Select all the expressions that have a value of 40 when x = 10.8.

Answer:

Area = x² + 7x

Step-by-step explanation:   5 15 8 19

Area = LW

Area = x(x+7)

Area = x² + 7x

We are given that Bank A charges ordinary interest for a loan of $11000 at a rate of 9% for a period of 90 days, we can calculate the total interest using the formula for ordinary interest, this is:

Replacing that we get:

Solving we get:

Now, bank B charges exact interest, the formula is:

Replacing we get:

solving the operation:

Therefore, she will pay less interest to Bank B. Bank B offers a better deal.

Answer:

\(w^{22}\)

Step-by-step explanation:

\((w^3)^4\cdot(w^5)^2=w^{3*4}\cdot w^{5*2}=w^{12}\cdot w^{10}=w^{12+10}=w^{22}\)

Answer:

see explanation

Step-by-step explanation:

vertical angles are angles on the opposite side at a vertex of 2 lines.

1 and 6 , 2 and 5 , 3 and 8 , 4 and 7 are all vertical angles

supplementary angles sum to 180°

adjacent angles on a straight line sum to 180°

1 and 2 , 3 and 4 , 5 and 6 , 7 and 8 are examples of supplementary angles.

Using quadratic function concepts, it is found that the true statements about the equation are:

A quadratic function is given according to the following rule:

\(y = ax^2 + bx + c\)

\(x_v = -\frac{b}{2a}\)

\(y_v = -\frac{\Delta}{4a}\)

\(\Delta = b^2 - 4ac\)

\(x_1 = \frac{-b + \sqrt{\Delta}}{2a}\)

\(x_2 = \frac{-b - \sqrt{\Delta}}{2a}\)

In this problem, the function is:

\(f(x) = x^2 - 6x + 2\)

The coefficients are \(a = 1, b = -6, c = 2\).

Since a > 0, the graph has a minimum value.

For the extreme value, we have that:

\(x_v = -\frac{b}{2a} = \frac{6}{2} = 3\)

\(\Delta = b^2 - 4ac = (-6)^2 - 4(1)(2) = 28\)

\(y_v = -\frac{\Delta}{4a} = -\frac{28}{4} = -7\)

Hence:

The extreme value is at the point (7,-3).

The solutions are:

\(x_1 = \frac{6 + \sqrt{28}}{2} = \frac{6 + 2\sqrt{7}}{2} = 3 + \sqrt{7}\)

\(x_2 = \frac{6 - \sqrt{28}}{2} = \frac{6 - 2\sqrt{7}}{2} = 3 - \sqrt{7}\)

The solutions are \(3 \pm \sqrt{7}\).

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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Answer:

A

Step-by-step explanation:

Given equation :

Evaluating the options

A (-2, 5)

The question is incomplete:

The cost of a parking permit consists of a one-time administration fee plus a monthly fee. A permit purchased for 12 months costs $660. A permit purchased for 15 months costs $810.

What is the administration fee?

Answer:

$60

Step-by-step explanation:

To calculate the administration fee, first you have to calculate the difference between the two permits and divide that by the month difference that is: 15-12= 3 to know the cost of the monthly fee:

$810-$660= 150

$150/3= $50

Now, you can multiply the monthly fee for 12 to know the total cost of the monthly fee for 12 months and then, subtract this from the cost of a permit purchased for 12 months to find the cost of the one-time administration fee:

$50*12= $600

$660-$600= $60

According to this, the administration fee is $60.

\(f(x)^{-1}\) =-5±\(\sqrt{x}\) for the domain [0, ∞). A function's domain is the set of potential inputs, or the set of input values for which the function is defined.

Since the term "domain" refers to a set of possible input data, the domain of a graph is composed of all the input data shown on the x-axis. The y-axis on a graph denotes the range of possible output values. Think about the equation y = f(x), where x and y are the independent and dependent variables. Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f. Choose the input values. Exclude any real numbers that produce a negative value in the radicand because there is an even root.

f(x)=\((x+5)^{2}\)

±\(\sqrt{f(x)}\)=x+5

x=-5±\(\sqrt{f(x)}\)

So, \(f(x)^{-1}\)=-5±\(\sqrt{x}\)

Because the domain of f(x) is (-5, ∞).

So,   \(f(x)^{-1}\) =-5±\(\sqrt{x}\)

Because x ≥ 0

So, the domain is [0, ∞).

(According to the mathematical algorithm).

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\(f(x)^1\) =-5±\(\sqrt{x}\) for the domain [0, ∞). A function's domain is the set of potential inputs, or the set of input values for which the function is defined.

