Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

Hint: Use the change of base formula: log base b of y equals log y over log b.

On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] =>  sinx = 0 and 2 cosx -1 =0

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]

sinx = 0 and 2 cosx -1 =0

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So, y = ab^x and y = ac^x are the exponential functions to represent the spread of Ben's and Carter's social media posts respectively.

An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).

For Ben's social media posts:

y = ab^x

For Carter's social media post:

y = ac^x

Please note that the value of a, b, and c will be different for Ben and Carter's post, as it will depend on the number of shares, likes, views, etc., and the rate of spread of the post.

This is an exponential function that represents the spread of Ben's social media posts and  Carter's social media post.

Complete Question:

1. Write an exponential function to represent the spread of Ben's social media post 2. Write an exponential function to represent the spread of Carter's social media post. 3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology. 4. Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers 5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is   . How does this graph compare with the original graph of Amber's photo share? 6. Based on your results, which students' post travels the fastest? How is this shown in the equation form of the functions? 7. If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions

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Answer:

She will earn $900.00 in 12 hours.

Step-by-step explanation:

Her unit rate is 75 dollars per hour.

375/5 = $75

75 x 12 = 900

Answer:  $900

Step-by-step explanation: 375/5x12.

Answer:

a = 191/81

Step-by-step explanation:

a+ 1 1/6 = 11 7/9

1 1/6 = 7/6

11 7/9 = 106/9

So, our equation is

a + 7/6 = 106/9

Subtract 7/6 from both sides

a = 191/81

So, the answer is

a = 191/81

The equation of the line is 3x + y - 11 = 0.

The slope-intercept formula y = mx + b is used when you know the slope of the line to be examined and the point given is also the y intercept (0, b). In the formula, b represents the y value of the y intercept point.

First we find the slope of the line y=-3x+10 by placing it into slope-intercept form:

y = -3 x + 10

Therefore, the slope of the line is m= -3

Now since the equation of the line with slope m passing through a point

(x₁ ,y₁) is y-y₁ = m(x-x₁)

Here the point is (1,8) and slope is m= -3, therefore, the equation of the line is:

y - 8 = -3(x - 1)

y - 8 = -3x +3

3x + y - 11 = 0

Hence, the equation of the line is 3x + y - 11 = 0.

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At the rate of 126cm/s is the area of the square increasing when the area of the square is 81cm2.

If each side of a square is increasing at a rate of 7 cm/s.

The area of the square increasing rate,

Area, A = s2

each side of the square is increasing at the rate of 7cm / s (= dx / dt).

s is the side length

=> dA/dt = 2s. ds/ dt

ds/dt = 7cm/s

Area of the square = 81 cm2

81 cm2 = s2

s = 9 cm

so, dA /dt = 2. 9. 7

               = 126 cm2/s

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By translating, stretching and contracting, or reflecting, two functions from the same function family can become one another. Any function from a function family can be obtained by applying one or more transformations to a parent function.

By altering the graph of the parent absolute value function, many other absolute value functions can be created. The resulting absolute value functions take the following form:

[tex]y = |x-h| + k[/tex], where h and k are real numbers.

Absolute value functions can be created using the same kinds of operations that produce new linear functions. They also have a similar impact on absolute value functions. The transformations may, however, appear differently graphically due to some important discrepancies between linear functions and absolute value functions.

Here are some of the transformations:

Vertical Transformations

Horizontal Transformations

This is how we graph the transformation of an absolute value function.

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The solution is given by the equation A = how many diet sodas there are in the fridge compared to how many regular sodas

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

The ratio of cows to pigs on a farm could be 1 to 3

So , the proportion is 1 : 3

Now , The ratio of chocolate chips to raisins in a cookie could be 5 to 9

So , the proportion is 5 : 9

Now , the number of diet sodas there are in the fridge compared to number of regular sodas is also a proportion

Hence , the proportion is number of diet sodas to number of regular sodas

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Answer:

16.74

Step-by-step explanation:

-1.8 times -9.3 will have a positive answer because 2 negative numbers will have a positive sum

  -1.8

x -9.3

---------

    5 4

1 6 2 0

---------

1 6 7 4 ||| add two decimal spaces

16.74

The solution to the differential equation y'' + y = sin2x is y = -2sin2x + (Acos2x + Bsin2x).

This differential equation can be solved by the method of variation of parameters. This method involves finding two arbitrary functions, U and V, such that U' = V and V' = -U + sin2x, so that the general solution of the differential equation is y = U + V. Solving the two equations yields U = Acos2x + Bsin2x and V = -2sin2x, where A and B are arbitrary constants. Substituting U and V into the general solution of the differential equation yields the final solution y = -2sin2x + (Acos2x + Bsin2x).

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Answer:

  see attached

Step-by-step explanation:

You want the graph of g(x) = -f(x-3), given the graph of the parent function f(x) = log₂(x).

The replacement of x with x-3 as the function argument causes the graph to be translated 3 units to the right.

