Which of the following is true regarding the solutions to the logarithmic equation below? 2log6(x) = 2 log6" (x?) =2 x^2 = 62 x^2 = 36 X= 6, -6
a. X=-6 are true solutions b. X=6 and X=-8 are extraneous solutions c. X-6 is a true solution and X=-6 is an extraneous solution d. X=6 is an extraneous solution and X=-6 is a true solution

Answer:

Step-by-step explanation:

Quadratic: binomial

Cubic: trinomial

Quartic: four terms

Quintic: five terms

8th degree: six terms

The inverse function of y = 2(x - 5)² is  [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

First to be an inverse function that function needs to one to one function, meaning every different preimage must correspond to a different image.

We can obtain the inverse of a function by switching the variables x and y with their respective positions and solving for y in terms of x.

Let, y = 2(x - 5)².

y/2 = (x - 5)².

Solving for 'x'.

[tex]x - 5 = \pm\sqrt\frac{y}{2}[/tex].

[tex]x = \pm\sqrt\frac{y}{2} + 5.[/tex]

Now, We have to interchange the positions of x and y.

[tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

So, The inverse of y = 2(x - 5)² is [tex]y = \pm\sqrt\frac{x}{2} + 5.[/tex]

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In his financial portfolio by adding an appreciating asset is mortgage

The term portfolio is defined as a collection of a wide range of assets that are owned by investors.

Here we have said collection of financial assets may also be valuables ranging from gold, stocks, funds, derivatives, property, cash equivalents, bonds, etc.

Here we have given that Your friend is confused about types of debts.

as per the definition of portfolio, here we must also understand the concept of financial portfolio,

The term financial portfolio is defined as  a collection of investments and holdings like stocks, bonds, mutual funds, commodities, crypto, cash, and cash equivalents.

Hence the correct option is (c).

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The tens digit of k when sum of its digits is 5 and tens digit of k + 6 is 3.

Let tens digit of k be x and units digit be y. Then

k = 10x + y

The sum of the tens digit of k and the units digit of k is 5, that is

x + y = 5

So possible combinations of (x, y) is (1, 4), (2, 3), (3, 2), (4, 1) and (5, 0).

The tens digit of k+6 is 3.

So x<=3.

14 + 6 = 20

23 + 6 = 29

32 + 6 = 38

So k is 32.

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The area of the octagon, to the nearest square centimeter, is 628 cm^2.

Octagon is a two-dimensional shape with eight sides and eight angles. It is a polygon with eight vertices, and it is one of the most widely recognized geometric shapes. It is often used in architecture, as well as in signage and logo designs. Octagons can also be found in nature, such as in the shape of honeycomb cells, some flower petals, and certain animal eyes.

To calculate the area of an octagon, we need to first calculate the length of the side. To do this we use the formula for the perimeter of an octagon: P = 8s, where s is the length of the side. Solving for s: s = P / 8.

The perimeter of the octagon is 80 cm. So the length of the side is 80 cm / 8 = 10 cm. Now we can use the formula for the area of an octagon: A = 2(1 + √2) s^2. Plugging in our value for s, we get: A = 2(1 + √2) (10 cm)^2 = 628.3 square cm. The area of the octagon, to the nearest square centimeter, is 628 cm^2.

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Answer: 8.7

Step-by-step explanation:

The remaining interior angle is [tex]95^{\circ}[/tex].

[tex]\frac{x}{\sin 33^{\circ}}=\frac{16}{\sin 95^{\circ}}\\\\x=\frac{16 \sin 33^{\circ}}{\sin 95^{\circ}}\\\\x \approx 8.7[/tex]

Answer:

Coupon A

Step-by-step explanation:

Coupon A takes 40% off

51 x .40= $20.40

Coupon B only gives a rebate for $18

Coupon A is $2.40 less than the price with coupon B

Therefore , the solution of the given problem of speed comes out to be

v=10mph is the michael speed in  water.

Distance-based speed is a gauge of how quickly something is moving. The amount of distance a moving object may move in a certain length of time depends on its speed. Speed is calculated using the following equation: velocity = distance x time. The most used units for gauging speed are meters per second (m/s), kilometers per hour (km/h), and kilometers per second (mph) (mph).

Here,

Given :The issue can be rapidly resolved after an equation has been established. Consider the equation time = distance/velocity. Let the speed of moving water equal v. The distance, 182 miles, will be the same both ways.

Downstream time =182/(v+3)

Downstream time + 12 = 182 (v-3)

Set t to the downstream time. Set t=t!

