How do I find the roots of a cubic equation?

The value off ARU based on the information will be 35°.

We know, the incenter of a triangle is the point of intersection of all the three interior angle bisectors of the triangle.

A)By property, AR is angle bisector of angle KRU.

Therefore m(<ARU) = m(<ARK) = 40°

m<ARU= 40°

B) The angle bisectors in a triangle are always concurrent and the point of intersection is known as the incenter of the triangle.

AU = AT = 20

Therefore,

AU = 20

C) AP is angle bisector of <QPR,

By definition of angle bisector

m<QPA = m<APR

3x+2 = 4x-9

4x-3x = 9+2

x =11

m<QPA = 3(11) +2 = 35°

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The value of the trigonometric ratios are

1. sin C = 21/29

2. sin C = 3/5

3. cos C = 12/13

4. cos C = 8/17

5. tan A = 12/35

6. tan X = 4/3

The trigonometry problem in a triangle is worked using an acronym SOH CAH TOA, this acronym means:

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

1. sin C

sin C = opposite / hypotenuse = 21/29

3. cos C = 12/13

cos C = adjacent / hypotenuse =  36/39 = 12/13 to the lowest term

6. tan X = 4/3

tan X = opposite / adjacent  = 36/27 = 4/3 to the lowest term

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The graph of g(x)=f(x)-d crosses the y-axis at (0,c-d).

What does y-intercept mean?

The point on a line where it crosses the y-axis is known as the y-intercept. To put it another way, it is the value of y when x is equal to 0.

It is given that graph  [tex]f(x)=ce^{x}[/tex] crosses the y-axis at (0,c).

Because at x=0,

[tex]f(0)=ce^{0}\\f(0)=c[/tex].

So, if g(x)=f(x)-d

[tex]g(x)=ce^{x}-d[/tex]

when x=0:

[tex]g(0)=ce^{0}-d\\g(0)=c-d[/tex]

So the graph of g(x)=f(x)-c touches the y-axis at (0,c-d).

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Answer:

3y(y + 4)

Explanation:

[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]

Answer:

The solution is 9,913 × 10⁸

Step-by-step explanation:

9,72 × 10⁸ and 1,93 × 10⁷

9,72 × 10⁸ + 1,93 × 10⁷

Factor the shape

= 10⁷ (9,72 × 10 + 1,93)

= 10⁷ (97,2 + 1,93)

= 10⁷ × 99,13

= 9,913 × 10⁸

The maximum number of hours is 1.6 hours and the minimum  number of hours is 1.6 hours.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, a plane is flying at a speed of 175 miles per hour.

The distance covered by the pilot, d = 250 ± 25 miles

We know that, speed = Distance/Time

The equation for the maximum number of hours is given as;

175 =(250+25)/t

t=275/175

t=1.6 hours

The equation for the minimum number of hours is given as;

175 =(250-25)/t

175=225/t

t=225/175

t=1.3 hours

Therefore, the maximum number of hours is 1.6 hours and the minimum  number of hours is 1.6 hours.

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The correct answer to the given question about all of the diagonals drawn from a vertex of an n-gon is option b) n-1

If all of the diagonals are drawn from a vertex of an n-gon, the number of triangles formed is equal to the number of non-diagonal sides of the n-gon. To see why, imagine selecting a vertex of the n-gon and drawing all of the diagonals from that vertex. Each diagonal connects that vertex to a non-adjacent vertex of the n-gon, which splits the n-gon into a series of triangles. The total number of triangles formed is equal to the number of non-diagonal sides of the n-gon, because each non-diagonal side forms one triangle with the selected vertex and one of its adjacent vertices. An n-gon has n sides, so the number of non-diagonal sides is equal to n - 3. This is because each vertex is connected to two adjacent vertices, so there are n - 2 diagonal sides emanating from the selected vertex, and the remaining n - 2 sides are non-diagonal. In addition, there are three sides at the selected vertex that are not counted as non-diagonal sides, so we subtract 3 from n - 2 to get n - 3. Therefore, the answer is (B) n - 1.

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The amount for first prize is $36 and second prize is $9.

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:

let the amount for Second price be x.

Then, amount of first Prize is 4x.

So, x+ x +x + 4x + 4x = 100

11x= 100

x= $9

So, the first prize would be (9 x 4)= $36

and, the second prize is $9 each.

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The total amount of time McKenna spends on her chores is 41/8 hours, or approximately 5.125 hours.

To find the total amount of time McKenna spends on her chores, we need to add up the time she spends mopping the floors and mowing and weeding the yard.

First, let's convert both the time spent mopping the floors and mowing and weeding the yard to a common denominator. The least common multiple of 4 and 8 is 8, so we can convert 7/4 hours to

7/4 * 2/2 = 7/2 hours.

