Alan bought 4 pounds of red apples and g pounds of green apples. Write an expression that shows how many pounds of apples Alan bought in all.

12m² is the area of the table top in rectangle .

What is a rectangle, exactly?

The parallel sides of a rectangle are equal to one another, and each of its four vertices is 90 degrees, making it a form of quadrilateral. As a result, it is sometimes referred to as an equiangular quadrilateral.

                               The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

area = length x width

We know that the width is 2 meters, and since the length is three times the width, the length would be 6 meters.

Therefore, the area of the table = 2 x 6 = 12 m2.

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Answer:

175 calories

Step-by-step explanation:

75 / 6 = 12.5

12.5 x 14 = 175

x = 12.5 x 14

The inequality best describes the number of paperback books 'p' and the number of hardback books 'h' that can be purchased for $45.00 or less

is 5p + 9h ≤ 45.  

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, Two types of books paperbacks are represented by 'p', and hardbacks are represented by 'h'.

Also, we can only buy two types of books for $45 or less.

Therefore, The inequality representing the context is,

5p + 9h ≤ 45.  (As the cost van be $45 or less not only less)

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The old tree in 54 feet height.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that Two apple trees are going next to each other

the oldest tree has a 36 ft Shadow

the smaller Creek has a 12-in shadow and the tree  is 8 ft tall.

We need to find the height of the older tree.

Let x be the height of older tree.

36/x=8/12

36×12=8x

432=8x

Divide both sides by 8

54=x

Hence, the old tree in 54 feet height.

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(-6,-5), (-2,3), (2,-5), (6,3) are the ordered pairs given on the graph.

In mathematics, a transformation is a process that changes the position, size, or orientation of a geometric shape or figure. The term is used in various branches of mathematics, including geometry, algebra, and calculus.

In geometry, transformations include translations, rotations, reflections, and dilations. A translation involves moving a shape a certain distance in a certain direction, while a rotation involves rotating a shape around a fixed point. A reflection involves flipping a shape over a line, and a dilation involves stretching or shrinking a shape by a given scale factor.

In algebra, transformations can involve changing the form of an equation, such as solving for a variable, transforming an equation into a different coordinate system, or solving a system of equations.

In calculus, transformations can involve changing the form of a function, such as finding its derivative or integral, or transforming a function from one coordinate system to another.

To find the ordered pairs that are on the transformations of the function, we can apply the transformations to the original point (-2, -1) to obtain the points on each transformation.

y = f(x-4) - 4: If we apply the x-4 transformation to the x-coordinate of the original point, we get -2-4 = -6. So, the point is (-6, f(-6) - 4).

y = f(x-4) + 4: The x-coordinate of the point is -6, so the point is (-6, f(-6) + 4).

y = f(x+4) - 4: If we apply the x+4 transformation to the x-coordinate of the original point, we get -2+4 = 2. So, the point is (2, f(2) - 4).

y = f(x+4) + 4: The x-coordinate of the point is 2, so the point is (2, f(2) + 4).

So, the ordered pairs that must be on each of the transformations of f(x) are:

y = f(x-4) - 4: (-6, f(-6) - 4)

y = f(x-4) + 4: (-6, f(-6) + 4)

y = f(x+4) - 4: (2, f(2) - 4)

y = f(x+4) + 4: (2, f(2) + 4)

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After dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).

The basic formula to find the scale factor of a figure is expressed as,

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.

Given that, the scale factor is k= 1/4.

From the given figure, vertices of triangle ABC are

A(0, 4), B(4, 4) and C(-4, -4)

After dilation with the scale factor 1/4, we get

A(0, 4)→1/4 (0, 4) =A'(0, 1)

B(4, 4)→1/4 (4, 4) =B'(1, 1)

C(-4, -4)→1/4 (-4, -4) =C'(-1, -1)

Therefore, after dilation with the scale factor 1/4 is A'(0, 1), B'(1, 1) and C'(-1, -1).

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Answer:

Step-by-step explanation:

Inverse variation functions have the form y = k / x, where k is a constant.

When k > 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k > 0, the hyperbola opens upwards and the two branches of the hyperbola move away from the x-axis as x increases. This means that as x increases, the value of y decreases. When x approaches 0 from the right, y approaches positive infinity, and when x approaches 0 from the left, y approaches negative infinity.

