6 as an addition of two whole number

In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

The volume of the box is calculated by multiplying the length, width, and height together. In this case, the measurements of the box are given as 10cm x 7cm x 4cm, so the volume of the box is:

volume = 10cm x 7cm x 4cm = 280cm³

However, since the measurements are given to the nearest centimeter, there is a slight degree of uncertainty in the exact measurements of the box. To calculate the upper and lower bounds for the volume of the box, we need to consider the possible variations in the measurements.

The upper bound for the volume would be calculated by taking the highest possible measurements for each dimension. So, if the length could be as much as 10.5cm, the width could be as much as 7.5cm and the height could be as much as 4.5cm. Then the upper bound for the volume would be:

Upper bound = 10.5cm x 7.5cm x 4.5cm = 382.125cm³

The lower bound for the volume would be calculated by taking the lowest possible measurements for each dimension. So, if the length could be as little as 9.5cm, the width could be as little as 6.5cm and the height could be as little as 3.5cm. Then the lower bound for the volume would be:

Lower bound = 9.5cm x 6.5cm x 3.5cm = 238.375cm³

In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

And the exact volume is 280cm³

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A formula with just one phrase where the unknown is squared and no terms where the unknown is raised to a power greater than 2 assumed: 3x* + 2kx+ 3= when compared to the quadratic equation ax2 + bx + c = 0, a = 3 b= 2kc= 3.

Given that the equation's roots are genuine and equal D=0 Discriminant, hence D = b2 - 4ac = 0 (2k) - 4.3.3 = 0 4k -36 = 0 4k -36 = 0 4k2 = 36 k'=9 taking square root on both sides k=3 or k=-3 as a result, the roots of the quadratic equation are real and equal for the values of k of 3, and -3.

When a polynomial is evaluated at x=2, the outcome is zero if the polynomial is divisible by (x-2). Therefore, we can substitute x = 2 into the polynomial 2kx-kx-8 and solve for k to find the value of k.

2k(2)^-k(2)-8 = 0 2

k(0.25) - 8 =0\s

k(0.25) = 8\sk=32 = 4

Therefore, k must be equal to 4 for the polynomial 2kx-kx-8 to be divisible by (x-2).

Complete question:

What is the value of K in the polynomial 3x2 2kx 3 The roots of the quadratic equation 3x2 2kx 27 are real and equivalent.

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The value of k when x = (-1/2) is a solution of the quadratic polynomial 3x² + 2kx - 3 = 0 is -2.

To find the value of k, we can substitute the value of x = (-1/2) into the equation and solve for k. So, we have:

3 * (-1/2)² + 2k * (-1/2) - 3 = 0

Expanding the square and substituting the value of x gives us:

-3/4 + k * (-1/2) - 3 = 0

Simplifying the left-hand side of the equation gives us:

k * (-1/2) = 3/4 + 3

Finally, solving for k by dividing both sides by -1/2 and simplifying gives us:

k = -2

Hence, the value of k when x = (-1/2) is a solution of the quadratic equation 3x² + 2kx - 3 = 0 is -2.

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Complete Question:

If x=(− 1/2), is a solution of the quadratic equation 3x^2 +2kx−3=0, find the value of k.?

Using trigonometric identities to decode, the secret message is

2 20-14-25-12 4-19-17 20-14-11-14-25 23-2-21-14-5 23-26-5-7-2-21-14-5! A Nerd who never makes mistakes!

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation.

The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities. Only for right-angle triangles do the trigonometric identities hold true.

All trigonometric identities are built upon the foundation of the six trigonometric ratios. It consists of sine, cosine, tangent, cosecant, secant, and cotangent. These right triangle sides—including the adjacent side, opposite side, and hypotenuse side—are used to define all of these trigonometric ratios. The six trigonometric ratios are the starting point from which all fundamental trigonometric identities are derived.

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Polynomials can be simplified by applying the distributive property to multiply the term outside the parentheses by everything inside the parentheses.

The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is f(x) = anxn + an-1xn-1+an-2xn-2+.....+a1x+a0

An expression made up of variables, constants, and exponents that are joined together via mathematical operations is referred to as a polynomial.

A polynomial must be simplified in two ways: Firstly, combine similarities, and secondly, rewrite the terms in descending order of exponent. A polynomial can be written in standard form. To write any polynomial in standard form, consider the degree of each term. Then, from highest to lowest, left to right, you write each term in order of degree.