Next, we can add the time spent on each chore:

7/2 hours + 27/8 hours = (14 + 27)/8 hours = 41/8 hours.

So, the total amount of time McKenna spends on her chores is 41/8 hours, or approximately 5.125 hours.

It is important to note that this calculation assumes that the time spent on each chore is a continuous amount of time, rather than broken up into smaller increments throughout the day.

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Answer:

red=7

pink=4

purple=15

dark pink=22

gray=18

Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.

To find the mass of the solution add the mass of salt and the mass of the solution. To find the concentration of the solution divide the salt mass by the total mass of the solution and multiply by 100.

Here we have  

Hugh poured 100 kilograms of water into 10 kg of salt.

After adding 100 kilograms of water to 10 kg of salt.  

The total mass of the solution = 100 + 10 = 110 kg

The concentration of salt

= [ Mass of salt/ Mass of solution] × 100

= [ 10/110] × 100 = 9.09%      

Therefore,

Hugh poured 100 kilograms of water into 10 kg of salt. He made 110 kilograms of 9.09 % salt solution.  

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Answer: 61 1/10

Step-by-step explanation:

9 2/5 x 6 1/2

The marked-up price of the discounted tablet computer is $298.35.

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

Given, During a sale, a store offered a 35% discount.

So, The discounted price of the computer tablet is,

= [(100 - 35)/100]×340.

= (65/100)×340.

= $221.

Now, The price is marked up by 35% which is,

= [(100 = 35)/100]×221.

= (135/100)×221.

= $298.35.

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Answer:

v=11

Step-by-step explanation:

Combined like terms and then divide at the end

Answer: V=11

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

The account that will yield the greatest future value is the first IRA. The difference in value would be $3,403.07.

The formula for calculating future value = annuity factor x monthly payments

Annuity factor = {[(1+r)^n] - 1} / r

Where:

Future value with monthly compounding: $416.66 x [{1.00208^360] - 1 }/0.00208] = $222,916.59

Future value with annual compounding: 5000 x [{1.025^30) - 1} / 0.0205] = $219,513.52

Difference in values = $222,916.59 - $219,513.52 = $3,403.07

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In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B as reflected line equation and explained as

When a shape is reflected in a line, it means that each point on the original shape is mapped to a corresponding point on the reflected shape that is symmetrical with respect to the reflecting line.

The line of reflection can be any straight line, and in this case, the line of reflection is given by the equation x = 2. To understand how the reflection works, imagine holding a mirror along the line x = 2 and placing Shape A on the mirror. The reflected shape, Shape B, would be the image that you see in the mirror. In mathematical terms, each point (x, y) on Shape A is mapped to a point (2 + (2 - x), y) on Shape B. This means that for each point on Shape A, we take its x-coordinate, subtract it from 2 to find the distance from the line of reflection, and then add that distance to 2 to find the x-coordinate of the corresponding point on Shape B. The y-coordinate remains the same.

The line of reflection acts as a dividing line between Shape A and Shape B, and the points on Shape B are exactly the same distance from the line of reflection as the points on Shape A, but on the opposite side. This means that Shape B is a perfect mirror image of Shape A, reflected across the line x = 2.

In summary, the reflection of Shape A in the line x = 2 maps each point on Shape A to a corresponding point on Shape B that is symmetrical with respect to the line of reflection. The result is a perfect mirror image of the original shape, reflected across the line.

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Variable and Coefficient of the given algebraic expression 3b + 6 is b and 3 respectively.

A variable is a symbol or letter that represents a value that can change or vary in a given context. Variables are often used to represent unknown or changing quantities in equations,

A coefficient is a numerical factor that is multiplied by a variable or variables in an algebraic expression. In other words, it is the number that appears in front of a variable.

3b + 6 identify the first term of the algebraic expression. Indicate whether the term is a variable term or a constant term. For a variable term, identify the variable and the coefficient of the term:

The first term of the algebraic expression 3b + 6 is 3b.

This is a variable term because it contains the variable "b".

The variable is "b" and the coefficient of the term is 3.

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From the given data points, about 50% of the data points are above the point 34.

Percentage defines the parts of a number per fraction of 100 or a part per 100. It is usually denoted by the symbol '%'.

Percentage of a number is calculated by dividing the number with the whole and then multiply with 100.

Given are a set of data points.

20  22  24  26  28  30  32  34  36  38  40  42  44  46  48  50

The numbers are in ascending order.

Total number of data points = 16

Data points above 34 are,

36  38  40  42  44  46  48  50

Number of data points which are above 34 = 8

Percent of numbers above 34 = (8 / 16) × 100 = 50%

Hence the percent of the data falls after 34 are 50%.

