what is the volume of the following rectangular prism

Step-by-step explanation:

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Using cosine law in the triangle given, the length of BC is 32 units

The law of cosines (also known as the cosine formula) is an equation that relates the lengths of the sides of a triangle to the cosine of one of its angles. It states that:

a² = b² + c² - 2(b)(c) Cos(A)

In the given problem, the data;

Substituting the values into the formula and solve for BC;

BC² = 29² + 23² - 2(29)(23) Cos 75

BC² = 1024.735393

BC = √1024.735393

BC = 32.01

BC ≈ 32

The length of side BC in the triangle is 32 units

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The sum of angles of a triangle formed in a spherical geometry exists equivalent to 180∘.

The sum of angles of a triangle formed in a spherical geometry exists equivalent to 180∘.

A category of non-Euclidean geometry, spherical geometry is a subset of elliptical geometry. Any type of geometry that is not founded on conventional planes is known as non-Euclidean geometry. Lines in non-Euclidean geometry are not always the usual straight lines found in Euclidean geometry (i.e., plane geometry).

We require opposing sides and angles in order to use the sine rule. We can utilise this knowledge to locate the side that is opposite the other angle if we know two angles and one of the sides opposite. Accuracy points may be lost because of this.

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The equation of line that passes through (2,3) and (-2,5) is y  = (-1/2)x + 4.

The point-slope form is expressed as;

( y - y₁ ) = m( x - x₁ )

Where m is slope, x₁ and y₁ are the coordinates of the point .

Given the data in the question;

Point 1 (2,3)

Point 2 (-2,5)

First, determine the slope.

Slope m = (y₂ - y₁)/(x₂ - x₁)

Slope m = ( 5 - 3 ) / ( -2  - 2)

Slope m = 2 / -4

Slope m = -1/2

Plug the slope m = -1/2 and point (2,3) into point-slope formula and simplify.

( y - y₁ ) = m( x - x₁ )

( y - 3 ) = (-1/2)( x - 2 )

y - 3 = (-1/2)x - (-1/2)2

y - 3 = (-1/2)x + 1

y = (-1/2)x + 1 + 3

y  = (-1/2)x + 4

Therefore, the equation of the line is y = (-1/2)x + 4.

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On solving the provided question, we can say that the linear function that can be formed y = mx + b, y = temperature, x = time

Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.

here,

the linear function that can be formed

y = mx + b

y = temperature

x = time

a and b = variables

for first data = 20 = 4m+b

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The relation which is a function among the given answer choices are Choices A and D.

It follows from the task content that the answer choices which represent a function be identified as required.

By definition, a function is a relation in which case, no one input value is assigned more than one output.

On this note, for Choice A; all input values have only one output value assigned to them and for Choice D; the graph represents a quadratic function in which case, each input value, x is assigned only one output value, y.

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Answer:

y = 7

Step-by-step explanation:

since the 2 triangles are congruent then corresponding angles are congruent , so

∠ R = ∠ F , that is

13y - 1 = 90 ( add 1 to both sides )

13y = 91 ( divide both sides by 13 )

y = 7

Answer:

Step-by-step explanation:

it do be a quadrilateral parallelogram and rhombus cause it do

Answer:

Step-by-step explanation:

We will use the triple integral in cylindrical coordinates to calculate the integral across the surface of the box in the illustration.

The integral is given by:

[tex]∫∫∫ {ze}^{2x} + y dzdydx[/tex]

Where x, y, and z are the coordinates and the limits of integration are

[tex]0 <= x <= 2, 0 <= y <= 3, and 0 <= z <= {ze}^{2x} + y[/tex]

We can change the integral into cylindrical coordinates by using the following change of variables:

x = rcosθ

y = rsinθ

z = z

The integral becomes:

[tex]∫(0 to 2)∫(0 to 3)∫(0 to ze^(2r cosθ) + r sinθ) rze^(2r cosθ) + r^2sinθ dzdrdθ[/tex]

Although the integral is challenging to calculate, this method will assess it. The region of integration can be determined by knowing the bounds of z, which would be beneficial given that the box is in rectangular coordinates.

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The estimated regression equation is d. ŷ = 145 + 20x₁ – 18x₂ + 4x₃

This equation is obtained from the coefficients given in the table. It is the equation that best predicts the value of the dependent variable (y) based on the values of the independent variables (x₁, x₂, and x₃).

The equation is in the form of y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, where β₀, β₁, β₂, and β₃ are the coefficients of the independent variables and ε is the error term. These coefficients represent the change in the dependent variable for a unit change in the independent variable, holding all other independent variables constant.

From the table, we can see that the value of β₀ = 145, which represents the predicted value of y when all independent variables (x₁, x₂, and x₃) are equal to zero.

The value of β₁ = 20 represents the change in the predicted value of y for a unit change in x₁, holding x₂ and x₃ constant. Similarly, the value of β₂ = -18 represents the change in the predicted value of y for a unit change in x₂, holding x₁ and x₃ constant, and the value of β₃ = 4 represents the change in the predicted value of y for a unit change in x₃, holding x₁ and x₂ constant.

So, the estimated regression equation is: ŷ = 145 + 20x₁ – 18x₂ + 4x₃.

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Answer:

34.

Step-by-step explanation:

The value of 7u + 6

=3u - 8 = 4

=3u = 4 + 8

=3u = 12

=3u/3 = 12/3

u = 4.

therefore u = 4

=7u + 6

=7(4) + 6

=28 + 6

=34.

