Write the value of the terms, given the
explicit formula:
1
f(n) = 18+ (n − 1)
2
a1
a 10
a 25
=
=
a 100

The value of the expression ( h o g)(0) is 5.

When two functions say f and g, are composed in such a way that h(x) = g(f(x)), a new function, h, is created. In this case, the function of g is being applied to the function of x. So, in essence, the output of one function is applied to the result of another.

Consider the two functions,

g(x) = 5x - 2 and h(x) = x² + 1

So,

( h o g)(x) = h(g(x))

( h o g)(x) = ( 5x - 2 )² + 1

( h o g)(x) = 25x² - 20x + 4 + 1

( h o g)(x) = 25x² - 20x + 5

( h o g)(0) = 25 × (0)² - 20 × (0) + 4 + 1

( h o g)(0) = 0 - 0 + 4 + 1

( h o g)(0) = 5

The value of the expression ( h o g)(0) is 5.

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The domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}

The domain and the range of a function are the set of input values and output values of the graph

We have the following ordered pairs of the function

(x, y) = {(2,-5) , (4,31), (11,-11), (-21,3)}

Remove the y values to determine the domain

x = {2, 4, 11, -21}

Remove the x values to determine the range

y = {-5, 31,-11,3}

Hence, the domain of the function is {2, 4, 11, -21} and the range is {-5, 31,-11,3}

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The correlation coefficient (r) is 0.9168.

The correlation coefficient can be improved by ignoring the bill for the month of July.

The 4th data point on the graph which indicates the month of July is the farthest away from the regression line in comparison to other points, and should not be included in the correlation coefficient improvement calculations for the electricity bill.

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Answer:

On the second reduction, she reduced 25% of the original T-Shirt's price. She should have reduced the price of the T-Shirt after one reduction.

Step-by-step explanation:

Answer:

W = 11/8 or 1 3/8

Step-by-step explanation:

The width of a vegetable garden is 1/4 times its length. If the length of the garden is 5 1/2 feet, what is the width in simplest form?

W=(1/4)(L)

width is 1/4 length

if the length is 5 1/2 ft

5 1/2 is equivalent to 11/2

W= (1/4)(11/2)

Multiply across.

W = 11/8 or 1 3/8

Answer:

-48

Step-by-step explanation:

[tex](-12)4\\(-12) \times 4\\= -48[/tex]

Answer: -48

Step-by-step explanation:

negative x negative x negative x negative = negative

12 x 4 = 48

remember the answer needs to be a negative

(-12)4 = -48

Answer:

[tex]\frac{-1}{2}[/tex]

Step-by-step explanation:

Slope is the change in y over the change in x.

The ordered pair is in the form (x,y).  The first number is the x value and the second number is the y value.  

for y;

-5 - 1 = -6

for x:

8 - (-4)

8 + 4

12

[tex]\frac{-6}{12}[/tex]  Which is the same as [tex]\frac{-1}{2}[/tex]  if we divide the top and bottom by 6

The amount in the account after 40 years will be $5800.

It should be noted that the interest is calculated as:

= (Principal × Rate × Time) / 100

= ($1000 × 12 × 40) / 100

= $480000 / 100

= $4800

Therefore, the amount in the account after 40 years will be:

= Principal + Interest

= $1000 + $4800

= $5800

Therefore, the amount in the account after 40 years will be $5800.

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Answer:

15-10-11-14

Step-by-step explanation:

15+10= 25

25+11= 36

36+14= 50

The temperature that water is increasing per minute is 2 degrees.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the digit above the line and the denominator is the number below the line. An example of a fraction is 3/7.

The first step is to determine what 2/5 of a minute is equivalent to in seconds.

1 minute = 60 seconds

2/5 x 60 = 24 seconds

The formula that can be used to determine the temperature that water is increasing per minute is :

Temperature increase per minute = (degree it rises to 2/5 of a minute x seconds in a minute) / seconds in 2/4 of a minute

(4/5 x 60) / 24 = 2 degrees

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Answer:

Step-by-step explanation:

Its not that hard.. just use your brain or wait for someone else.

 The value of the simplified expression is 8√3

 Simplification is a process of reducing terms to expressions, which do not generate changes or values.

 Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.

 As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.

    Since there are no denominators, we will only decompose the square root into factors for simplicity

2(2√3) - 4(3√3)

4√3 - 12√3

8√3

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After simplifying 2√12 -4√27 the answer will be -8√3.

