vertical angles 4x+7 and [5(x-4)] what is the value of x

Answer:

x = 58

Step-by-step explanation:

that is a 90 degree angle - 32 degrees = 58 degrees

The number of nickels and dimes that Ariana has are 58 and 91

Linear Equation:

The polynomial equation with 1 degree representing an unknown quantity is known as a Linear equation. Here to represent the unknown quantity we will use variables like x, y, z .... etc.

From the given problem,

The amount that Ariana = $12.00

As we know 1 dollar = 100 cents

⇒ $12.00 = 12 × 100 = 1200 cents  

Total number of nickels and dimes = 149

Since we don't know the number of nickels and dimes we will represent them with variables x and y respectively.

The amount of x nickels coins

= x × 5 cents = 5x cents   [ ∵ nickels = 5 cents ]  

The amount of y dimes coins

= y × 10 cents = 10y cents   [ ∵ dimes = 10 cents ]  

From the above calculations the equation that can be formed

Total amount that Ariana is 5x + 10y = 1200 cents

=> x + 2y = 240 ----- Equation (1)  

Total number of coins is  x + y = 149 ----- Equation (2)    

Now solve (1) and (2) to find the number of each coin  

Do (1) - (2)

=> x + 2y - [ x + y ] = 240 - 149

=> x + 2y - x - y  = 91  

=> y  = 91      

Substitute y = 91 in Equation (2)      

(2) => x + 91 = 149

=> x = 58

The number of nickels and dimes that Ariana has are 58 and 91

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Significant independent variables makes a good regression model.

A reasonable high R-squared score makes sense if your regression model includes independent variables that are statistically significant. According to the statistical significance, shifts in the dependent variable are correlated with changes in the independent variables.

Accordingly, a high R-squared value shows that your model adequately accounts for the variation in the dependent variable.

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Answer:

-3, -2.5, -3/4, 0.8, 2.5, 6 1/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/2 = 0.5

6 = 6

6 + 0.5 = 6.5

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

1/4 = 0.25

-1/4 = -0.25

-3/4 = -0.75

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

Hope this helps! <3

A coordinate system is a two-dimensional number line, for example, two perpendicular number lines or axes.

This is a typical coordinate system:

coordinate plane1

The horizontal axis is called the x-axis and the vertical axis is called the y-axis.

The center of the coordinate system is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0).

An ordered pair contains the coordinates of one point in the coordinate system. That is named by its ordered pair of the form of (x, y).

The first number corresponds to the x-coordinate and the second to the y-coordinate.

To graph a point, we have to draw a dot at the coordinates that correspond to the ordered pair. It is one of the best ways to start at the origin.

The x-coordinate shows how many steps have to take from positive to negative on the x-axis, the same as the y-coordinate tells how to have many steps from positive to negative on the y-axis.

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The value of b is given as follows:

b = 18.

Similar triangles are triangles that share these two features presented as follows:

The bisection, represented by the altitude segment in this triangle, divides the triangle into two similar triangles, hence the equivalent side lengths are given as follows:

Then the proportional relationship for these side lengths is given as follows:

b/(28 - b) = 27/15

Applying cross multiplication, the value of b is obtained as follows:

15b = 27(28 - b)

42b = 27 x 28

b = 27 x 28/42

b = 18.

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The perimeter of the quadrilateral illustrated is 30cm.

The information is incomplete. Therefore, an overview will be given. It should be noted ha perimeter simply means the addition of the sides given.

Let's assume that that we've a rectangle with length and width of 10 and 5cm.

The perimeter will be:

= 2(l + w)

= 2(10 + 5)

= 30cm

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Answer:

x = 27.6907 units

Step-by-step explanation:

cos (62) = 13/x

x cos (62) =13

13 / cos(62)=x

x is 27.6907 units

Answer:

1) Heredity, also called inheritance or biological inheritance, is the passing on of traits from parents to their offspring; either through asexual reproduction or sexual reproduction, the offspring cells or organisms acquire the genetic information of their parents.

2) Looking more like one parent or the other is dependent on the gene versions each parent has. And which ones happen to get passed down. We have two copies of each of our chromosomes and so have two copies of each of our genes.

