Solve 5^x − 4 = 7 for x using the change of base formula log base b of y equals log y over log b.

Answer:To determine if the function is a minimum or maximum value, we need to find its second derivative and see if it is positive or negative. If the second derivative is positive, the function is a minimum value, if it's negative, the function is a maximum value.

The second derivative of the given function is a constant (2), which means it is always positive. Therefore, the function g(x)=x^2+6x+8 is a minimum value.

The minimum value occurs at the vertex of the parabolic shape of the function, which can be found using the formula: x = -b / 2a, where a, b, and c are the coefficients of the function g(x) = ax^2 + bx + c. Plugging in the values, we get x = -6 / 2 * 1 = -3.

The minimum value of the function can be found by substituting the x value back into the function: g(-3) = (-3)^2 + 6(-3) + 8 = 9.

So the minimum value of the function g(x) = x^2 + 6x + 8 is 9, and it occurs at x = -3.

Step-by-step explanation:

Answer:

The function doesn't have maximum value, as it is always increasing, although it has minimum value which is -b/2a, in this case -3 is a minimum value

The solution of the composite function fog(x) = 3x + 3 at x > 2.

Let the two function f(x) and g(x) generate a new function h(x) using an operation.

The operation is composition of functions and h(x) is a composite function.

We have three piecewise function.

First we have to show that,

the composite function,

fog(x) at x > 2.

For that,

g(x) at x > 2 is,

g(x) = 3x.

Now, f(g(x)),

= f(3x)

= 3x + 3 at x > 2.

Therefore, the function is fog(x) = 3x + 3.

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The complete question:

Find the fog(x) at x > 2

Standard form of the line passing through the points (-2, -3) and (4, -7) is,

⇒ y = - 2/3x - 13/3

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-2, -3) and (4, -7).

Now,

Since, The equation of line passes through the points (-2, -3) and (4, -7).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (- 7 - (-3)) / (4 - (-2))

m = - 4 / 6

m = - 2/3

Thus, The equation of line with slope - 2/3 is,

⇒ y - (-3) = - 2/3 (x - (-2))

⇒ y + 3 = - 2/3 (x + 2)

⇒ y + 3 = - 2/3x - 4/3

⇒ y = - 2/3x - 4/3 - 3

⇒ y = - 2/3x - 13/3

Therefore, The equation of line passes through the points (-2, -3) and

(4, -7) will be;

⇒ y = - 2/3x - 13/3

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The vehicle in motion produces 44000 joules of kinetic energy.

Kinetic energy is a type of power that a moving object or particle possesses.

An item accumulates kinetic energy doing work, which involves the transfer of energy, is done on it by exerting a net force.

Given, The formula for kinetic energy is, K = (1/2)mv².

The vehicle has a mass of 2200 kilograms and a velocity of 20 m/s.

So, Replacing the values in the formula will yield the result.

K = (1/2)mv².

K = 1100×400.

K = (1/2)×2200×(20)².

K = 44000 joules.

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Answer:

699.626 kilopascals after 4 minutes

Step-by-step explanation:

We can use the formula for simple interest to calculate the tire pressure after 4 minutes. Let's call the initial pressure "P", the rate of loss "r", and the time elapsed "t".

P = P * (1 - r)^t

Where r is the rate of loss in decimal form and t is the number of minutes elapsed.

Substituting the given values, we have:

P = 1,060 * (1 - 0.10)^4

P = 1,060 * (0.9)^4

P = 1,060 * 0.6561

P = 699.626 kPa

Therefore, the tire pressure will be 699.626 kilopascals after 4 minutes.

Inequalities help us to compare two unequal expressions. The point which satisfy both inequalities is (5,0)

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

For a point to be the solution of the system of inequalities, the point when substituted in the inequalities must satisfy both the given inequalities.

A. (2, -6)

y > (-3/2)x + 6

-6 > (-3/2)2 + 6

-6 > 3. this is false

y > x - 6

-6 > 2 - 6

-6 > -4 this is false

Since the both inequality is not satisfied, therefore, the given point is not the solution.

B. (10, -5)

y > (-3/2)x + 6

-5 > (-3/2)10 + 6

-5 > -9. this is true

y > x - 6

-5 > 10 - 6

-5 > 4 this is false

Since the second inequality is not satisfied, therefore, the given point is not the solution.

C. (5, -0)

y > (-3/2)x + 6

0 > (-3/2)5 + 6

0 > -1.5. this is true

y > x - 6

0 > 5 - 6

0 > -1 this is false

Since both the inequality are satisfied, therefore, the given point is the solution.

