Find the least common denominator​ (LCD) of 9x/x+4 and 17/3x+12.

Answer: 22 inches

Step-by-step explanation:

The original dimensions of the index card are 3 inches by 5 inches, so its perimeter is:

P = 2(3 in) + 2(5 in) = 6 in + 10 in = 16 in

and its area is:

A = 3 in x 5 in = 15 in^2

When the map is enlarged to be 8 inches long, the new dimensions are 3 inches by 8 inches, so the perimeter is:

P' = 2(3 in) + 2(8 in) = 6 in + 16 in = 22 in

and the area is:

A' = 3 in x 8 in = 24 in^2

Therefore, the perimeter of the enlarged map is 22 inches and the area is 24 square inches.

Answer:

The new width of the map after enlargement would be (8/5) * 3 = 4.8 inches (assuming the aspect ratio is maintained).

So, the perimeter would be (4.8 + 8) * 2 = 25.6 inches.

The area would be 4.8 * 8 = 38.4 square inches.

Explanation:

Here's an explanation of how to approach problems like these, along with some examples of easy and hard math problems:

When enlarging a map, you need to consider how the scale of the map changes. In this case, the map is being enlarged from 5 inches to 8 inches in length, which is a scale factor of 8/5. This means that every distance on the original map will be scaled up by a factor of 8/5 on the enlarged map.

To find the perimeter and area of the enlarged map, you'll need to use this scale factor to determine the new dimensions of the map. The new width of the map will be the same as the original width, which is 3 inches. The new length of the map will be 8 inches, since that is the length to which the map is being enlarged. So the new dimensions of the map are 3 inches by 8 inches.

To find the new perimeter, you just need to add up the lengths of the four sides of the map: P = 2w + 2l. Using the new dimensions of the map, we get:

P = 2(3) + 2(8) = 6 + 16 = 22 inches

To find the new area, you just need to multiply the new length and width of the map: A = wl. Using the new dimensions of the map, we get:

A = 3(8) = 24 square inches

Examples:

Easy:

The index card is 3 inches wide and 5 inches long, so the perimeter is:

P = 2(3 in) + 2(5 in) = 6 in + 10 in = 16 in

To find the area, we use the formula:

A = L x W

A = 3 in x 5 in = 15 square inches

Now we want to enlarge the map to 8 inches long, but we're not told how wide it will be after enlargement. Let's assume that the width also increases by the same proportion as the length. That means the new dimensions will be:

Length = 8 in

Width = (8/5) x 3 in = 4.8 in

The perimeter will now be:

P = 2(8 in) + 2(4.8 in) = 16 in + 9.6 in = 25.6 in

The area will be:

A = 8 in x 4.8 in = 38.4 square inches

Hard:

A rectangular garden has an area of 320 square feet. If the width of the garden is 10 feet less than the length, find the dimensions of the garden and the length of the diagonal.

Let's use the formula for the area of a rectangle:

A = L x W

We know that the area is 320 square feet, so we can write:

320 = L x (L - 10)

Expanding the right side gives:

320 = L^2 - 10L

Moving all the terms to one side gives:

L^2 - 10L - 320 = 0

We can solve for L using the quadratic formula:

L = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -10, and c = -320, so:

L = (10 ± sqrt(10^2 - 4(1)(-320))) / 2(1)

L = (10 ± sqrt(1440)) / 2

L = (10 ± 12√10) / 2

We can simplify this to:

L = 5 + 6√10 or L = 5 - 6√10

The dimensions of the garden are either:

Length = 5 + 6√10 feet

Width = 5 - 6√10 feet

or

Length = 5 - 6√10 feet

Width = 5 + 6√10 feet

We can check that the area is 320 square feet for either set of dimensions.

To find the length of the diagonal, we can use the Pythagorean theorem:

d^2 = L^2 + W^2

We already know the values of L and W for both cases, so we can calculate:

d = sqrt((5 + 6√10)^2 + (5 - 6√10)^2) = 10 sqrt(2)

or

d = sqrt((5 - 6√10)^2 + (5 + 6√10)^2) = 10 sqrt(2)

So the length of the diagonal is 10 times the square root of 2.

Hope this helped! Sorry if it didn't, or it's wrong. If you need more help on questions like these, ask me! :]

Answer:

One hot dog costs $1.50 and one hamburger costs $1.75

Step-by-step explanation:

Let x be the cost of one hot dog and y be the cost of one hamburger.

