k). We can just take (3i + 3j - k) as our second vector.

Now, we can find the normal vector of the plane by taking the cross-product of two vectors that we just found, we get:

n = (2i - j + 3k) * (3i + 3j - k)

= -6i - 7j - 9k

Therefore, the equation of the plane pi is: -6x-7y-9z=0.

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Use ≈ 3.14 and round your answer
to the nearest hundredth.
10 ft
6 ft
square feet

Answers

The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

We know that,

In geometry, a cylinder is one of the basic 3d shapes with two parallel circular bases at a distance. A curving surface connects the two circular bases at a predetermined distance from the centre. The axis of the cylinder is the line segment connecting the centres of two circular bases. The height of the cylinder is defined as the distance between the two circular bases. One real-world example of a cylinder is an LPG gas-cylinder.

The surface area of this cylinder is defined as the product of the radius of the base and the height of the cylinder.

The surface area of this cylinder = (2π x r)h

We have given a radius of the base is 8 cm and the height of the cylinder is 10 cm.

The surface area of this cylinder = (2π x r)h

= (2π x 8)10

= (50.24)10

= 502.4

Thus, The surface area of the cylinder has a radius of 8cm and a height of 10 cm is 502.4 square centimeters.

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The complete question is attached below:

What is the slope of this line?

A line passing through the points (negative 4, negative 3) & (0, 1).

© 2017 StrongMind. Created using GeoGebra.


Enter your answer as a number, like this: 42

Or, if the slope is undefined, enter a lowercase letter "u," like this: u

Answers

Answer:

[tex]m = \frac{1 - ( - 3)}{0 - ( - 4)} = \frac{4}{4} = 1[/tex]

the graph of a quadratic function has a y intercept at (0,3) and its vertex at (4,8 1/3) what are its x intercepts in order from least to greatest

can you also explain the steps?

Answers

The x-intercepts, in order from least to greatest, are (2.46, 0) and (5.54, 0).

Use the vertex form of a quadratic function, which is [tex]y = a(x-h)^2 + k,[/tex] where (h, k) is the vertex and "a" is the coefficient of the[tex]x^2[/tex]term. Since the vertex is at (4, 8 1/3), the quadratic function's equation is y = a(x-[tex]4)^2 + 8 1/3.[/tex]

Use the y-intercept to find the value of "a".

The y-intercept is (0,3), so when x=0, y=3.

Plugging these values into the equation above, we get: [tex]3 = a(0-4)^2 + 8 1/3[/tex].

Simplifying, we get 3 = 16a + 25/3, or 9/3 = 16a. Therefore, a = 9/48 or a = 3/16.

To obtain the complete equation, enter the value of "a" into the vertex form equation: [tex]y = (3/16)(x-4)^2 + 8 1/3.[/tex]

To find the x-intercepts, set y = 0 and solve for x.

The equation becomes: [tex]0 = (3/16)(x-4)^2 + 8 1/3[/tex].

Subtracting 8 1/3 from both sides, we get: [tex]-8 1/3 = (3/16)(x-4)^2[/tex]. Multiplying both sides by -1, we get: [tex]8 1/3 = (3/16)(x-4)^2.[/tex]

Take the square root of both sides to isolate[tex]x-4: \sqrt{(8 1/3) } = \sqrt{((3/16)(x-4)^2)}[/tex] Simplifying,

we get: [tex]\sqrt{(25/3)} = (3/4)(x-4).[/tex]

Solving for x, we get two solutions: [tex]x = 4 + 4\sqrt{(3)/3 } or x = 4 - 4\sqrt{(3)/3 }[/tex]

Sort the answers in order of best to worst. The x-intercepts are (2.46, 0) and (5.54, 0) because the first answer is around 5.54 and the second solution is roughly 2.46.

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Find the area of a triangle whose base (b) is 5 feet and whose height (h) is 2 ft.
(a) 5ft.²
(b) 20ft.²
(c) 100ft.²
(d) 3.5ft.²​

Answers

Answer:

(a) 5 ft^2

Step-by-step explanation:

The formula for area of a triangle is given by the formula,

A = 1/2bh, where

A is the area in square units,b is the base,and h is the height.

Thus, we can plug in 5 for b and 2 for h in the formula to find the area of the triangle in square feet:

A = 1/2(5)(2)

A = (5/2)(2)

A = 10/2

A = 5

Thus, the area of a triangle whose base is 5 ft and whose height is 2 ft is 5 ft^2

can u give me an answer

Answers

Answer: 0 , 5

Step-by-step explanation:

Imagine a plane taking off, first it drives to gain speed then flies, thats what you can use for coordinates.

X is the driving and Y is the flight.

The X is at 0, and the Y is at 5.

Find the area of the shape

Answers

The area of the given figure with rectangle and triangle is 27.5 square centimeters.

The given figure has a rectangle and two triangles.

