which value of ₓ is the solution to this equation?
5ₓ²=30ₓ-45
A.ₓ=3 C.3√7

B.49√3 D.21√7

Answer:

Step-by-step explanation:

The given parameters are:

10% on the first $25,000 of income

20% on income above $25,000

The above means that;

T(x) = x * 10%, when x <= 25000

T(x) = x* 20%, when x > 25000

Evaluate the products

T(x) = 0.1x, when x <= 25000

T(x) = 0.2x, when x > 25000

In this case, x = 60000

60000 > 25000

So, we have:

T(60000) = 0.2 * 60000

Evaluate

T(60000) = 12000

Hence. if a person has income of $60,000, their income tax be under the proposal would be $12000

Answer:The problem says that income up to $25,000 will be taxed at 10%. This is the first tier (or bracket). People who make more than $25,000, will pay 10% of their initial $25,000, and the higher rate of 20% on any income above $25,000. This is the second tier.

Let's calculate the amount of tax in this particular case. For a person making $60,000, they'll pay 10% of the first $25,000, and then 20% of the additional $35,000. We have,

Total Income Tax=Tax from Tier 1+Tax from Tier 2=10100⋅$25,000+20100⋅($60,000−$25,000)=$2,500+$7,000=$9,500.

Under the proposal, this person will pay $9,500 in taxes.

The amount of money that is compounded monthly for 30 years will be $17,153.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

If $10,000 is deposited into a savings account that pays 1.8% annual interest.

Then the rate is given as,

r = 1.8% / 1200

r = 0.0015

Then the number of years is given as,

n = 30 x 12

n = 360

Then the amount of money that is compounded monthly for 30 years is given as,

A = $10,000 × (1 + 0.0015)³⁶⁰

A = $10,000 × (1.0015)³⁶⁰

A = $10,000 × 1.715

A = $17,153

The amount of money that is compounded monthly for 30 years will be $17,153.

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The equation of the sphere with center coordinates  (4, −12, 8) and radius 10 is x² -8x + y² + 24y + z² -16z + 124 =0 .

And different plane equations are :

Intersection with xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

Intersection with yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

Intersection with zx plane :( x - 4 )² +  ( z - 8 )² = -44

Equation of the sphere with center coordinates (4, −12, 8) and radius 'r' = 10 is :

( x - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒ x² -8x + y² + 24y + z² -16z + 224 = 100

⇒x² -8x + y² + 24y + z² -16z + 124 =0

Intersection with xy-plane

z = 0

( x - 4 )² + ( y + 12 )² + ( 0 - 8 )² = 10²

⇒( x - 4 )² + ( y + 12 )² = 6²

Circle with center ( 4,-12) and radius 6.

Intersection with yz-plane

x = 0

( 0 - 4 )² + ( y + 12 )² + ( z - 8 )² = 10²

⇒( y + 12 )² + ( z - 8 )² = (√84)²

Circle with center ( -12, 8) and radius √84.

Intersection with zx-plane

y = 0

( x - 4 )² + ( 0 + 12 )² + ( z - 8 )² = 10²

⇒( x - 4 )² +  ( z - 8 )² = -44

Not possible as radius cannot be negative.

Therefore, the equation of the sphere with the given center and radius is equal to x² -8x + y² + 24y + z² -16z + 124 =0 and equation of the intersection of different planes are:

xy-plane : ( x - 4 )² + ( y + 12 )² = 6²

yz plane :( y + 12 )² + ( z - 8 )² = (√84)²

zx plane :( x - 4 )² +  ( z - 8 )² = -44

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Answer:

[tex]\Huge \boxed{\textbf{F. One solution}}[/tex]

Step-by-step explanation:

To find the number of solutions for the given equation, we can start by simplifying and solving the equation.

First, distribute the 7 on the left side of the equation:

Now, subtract 5x from both sides:

Next, subtract 14 from both sides:

Finally, divide by 30:

Simplifying the fraction, we get:

Since we found a unique value for x, the equation has only one solution.

Therefore, the correct answer is option F.

