A right triangle has a leg length of square root of 11 and a hypotenuse length of 9. Determine the length of the other leg of the right triangle.

For the given expression 300 - 5x , Diana's saving after five weeks is equal to 275 dollars.

As given in the question,

Given expression to represent the Diana's saving is written as:

300 - 5x

Where 'x' represents the number of weeks.

Now the Diana's savings after five weeks is given by :

Here x = 5

Substitute the value of x in the given expression 300 - 5x we get,

300 - 5x

= 300 - 5( 5 )

= 300 - 25

= 275 dollars

Therefore, the Diana's savings as per the given expression 300 - 5x after five weeks is equal to 275 dollars.

The above question is incomplete, the complete question is:

Diana's savings at the end of each week can be described by the expression (300-5x) dollars where x represents the number of the week.

What is her savings after five weeks in dollars?

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Answer:

-16

Step-by-step explanation:

Answer:

the answer is 16

by substitution

you will get the answer

leap years

Answer:

2004, 2008, 2012, 2016, 2020, 2024, 2028, 

Using the substitution method we will see that the solution is:

a = 69

b = 55.5

Here we want to solve the system of equations below:

-3a + 4b = 15

5a - 6b = 12

We can isolate one of the variables in one of the equations, I will isolate b on the first one.

4b = 15 + 3a

b = (15 + 3a)/4

Now we can replace this on the other equation:

5a - 6*(15 + 3a)/4 = 12

Now we can solve that equation for a.

5a - (6/4)*15 - (6/4)*3a = 12

5a - (3/2)*15 - (9/2)*a = 12

(1/2)*a = 12 + (3/2)*15

a = 2*(12 + (3/2)*15)

a = 24 + 45

a = 69

And the value of  b is:

b = (15 + 3a)/4

b = (15 + 3*69)/4 = 55.5

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Answer:

5h - 2(2j+k)

Step-by-step explanation:

Best we can do here is 5h - 2(2j-k) but there's no simplifying further

The percent change in the blu-ray player decreased by 20%.

A percentage is a figure or ratio that can be stated as a fraction of 100.

If we need to determine the percentage of the given number, we divide the number by its whole number and multiply it by 100. As a result, the percentage is one part in one hundred. "Per 100" is short for "per percent." It is represented by the symbol "%".

Given the cost price of a Blu-Ray player = $300

the selling price of a Blu-Ray player = $240

loss = $300 - $240

loss = $60

Decrease in percent  = 100*(loss)/cost price

Decrease in percent  = 100*(60)/300

Decrease in percent  = 20%

Hence there is a decrease of 20%.

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Answer:

b

Step-by-step explanation:

hopefully this helps

The length of the ribbon that Regina needed is 38.10 inches

The measurement of the circle's boundaries is known as the circumference or perimeter of the circle. The circumference of a circle is its length when it is opened up and drawn as a straight line. Units like cm or unit m are typically used to measure it.

The formula for the Circumference of the circle is given by

where 'r' is the radius of the circle.

Here we have

Regina is tying a bow around a soccer ball to give to her sister.

The ribbon must be 10 inches longer than the circumference of the ball

Length of the ribbon = Circumference of ball + 10 inches

Given the radius of the ball, r = 4.5 inches  

Circumference of ball = 2(3.14)(4.5) = 28.26 inches

So, Length of the ribbon = 28.26 inches + 10 inches = 38.10 inches

Therefore,

The length of the ribbon that Regina needed is 38.10 inches.

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The value of f(7.5) of the exponential function is 86.84

The general form of an exponential function is given by:

f(x) = abˣ

Since f(x) is an exponential function, and f(4)=21 and f(4.5)=47. We can write that:

21 = ab⁴   --- (1)

47 = ab⁴°⁵  --- (2)

Divide (2) by (1):

47/21 = b⁴°⁵⁻⁴

47/21 = b⁰°⁵

b =√(47/21)

b = 1.50

Put b = 1.5 into (1):

21 = ab⁴

21 = a(1.5)⁴

a = 21/(1.5)⁴

a = 4.15

So the exponential function f(x) = 4.15(1.50)ˣ

To find the value of f(7.5), put  x = 7.5 into the exponential function:

f(x) = 4.15(1.50)ˣ

f(7.5) = 4.15(1.50)⁷°⁵

f(7.5) = 86.84

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The answer(s) to the initial equation is/are  -5 - √21/2 , -5 + √21/2.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

A statement is not an equation if it has no "equal to" sign. 