The replacement of f(x) with -f(x) causes the graph to be reflected over the x-axis.

The translated, reflected graph is shown in blue in the attachment.

The coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

Given are the coordinates of the vertices of ΔRST are R(1, 6), S(5, 3), and T(3,-2).

The rule for a reflection over the x -axis is (x, y) →(x, −y). Now we can write the coordinates of the reflection as -

R' (1, -6)

S' (5, -3)

T' (3, 2)

The graph is attached.

Therefore, the coordinates of the reflected points are R' (1, -6), S' (5, -3), T' (3, 2) and the graph is attached.

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If star A is closer to us than star B, then Star A's parallax angle is: Larger than that of Star B.

Hence, option (A) is correct choice.

The parallax of a star at a distance of 10 parsecs would be 0.1′′ since parallax is inversely proportional to distance. The parallax of Proxima Centauri, a star in the triple system of Alpha Centauri, is 0.76813′′, indicating that it is 4.24 light-years away from Earth at a distance of 1/0.76813, or 1.302 parsecs.

The apparent shift in an object's location caused by a change in the observer position is known as parallax. This apparent shift is measured (in arc seconds) is reversed to provide the distance from the background stars (in parsecs).

The definition of an object's absolute magnitude is the apparent magnitude the object would have if it were observed at a distance of precisely 10 parsecs (32.6 light-years), without light extinction.

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The simplification of all the given algebra fractions are;

1) a/c

2) (a - b)/(a - 1)

3) (x + 1)/(x - 4)

An algebraic fraction is defined as a fraction whose numerator and denominator are algebraic expressions.

1) (abc + ab²)/(b²c + bc²)

Factorizing numerator and denominator gives;

ab(c + b)/bc(b + c)

b(b + c) will cancel out to get; a/c

2) (a² - b²)/(a² - a + ab - b)

Factorizing numerator and denominator gives;

[(a + b)(a - b)]/[a(a - 1) + b(a - 1)]

= [(a + b)(a - b)]/(a + b)(a - 1)

(a + b) will cancel out to get;

(a - b)/(a - 1)

3) (x² - 2x - 3)/(x² - 7x + 12)

Expanding the numerator and denominator gives;

(x² - 3x + x - 3)/(x² - 4x - 3x + 12)

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

(x - 3) will cancel out to get;

(x + 1)/(x - 4)

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The equivalent quadratic equation to  (x - 2)(x + 9) = 0 is x² + 7x - 18 = 0.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

We know if α and β are the roots of a quadratic equation ax² + bx + c = 0,

Then we can construct the equation by the factors (x - α)(x - β).

Given, We have to construct a quadratic equation with (x - 2)(x + 9) = 0.

Now, Multiply the terms we have,

x² + 9x - 2x - 18 = 0.

x² + 7x - 18 = 0.

So, Our required quadratic equation is x² + 7x - 18 = 0.

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Answer:

2A/h - b2= b1

Step-by-step explanation:

In order to get the value of n, which is what we are trying to find, it is important to know how to isolate the variable.

When something is added to n, you subtract to isolate n. Going with this logic, you would multiply by a number if you wanted to isolate n with a fraction.

[tex]\frac{n}{5}+4=-4[/tex]

The first step would be to get rid of the 4 on the left side so we can work on the variable. We can do this by subtracting both sides by 4, so the left side cancels out to 0.

[tex]\frac{n}{5}+4-4=-4-4[/tex]

[tex]\frac{n}{5} =-8[/tex]

Next, we can multiply both sides by 5, so we can isolate the variable, because it is being divided by 5.

[tex]\frac{n}{5} *5=-8*5[/tex]

n=-40

The L.C.M. defines the least number that is exactly divisible by two or more numbers, whereas the G.C.F. defines the greatest factor present between any given pair of two or more numbers.

LCM is also known as the Least Common Multiple (LCM), and HCF is also known as the Greatest Common Factor (GCF).

The highest common factor (HCF) between two or more numbers is two or more. The LCM, on the other hand, is the lowest common multiple that exactly divides these two figures. The greatest common factor between any two numbers is also known as HCF. Between two or more numbers, LCM is also known as Least Common Divisor.

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If triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

Two or more expressions with an Equal sign is called as Equation.

Let us consider the number be x

tripple of a number added to its half part

3x+x/2

Difference between four times the number and 12

4x-12

So tripple of a number added to its half part its equal to the difference between four times the number and 12

3x+x/2=4x-12

6x+x=2(4x-12)

Apply distributive property on RHS

7x=8x-24

Subtract 7x on both sides and add 24

24=x

Hence, if triple of a number added to its half part its equal to the difference between four times the number and 12 then the number is 24.

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100

Step-by-step explanation:

because after 105 it's 100

The system y = 3x + 4 and 6x - 2y = 8 has no solutions.

A system of equations is a set of equations with multiple variables. To determine the number of solutions for a system of equations, one can use the following methods: graphing, substitution, or elimination. In this case, we can use the elimination method by adding or subtracting the equations to eliminate one of the variables.