3) Nurture refers to all the environmental variables that impact who we are, including our early childhood experiences, how we were raised, our social relationships, and our surrounding culture. Nurture assumes that correlations between environmental factors and psychological outcomes are caused environmentally. For example, how much parents read with their children and how well children learn to read appear to be related. Other examples include environmental stress and its effect on depression.

4) Sea turtles use two cues to find the ocean after they hatch. One is light. The surface of the ocean reflects light. The hatchlings look for the twinkling of the sun or moon light bouncing off the ocean.

Step-by-step explanation:

Answer:1).Although an individual gene may code for a specific physical trait, that gene can exist in different forms, or alleles. One allele for every gene in an organism is inherited from each of that organism's parents. ... Alleles produce phenotypes (or physical versions of a trait) that are either dominant or recessive.

2). Boys and girls are equally likely to get DNA from their grandmother as they are to get DNA from their grandfather. Take a look at a real example of the DNA that two siblings share with each of their grandparents. As you can see, they did not inherit exactly 25% of genetic information from each grandparent.

3). Nurture is the process of caring for and encouraging the growth or development of someone or something.

4). Sea turtles use two cues to find the ocean after they hatch. One is light. The surface of the ocean reflects light. The hatchlings look for the twinkling of the sun or moon light bouncing off the ocean.

Step-by-step explanation

Answer:

the answer is 1.414,3.142,4.5

1. The values that could represent the number of participants making the donation are options (e) 10 and (f) 150.

2. The set of numbers that best describes the numbers chosen in the above MCQ is option (d) whole numbers.

1. The number of participants making the donation should be a positive whole number. So, among the given options:

a. √5 (irrational)

b. 0 (not positive)

c. 3/8 (not a whole number)

d. 2.7 (not a whole number)

e. 10 (positive whole number)

f. 150 (positive whole number)

The values that could represent the number of participants making the donation are: e. 10 and f. 150.

2. The set of numbers that best describes the numbers chosen in the above MCQ is:

d. whole numbers.

The reason is that whole numbers include all positive integers (including 10 and 150), as well as zero. Whole numbers are a subset of both counting numbers (positive integers) and rational numbers, and they belong to the set of real numbers.

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The complete question is:

Your school is sponsoring a charity race. If each participant made a donation d of $ 15.50 to a local charity, which subset of real numbers best describes the amount of money raised?

1. circle the values below that could represent the number of participants making the donation.

a. \sqrt{5}

b. 0

c. 3/8

d. 2.7

e. 10

f. 150

2. circle the set of numbers that best describes the numbers you chose in the above mcq.

a. counting numbers.

b. rational numbers.

c. real numbers.

d. whole numbers.

Answer:

x + 3

Step-by-step explanation:

x - 117 + 120

= x + ( 120 - 117 )

= x + 3

The statement "Gasoline is an ideal fuel for transportation because it has a high energy density and is highly portable" is completed correctly by the information in option (a): "high; flammable."

Gasoline is known for its high energy density, meaning it contains a significant amount of energy per unit volume. This characteristic allows vehicles to carry a sufficient amount of fuel for long-distance travel without requiring excessive storage space. Additionally, gasoline is highly portable due to its liquid form, which makes it easy to transport and dispense into vehicles.

Regarding the biggest concern associated with the use of petroleum, the correct option is (c): "carbon dioxide emissions." When petroleum products like gasoline are burned, they release carbon dioxide (CO2) into the atmosphere. CO2 is a greenhouse gas that contributes to global warming and climate change. The combustion of petroleum fuels, especially in the transportation sector, is a major source of CO2 emissions.

While other concerns such as air pollutants (particulates in the air) and environmental impacts (ground level emissions, oil spills) are also associated with petroleum use, the significant contribution of CO2 emissions to climate change makes it the most pressing concern. Addressing carbon dioxide emissions from the burning of petroleum fuels is essential to mitigate the impact of transportation on climate change and promote the use of more sustainable and cleaner energy sources.

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(a) There are 126 proper subsets of set A.

(b) There are 128 subsets of set A, including the empty set and the set A itself.

(a) To find the total number of proper subsets of set A, we need to exclude the empty set and the set A itself.