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________________________________________________________

Answer:

a) 4

b) 2

Step-by-step explanation:

I use this sentence to remember quadrants:

All Students Take Coffe

- All trigs are positive in 1 Quadrant

- Sin and (cosine) is positive in 2 quadrant

-Tan and (Cotan) are positive in 3 quadrant

- Cos and (Sec) are positive in 4 quadrant

all other trigs other than those are negative.

a) cos is positive in 1 and 4 quadrant. Csc is reciprocal of Sin and is negative in 3 and 4 quadrant. 4th quadrant satisfies both conditions.

b) csc  is reciprocal of Sin and is positive in 1 and 2 quadrants. Sec is reciprocal of Cos and is negative in 2 and 3 quadrant. 2nd quadrant fulfills both conditions.

If there is no solution to the system of equations, it signifies that the equations describe two parallel lines in the two-dimensional plane. This indicates that the lines will never meet because they have the same slope but separate y-intercepts. This signifies that the two lines are geometrically distinct and will never intersect.

A geometric significance is a geometric aspect or quality of a form or item. This encompasses the object's size and orientation, as well as its symmetry and proportions. Several areas, including architecture, engineering, graphic design, and mathematics, rely on geometric importance. In architecture, for example, the size and direction of a structure may be utilised to decide how much light it receives and how much shade it casts. The geometry of an item can be used to determine its strength, stiffness, and durability in engineering. The symmetry and dimensions of an object may be employed in graphic design to produce an appealing and balanced design.

The given question states that when there are no solutions to a system of K equations in two variables, it means that the lines associated with those equations are either parallel or coincident. Geometrically, this means that the lines are not intersecting, which implies that the two variables cannot simultaneously satisfy all of the equations.

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The Cartesian, or rectangular, coordinate system is composed of an x-axis that runs horizontally and a y-axis that goes vertically.

The rectangular coordinate system of the Cartesian plane, which bears Rene Descartes' (1596–1650) name, assigns each point in the plane a pair of integers.

An x-axis that runs horizontally and a y-axis that runs vertically make up the Cartesian, or rectangular, coordinate system. The origin is the place where the two axes meet. Any point can be characterized by its distance from the origin along the x-axis and along the y-axis, and this distance is represented by the symbol (x, y).

A two-dimensional coordinate plane produced by the intersection of the x- and y-axes is known as the cartesian plane in mathematics. At the location known as the origin, the x- and y-axes cross perpendicularly.

Therefore, the correct answer is option D. A graph used in mathematics to plot points.

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Answer:

The model shows that there are 9 pieces that are each ft long.​. The model shows that there are 9 pieces that are - 1.

If my bowl of easter candy has colorful foil-wrapped chocolate eggs. there are 5 gold, 7 blue, and 10 pink. The probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil is 0.45.

Total color = 5 gold + 7 blue + 10 pink

Total color = 22

Now let find the probability that she reaches in without looking and gets a chocolate candy wrapped in pink foil

Probability (pink) = 10/22

Probability (pink) = 0.45

Therefore the  probability of Callie Brooke getting a pink foil-wrapped chocolate egg is 10/22, or approximately 0.45.

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C is equidistant to the following points:  CL=CM=CN

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

One of the triangle's centers where the bisectors of the inner angles converge is known as the incline

The circumcenter of a triangle, which is equal distances from all the vertices, is where the perpendicular bisectors of the triangle meet.

so, C is equidistant to the following points:  CL=CM=CN

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The plan cost same for 800 minutes.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Plan A costs $12 plus an additional $0.14 for each minute of calls.

Plan B costs $28 plus an additional $0.12 for each minute of calls.

let the number of minutes for which two plans are equal be x.

so, 12 + 0.14x = 28 + 0.12 x

12 - 28 = 0.12x - 0.14x

-16 = -0.02x

x= 800 minutes

and, the plan cost

y = 12 + 0.14x

y = 12 + 0.14(800)

y = $124

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a. f(x) = 1.8x.

b. f(x) = 1.35x.

c. f(150) = 1.35×150 ⇒ f(150) = 202.5.

d. The order in which the adjustments are applied doesn't make any difference.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, A department store has marked down its merchandise by 25%. It later decreases by $5 the price of items that have not sold.

Let, 'x' be the price of the merchandise.

So, After adding 80% to its cost it becomes [(100 + 80)/100]×x = 1.8x.

Later it decreases by 25% the price of items that don't sell quickly.

