Find the missing variable and indicated
angle measure.
X =
G
50°
K
H
28°
(15x-3)°
m2KHL =
J
O

Given vectors are, u = (6,1,6), v = (1,-1,4) and w = (1,4,7) and a vector (23, 10, 23).We need to express (23, 10, 23) as a linear combination of u, v and w.

To find the coefficients, we use matrix notation.
Let A be a matrix containing u, v and w as its column matrices, and X be a matrix containing the coefficients.
Then,AX = B Where A = [u | v | w]X = [a | b | c]B = (23, 10, 23)
Therefore, [u | v | w][a | b | c] = (23, 10, 23)⇒ a(u1) + b(v1) + c(w1) = 23a(6) + b(1) + c(1) = 23⇒ 6a + b + c = 23⇒ a(u2) + b(v2) + c(w2) = 10a(1) - b(1) + c(4) = 10⇒ a - b + 4c = 10⇒ a(u3) + b(v3) + c(w3) = 23a(6) - b(4) + c(7) = 23⇒ 6a - 4b + 7c = 23
The above system of linear equations can be solved using Gaussian elimination method.
The row echelon form of the augmented matrix [A | B] is, [6 1 1 | 23][1 -1 4 | 10][0 0 2 | 9]
The solution is, c = 9/2, b = -3, and a = 1/2.
Therefore, (23, 10, 23) = (1/2)u - 3v + (9/2)w can be written as a linear combination of u, v and w.

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The domain of f⁻¹(x) is [0, ∞) and the range of f⁻¹(x) is [-3, ∞).

The function f(x)=(x+3)² is not one-to-one, as it is a quadratic function and has a parabolic shape. However, we can restrict the domain of the function so that it is one-to-one and increasing. One way to do this is to restrict the domain to be greater than or equal to the x-coordinate of the vertex of the parabola. The vertex of the parabola is at (-3, 0), so we can restrict the domain to be x ≥ -3. In interval notation, this is [-3, ∞).

The inverse function of f(x) can be found by switching the x and y values and solving for y. This gives us:

x = (y+3)²

√x = y+3

y = √x - 3

So the inverse function is f⁻¹(x) = √x - 3. The domain of the inverse function is the range of the original function, and the range of the inverse function is the domain of the original function. Therefore, the domain of f⁻¹(x) is [0, ∞) and the range of f⁻¹(x) is [-3, ∞).

In summary:

f(x)'s domain: [-3, ∞)

f⁻¹(x)'s domain: [0, ∞)

f(x)'s range: [0, ∞)

f⁻¹(x)'s range: [-3, ∞)

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The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. In a box plot, we draw a box from the first quartile to the third quartile.

The given data set is,

14, 13, 13.5, 16, 14, 15.5, 14.5.

Hence, We get;

Order of data is,

⇒ 13, 13.5, 14, 14, 14.5, 15.5, 16.

Here, minimum is 13

Maximum is 16

Median is 14

Lower quartile range(Q1) is 13.5

Upper quartile range(Q3) is 15.5

Therefore, The box plot for given minimum, maximum, median, Q1 and Q3  is plotted below.

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A) The probability of the sample obtained having a mean altruism score lower than 72 is 0.9474. B) The probability of the sample obtained having a mean altruism score between 67 and 73 is 0.3584. C) The sample size (n) should be at least 207 in order to have a probability of 0.8 for a sample mean no greater than 67.

A. We can use the Central Limit Theorem to calculate the probability of the sample obtained having a mean altruism score lower than 72.

The Central Limit Theorem states that the mean of a sample of size n will be approximately normally distributed with a mean of μ and a standard deviation of σ/√n.

In this case, the mean of the sample will be approximately normally distributed with a mean of 66 and a standard deviation of 11.5/√27 = 2.214. Using the z-score formula, we can calculate the z-score for a sample mean of 72:
z = (72 - 66)/(11.5/√27) = 1.62
Using a z-table, we can find the probability of the sample mean being lower than 72:
P(z < 1.62) = 0.9474
Therefore, the probability of the sample obtained having a mean altruism score lower than 72 is 0.9474.

