Given g (x) = -x-4 , find g(-2)

Answer:

[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]

[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]

[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]

[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]

[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Step-by-step explanation:

Question 1

[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]

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Question 2

[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]

--------------------------------------------------------------

Question 3

[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]

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Question 4

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]

Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.

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Question 5

[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]

[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]

Answer:

It is everything that's bigger then (0,-3),

Picture under ↓

It's a bad drawing.

The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.

An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.

here, we have,

For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (-2,0)

Now, putting x=0, we get:

The point will be: (0,4)

Now as the sign of inequality is >, the line of graph will be dotted.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be away from the test point.

Similarly, finding the points for the inequality , we let the inequality as:

Putting y=0, we get:

The point will be: (6,0)

Now, putting x=0, we get:

The point will be: (0,6)

Now, as the sign of inequality is of , the line of graph will be solid.

Taking a test point (0,0) to find the shaded region, substituting this in the inequality,

So, the shaded region will be towards the test point.

The resulting graph is attached after the solution.

The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.

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The scores of two groups can be compared using coefficient of variation;

Coefficient of variation (C.V.) = (Standard Deviation/ Mean) × 100%;

For Data set 1;

Standard deviation = 3.6

Mean = 35.3

C.V. = (3.6/35.3) × 100%;

       = 10.19%

For Data set 2;

Standard deviation = 0.5

Mean = 34.1

C.V. = (0.5/34.1) × 100%;

       = 1.46%

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The values of x and y are;

If a, b, and r are all real numbers that are not equal to zero, then;

ax + by = c depicts a two-variable linear equation.

For the given equations;

(7y-4)° = 59⁰ and (3y - 5)° = (12x + 3)º

Consider (7y-4)° = 59⁰;

Simplifying;

7y = 59 + 4

7y = 63

y = 9

Put y = 9 in the second equation;

(12x + 3)º = (3y - 5)°

12x + 3 = 3×9 - 5

Further simplifying;

12x = 27 - 8

12x = 19

x = 19/12

Thus, the values obtained for x and y are  x = 19/12° and y = 9°.

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The correct question is-

Find the values of x and y.

(7y-4)° = 59⁰

(3y - 5)° = (12x + 3)º

Answer:

-3

Step-by-step explanation:

4+(-7), In math you always have to do parentheses first. But, 4+(-7) equals -3 because -7 is bigger than 4. So it equals -3.

The volume required for a 5% solution is 5.7 L, while a 40% solution requires 4.3 L for the experiment.

A percentage is a fraction of a whole represented as a number ranging from 0 and 100.

The equation should be as follows:

If 'x' is the volume of a 40% solution, then the volume of a 5% solution is:

10 L = 40% solution volume + 5% solution volume

10 L = x + 5% volume of solution

10 L - x = 5% solution volume

The volume would then be calculated as follows:

(volume 20% × concentration 20%) = (volume 40% × concentration 40%)           + (volume 5% × concentration 5%)

10 litre × 20% = x litre × 40% + (10- x) litre × 5%

10 L ×  20% = x litre  × 35% + 10 litre × 5%

x litre × 35 = 10 L × 20 - 10 L × 5

                 = 10 L × 15

x litre = 10 L × 15/35

x litre = 4.28 L

x litre = 4.3 L

40% solution volume = 4.3 L

The volume of 5% solution is equal to 10 L - 4.3 L = 5.7 L.

Thus, the volume of 5% solution  requires is 5.7 L and volume of 40% solution required is 4.3 L.

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Answer:

y = [tex]\frac{16}{11}[/tex]x - [tex]\frac{-56}{11}[/tex]

Step-by-step explanation:

First find the slope.  The slope is the change in y over the change in x

[tex]\frac{8 - (-8)}{9 - (-2)}[/tex] = [tex]\frac{8+8}{9+2}[/tex] = [tex]\frac{16}{11}[/tex]

Next, find the y-intercept.  Use the slope and one of the points.  It does not matter which point that you use.  I will use the point (9,8)

y = mx + b

8 = [tex]\frac{16}{11}[/tex](9) + b

8 = [tex]\frac{144}{11}[/tex] + b  Subtract 144/11 from both sides

[tex]\frac{-56}{11}[/tex] = b

The derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

Derivative of a function f(x) is defined as the rate of change of that function with respect to x at a point in its domain.

For Example , Derivative of [tex]3x^{2} =6x[/tex].

Product Rule of Differentiation

Let f(x) and g(x) be any two function. The derivative of their will be

F(x)=f(x)*g(x)

[tex]F'(x)=f(x)*g'(x)+g(x)*f'(x)[/tex]

Given y=(sin(7x))ln(x)

[tex]y'=Sin(7x)*\frac{d}{dx} ln(x)+ln(x)*\frac{d}{dx}Sin(7x)[/tex]

[tex]y'=Sin(7x)*\frac{1}{x} +ln(x)*Cos(7x)*7[/tex]

[tex]y'=\frac{Sin(7x)}{x} +7*ln(x)*Cos(x)[/tex]

Therefore , the derivative of the function y = (sin(7x))ln(x) is [tex]\frac{Sin(7x)}{x} +7*ln(x)*Cos(7x)[/tex]

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The area of the rectangular-shaped building is 2448 square feet.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle.

Given that a rectangular-shaped building that is 34 feet wide and 72 feet long. The area of the rectangle will be calculated as below:-

Area of rectangle = Length x width

Area of rectangle = 34 x 72

Area of rectangle = 2448 square feet

Therefore, the area of the rectangular-shaped building is 2448 square feet.

