I need help with this problem.

x = x² - 22 · x + 141 + x - 11 ÷ 2

your answer will be

10 or 13

Step-by-step explanation:

This is your question just a little different

ANSWER:

STEP-BY-STEP EXPLANATION:

When two lines are parallel the slope is the same.

Therefore, the slope, m = -4

Now, we must calculate the y-intercept, which we calculate starting from the equation in its slope-intercept form, like this

Therefore the equation would be

By translation, the image of the triangle X is equivalent to the triangle E.

Herein we find the representation of a triangle, whose vertices are described below:

A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)

Whose image must be determined by a rigid transformation known as translation:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the images of the vertices of the triangle:

A'(x, y) = (5, 5) + (4, - 3)

A'(x, y) = (9, 2)

B'(x, y) = (5, 6) + (4, - 3)

B'(x, y) = (9, 3)

C'(x, y) = (7, 5) + (4, - 3)

C'(x, y) = (11, 2)

Therefore, the triangle E is the image of the triangle X.

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Answer:

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

15 is the total number of all possible combinations for choosing 2 elements at a time from 6 distinct elements without considering the order of elements in statistics & probability surveys or experiments.

a. About 50% of the students scored less than 78.

b. Approximately 68% of the students scored between 75 and 78.

c. Approximately 95% of the students scored between 72 and 81.

d. Approximately 99.7% of the students scored between 69 and 75.

a) The normal curve is symmetrical, meaning that the area to the left of the mean is equal to the area to the right of the mean. Since the mean score is 78, 50% of the students scored above 78 and 50% scored below 78.

b) To apply the Empirical Rule, we will assume that 68% of the data falls within one standard deviation of the mean, which in this case is 3 points. So, 68% of the students scored between 75 and 81.

c) The percentage of students who scored between 72 and 81 can be found by subtracting the area to the left of 72 from the area to the left of 81. Using the Empirical Rule, we know that 95% of the observations are within two standard deviations of the mean, so the area between 72 and 81 is equal to 95%.

d) The percentage of students who scored between 69 and 75 can be found by subtracting the area to the left of 69 from the area to the left of 75. Using the Empirical Rule, we know that 99.7% of the observations are within three standard deviations of the mean, so the area between 69 and 75 is equal to approximately 99.7%.

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a) To re-express the given differential equation as a first-order differential equation using matrix and vector notation, we can rewrite it in the form:

\(x' = Ax\)

where x is a vector and A is a square matrix.

b) To determine the stability of the system obtained in part (a), we need to analyze the eigenvalues of matrix A.

If all eigenvalues have negative real parts, the system is stable.

If at least one eigenvalue has a zero real part, the system is neutrally stable.

If at least one eigenvalue has a positive real part, the system is unstable.

c) To compute the eigenvalues and eigenvectors of matrix A, we solve the characteristic equation

\(det(A - \lambda I) = 0\),

where λ is the eigenvalue and I is the identity matrix.

By solving this equation, we obtain the eigenvalues.

Substituting each eigenvalue into the equation

\((A - \lambda I)v = 0\),

where v is the eigenvector, we can solve for the eigenvectors.

d) Once we have computed the eigenvalues and eigenvectors of matrix A, we can construct the diagonalization relationship as follows:

\(A = PDP^{(-1)}\)

where P is a matrix whose columns are the eigenvectors of A, and D is a diagonal matrix whose diagonal elements are the eigenvalues of A.

To show that this relationship is valid, we can compute \(PDP^{(-1)}\) and verify that it equals A.

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Answer: $980

$25480

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

The sum of payments made n times per year for t years and earning annual interest rate r is the value of a single payment multiplied by k, where ...

  k = ((1 +r/n)^(nt) -1)/(r/n)

__

Problem 1

The multiplier k is ...

  k = ((1 +0.08/4)^(4·25) -1)/(0.08/4) ≈ 312.232306

Then the quarterly deposit needs to be ...

  $300,000/312.232306 ≈ $960.82

The sum of the 100 quarterly payments is ...

  100 × $960.82 = $96,082

So, the amount of interest earned is ...

  $300,000 -96,082 = $203,918

__

Problem 2

The multiplier k is ...

  k = ((1 +0.072/12)^(12·30) -1)/(0.072/12) ≈ 1269.22544

Then the balance resulting from monthly deposits of $250 will be ...

  $250 × 1269.22544 = $317,306.36

The total of the 360 payments is $90,000, so the interest earned is ...