On the other hand, when k < 0, the graph of the inverse variation function is a hyperbola that opens upwards or downwards, depending on the sign of k. When k < 0, the hyperbola opens downwards and the two branches of the hyperbola move toward the x-axis as x increases. This means that as x increases, the value of y increases. When x approaches 0 from the right or left, y approaches negative infinity.

In both cases, the inverse variation function is undefined for x = 0, as division by zero is undefined.

The slope of a straight line that is parallel to the vertical axis is zero.

A slope of zero indicates that the line is flat and has no incline or decline. In a two-variable diagram, this means that there is no relationship between the two variables, as a change in one variable does not affect the value of the other. A line with a slope of zero is a horizontal line, and its equation is of the form y = b, where b is a constant value.

In contrast, a line with an infinite slope (or vertical line) would indicate a perfect correlation between the two variables, such that a change in one variable would result in an infinite change in the other. A line with a finite positive or negative slope would indicate a direct or inverse relationship between the two variables, respectively.

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[tex]-4z+31\geqslant 17z+23\implies 31\geqslant 13z+23\implies 8\geqslant 13z\implies \cfrac{8}{13}\geqslant z[/tex]

Answer:

1,325,000,000 people

Step-by-step explanation:

Million = 1,000,000

Number = 1,324,671,354

The 1st 4 is in the millionth place. 6 > 4 so round 4 up to 5.

Rounded = 1,325,000,000 people

Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.

Deformations are four alternative approaches that can be utilized to change a point, line, or mathematical figure's orientation and/or shape. Both the Pre-Image, who describes the shape of the object there at initial state, and the Photograph, which describes the final state and location of the object following change, are words. Translations, reflection, and dilations are the three types of transformations that can be differentiated. A function can undergo two different types mathematical transformations: vertical (it affects the y-values) and sideways (affects the x-values). Its function's equation is provided below, and it comprises the share the information variables (a, b, h, and k). modifying the log.  observation. even by square root, invert.

given

From the figure RSTU to R'S'T'U' R moved from P(5,2) to P(-3,0), translating 8 units to the left.

Hence, 5-(-3)= 8 = 2-0 = 0.

Down two units.

as well as reflection on the y axis.

Figure RSTU is transformed into Figure R1 S T 1 U1 by moving down two units and reflecting on the y axis.

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The distance the plane traveled from point A to point B is 10,802.1 feet.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Given the height of the plane = 5925 feet

let the distance between A to B be x and distance from B to the position of the plane is y as shown in the image,

angle of elevation from point A = 16°

the angle of elevation from point B = 31°

using trigonometric functions,

tanα = perpendicular/base

base =  x + y

perpendicular = 5925 feet

tan(16) = 5925/(x + y)

x + y = 5925/tan(16)

y  = 5925/tan(16) - x.........(1)

and tan(32) = 5925/y

y = 5925/tan(32)

substitute the value of y from equation 1

5925/tan(16) - x = 5925/tan(32)

5925/tan(16) - 5925/tan(32) = x

x = 10,802.1 feet

Hence the distance covered by points A to B is 10,802.1 feet.

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The graph for the functions is attached.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.

Given

A: graph of y = f(x)

since the graph is in form of a parabola so the function is a quadratic function,

f(x) = ax² + bx + c

the vertex of the graph is at (2, 0)

here in the given curve, the value of the y-axis is 0,

and y = f(x) - 3

in the equation y = f(x) - 3

the shape of the curve will be the same but only change in the vertex of the curve, the new vertex for the curve is (2, -3)

for x = 0 y = -3.

B: given y =g(x)

the graph shows the negative cubic function,

g(x) = -x³

and y = g(x + 4)

= -(x + 4)²

the graph will shift towards 4 units left.

Hence the graph is attached for both equations.

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The product which cost less is Tide which has a cost value of $15.99 with 20% off.

This is referred to as the expenditure required to create and sell products and services, or to acquire assets.

Tide was $15.99 with 20% off which when calculated = 20/100 × $15.99 = $3.198.

Gain was $17.55 with 25% off which when calculated = 25/100 × $17.55 =  $4.388.

Therefore the cheaper alternative will be Tide detergent.

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The full question:

Mrs. Klein went to Target in search of a good deal on laundry detergent (Owen is one messy boy!). She found Tide was $15.99 with 20% off. Gain was $17.55 with 25% off. She has a target red card and gets 5% off her total purchase. which one of the products costs less?