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The most are $13.75 if she wants to give all of her friends a gift.

Ryan has an $800 present budget. She had already made up her mind to use $25 to buy her granny a vehicle. The remaining funds will be used to buy gifts for her four friends. She will invest the same sum of money in each present for a buddy.

Okay, so she would have 55 dollars left over after spending 25 of her 80 dollars.

She will distribute her 55 bucks among her four buddies equally now that she has them.

55/4 = 13.75

She could only afford to offer them a maximum of $13.75

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The factors of 50 are the natural numbers that divide the original number, evenly. They are 1,2,5,10,25 and 50.

Herbal numbers are a set of fine integers, frequently used for counting and ordering. They consist of the numbers 1, 2, 3, four, 5, and so on. The set of natural numbers is denoted by way of the symbol N. they are also called counting numbers. natural numbers are used in lots of regions of arithmetic, inclusive of number concepts and combinatorics.

They play a critical function in the look at algorithms and information structures. moreover, herbal numbers are used in lots of areas of physics and engineering, inclusive of the look at vibrations and waves. They may be also used in laptop technological know-how and programming, where they are regularly used to symbolize the number of objects in a listing or array. natural numbers are an essential idea in arithmetic, and they may be used in many areas of technological know-how, technology, and normal existence.

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Answer:

a) Tandeka will be in the middle of a circuit as the time runs out.

b) Tandeka began the last circuit after 7 minutes.

c) Lerato played 2 more games than Tandeka.

Explanation:

a) To determine which player will be in the middle of a circuit when the 12 minutes are up, we need to figure out which player completes the most circuits in 12 minutes. We can use the formula: time available / time per circuit = number of circuits completed. In this case: 12 minutes / 2 minutes per circuit = 6 circuits for Lerato, 12 minutes / 3 minutes per circuit = 4 circuits for Jarrod, 12 minutes / 4 minutes per circuit = 3 circuits for Ian, 12 minutes / 5 minutes per circuit = 2.4 circuits for Tandeka. Tandeka completes 2 full circuits, and starts the third one, hence she will be in the middle of a circuit when the time runs out.

b) To determine when Tandeka began the last circuit, we need to figure out how many minutes were left when she completed the second circuit. We know that Tandeka completes 2 full circuits in 10 minutes (2 x 5 minutes). So, the last circuit starts after 12 minutes - 10 minutes = 2 minutes

c) To determine how many more games Lerato played than Tandeka, we can subtract the number of games Tandeka played from the number of games Lerato played: 6 games - 4 games = 2 games.

Step-by-step explanation:

The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1.

Now, After the reflection, the triangle will be inverted and the measure of angle: A should be equal to A", B should be equal to B", and C should be equal to C".

Now, The dilation factor is less than 1 and greater than 0. So, the reflected triangle should shrink its size.

Therefore, The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

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The 45-45-90 triangle has two congruent sides and one right angle, with each angle measuring 45°. The sides are perpendicular to each other and the length of the hypotenuse is equal to the square root of 2 times the length of a leg.

The 30-60-90 triangle has one right angle and two sides that are proportional. The shortest side is half the length of the hypotenuse and the middle side is equal to the shortest side times the square root of 3. The two acute angles in the triangle measure 30° and 60°, respectively.

In conclusion, both 45-45-90 and 30-60-90 triangles are special right triangles with distinct relationships between their sides and angles.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.

What is system of equations?

A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.

A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.

According to given question, x represents the number

So, The number would be 6x ≥ 8x - 4

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Answer: option 1

Step-by-step explanation: as when you try to simplify you get the values in option 1

Answer: 1

Step-by-step explanation:

The notation "FG)(x" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F". The notation for this is usually represented as "F(G(x))", where "x" is the input for both functions.

The rule for this notation is that the innermost function is applied first. In this case, the function "G" is applied to the input "x" first, and then the output of that function is used as the input for the function "F". The composition of the functions F and G is denoted by the notation F(G(x)) and the result of this notation is a new function obtained by applying F to the result of G on x.

The function "F" is applied to the output of the function "G", meaning that the output of the function "G" is used as the input for the function "F".. For example, if the function "F" is applied to the input "x" first, followed by the function "G", the notation would be represented as "G(F(x))", and the resulting function would be different.

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The statue of the cat is 14 meters tall.