D. (-10, -4)

y > (-3/2)x + 6

-4 > (-3/2)-10 + 6

-6 > 21. this is false

y > x - 6

-4 > -10 - 6

-6 > -16 this is true

Since the first inequality is not satisfied, therefore, the given point is not the solution.

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The correct statement is,

⇒ A coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points

(0, 27) and (2, 21).

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The table shows the relationship between the number of days she has been selling cookies and the total number of boxes remaining.

Girl Scout Cookie Fundraiser

Time (in days)          1   3   4   7

Number of Boxes   24 18  15  6

Now, Take two points for the line is, (1, 24), (3, 18)

Hence, The graph of equation is,

⇒ y - 24 = (18 - 24) / (3 - 1) (x - 1)

⇒ y - 24 = - 6/2 (x - 1)

⇒ y - 24 = - 3 (x - 1)

⇒ y - 24 = - 3x + 3

⇒ y = - 3x + 3 + 24

⇒ y = - 3x + 27

Thus, A coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (0, 27) and (2, 21).

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Answer:

(0, 27) and (2, 21).

Step-by-step explanation:

Then the 3 integer even numbers are:

-24, -22, -20

We know that the sum of 3 consecutive even numbers is -78, that can be written as:

x + (x + 2) + (x + 4) = -78

Now we can solve that equation for x:

3x + 6 = -78

3x = -78 - 6 = -72

x = -72/3 = -24

The next even integer is:

-24 + 2 = -22

-24 + 4 = -20

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The three consecutive integer even numbers are -24, -22, -20

From the question, we have the following parameters that can be used in our computation:

The sum of three consecutive even integers is -78

Represent the smallest integer with x

So, we haee the following equation:

x + (x + 2) + (x + 4) = -78

Evaluate the like terms

3x + 6 = -78

So, we have

3x = -72

Divide both sides by 3

x = -72/3 = -24

This means that the next integers are

-24 + 2 = -22

-24 + 4 = -20

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The values of the function are

a) f(-1)+ f(2) = 32

b)  f(-1) - f(2) = -30.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f( x ) = 3x² + 7x + 5

a) f(-1)+ f(2)

=  3(-1)² + 7(-1) + 5 +  3(2)² + 7(2) + 5

= 3 -7 + 5 +12 + 14 + 5

= 32

So, the value of f(-1)+ f(2)= 32

b)  f(-1) - f(2)

=  3(-1)² + 7(-1) + 5 -{  3(2)² + 7(2) + 5}

= 3 -7 + 5 -{12 + 14 + 5}

=-30

So, the value of  f(-1) - f(2)= -30.

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The expression ⅘ x 50 represents the multiplication of a fraction and a whole number, and the answer is 40.

The expression "⅘ x 50" is a mathematical equation that represents a multiplication operation. The symbol "x" represents the multiplication operator. In this expression, the first number, ⅘, represents a fraction, while the second number, 50, represents a whole number.

When solving the expression, we first simplify the fraction ⅘ by dividing the numerator (4) by the denominator (5). This results in a decimal value of 0.8. Then, we multiply the decimal by 50 to obtain the final answer. 0.8 x 50 = 40.

So, the expression "⅘ x 50" equals to 40. This means that if we have 4 out of 5 equal parts of a whole, and the whole is equal to 50 units, then each part is equal to 40 units

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The limit of f(x) is 2, which means that as x approaches infinity, f(x) approaches 2. This implies that f(x) has a vertical asymptote at x = 2, but does not have a horizontal asymptote at y = 2, and is never equal to 2.

The limit of a function is the value that the function approaches as the argument approaches infinity. In the case of f(x), the limit is 2. This means that as x gets larger and larger, the value of f(x) gets closer and closer to 2. This implies that f(x) has a vertical asymptote at x = 2, meaning that the function approaches this value, but never reaches it. It does not have a horizontal asymptote at y = 2, meaning that the function does not approach this value as x gets larger. Additionally, the limit of f(x) is not -2, meaning that the function does not approach this value as x gets larger. Lastly, f(x) is continuous at x = 0, meaning that there is no discontinuity at this point in the graph.

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Answer:

Step-by-step explanation:

A convex octagon can be split into a set of triangles by connecting its vertices in a way that each vertex is connected to its neighboring vertices.

There are several ways to split a convex octagon into triangles, but a common approach is to use the ear clipping algorithm, which involves finding triangles that have their vertices on the octagon's perimeter and have no other vertices inside the triangle.