The man can wear 27 different shirt and tie combinations.

Therefore the answer is 27.

The number of different shirt and tie combinations that a man can wear can be calculated by multiplying the number of choices for each item.

Number of choices for shirts = 3

Number of choices for ties = 9

Since the man has three different shirts and nine different ties, and each shirt can be paired with any one of the nine ties, the number of combinations is:

Combinations = 3 * 9 = 27

So the man can wear 27 different shirt and tie combinations.

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Step-by-step explanation:

The frequency of the first harmonic of a string fixed at both ends can be determined using the formula:

f = (1 / 2L) * √(T / μ)

where f is the frequency, L is the length of the string, T is the tension, and μ is the linear mass density. Plugging in the given values:

f = (1 / 2 * L) * √(100 N / 2 kg/m)

= (1 / 2 * L) * √(50 N/m)

So, the frequency of the first harmonic depends on the length of the string, which is not specified in the problem.

Answer:

Step-by-step explanation:

The frequency of the first harmonic of a string fixed at both ends can be calculated using the formula:

f = (1 / 2L) * (T / μ)^(1/2)

where:
f = frequency
L = length of the string
T = tension
μ = linear density of the string

Plugging in the values:
f = (1 / 2 * L) * (100 N / 2 kg/m)^(1/2)
f = (1 / 2L) * (10 N/kg)^(1/2)

We don't have the length of the string, L, so we can't calculate the frequency.

The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.

The amount of baking powder per unit of flour is the unit rate for baking powder and flour. The amount of flour in this situation equals 1 2/3 cups. We must change the baking powder measurement to the same unit as the flour measurement in order to calculate the unit rate.

For every 1 2/3 cups of flour, 1/4 teaspoon of baking powder should be used as follows:

1/4 teaspoon / (1 2/3 cups)

By changing the numerator and denominator of the fraction on the right side to a standard unit, such as teaspoons, we may make it simpler. 1 2/3 cups equal 48 teaspoons, so:

1/4 teaspoon / (1 2/3 cups) = 1/4 teaspoon / (48 teaspoons)

The ratio of baking powder to teaspoons is as follows:

1/4 teaspoon / (48 teaspoons) = 1/192 teaspoon per teaspoon

So The ratio of baking powder to flour is 1/192 teaspoon of baking powder for every teaspoon of flour.

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The expression that represents the amount in dollars the salesperson makes, before taxes, would be equal to 7x + 100 = 40.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol that can also be used to indicate the logical syntax's order of operations and other features.

Given that car sales person makes $7.00 per hour plus $100.00 for every car sold.

Therefore, we have,

7x + 100 = 40

The expression that represents the amount in dollars the salesperson makes, 7x + 100 = 40.

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The measure of the angles of the triangles are 90° , 67.380° and 22.620°

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔPQR

Now , the measure of ∠PQR = 90°

The measure of side PR = 13 cm

The measure of side PQ = 5 cm

The measure of side QR = 12 cm

From the law of sines , we get

a / sin A = b / sin B = c / sin C

Substituting the value sin the equation , we get

12 / sin P = 13 / sin 90°

From the trigonometric relations , sin 90° = 1

So , Multiply by sin P on both sides of the equation , we get

sin P = 12/13

Taking inverse on both sides of the equation , we get

sin⁻¹ ( 12/13 ) = 67.380°

Therefore , the measure of ∠QPR = 67.380°

And , the measure of ∠PRQ = 180 - ( 90° + 67.380° )

The measure of ∠PRQ = 22.620°

Hence , the angles of triangles is solved

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The letters in the word MIAMI are rearranged at random so that every possible anagram is equally likely. The probability that it still spells MIAMI is 1/5.

Let us count the total number of ways MIAMI can be arranged regardless of condition.

There are 2 M’s 2 I’s 1 A in word.

Total ways of arrangement will be = 5!/2!2!

​Total ways of arrangement will be = (5 × 4 × 3 × 2!)/2! × 2 × 1

Total ways of arrangement will be = 5 × 2 × 3

Total ways of arrangement will be = 30 ways

Now, ways in which all similar words are together, thus we have to consider 2M's as one unit, similarly 2 I's as a unit, so number of ways will be 3!.

Thus, the probability will be = 3!/30

The probability will be = (3 × 2 × 1)/30

The probability will be = 6/30

The probability will be = 1/5

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Answer:

14√2

Step-by-step explanation:

28/√2

Since you can't have a square root as the denominator of a fraction, we must multiply the denominator and the numerator to get rid of the square root.

