Rectangles S and T are similar. If the area of rectangle S is 150, what is the area of rectangle T?

The equivalent fractions are A = { 100 / 20 , 150 / 30 }

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fractions be represented as A

Now , the value of A is

A = 50/10

On simplifying , the fraction , we get

The value of A = 5/1

Now , the equivalent fractions of A are

Multiply the numerator and denominator of the fraction by 2 , we get

A = 100/20

Multiply the numerator and denominator of the fraction by 3 , we get

A = 150/30

Hence , the equivalent fractions are 5/1 , 100/20 and 150/30

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Answer: 480

Step-by-step explanation:

20 times 24 is 480

In the case of 9 x 9, using the Commutative Property, we can rewrite it as 9 x 9 = 9 x 9. The product of these two factors is 81, which is the same regardless of the order of the factors.

The Commutative Property of Multiplication is one of the fundamental properties of arithmetic. It states that the order of the factors in a multiplication expression does not affect the product. In other words, you can multiply two numbers in any order and still get the same result.

For example, if you have the multiplication expression 2 x 5, you can switch the order of the factors and write it as 5 x 2, and the result is still the same:

2 x 5 = 5 x 2 = 10

Similarly, for the expression 3 x 4, you can switch the order of the factors and write it as 4 x 3, and the result is still the same:

3 x 4 = 4 x 3 = 12

The Commutative Property is a fundamental property of multiplication, and it is used in many mathematical operations, including simplifying expressions, solving equations, and more.

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Answer:

Step-by-step explanation:

here are the steps to solve this problem:

Draw a line segment MO and a point N on it, such that N is between M and O. Label the length of MN as 2x, the length of NO as x-2, and the length of MO as 2x-9.

Write the equation that relates the lengths of MN, NO, and MO. This equation is MO = MN + NO, since MO is the sum of MN and NO.

Substitute the given expressions for MN, NO, and MO into the equation from step 2. We get:

2x-9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x-9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

-x = 7

Divide both sides of the equation by -1 to isolate x. We get:

x = -7

Check the solution by plugging it back into the original equation. We get:

2(-7)-9 = -23

2(-7) + (x-2) = -16

The two sides of the equation are not equal, so x = -7 is not a valid solution.

Recheck the original problem to see if there was an error in the given values, or if the problem was written incorrectly. We notice that the values of MN, NO, and MO are all positive, so x cannot be negative. Therefore, we assume that there was an error in the given solution for MO, and that it should be 2x+9 instead of 2x-9.

Rewrite the equation from step 2 with the corrected value for MO. We get:

2x+9 = 2x + (x-2)

Simplify the equation by combining like terms. We get:

2x+9 = 3x-2

Bring all the x terms to one side of the equation and all the constant terms to the other side. We get:

x = 11

Check the solution by plugging it back into the original equation. We get:

2(11) + (x-2) = 22 + 9 = 31

2(11) + (11-2) = 20 + 9 = 29

The two sides of the equation are not equal, so x = 11 is not a valid solution.

Recheck the original problem to make sure there are no other errors. We notice that the length of MN is given as 2x, but we haven't yet found the value of x. This means we need to solve the equation from step 11 for the value of 2x:

2x = 2(11) = 22

Therefore, the numerical length of MN is 22.

At the Culver City Trampoline Park, customers leave their shoes in cubbies shaped like rectangular prisms while they jump. Each cubby is 11 inches deep, 6 inches tall, and has a volume of 396 cubic inches. So, each cubby is 6 inch wide.

Three-dimensional space is quantified by volume. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or American customary units. 

Every object in three dimensions takes up that space. The volume of that kind of area is the one being measured. The area covered by such an object's boundaries in three-dimensional space generally said to as the volume. Other term for it would be an object's capacity.

Given that,

Each cubby is 11 inches deep,

6 inches tall, and

has a volume of 396 cubic inches.

Volume of rectangular prism = L × W × h

or, 396 = 11 × W × 6

or, W = 396 / 66

or, W = 6 inch

Thus, each cubby is 6 inch wide.

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a) The linear function is defined as follows: y = 1 - 0.2x.

b) The slope and the intercepts are interpreted as follows:

c) The battery power is at 75% after 1.25 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:

m = -1/5

m = -0.2.