According to our question-

Use the substitution u = x + 4 to solve the problem

(x + 4)2 - 3(x + 4) - 3 = 0 The equation will then look at that.

further solving gives,

x1 = -5 - √21/2 , x2 = -5 + √21/2.

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The Graph to the y≥2 and y<4 is attached below.

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

The Inequalities are:

y≥2

y<4

Now, if plot these inequalities in the graph we get

The y≥2 will have the shaded on the upper part where y= 2, 3, 4, and so on.

Now,  y < 4 will have the shaded on the lower part of graph where y= 3, 2, 1, 0, -1, -2 and so on.

Now, The shaded region shown the common point between both inequality which is y= 2, 3 4.

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Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.

Here,

At time zero, Kadeesha stepped outside and drove 3 minutes at a speed of 1 block per minute to the store.

after traveling six blocks at her normal speed of three blocks per minute

She spent 5 minutes stopping at the bank as a result. She then sped home at a rate of three blocks per minute.

She therefore begins at (19,8), travels 8 blocks back in 2 minutes, and ends at (21,0).

Therefore ,As a result, the answer to the above  equation is: She starts at (19,8), travels 8 blocks back in 2 minutes, and ends up at (21,0).

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On solving the provided question, we can say that by trigonometry angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

by trigonometry

B = 50m

P = 28m

Tan(x) = 50/281.7857142857 = 1.2

angle of evolution = x = [tex]tan^{-1}(1.2)[/tex]

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The right answer is option c, which displays the relation as a set of ordered pairs in the coordinate plane, with points at (-2, 1), (0, -1), and (2, 3). (2, -3).

When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.

given

We have the ordered pair provided by the pair that complies with a set of requirements given that the points are on a coordinate plane.

The most appropriate set of coordinates that make up an ordered pair in the question are (-2, -1), (0, 1), and (2, 3).

The points are colinear because the slope between (-2, -1) and (0, 1) is the same as the slope between (-2, -1) and (y), and each x-coordinate term is less than the y-coordinate term by 1. (2, 3).

The right answer is option c, which displays the relation as a set of ordered pairs in the coordinate plane, with points at (-2, 1), (0, -1), and (2, 3). (2, -3).

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The measure of internal angle m∠V = 103°

The sum of the interior angles of a polygon is given by the formula

Sum of Interior angles of a polygon with n sides is

nθ = 180 ( n - 2 )

where n is the number of sides

θ = angle in degrees

Given data ,

Let the sum of interior angles of the polygon be S

Now , the number of sides of the polygon n = 6 sides

So , Sum of Interior angles of a polygon with n sides is

nθ = 180° ( n - 2 )

Substituting the values in the equation , we get

nθ = 180° ( 6 - 2 )

nθ = 180° x 4

nθ = 720°

Therefore , the value of S = 720°

Now , the sum of measures of internal angles inside the polygon is

m∠S = 90°

S = 90° + ( 9x - 19 )° + 111° + ( 5x + 8 )° + 128° + ( 7x + 3 )°

On simplifying the equation , we get

( 9x - 19 )° + ( 5x + 8 )° + ( 7x + 3 )° + 329° = 720°

Subtracting 329° on both sides of the equation , we get

( 9x - 19 )° + ( 5x + 8 )° + ( 7x + 3 )° = 391°

And , on further simplification , we get

21x - 8 = 391

Adding 8 on both sides , we get

21x = 399

Divide by 21 on both sides , we get

x = 19

Now , the measure of m∠V = ( 5x + 8 )°

Substitute the value of x in the equation , we get

The measure of m∠V = ( 5 ( 19 ) + 8 )°

The measure of m∠V = 103°

Hence , the measure of angle m∠V = 103°

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Answer:

Step-by-step explanation:

I had to do this like 3 times; hope this helps!! Remember both parts are 3d spaces.

Basically I did whole box - part of the box

Remember your formulas !! <3

The number line that represents the solutions that is n > 3 is number line 1.