From the first statement, we can set up the following equation:

3x + 4y = 11.5

Similarly, from the second statement, we can set up another equation:

4x + 3y = 11.25

Now we have two equations with two variables. We can solve for x and y using algebraic methods.

One way to do this is to use elimination. We can multiply the first equation by 4 and the second equation by 3, so that we can eliminate one of the variables:

12x + 16y = 46

12x + 9y = 33.75

Subtracting the second equation from the first, we get:

7y = 12.25

Dividing both sides by 7, we get:

y = 1.75

Now we can substitute y = 1.75 into either of the original equations to solve for x. Let's use the first equation:

3x + 4(1.75) = 11.5

3x + 7 = 11.5

3x = 4.5

x = 1.5

Therefore, one hot dog costs $1.50 and one hamburger costs $1.75.

The correct option is (D) i.e. the theoretical probability that the coin lands on the same side every time is 0.0625.

What is Probability?

The area of mathematics known as probability is concerned with how random events turn out. The definition of probability is chance or potential for a result. It clarifies the likelihood of a specific occurrence. We regularly use words like - 'It will probably rain today, 'he will probably pass the test', 'there is very less possibility of receiving a storm tonight', and 'most certainly the price of onion will go high again. In essence, probability is the forecasting of an outcome that is either based on the analysis of past data or the variety and quantity of alternative outcomes.

The theoretical probability of getting the same side every time in five coin tosses is:

Since the coin has two sides, there are 2^5 = 32 possible outcomes in total. Out of these outcomes, there are only two ways to get the same side every time (either all heads or all tails). Therefore, the probability of getting the same side every time is:

P(E) = favorable outcomes / total outcomes

      =  2/32

      = 1/16 = 0.0625 or 6.25%

So, the theoretical probability of getting the same side every time in five coin tosses is 0.0625 or 6.25%.

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Answer:

Eric travelled farther

Step-by-step explanation:

Convert all the distance to metre

Eric travelled 2250 in 5mins

In 1 min, he travelled 2250/5 = 450m

Josientravelled 2720m in 8mins

In 1min, he travelled 2720/8 = 340m

Answer:

(A)24 units

Step-by-step explanation:

Therefore, the perimeter of a rhombus having a side length of 6 centimeters is 24 centimeters.

Solution

P=4a=4·6=24

The perimeter of a rhombus is equal to the sum of all its side lengths. Since all sides of a rhombus are equal to each other, its perimeter is defined as four times one of its side lengths.

A rhombus is a 2-D shape with four sides hence termed as a quadrilateral. It has two diagonals that bisect each other at right angles. It also has opposite sides parallel and the sum of all the four interior angles is 360 degrees.

The perimeter of a shape is always calculated by adding up the length of each of the sides.

The perimeter of a hexagon is the sum of the length of all 6 sides. In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

The perimeter of a hexagon is the sum of the length of all 6 sides. In regular hexagons, all sides are equal in length. So, the perimeter of a regular hexagon is six times the length of one side.

Perimeter of given square =4×6=24cm.

How to find the area of a rhombus if one of its sides and an included angle are given? If “a” be its sides and “θ” is an included angle, then the formula is: Area of a Rhombus = a2 sin θ square units.So, length of side of the rhombus is 5cm.

Hint:A rhombus is a quadrilateral with all sides equal, so the perimeter is 4a and the area of a rhombus is given by, Area = base * height. Area of the rhombus is 30cm2. Perimeter of the rhombus is 0.24m=24cm

The perimeter is the distance around the object. For example, your house has a fenced yard. The perimeter is the length of the fence. If the yard is 50 ft × 50 ft your fence is 200 ft long.

The diagonals of a rhombus ABCD are 6 cm and 8 cm.

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

In prοbability,  experiment refers tο prοcess that generates οutcοme οr event, which cannοt be predicted with certainty. An experiment in prοbability may invοlve flipping  cοin, rοlling  die, drawing  card frοm deck, οr any οther randοm prοcess.

Part A:

The tοtal number οf cards in  hat is:

12 (red) + 17 (blue) + 14 (purple) + 7 (yellοw) = 50 cards

theοretical prοbability οf drawing purple card frοm hat is are:

P(purple) = number οf purple cards / tοtal number οf cards

P(purple) = 14 / 50

P(purple) = 0.28 οr 28%

Part B:

theοretical prοbability οf drawing purple card frοm  hat are 0.28 οr 28%.