The area of the rectangle is length times width

Length = 5 cm

Width = 4 cm

Area of rectangle = 5×4

=20 square centimeters

Area of triangle =1/2 base ×height

=1/2×2.5×3

=3.75  square centimeters

As there are two triangles, 2(3.75)=7.5   square centimeters

Total area = 20+7.5

=27.5 square centimeters

Hence, the area of the given figure with rectangle and triangle is 27.5 square centimeters.

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Susie paid 2/5 of the price of her movie ticket. Her parents paid the remaining portion of the movie ticket price. What decimal is equivalent to the fraction of the price of the movie ticket Susie paid?


17 points!!

Answers

To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, the decimal equivalent to 2/5 is 0.4.

Thanks to the other user

To find the decimal equivalent of 2/5, you can divide the numerator (2) by the denominator (5):

2 ÷ 5 = 0.4

Therefore, the decimal equivalent to 2/5 is 0.4.

(Mines) Simple Equation2/5 which is know as 2 ÷ 5 is 0.4TipWhenever you see a fraction like 2/5 just divide and it will turn into decimal.

Solve each equation by completing the square. Round to the nearest
necessary.

2x² - 2x +7=5

-2x^2 + 10x =14

4x^2 + 6x = 12

Answers

All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

Given that;

Expressions are,

⇒ 2x² - 2x + 7 = 5

⇒ -2x² + 10x = 14

⇒ 4x² + 6x = 12

Now, We can completing the square each equation as;

⇒ 2x² - 2x + 7 = 5

⇒ x² - x + 7/2 = 5/2

⇒ x² - x + 1/4 - 1/4 + 7/2 = 5/2

⇒ (x - 1/2)² = 1 + 1/4

⇒ (x - 1/2)² = 5/4

⇒ -2x² + 10x = 14

⇒ - x² + 5x = 7

⇒ x² - 5x = - 7

⇒ x² - 5x + 25/4 - 25/4 = - 7

⇒ (x - 5/2)² = - 7 + 25/4

⇒ (x - 5/2)² = - 3/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ 4x² + 6x = 12

⇒ (2x)² + 2×2x×3/2 + 9/4 -9/4 = 12

⇒ (2x + 3/2)² = 12 + 9/4

⇒ (2x + 3/2)² = 57/4

Thus, All the expressions after completing the square each equation are,

⇒ (x - 1/2)² = 5/4

⇒ (x - 5/2)² + 3/4 = 0

⇒ (2x + 3/2)² = 57/4

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Convert the polar representation of this complex number into its standard form. A 4-451 B. -43-4/ C. -8√5 +8/ D. 4-4√3 i ​

Answers

The complex number in standard form is written as:

Z =  1.99 + i*0.201, so the correct option is a

How to write the complex number in standard form?

Remember that a complex number can be written in standard form as:

Z = a + b*i

And in polar form the notation is (R, θ):

[tex]Z = R*e^{i*\theta} = R*cos(\theta) + i*R*sin(\theta)[/tex]

Here we have the complex number:

Z = 2(cos(11pi/6) + i*sin(11pi/6))?

So here we just need to solve these expressions, we will get:

Z = 2*(0.995 + i*0.100)

Z =  1.99 + i*0.201

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Complete question:

"Convert the polar representation of this complex number into its standard form: z = 2(cos 11pi/6+ i sin 11pi/6)? "

The following transactions were completed by the company:


The company completed consulting work for a client and immediately collected $5,600 cash.
The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.
The company paid an assistant $1,450 cash as wages for the period.
The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.
The company paid $720 cash for this period's cleaning services.

Answers

In accounting, the accounting equation is a fundamental principle that describes the relationship between a company's assets, liabilities, and equity. This equation is represented as Assets = Liabilities + Equity. Every financial transaction that a company undertakes has an impact on at least two of the components of the accounting equation.

Transaction Analysis:

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

This transaction increases both cash and revenue. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$5,600

Revenue: +$5,600

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

This transaction does not impact any account initially. Revenue will increase when payment is received.

Accounts Affected:

Accounts Receivable: +$4,100

Revenue: +$0

c. The company paid an assistant $1,450 cash as wages for the period.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$1,450

Expenses: +$1,450

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b.

This transaction increases cash and decreases accounts receivable. There is no impact on liabilities or equity.

Accounts Affected:

Cash: +$2,050

Accounts Receivable: -$2,050

e. The company paid $720 cash for this period's cleaning services.

This transaction decreases cash and increases expenses. There is no impact on liabilities or equity.

Accounts Affected:

Cash: -$720

Expenses: +$720

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Complete Question

The following transactions were completed by the company

a. The company completed consulting work for a client and immediately collected $5,600 cash earned.

b. The company completed commission work for a client and sent a bill for $4,100 to be received within 30 days.

c. The company paid an assistant $1,450 cash as wages for the period.

d. The company collected $2,050 cash as a partial payment for the amount owed by the client in transaction b

e. The company paid $720 cash for this period's cleaning services  Required: Enter the impact of each transaction on individual items of the accounting equation. (Enter decreases to account balances with a minus sign.)