Any real number can be represented in two dimensions using a number line. Any number on the number line with a solid circle next to it means to include that number followed by the rest of the values, and any number with a hollow circle means to exclude that value from the list before the rest of the values.

The solutions represented by number line 1 are those where n>3. By using special representational techniques, number lines are used to represent real numbers. This was Illustrated in number line 1.

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Answer:

m=55

Step-by-step explanation:

Since one line equals 180 degrees, 180-125=55

Answer:

(1) -4n-5

(2) 15r

(3) 12x-9

(4) 12r-20

(5) 10n-13

(6) 42n^2+21n

(7) 10a^2-100ab

(8) 3n^3-18n^2+15n

(9) 9v^2+24v-15

(10) 9v^2u^2 + 9uv^3- 45v^4

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A. Simplifying an algebraic expression means combining any like terms, which are terms that have the same variable and exponent. In these problems, we are asked to simplify the expressions by combining like terms.

1. n + 4 − 9 − 5n = n - 5n + 4 - 9 = -4n - 5

The first step is to combine the like terms which are n and -5n, we get -4n then we combine -9 and 4 and we get -5.

2. 12r + 5 + 3r – 5 = 12r + 3r + 5 - 5 = 15r

The first step is to combine the like terms which are 12r and 3r, we get 15r then we combine 5 and -5 and we get 0

3. −3x − 9 + 15x = 15x - 3x - 9 = 12x - 9

The first step is to combine the like terms which are 15x and -3x, we get 12xthen we combine -9 and 0 and we get -9

4. 12r - 8 - 12 = 12r - 12 - 8 = 12r - 20

The first step is to combine the like terms which are 12r and -12, we get 12r-12 then we combine -8 and 0 and we get -20

5. n - 10 + 9n - 3 = n + 9n - 10 - 3 = 10n - 13

The first step is to combine the like terms which are n and 9n, we get 10n then we combine -10 and -3 and we get -13

B. In these problems, we are asked to multiply the expressions.

6. 7n(6n + 3) = 42n^2 + 21n

In this example we have 7n multiplied by the expression 6n + 3, the distributive property is used to multiply 7n by each term in the parenthesis (6n and 3)

7n * 6n = 42n^2

7n * 3 = 21n

7. 10a( a − 10b) = 10a^2 - 100ab

In this example we have 10a multiplied by the expression a - 10b, the distributive property is used to multiply 10a by each term in the parenthesis (a and -10b)

10a * a = 10a^2

10a * -10b = -100ab

8. 3n( n2 − 6n + 5) = 3n^3 - 18n^2 + 15n

In this example we have 3n multiplied by the expression n^2 − 6n + 5, the distributive property is used to multiply 3n by each term in the parenthesis (n^2, -6n and 5)

3n * n^2 = 3n^3

3n * -6n = -18n^2

3n * 5 = 15n

9. 3(3v^2 + 8v - 5) = 9v^2 + 24v - 15

In this example we have 3 multiplied by the expression 3v^2 + 8v - 5, the distributive property is used to multiply 3 by each term in the parenthesis (3v^2, 8v and -5)

3 * 3v^2 = 9v^2

3 * 8v = 24v

3 * -5 = -15

10. v^2( u^2 + uv − 5v^2) = 9v^4 + 9

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To convert a number to base 12, you can use the process of repeated division and remainder.

To convert a number to base 12, you can use the process of repeated division and remainder with these:

1. Divide the number by 12, and keep track of the remainder.

2. Replace the original number with the quotient from step 1.

3. Repeat steps 1 and 2 until the quotient is 0.

4. The remainders from each step form the digits of the base-12 representation of the original number, with the last remainder being the least significant digit.

For example, to convert the number 35 to base 12:

35 / 12 = 2 remainder 11

2 / 12 = 0 remainder 2

So the base-12 representation of 35 is "23".

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According to the given information in the question the water level drop -0.15 each​ hour.

You must add "an" before words that begin with any of the five vowels, a, e, I, o, or u. However, how you say it is more important than how you spell it. Examples are "a history" and "an hour" (both of which begin with a vowel sound) (because history begins with a consonant sound).