For simplicity, we should basically convert the square root into its factors.

Now we know that the prime factorization of 12 is, 12 =1×2×2×3.

and for 27 it is 27=3×3×3.

Now 2√12 =2[tex]\sqrt{2^2.3}[/tex]=4√3.

And, 4√27 = 4[tex]\sqrt{3^2.3}[/tex]=12√3.

∴2√12 - 4√27

=4√3 - 12√3

=-8√3 .

∴2√12 - 4√27 =-8√3 .

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Answer:

2 real different roots

Step-by-step explanation:

Discriminant determines the number of real solutions of a quadratic equation. The formula of discriminant goes by:

[tex]\displaystyle{D = b^2-4ac}[/tex]

The formula is derived from a quadratic formula which is:

[tex]\displaystyle{x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

The expression inside the square root is discriminant. The discriminant says that:

From the equation [tex]\displaystyle{x^2+5x-14}[/tex], determine the coefficients of equation:

Therefore, substitute the coefficients’ values in the discriminant:

[tex]\displaystyle{D=5^2-4(1)(-14)}\\\\\displaystyle{D=25-4(-14)}\\\\\displaystyle{D=25+56}\\\\\displaystyle{D=81}[/tex]

Since the discriminant is greater than 0, we can conclude that this equation will have 2 real different roots.

Answer: the answer is (6,1)

Step-by-step explanation:

Answer:

(4, 3)

Step-by-step explanation:

If you are moving 2 units left, the x coordinate is shifted to the left by 2 units, the y coordinate remains the same.

A shift to the left means a decrease in the x-coordinate value so new
x-coordinate is 6- 2 = 4 , y coordinate is still 3 so you end up at point (4, 3)

Answer: 10^-5 = 1/10^5

Step-by-step explanation: Every time you see a negative exponent, it would be 1/10^ (exponent number)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{10^{-5}}\\\\\mathsf{= \dfrac{1}{10\times10\times10\times10\times10}}\\\\\mathsf{= \dfrac{1}{100\times100\times10}}\\\\\mathsf{= \dfrac{1}{10,000\times10}}\\\\\mathsf{= \dfrac{1}{100,000}}\\\\\mathsf{= \dfrac{1}{10^5}}[/tex]

[tex]\huge\text{Thus, your answer should be: \boxed{\mathsf{\dfrac{1}{10^5}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The simplest form of the expression is 4 x²  .

We have given an expression √8 x² . √2 x²  .   .....(1)

On multiplying , we get

√8 x² . √2 x² = √16 x⁴

On simplifying , we get

√16 x⁴ =  √ 4 × 4 × x² × x²

           = 4 x²

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Answer:

[tex]\frac{1}{4}[/tex] (t + 9) ≤ 9

Step-by-step explanation:

One-fourth multiplied by sum of t and 9 is at most 9

One-fourth [tex]\frac{1}{4}[/tex]

sum of t and 9 = t + 9

at most 9 = ≤ 9

Value of x = 2/3.

✓(6 - 3x) - 2 = 0

Adding 2 to both sides of the equation

✓(6 - 3x) - 2 + 2 = 0 + 2

✓(6 - 3x) - 2 = 2

Now, tor remove the square root from the Left Hand Side of the equation, square both the sides of the equation.

(✓(6 - 3x))² = 2²

6 - 3x = 4

3x = 6 - 4

3x = 2

x = 2/3

Thus, the value of x is 2/3.

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The value of y in the triangle is 7.5

The given parameter is the triangle

On the triangle, we have the following equivalent ratio

y : 8 = y + 15 : 20

Express as fraction

y/8 = y + 15/20

Cross multiply

20y = 8y + 90

Collect the like terms

20y - 8y = 90

Evaluate

12y = 90

Divide by 12

y = 7.5

Hence, the value of y in the triangle is 7.5

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Answer:

wait first of all where did they put grandma?

The function that models the change in the animal population is

                   [tex]F(x) = x ( 1+ r)^{t}[/tex]

According to the question we have been given that

        population decreases = 3.5% per year

         Number of animals counted = 80

The formula to be used is

       [tex]F(x) = x (1 + r)^{t}[/tex]           (1)

where,  F(x) = amount of animals counted after t years

              x = initial amount of animals

               r = decrease or increase rate of animal species.

               t = time

Now according to the question,

           r = -0.035

           x = 80

Putting the required values in equation (1) we get  

      [tex]F(x) = 80 (1 - 0.035)^{t}\\ F(x) = 80 (0.965)^{t}[/tex]

Thus above is the required function that models the change in the animal population.

