The length of the longer leg of a right triangle is 20cm more than twice the length of the shorter leg. The length of the hypotenuse is 22cm more than twice the length of the shorter leg. Find the side lengths of the triangle.

Answer:

$40.00 is the answer

Step-by-step explanation:

also can you mark me as a brainlist if you get a chance

Answer: $40.00

Step-by-step explanation:

12 is 30% of 40

Answer:

Step-by-step explanation:

The equation f(x) = 3x^2 + 4x + 3 is a quadratic function. Here are three ways this equation can be used in the real world:

In physics, this equation can be used to model the height of an object thrown into the air. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the height of the object at any given time x, where x is the time elapsed since the object was thrown. The coefficient 3 in the equation represents the acceleration due to gravity, and the other terms represent the initial height and velocity of the object.

In economics, this equation can be used to model the profit of a company. If x represents the number of units sold, then f(x) = 3x^2 + 4x + 3 can be used to calculate the profit made by the company at any level of sales. The coefficient 3 in the equation represents the fixed costs of the company, while the other terms represent the variable costs and revenue.

In engineering, this equation can be used to model the trajectory of a projectile. The equation f(x) = 3x^2 + 4x + 3 can be used to calculate the distance traveled by a projectile at any given time x, where x is the time elapsed since the projectile was launched. The coefficient 3 in the equation represents the initial velocity of the projectile, and the other terms represent the effects of air resistance and gravity.

The value of x in the circle is 180° - 85° = 95°. The Cyclic Quadrilateral Theorem states that the sum of any opposite angle pair within a cyclic quadrilateral is additional,

Given

Angle = 85°

Required to find the opposite angle to 85° which is x

x = 180° - 85°

x= 95°

Thus, the quadrilateral is inscribed in a circle. Due to the shape being a quadrilateral, it is presumed that the angle in the middle is supplementary and adds up to 180° 180° 180°. The opposing angles in a quadrilateral are presumed to be equal since angles in the same segment are equal.

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When creating a rubric or criteria for grading students, it is important to establish clear expectations and criteria that align with the learning objectives of the assignment or task. Here is a suggested rubric format:

1. Content Knowledge: Assess the depth and accuracy of the student's understanding of the subject matter.

2. Organization and Structure: Evaluate the clarity and logical flow of the student's work, including the use of headings, subheadings, and transitions.

3. Research and Evidence: Consider the quality and relevance of sources used, as well as the integration of evidence to support arguments or claims.

4. Critical Thinking: Assess the student's ability to analyze, evaluate, and synthesize information, demonstrating higher-order thinking skills.

5. Writing Mechanics: Evaluate the student's grammar, spelling, punctuation, and overall writing style.

6. Creativity and Originality: Acknowledge unique or innovative ideas, approaches, or perspectives.

7. Presentation (if applicable): Assess the student's ability to effectively present their work, including visual aids, organization, and delivery.

Each criterion should have specific descriptors or levels of achievement (e.g., Excellent, Good, Fair, Poor) that clearly communicate expectations. It is also helpful to assign weights to each criterion to reflect their relative importance.

Providing detailed feedback and examples can further enhance the usefulness of the rubric for students' understanding and improvement.

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The mean, median, mode and range of the data are 68.58, 68, 68 and 17 respectively.

A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.

1. The mean of the data is;

mean = 62 + 63 + 65 + 66 + 68 + 68 + 68 + 70 +  70 + 72 + 72 + 79 / 12

mean = 68.58

2. The median of the data = 68

3. The mode of the data = 68

4. The range of the data = 17

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Answer:

2715

Step-by-step explanation:

10860/4 = 2715

if im wrong smite me

Answer: 2(x+3)(x+2)

Step-by-step explanation:

The chord in this circle is RS while the radius of the circle is QT. If the diameter of the circle is 28 cm, then the radius will be 14 cm.

The chord of a circle refers to the line that connects two parts of the circle. In the diagram provided, points RS represent the chord of the circle. Also, the diameter of a circle are the points that run between two segemnts of the circle's center.

In this circle these are points GP. The radius is gotten by dividing the diameter by 2, so the radius of the given diameter is 28/2 = 14.