B. We can use the Central Limit Theorem to calculate the probability of the sample obtained having a mean altruism score between 67 and 73. The mean of the sample will be approximately normally distributed with a mean of 66 and a standard deviation of 11.5/√34 = 1.971. Using the z-score formula, we can calculate the z-scores for a sample mean of 67 and 73:
z1 = (67 - 66)/(11.5/√34) = 0.338
z2 = (73 - 66)/(11.5/√34) = 2.374
Using a z-table, we can find the probability of the sample mean being between 67 and 73:
P(0.338 < z < 2.374) = P(z < 2.374) - P(z < 0.338) = 0.9909 - 0.6325 = 0.3584
Therefore, the probability of the sample obtained having a mean altruism score between 67 and 73 is 0.3584.

C. We can use the Central Limit Theorem to calculate the sample size (n) such that the probability of randomly drawing a sample of children of the sample size (n) from this target population will have a probability of 0.8 for a sample mean no greater than 67. The mean of the sample will be approximately normally distributed with a mean of 66 and a standard deviation of 11.5/√n. Using the z-score formula, we can calculate the z-score for a sample mean of 67:
z = (67 - 66)/(11.5/√n) = 0.8
Solving for n, we get:
n = (11.5/(0.8*(67 - 66)))^2 = 206.13
Therefore, the sample size (n) should be at least 207 in order to have a probability of 0.8 for a sample mean no greater than 67.

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Answer:

x=55°, y=35°

Step-by-step explanation:

The angle between x and 35° is a right angle.

A right angle equals 90°.

Therefore. 90=x+35

x=55°

Now that x is known, we can find y.

The angle made between the x and y axis is 90°.

Therefore, 90=x+y

90=55+y

y=35°

Answer:

X=55° and Y=35° ................................

It is unlikely that the projected rebounds in 15 shots will actually happen.

Total shots fired equals 10.

To find that there were 15 shots total.

Consider S to be the likelihood that your team will rebound and miss a shot.

P(S) = Number of rebounds / Total Number of outcomes

P(S) = 7/15

P(S) = 0.46

Consequently, it is unlikely that the projected rebounds in 15 shots will actually happen.

Thus, it is unlikely that the projected rebounds in 15 shots will actually happen.

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The complete question is-

During a basketball game, you record the number of rebounds from missed shots for each team.  How many rebounds should your team expect to have in 15 missed shots?

Picture for question is attached.

Therefore, the length of the other side of Ross's garden is approximately 13.7 feet.

A rectangle is a four-sided flat shape with four right angles (90-degree angles) between opposite sides. It is a type of quadrilateral, which means it has four sides. In a rectangle, the opposite sides are equal in length and parallel to each other, which makes it different from a square, where all sides are equal in length. The area of a rectangle can be found by multiplying the length by the width, and the perimeter can be found by adding up the lengths of all four sides.

Here,

Let the length of the other side of the garden be x feet.

Using the Pythagorean theorem, we have:

x² + 30² = 33²

Simplifying the equation:

x² = 33² - 30² = 1089 - 900

= 189

Taking the square root of both sides:

x = √189 ≈ 13.7 feet

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Answer: See the Picture.

Step-by-step explanation:

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Answer:

x < 5

Step-by-step explanation:

2x - 3 < x + 2 ≤ 3x + 5

2x - 3 < x + 2 and x + 2 ≤ 5

x < 5 and x ≤ 3

Answer: x < 5

Therefore , the solution of the given problem of unitary method comes out to be Browns books are less expensive than Noble books at $5.50 each.

Take the lengths of this minute subsection and split the sum by two to complete a task using a unitary variable technique. The unit technique, in a nutshell, removes a wanted item both from the specific sets and color subsets. For instance, 40 pencils will cost Rs/kg ($1.01). It's possible that one country will have total influence over the approach taken to accomplish this. Almost every living creature has a distinctive quality. There are unanswered questions and changes (mathematics, algebra).

Here,

We must ascertain the price per book for each retailer in order to evaluate the costs of Browns and Noble books.