Hence,

28 x √2 , √2 x √2

Your problem would now be:

28√2 / 2

Reduce the fraction by canceling out the common factor of 2

ANS = 14√2

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Answer: 40 degrees

Step-by-step explanation:

m/CBA = m/CED

16 + 6x = 48 - 2x; add 2x on both sides and subtract 16 on both

8x = 32; divide 8 on both sides to isolate the x

x = 4

m/CBA = 16+6(4) = 40

the expression 24x - 48 is equivalent to 36x + 12

The label 24x - 48 applies to the expression because it is the same as itself. The value obtained by multiplying 24 by x and then taking 48 out is represented by this expression.

The label "36x + 12" applies to the expression because it is the same as itself. The value generated by multiplying 36 by x and then adding 12 is represented by this expression.

Since the formulations in both situations have distinct coefficients for x and various constant terms, they are not comparable to one another. Since both expressions are equal to one another, the term "neither" does not apply to them.

Therefore, the expression 24x - 48 is equivalent to 36x + 12

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Step 1: Calculate the number of laps the cars have completed. To calculate the number of laps the cars have completed, divide the total time (150 seconds) by the time it takes car A to complete one lap (30 seconds), which gives us a total of 5 laps.

Step 2: Calculate the possible times for car B. To calculate the possible times for car B, we need to find out how many times car B must complete a lap in order to keep up with car A. Since car A takes 30 seconds to complete one lap and the cars have completed 5 laps in 150 seconds, car B must take the same amount of time as car A, i.e. 30 seconds, in order to keep up with car A. Therefore, the possible times for car B are 30, 60, 90, and 120 seconds.

Therefore, the four possible times that car B could take to complete one lap are 30, 60, 90, and 120 seconds.

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Answer:

0.0000000105

Step-by-step explanation:

Simply move the decimal 8 places to the left, since it is a negative exponent.

The area of the figure as a monomial with the sides [tex]p^{2} q^{4}[/tex] and [tex]p^{2} q^{4}[/tex] is [tex]p^{4} q^{8}[/tex].

As per the given data we to express the area of the figure as a monomial.

Figure attached at the end of solution.

A polynomial with only one term is called a monomial. An algebraic expression known as a monomial has only one term but might have more than one variable and a higher degree.

As the sides are equal we use the area of the square formula.

Area of the square formula:

The formula for the area of a square is side × side

Simple multiplication is the answer to the equation.

Area of the given figure:

= [tex]p^{2} q^{4} \times p^{2} q^{4}[/tex]

= [tex]p^{4} q^{8}[/tex]

[tex]p^{4} q^{8}[/tex] is a monomial as it is expressed as a single term.

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Answer:

5

Step-by-step explanation:

The midpoint of AC is (2,0), and the midpoint of BC is (0,2.5). The third vertex of triangle DEC is E, the midpoint of AB, which can be found using the midpoint formula:

E = ( (A_x + B_x) / 2, (A_y + B_y) / 2 )

= ( (0 + 2) / 2, (0 + 5) / 2 )

= (1, 2.5)

So the vertices of triangle DEC are (0, 2.5), (2, 0), and (1, 2.5). The area of triangle DEC is half the area of triangle ABC, which is (4 * 5) / 2 = 10. So the area of triangle DEC is 10 / 2 = 5.

Answer:

$49.59

Step-by-step explanation:

$20.75+$10.59+$18.25=$49.59

The values that are solutions to inequality are -6 and 5.

Options A and D are the correct answer.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

x² + 3x - 4 > 0

Now,

Substituting x = -6, -2, 0, 5

(-6)² + 3(-6) - 4 > 0

36 - 18 - 4 > 0

36 - 22 > 0

14 > 0

True.

x² + 3x - 4 > 0

(-2)² + 3 x (-2) - 4 > 0

4 - 6 - 4 > 0

-6 > 0

This is not true.

x² + 3x - 4 > 0

0 + 3 x 0 - 4 > 0

0 + 0 - 4 > 0

-4 > 0

This is not true.

x² + 3x - 4 > 0

5² + 3 x 5 - 4 > 0

25 + 15 - 4 > 0

40 - 4 > 0

36 > 0

This is true.

Thus,

-6 and 5 are the solutions to inequality.

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