1.what is the question of f(x)
2. Height of the tunnel if the road is 14ft wide by 7 ft shoulders

[tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.

Now,

For example, let x = 0.1

Then, [tex]ln(e^{(0.1)}) = 0.1 < 1[/tex]

For example, let x = 2

Then, [tex]ln(e^2) = 2 > 1[/tex]

Hence, [tex]ln(e^x) \geq 1[/tex] is sometimes true, by seen by operations on logarithm.

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If the two functions be f(x) = 3x² - 11x - 4 and g(x) = 3x + 1 then

(fg)(x) = f(x)g(x) = [tex]$$9x^3[/tex] - 30x² - 23x - 4

(f/g)(x) = f(x)/g(x) = x - 4

Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.

Function composition is a mathematical operation that takes two functions f and g and produces a function h = g f such that h(x) = g(f(x)). The function g is applied to the result of applying the function f to x in this operation.

Let the two functions be f(x) = 3x² - 11x - 4 and g(x) = 3x + 1.

(fg)(x) = f(x)g(x)

= (3x² - 11x - 4) (3x + 1)

simplifying the above equation, we get

= 3x² [tex]*[/tex] 3x + 3x² [tex]*[/tex] 1 - 11x [tex]*[/tex] 3x - 11x [tex]*[/tex] 1 - 4 [tex]*[/tex] 3x - 4 [tex]*[/tex] 1

= [tex]$$9x^3[/tex] - 30x² - 23x - 4

Therefore, (fg)(x) = f(x)g(x) = [tex]$$9x^3[/tex] - 30x² - 23x - 4

(f/g)(x) = f(x)/g(x)

Where, f(x) = 3x² - 11x - 4 and g(x) = 3x + 1.

f(x)/g(x) =  (3x² - 11x - 4)/(3x + 1)

= [(3x + 1)(x - 4)]/(3x + 1)

canceling the common factors we get

= x - 4

Therefore, f(x)/g(x) = x - 4

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Answer:

Step-by-step explanation:

90-degree rotation

Let me explain, you see point B? Yeah, okay. 90 degrees is a right angle, so you see how the replica blue B is on the line a right angle from it?

That's how you figure that out, if the point is on a line 90 degrees from it it's a 90-degree rotation

If you remain confused please don't hesitate to ask :))

Answer:

9.5

Step-by-step explanation:

[tex]\frac{KQ}{BK} = \frac{?}{?}\\ KQ = \frac{BK}{2}\\KQ = \frac{19}{2}\\KQ = 9.5[/tex]

Answer:

17.

Step-by-step explanation:

Multiply rate by 2

8 1/2 * 2 = 17

The possible values of angles A and C are;

60° and 70° or 55° and 75°

An acute triangle is a triangle that has all the measures of its angles to be less than 90°.  This means that none of the angles is greater than 90°

Since sum of the angles in a triangle is equal to 180°, then it means that;

∠A + ∠B + ∠C = 180°

We are given that;

∠B = 50°

Thus;

50° + ∠A + ∠C = 180°

∠A + ∠C = 180° - 50°

∠A + ∠C = 130°

It should be noted that all the angles of the acute triangle are also different.

Thus, the possible values of A and C are 60° and 70° or 55° and 75° because their sum must be equal to 130°

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12 x 5 = 60

10x 6= 60

so 5 packs of pencils and 6 packs of erasers.

Answer:

x = -6/5

Step-by-step explanation:

Find the value of x.

-2x = 3x + 6​

Subtract 3x from each side

-2x-3x = 3x-3x + 6​

-5x = 6

Divide each side by -5

-5x/-5 = 6/-5

x = -6/5

Step-by-step explanation:

It is here that equilibrium level of income is established because what the savers intend to save becomes equal to what the investors intend to invest. Sum and substance is that if planned saving and planned investment are equal, then output, income, employment and price level will be constant.Kindness is defined as the quality of being friendly, generous, and considerate. Affection, gentleness, warmth, concern, and care are words that are associated with kindness

Answer:

[tex]3\sqrt{5}[/tex]

Step-by-step explanation:

Factor out a [tex]\sqrt{5}[/tex] from the [tex]\sqrt{80}[/tex], and you will get [tex]\sqrt{5} * \sqrt{16}[/tex]

Then you get: [tex]4\sqrt{5}[/tex], since the square root of 16 is just 4. Then we have this expression:

[tex]4\sqrt{5} -\sqrt{5}[/tex], which gives us [tex]3\sqrt{5}[/tex].

Hope this helps

Answer:

28y-196

Step-by-step explanation:

28(y-7)

Multiply y and -7 by 28.

(28*y)-(7*28)

Simplify.

28y-196

The solution of 4+√3 x+5=7  is x = ( - 2 ) / [tex]\sqrt{3}[/tex] .

Linear Equation : An equation ( containing equal to = sign ) is called a linear equation if the highest power of variable is 1 . In order to solve linear equation in 1 variable 1 equation is enough .