Answer: 104

Step-by-step explanation:

Angles at a line are equal to 180 degrees so:

180 = 72 + (x + 4)

180 = x + 76

180 -76 = x + 76 -76

104 = x

Answer: 750

Step-by-step explanation:

5/7 = women

2/7 = men (to get 2/7, 7/7 - 5/7 and you get 2/7)

5/7 x 1050

= 5 x 1050/7

= 5250/7

=750

The / means divide

Answer:

156 1/4

Step-by-step explanation:

Assume the room is a square.

side = 12 1/2 ft

area = (side)²

area = (12 1/2 ft)²

area = (12 1/2 ft) × (12 1/2 ft)

area = (144 + 6 + 6 + 1/4) ft²

area = 156 1/4 ft²

The equivalent fraction of -3/2 is the fraction -6/4

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

numerator negative 3 and denominator 2

Express the fraction properly

So, we have

-3/2

Multiply the numerator and the denominator by a constant (say 2)

So, we have

-6/4

This implies that -6/4 is equivalent to 3/2

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Answer:

(6)×(5)-1)3

6×5-3

30-3

=27

The number of different functions with the given domain, target and additional properties is as follows:

(a) There are infinitely many different functions, as there is no additional property given that could have the domain (0,1) and the target {0,1}.

(b) The only one-to-one function with the domain (0,1) and the target {0,1} is the identity function, f(x) = x. The additional property is that the function is one-to-one.

(c) The function f has a target of and a domain of (0,1) and (0,1). There are an infinite number of possible functions that could have this domain and target because no additional property is provided.

(d) There are infinitely many different one-to-one functions that could have the domain (0,1) and the target (0,1).

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Answer:

A) [tex]108^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle 1+m\angle 2=180^{\circ} \\ \\ 72^{\circ}+m\angle 2=180^{\circ} \\ \\ m\angle 2=108^{\circ}[/tex]

Answer:

BC = 8

Step-by-step explanation:

If AC is the perpendicular bisector of BD then

BC = CD = BD/2

BD/2 = 8

So BC = 8

Answer:

the answer is

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

The value of x for which the rational expression equals to zero is -4

An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, whereas B is a constant. A linear equation with two variables has the standard form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

A linear equation is an algebraic equation in which each term has an exponent of 1, and which, when plotted on a graph, always yields a straight line. It is called a "linear equation" for this reason.

The equation is

2 - x +x/2 + x = 0

⇒ x/2 = -2

⇒ x = -4

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Answer:

A) The relation is a function.  Every input (x) and only one output (y)

B) Domains are the x values: 1,2,3,4,5,6

The Ranges are the y values: 1,4,9,16,25,36

Step-by-step explanation:

You can use the same name (identifier). It may be a different object. They both loop will not affect each other.

Inside the inner or second loop, there is no way to refer to the object used in the first loop (unless you make special bread for that, as by providing a pointer to it).

This is Normally bad style, is prone to confusion, and should be avoided.

The objects are different only if the inner one is defined alone, as with the int I you have shown. If the same name is used without shaping a new object, the loops will use the same object and will interfere with each other.

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The concept given is a Probability, It is a branch of mathematics that deals with the occurrence of a random event. The answer is P(A|B)=P(B|A).

Probability is the branch of mathematics concerning numerical descriptions of how probable an event is to do, or how likely it's that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

Inverse probability is the probability of unobserved effects; or, more technically, the probability distribution of an unobserved variable. It's generally considered an obsolete term.

In probability proposition and statistics, an inverse distribution is the distribution of the complementary of an arbitrary variable. Inverse distributions arise in particular in the Bayesian environment of previous distributions and posterior distributions for scale parameters.

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Answer:

[tex]x + 2 = 8 - x \\ \\ \dashrightarrow \: x + x = 8 - 2 \\ \\ \dashrightarrow \: 2x = 6 \\ \\ \dashrightarrow \: x = 3[/tex]

hope helpful ;-;

Answer:

Step-by-step explanation:

x+2=8-x what is the answer to this?

x + 2 = 8 - x

x + x = 8 - 2

2x = 6

x = 3

----------------------------

check

3 + 2 = 8 - 3

5 = 5

When an equation simplifies to 0=0 then it has true for all real numbers or else it does not have solution.

Two or more expressions with an Equal sign is called as Equation.

3x +6 = 2x +10 +x -4

Subtract (3x+6) from both sides:

(3x +6) -(3x +6) = (2x +10 +x -4) -(3x +6)

0 = x(2 +1 -3) +(10 -4 -6)

0 = 0

0 = 0 . . . . has "all real numbers" as a solution set

6x +2 -2x = 4x +1

Subtract (4x+1) from both sides:

(6x +2 -2x) -(4x +1) = (4x +1) -(4x +1)

x(6 -2 -4) +(2 -1) = 0

0x +1 = 0

1 = 0

Does not have "all real numbers" as a solution set. There is no solution

Hence, when an equation simplifies to 0=0 then it has true for all real numbers or else it does not have solution.

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Answer:

203, 230, 320, 302, 140, 410, 104, 401

Step-by-step explanation:

To meet the criteria, we have to think of all the ways we can use three distinct numbers, with one of the numbers being odd, which adds up to 5:

1 + 4 + 0 = 5

2 + 3 + 0 = 5

Subsequently, use the numbers we found and rearrange them to form three-digit numbers.