  $317,306.36 -90,000 = $227,306.36

_____

Additional comment

In the case of Problem 1, the deposit amount is rounded down to the nearest cent. This means that the account balance at the end of 25 years will be slightly less than $300,000. The difference is on the order of $0.96. This means both the account balance and the actual interest earned are $0.96 less than the amounts shown above.

In many of these school calculations, we ignore the effect of rounding the payment values. Similarly, we ignore the effect of rounding the account balance values for each monthly or quarterly statement. In real life, the final payment of a series is often adjusted to make up the difference caused by this rounding.

Also worthy of note is that the calculations here assume the payments are made at the end of the period, not the beginning. That makes a difference.

Answer:

Step-by-step explanation:

D

Answer:

X=-2 x=1 x=3 and x=-1

Step-by-step explanation:

When the problem asks you to find the zeros all they are asking for is the solution so to solve all you need to do is set each individual piece equal to zero.

Answer:

72°

Step-by-step explanation:

4+2+6+8=20

360÷20=18

AC=4x18=72

Using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

What is meant by the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. This method allows us to calculate both the value of many units from the value of one unit and the value of one unit from the value of many units. In the unitary technique, the value of a unit or one quantity is always counted first, and the values of additional or fewer quantities are then determined. This method is known as the unitary method for this reason.

Given,

The cost of an ounce of medium soft serve = $0.56

The amount of soft serve in a medium size  = 6.5 ounces

We are asked to find the cost of the total amount of soft serve in a medium size.

This can be done using the unitary method.

If 1 ounce = $0.56

Then for 6.5 ounces, the cost is = 6.5 * 0.56 = $3.64

Therefore using the unitary method, we found out that the cost of 6.5 ounces of a medium soft serve is $3.64.

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A = 14°

Step-by-step explanation:

We can use sine law in this situation, where

\(\dfrac{\sin A}{a} =\dfrac{\sin B}{b}\)

where a and b are the lengths of the sides opposite the corresponding angles. From the given diagram, we can see that

\(\dfrac{\sin A}{7\:\text{yd}} = \dfrac{\sin 75°}{28\:\text{yd}}\)

or

\(\sin A = \dfrac{7}{28}\sin 75° = 0.241\)

Solving for the angle A, we get

\(A = \sin^{-1}(0.241) = 14°\)

To make this problem solvable, I have replaced the 't' in the second equation for a 'y'.

Answer:

x = -9

y = 2

Step-by-step explanation:

Solve the system:

2x + 3y = -12       [1]

2x + y = -16       [2]

Subtracting [1] and [2]:

3y - y = -12 + 16

2y = 4

y = 4/2 = 2

From [1]:

2x + 3(2) = -12

2x + 6 = -12

2x = -18

x = -18/2 = -9

Solution:

x = -9

y = 2

Answer: 3?

Step-by-step explanation:

Im wrong :)

The length of the base of the triangle is 8 yards whose height is half of 28 yards.

A triangle is a two-dimensional geometric shape that is formed by three straight lines that connect three non-collinear points. These three lines are called the sides of the triangle, and the points where the sides meet are called the vertices of the triangle.

The following formula provides the area of a triangle:

Area = (1/2) x base x height

We are given that the height of the triangle is half of 28 yards, which is:

height = 1/2 x 28 = 14 yards

We are also given that the area of the triangle is 56 square yards. Substituting these values into the formula for the area, we get:

56 = (1/2) x base x 14

Simplifying this equation, we get:

56 = 7 x base

Dividing both sides by 7, we get:

base = 8

Therefore, the length of the base of the triangle is 8 yards.

The vertices are typically denoted by letters, such as A, B, and C. The three angles formed by the sides are also part of the triangle.

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The radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis is 27\(a^{\frac{3}{2}\).

To find the radius of curvature of the curve \(a^{2y\)=x³-a³ at the point where the curve intersects the x-axis, we need to first find the equation of the curve and then determine the value of y and its derivative at that point.