Hence the function is:

y = -0.2x + 1.

The battery power is of 75% = 0.75 when y = 0.75, as follows:

0.75 = -0.2x + 1

0.2x = 0.25

x = 0.25/0.2

x = 1.25 hours.

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Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

A triangle is a closed geometric figure that is formed by connecting three straight line segments called sides. These sides meet at three points called vertices. Triangles are one of the simplest and most fundamental shapes in geometry and can be found in many natural and man-made objects.

Triangles can be classified into different types based on their sides and angles.

By sides:

Equilateral triangle: all three sides are equal in length.

Isosceles triangle: two sides are equal in length.

Scalene triangle: all three sides are different in length.

By angles:

Acute triangle: all three angles are acute (less than 90 degrees).

Right triangle: one angle is a right angle (exactly 90 degrees).

Obtuse triangle: one angle is an obtuse angle (greater than 90 degrees).

Triangles have many properties and are used in various fields such as architecture, engineering, physics, and mathematics. They are also commonly used in trigonometry to solve problems involving angles and distances.

We can use the Pythagorean theorem to find the value of z:

[tex]AC^2 = AD^2 + DC^2[/tex]

Since BD is perpendicular to AC, we know that DC = BC. We can also use the fact that AB and BD are altitudes of triangle ABC to find the area of the triangle in two different ways:

Area of triangle ABC = 1/2 * AB * BD = 1/2 * AC * AD

Substituting the given values, we get:

1/2 * 10 * BD = 1/2 * z * 8

Simplifying this equation, we get:

BD = 4z/5

Substituting this expression for BD into the area formula, we get:b

1/2 * 10 * (4z/5) = 1/2 * z * 8

Simplifying and solving for z, we get:

20z/25 = 4z

16z = 100

z = 6.25

Therefore, the value of z is 6.25.

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The correct calculation of the average is given as 0.2546

The average is a measure of central tendency that represents the typical value in a set of data. It is also known as the arithmetic mean and is calculated by adding up all the values in a set of data and then dividing the sum by the total number of values in the set.

The calculation of the average would be gotten by the number of hits / by the total bats that he had

This is given as

151 / 593

= 0.2546

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The equation and solution to find the length of mis teak wood piece is x/3=8 and 24;

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas;

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely;

We are given:

The length of oak wood is 8inches

Teak wood/3= oak wood

So,

Let the length of teak wood be x;

Now,

x/3=8

x=3x8

x=24

Therefore, by algebra the length of teak wood will be 24;

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The composite function (fg)(0) has a value of -4

From the question, we have the following parameters that can be used in our computation:

The graph

Also, we have

(fg)(0)

The notation (fg)(x) represents the composite function of two functions f(x) and g(x), where one function is applied to the result of the other function.

The formula for (fg)(x) is:

(fg)(x) = f(g(x))

So, we have

(fg)(0) = f(g(0))

This gives

(fg)(0) = f(3)

(fg)(0) = -4

Hence, the value is -4

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The area of the ENTIRE rectangle would be: Area = Base * Height

I think you can see that the triangle is 1/2 of the rectangle. so the

    The area of the right triangle would be: Area = 1/2 * base * height

if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

If the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

Triangle is a three-sided geometric shape that has three angles and three sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. A triangle can be classified as either right, obtuse, or acute depending on the measure of its angles. Right triangles have one right angle, obtuse triangles have one obtuse angle, and acute triangles have three acute angles.

The area of a right triangle can be found by using the formula A=1/2bh, where b is the base of the triangle and h is the height. In this example, the base, b, is 6 inches. To find the height, h, we can solve the equation for h: h = 2A/b, where A is the area of the triangle.

Therefore, if we know the area of the triangle, A, we can find the height, h, of the triangle by plugging in the values and solving for h. For example, if the area of the triangle is 18 square inches, then h = 2(18)/6 = 6 inches.

The area of a right triangle can be found by using the formula A=1/2bh and plugging in the known values of b and h. In this example, if the base, b, is 6 inches, and the area, A, is 18 square inches, then the height, h, of the triangle is 6 inches.

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The two numbers are 10 and 12

A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.

The two numbers that have their highest factor as 2 are 4 and 6, 6 and 8, 8 and 10 and 10 and 12.