182/(v+3) = 182/(v-3) - 12

Denominators are eliminated by dividing both side by (v+3) (v-3).

12v2 turns out to equal 1200.

Hence, v=10 mph!

Therefore , the solution of the given problem of speed comes out to be

v=10mph is the michael speed in  water.

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The geometric series is 6, -30, 150, -750, 3750, -18750 and the sum of the geometric series is -15624.

A geometric series is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio.

The geometric series that starts with 6, ends with -18,750, and has a common ratio of -5 is:

6, -30, 150, -750, 3750, -18750.

The sum of the geometric series is the sum of all the terms in the series. To find the sum of the series, you can use the formula:

S = a(1 - rⁿ)/(1 - r)

Where:

S is the sum of the series

a is the first term of the series

r is the common ratio

n is the number of terms in the series

In this case, a = 6, r = -5 and n = 6. Thus:

S = 6(1 - (-5)⁶)/(1 - (-5))

S = 6(1 - 15625)/(1 + 5)

S= 6(-15624)/6

S = -15624

Thus, the sum of the geometric series is -15624.

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Answer: 18

unclear but appears its 18.

Step-by-step explanation:

Because x is 7; 4x+8/2 = 36.

but its not clear what is being halved: 8 or (4x+8)? so answer could be 32 as well.

Answer: x= 337/70 or 4 57/70

Step-by-step explanation:

The area of the given prism is equal to 1,920 in³.

What is a rectangular prism?

A rectangular prism is simply a three-dimensional solid shape which with six faces that are rectangles.

We have given,

length l = 8  in.

width w = 12 in,

height h = 20 in.

The volume of a prism is defined as the total space occupied by the three-dimensional object.

The volume of a rectangular prism is given by A = l * w * h,

where 'l' is the length of the prism, 'w' is the width, and 'h' is the height.

so, A = 8 * 12 * 20 = 1,920 in³.

A = 1,920 in³.

Therefore, the area of the given prism is equal to 1,920 in³.

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The relationship between the expressions is that these are inverses.

Here we want to find the relationship between:

logₐ(n) = logₙ(a)

(I changed the variable b for n)

Remember the definition of a logarithm with a base, we can rewrite it as:

logₐ(n) = ln(n)/ln(a)

If we write both of the expressions in that form, we will get:

logₐ(n) = logₙ(a)

ln(n)/ln(a) = ln(a)/ln(n)

So, as you can see, the two expressions are inverses, that is the relation.

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Quadrilateral LMNP has four vertices at the coordinates: L(-4,3), M(2,7), N(9,3), and P(-3,-5).

These vertices can be plotted on to  a Cartesian coordinate plane in order  to form a quadrilateral shape. The shape of the quadrilateral which  can be determined by the relative positions of its one of vertices, such as whether to check  it is a rectangle, square, parallelogram, or any other type of quadrilateral as such . However, without more information or proper data , it is not possible to determine whether the quadrilateral is having  the exact shape of quadrilateral LMNP from just its vertices or not .It is a type of polygon which contains  4 sides, 4 vertices and 4 angles. To make a one  quadrilateral and contains four non-collinear points which  are joined and the sum of all the interior angles and exterior angles is always equal to 360 degrees as we know . The word ‘Quadrilateral’ was initiated  from Latin words ‘Quadra’ and ‘Latus’ which meant four and sides respectively.

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Ram and Shyam laid 80 and 170 bricks respectively.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, Two workers laid 250 bricks. If Ram had laid twice as many as he did and Shyam had laid half as many as Ram did, there would have been 50 bricks left over.

Let each of them initially laid x and y bricks,

Therefore, establishing the equations,

x + y = 250....(i)

According to later condition,

2x + x/2 = 200

4x + x = 400

5x = 400

x = 80

Put x = 80, in equation (i)

80 + y = 250

y = 170

Hence, Ram and Shyam laid 80 and 170 bricks respectively.

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Answer: The correct equation that matches the statement "The product of a number, x, and 0.28 is 13.44" is:

0.28x = 13.44

This equation states that when a number x is multiplied by 0.28, the result is 13.44.

Step-by-step explanation:

The system of inequalities that models this situation is given as follows:

One possible solution is given as follows:

(9,4).

Meaning that he works 9 hours lifeguarding and 4 hours clearing tables.

The variables for the system of inequalities in this problem are given as follows:

The number of hours cannot be negative, hence the first two restrictions are given as follows:

He can work a maximum of 14 total hours, hence:

x + y ≤ 14.

He must earn no less than $180, hence, considering the rates for each job, we have that:

18x + 10y ≥ 180.