Solving linear eq . in 1 variable

4+√3 x+5=7

√3 x = 7 - 5 - 4

x = ( - 2 ) / [tex]\sqrt{3}[/tex]

Hence , the solution of 4+√3 x+5=7  is x = ( - 2 ) / [tex]\sqrt{3}[/tex] .

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The expression ∛(a)⁷  raised to a single rational exponent is  [tex]a^{\frac{7}{3} }[/tex] .

A rational number is one that can be defined as the ratio or fraction a/b of two numbers, where a and b are the numerator and denominator, respectively. Here the integer numbers a and b are co prime numbers.

For example 8/7 is a rational number and all integers are rational numbers.

Any combination of terms that have undergone operations like multiplication,addition, subtraction, division is known as an algebraic expression.

it is given that the expression is of the form ∛(a)⁷ .

We know that the n-th root of a variable x ([tex]\sqrt[n]{x}[/tex]) can also be written as

[tex]x^{\frac{1}{n} }[/tex].

Therefore  ∛(a) can be written as [tex]a^{\frac{1}{3} }[/tex] . Now the complete expression is ∛(a)⁷.

So [tex](a^{\frac{1}{3} })^7=a^{\frac{7}{3} }[/tex] and we know that 7/3 is a rational number.

Therefore the expression can be written as [tex]a^{\frac{7}{3} }[/tex] using rational exponents.

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To receive the greatest discount, the customer should first apply the membership discount and then take the rebate.

We are given that:

Rebate a customer receives if he buys a regular priced CD at $ 13 each = $ 5.

If a customer registers for the store member, he get a discount = 15 %.

Now, let the regular priced CD purchased be x and the application for store member be y.

So, the functions will become:

For rebate:

R (x) = 5 x

For discount:

M (y) = 15 % of x

M (y) = 0.15 x

Now, the amount a customer has to pay if she takes the membership and then takes the rebate =(1 − 0.15) (13 x) − 5 x = 6.05 x

And, if he takes the rebate first and then take the membership, he pays = (13 - 5 x)( 1 - 0.15) = 6.8 x

Therefore, we get that, to receive the greatest discount, the customer should first apply the membership discount and then take the rebate.

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The width of the rectangle is: 3 meters.

Perimeter of a rectangle is determined using the formula:

Perimeter = 2(length + width)

Given the parameters below:

Width of the rectangle = w meters

Length of the rectangle = 2w - 3 meters

Perimeter of the rectangle = 24 meters

Therefore:

2((2w - 3) + w) = 24

Solve for w (width of the rectangle)

2((2w - 3 + w) = 24

2(3w - 3) = 24

6w - 6 = 24

6w = 24 - 6

6w = 18

6w/6 = 18/6

w = 3

Therefore, the width of the rectangle is: 3 meters.

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Answer:

The value behind a decimal point isn't increased by zeros, zeros are actually just placeholders

Step-by-step explanation:

Answer:

tan4θ=(4tanθ−4tan^3θ)/(1−6tan^2θ+tan^4θ)

Step-by-step explanation:

A linear equation that relates the cost of c in dollars of renting a truck to the number x of miles driven is c = 0.09x + 39, and the cost of renting the truck if the truck is driven 187 miles and 319 miles is equal to $55.83 and $67.71 respectively.

If the rental company rents a truck by charging $34 and 0.09$ per mile, the liner equation can be given as

c = 0.09x + 39

where c represents the cost in dollars of renting the truck and x represents the number of miles

If the truck is driven 187 miles, it can be calculated using the linear equations as follows,

c = 0.09x + 39

As x = 187

c = 0.09 (187) + 39

c = 16.83 + 39

c = 55.83

If the truck is driven 319 miles, it can be calculated using the linear equations as follows,

c = 0.09x + 39

As x = 319

c = 0.09 (319) + 39

c = 28.71 + 39

c = 67.71

Hence the cost in dollars of renting the truck if the truck is driven 187 miles and 319 miles is calculated to be 55.83 and 67.71 respectively.

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The child that will have a greater percentage of increasing amounts is; The child with original amount of $500

The amount that has increased from the initial number to the final number in terms of 100 parts of the original is essentially what the concept of percentage increase refers.

We are given that the original amount found in their savings account are;

First child; A = $500

Second child; B = $300

Thus the first child denoted by A has greater amount in savings compared to the second child and as such child A will have a greater percentage of increasing amounts.

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Answer: The older child.

Step-by-step explanation: The original amounts in their savings accounts

were $500 and $300, respectively.

Answer:

x=7 -2x+4=-10

-2x+4-4=-10-4

Step-by-step explanation:

this should be right pick me brainliest

Confirmed Solution:

[tex]x=7[/tex]

Further Explanation:

Displayed Above

Hope this helps!

The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)

Transformation is the movement of a point from its initial location to a new location. Types of transformations are rotation, translation, reflection and dilation.