When the curve intersects the x-axis, y=0. Therefore, we have:

a⁰ = x³ - a³

x³ = a³

x = a

Next, we need to find the derivative of y with respect to x:

dy/dx = -2x/(3a²√(x³-a³))

At the point where x=a and y=0, we have:

dy/dx = -2a/(3a²√(a³-a³)) = 0

Therefore, the radius of curvature is given by:

R = (1/|d²y/dx²|) = (1/|d/dx(dy/dx)|)

To find d/dx(dy/dx), we need to differentiate the expression for dy/dx with respect to x:

d/dx(dy/dx) = -2/(3a²(x³-a³\()^{\frac{3}{2}\)) + 4x²/(9a⁴(x³-a³\()^{\frac{1}{2}\))

At x=a, we have:

d/dx(dy/dx) = -2/(3a²(a³-a³\()^{\frac{3}{2}\)) + 4a²/(9a⁴(a³-a³\()^{\frac{1}{2}\)) = -2/27a³

Therefore, the radius of curvature is:

R = (1/|-2/27a³|) = 27\(a^{\frac{3}{2}\)

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To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).

Assuming the height of the rectangular prism is h inches.

According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.

The total surface area of the rectangular prism is given by the formula:

Surface Area = 2lw + 2lh + 2wh

Substituting the values, we have:

576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)

576 = 8h² + 4h² + 4h²

576 = 16h² + 4h²

576 = 20²

h² = 576/20

h² = 28.8

h = √28.8

h = 5.37

The height of the prism is approximately 5.37 inches.

The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.

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The value of x that satisfies the given statement is 5.

The given statement can be written as an equation:

The excess of 15 over x is 10

15 - x = 10

To solve for x, we can isolate the variable on one side of the equation. Adding x to both sides, we get:

15 - x + x = 10 + x

Simplifying the left side, the x terms cancel out:

15 = 10 + x

Subtracting 10 from both sides, we get:

15 - 10 = x

Simplifying the left side, we get:

5 = x

x = 5

Therefore, the value of x is 5.

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Answer:

2100

Step-by-step explanation:

Answer:

3.025 as a fraction is 121/40

check your textbook for the remainder theorem, where it states that for a factor (x-5) of f(x) then the remainder will be 0, thus f(5) = 0, what the heck all that means?

well, it means that if we evaluate f(5) our result should be 0, so

\(\stackrel{factor}{(x-5)}\hspace{5em}f(5)=(5)^3-7(5)^2+(5)+a=0 \\\\\\ 0=(5)^3-7(5)^2+(5)+a\implies 0=125-175+10+a \\\\\\ 0=-40+a\implies \boxed{40=a}\)

186 cm³ will be the surface area of the given figure.

To calculate the surface area of the given figure, we need to add the surface area of two cubes and reduce the area of the hidden part.

Thus,

Total surface area = Surface area of bigger cube + surface area of the smaller cube - 2* surface area of the hidden part.

So,

Total surface area = 6*(5*5)+6*(3*3)-2*(3*3)

Total surface area = 150+54-18

Total surface area = 186

Therefore, the surface area of the given figure will be 186 cm³.

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Answer:

To get the additive inverse of a positive number you put a minus in front of it and to get the additive inverse of a negative number, you remove the minus to make it a positive number.

Answer:

It 2/4

Step-by-step explanation:

t 2/4 because on the graph the lines is on 2/4

The most appropriate choice for corrosponding angle will be given by-

x = 2 is the correct answer

What is corrosponding angle?

At first we need to understood what is angle, parallel lines and transversal

Angle

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Parallel lines

Two lines are said to be parallel if on extending them indefinitely, they will never intersect

Transversal

Transversal is a line that intersects two or more parallel lines

Corrosponding angle

The angles formed in the same position on the same side of transversal when a transversal cuts two or more parallel lines

Here,

(7x + 3)° and (8x + 1)° are corrosponding angles.

Lines m and n are parallel.

So corrosponding angles are equals

By the problem,

(7x + 3) = (8x + 1)

8x - 7x = 3 - 1

x = 2

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The reason that justifies the second statement "Angle L is congruent to angle T" is:

In a parallelogram, opposite angles are congruent.

Option C is the correct answer.

A parallelogram is a quadrilateral that has two pairs of parallel sides.

In a parallelogram, opposite sides and angles are equal.

The adjacent angles add up to 180 degrees.

We have,

Parallelogram LENS and parallelogram NGTH

Now,

Parallelogram LENS:

∠L = ∠N _____(1)

Opposite angles are equal.

Parallelogram NGTH:

∠N = ∠T ______(2)

Opposite angles are equal.

Now,

∠ENS = ∠GNH

Vertical angles are equal.

So,

From (1) and (2).

∠L = ∠T

Angle L is congruent to angle T

Thus,

Angle L is congruent to angle T

[ In a parallelogram, opposite angles are congruent ].

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