For example, if the vertices of the octagon are given by v1, v2, v3, v4, v5, v6, v7, and v8, then we can split the octagon into the following triangles:

(v1, v2, v3), (v3, v4, v5), (v5, v6, v7), (v7, v8, v1), (v2, v3, v5), (v4, v5, v7),

(v6, v7, v1), and (v8, v1, v3).

Each of these triangles has three vertices that are connected to form a closed polygon, and together they form the entire convex octagon. By splitting the octagon into smaller triangles, it is easier to perform computations, such as finding the area or the normal vectors of the octagon's surface.

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Answer:

Second option:

[tex]\boxed{ \$6,671.67}[/tex]

Step-by-step explanation:

The equation for the amount accrued at 5.4% interest compounded semi-annually(twice a year) for an initial investment P for t years is already given:

[tex]A = P\left(1 + \dfrac{0.054}{2}\right)^{2t}[/tex]

Plug in
P = $3000
t = 15 years

[tex]A = 3000\left(1 + 0.054\right)^{2\cdot 15}\\\\A = 3000(1 + 0.027)^{30}\\\\A = 3000(1.027)^{30}\\\\A = 3000 (2.22389)\\\\A = \$6,671.67[/tex]
This is the second option

The equation of the function is f(x) = 4x + 11

From the question, we have the following parameters that can be used in our computation:

f(-2)=3, and f(4)=5

A linear function is represented as

y = mx + c

So, we have

-2m + c = 3

4m + c = 5

When solved, we have

2m = 8

This gives

m = 4

So, we have

c = 3 + 2m

c = 3 + 8 = 11

So, the function is

f(x) = 4x + 11

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Answer:

Step-by-step explanation:

110 x 0.20 = 22

your total is 132

Answer:

Therefore you will be able to get 6 * 3 different pizzas = 18 pizza combinations.

Answer: 12

Step-by-step explanation:

The length of the radius, diameter, and circumference are 78.5 and 31.4.

Supposing that a considered circle has its radius of 'r' units.

Then, its area and circumference is given as:

[tex]Area = \pi r^2 \: \rm unit^2 Circumference = 2\pi r \: \rm units[/tex]

Radius of a circle is half of its diameter.

Given;

Let the diameter be 10cm

Radius=d/2

=10/2=5

Diameter=10

Circumference=2pi*r

=2*3.14*5=31.4

Area= pi*r^2*

=3.14*5*5=78.5

Therefore, the area and circumference will be 78.5 and 31.4.

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The fraction in simplest form is, 5/12.

A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.

We have to given that;

All the fractions are,

⇒ 2/10, 5/12, 3/6, 4/8

Now, We know that;

The fraction is in simplest form if the GCD of denominator and numerator is 1.

So, By all the fractions;

⇒ 5/12

Clearly, GCD of 5 and 12 are 1.

Hence, The fraction in simplest form is, 5/12.

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The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: The measure of the frame is 8.5 inches and 11 inches

a) if the frame is 4 papers long then we  have the length of the frame as

11×4=44 inches (since he lays the paper along the edge of frame)

We know 1 inch= 0.0833 foot

Thus      44 inches= 3.66667 foot

b) Again if he lays the paper along the short edge than the width of the frame is 3×8.5=25.5 inches

∴25.5 inches= 2.125 feet

Hence, The measure of the frame in feet of the length and width are 3.667 feet and 2.125 feet respectively.

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The missing marginal costs and benefits values are the following

Marginal benefit = $ 30

Marginal benefit = $25

See above we have a table with columns total cost, marginal cost , total benefits and marginal benefits. We have to determine the values in place of question mark (?) . Marginal benefit and marginal cost are two measures of how the price or value of a product changes.

Now, Marginal cost and benefits for row 2

change in total cost = 125- 100 = 25

change in units = 2 - 1 = 1

So, marginal cost = 25/1 = $25

Marginal benefit = change in total benefits/ change in units

= (150 - 120)/2-1 = 30/1 = $ 30

Change in total cost = 140 - 125 = 15

Change in units = 3 - 2 = 1

Change in total benefit = 175 - 150 = 25

So, marginal cost = 15/1 = $15

Marginal benefit = 25/1 = $25

Change in total cost = 160 - 140 = 20

Change in units = 4 - 3 = 1

Change in total benefit = 190 - 175= 15

So, marginal cost = 20/1 = $20

Marginal benefit = 15/1 = $15

Hence, we get all the values of question mark.