Given that set A has 7 elements, the total number of proper subsets can be calculated using the formula 2ⁿ - 2.

where n is the number of elements in the set.

The number of elements in set A is 7, so the total number of proper subsets of A is:

2⁷ - 2 = 128 - 2

= 126.

Therefore, there are 126 proper subsets of set A.

(b) To find the total number of subsets of set A, we need to include the empty set and the set A itself.

Using the same formula, the total number of subsets can be calculated as 2ⁿ, where n is the number of elements in the set.

The number of elements in set A is 7, so the total number of subsets of A is:

2⁷ = 128.

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Answer:

using pythagoras theorem

h^2=p^2+b^2

h^2=12^2+9^2

h^2=144+81

h^2=225

h=\(\sqrt{225}\)

h=15

Step-by-step explanation:

Answer:

i think it is A

Step-by-step explanation:

Answer:

A)  m = 1300 - 35(8)

Step-by-step explanation:

If your savings account has $1300 in it, and 35 is being taken away every month for 8 months, then you would multiple the months by the amount of money being taken away then subtract the amount from the total amount of money in her account. There for 'm = 1300 - 35(8)'.

Answer:

x=30 cm

y=24 cm

Step-by-step explanation:

y=24 cm

x=√(24²+18²)=√[6²(4²+3²)]=6√(16+9)=6√25=6×5=30 cm

Answer:

Step-by-step explanation:

P is the exterior point to the circle with centre O

Radius = 5cm

Length of the tangent = 12 cm

Distance between the point and centre of the circle = x cm

We know that

The angle between the radius of the circle and the tangent at the point of contact is 90°

By Pythagoras Theorem

Hypotenuse² = Side²+Side²

⇛OP² = OT1² +PT1²

⇛x² = 24²+18²

⇛x² = 576+324

⇛x² = 900

⇛x² = 30²

⇛x = √(30)²

⇛x = √(30*30)

We know that

The lengths of tangents drawn from the exterior point to the circle are equal.

PT1 = PT2

Answer: Hence, the value of x=30cm and y = 18cm.

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The statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

Let {v₁, v₂, ...., vp} be a set of p vectors in Rⁿ, then the following are equivalent statements:

1. The set of vectors is linearly dependent.

2. There exist constants c₁, c₂, ... cp, not all of them zero, such that:

c₁v₁+c₂v₂+...+cpvp = 0 (zero vector)

For the above to be possible, the following must hold true: p≥n

Because in Rⁿ, each vector has n components.

So, the total number of unknowns is p, while the total number of equations that we have is n.

Hence p≥n for the system of linear equations above to have a non-zero solution.

Hence, the statement "If a set of vectors {v₁, v₂, ...., vp} in Rⁿ is linearly dependent, then p>n" is False.

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The complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

What is the congruent triangle?

The triangles are congruent regardless of how they are rotated or flipped. The symbol “≅” is frequently used to express the congruence of two items. In the diagram given, ΔABC ≅  ΔXYZ.

The corresponding angles and the sides of the triangles are also congruent with each other.

We have given,

all the corresponding congruent angles and sides. Then the triangle congruence statement.

a)

∠A ≅ ∠Y

∠B ≅ ∠Z

∠C ≅ ∠X

b)

AB ≅ YZ

AC ≅ XY

BC ≅ XZ

c)

ΔABC ≅  ΔXYZ.

Therefore, the complete triangle congruence statement are:

a) ∠A ≅ ∠Y, ∠B ≅ ∠Z, ∠C ≅ ∠X

b) AB ≅ YZ, AC ≅ XY, BC ≅ XZ

c) ΔABC ≅  ΔXYZ.

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The given vector field is F = x²yzi + xy²zj + xyz²k.

We have to find the div F and curl F of the vector field.

Div F of the given vector field F = x²yzi + xy²zj + xyz²k

The formula to find the div F is given below:div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z, where F = P i + Q j + R k

Now, let's find div F∂P/∂x = 2xyz∂Q/∂y

= x²z + 2xyz∂R/∂z

= xy² + 2xyz

Therefore,div F = ∂P/∂x + ∂Q/∂y + ∂R/∂z

= 2xyz + x²z + 2xyz + xy²

= x²z + xy² + 4xyz

This is the required div F of the given vector field.

