Please help.
Is Algebra.

The value of [tex]f^{-1}(49)[/tex] is 4

The given function is:

[tex]f(x)=(x+3)^2[/tex]

Let f(x) be represented by y

[tex]y=(x+3)^2[/tex]

Make x the subject of the formula

[tex]\sqrt{y} =x+3[/tex]

Subtract 3 from both sides

[tex]x=\sqrt{y} -3[/tex]

Replace x by [tex]f^{-1}(x)[/tex] and let y be replaced by x

[tex]f^{-1}(x)=\sqrt{x} -3[/tex]

Substitute x = 49 into the inverse function

[tex]f^{-1}(x)=\sqrt{49} -3\\\\f^{-1}(x)=7-3\\\\f^{-1}(x)=4[/tex]

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Answer:

as x is approaching positive infinity, y approaches positive infinity

as x is approaching negative infinity, y is approaching negative infinity

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

An even number can be defined as a type of number which is divisible by two (2) without any remainder.

Since this 2-digit numbers are even and its digits are distinct, we can infer and logically deduce the following points:

By counting all the even 2-digit numbers between 10 and 100, there are 41 even and distinct digits.

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The ratio of the lemon water is 10:1

From the information, we have that;

The ratio of water to strawberry juice  is 2 : 1

That of strawberry juice to lemon juice is 5: 1

The, we have that of water to lemon juice to be 10: 1 when compared

Hence,  the ratio of the lemon water is 10: 1

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There are 0 intersections between the railroad and the highway and there are 2 intersections between the railroad and the turnpike

From the graph, we have the following points on the railroad

(x, y) = (3, 3) and (0, 5)

The slope is calculated as:

m = (y2 - y1)/(x2 - x1)

This gives

m = (5 -3)/(0 - 3)

Evaluate

m = -2/3

The equation is then calculated as:

y = mx + b

This gives

y = -2/3x + b

Substitute (0, 5)

5 = -2/3 * 0 + b

This gives

b = 5

Substitute b = 5 in y = -2/3x + b

y = -2/3x + 5

Multiply through by 3

3y = -2x + 15

Rewrite as:

2x + 3y = 15

The equation of the highway's path is

2x+3y=21

So, we have:

2x+3y=21

2x + 3y = 15

Subtract the equations

2x - 2x + 3y - 3y = 21 - 15

Evaluate

0 = 6

The above equation is false because 0 and 6 are not equal.

This means that the system of equations have no solution

Hence, there are 0 intersections between the railroad and the highway.

Here, we have

y = x^2 and 2x + 3y = 15

Substitute y = x^2 in 2x + 3y = 15

2x + 3x^2 = 15

Rewrite as:

3x^2 + 2x - 15 = 0

Calculate the discriminant using

d =b^2 - 4ac

This gives

d = 2^2 - 4 * 3 * -15

Evaluate

d = 184

The discriminant d is greater than 0.

This means that the equation has 2 real solutions

Hence, there are 2 intersections between the railroad and the turnpike

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Answer:

Step-by-step explanation:

Answer:

Refer to the attached image!!

Hope it helps!

Answer:

$0.45.

Step-by-step explanation:

Total amount of money held by all 5 children

= 5 * 0.50 = $2.50.

After 0.25 is lost the total = $2.25.

So the new average = 2.25 / 5

= $0.45.

The value of Mario's car after 5 years is $8,249.

Deprecation is when the value of an asset declines with the passage of time as a result of wear and tear.

V = 15,999 − 1,550t

V = 15,999 − 1,550(5)

V = 15,999 - 7,750

V =$8,249

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Answer:

Domain: All real numbers (infinite) Range: [tex]y \leq -4[/tex]

Step-by-step explanation:

For the domain, the x-axis will continue to be used for the parabola, because the parabola can go on forever and can use an x- value on the x-axis. For the range, the largest number the parabola will go up to is -4. Therefore, if that is the highest point/ where the vertex is, the highest point on the y-axis is -4, resulting in the answer y can be equal to or less than -4 (y [tex]\leq[/tex] -4), since the parabola will continue to go down with the reflection over the x-axis.

Answer:

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

Step-by-step explanation:

using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇒ x = [tex]b^{n}[/tex]

given

[tex]log_{2x}[/tex] (x² - 5x + 17) = 3x , then

x² - 5x + 17 = [tex](2x)^{3x}[/tex]

[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 10 {}^{5} ) \sdot(2 .3 \times {10}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: (1.6 \times 2.3) \sdot(10 {}^{5} \times 10 {}^{1} )[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3.68 \times 10 {}^{6} [/tex]

The correct order to express cos3x in terms of cosx is; As shown in steps 1 to 9 below.

The steps to simplify the trigonometric identities cos 3x in terms of cos x are as follows;

Step 1; cos x = cos(2x + x)

Step 2; cos(2x) cosx - sin(2x) sinx

Step 3; 1 - 2sin^2x(cosx) -(2sinxcosx)sinx

Step 4; cosx - 2sin²x cosx - 2sin²x cosx

Step 5; cosx - 4sin²x cosx

Step 6; cosx( 1 - 4sin²x)

Step 7; cosx{1 - 4(1 - cos²x)}

Step 8; cosx{-3 + 4cos²x}

Step 9; 4cos³x - 3cosx

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Answer:

x is 14

1st is 14

2nd is 20

Step-by-step explanation:

4/7 (x ) = (34 - x )(2/5)

4x/7 + 2x/5 = 34 x 2/5 = 68/5

34x/35 = 68/5

x = 14

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Answer:

No it isn't

As the variable "x" has root in it which means it isn't a whole number and for a expression to be a polynomial the variable must be whole no.

Hope it helps you!