Translation is the movement of a point either up, down, left or right in the coordinate plane.

The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)

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When written as a fraction, 0.116 can be found to be the equivalent of 29 / 250

The value of 0.116 has 3 decimals after the decimal point. This means that it is a thousandth decimal.

The fraction form is therefore:
= 116/1,000

You can then take this to be simplest form:
= (116 / 2) / (1,000 / 2)

= 58 / 500

= (58 / 2) / (500 / 2)

= 29 / 250

In conclusion, 0.116 = 29/250

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Answer:

√50, 7.6, √65, √78.8, 8.2

Step-by-step explanation:

might be wrong but i'm pretty sure this is it

According to  the solving the estimated sum of the numbers:

To estimate implies to come up with a solution that is close but not accurate. It's a reasonable solution to a problem. A sum is the solution to an addition issue. A difference is a solution to a subtraction issue.

To get the total, we round each number to the closest tenth and then add the rounded figures. Let us calculate 38 + 23. 38 is more like 40 than 30. As a result, 38 is rounded up to 40.

1 435 + 678 + 925 =  2,038

on round of  = 2040

2.359 + 814 + 207 = 1,380

on round of  = 1380

3. 6428 + 7154 + 9345 = 22,927

on round of  = 22930

4. 2987 + 6873 + 4555 = 14,415

on round of  = 14420

5. 6759 + 8210 + 7642 = 22,611

on round of  = 22610

2,040

1,380

22,930

14,420

22,610

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I understand that the question you are looking for is:

Estimate the sum:

1 435 + 678 + 925 =

2.359 + 814 + 207 =

3. 6428 + 7154 + 9345 =

4. 2987 + 6873 + 4555 =

5. 6759 + 8210 + 7642 =

Answer:

7.07070707E15

Step-by-step explanation:

Value for (f⁰g)(-2) = -6/3

Given :

             g(x) = 3x + 2

              f(x) =  (x-2)/3        

Now,

(f⁰g)(x) = f(g(x))

(f⁰g)(-2) = f(g(-2))

substitute x = -2

g(-2) = 3(-2) + 2 = -4

f(g(-2)) = f(-4)

(f⁰g)(-2) = f(-4) =  -6/3

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The three consecutive odd integers are 17, 19 and 21 respectively.

Linear equations are equations that has a leading degree of 1. Given the three consecutive odd numbers to be

2x+1, 2x+3 and 2x+5

If the sum of the smallest number and middle number is 27 less than three times the largest number, then;

2x + 1 + 2x + 3 = 3(2x+5) - 27

Simplify

4x + 4 = 3(2x) + 3(5) - 27

4x + 4 = 6x + 15 - 27

4x - 6x = 15 - 27 - 4

-2x = -16

x = 16/2

x = 8

Determine the numbers

Smallest number = 2x + 1

Smallest number = 2(8) + 1 = 17

Middle number = 2x + 3

Middle number = 2(8) + 3

Middle number = 19

Largest number = 2(8) + 5

Largest number = 21

Hence the three consecutive odd integers are 17, 19 and 21 respectively.

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The median of the data is 4.

The mean of data is the ratio of the sum of observations to the total number of observations. The Median is defined as the middle value of data.

Data:23,25,32,35,36,25,27.

The mean of the data is, 

[tex]Mean = \frac{Sum \: of \: observation }{Total \: number \: of \: observation}[/tex]

= 23+25+32+25+36+27+27 7 

=29 

The mean of the data is 29.

The median of the data is, 

Arranging the data in ascending order, 

23,25,25,27,32,35, 36 

[tex]Meadian= \frac{n+1}{ 2} = \frac{ 7+1}{ 2 }[/tex]

= 4 

Therefore, the median of the data is 4.

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The correct option for the end behaviour of function is option C. As x approaches positive infinity, g(x) approaches positive infinity.

We have been assigned the following function:

g(x) = 1/2|x - 3| - 7

Behavior at the end:  As x approaches negative and positive infinity, the limit of g(x) is reached.

Infinity minus one:

lim g(x) =   lim      1/2|x - 3| - 7

x → -∞          x → -∞

lim g(x) =  1/2|-∞ - 3| - 7   = | -∞ |  = ∞

x → -∞        

Thus, the negative end behaviour is ∞ .

Infinity plus one:

lim g(x) =   lim      1/2|x - 3| - 7

x → ∞          x → ∞

lim g(x) =  1/2|∞ - 3| - 7   = | ∞ |  = ∞

Thus, positive end behaviour is also  ∞ .

As a result, it approaches positive infinity in both cases, and the correct option is C.

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The correct question is-

Which statement describes the end behavior of this function?

g(x) = 1/2|x - 3| - 7

A. As x approaches positive infinity, g(x) approaches negative infinity.

B. As x approaches negative infinity, g(x) approaches negative infinity.

C. As x approaches positive infinity, g(x) approaches positive infinity.

D. As x approaches negative infinity, g(x) is no longer continuous.