Two of Brown's books cost $11, so each volume costs $5.50 (11/2 = 5.50).

Five novels from Barnes & Noble cost $31, making each book $6.20 (31/5 = 6.20).

Browns books are less expensive than Noble books, which cost $6.20 per volume, at $5.50 each.

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The minimum amount of money Camille could have is 0 dollars if she doesn't buy anything, and the maximum amount of money she could have is 166 dollars if she buys the maximum quantity of each item.

To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.

Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.

We are given that;

The prices of different items at a garage sale: pants, shirts, shorts, and belts.  

Camille can buy up to 5 shirts.

Now,

If Camille buys 5 shirts, she would spend 5 * 6 = 30 dollars on shirts. Since she can buy up to 5 shirts, she may spend less than 30 dollars if she buys fewer shirts.

She can buy up to 10 pants, which would cost her 10 * 8 = 80 dollars.

She can buy up to 5 shorts, which would cost her 5 * 4 = 20 dollars.

She can buy up to 12 belts, which would cost her 12 * 3 = 36 dollars.

30 + 80 + 20 + 36 = 166 dollars

Therefore, by the  maxima and minima the answer will be 166 dollars if she buys the maximum quantity of each item.

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An EM wave is written line E = E0 sin(kx - ωt) and EM wave equation is written as ∂²E/∂x² = μ₀ε₀∂²E/∂t²

An electromagnetic wave (EM wave) is a type of wave composed of an electric field and a magnetic field that propagate at the speed of light. The equation for an EM wave is given by E = E0 sin(kx - ωt), where E0 is the peak electric field, k is the wavenumber, ω is the angular frequency, x is the position, and t is time.

An ELECTROMAGNETIC WAVE, or EM wave, is a type of wave that travels through space and carries energy from one point to another. EM waves are created when electric and magnetic fields interact with one another. These waves are categorized by their frequency, which determines their energy and their wavelength.

The EM wave equation, also known as the wave equation, is used to describe how EM waves propagate through space. The equation is typically written in the form:

∂²E/∂x² = μ₀ε₀∂²E/∂t²

Where E is the electric field, μ₀ is the permeability of free space, ε₀ is the permittivity of free space, x is the position, and t is the time. This equation shows how the electric field changes over time and space, and is used to predict the behavior of EM waves.

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To solve the given linear system, we can use the Gaussian elimination method. This method involves reducing the given matrix to a row echelon form and then solving for the variables using back substitution.

Step 1: Reduce the given matrix to a row echelon form by performing elementary row operations.
\[ \left[\begin{array}{rrr|r} 6 & 2 & -3 & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
We can start by dividing the first row by 6 to get a leading 1:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ -5 & 3 & 9 & 0 \\ 2 & -7 & -1 & 0 \end{array}\right] \]
Next, we can add 5 times the first row to the second row and subtract 2 times the first row from the third row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & \frac{16}{3} & \frac{17}{2} & 0 \\ 0 & -\frac{23}{3} & 0 & 0 \end{array}\right] \]
Finally, we can multiply the second row by $\frac{3}{16}$ and the third row by $-\frac{3}{23}$ to get a leading 1 in each row:
\[ \left[\begin{array}{rrr|r} 1 & \frac{1}{3} & -\frac{1}{2} & 0 \\ 0 & 1 & \frac{51}{32} & 0 \\ 0 & 1 & 0 & 0 \end{array}\right] \]

Step 2: Use back substitution to solve for the variables.
From the third row, we have:
$x_2 = 0$
Substituting this into the second row gives us:
$x_3 = 0$
And substituting these values into the first row gives us:
$x_1 = 0$
Therefore, the solution to the given linear system is:
$x_1 = 0$, $x_2 = 0$, and $x_3 = 0$

This means that the given linear system has a unique solution at the origin.

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Answer:

C. Exchange the $100 bill for ten $10 bills.

Since the money is to be divided among 4 people, it is easier to divide it if the money is in equal denominations. Therefore, the first step should be to exchange the $100 bill for ten $10 bills, so that each person can receive an equal share of $25. This way, we can avoid having to deal with different denominations while dividing the money among the four people.