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Answer:

C

Step-by-step explanation:

using the sine ratio in the right triangle

sin P = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{QR}{PQ}[/tex] = [tex]\frac{12}{13}[/tex] , then

∠ P = [tex]sin^{-1}[/tex] ( [tex]\frac{12}{13}[/tex] ) ≈ 67° ( to the nearest degree )

The probability that Julie will be a captain, given that she makes the team is 1/3.

Given,

Number of students trying out for a soccer team = 40

Case of probability,

P(A) = n(A)/n(S)

n(A) = number of favourable outcomes, n(S) is the total number of events in the sample space.

Given ,

18 of 40 students will make the soccer team.

⇒ n(S) = 18

Let event A: Julie will be a captain, given that she makes the team

⇒ n(A) = 3

So, the probability that Julie will be a captain, given that she makes the team,

= P(A) = n(A)/n(S)

= P(A) = 3/18

= P(A) = 1/6

Therefore, the probability that Julie will be a captain, given that she makes the team is 1/3.

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To answer the given questions, let's use conditional probability based on the information provided:

a. To find the probability that the selected student does not get a scholarship, given that they cannot get a job within 2 months after graduation, we can use Bayes' theorem. Let's denote the events as follows:

A: Not getting a scholarship

B: Not getting a job within 2 months after graduation

We want to find P(A|B), which is the probability of not getting a scholarship given that the student cannot get a job within 2 months. According to the given information, 25% of students who cannot get a job within 2 months get at least one university scholarship.

Using Bayes' theorem:

P(A|B) = (P(B|A) * P(A)) / P(B)

P(B|A) is the probability of not getting a job within 2 months given that the student does not get a scholarship. Since this information is not provided, we cannot determine this probability.

b. To find the probability that the selected student gets no university scholarship, we can use the law of total probability. Let's denote the events as follows:

A: Not getting a scholarship

B: Getting a job within 2 months after graduation

C: Not getting a job within 2 months after graduation

We want to find P(A), the probability of not getting a university scholarship. According to the given information, 60% of students get a job within 2 months after graduation, and among those students, 70% get at least one university scholarship. For students who cannot get a job within 2 months, 25% get at least one university scholarship.

Using the law of total probability:

P(A) = P(A|B) * P(B) + P(A|C) * P(C)

We don't have the values for P(A|B) or P(B) and P(A|C) or P(C), so we cannot calculate the exact probability of not getting a university scholarship.

Therefore, without additional information or values for conditional probabilities, we cannot provide specific numerical answers to these questions.

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Answer:

wheres it at?

Step-by-step explanation:

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The solution of the equation will be; [tex]\dfrac{1}{3y} (\dfrac{x + 9xy + 9y}{x + 2} )[/tex]

Since we know that equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation that is a statement with two equal sides and an equal sign in between.

We are given the equation as;

[tex]3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3} (\dfrac{x}{xy + 2y} )[/tex]

Taking y common as;

[tex]3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3} (\dfrac{x}{xy + 2y} )\\\\\\3(\dfrac{x+ 1}{x+ 2} )+ \dfrac{1}{3y} (\dfrac{x}{x + 2} )\\\\\\ \dfrac{1}{3y} (\dfrac{x + 9xy + 9y}{x + 2} )[/tex]

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3/5 and -3/4 are the x and y-intercept of the line respectively

Given the coordinate points (−1, −2) and (3, 3), we need to determine the x and y-intercept

The equation of a line in slope intercept form is y = mx + b where:

m is the slope

b is the intercept

For the slope:

slope = 3-(-2)/3-(-1)
Slope = 5/4

For the y- intercept

3 = 5/4(3) + b

3 = 15/4 + b

b = 3 - 15/4

b = -3/4

Hence the equation of the line is. y = 5/4 x - 3/4

For the x-intercept

The x-intercept is the point where y = 0

0 = 5/4 x - 3/4

5/4 x = 3/4

5x = 3

x = 3/5

Hence the x- and y-intercepts of the line are 3/5 and -3/4 respectively.

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A surveyor plays a crucial role in land surveying and mapping, using various tools and techniques to accurately measure and analyze land features.

Trigonometric functions are fundamental mathematical tools that surveyors rely on to solve problems involving angles, distances, and elevations. By employing trigonometry, surveyors can determine the precise locations of points, measure distances between objects, and calculate elevations with accuracy and efficiency. This essay will explore how surveyors utilize trigonometric functions in their work, highlighting key vocabulary words and providing three detailed examples.