Since the term "domain" refers to a set of possible input data, the domain of a graph is composed of all the input data shown on the x-axis. The y-axis on a graph denotes the range of possible output values. Think about the equation y = f(x), where x and y are the independent and dependent variables. Think about the equation y = f(x), where x and y are the independent and dependent variables. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f. Choose the input values. Exclude any real numbers that produce a negative value in the radicand because there is an even root.

f(x)= \((x+5)^2\)

±\(\sqrt{f(x)}\)=x+5

x=-5±\(\sqrt{f(x)}\)

So, \(f(x)^-^1\) =-5±\(\sqrt{x}\)

Because the domain of f(x) is (-5, ∞).

So,  \(f(x)^-^1\)  =-5±\(\sqrt{x}\)

Because x ≥ 0

So, the domain is [0, ∞).

(According to the mathematical algorithm).

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i cant see anything but dashes..

Answer:

\(AD = 403.75\)

\(CD = 115.70\)

\(BD = 294.93\)

Step-by-step explanation:

Given

The above triangle

Solving (a): AD

To solve AD, we consider triangle ACD.

Using cosine formula:

\(cos(\angle A) = \frac{AD}{AC}\)

Where:

\(\angle A =16\)

\(AC = 420\)

So:

\(cos(16) = \frac{AD}{420}\)

\(AD = 420 * cos16\)

\(AD = 420 * 0.9613\)

\(AD = 403.75\)

Solving (b):  CD

Here, we make use of Pythagoras theorem:

\(AC^2 = AD^2 + CD^2\)

So:

\(420^2 = 403.75^2 + CD^2\)

\(176400 = 163014.0625 + CD^2\)

\(CD^2 = 176400 - 163014.0625\)

\(CD^2 = 13385.9375\)

\(CD = \sqrt {13385.9375\)

\(CD = 115.70\)

Solving (c): BD

Here, we make use of Pythagoras theorem:

\(AB^2 = AD^2 + BD^2\)

\(BD^2 = AB^2 - AD^2\)

\(BD = \sqrt{AB^2 - AD^2\)

\(BD = \sqrt{500^2 - 403.75^2\)

\(BD = \sqrt{86985.9375\)

\(BD = 294.93\)

Answer:

The answer is d

Step-by-step explanation:

This table shows the frequency of each number obtained after throwing the die 35 times

To prepare a frequency table based on the numbers obtained from throwing a die 35 times, we can list the numbers from 1 to 6 and count the frequency of each number.

Numbers: 1, 2, 3, 4, 5, 6

Frequency: 5, 14, 6, 4, 5, 1

Based on the given numbers, the frequency table would look like this:

Number   | Frequency

1                      5

2                     14

3                      6

4                      4

5                      5

6                       1

This table shows the frequency of each number obtained after throwing the die 35 times.

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Answer:

5.08

Step-by-step explanation:

2.17+2.91 = 5.08

Answer:

multiply each by -1

-5/6 x -1 = 5/6

-7 3/8 x -1 = 7 3/8

-3/11 x -1 = 3/11

Step-by-step explanation:

On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

B) 40 feet

Step-by-step explanation:

Essentially, there are two similar right triangles in the given problem.

base_L = Base [larger triangle] = 60 ft

base_S = Base [smaller triangle] = 6 ft

x = leg (larger triangle)

y = leg (smaller triangle) = 4 ft

Using the given proportion to solve for the value of x:

\(\frac{x}{base_{_L} } = \frac{y}{base_{_S} }\)

\(\frac{x}{60ft} = \frac{4 ft}{6 ft}\)

6x = 240

Divide both sides by 6:

6x/6 = 240/6

x = 40

Answer:

Median: 3,3,4,5,6,7,10,11,12

Answer:

6

Step-by-step explanation:

We need to arrange the numbers 3, 11, 6, 5, 4, 7, 12, 3 and 10  in increasing order

3, 3, 4, 5, 6, 7, 10, 11, 12

Next, we need to find such a number so that it is middle one and hase equal amount of number on either side of it

median = 6

First, notice that both triangles are congruent. Corresponding parts of congruent triangles are also congruent.

Identify the corresponding parts of the triangle to find which parts are congruent.

The correspondence between the vertices of the triangle is such that:

Which means that the following segments are congruent:

And the following angles are congruent:

From the given options, check the ones that show a correct congruence relation between the parts of the triangles.

Therefore, the correct options are:

- Segment JL is congruent to segment JK.

- Segment HL is congruent to segment KI.

- Angle LJH is congruent to angle KJI.

To find a particular solution of the non-homogeneous equation and the general solution of the equation, we can use the method of variation of parameters.