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keeping in mind that a line with an undefined slope is always a vertical line, check the picture below.

now, we could use those two points from that line and check its slope

[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{6}}} \implies \cfrac{4 +2}{0}\implies \cfrac{6}{0}\implies und efined[/tex]

The equation of the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

Inverse functions are the opposite of an original equation. This means that for a function f(x), the inverse of the function f(x) is f-(x); it also represents the opposite function

The function f(x) is given as

f(x) = x^2 - x - 2

Start by expressing the above function in vertex form

Using a graphing calculator, we have

f(x) = (x - 0.5)^2 - 2.25

As a general rule, we start by writing f(x) as a variable (say f(x) = y).

So, the equation of the function becomes

y = (x - 0.5)^2 - 2.25

The next step is to switch/swap the positions of x and y in the above equation y = (x - 0.5)^2 - 2.25

The equation becomes

x = (y - 0.5)^2 - 2.25

Add 2.25 to both sides

So, we have

(y - 0.5)^2 = x + 2.25

Take the square root of both sides

y - 0.5 = √x + 2.25

Add 0.5 to both sides

So, we have

y = 0.5 + √x + 2.25

Express as an inverse function

f'1(x) =  0.5 + √x + 2.25

Hence, the inverse function of the function f(x) = x^2 - x - 2 is f'1(x) =  0.5 + √x + 2.25

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The simplified form of the real root  4√810,000 is 3600.

To simplify simply means to make something easier. In mathematics, simplifying an expression, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

By considering the given root

4√810,000

=4x 900

=3600

Making something simpler means making it less complicated or cluttered. When you explain a complex mathematical concept to a child in terms they can easily understand, you are simplifying. When you eliminate many of the activities that were keeping you busy and stressed out, you have simplified.

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Using the vertical line test, we conclude that the relation that is a function is the bottom right one.

A relation is a function only if all the inputs are mapped into a single output.

If we have the graph of a relation, it only will be a function if it passes the vertical line test.

This means that if we draw any vertical line on the coordinate axis, and it intercepts the graph of the relation more than once, then it is not a function.

With that we can see that the first 3 options are not functions, and the last one (bottom right) it is a function.

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Let's call the entire angle between the 10 and 5 sides to be x

Applying to cosine rule:

[tex]9 {}^{2} = 10 {}^{2} + 5 {}^{2} - 2(10)(5)cos(x) \\ 81 = 100 + 25 - 100cos(x) \\ 100cos(x) = 125 - 81 \\ cos(x) = \frac{44}{100} = 0.44 \\ x = arccos(0.44)\approx63.9[/tex]

We can conclude that the angle inside the small triangle is half of x, which i will denote by y

[tex]y = \frac{x}{2} = \frac{63.9}{2} = 31.95[/tex]

Similarly to find the angle which i will denote by z at the right lower corner of the small or large triangle, apply the cosine law again:

[tex]10{}^{2} = 5 {}^{2} + 9 {}^{2} - 2(9)(5)cos(z) \\ 100 = 25 + 81 - 90cos(z) \\ 90cos(z) = 106 - 100\\ cos(z) = \frac{6}{90} = 0.06666 \\ z = arccos(0.06666)\approx86.2[/tex]

The last angle in our small triangle which i will denote by w, will be 180 minus z and y

[tex]w = 180 - (y + z) \\ w = 180 - (31.95 + 86.2) \\ w = 61.85[/tex]

Let t be our missing side,

applying the law of sines:

[tex] \frac{5}{sin(w)} = \frac{t}{sin(y)} \\ t = \frac{5sin(y)}{sin(w)} = \frac{5sin(31.95)}{sin(86.2)} [/tex]

[tex]t \approx2.652[/tex]

Answer:

11.5307692308

Step-by-step explanation:

Answer:

Around $79.88

To cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.

So,

When z "varies jointly" with x and y, the following formula can be used to describe it:

z = kxy

Here, we have mulch bags (n) that vary with the area (a) and depth (d), both in feet.

The information provided allows us to calculate the value of k.

Now we can fill in the blanks with the other values of interest.

Therefore, to cover 200 ft2 to a depth of 4 inches, we'll need 22(2/9) bags of mulch.

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