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The interest owed is $40

Interest is the amount of money paid when a loan is collected

The amount is $500

The interest rate is 8%

Therefore the interest owed can be calculated as follows

= 8/100 × 500

= 0.08 × 500

= 40

Hence the interest owed is $40

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The answer is option C, No; the graph fails the vertical line test.

The graph given doesn't show a function.

The method that is used to determine whether a given graph is a function or not is called the vertical line test. In this test, a vertical line is drawn at an arbitrary point x. If this line touches the given graph at more than 2-points, then the given graph is not a function.

In the given graph, if we draw a vertical line for any x > -1, then this vertical line touches the graph at more than two points.

In other words, for any value x > -1, the corresponding value of y is not unique.

So, the answer is option C, No; the graph fails the vertical line test.

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Answer:

First term = 53,

Step-by-step explanation:

a10 = a1 + (10 - 1)d so:

98 = a1 + 9*5

a1 = 98 - 45

    = 53,

The graph of the given piecewise function is plotted at the end of the answer.

A piecewise function is a function that has different definitions, depending on the input.

From the definition in the problem, we have that:

Considering these three definitions, the graph is given at the end of the answer, with the legend of the closed interval given in the text.

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The original price of the bed was £330.

From the question, we are to determine the original price of the bed.

Let the original price of the bed be x

From the given information,

The current sale price of the bed is £257.40, and this price is a saving of 22% on the original price

Then,

We can write that

x - 22% of x = £257.40

Thus,

x - 0.22x = £257.40

0.78x = £257.40

x = £257.40/0.78

x = £330

Hence, the original price of the bed was £330.

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Answer:330

Step-by-step explanation:

easy way to do this:

1. ok so you know 100%=x and 100-22=73 so that means that 73%=2570.40

2. so write them with the known above the unknown: 100%=x

                                                                                          78%=2457.40

3. no cross multiply like this [tex]\frac{100X257.40}{78}[/tex] imagine the multiplication sign is the X here( the app didn't let me change that?)

4. the solution equals 330 which the answer

5. YOU DID IT!!

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

In order to determine if the function f(x) and g(x) are inverses of each other, the composite function f(g(x)) = g(f(x))

Given the function

f(x)= 5-3x/2 and

g(x)= 5-2x/3

f(g(x)) = f(5-2x/3)

Substitute

f(g(x)) = 5-3(5-2x)/3)/2

f(g(x)) = (5-5+2x)/2

f(g(x)) = 2x/2

f(g(x)) = x

Similarly

g(f(x)) = 5-2(5-3x/2)/3

g(f(x)) = 5-5+3x/3

g(f(x)) = 3x/3

g(f(x)) =x

Since f(g(x)) = g(f(x)) = x, hence the function f(x) and g(x) are inverses of each other.

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Answer:

c

Step-by-step explanation:

because 7 of the 12 sections are shaded in blue.

Answer:

0

Step-by-step explanation:

As x aproaches a, (x-a) will aproach 0, so the numerator will aproach 0, and because 0 divided by anything=0, the whole function will become 0. So, the answer is 0.

Answer:

16

Step-by-step explanation:

Answer: 20

Step-by-step explanation:

Answer:

12 1/2

1/6

Step-by-step explanation:

5/6 x 15/1

2/3 x 1/4

These forecasts illustrate bias.

Therefore, these forecasts illustrate bias.

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The x- and y-intercepts of the function both are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The relationship between the quantity of Fun Pass tickets sold and the amount of the overall sales are represented on the given graph.

Positive and negative functions are performed here, and the meanings are interpreted in the context of the situation.

Therefore, the x- and y-intercepts of the function are zero which represents when sold 0 tickets are, the value of sales is 0 and when the value of sales is 0, the number is 0.

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The number of possible outcomes is 81

Count of Outcomes :

In the domain of Statistics, the number of possible outcomes for a given help in determining the overall size of the universe of outcomes. From such a universe, one can ascertain the probability or likelihood of desirable outcomes in terms of percentage or fraction.

Let's come to the solution of the question:

Here, the number of possible outcomes for each game is 3 (win, lose, tie).

The total number of possible outcomes is given by:

= Number of outcomes for 1st game * Number of outcomes 2nd game

= 3*3*3*3

=81

Hence, The number of possible outcomes is 81

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Miranda made error by combining unlike terms, She added 5x and 9y then subtracted 4 from the answer. Answer is already in simplified form, it cannot be simplified further.

Like terms are ones whose exponent power and variables are the same. These variables' coefficients could differ. Terms that are comparable to one another are known as algebraic terms. As an illustration, consider the algebraic statement 8y + 2y, where y is the same variable as in the expression but has different coefficients.

Terms that have variables and exponents that differ from one another are said to be unlike terms. In contrast to terms, an expression is known to obtain when the coefficient, variables (in this case, two variables), and exponent powers (if any) are all distinct. Contrary to algebraic terms, the algebraic formula 3x + 9y is known as, where x and y are two separate variables with different coefficients.

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Answer:

good question it is very hard question

Answer:

-1, 2

Step-by-step explanation:

Plug the "x" on the top row into the "x" on the equation.

y = 3(0) - 1 = -1

y = 3(1) - 1 = 2

The midpoint of line segment AB is (2, 5)

The coordinates are given as:

A= (-1,3)

B = (5.-7)

The midpoint of line segment AB is calculated as

Midpoint = 0.5 * (x1 + x2, y1 + y2)

So, we have:

Midpoint = 0.5 * (-1 + 5, 3 + 7)

Evaluate

Midpoint = (2, 5)

Hence, the midpoint of line segment AB is (2, 5)

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