3 1/5 + 1 3/7

To add these two fractions, we need to find a common denominator. The least common multiple of 5 and 7 is 35.

3 1/5 = 16/5

1 3/7 = 10/7

16/5 + 10/7 = (16/5) * (7/7) + (10/7) * (5/5) = 112/35 + 50/35 = 162/35

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1.

162/35 = 4 22/35

This expression does not equal 4 4/12.

1 11/12 + 2 1/4

Again, we need to find a common denominator to add these two fractions. The least common multiple of 4 and 12 is 12.

1 11/12 = 23/12

2 1/4 = 9/4

23/12 + 9/4 = (23/12) * (1/1) + (9/4) * (3/3) = 23/12 + 27/12 = 50/12

We can simplify this fraction by dividing both the numerator and denominator by their GCF, which is 2.

50/12 = 4 2/12

This expression does equal 4 4/12.

Fοr the inequality the sοlutiοn set is x > -2.

In Algebra, an inequality is a mathematical statement that uses the inequality symbοl tο illustrate the relatiοnship between twο expressiοns. An inequality symbοl has nοn-equal expressiοns οn bοth sides. It indicates that the phrase οn the left shοuld be bigger οr smaller than the expressiοn οn the right, οr vice versa.

Tο sοlve the inequality, we can fοllοw these steps -

Subtract 3/2 frοm bοth sides -

-x/2 < 5/2 - 3/2

-x/2 < 2/2

-x/2 < 1

Multiply bοth sides by -2 (and flip the inequality since we're multiplying by a negative number) -

x > -2

The graph is drawn fοr the sοlutiοn.

The circle οn the left endpοint is nοt filled because the inequality is strict (i.e., nοt less than οr equal tο).

The arrοw οn the right endpοint is filled because the sοlutiοn set includes all values greater than -2.

Therefοre, the sοlutiοn set is all real numbers greater than -2, which can be represented οn a number line as a ray starting at -2 and mοving tοwards pοsitive infinity.

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  All zeros of polynomial functions  -3/2 , 5i and -5i

Zeros of polynomial are the points where the polynomial equals zero on the whole. In simple words, we can say that zeros of polynomial are values of the variable such that the polynomial equals 0 at that point. Zeros of a polynomial are also referred to as the roots of the equation and are often designated as α, β, γ respectively. Some of the methods used to find the zeros of polynomial are grouping, factorization, and using algebraic expressions.

2x^3+3x^2+50x+75 equal to 0

2x^3+3x^2+50x+75 = 0

⇒ x^2 (2x + 3) + 25 (2x + 3) = 0

⇒ (2x + 3) (x^2 + 25 ) = =

If any individual factor on the left side of the equation is equal to  0, the entire expression will be equal to 0

2x + 3 = 0

x^2 + 25 = 0

so, x = -3/2  and x = 5i and -5i

The final solution is all the values that make  2x^3+3x^2+50x+75 = 0

x = -3/2 , 5i and -5i

Hence, all zeros of polynomial functions  -3/2 , 5i and -5i

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The answer of set U by listing its elements is {-3, -2, -1}

To rewrite the set U by listing its elements, we need to identify the integers that fall within the given range of -3<=z<=-1.

The appropriate set notation for listing the elements of a set is {element1, element2, element3, ...}.

So, the integers that fall within the given range are -3, -2, and -1.

Therefore, we can rewrite the set U as:

U = {-3, -2, -1}

This is the answer in the appropriate set notation, listing the elements of the set U.

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Answer:When we choose a dime from the box, there are two coins left, one penny and one nickel. Since we do not replace the dime, the probability of choosing a penny next is 1/2.

Therefore, the probability of choosing a dime first and a penny second is:

P(dime first and penny second) = P(dime first) * P(penny second | dime first)

= (1/3) * (1/2)

= 1/6

So, the answer is A. 1/6.

Step-by-step explanation:

Assuming the lines, which appear to be diameters, are actual diameters. The value of x is 10.63.