If the ladder is 6 meters tall and it casts a shadow that is 3 meters long and the statue of a cat casts a shadow that is 7 meters long, then we can use the concept of similar triangles to determine the height of the statue of the cat.

The ratio of the height of the ladder to the length of its shadow is 6/3 = 2.

We can also assume that the ratio of the height of the statue of the cat to the length of its shadow is also 2.

so, the height of the statue of the cat can be calculated by:

height of statue of the cat = (2 * shadow length of the statue of the cat) = (2 * 7) = 14 meters

Therefore the statue of the cat is 14 meters tall.

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The equivalent function when the number of bacteria in a lab experiment can be modeled by the function is P(t) = 1161(9)^t

A function illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the situation.

Here, we are given that the number of bacteria in a lab experiment can be modeled by the function given as P(t) = 43(39^(2t + 3)

This will be:

= 43 × 3³ × 3(^2t)

= 1161 × 3²^t.

P(t) = 1161(9)^t

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A horizontal line at y=4 has the following formula: Nothing slopes. The y-intercept is at 4.0.

What are the intercepts and slopes?

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

The slope conveys how quickly the dependent variable shifts in response to changes in the independent variable. Mathematicians and economists frequently use the Greek capital D or D to denote change. The change in the horizontal axis, x, is contrasted with the change in the vertical axis, y.

Negative values are below the origin on the x-axis and to the left of the origin on the y-axis. If the y-coordinate is negative, go downhill; if the x-value is negative, start at the origin and travel to the left.

Line graphs, often referred to as XY graphs, are used to graphically display data (the results of an experiment) to show how multiple aspects, such as time and the severity of the disease, are related.

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Answer: $22.5

Step-by-step explanation:

refer to the image to see the steps and explanation

The value of third angle is 30 and we can find using angle sum property.

The triangle's angles can be added up to equal 180 degrees, according to the angle sum property of triangles. A triangle has three sides, one at each vertex, and three angles. The total of the interior angles in any triangle, whether acute, obtuse, or right, is 180 degrees.

One of the most commonly employed properties in geometry is the angle sum property of a triangle. Calculating the unknown angles is primarily done using this characteristic. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.

Given

The two angles are given as 102 and 48

we need to find the third angle

Let the third angle be a then

using the angle sum property we get

102 + 48 + a = 180

a = 30

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The value of k for which the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 have infinitely many solutions is 4.

To solve this question, we need to find the value of k for which the two equations are equivalent. Equivalence means that the coefficients of x and y are the same and the constant terms are the same.

From the given equations, we can see that the coefficients of x and y are the same in both equations, which is 6x. The constant terms, however, are different. The first equation has a constant term of -8, while the second equation has a constant term of -16.

To make the equations equivalent, we need to make the constant terms the same. We can do this by dividing the second equation by 2. This gives us 6 ky - 8 = 0. We can see that the constant term is now the same as the first equation. Therefore, the value of k that makes the equations equivalent is k = 4.

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The complete question is:

For what value of k do the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 has infinitely many solutions?

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Answer:

We can use the chain rule to find the derivative of y with respect to x.

The chain rule states that if y = f(u) and u = g(x), then dy/dx = dy/du * du/dx

y =sin x sec (90-x)

dy/dx = cos x sec (90-x) * d/dx(sec (90-x)) - sin x tan (90-x) sec (90-x) * d/dx(90-x)

let us calculate the second derivative

du/dx = -cos(90-x)

d²y/dx² = -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) - cos x sec (90-x) * (-sin (90-x))

= -sin x sec (90-x) * cos (90-x) - cos x tan (90-x) sec (90-x) * cos (90-x) + cos x sec (90-x) * sin (90-x)

= -sin x sec (90-x) * cos (90-x) + cos x tan (90-x) sec (90-x) * sin (90-x)

= -(sin^2 x + cos^2 x) sec (90-x) tan (90-x)

= -sec^2 (90-x) tan (90-x)

So, the value of the second derivative of y with respect to x is -sec^2 (90-x) tan (90-x)

Step-by-step explanation:

Substitute y = 0 and solve for x to find the x-intercept, and do the same for the y-intercept.

Examples on the Y Intercept Using the y-intercept formula, we can find the y-intercept of a function by substituting x = 0 and solving for y; consequently, the given function lacks a y-intercept. 2nd Example: Find the value of "a" if the y-intercept of a function y = a (x - 1) (x - 2) (x - 3) is (0, 12).