Answer:

yes

Step-by-step explanation:

A polynomial is an algebraic expression of two or more terms

[tex]x^{2} +4\sqrt{x}[/tex]  It is an algebraic expression of two terms, It is more common to label it binomial, but it is also a polynomial.

Hope this helps

The length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.

The area of a figure is the total space enclosed in two dimensions within its boundary.

The area of a rectangle is given as, area = length*width.

In the question, we are given that the area of a rectangle is represented by 25x³y⁶ and its width is represented by 10xy, and are asked to express the length of this rectangle in terms of x and y.

We know that the area of a rectangle is given as, area = length*width.

Substituting the known values in the equation, we get:

25x³y⁶ = length*10xy.

Rearranging this equation, we get:

length = 25x³y⁶/10xy = (5x²y⁵)/2 = 2.5x²y⁵.

Thus, the length of the rectangle in terms of x and y, given that its area is represented by 25x³y⁶ and its width is represented by 10xy is 2.5x²y⁵.

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Answer:

[tex]g(f(x))=25x^2-15x-7[/tex]

domain: (-∞,∞)

Step-by-step explanation:

g of f means plug the function f(x) in to x in the function g(x)

[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]

since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)

The required equation based on the information given is y =0.433x + 24.493

It should be noted that one can simply copy and paste the data set into excel sheet

Then, use intercept and the slope formula to find slope and intercept. We will have

slope = SLOPE(y values, x values)

= 0.433

intercept = INTERCEPT(y values, x values)

= 24.493

Therefore, the required equation is y =0.433x + 24.493

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Answer:

the red curve is a hyperbola

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

The volume of a cylinder is calculated using the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.

The expression used by Aiden to calculate the volume of a cylinder is π(16)(12), or, π(4²)(12).

Comparing this expression with the general formula of the volume of a cylinder, V = πr²h, where V is its volume, r is its radius, and h is its height, we can say that the radius can be 4 units and the height can be 12 units.

Assuming the units to be cm, we can say that:

The dimensions of the given cylinder are that its height is 12cm, while its base radius is 4cm, which implies its diameter is 8 cm.

Thus, the first option, The height is 12 cm, and the diameter of the base is 8 cm, is the right choice.

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The complete question is:

Aiden evaluated the expression π(16)(12) to find the volume of a cylinder. What could be the dimensions of the cylinder?

The height is 12 cm, and the diameter of the base is 8 cm.

The height is 12 cm, and the area of the base is 16 cm².

The height is 16 cm, and the diameter of the base is 6 cm.

The height is 16 cm, and the area of the base is 12 cm².

The average rate of change in weight is 3/8.

According to the statement

Weight of baby during birth = 3 kg

Weight of baby after 8 months = 6 kg

Average rate of change of in weight is calculated by

Average rate = Increased weight - Real weight / Time period

Average rate = 6-3 / 8

Average rate = 3/8

So, the average rate of change in weight is 3/8.

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Using percentage of its total accounts the $50,000 is the amount to be uncollectible. The amount of $50,000 will be reported as an allowance for uncollectible accounts for the Year 2 on December 31 in the balance sheet.

According to the question,

Under the approach of the balance sheet, the ending balance of the allowance for the uncollectible accounts is the percentage (%) of the ending balance of the accounts receivable.

The amount of uncollectible accounts should reflect the aggregate needed ending balance of the allowance which amounts to $50,000.

Hence, using percentage of its total accounts the $50,000 is the amount to be uncollectible.

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The number of visitors to the homepage of an online magazine in the year 2005 is 3527

An equation is an expression that shows the relationship between two or more number and variables.

Let y represent the total number of visitors x years since 2000. Hence:

y = 1100.74x - 1976.47

In the year 2005 (x = 5):

y = 1100.74(5) - 1976.47 = 3527.23

The number of visitors to the homepage of an online magazine in the year 2005 is 3527

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By applying the law of cosine, the length of side BM is equal to 7.05 cm..

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides. Also, some examples of a polygon include the following:

Note: The number of sides (n) of a pentagon is 5.

In Geometry, the interior angle of both a regular and irregular polygon is given by this formula:

Interior angle = 180 × (n - 2)/n

Interior angle = 180 × (5 - 2)/5

Interior angle = 180 × 3/2

Interior angle = 108°.

For the central angle, we have:

Central angle, O = 360/5

Central angle, O = 72°.

By applying the theorem of intersecting secants, angle OCB will be given by this formula:

<OCB = ½ × (180 - 72)

<OCB = ½ × 108

<OCB = 54°.

In order to determine the length of side BM, we would apply the law of cosine:

cos(θ) = Adj/Hyp

cos54 = BM/12

BM = 12 × cos54

BM = 12 × 0.5878

Side BM = 7.05 cm.

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Answer:

x ^ (1/3)

Step-by-step explanation:

solution:

the answer is in the picture I have sent.

I hope this will help you

Answer:

Exact form: 19 multiply 4200^28 + 1972^31 / 19

Decimal form: 3.55481422 multiply 10^101

Answer:

a₃₂ = 131

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 7 and d = 4 , then

a₃₂ = 7 + (31 × 4) = 7 + 124 = 131

Answer:

I don't understand what the question is what do you need to find?

If the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is: D. random.

A fair coin can be defined as an idealized type of coin that has an equal probability of revealing both heads and tails when randomly flipped or tossed by anybody.

This ultimately implies that, the outcome of flipping a fair coin is generally going to produce only one of two results and these include the following:

In this context, we can infer and logically conclude that if the distribution of heads and tails of a fair coin is very regular in a large number of flips, then flipping a fair coin is considered as being random.

In conclusion, it is important to note that a fair coin is considered as being random when the distribution of heads and tails of a fair coin is very regular in a large number of flips.

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