So, It has a value of (75/100)×1.8x = 1.35x.

a. A function f(x) to represent the price after the 80% markup is.

f(x) = 1.8x.

b. A function g(x) to represent the price after the 25% markdown is,

f(x) = 1.35x.

c. A composition function to find the price of an item after both price adjustments that originally the boutique $150 is,

f(150) = 1.35×150.

f(150) = 202.5.

d. Let, The price of the item be $100, after 80% makeup it would be

$180 and after 25% markdown it would be $135.

Again 25% markdown on $100 is $85 and an 80% markup is

75×1.8 = $135 hence no difference.

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Ian would have $16 left in his checking account.

Here is the working:

$28 (starting amount) - $12 (check written)

= $16 (remaining amount)

The answer to your question is true

Answer:

true, the square root of 361 is 19

Step-by-step explanation:

(  ﾟｰﾟ)ﾉ

Circle Detection Algorithm is a highly efficient and effective solution to finding the most number of points that lie on any one circle in a 2D real plane.

The algorithm to solve this problem is known as the "Circle Detection Algorithm." This algorithm starts by considering three points randomly selected from the given N points.

Next, the algorithm checks the number of points that lie on this circle. If this number is greater than the current maximum, then this circle becomes the new candidate for the circle that contains the most number of points.

To ensure that the algorithm is efficient, it is important to choose the points randomly, as this reduces the chances of getting stuck in a local maximum.

The mathematical formula to calculate the center and radius of the circle that passes through three points (x₁, y₁), (x₂, y₂), and (x₃, y₃) is given by:

x = ( (y₂ - y₁)(y₃² - y₁² + x₃² - x₁²) - (y₃ - y₁)(y₂² - y₁² + x₂² - x₁²) ) / (2 * (x₃ - x₁)(y₂ -y₁) - 2 * (x₂ - x₁)(y₃ - y₁) )

y = ( (x₂ - x₁)(x₃² - x₁² + y₃² - y₁²) - (x₃ - x₁)(x₂² - x₁² + y₂² - y₁²) ) / (2 * (y₃ - y₁)(x₂ -x₁) - 2 * (y₂ - y₁)(x₃ - x₁) )

r = √(x₁ - x)² + (y₁ - y)²

Once the center and radius have been calculated, the algorithm can easily check the number of points that lie on the circle by calculating the distance of each point from the center and checking if it is equal to the radius.

Complete Question:

Given N points on the 2D real plane, what is the most efficient algorithm to find the most number of points that lie on any one circle?

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The probability of not rolling doubles on one roll of two fair six-sided dice is 5/6.

Hence, the probability of rolling doubles is 1/6. The probability of not rolling doubles in three rolls is (5/6)^3. So, the probability of rolling doubles on the third roll is 1 - (5/6)^3. This is the same as (1/6) (5/6)^2. So the correct answer is (d) (1/6) (5/6)^2.

The probability of rolling a specific number on one fair six-sided die is 1/6.

In this problem, we are looking for the probability of rolling doubles (i.e. getting the same number on both dice) in three rolls.

The probability of not rolling doubles in one roll is 5/6 (since there are five outcomes that are not doubles, out of a total of 6 possible outcomes).

The probability of not rolling doubles in three rolls is (5/6)^3, which represents the chance of not rolling doubles in three independent rolls, each with a 5/6 probability of not rolling doubles.

To find the probability of rolling doubles in three rolls, we subtract the probability of not rolling doubles in three rolls from 1:

P(rolling doubles in three rolls) = 1 - (5/6)^3 = (1/6) (5/6)^2

So, the correct answer is (d) (1/6) (5/6)^2.

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A sales presentation aims to attract and compel the audience to whom the presentation is made.

Creating a sales presentation involves several steps:

Define the goal and audience of the presentation: Before creating the presentation, it is important to understand the goal of the presentation, and the target audience it is meant for. This will help you tailor the content of the presentation to the specific needs and interests of the audience.

Research the product or service: Understand the product or service you are selling inside and out. This will help you answer any questions that may come up during the presentation and show that you are an expert on the subject.

Create an outline: Once you have a clear understanding of your audience and the product or service, create an outline for the presentation. This will help you organize your thoughts and stay on track during the presentation.

Create compelling content: Use persuasive language and storytelling to create content that is engaging and easy to understand. Use statistics, testimonials, and visual aids to support your points.

Design the visual aids: Use charts, graphs, images, and other visual aids to supplement the text of your presentation. Make sure that the visual aids are clear and easy to understand, and that they support the points you are making.