First, let's find the Wronskian of the homogeneous solutions y1(x) and y2(x):

W(y1, y2) = | y1 y2 |

| y1' y2' |

We have y1(x) = sin(x) / √x and y2(x) = cos(x) / √x. Differentiating these functions, we get:

y1'(x) = (cos(x) / √x - sin(x) / (2√x^3))

y2'(x) = (-sin(x) / √x - cos(x) / (2√x^3))

Substituting these values into the Wronskian:

W(y1, y2) = | sin(x) / √x cos(x) / √x |

| (cos(x) / √x - sin(x) / (2√x^3)) (-sin(x) / √x - cos(x) / (2√x^3)) |

Expanding the determinant:

W(y1, y2) = (sin(x) / √x) * (-sin(x) / √x - cos(x) / (2√x^3)) - (cos(x) / √x) * (cos(x) / √x - sin(x) / (2√x^3))

Simplifying:

W(y1, y2) = -1 / (2√x)

Now, we can find the particular solution using the variation of parameters formula:

y_p(x) = -y1(x) * ∫(y2(x) * g(x)) / W(y1, y2) dx + y2(x) * ∫(y1(x) * g(x)) / W(y1, y2) dx

Here, g(x) = 3x√xsin(x). Substituting the values:

y_p(x) = -((sin(x) / √x) * ∫((3x√xsin(x)) * (-1 / (2√x))) dx + (cos(x) / √x) * ∫((3x√xsin(x)) / (2√x)) dx

Simplifying the integrals:

y_p(x) = -(∫(-3sin^2(x)) dx) + (∫(3xcos(x)sin(x)) dx)

Integrating:

y_p(x) = 3/2 (xsin^2(x) - cos^2(x)) - 3/2 (xcos^2(x) + sin^2(x)) + C

Simplifying:

y_p(x) = 3x(sin^2(x) - cos^2(x)) + C

The general solution of the equation is given by the sum of the homogeneous solutions and the particular solution:

y(x) = C1 * (sin(x) / √x) + C2 * (cos(x) / √x) + 3x(sin^2(x) - cos^2(x)) + C

where C1, C2, and C are arbitrary constants.

Answer:

Step-by-step explanation:

Sjaoa

The required cross-sectional area in a wireway is 12.8 In squared.

The percentage is defined as a ratio expressed as a fraction of 100.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

+ Addition operation: Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.

for example 4 -2 = 2

We have been given an 8"×8"×6' long wireway the conductors can occupy.

Since the NEC permits 20% of the cross-sectional area in a wireway to be occupied by conductors

So the required cross-sectional area in a wireway is

⇒ 20 % of ( 8"×8" )

⇒ 0.20 × (64 )

⇒ 12.8 In squared

Thus, the required cross-sectional area in a wireway is 12.8 In squared.

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The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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Answer:

x = 3/2 or x = -1

Step-by-step explanation:

2x² - x - 3 = 0

2*(-3) = -6

Factors of -6:

(-1, 6), (1, -6), (-2, 3), (2, -3)

We need to find a pair that adds up to the co-eff of x which is (-1)

Factors :(2,-3)

2 - 3 = -1

so, 2x² - x - 3 = 0 can be written as:

2x² + 2x - 3x - 3 = 0

⇒ 2x(x + 1) -3(x + 1) = 0

⇒ (2x - 3)(x + 1) = 0

⇒ 2x - 3 = 0 or

x + 1 = 0

⇒ 2x = 3 or x = -1

⇒ x = 3/2 or x = -1

Answer:

125.4

Step-by-step explanation:

Given

\(Number = 125.3546\)

Required

Round to 1 decimal place

Up till the first decimal place, the number is:

\(Number = 125.3\)

The digit after .3 is 5

The conditions for approximation are:

In this case: 5 > 4, so we approximate to 1

Add this "1" to the last digit of 125.3. This becomes 125.4

Hence: when the number is approximated to 1 decimal place, the digit is 125.4

The average retail value of the SUV is,

⇒ $9,455

We have to given that;

A used-vehicle guide shows the average retail value is $9,480. Add $150 for air-conditioning, $75 for anti-lock brakes, and $150 for the Global Positioning System (GPS). Subtract $100 for a manual transmission and $300 for excessive mileage.

Hence, The average retail value of the SUV is,

⇒ 9,480 + 150 + 75 + 150 - 100 - 300

⇒ $9,455

Thus, The average retail value of the SUV is,

⇒ $9,455

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Answer:

x = ±8

Step-by-step explanation:

The given equation is :

\(3x^2-192=0\)

We can use the Square root Property to solve it.

Adding 192 both sides,

\(3x^2-192=0\\\\3x^2=192\)

Dividing both sides by 3.

\(x^2=64\\\\x=\sqrt{64} \\\\x=\pm 8\)

So, the value of x is equal to +8 and -8.

Answer:

6,000 in scientific notation is 6⋅103