O EXPONENTIAL AND LOGARITHMIC FUNCTIONSExpanding a logarithmic expression: Problem type 1

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given function.

STEP 2: Explain the means to use to find the required values

Since we were given a graph and can not use a caculator, we will be using the graph to get the values.

STEP 3: Plot the given function on a graph

STEP 4: Get the domain of the function

Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.

STEP 5: Get the Range of the function

The range is all y-values or outputs of a function.

STEP 6: Get the value on which the function is increasing on

STEP 7: Get the value on which the function is decreasing on

STEP 8: Get the values of the asymptotes

An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.

Answer:

1-4<58

Step-by-step explanation:

poor Greg is broke and yea

The number of hamburger is 350 and the number of cheeseburger is 282.

It should be noted that an expression is simply used to show the relationship between the variables.

In this case, the local hamburger shop sold a combined total of 632 hamburgers and cheeseburgers on Saturday and there were 68 fewer cheeseburgers sold than hamburgers.

Let Cheeseburger = x

Hamburger = x + 68

This will be:

x + x + 68 = 632

2x + 68 = 632

2x = 632 - 68

2x = 564

x = 564/2

x = 282

Cheeseburger = 282

Hamburger = x + 68 = 282 + 68 = 350

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Answer:

she needs to make 11 bars

Step-by-step explanation:

42-20

22

each bar is 2 servings so

22÷2

11 bars

The value of the function when x is equivalent to 2043 is 4089.

Linear equations are equation that has a leading degree of 1. Given the linear equation;

3x+7x-28+31-8x

Collect the like terms

3x+7x-28+31-8x

3x+7x-8x-28+31
10x-8x-28+31

2x+3

If the value of x is 2043, substitute;

2x+3 = 2(2043) + 3

2x + 3 = 4086 + 3
2x + 3 = 4089

Hence the value of the function when x is equivalent to 2043 is 4089.

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Answer:

x = 11

Step-by-step explanation:

7X = 77

divide both sides by 7

x = 11

After t hours, the population is 3(2^2t).

After 7 hours, the population is 3(2^14).

In 2.33 minutes, the population would be 21.

The following formula is used to calculate the bacteria population:

The formula for calculating future value is as follows:

FV = P (1 + r)^n

Where:

FV stands for Future Value.

P = Present value of three

R = growth rate = 100%

(hours x 60 minutes) / 30 = 2t = time

3(2^2t) = population in t hours

3(2 ^14) = population in 7 hours

The population of time would be 21 =[( FV /PV) / r] X 30.

2.33 minutes = ( 21 / 3) / 3.

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The vertex and range of y = (x + 2) - 3 is [tex]$(0,-1) ;-3 \leq y < \infty[/tex]

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Matching the specific Polygons with their descriptions, we have;

15-gon → An exterior angle measures 24°

16-gon → The Sum of interior angles is 2520°

12-gon → An interior angle measures 150°

18-gon → An interior angle measures 160°

The formula for sum of interior angles of a Polygon is;

S = (n - 2) * 180

where n is number of sides of polygon. Thus;

1) For a 15 sided polygon;

Sum = (15 - 2) * 180

Sum = 13 * 180

Sum = 2340

Sum of exterior angles of a polygon is; 360°

Thus, external angles = 360/15 = 24°

2) For a 16 sided polygon;

Sum of interior angles = (16 - 2) * 180 = 2520°

3) The value of the interior angles of a polygon with 12 sides is;

(12 -2) * 180/12 = 150°

4)  The value of the interior angles of a polygon with 18 sides is;

(18 - 2) * 180/18 = 160°

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The correct options regarding the functions are given as follows:

1. C. y = -2x - 7/9, m = -2, b = -7/9.

2. A. y = 1400x + 5000, 10,600 lbs.

3. A. t = 0.75m + 12, $23.25.

4. A. y = (x - 2) - 3.

5. B. 302.5 miles.

In slope-intercept formula, a linear function is given as follows:

y = mx + b.

In which:

For this problem, the equation is:

-18x - 9y = 7.

Then:

9y = -18x - 7

y = -2x - 7/9, which slope -2 and intercept -7/9.

Thus option C is correct.

The table represents a linear function, in which:

Thus the function is:

y = 1400x + 5000.

In four weeks, x = 4, hence the amount is of:

y = 1400(4) + 5000 = 10600.

Which means that option A is correct.

Also a linear function, in which:

Hence the function is:

t = 0.75m + 12.

For 15 miles, the cost is given as follows:

t = 0.75(15) + 12 = $23.25.

Which means that option A is correct.

In this graph, we have a concave up parabola with vertex at (2,-3), hence the rule is:

y = (x - 2) - 3.

Which means that option A is correct.

The distance function after t hours is given by:

d = 45t + 100.

Hence, after 4.5 hours, as 1/2 = 0.5, the distance is of:

d = 45(4.5) + 100 = 302.5 miles.

Which means that option B is correct.

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The given expression is

Where n = 1/5.

Let's replace the variable for its value.

First, we solve the product.

Then, we sum fractions. Notice that we just have to sum numerators because the denominators are equal.