The numbers above which have least common multiple of 60 are

multiple of 4: 4,8,12,16,20,24,28,32,36,40,44,48,52,56,60

multiple of 6; 6,12,18,24,30,36,42,48,54,60

multiple in of 10: 10,20,30,40,50,60

multiple of 12: 12,24,36,48,60.

The least common multiple of 6 and 10 is 30

but the least common multiple of 12 and 10 is 60

therefore the two numbers are 12 and 10.

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a. The exact value of tan(cos⁻¹(-16/19)) in simplified radical form is -3/16.

b. sin⁻¹(tan(2π/3)) is undefined and does not have an answer.

a. We know that cos(cos⁻¹(x)) = x and hence cos(cos⁻¹(-16/19)) = -16/19.

Let θ = cos⁻¹(-16/19), then we have

cos(θ) = -16/19 and

sin(θ) = √(1 - cos²(θ))

= √(1 - (16/19)²)

= 3/19 (using the Pythagorean identity).

Now, we can use the identity tan(θ) = sin(θ)/cos(θ) to find the value of tan(cos⁻¹(-16/19)):

tan(cos⁻¹(-16/19))

= sin(θ)/cos(θ)

= (3/19) / (-16/19)

= -3/16.

Therefore, the exact value of tan(cos⁻¹(-16/19)) is -3/16 in simplified radical form.

b. The range of the function tan(x) is (-∞, ∞), which means that it can take any value. However, the range of the function sin⁻¹(x) is [-π/2, π/2], which means that it can only take values between -π/2 and π/2. In particular, sin⁻¹(x) is not defined for |x| > 1, since there is no angle whose sine is greater than 1 or less than -1.

Let's consider sin⁻¹(tan(2π/3)). We know that tan(2π/3) is undefined, since the tangent function has vertical asymptotes at odd multiples of π/2 (including 2π/3).

Therefore, sin⁻¹(tan(2π/3)) is also undefined and does not have an answer.

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Answer:

To determine how many loaves will not meet quality standards on Tuesday, we need to count the number of integers in the sample that are between 1 and 50, inclusive. From the given sample, we can see that there are 2 integers that fall between 1 and 50: 47 and 4. Therefore, we can predict that 2 loaves will not meet quality standards on Tuesday.

To calculate the difference between the number of sub-standard loaves produced on Monday and the number predicted to be sub-standard on Tuesday, we need to subtract the number of sub-standard loaves on Monday from the number predicted for Tuesday.

Number of sub-standard loaves on Monday = 50

Number predicted to be sub-standard on Tuesday = 2

Difference = 2 - 50 = -48

The difference is -48, which means that there were 48 fewer sub-standard loaves predicted on Tuesday than the number produced on Monday.

The maximum height of the ball from the maximum compression of the spring is 13.39 m

Maximum height is the highest displacement of the object.

Since a spring of spring constant 504 N/m is compressed 7.66 cm by a ball of mass 11.2 g. If the ball is shot straight into the air, we desire the maximum height of the ball.

Using the law of conservation of energy, the elastic potential energy lost by the spring, E equals the gravitational potential energy gained by the ball, E'

So, E = E'

1/2kx² = mgh where

Making h subject of the formula, we have that

h = kx²/2mg

So, substituting the values of the variables into the equation, we have that

h = kx²/2mg

h = 504 N/m × (0.0766 m)²/(2 × 0.0112 kg × 9.8 m/s²)

= 504 N/m × 0.00586756 m²/(2 × 0.0112 kg × 9.8 m/s²)

= 2.95725024 Nm/(0.21952 kgm/s²)

= 13.47 m

So, the maximum height from the springs compression is H = h - x = 13.47 - 0.0766 m

= 13.3934 m

≅ 13.39 m

So, the maximum height is 13.39 m

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Answer:

The solution is 1/8

Step-by-step explanation:

[tex] \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{x - 16} \\ \\ \sf {a}^{2} - {b}^{2} = (a - b) (a + b)\\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \sqrt{x} - 4 }{( \sqrt{x} - 4) \times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{ \cancel{\sqrt{x} - 4} }{(\cancel{ \sqrt{x} - 4) }\times ( \sqrt{x} + 4)} \\ \\ \sf \displaystyle \lim_{x \to 16}  \sf \frac{1}{ \sqrt{x} + 4} \\ \\ \sf \frac{1}{ \sqrt{16} + 4} \\ \\ \sf \frac{1}{ 4 + 4} \\ \\ \sf \frac{1}{8} [/tex]

Answer:

help with what?