Any straight line that connects two points on a circle's circumference and goes through the circle's center. The length of such a line in geometry. The greatest separation possible between any two points in a metric space (geometry).

Exterior angles are 128, 32, and 45

Interior angles are 11x+4 and 85

Exterior angles = interior angles

128 + 32 + 45 = 11x+4 + 85

205 = 11x + 88

11x = 205 - 88 = 117

x = 117/11

x = 10.63

Therefore, the value of x is 10.63.

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To find the altitude of the spherical segment, we need to use the formula for the total surface area of a spherical segment, which is given by:
A = 2πR(r + h), where R is the radius of the spherical surface, r is the radius of the base, and h is the height of the segment.

We are given that the total surface area of the spherical segment is 7 times greater than the surface area of the sphere inscribed in it, which means that:
7(4πR^2) = 2πR(r + h)
Simplifying this equation gives us:
14R = r + h

We are also given that the radius of the spherical surface is equal to R, which means that r = R. Substituting this into the equation gives us:
14R = R + h
Solving for h, we get:
h = 14R - R
h = 13R
Therefore, the altitude of the spherical segment is 13R.

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The values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

To find two numbers a and b such that the system of linear equations is inconsistent, we need to make sure that the two equations have the same slope but different y-intercepts. This will result in the two equations being parallel to each other and never intersecting, making the system inconsistent.

The first equation is: ax - 3y = 2. We can rearrange this equation to solve for y and find the slope:

3y = ax - 2
y = (a/3)x - (2/3)

The slope of this equation is a/3.

The second equation is: -4x + 5y = b. We can rearrange this equation to solve for y and find the slope:

5y = 4x + b
y = (4/5)x + (b/5)

The slope of this equation is 4/5.

For the system to be inconsistent, the slopes need to be equal. So we can set a/3 = 4/5 and solve for a:

a/3 = 4/5
a = 12/5

Now we need to find a value for b that will result in a different y-intercept. We can do this by plugging in the value of a into one of the equations and choosing a different value for the y-intercept:

y = (12/5)(1/3)x - (2/3)
y = 4x - (2/3)

If we choose a different value for the y-intercept, such as -1, we can solve for b:

y = 4x - 1
5y = 20x - 5
b = 20x - 5y

So the values of a and b that will result in an inconsistent system are a = 12/5 and b = 20x - 5y.

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1. 286

2. False

3. 84

1. The number of non-negative integer solutions of x1​+x2​+x3​+x4​=10 is 286.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10. The reason is that the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. The number of positive integer solutions of x1​+x2​+x3​+x4​=10 is 84.

1. To find the number of non-negative integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n+k-1, k-1) = C(10+4-1, 4-1) = C(13, 3) = 286

Therefore, there are 286 non-negative integer solutions of x1​+x2​+x3​+x4​=10.

2. The answer to the above question is not the same as the number of non-negative integer solutions of x1​+x2​+x3​≤10 because the first equation has 4 variables, while the second equation has only 3 variables.

Therefore, the number of solutions will be different.

3. To find the number of positive integer solutions of x1​+x2​+x3​+x4​=10, we can use the formula: C(n-1, k-1) = C(10-1, 4-1) = C(9, 3) = 84

Therefore, there are 84 positive integer solutions of x1​+x2​+x3​+x4​=10.

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The solutions to the equations are;

1) {-2, 1/2}

2) {0, -2}

The zero product property is a fundamental property of algebra that states that if the product of two or more factors is equal to zero, then at least one of the factors must be zero. In other words, if a × b = 0, then either a = 0, b = 0, or both a and b are equal to zero.

Using the zero product property;

2x - 1 = 0

x = 1/2

x + 2

x = -2

The solution is;

{-2, 1/2}

Again for x(x + 2) = 0

x = 0

x + 2 = 0

x = -2

The solution is;

{0, -2}

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Answer:

Z= 6

Step-by-step explanation:

Z + 9 = 15

- do the inverse (opposite) operation

15 -9 = 6

9 -9 * cancel out *

Z = 6

CHECK:

6 +9 = 15

TRUE

The polynomial g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial with 4 terms.