Next, let's find the curl F of the given vector field F = x²yzi + xy²zj + xyz²k.

The formula to find the curl F is given below:curl F = ( ∂R/∂y - ∂Q/∂z )i + ( ∂P/∂z - ∂R/∂x )j + ( ∂Q/∂x - ∂P/∂y )k

Now, let's find the curl F of the given vector field∂R/∂y = xz²∂Q/∂z

= xy²∂P/∂z

= 2xyz∂R/∂x

= yz²∂Q/∂x

= 2xyz∂P/∂y

= x²z

Therefore,curl F = ( ∂R/∂y - ∂Q/∂z )i + ( ∂P/∂z - ∂R/∂x )j + ( ∂Q/∂x - ∂P/∂y )k

= (xz² - xy²) i + (2xyz - yz²) j + (xy² - x²z) k

Therefore, the curl F of the given vector field is (xz² - xy²) i + (2xyz - yz²) j + (xy² - x²z) k.This is the final answer.

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Answer:

1512 cm³

Step-by-step explanation:

Formula

Volume of right rectangular prism = Length × Breadth × Height

As given

Two blocks of wood are shaped as right rectangular prisms.

The smaller block has a length of 9 cm, a width of 3 cm, and a height of 7 cm.

As given

The dimensions of the larger block are double the dimensions of the smaller block.

Length of the larger block = 2 × Length of the smaller block

                                           = 2 × 9

                                           = 18 cm

Breadth of the larger block = 2 × Breadth of the smaller block

                                           = 2 × 3

                                           = 6 cm

Height of the larger block = 2 × Height of the smaller block

                                           = 2 × 7

                                           = 14 cm

Put in the formula

Volume of larger wooden block = 18 × 6 × 14

                                                    = 1512 cm³

Therefore the volume of the wooden block is 1512 cm³ .

Answer:

1,512 that’s the answer because u said double

e

d and 9 x 2 is 18,3 x 2 is 6, 7 x 2 is 14.Thani would muliply 18 x 6 x 14 that would get u https 1,512

Step-by-step explanation:

¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

i. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx (5 marks)

Proof:

1. ∃x(Fx & Gx) [Premise]

2. Fx & Gx [∃-Elimination, 1]

3. ∃xFx [∃-Introduction, 2]

4. ∃xGx [∃-Introduction, 2]

5. ∃xFx & ∃xGx [Conjunction Introduction, 3 and 4]

6. ∃x(Fx & Gx) ⊢ ∃xFx & ∃xGx [1-5, Modus Ponens]

ii. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px (5 marks)

Proof:

1. ¬ 3x(Px v Qx) [Premise]

2. ¬ Px v ¬ Qx [DeMorgan’s Law, 1]

3. Vx ¬ Px [∀-Introduction, 2]

4. ¬ 3x(Px v Qx) ⊢ Vx ¬ Px [1-3, Modus Ponens]

iii. ¬ Vx(Fx → Gx) v 3xFx (10 marks; Hint: To derive this theorem use RA.)

Proof:

1. ¬ Vx(Fx → Gx) v 3xFx [Premise]

2. (¬ Vx(Fx → Gx) v 3xFx) → (¬ Vx(Fx → Gx) v Fx) [Implication Introduction]

3. ¬ Vx(Fx → Gx) v Fx [Resolution, 1, 2]

4. (¬ Vx(Fx → Gx) v Fx) → (Fx → Gx) [Implication Introduction]

5. Fx → Gx [Resolution, 3, 4]

6. ¬ Vx(Fx → Gx) v 3xFx ⊢ Fx → Gx [1-5, Modus Ponens]

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Answer: 9

Step-by-step explanation:

Answer:

θ = π/3 and 5π/3

Step-by-step explanation:

x = r cos θ and y = r sin θ.  Therefore:

dy/dx = (dy/dθ) / (dx/dθ)

dy/dx = (r cos θ + r' sin θ) / (-r sin θ + r' cos θ)

In this case, r = 1 + cos θ and r' = -sin θ.