We can solve for the y-intercept in the slope-intercept equation y=mx+b by first determining the slope between two points on a line and then writing an equation for that line.

The slope-intercept form is used to write the line's equation, which looks like this: y is equal to mx + b, where m is the slope and b is the y-intercept. We can see that the line has a slope of 6 in our equation, which is y = 6x + 2.

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Answer:

  1/5

Step-by-step explanation:

You want the slope of line AB, given A(-2, 2) and B(3, 3).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -2)/(3 -(-2)) = 1/5

The slope of the line AB is 1/5.

__

Additional comment

You can also find the slope by counting the grid squares. Point B is 1 up and 5 over from point A, so the slope is rise/run = 1/5.

Answer:

The GCF of 36 and 69 is 3

Step-by-step explanation:

hope this helps

The SSA theorem tells us that if two angles and a non-included side of one triangle are congruent to two angles and also the corresponding non-included side of another triangle, then it is claimed that the two triangles supplied are congruent to one another.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are similar objects. To put it another way, if two triangles are similar, then their respective sides are proportionately equal and their corresponding angles are congruent.

The SSA congruence rule is not a reliable standard for determining if two triangles are congruent to one another.

Hence, there is no such SSA similarity from which you can make predictions that whether the two triangles are similar or not.

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Answer:

side length of square C is 5 ft

Step-by-step explanation:

A, B andC are the areas of the sides of a right triangle.

C is the square on the hypotenuse of the right triangle.

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

C² = A² + B² = 9 + 16 = 25 ft²

the area of a square is  s² , where s is the side length, then

s² = 25 ( take square root of both sides )

s = [tex]\sqrt{25}[/tex] = 5 ft

The solution of |( 2x-3 )|= 7 is 5.

|(2x – 3)| = 7

2x = 7+3

2x = 10

x=5

In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.

solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.

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Complete Question:

What is the solution of |( 2x-3 )|= 7?

The number of images formed by using the angle 120° is 3 or 30° is 11.

Angle in math is defined as the image formed when two rays are joined together at a common point and the common point here is called node or vertex and the two rays are called arms of the angle.

Here we have given that 120 degree and 30 degree object is placed symmetrically with respect to both the mirrors.

As we all know that the formula number of images formed between two mirrors kept at some angles is written as,

=> n = (360 / θ) - 1

Here we have  n is the number of images and θ is the angle between the mirrors.

The value of θ is 120 or 30.

If the angle is 120, then the number of image is calculated as,

=> n = (360 / 120) - 1

=> n = 3 - 1 = 2

Where as the angle is 30, then the number of image is calculated as,

=> n = (360 / 30) - 1

=> n = 12 - 1 = 11

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The ounces of the watermelon sugar scrub per dollars is 1.1 ounces per dollars.

The store charges $12.65 for a 14 oz container of watermelon sugar scrub. The amount in ounces of watermelon sugar scrub per dollars can be calculated as follows:

12.65 dollars = 14 ounces

1 dollars = ?

cross multiply

Hence,

amount of ounces of watermelon sugar scrub per dollars  = 14 × 1 / 12.65

amount of ounces of watermelon sugar scrub per dollars  = 14/ 12.65

amount of ounces of watermelon sugar scrub per dollars  = 1.10671936759

amount of ounces of watermelon sugar scrub per dollars  = 1.1 ounces per dollars

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The one-to-one function is also called the injective function.

The one-to-one function is a special function that maps every element of the range to exactly one element of its domain.

we can define one to one function as:

function g: D -> F is said to be one-to-one if

g(x₁) = g(x₂)

⇒ x₁=x₂

for all elements x₁ and x₂ ∈ D., A one-to-one function is also considered an injection, a function is injective only if it is one-to-one.

There are some examples of injective functions:

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The expression that represents the height of the cylinder in terms of its radius is 3r - 5.

The cylinder's radius is specified in "r" units.

So, In comparison to its radius, r, a cylinder's height, h, is five units less.

The radius times three will be denoted by the unit "3r."

and

The radius reduced by 5 units will be shown as "3r - 5" units.

The height "h" of the cylinder is equal to 5 units less than 3 times the radius, hence the final equation is,

h = 3r-5

Thus, the expression representing the height of the cylinder in terms of the radius is h = 3r-5

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