One of the primary applications of trigonometry in surveying is angle measurement. Surveyors use the concept of trigonometric ratios, such as sine, cosine, and tangent, to determine angles between reference points. By measuring the lengths of sides in a triangle formed by the surveyor's position and the target point, trigonometric functions enable them to calculate the unknown angles. For instance, when surveying a land boundary, a surveyor may use the tangent function to determine the angle of deflection between two adjacent lines, helping establish accurate boundary lines.

Another crucial application of trigonometry in surveying is distance measurement. By utilizing trigonometric principles, surveyors can measure distances that are difficult or impractical to physically traverse. For instance, when faced with measuring the width of a river or the height of a tall structure, a surveyor can employ trigonometry along with the concept of similar triangles. By measuring the angles of elevation or depression from the surveyor's position to the target point and knowing the distance between two reference points, they can calculate the unknown distance using trigonometric functions like sine or tangent.

Elevation determination is yet another area where surveyors rely on trigonometric functions. By combining angle measurements and distance measurements, surveyors can determine the elevation of a specific point above a reference level. For example, when conducting a topographic survey to create a contour map, surveyors measure the angles of elevation or depression to various points on the terrain. By applying trigonometry, they can calculate the differences in elevations between these points and establish contour lines representing the shape and relief of the land.

In conclusion, trigonometric functions are indispensable tools for surveyors in their day-to-day work. Angle measurement, distance measurement, and elevation determination are just a few examples of how surveyors employ trigonometry to accomplish accurate and precise land surveying. By understanding trigonometric concepts and utilizing key vocabulary words such as sine, cosine, tangent, angles of deflection, and angles of elevation, surveyors can confidently carry out their tasks, ensuring reliable measurements and mapping of land features. Trigonometry empowers surveyors to overcome challenges in measuring angles, distances, and elevations, contributing to the accurate representation of the physical world and supporting various engineering and construction projects.

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The data given is an example of a B. Quadratic regression.

The r-squared ( r ²) value is a statistical measure that represents the proportion of the variance for a dependent variable that's explained by an independent variable or variables in a regression model.

The r² values are highest for the quadratic model (r ² = 0. 997), meaning this model explains the most variance in your data compared to the linear (r² = 0. 808) and exponential models (r ² = 0. 813). Thus, the data are best modeled with a quadratic regression.

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The total mass of the four packages is given as follows:

37.67 kg.

The total mass of the four packages is obtained adding the masses of each package given on the table for this problem.

From the table given in this problem, the mass for each package is given as follows:

Hence, adding these amounts, the total mass of the package is obtained as follows:

3.94 + 14.81 + 11.27 + 7.65 = 37.67 kg.

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Step-by-step explanation:

Let's denote the number of hours Nathan works delivering pizzas as "x" and the number of hours he works babysitting as "y." We can set up the following system of inequalities:

Nathan's total earnings should be at least $40:

10x + 5y ≥ 40

Nathan's total working hours should be less than six hours a week:

x + y < 6

These two inequalities represent the given conditions that Nathan wants to make at least $40 and work for less than six hours a week.

Answer:

123

Step-by-step explanation:

Add 6 to the first number to get the second number.

Add 3 to the second number to get the third number.

Multiply the third number by 4 to get the fourth number.

Add 5 to the fourth number to get the fifth number.

Using this pattern, we can find the next number in the sequence by following the same rule:

Multiply the fifth number by 2 and then subtract 7 to get the next number.

So, the next number in the sequence is:

65 x 2 - 7 = 123

Answer: p(x) = f(x+8)-6

Step-by-step explanation:

Answer:  C f(x+8)-6

Step-by-step explanation:

You went left 8 or -8 in x direction, take opposite sign for x

also down 6 or -6 in y direction, take sign as is.

f(x+8)-6

The coordinates of the hole of the rational function are (-3, -3).

Here we have the following rational function:

[tex]f(x) = \frac{x^2 + 3x}{x + 3}[/tex]

The hole is when the denominator becomes zero, that is at x = -3

Now, we can rewrite the numerator as:

x² + 3x = x*(x + 3)

Then we can rewrite the function as:

[tex]f(x) = \frac{x^2 + 3x}{x + 3} = \frac{x*(x + 3)}{x + 3} = x[/tex]

Evaluating that in x = -3 we get f(x) = -3, then the coordinates of the hole aer (-3, -3).