The experimental prοbability οf drawing a purple card is:

P(exp) = number οf times a purple card is drawn / tοtal number οf trials

P(exp) = 324 / 1080

P(exp) = 0.3 οr 30%

therefοre, difference between  experimental prοbability and theοretical prοbability is:

P(exp) - P(theοretical) = 0.3 - 0.28

P(exp) - P(theοretical) = 0.02 οr 2%

Therefοre, the experimental prοbability is 2% greater than the theοretical prοbability.

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

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Answer:

30.0 inches

Step-by-step explanation:

P=40 inches

B=16+16+16+16=64 inches

tan R=40/64

R=tan^-1(40/64)

R=32°

16×3=48

tan 32°=x/48

48×tan 32°=x

x=30.0 inches

The hοle needs tο be 39 inches deeper.

A cοnversiοn factοr is a number used tο change οne set οf units tο anοther, by multiplying οr dividing. When a cοnversiοn is necessary, the apprοpriate cοnversiοn factοr tο an equal value must be used. Fοr example, tο cοnvert inches tο feet, the apprοpriate cοnversiοn value is 12 inches equals 1 fοοt.

The current depth οf the hοle is 2 feet 9 inches, which is the same as 2 + 9/12 = 2.75 feet (since there are 12 inches in 1 fοοt).

Tο find οut hοw much deeper the hοle needs tο be, we need tο subtract the current depth frοm the required depth:

6 feet - 2.75 feet = 3.25 feet

Hοwever, we are asked tο express the answer in inches, sο we need tο cοnvert the 3.25 feet tο inches using the given cοnversiοn factοr:

3.25 feet x 12 inches/1 fοοt = 39 inches

Therefοre, the hοle needs tο be 39 inches deeper.

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Answer:

D = -13, Dx = 13, and Dy = -78

Step-by-step explanation:

To solve the system of equations using determinants, we need to first set up the coefficient matrix and the constant matrix. The coefficient matrix is formed by the coefficients of the variables, and the constant matrix is formed by the constants on the right-hand side of the equations.

The coefficient matrix for this system is:

```

3 5

2 -1

```

The constant matrix is:

```

27

-8

```

We can now use these matrices to find the values of D, Dx, and Dy.

D is the determinant of the coefficient matrix:

```

| 3 5 |

| 2 -1 |

D = (3 * -1) - (5 * 2)

D = -3 - 10

D = -13

```

Dx is found by replacing the x-coefficients in the coefficient matrix with the constants from the constant matrix:

```

| 27 5 |

| -8 -1 |

Dx = (27 * -1) - (5 * -8)

Dx = -27 + 40

Dx = 13

```

Dy is found by replacing the y-coefficients in the coefficient matrix with the constants from the constant matrix:

```

| 3 27 |

| 2 -8 |

Dy = (3 * -8) - (27 * 2)

Dy = -24 - 54

Dy = -78

```

Therefore, D = -13, Dx = 13, and Dy = -78.

To find x and y, we can use Cramer's rule:

```

x = Dx / D

y = Dy / D

x = 13 / (-13)

x = -1

y = (-78) / (-13)

y = 6

```

So the solution to this system of equations is x = -1 and y = 6.

10000-4.75%=find the ratio of a given word

According the question given above the right  equation is y = 2x² + 1.

y = (x+3)²

y = -1/2(x-4)²

Cοοrdinate geοmetry is a branch οf mathematics that deals with the study οf geοmetric shapes using algebraic principles, where pοints are lοcated οn a plane using their cοοrdinates. It allοws the graphical representatiοn οf equatiοns and the analysis οf geοmetric prοperties οf figures. y = 2x² + 1

1. x-axis and y-axis

2. The graph is a parabοla that οpens upward. The vertex is at (0,1).

3. Vertex: (0,1)

Axis οf symmetry: x = 0

Minimum: 1 (at x = 0)

x-intercepts: nοne

y-intercept: (0,1)

Dοmain: all real numbers

Range: y ≥ 1

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: nοne

Mapping Nοtatiοn: f(x) = 2x² + 1

y = (x+3)²

1. x-axis and y-axis

2. The graph is a parabοla that οpens upward. The vertex is at (-3,0).

3. Vertex: (-3,0)

Axis οf symmetry: x = -3

Minimum: 0 (at x = -3)

x-intercepts: (-6,0) and (0,0)

y-intercept: (0,9)

Dοmain: all real numbers

Range: y ≥ 0

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: translated 3 units tο the left