Rehearsal: Practice the presentation several times before delivering it. This will help you build confidence and ensure that the presentation flows smoothly.

Delivery: During the presentation, engage with the audience and be responsive to their questions and feedback. Make sure that you are well-prepared and that you stay on track.

Follow-up: After the presentation, make sure to follow up with the audience and address any remaining questions or concerns they may have.

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Answer:614

Step-by-step explanation:

The maximum number of boxes that can fit in the trailer can be calculated by dividing the volume of the trailer by the volume of each box.

First, we need to convert the dimensions of the boxes and the trailer to the same unit, such as cubic feet. The volume of each box is given by:

V_box = (1 1/2 ft)^3 = (1.5 ft)^3 = 3.375 ft^3

Next, we calculate the volume of the trailer:

V_trailer = 28 ft * 8 1/2 ft * 9 1/6 ft = 2070 ft^3

Finally, we divide the volume of the trailer by the volume of each box to find the maximum number of boxes:

N_boxes = V_trailer / V_box = 2070 ft^3 / 3.375 ft^3 = 614.07 boxes

Since we can only fit whole boxes in the trailer, the maximum number of boxes that will fit is 614.

The point of intersection of the lines given is (1,4,2) and the plane determined is -3y +2z+8 = 0.

Let us first define the lines as -

L1 = x=3t+1, y=4t+4, z = 6t + 2

L2 = X=s+2 y=2s+6, z = 3s - 1

We have to find the intersection so -

= 3t+1 = s+2 ⇒ 3t - s - 1 = 0

= 4t+4 = 4t+4 ⇒ 4t - 2s - 2 = 0

= 6t + 2 = 3s - 1 ⇒ 6t - 3s + 3 = 0

Now, if we input the values of t and s as given in the question i.e., t = 0 and s = -1, we get -

= x = 1

= y = 4

= z = 2

These are the points of intersections of the given lines.

Now, the direction vector of L1 = (3,4,6) and L2 = (1,2,3)

So, the normal vector to the plane can be calculated using the determinant method.

[tex]\left[\begin{array}{ccc}i&j&k\\3&4&6\\1&2&3\end{array}\right][/tex]

On solving this, we get  = -3j + 2k

The equation of the plane is -

= 0(x-1) - 3(y-4) + 2(z-2) = 0

= -3y +2z+8 = 0

The complete question that you might be looking for is given below -

Find the point of intersection of the lines given below and then find the plane determined by these lines x=3t+1, y=4t+4, z = 6t + 2, 0<t< 0 X=s+2 y=2s+6 2 = 3s - 1 , C < 5 < 0

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The volume of the solid is 1789.33

For a circle of radius 11, we have the following equation:

x²+y²=11²

x²+y²=121

Now, making it explicit for x:

[tex]x=\sqrt{121-y^2}[/tex]

Then, if we consider that for a height y, the length x is double, we have that the length of each cross-section is given by:

[tex]s=\sqrt[2]{81-y^2}[/tex]

With this, we can propose the following integral to obtain the volume that they are asking us:

[tex]\int\limits^1_0 {s^2} \ \, dy \\\int\limits^1_0 ({\sqrt[2]{121-y^2})^2 } \, dy\\\\\int\limits^1_0 {4*(121-y^2)} \, dy\\\\4*(121y-\frac{y^3}{3} )[/tex]

Finally, calculating, we have that the volume is V=1789.33

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Answer:

-2 <n>5 I believe? that's all I know

Answer:

below

Step-by-step explanation:

For the LEFT part

n < -2      or     -2 > n

for the RIGHT part

n>5  

combine these two to get       -2 > n > 5

The method to calculate the reference angle is discussed below.

Reference Angle is the acute angle between the terminal side and the

x - axis.

Given is reference angle.

You determine a reference angle by looking at the terminal side of the angle you're working with and its relation with the positive or negative x-axis (depending on which quadrant the terminal side is in).

Therefore, the method to calculate the reference angle is discussed above.

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{Question in english -

How is a reference angle calculated?}

Answer: 400 ft

Step-by-step explanation:

Since the triangles are Congruent Triangles (similar)

x/40  =  50/5

Cross multiply

5x = 2000

divide both sides by 5

5x/5 = 2000/5

x = 400 ft

Yes, b(-6, 9, 2) is in the span of the other given vectors [tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6).

b as a linear combination of the other vectors [tex]a_1[/tex] and [tex]a_2[/tex]

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

A vector is a quantity that has magnitude and direction.