Step-by-step explanation:

you did not ask a question?

good luck....

Answer: 48%

Step-by-step explanation:

Answer:

Step-by-step explanation:

cos(2[tex]\sqrt{23}[/tex]/24)=β

0.9999=β

1=β

Answer:

graph linked

Step-by-step explanation:

Answer:

x= −1088

Step-by-step explanation:

Answer:

-1088

Step-by-step explanation:

-17      =    x/64

*64           *64

-1088 = x

Answer:

Step-by-step explanation:

To solve the equation (-1)/(x-5) = 2/(x+4), we can start by cross-multiplying:

(-1)(x+4) = 2(x-5)

Expanding both sides and simplifying, we get:

-x - 4 = 2x - 10

Bringing all the x terms to one side and all the constant terms to the other, we get:

3x = 6

Dividing both sides by 3, we get:

x = 2

So the solution to the equation is x = 2. However, we need to check if this value of x makes the denominators of the original equation non-zero. Plugging x = 2 into the original equation, we get:

(-1)/(2-5) = 2/(2+4)

Simplifying, we get:

1/3 = 1/3

Since both sides are equal, the solution x = 2 satisfies the original equation. Therefore, the only solution to the equation is x = 2.

Answer: x = 2

Step-by-step explanation:

    [tex]\boldsymbol{\sf{The\:exercise\:is \longmapsto \ \dfrac{-1}{x-5}=\dfrac{2}{x+4} }}[/tex]

We cross multiply.

     -(x + 4) = 2(x - 5)

We apply the multiplicative law of distribution.

       -x -4 = 2(x - 5)

       -x - 4 = 2x - 10

We rearrange the unknown terms to the left side of the equation.

       -x - 2x = -10 + 4  <===Combine as terms===> -3x = -10 + 4

We calculate -10 + 4 = -6.

       -3x = -6

We divide both sides of the equation by the coefficient of the variable.

       [tex]\boldsymbol{\sf{x=\dfrac{-6}{-3} \iff \ x=\dfrac{6}{3} }}[/tex]

      x = 2

The greatest distance, in feet, a person could be from the lamp and be detected is: B. 12 ft

The equation (x+16)² + (y-13)² = 36 describes a circle with center (-16,13) and radius 6. The motion detector on the lamp post can detect motion within this circle.

To find the greatest distance a person could be from the lamp and still be detected, we need to find the diameter of the circle, which is equal to twice the radius. Therefore, the greatest distance a person could be from the lamp and still be detected is 2(6) = 12 feet.

Therefore, the correct answer is B) 12 ft.

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The solution is, the value  of the function when x = -2 is -4.

An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

here, we have,

Given the expression

h(x) = -x^2 +4x

h(-2) = (-2)^2 + 4(-2)

h(-2) = 4  + (-8)

h(-2) = 4 -  8

h(2) = -4

Hence the value of the function when x = -2 is -4.

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Based on the information in the passage, we will most likely expect the following to happen:

C. Elizabeth and Joelle will remain friends despite the sport they play.

The passage being referred to in this question is "Sliding into Home" by Dori Hillestad Butler. It tells the story of two girls named Elizabeth Shaw and Joelle Cunningham who chose different sports but remained determined to be friends despite this.

While Joelle enjoyed playing baseball, Elizabeth was better at Softball. Despite Elizabeth's encouragement for Joelle to play Softball, Joelle insisted on her favorite game but they remained friends regardless.

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The probability of the event between two and five lines, inclusive, are in use is 0.85.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

Given that,

x         0         1         2       3        4         5         6

p(x)   0.12    0.18   0.20  0.20  0.20   0.07   0.03

a) At most three lines are in use

Here we need to find the probability for x≤3.

P(x≤3)=P(x=0)+P(x=1)+P(x=2)+P(x=3)

= 0.12+0.18+0.20+0.20

= 0.70

b) Fewer than three lines are in use

Here we need to find the probability for x<3.

P(x<3)=P(x=0)+P(x=1)+P(x=2)

= 0.12+0.18+0.20

= 0.50

c) At least three lines are in use

Here we need to find the probability for x≥3.