We know that he scored 879 points in 34 games, so we can calculate the average rate as:

At this rate, we can calculate the total points P by multiplying the rate r by the number of games n:

We can calculate how many games are needed for P=1500 as:

For n=82 games, the expected number of points P is:

Answer:

a) It will take him approximately 58 games to score 1500 points.

b) At this rate, he would score approximately 2120 points in the the entire season.

INFORMATION:

We have the following figure

And we must find its surface area

STEP BY STEP EXPLANATION:

To find the surface area of the triangular prism, we can divide the figure in:

- The two triangle bases:

We have the next triangle in the two bases:

We can calculate the area of the triangle

Since we have the same triangle in the two bases, the total area of the two triangles would be

-

% of the burger restaurants worldwide were in that country in 2016 =

= 12994/ 34602 X 100

= 37.55 %

Answer: m = -3/5

Step-by-step explanation:

Given:

Number of friends = 5

Total amount they earn = $33.75

Let's find how much each friend earn.

To find the amount each friend earn, take the formula below:

Substitute values into the equation above and evaluate:

Therefore, each friend earns $6.75

ANSWER:

$6.75

Answer: $6.75

Step-by-step explanation: Divided 33.75 by 5 which is equal to $6.75

Explanation:

The expression is given below as

Concept:

The sum of two or more like terms is a single like term; but the two unlike terms cannot be added together to get a single term. Suppose, to find the sum of two unlike terms x and y, we need to connect both the terms by using an addition symbol and express the result in the form of x + y.

In this case,

The terms given ( 3m and n ) are unlike terms and as such the expression cannot be simplified further

Hence,

The final answer is

such

The area of a trapezoid is given by:

where b1 and b2 are the bases of the trapezois and h is the height. In this case we have that A=198, b1=15 and h=12, plugging this values into the equation above and solving for b2 we have:

Therefore b2 is equal to 18 m

we have that

the equation of the line in slope intercept form is

y-=mx+b

we have

m=2

b=3/2

substitute

y=2x+3/2

answer is option C

Given: 8abcd

The number of degrees is the sum of the exponent of each variable in the monomial

The answer is 4

Fair price to play this game is $16.72

To find the fair price, we divide the total amount by the number of bill denominations given

Fair price to play this game is $16.72

Explanation:

Mr. Coffey bought a house for $195,000 with a 20% down payment.

A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.

He bought the bouse for $156,000.

5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.

He would pay $8,190 every 30 years. (if this was the interest rate.)

Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.

He would pay $2,047.50 every 30 years. (if this was the interest rate.)

There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years.

F(x) is blue and G(x) is red

Have to find at which point both functions have the same value, or the same in which point both lines intercept

and looking at the graph ,theres only one point where both are equal. Its the point x= 2 y=0.

so the correct answer is f(2) = g(2)

The given function 8x^2+8x-22 rewritten using the completing the square method is (x+1/2)^2 = 3

By altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach.

Given the quadratic equation below;

8x^2+8x-22 = 0

This can be simplified into the equation below;

8x^2+8x-22 = 0

4x^2+4x-11 = 0

Add 11 to both sides of the equation

4x^2+4x-11 + 11= 0 + 11

4x^2+4x = 11

Factor out 4x from the expression;

4(x^2+1) = 11

(x+1/2)^2 = 11/4 + 1/4

(x+1/2)^2 = 12/4

(x+1/2)^2 = 3

Hence the expression in the form of (x-p)^2=q is (x+1/2)^2 = 3

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From the information given, the area of the kitchen is 54 square feet and it is 9 times as many square feet as does Tina's pantry. This means that the area of Tina's pantry is

54/9 = 6 square feet

If the pantry is 2 feet wide, we would determine its length by applying the formula for determining the area of a rectangle which is expressed as length * width

Therefore,

2 * length = 6

length = 6/2 = 3 feet

Length of the pantry is 3 feet

The equation of a straight line is y = mx + b where m is the slope and b is the y-intercept then the two points exist (0, -2) and (6, 0).

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

The equation of a straight line is:

y = mx + b where m is the slope and b is the y-intercept.

Therefore, the equation for this line is:

y = (1/3)x - 2

To graph it we can identify two points on the line and connect them.

If x = 0, then y = -2 this is the y-intercept given in the problem.

If x = 6, then y = 0 this is the x-intercept

Therefore, the two points exist (0, -2) and (6, 0).

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We are given the information that the equation of the line is of the form:

y = a x + b

where a is a negative number and b is a positive number.

And we are asked to select among a number of options that represent the situation.

SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.

SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and dropping from left to right Therefore option b is also discarded because that represents a line going up from left to right.

Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.

The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)

Then, please mark the last option (d) as the correct answer.

Solution

For this case we need to sort the values and we have:

Studied

79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100

Q3= 98.25

Q1= 89

Therefore IQR = 98.25-89= 9.25

Not Studied

45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91

Q3= 87.5

Q1= 70.25

Therefore IQR = 87.5-70.25= 17.25

From the results obtained we can conclude that the students who not studied havve larger variability compared to those who studied

Answer:

Step-by-step explanation:

The distance from the center to the chord is the perpendicular bisector of the chord.

The three segments form a right triangle:

a) Use Pythagorean to find the radius:

b) Let the half-chord is x cm long. Use Pythagorean to find the missing leg:

The length of the chord is:

The surface area of a rectangular prism can be represented below

Therefore,