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Answer: 2021

Step-by-step explanation:

Answer:

56 is 40% of the original number

Step-by-step explanation:

Let [tex]n[/tex] represent the original number

We are given that  

30% of number is 42

70% of the same number is 98

Lets convert the precents to decimals

30% as a decimal is [tex]0.3[/tex]

70% as a decimal is [tex]0.7[/tex]

We can create an equation for each scenario

[tex]0.3n=42\\0.7n=98[/tex]

We can choose either one to evaluate [tex]n[/tex].

[tex]0.3n=42[/tex]

Lets solve for [tex]n[/tex].

Divide both sides by [tex]0.3[/tex].

[tex]n=\frac{42}{0.3}[/tex]

Evaluate [tex]\frac{42}{0.3}[/tex].

[tex]n=140[/tex]

Now that we know what the original number is we can calculate what 40% of the number is.

40% as a decimal is [tex]0.4[/tex].

[tex]140*0.4=56[/tex]

Null hypothesis: Proportion of residents favoring annexation <= 72%. Alternative hypothesis: Proportion of residents favoring annexation > 72%

The null hypothesis is that the proportion of residents who favor annexation is equal to or less than 72%. The alternative hypothesis is that the proportion of residents who favor annexation is greater than 72%.

To determine if there is sufficient evidence to support the mayor's claim, a hypothesis test should be performed. A common approach is to use a one-sample proportion test. This test compares the proportion of residents who favor annexation in a sample to the hypothesized proportion of 0.72.

Assuming a significance level of 0.05, if the p-value is less than 0.05, then there is sufficient evidence to reject the null hypothesis and conclude that the proportion of residents who favor annexation is greater than 72%.

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Thus, the required rest stops are approximately 4.09 miles apart on the new map.

The scale factor is defined as the ratio of the modified change in length to the original length.

Here,
The total length of the highway in miles can be found by using the scale of the original map. Since 2 inches on the map represent 33 miles in reality, 6 inches on the map represent:

= 6 inches × (33 miles/2 inches) = 99 miles

Since there are 11 equally spaced rest stops along the highway,

= (99 miles)/(11 intervals) = 9 miles per interval

To create the new map with a scale of 1 inch = 30 miles, we need to use a scale factor of (1/2) × (30/33) = 15/33.

Therefore, the distance between each rest stop on the new map can be found by multiplying the distance between rest stops on the old map by the scale factor,

= (9 miles per interval) × (15/33) = 4.09 miles per interval

So, the required rest stops are approximately 4.09 miles apart on the new map.

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Just multiply each side by side

Step-by-step explanation:1.Times one side by another

2. Times your answer by the third side

The probability that the person belonged to Group A is given as follows:

Probability = number of people in Group A that ate at least 7 vegetables / total number of people that ate at least 7 vegetables.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The outcomes for this problem are given as follows:

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If discount offered is 25% then the discount on the bike is $112.50 by multiply the rate by the original price.

What is discount price?

Discount pricing is a type of promotional pricing strategy where the original price for a product or service is reduced with the aim of increasing traffic, moving inventory, and driving sales.

According to the question:

Ken bought a bike that was priced at $450

Discount percentage offered to him is 25%

To find the discount price, first the rate is usually given as a percent.

To find the discount, multiply the rate by the original price.

Discount = [tex]450 \times \frac{25}{100}[/tex]

Therefore the discount on the bike is $112.50

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Answer:

x = -0.01835

Step-by-step explanation:

1) Isolate the term with the variable, 910x, by subtracting 45 on both sides:

2) Divide both sides by 910 to solve for x

Answer:

The monthly fee is [tex]\boxed{\$\;3.00}[/tex] and the yearly fee is [tex]\boxed{\$\;12.00}[/tex]

Step-by-step explanation:

The graph is a straight line whose equation can be represented in general terms as

y = mx + b

m = slope which is the rate of change of y with respect to x
b = y-intercept which is the value of y when x = 0; also the y-value where the line crosses the y-axis

To find m:

To find b:

So the equation of the line is
y = 3x + 12

In this context 3 represents the monthly fee since for 1 month, the cost goes up by $3

The constant 12 represents the yearly cost of membership which is the amount incurred regardless of how long you are with the music group

Answers
Monthly fee: $3
Yearly fee = $12

If the adult men have a height with mean as 69 inches , standard deviation as 2.8 inches , then the z-score for 63.4 inches tall man is     .

To find the z-score of a man 63.4 inches tall, we  use the formula: z = (x - μ)/σ  ;

where x is = the individual height, μ is = the mean height, and σ is = the standard deviation.

Substituting the values, we get  ;

⇒ z = (63.4 - 69.0)/2.8  ;

Simplifying, we get:

⇒ z = -5.6/2.8 = -2  .

⇒ z = -2  .

Therefore, the z-score of a man 63.4 inches tall is -2 which means that the man's height is 2 standard deviations below the mean height of adult men.

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