If we add the two equations, we get y = 3x + 4 + 6x - 2y = 8, which results in 3x + 4 = 8. This is an inconsistent equation and does not have any solutions. Therefore, the system y = 3x + 4 and 6x - 2y = 8 has no solutions.

This shows that the system is inconsistent, which means that there's no solution that satisfies both equations.

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Step-by-step explanation:

1:13

2:26

3:39

4:52

5:65

6:78

Rule - ×13

Answer:

6.3

Step-by-step explanation:

This is a right triangle, so in order to solve you can use the Pythagorean theorem; which is a² + b² = c² (The hypotenuse, or the longest side, equals C.  A and B equal the legs, or the shorter sides.)  So once you plug in the values, your equation should look like this:

3² + b² = 7²

Square each side, or in other words multiply it by itself.  

9 + b² = 49

Subtract 9 from both sides.  

b² = 40

Take the square root of 40 and your done!

b = 6.3

I hope this helped you!  :)

Answer:

O hrs and 30 minutes is the answer

Step-by-step explanation:

want proof?

Answer:

  about 0.04878 hours ≈ 2 minutes 56 seconds

Step-by-step explanation:

You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.

The speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:

  closing speed = 83 km/h + 40 km/h = 123 km/h

The time it takes to close the 6 km gap is ...

  time = distance/speed

  time = (6 km)/(123 km/h) ≈ 0.04878 h

Converted to minutes and seconds, that is about ...

  0.04878 h ≈ 2 minutes 55.6 seconds

It will be about 2 minutes 56 seconds before the boat and whale meet.

__

Additional comment

NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.

Answer:

y = -3x -27

Step-by-step explanation:

Parallel lines have the same slope.  So the slope will be -3

We need to solve for the y-intercept.  Us the x and y values from the point (-6,-9) to find the y-intercept

m = -3 given

y = -9  from the point( -6,-9)

x = -6  from the point (-6,-9)

y = mx + b  substitute in what you know and solve for b

-9 = (-3) (-6) + b

-9 = 18 + b  Subtract 18 from both sides

-9 -18 = 18 - 18 +b

-27 = b

The equation of the line is y = -3x -27

On observing the provided question we can say that - the function f(x) = a^x is Range : (−∞,∞) or all real numbers

Range: the discrepancy between the top and bottom numbers. To get the range, locate the greatest observed value of the number and deduct the least observed value (the minimum). The data points between the two extremes of the distribution are not taken into consideration by the range; just these two values are considered. Between the lowest and greatest numbers, there is a range. Values at the extremes make up the range. The data set 4, 6, 10, 15, 18, for instance, has a range of 18-4 = 14, a maximum of 18, a minimum of 4, and a minimum of 4.

The answer to the question is that all real numbers or (−∞,∞)

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The general solution to the given differential equation is y = c₁e⁻t + c₂te⁻t + t².

The given differential equation can be written as y'' - y' - 2y = -2t + 4t², which is a second-order linear differential equation with constant coefficients. To solve this equation, the first step is to solve the associated homogeneous equation, which is y'' - y' - 2y = 0. This homogeneous equation can be solved by using the characteristic equation, r² - r - 2 = 0, which has two roots, r = 2 and r = -1.

The general solution of the homogeneous equation is then y = c₁e²t + c₂e⁻t. To find the particular solution of the non-homogeneous equation, the method of undetermined coefficients is used. Since the non-homogeneous term is 4t², the particular solution of the non-homogeneous equation is yp = t².

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a) The probability that a student will study and will pass is 0.765.

b) The probability that a student will pass is 0.715.

What is probability?

Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.

Define some events -

A: A  student studies.

B: A student will pass.

Given that P(A)=0.85 and

P(B|A)=1-P([tex]\bar{B}[/tex]|A)

=1-0.10

=0.90

a) P(a student will study and will Pass)= P(A∩B)

= P(A)·P(B|A)

= 0.85×0.90

= 0.765

b) Given that P( student will either study or pass), the probability is -

=P(A∪B)= 0.8 then P(a student will pass)

=P(B)

It is known that P(A∪B)= P(A)+P(B)-P(A∩B)

Then P(B)=P(A∪B) -P(A) +P(A∩B)

=0.8-0.85 + 0.765

=0.715

Therefore, the probabilities are 0.765 and 0.715.

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Answer:

37/56

Step-by-step explanation:

Answer: 3/5 = 0.6

Step-by-step explanation:

1. 2 2/5 x 1/4 = 12/20

2. 2 times 5 over 5 + 2/5 = 10 + 2 over 5 = 12/5

3. 12/5 times 1/4 = 12/20

4. 12/20=3/5

The solution of the inequality is,

⇒ x > - 5

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ - 4x + 3 < 23

Now,

Since, The inequality is,

⇒ - 4x + 3 < 23

Solve as;

⇒ - 4x < 23 - 3

⇒ - 4x < 20

⇒ - x < 5

⇒ x > - 5

Thus, The solution is,

⇒ x > - 5

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