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Complete question:

Find Out the missing marginal costs and benefits in the above table. (see question marks) unit total cost marginal cost total benefit marginal benefit 1 100 100 120 120 2 125 ? 150 ? 3 140 ? 175 ? 4 160 ? 190 ?

1) The independent variable is ''Day'' shown in x - axis.

2) Days shows on x - axis are incorrectly arranged.

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

We have to given that;

The graph is shown in graph.

On the graph;

Day is shown in x - axis.

And, Earnings shown in y - axis.

Now, We know that;

The independent variable is shown in x - axis.

Hence, The independent variable is Day.

And, One wrong thing in graph is,

Days shows on x - axis are incorrectly arranged.

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The equation that represents the relationship between the distance of Tamara and Marcia is y = x-4

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1.

let x represent the kilometers covered by Tamara and y by the kilometers covered by Marcia.

x+y = k

x = k/2

x = Y+2

Y+2 = K/2

2Y+4 = K

x+ y = 2y+4

collect like terms

2y -y = x-4

y = x-4

therefore the linear equation they represents the relationship between the distances each girl has run is y = x-4

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The value of x from the equation is 18. Option E

It is important to note that algebraic expressions are expressions with variables, terms, coefficients, constants and factors.

They are also made up of operations, such as addition, multiplication, division, subtraction, floor division, parentheses, bracket.

From the information given, we have that;

3√x - 2 + 7 = 19

Take the following steps

collect like terms

3√x-2 = 19   - 7

add the like terms

3√x -2 = 12

Divide  both sides by 3

√x - 2 = 4

Find the square of both sides

x - 2 = 16

x = 18

Hence, the value is 18

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Number 10⁻² is 100 times as great as 10⁻⁴.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Numbers are 10⁻² and 10⁻⁴.

Let number 10⁻² is x times great as 10⁻⁴.

Hence, We can formulate;

⇒ 10⁻² = x × 10⁻⁴

⇒ x = 10⁻² / 10⁻⁴

⇒ x = 10⁻²⁺⁴

⇒ x = 10²

⇒ x = 100

Thus, Number 10⁻² is 100 times as great as 10⁻⁴.

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The amount he should invest today is $279,229.23.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

A = $460,000

r = 4.59%

t = 11 years

Semi-annually.

So,

n = 2

Now,

A = P [tex](1 + r/n)^{nt}[/tex]

460,000 = P [tex](1 + 0.0459/2)^{22}[/tex]

P = 460,000 / [tex]0.02295^{22}[/tex]

P = $279,229.23

Thus,

He should invest $279,229.23 today.

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Answer: 39 in^2

Step-by-step explanation: To find the area of this polygon, we can break it down into two triangles and one rectangle. The following formulas are to solve for the area of each polygon:

Area of a Triangle: A = b x h / 2

Area of a Rectangle: A = l x w

We can plug in the values by what we are given. The triangle to the top has a base of 6 in and a height of 5 in. We can multiply these to get 30 in but cut it in half to get 15 in. The second triangle has a base of 3 in and a height of 4 in, so when we multiply, we get 12 in / 2 to get 6 in. The rectangle's length is 6 in and the width is 3 in. So, 6 x 3 is 18. Add all these values together, and you get 39 in^2.

Let me know if this is right! :)

The probability mass function (PMF) of N can be determined by finding the probability that N = k, for each k = 1, 2, 3, ....

Let p_k = P(N = k) be the probability that the first bid that is better than the initial bid X_0 is the kth bid. We can calculate p_k as follows:

p_k = P(X_k > X_0, X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0) = P(X_k > X_0 | X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0) * P(X_1 < X_0, X_2 < X_0, ..., X_{k-1} < X_0)

Since X_0, X_1, ... are independent and identically distributed, we have:

p_k = P(X_k > X_0) * (P(X_1 < X_0))^{k-1}

To find the mean E[N], we need to calculate the expected value of N. The expected value of N is given by:

E[N] = 1 * p_1 + 2 * p_2 + 3 * p_3 + ... = ∑_{k=1}^∞ k * p_k

Since p_k = P(X_k > X_0) * (P(X_1 < X_0))^{k-1}, we can write E[N] as:

E[N] = ∑_{k=1}^∞ k * P(X_k > X_0) * (P(X_1 < X_0))^{k-1}

To find E[N], we need to know the distribution of X_0, X_1, .... Unfortunately, without further information on the distribution of X_0, X_1, ..., it is not possible to determine the PMF of N or the mean E[N].

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