Hipparchus recommended splitting the day into 24 require longer hours depending on the 12 days of daylight and 12 hours or darkness observed on solstice days. Hipparchus' work mostly occurred between 147 and 127 B.C.

rate = (change in water level) / (time elapsed)

rate = (4/25) / (-2.64)

rate = -0.15

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Answer:

  2

Step-by-step explanation:

You want the count of negative terms in the simplified form of -3x² + 2y² + 5xy - 2y + 5x² - 3y².

The expression is simplified by combining like terms.

  -3x² + 2y² + 5xy - 2y + 5x² - 3y² = (-3+5)x² +5xy +(2-3)y² -2y

  = 2x² +5xy -y² -2y

There are two negative terms in the simplified expression.

Option A) 59.6 is correct.

How to calculate Distance?

Using the distance formula: This method is also used to find the distance between two points in a plane. The formula is: distance = √((x2 - x1)² + (y2 - y1)²)

To find the distance between the man and the cliff, we can use trigonometry. We know that the angle of elevation is 40° and the height of the cliff is 50 m. We can use the tangent function to find the distance.

distance = (height of cliff) / (tangent of angle of elevation)

distance = 50 m / (tan 40°)

distance = 50 m / 0.8391

distance = 59.6 m

So, the distance between the man and the cliff is approximately 59.6 meters.

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The linear, quadratic and exponential functions form a set because they differ only in the values of exponents.

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Choose a set among the 4 sets.

Let us choose set 2.

Linear Function :

Linear functions are functions whose variable has the highest degree equal to 1. The graph of the linear function is a line.

Standard form of linear equation is y = mx + c.

For example, let f(x) = 5x + 2.

Quadratic Function :

Quadratic functions are functions whose variable has the highest degree of 2. The graph of quadratic function is a parabola.

Standard form of quadratic function is y = [tex]ax^{2} +bx+c[/tex]

For example, let f(x) = [tex]2x^{2} +4x-5[/tex]

Exponential function :

Exponential functions are functions where the variable lies in the exponent. The graph of exponential functions makes a curve which grows steeper over time.

Standard form of exponential function is y = [tex]e^{x}[/tex]

For example, let f(x) = [tex]2^x[/tex]

Hence these formed into a group because of they are different type of functions which differ in the exponents.

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We can summarize the relationships among these shapes as:

Quadrilaterals --> Parallelograms --> Rhombuses

--> Trapezoids --> Isosceles Trapezoids

--> Rectangles --> Squares

--> Kites

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Answer:

Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents.

The building have to rent 14 offices with area 500 ft² each so that the total acquired space is  7000 ft².

What is division?

One of the four fundamental mathematical operations—the others being addition, subtraction, and multiplication—is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

The area of one office is 500 ft².

The total space acquired by the office building is 7000 ft².

To find the number of offices the building is renting, use the formula of division -

Number of office = Total space rented / Area of one office

Let the value of number of office rented be x.

Substituting the values in the equation -

x = 7000/500

x = 14

Therefore, the number of offices being rented is 14.

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Yes, mathematics plays a crucial role in the insurance industry. Actuarial science, which uses mathematical and statistical methods to assess and manage risk, is the foundation of the insurance industry.

Actuaries use mathematical models to calculate the likelihood of future events, such as accidents, illnesses, or natural disasters, and use this information to price insurance policies and estimate the company's potential losses.

The insurance industry also uses mathematical models to assess and manage the risk of potential losses, set prices for their products, and make investment decisions. For example, insurance companies use simulations to estimate the likelihood of different scenarios and the potential impact on their financials.

Additionally, underwriters use mathematical models to assess the risk of insuring a particular individual or business, they take into account factors such as the individual's age, health, and occupation when determining the price of the policy.

Insurance companies also use statistical models and Machine learning algorithms to detect patterns of suspicious behavior that could indicate fraud.

In summary, the mathematical basis for insurance is the use of mathematical and statistical models and techniques, such as probability and statistics, to assess and manage risk and make financial decisions in the insurance industry.

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Answer:

the answer is A. 64:343.

Step-by-step explanation:

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding side lengths. Since the scale factor of the two cylinders is 4:7, the ratio of their corresponding radii is 4:7 and the ratio of their heights is also 4:7.

So, the ratio of their volumes is (4/7)^3 = (64/ 343) = 64:343

So, the answer is A. 64:343.