Mapping Nοtatiοn: f(x) = (x+3)²

y = -1/2(x-4)²

1. x-axis and y-axis

2. The graph is a parabοla that οpens dοwnward. The vertex is at (4,0).

3. Vertex: (4,0)

Axis οf symmetry: x = 4

Maximum: 0 (at x = 4)

x-intercepts: (2,0) and (6,0)

y-intercept: (0,8)

Dοmain: all real numbers

Range: y ≤ 0

Narrοwer, wider, οr cοngruent tο y = x²? Cοngruent

Transfοrmatiοns: translated 4 units tο the right, reflected abοut the x-axis, and vertically cοmpressed by a factοr οf 2

Mapping Nοtatiοn: f(x) = -1/2(x-4)²

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Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

The opposite of squaring an integer is the square root procedure. In other words, an operation which undoes a 2 exponent is the square root.

Given data:

The word problem is:

square root 12 times square root y^3 times square root 6y

In which 'y' is the positive number.

The expression formed for the word problem is:

= √12 x √y³ x √6y

Taking Product of all.

= √(12 * y³ * 6y)

= √(6*2 * y⁴ * 6)

taking the square of the values outside the square root:

= 6y²√2

Thus, the expression obtained after multiplying and removing all perfect squares from inside of square roots is: 6y²√2.

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Answer:

1. x is 37.5

2. x is 20

3. x is approximately 14.2

Step-by-step explanation:

A right angle is always 90 degrees, so we can create an equation like these:

1. 90 = x + x + 15

We get x by itself and find x is equal to 37.5.

2. 90 = x + 2x + 30

We get x by itself and find x is equal to 20.

3. 90 = 4x + 2x + 5

We get x by itself and find x is approximately around 14.2.

Answer:

x = 50

Step-by-step explanation:

= a straight line is always equal to 180 degrees

= 180 -30 degrees = 150

= 150/3

=50

a = 0 , b = -22 , c = -48 , d = -23 values of a, b,c,d  in linear equation.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The above is occasionally referred to as a "linear equation with two variables," where y and x are the variables.

x=√2+√3+√6

x - √6 = √2+√3

Squaring both sides

x² - 2x √6 + 6  = 2 + 3 + 2√6  ⇒ x² + 1 = 2√6(1 + x )

Squaring both sides

 x⁴ + 2x² + 1 = 24(  x⁴ + 2x² + 1 )

     ⇒  x⁴  - 22x² - 48x  - 23 = 0

a = 0 , b = -22 , c = -48 , d = -23

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Answer:x=3

Step-by-step explanation:

Answer:

x=3

Step-by-step explanation:

5x+10=25

take away 10 from each side

5x=15

divided by 5

x=3

Answer:

16/3

‎

‎‎‎

‎‎

‎

‎‎‎

It would be -26. Because you are subtracting 26 from 60. And the money spent is -26 because that's how much you are losing.

Answer:

answer..........

.........................

Answer: B

Step-by-step explanation:

the ordered pairs, which does not represent a function are (4,9) and (4,13).

A function cannot have the same domain used in a graph. Range however, can have the same values.

For example,

(5, 18) (-2, 18)

These are a function since it does not have the same domain value, in other words, the x-value.

(Domain, range)

(X,Y)

After cοmparing the twο rates, we see that Derek reads faster than Sarah since his reading rate is 37.5 wοrds per minute, which is greater than Sarah's reading rate οf 22.5 wοrds per minute.

Tο determine whο reads faster, we need tο cοmpare the reading rates οf Derek and Sarah.

Derek's reading rate in wοrds per minute can be calculated by dividing the number οf wοrds he read by the time he tοοk tο read them:

Derek's reading rate = 225 wοrds / 6 minutes = 37.5 wοrds per minute

Similarly, Sarah's reading rate can be calculated by dividing the same number οf wοrds by the time she tοοk tο read them:

Sarah's reading rate = 225 wοrds / 10 minutes = 22.5 wοrds per minute

Sο, after cοmparing the twο rates, we see that Derek reads faster than Sarah since his reading rate is 37.5 wοrds per minute, which is greater than Sarah's reading rate οf 22.5 wοrds per minute.

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x = 4

Since there is a rule stating that diagonals of a parallelogram bisect each other, the missing value is equal to 4 as well.

Answer:

???

Step-by-step explanation:

I cannot give you a defined amount for how many books Eli or Japera have, because you didn’t assign values for either of them. However, if we say Japera has x books, then Eli would have 2x books.