I have been doing this for 4 hours and still can’t figure these out

Answers

The equation of the line is y = x/7 - 1/7

What is equation of a line?

The equation of a straight line is y=mx+c . Where m is the gradient or slope and c is the height at which the line crosses the y -axis, also known as the y -intercept.

The equation of a line can be expressed as;

y-y1 = m(x -x1)

where m is the slope

The slope = 1/7

x1 = 8 and y1 = 1

Therefore;

y -1 = 1/7( x -8)

7(y-1) = x-8

7y -7 = x-8

collecting like terms

7y = x - 8+7

7y = x -1

y = x/7 -1/7

The intercept is -1/7 and the slope is 1/7

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The rear window of Alex's van is shaped like a trapezoid with an upper base

measuring 36 inches, a lower base measuring 48 inches, and a height of 21 inches.

An 18-inch rear window wiper clears a 150° sector of a circle on the rear window, as

shown in the diagram below.

36 in.

21 in.

150 degrees

18 in.

48 in.

a. What is the area, in square inches, of the entire trapezoidal rear window? Show or explain how you got your answer.

b. What fractional part of a complete circle is cleared on the rear window by the 18-inch wiper? Show or explain how you got your answer.

c. What is the area, in square inches, of the part of the rear window that is cleared by the wiper? Show or explain how you got your answer.

d. What percent of the area of the entire rear window is cleared by the wiper? Show or explain how you got your answer.

Answers

a) The area of the entire trapezoidal rear window =  882 sq.in.

b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12

c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.

d) The percent of the area of the entire rear window is cleared by the wiper =  48.09%

We know that the formula for the area of trapezoid,

A = ((a + b) / 2) × h

Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in

Using above formula, the area of the entire trapezoidal rear window would be,

A = ((36 + 48) / 2) × 21

A = 882 sq.in.

Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.

We know that the measure of entire circle = 360°

So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,

150° / 360° = 5/12

Now we need to find the area of the part of the rear window that is cleared by the wiper.

We know that the formula for the area of sector of a circle is:

A = (θ/360) × πr²

Here, the central angle θ = 150° and radius r = 18 in.

A = (θ/360) × πr²

A = (150/360) × π × 18²

A = 424.12 sq. in.

Now we need to find the percent of the area of the entire rear window is cleared by the wiper.

P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100

P = (424.12 / 882) × 100

P = 48.09%

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Help with number 8 please

Answers

The simplification of the expression, ∛8x⁴y⁸ / 125 is [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex].

How to solve an exponential expression?

The exponential expression can be solved as follows:

Therefore, let's simplify the expression.

To simplify the expression we have to deal with the exponential by applying it laws and also the cube root.

∛8x⁴y⁸ / 125

let's solve them individually,

125 = 5³ = 5 × 5 × 5

8 = 2³ = 2 × 2 × 2

Therefore,

∛8x⁴y⁸ / 125 = [tex]\frac{2\sqrt[3]{x^{4}y^{8} } }{5}[/tex]

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Hello! Find Domain and range, thank you :-)

Answers

Domain: (-1, infinity]
Range:[-infinity,3)

You may want to check your notation with this as I am rusty with interval notation but here are the answers.

task1 part b evaluate

Answers

The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

We have to given that,

Expression to solve,

⇒ ∫ (0 to 10) (x + 1) dx

Now, We can simplify as,

⇒ ∫ (0 to 10) (x + 1) dx

⇒ ∫ (0 to 10) (x) dx + ∫ (0 to 10) dx  

⇒ (x² / 2)₀¹⁰ + ((x)¹⁰₀

⇒ 1/2 (10² - 0) + (10 - 0)

⇒ 1/2 × 100 + 10

⇒ 50 + 10

⇒ 60

Therefore, The solution of expression ∫ (0 to 10) (x + 1) dx is,

⇒ 60

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i need some help on this please

Answers

Using the intersecting chord theorem, we can calculate the value of x as: 12

How to solve the Intersecting chord theorem?

The intersecting chord theorem states that If two chords intersect in a circle , then the products of the measures of the segments of the chords are equal.

Applying the intersecting chord theorem to the two chords of the circle, we can say that:

3x = (9 * 4)

3x = 36

x = 36/3

x = 12

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find the numerical value of the log expression

Answers

Answer:

Step-by-step explanation:

The numerical value of the given log expression is -73.

From definitions of logarithms, we know that :

[tex]log(a*b) = log(a) + log(b)\\log(a / b) = log(a) - log(b)[/tex]

[tex]log(a^n) = n*log(a)[/tex]

Therefore,

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*log(b) - 8*log(a) - 5*log(c)[/tex]

substituting the given values

[tex]log(a) = 10\\log(b) = 9\\log(c) = 1\\[/tex]

we get the value of the given expression

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = \frac{4}{3}*9 - 8*10 - 5*1[/tex]

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = 12 - 80 - 5[/tex]

[tex]log(\frac{\sqrt[3]{b^4}}{a^8c^5 }) = -73[/tex]

Therefore the numerical value of the given log expression is -73.

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