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Answer:

The car is moving 15 degrees South of East. This means that it is moving in a direction that is 75 degrees from the positive x-axis.

The velocity vector of the car can be broken down into its components in the x and y directions as follows:

vx = v * cos(theta) = 68 * cos(75) = 17.3 mph

vy = v * sin(theta) = 68 * sin(75) = 66.3 mph

where

v = 68 mph (magnitude of velocity)

theta = 75 degrees (angle of velocity vector with respect to the positive x-axis)

Therefore, the car is moving 17.3 mph in the Eastern direction and 66.3 mph in the Southern direction.

The correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.

To determine the number of votes an ice cream would need to accumulate in order to be the majority winner, we should analyze the preference schedule provided.

Looking at the preference schedule, we can see that there are four ice cream flavors:

Chocolate (C), vanilla (V), strawberry (S), and pistachio (P).

Each row represents the rankings given by Janice's friends.

To be the majority winner, an ice cream flavor would need to accumulate more votes than any other flavor.

In this case, we can determine the highest number of votes an ice cream flavor can receive by considering the first-place line in the preference schedule.

From the first-place line, we can see that the maximum number of votes any flavor has received is 9.

Therefore, an ice cream flavor would need more than 9 votes from the first-place line to be the majority winner.

Based on the given options, the correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.

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Answer:

d. Certain

Andres will always roll a number greater than or equal to 1 since 1 is the lowest number on the die. Therefore, the probability of rolling a number greater than or equal to 1 is certain.

The correct answer is 4,128 square inches.

To determine the amount of material needed to replace the felt cover on the pool table, we need to calculate the surface area of the table.

The pool table has dimensions of 86 inches in length and 48 inches in width.  

Surface area is the measure of the total area of the external or exposed surfaces of a three-dimensional object.

It represents the sum of the areas of all the faces or surfaces of an object, including its top, bottom, and sides.

Surface area is typically measured in square units such as square inches, square centimeters, or square meters.

To find the surface area, we multiply these two dimensions together:

Surface area = Length [tex]\times[/tex] Width

Surface area = 86 inches [tex]\times[/tex] 48 inches

Surface area = 4,128 square inches.

Therefore, the correct answer is 4,128 square inches.

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Answer:

  1650 calories

Step-by-step explanation:

You want to know how many calories are burned in 3 hours of walking if 550 calories are burned each hour of walking.

The total number of calories burned is the product of the number burned per hour and the number of hours:

  (550 cal/h)·(3 h) = 550·3 cal = 1650 cal

The woman burned 1650 calories after walking 3 hours.

__

Additional comment

As with most rate problems, the quantity is the product of the rate and the time.

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The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

We have to given that,

All the numbers are,

⇒ 5⁰

⇒ |2|

⇒ (- 1/2)²

⇒ 5/8

⇒ 30%

Now, We can simplify each as,

⇒ 5⁰

⇒ 1

⇒ |2|

⇒ 2

⇒ (- 1/2)²

⇒ 1/4

⇒ 0.25

⇒ 5/8

⇒ 0.625

⇒ 30%

⇒ 30/100

⇒ 0.3

Hence, Ascending order is,

0.25, 0.3, 0.625, 1 , 2

Or,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

Thus, The value of ascending order of numbers are,

⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|

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Answer:

Yes

Step-by-step explanation:

These are the rules regarding polynomial graphs and their real zeros (solutions)

In the above graph we see that the graph touches the x-axis at x = 3. This means (x - 3)ᵃ  is a factor of the polynomial where p is an even number (2, 4, 6 etc)

That means x = 3 is a repeated real solution. It appears that the multiplicity is 2 so one factor of the polynomial is (x - 3)²

More inf o(ignore if you want)

The other real roots are x = -1 and x = 5 because the graph crosses the x axis at these two values of x. So the multiplicity of both factors ( x + 1) and (x - 5) is odd. Since at the crossover point, the graph is almost linear, we can safely assume that the multiplicity of the graph is odd at these points and equal to 1

Therefore the polynomial can be factored as
(x + 1)(x - 5)(x -  3)²

The degree of the polynomial is the sum of the multiplicities and is equal to 1 + 1 + 2 = 4 so it is a quartic polynomial of the form ax⁴ + bx³ + cx² + dx + e