dy/dx = ((1 + cos θ) cos θ + (-sin θ) sin θ) / (-(1 + cos θ) sin θ + (-sin θ) cos θ)

dy/dx = (cos θ + cos²θ − sin²θ) / (-sin θ − sin θ cos θ − sin θ cos θ)

dy/dx = (cos θ + cos²θ − (1 − cos²θ)) / (-sin θ (1 + 2 cos θ))

dy/dx = (cos θ + 2 cos²θ − 1) / (-sin θ (1 + 2 cos θ))

The tangent line is horizontal when the numerator of dy/dx is 0 and the denominator of dy/dx is not 0.

0 = 2 cos²θ + cos θ − 1

0 = (cos θ + 1) (2 cos θ − 1)

cos θ = -1 or 1/2

θ = π/3, π, 5π/3

0 = -sin θ (1 + 2 cos θ)

sin θ = 0 or cos θ = -1/2

θ = 0, 2π/3, π, 4π/3

Therefore, the answer is θ = π/3 and 5π/3.

The length of a side of the picture is 3.39 centimeters. The area of a frame is calculated by multiplying the width of the frame by the perimeter of the picture.

Let x be the length of a side of the picture. The area of the picture is x². The area of the frame is 2x. The total area is x² + 2x.

We are given that the area of the picture is 2/3 of the total area. This means that x² = 2/3(x² + 2x).

Solving for x, we get x = 3.39 centimeters.

Here are some additional explanations:

The area of a square is calculated by multiplying the length of one side by itself.

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According to Newton's second law

\(\\ \sf\longmapsto F=ma\)

\(\\ \sf\longmapsto m=\dfrac{F}{a}\)

\(\\ \sf\longmapsto m=\dfrac{0.02}{8}\)

\(\\ \sf\longmapsto m=0.0025kg\)

\(\\ \sf\longmapsto m=2.5g\)

Done

Answer:

the length of the gym will be 80 feet

Step-by-step explanation:

To solve the given system of differential equations, we can use the substitution method to obtain first-order linear differential equations and solve them for x and y. Alternatively, we can apply the operator method to rewrite the system as a second-order linear differential equation.

To solve the given system of differential equations using three different methods - substitution method, operator method, and eigen-analysis method - we start by representing the system in matrix form: Let X = [x y]' and X' = [x' y']'. The given system can be written as: X' = A * X + B, where A is the coefficient matrix and B is the vector of constants.

Substitution Method:

In this method, we substitute the expressions for x' and y' from the given system into the equations and solve for x and y. By substituting the given expressions, we obtain two first-order linear differential equations. We can then solve these equations using standard methods such as separation of variables or integrating factors to find the solutions for x and y.

Operator Method:

The operator method involves defining operators D = d/dt and E = d/de, where t is the independent variable and e is the exponential function. We can rewrite the given system as a single second-order linear differential equation in terms of these operators. By manipulating the equations using operator algebra, we can find the characteristic equation and the solutions for x and y.

Eigen-analysis Method:

The eigen-analysis method involves finding the eigenvalues and eigenvectors of the coefficient matrix A. By calculating the eigenvalues, we can determine the type of critical points in the system. The eigenvectors corresponding to the eigenvalues provide the basis for the solutions. Using the eigenvalues and eigenvectors, we can construct the general solution for the system. Lastly, the eigen-analysis method helps us determine the critical points and construct the general solution using eigenvalues and eigenvectors.

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As the inventor of an underwater diving apparatus for my dog, the plaque on my wall acknowledging my achievement is a source of pride and accomplishment. The fact that I was awarded a US patent for my invention means that I am legally recognized as the creator of this unique device. This provides me with a sense of ownership and protects my invention from being copied or stolen by others.
Personally, the patent gives me the satisfaction of knowing that my idea has been officially recognized as innovative and useful. It also opens up opportunities for me to potentially profit from my invention, as Happy Dogs Inc. owns the legal rights to the patent and is selling the device on Amazon. This could potentially lead to financial benefits and further recognition in the field of inventing. Overall, the patent is a defining moment in my career as an inventor and has provided me with a sense of accomplishment and pride.

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