Also, he must work no more than 10 hours lifeguarding and no less than 3 hours clearing tables, hence:

The shaded region represents all possible solutions for the system of inequalities.

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The answer and prove are AD = RC, <A≅<R, <AMD≅<RMC

the table shows the statement and the reasons for the proves of congruency of the angles and triangles

The table appears as follows

sn                  Statement                               Reason

1                     AD = RE                                 Given

2                   <A ≅<R                                    Given

3                     <AMD ≅<RMC                      Vertically opposite angles

4                     ΔMAD≅ΔMRC                      Congruent by ASA or SSA

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Answer:

Step-by-step explanation:

Unfortunately, without more information, it is not possible to accurately predict the number of pounds someone would be overweight if they spent 8 hours per day using a computer. The graph provided does not provide enough data to make an accurate prediction. It is possible, however, to make an educated guess based on the graph. Looking at the graph, it appears that someone who spends 8 hours per day on the computer would likely be somewhere between 20 and 40 pounds overweight.

A cone has a radius of 5.1 m and a slant height of 10.9 m. So the surface area of the cone is 87.3834 π m².

These are the specified parameters:

Radius (r) = 5.1 m

Cone height (h) = 10.9 m

Find the length of the cone painter's line (s)

s² = r² + h²

   = 5.1² + 10.9²

   = 26.01 + 118.81

   = 144.82

s = √144.82

s = 12.034

Find the surface area of the cone

A = πr (r + s)

   = π × 5,1 (5.1 + 12.034) m²

   = 5.1 π (17.134) m²

   = 87.3834 π m²

Which would increase the cone's surface area more is doubling the radius.

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When plotting points on a quadratic inequality, the "included" points refer to the points that satisfy the inequality, and the "not included" points refer to the points that do not satisfy the inequality.

Generally, A quadratic inequality is an inequality that can be written in the form of

ax^2 + bx + c > 0 or ax^2 + bx + c < 0,

where a, b, and c are constants and x is a variable.

These types of inequalities can be solved using the same methods as solving quadratic equations, with the added step of testing the solutions in the original inequality to determine whether they are valid solutions.

Simply put, an equation of the kind with the greatest degree two and no equal sign is known as a quadratic inequality. There is a technique for resolving quadratic inequalities called the wavy curve approach. It is the same to solve quadratic equations as it is to solve quadratic inequalities.

For example, if the inequality is "y > x^2," the points that are above the parabola y = x^2 would be included, and the points that are below the parabola would be not included.

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The next year's population will be 140,014. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

For all real numbers, there are four fundamental mathematical operations that are:

1. The sum of the numbers is achieved through addition ('+').

2. Subtraction with the sign "-," which yields the numbers' differences.

3. Multiplication('×') when the result is the product of the numbers.

4. Division ('÷'), which yields the numbers' quotient.

We are given that the population of a city increases by 2.2% per year and this year's population is 137,000.

Let the population of next year be 'x'

So, we get

⇒137,000 + 137,000(2.2%) = x

⇒137,000 + 3014 = x

⇒140,014 = x

Hence, the next year's population will be 140,014.

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Answer: 25q and 3d

Step-by-step explanation:

23 dimes and 17 quarters equal $6.55.

To find the number of dimes and quarters which equals $6.55, we can use the following method:

Let D = number of dimes

Let Q = number of quarters

40 coins  ==>  D + Q = 40  ==>  D = 40 - Q

$6.55 total  ==>  10*D + 25*Q = 655

After the value for D is substituted in the second equation,

10*(40 - Q) + 25*Q = 655

400 - 10*Q + 25*Q = 655

15*Q = 255

Q = 17

i.e., D = 40 - 17 = 23

Check:  23 dimes = $2.30

           17 quarters = $4.25

           Total = $6.55 

Therefore, 23 dimes and 17 quarters equal $6.55.

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Answer: -8

Step-by-step explanation:

As a result, from the equation a 0.622-gram sample of gas with a 2.4-liter volume and 287 K and 0.850 atm has a 7.18-gram molar mass.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14.

An ideal gas is a gas in which the particles (a) do not attract or repel one another and (b) take up no space (have no volume).

[tex]V = 2.4 L = 0.0024\\P = 86126.25 Pa\\T = 287 K\\m = 0.622\\R = 8.314[/tex]

The ideal gas equation is given below.

[tex]n = PV/RT\\n = 86126.25 x 0.0024 / 8.314 x 287\\n = 0.622 / molar mass (n = Avogardos number)\\Molar mass = 7.18 g[/tex]

As a result, a 0.622-gram sample of gas with a 2.4-liter volume and 287 K and 0.850 atm has a 7.18-gram molar mass.