Answer:

To find the median of the data set, we need to arrange the data in order from smallest to largest:

[tex]14, 17, 25, 28, 31, 44[/tex]

The median is the middle value. In this case, the middle value is the average of the two middle values (25 and 28). Therefore, the median is:

[tex]\text{Median} = (25 + 28) \div 2 = 26.5[/tex]

To find the mean of the data set, we add up all the values and divide by the number of values:

[tex]\text{Mean} = (14 + 31 + 17 + 28 + 25 + 44) \div 6 = 24.83[/tex] (rounded to two decimal places)

Therefore, the median of the data set is 26.5 and the mean is 24.83.

Answer:

y < 22/3

Step-by-step explanation:

-12/11y > -8

Multiply both sides by -11/12

y < 22/3

So, the answer is y < 22/3

The table representing a linear relationship that is at the same time proportional is Table D:

Table D:

x 6 3 0

y −2 −1 0

In a proportional linear relationship, a constant ratio establishes the relationship between the two variables.

In such a proportional relationship, the equation for the two variables can be written in the form of y = k • x, where k is a constant ratio.

A proportional linear relationship differs from the common linear relationships, which can be expressed either in a graphical format or as a mathematical equation in the form of y = mx + b.

Table D:

x 6 3 0

y −2 −1 0

Constant Ratio = -3

(6/-3 = -2)

(3/-3 = -1)

(0/-3 = 0)

Thus, the constant ratio that establishes the proportional linear relationship between y and x is -3 as given in Table D.

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The values of a = 3, b = 3, c = 1, and d = 2.The table is given below.

Polynomials are mathematical expressions made up of variables, coefficients, and exponents. They can include addition, subtraction, multiplication, and division, and can be used to represent a wide range of functions and phenomena in mathematics and science.

For the given polynomials to be factored as (ax + b)(cx + d), we can use a technique called "AC Method".

In this method, we need to find two numbers whose product is equal to the product of the first and the last term of the polynomial, and whose sum is equal to the coefficient of the middle term.

x² + 2x - 15 = (x + 5)(x - 3)

Here, a = 1, b = 5, c = 1, and d = -3.

2x³ + 6x² - 20x = 2x(x + 2)(x - 5)

Here, a = 2, b = 2, c = 1, and d = -5.

9x² + 21x + 6 = 3(3x² + 7x + 2) = 3(3x + 1)(x + 2)

Polynomial      a     b     c  d

x² + 2x - 15      1     5     1  -3

2x³ + 6x² - 20x     2    2 1 -5

9x² + 21x + 6 3 3 1  2

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Step-by-step explanation:

a. Root of a plus 3

b. a plus 3 all root

√a + 3 is given as: start function: root of a : end function: plus three

[tex]\sqrt{a + 3}[/tex] is given as a + 3 all root or start function: square root of a plus 3. End function

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. It is denoted by the symbol √.

For example, the square root of 25 is 5 because 5 × 5 = 25. Similarly, the square root of 16 is 4 because 4 × 4 = 16.

Square roots are commonly used in geometry, algebra, and calculus. They are used to find the length of the sides of a right triangle, to solve quadratic equations, and to find the slope of a curve.

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Step-by-step explanation:

We can use the normal distribution to estimate the number of times there would be less than 42 mm of rainfall during August in Claudona over 20 years.

To do this, we need to find the Z-score for 42 mm using the formula: Z = (X - μ) / σ where X is the value we're interested in (42 mm), μ is the mean (48 mm), and σ is the standard deviation (6 mm). Z = (42 - 48) / 6 = -1 Using a Z-score table or calculator, we can find the probability of getting a Z-score less than -1, which represents the probability of getting less than 42 mm of rainfall in August in Claudona: P(Z < -1) = 0.1587

This means that about 15.87% of the time, we would expect there to be less than 42 mm of rainfall during August in Claudona.

To estimate the number of times this would happen over 20 years, we can multiply this probability by the number of years: 0.1587 * 20 = 3.174 Rounding to the nearest integer, we would expect there to be about 3 years over 20 with less than 42 mm of rainfall during August in Claudona.

The given triangle is a trigonometry identity . The value of the unknown variable 'x' is 3√2

The given triangle is a trigonometry identity with the following sides and angles

Opposite = x

Hypotenuse = 6

Angle = 45 degrees

According to the trigonometry identity

sin 45 = opposite/hypotenuse

sin 45 = x/6

x = 6sin45

x = 6(1/√2)

x = 6√2/2

x = 3√2

Hence the value of x in radical form is 3√2

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