P(x≥3)=P(x=3)+P(x=4)+P(x=5)+P(x=6)

= 0.20+0.20+0.07+0.03

= 0.50

d) Between two and five lines, inclusive, are in use

Here we need to find the probability for 2≤x≤5.

P(2≤x≤5)= P(x=2)+P(x=3)+P(x=4)+P(x=5)

= 0.18+0.20+0.20+0.20+0.07

= 0.85

Therefore, the probability of the event between two and five lines, inclusive, are in use is 0.85.

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A fraction of [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.

If there are 70 vegetables altogether, then there are 10 potatoes.

Fractions are type of numbers which are written in the form p/q, which implies that p parts in a whole of q.

Here p, called the numerator and q, called the denominator, are real numbers.

Some of the values are missing here.

Given that,

Aziz grows vegetables in his garden.

Let the total number of vegetables be x.

Assuming [tex]\frac{1}{2}[/tex] of the vegetables grow underground.

Number of underground vegetables =  [tex]\frac{1}{2}[/tex] x

Assuming,  [tex]\frac{2}{7}[/tex] of these underground vegetables, are potatoes.

Number of potatoes = [tex]\frac{2}{7}[/tex] × ( [tex]\frac{1}{2}[/tex] x ) = [tex]\frac{1}{7}[/tex] x

So, [tex]\frac{1}{7}[/tex] of all the vegetables are potatoes.

If there are 70 vegetables altogether,

Number of potatoes = [tex]\frac{1}{7}[/tex] x =  [tex]\frac{1}{7}[/tex] × 70 = 10

Hence of the total vegetables of 70, 10 are potatoes.

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We kindly invite to see the image attached below to know the representation of the parabola according to its features.

A parabola is the graphic representation of any quadratic equation, that is, a polynomial of the form y = a · x² + b · x + c, where a, b, c are real coefficients. An alternative presentation is the vertex form:

y - k = C · (x - h)²

Where:

The procedure to sketch the parabola according to its features is described below:

Step 1 - Determine the y-intercept:

y = 6 · 0² - 17 · 0 + 12

y = 12

Step 2 - Determine the x-intercepts.

6 · x² - 17 · x + 12 = 0

6 · [x² - (17 / 6) · x + 2] = 0

6 · (x - 3 / 2) · (x - 4 / 3) = 0

x = 3 / 2 or x = 4 / 3

Step 3 - Determine the coordinates of the vertex:

y = 6 · x² - 17 · x + 12

y = 6 · [x² - (17 / 6) · x + 2]

y + 6 · (1 / 144) = 6 · [x² - (17 / 6) · x + 2 + 1 / 144]

y + 1 / 24 = 6 · [x² - (17 / 6) · x + 289 / 144]

y + 1 / 24 = 6 · (x - 17 / 12)²

(h, k) = (17 / 12, - 1 / 24)

Steps 4 & 5 - Add the points on Cartesian plane and match the resulting curve.

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Answer:

y=2x-10

Step-by-step explanation:

since the lines are parallel, then their gradients are equal, that to say both lines have the gradient of 2. The following step is to work out the value of c using the equation y= mx+c. Then substitute the values of given points and it will be 2=2(6)+c, and c=-10

then you find an equation

Explanation:

The line y = 2x+4 has the slope 2. Compare that equation to y = mx+b

Parallel lines have the same slope.

The answer will be of the form y = 2x+b, where the b value will be something other than 4. Otherwise, we'll end up with the same exact equation.

To find this new b value, we plug in x = 6 and y = 2. These values are from the point (6,2).

Let's solve for b.

y = 2x+b

2 = 2*6+b

2 = 12+b

b = 2-12

b = -10

We go from y = 2x+b to y = 2x-10 as the final answer.

You can use a tool like GeoGebra to confirm the answer is correct.

The x and y values are x=5 and y= -2

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

y=4x-22 ----(1)

2x+3y=4------(2)

Substitute (1) into (2)

=> 2x+3(4x-22)=4

=> 2x+12x-66 = 4

=> 14x = 4+66

=> 14x = 70

=> x=70/14 = 5

(1) => y=4*5-22 = 20 - 22 = -2

So, the x and y values are x=5 and y= -2

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