To prove its degree using successive differences, we first need to find the successive differences of the polynomial's y-values for consecutive x-values. We can do this by substituting x-values into the polynomial and finding the differences between the resulting y-values.

For x=0, g(x)=0^(3)+3(0^(2))-0-3=-3
For x=1, g(x)=1^(3)+3(1^(2))-1-3=0
For x=2, g(x)=2^(3)+3(2^(2))-2-3=11
For x=3, g(x)=3^(3)+3(3^(2))-3-3=30

The first successive difference is 0-(-3)=3
The second successive difference is 11-0=11
The third successive difference is 30-11=19

Since the successive differences are not constant, we need to find the successive differences of the successive differences.

The first successive difference of the successive differences is 11-3=8
The second successive difference of the successive differences is 19-11=8

Since the successive differences of the successive differences are constant, the degree of the polynomial is 3, which is one less than the number of times we had to find successive differences. This confirms that g(x)=x^(3)+3x^(2)-x-3 is a cubic polynomial.

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The multiplication equation that can be used to determine the number of people who contributed to the cost of the season ticket package is: $745 = $186.25 x 4.

To write a multiplication equation that can be used to determine the number of people who contributed to the cost of the season ticket package, we can use the following equation:

Total Cost = Cost per Person x Number of People

In this case, the total cost is $745 and the cost per person is $186.25. We can plug these values into the equation to get:

$745 = $186.25 x Number of People

To solve for the number of people, we can divide both sides of the equation by $186.25:

Number of People = $745 / $186.25

Number of People = 4

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The value of x for the given equations are a. 10, b. -7, c = -8, d. 5.

Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics. One or more variables are identified as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root.

Given that,

2(x-3) = 14

2x - 6 = 14

2x = 20

x = 10

b. -5(x - 1) = 40

-5x + 5 = 40

-5x = 35

x = -7

c. 12(x + 10) = 24

12x + 120 = 24

12x = 24 - 120

x = -8

d. (x + 6) = 11

x = 11 - 6

x = 5

Hence, the value of x for the given equations are a. 10, b. -7, c = -8, d. 5.

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Maria has $22,000 invested in account A and $8,000 invested in account B.

Let's begin by setting up a system of equations to solve for the amount Maria has invested in each account. Let x be the amount invested in account A and y be the amount invested in account B. Since Maria has a total of $30,000 invested in both accounts, we can write the first equation as:

x + y = 30,000

Next, we can write an equation to represent the total annual interest earned from both accounts:

0.045x + 0.038y = 1,294

Now, we can use the substitution method to solve for x and y. We'll rearrange the first equation to solve for x:

x = 30,000 - y

Then, we'll substitute this value of x into the second equation:

0.045(30,000 - y) + 0.038y = 1,294

Simplifying the equation gives:

1,350 - 0.045y + 0.038y = 1,294

Combining like terms and isolating y gives:

0.007y = 56

y = 8,000

Now, we can substitute this value of y back into the first equation to solve for x:

x = 30,000 - 8,000

x = 22,000

So, Maria has $22,000 invested in account A and $8,000 invested in account B.

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The axis of symmetry of the parabola defined by the equation x=(1)/(36)y^(2)-(1)/(18)y+(37)/(36) is the vertical line x = (37)/(36). This is because the equation is in the form of y = ax^2 + bx + c, and the axis of symmetry is x = -b/2a. In this case, a = (1)/(36), b = -(1)/(18) and c = (37)/(36).

Therefore, the axis of symmetry is x = -(1)/(36) x -(1)/(18) = (37)/(36). This axis of symmetry divides the parabola into two symmetric halves and it is also the x-coordinate of the vertex of the parabola.

The vertex is the highest or lowest point of the parabola and it is the point of intersection between the axis of symmetry and the parabola. To find the y-coordinate of the vertex, we can substitute the x-coordinate of the vertex into the equation, which gives us y = (1)/(72) + (37)/(36) = (109)/(72). Therefore, the coordinate of the vertex is (37/36, 109/72).

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