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Answer:

To solve this problem, we will use the following steps:

Step 1: Since a pair of dice are tossed, we have 36 possible outcomes (6 outcomes for each die).

Step 2: To find the probability that doubles are rolled, we can find the number of outcomes that result in doubles and divide that by the total number of possible outcomes.

Step 3: To find the probability that the sum on the two dice is less than 7, we can find the number of outcomes that result in a sum of less than 7 and divide that by the total number of possible outcomes.

Step 4: We will use this probability to find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7.

Step 5: To find the number of outcomes that result in doubles, we can consider rolling (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) which are 6 outcomes.

Step 6: To find the number of outcomes that result in a sum of less than 7, we can consider rolling (1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (2,5), (3,1), (3,2), (3,3), (3,4), (4,1), (4,2), (4,3), (5,1), (5,2) which are 18 outcomes.

Step 7: To find the conditional probability of rolling doubles, given that the sum on the two dice is less than 7, we can find the number of outcomes that result in doubles and sum less than 7 which are (1,1), (2,2), (3,3), (4,4), (5,5) which are 5 outcomes.

Step 8: We can calculate the probability by dividing the number of outcomes that result in doubles and sum less than 7 by the number of outcomes that result in a sum less than 7.

5/18 = 0.278

Final Answer: The probability of rolling doubles, given that the sum on the two dice is less than 7, is 0.278 or 27.8%.

Data set 2 is not a function, while data set 1 is a function. To turn the data set that is not a function into a function, the point (3,0) can be changed so the x-value is not equal to 1, 3, 5 or 7.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

In input-output format, the points in these relations are given as follows:

(x,y).

Hence a data-set will represent a function if each value of x is mapped to a single value of y.

This means that data-set 1 represents a function, while data-set 2 does not, as the value of x = 3 is mapped to both y = 2 and y = 0.

The data-set 2 will represent a function if one of the x-coordinates of 3 is changed to another x-coordinate, that is also different of the other x-coordinates of the table.

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The width and length of the rectangle is 4.5ft and 12ft.

Width of a rectangle = b = x ft.

Length of a rectangle = l = (2x+3) ft.

Area of the rectangle = l×b = 54 sq.ft.

                                    = x (2x + 3) = 54

                                    = 2x² + 3x = 54

                                      (2x-9)(x+6) = 0

The size of a patch on a surface is determined by its area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area can be interpreted as the quantity of material with a specific thickness required to create a model of the shape or as the quantity of paint required to completely cover a surface in a single coat.

 It is the two-dimensional equivalent of the volume of a solid or the length of a curve, both of which are one-dimensional concepts (a three-dimensional concept).

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The square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

Square is a two-dimensional shape with four equal sides and four right angles. It is one of the most common shapes in geometry. Squares have many practical uses, such as in forming grids, creating patterns, and making tiling. Squares are also used in art and architecture, as well as in construction, mathematics, and science.
To solve this problem, we will use the formula for the volume of a rectangular box, V = lwh. We can substitute the given values to solve for x. First, we will find the length and width of the box after the square corners are cut out:

Length = 20 - 2x

Width = 14 - 2x

Now, substituting these values into the volume formula, we get:

288 = (20 - 2x)(14 - 2x)h

Expanding and simplifying, we get:

288 = 280 - 56x + 4x^2

Subtracting 280 from both sides, we get:

8 = -56x + 4x^2

Solving for x, we get:

4x^2 - 56x + 8 = 0

Using the quadratic equation, we get x = 2.4 or x = 0.4

Since x must represent a length, we can discard the negative solution, x = 0.4. Therefore, the square that must be cut from each corner of the cardboard to form a box with a volume of 288 cubic inches is 2.4 inches on each.

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The value of (x + y) is 25.

What is solving an equation?

We must use arithmetic operations to separate the variables in order to solve any equation.

The same number is added on both sides.

Taking away the same number from both sides.

using the same number on both sides of the multiplication.

using the same number on both sides to divide.

Consider, the given equations

2x^2 - 2y^2 = 125              ..(1)

x - y = 2.5                           ..(2)

From equation (1)

x^2 - y^2 = 125/2

By using:  [tex]a^2 - b^2 = (a - b)(a + b)[/tex]

⇒  (x - y)(x + y) = 125/2

Given:  (x - y) = 2.5

⇒ 2.5*(x + y) = 125/2

           (x + y) = 125/(2*2.5)

            x + y = 125/5

            x + y = 25

Hence, the value of (x + y) is 25.

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