We say that a vector u spans vectors v, w if u = av + bw where a and b are scalars.

As per the given data:

[tex]a_1[/tex] = (-1, 3, -1), [tex]a_2[/tex] = (-2, -3, 6), b = (-6, 9, 2)

We need to write vector b as a linear combination of vectors [tex]$a_1[/tex] and  [tex]a_2$[/tex].

Let c and d be scalars.

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

(-6, 9, 2) = c(-1, 3, -1) + d(-2, -3, 6)

(-6, 9, 2) = (-c - 2d, 3c - 3 d, -c + 6d)

-6 = -c - 2d........(i),

9 = 3c - 3d ...... (ii),

2 = -c + 6d .......(iii)

b = c [tex]a_1[/tex] + d [tex]a_2[/tex]

On solving equations (i) and (ii), we get c = 4, d = 1

Now, we will check if c = 4, and d = 1 satisfy equation (iii).

= - c + 6d

= -4 + 6(1)

= -4 + 6

= 2

As it satisfies this equation, so b is a linear combination of [tex]$a_1[/tex] and [tex]a_2[/tex]

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Determine if b is in the span of the other given vectors. If so, write b as a linear combination of the other vectors.  (if b cannot be written as a linear combination of the other two vectors, enter done in both answer blanks.) a1=[-1 3 -1],a2=[-2 -3 6],b=[-6 9 2]

The compound inequality for the graph shown above include the following:

x < -2.

x > 5.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numerical values that are placed at equal intervals along its length.

Generally speaking, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.

Since the point is at -2 and the arrow points to the left of the number line, it represents the less than (<) inequality symbol and should be written as x < -2.

Additionally, the second point is at 5 and the arrow points to the right of the number line, it represents the greater than (>) inequality symbol and should be written as x > 5.

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The correct answer is option A. 110 snacks have between 100 and 120 mg of sugar.

A bar in a histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar. So, the statement that best describes the meaning of one of the bars in the histogram is: 110 snacks have between 100 and 120 mg of sugar.

In summary, the bar in the histogram represents a range of values and the height of the bar represents the frequency of the values in that range. In this case, the bar represents the range of values between 100 and 120 mg of sugar and the height of the bar represents the frequency of snacks with that amount of sugar.

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The other way of representing the given function is f(x) = 2 - 8/(x+4).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, rational function f(x)=2x/x+4

Using Long division:

x + 4) 2x      ( 2

         2x + 8

-------------------------

                -8

The remainder is -8.

Since the Degree of the remainder is less than the degree of the divisor then we are done.

Now using,

Dividend = divisor* quotient + remainder

=> 2x = 2 * (x+4) -8

Thus, f(x) = 2 - 8/(x+4)

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The infinite series, [tex]ln(6)/6 + ln(7)/7 + ln(8)/8 + ln(9)/9 + ln(10)/10 + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx\\ [/tex] is diverges as the integral diverges.

We know that the Integral test : Suppose that f(x) is a continuous, positive and decreasing function on the interval [ k,∞) and that f(n)= a, then

If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is convergent then the series, [tex] \sum_{n = 1}^{ \infty } a_{n}[/tex]

If [tex] \int_{k}^{ \infty } f(x)dx[/tex] is divergent so is [tex]\sum_{n = 1}^{ \infty } a_{n}[/tex].

We have an integral equals to an infinite series [tex] \frac{ln(6)}{6} + \frac{ln(7)}{7} + \frac{ln(8)}{8} + \frac{ln(9)}{9} + \frac{ln(10)}{10} + ... = \int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx \\ [/tex]

[tex]\int_{1}^{ \infty } \frac{ln(x + 5)}{ (x + 5 )}dx = {\lim_{k-> \infty } \\}\int_{1}^{k} \frac{ln(x + 5)}{ (x + 5 )}dx [/tex]

[tex]= {\lim_{k-> \infty } \\}[ \frac{ {(ln(x+5))}^{2} }{2} ]_{1}^{k}\\ [/tex]

[tex] = \infty [/tex]

This implies that the integral diverges, so by integral test the series also diverges.

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