Find the inverse of each function:
y = log5 (4x + 1)
y = log3 (2^x + 8)
y = log4 (-2x + 9)
y = 5^x + 9/2
y = 10^x + 3/ -3
y = log5 (-4x + 10)

The given function, f(x) = x + 4 is increasing on the entire interval of 2≤x≤5

From the question, we are to determine if the given function is increasing or decreasing over the given interval

The given function is

f(x) = x + 4

To determine if the function f(x)=x+4 is increasing or decreasing on the interval of 2≤x≤5, we need to look at the sign of the first derivative of the function on that interval.

The first derivative of the function is

f'(x) = 1

Which is always positive

This means that the function is increasing on the entire interval of 2≤x≤5.

To justify this, we can also look at the graph of the function, which is a straight line with a positive slope. Any line with a positive slope is always increasing, so this confirms our conclusion that the function is increasing on the given interval.

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Answer:

First, subtract 10x on both sides so you get

12=10x-2

Then add 2 odd both sides

14=10x

Then divide both sides by 10

14/10= 10X/10

So you get x=1.4

Answer:

Step-by-step explanation:

Multiply each then divide by the first number you started off with.

Based on the given information, the cost of a pound of pistachios and a pound of cashews is $7.875 and $5.50, respectively.

To find the cost of a pound of pistachios and the cost of a pound of cashews, we can use a system of equations.

Let's let P represent the cost of a pound of pistachios and C represent the cost of a pound of cashews.

Then we can write two equations based on the information given:

4P + 1C = 37

3P + 3C = 48

Now we can use the elimination method to solve for one of the variables.

Let's multiply the first equation by -3 to eliminate the P variable:

-12P - 3C = -111

3P + 3C = 48

Adding these two equations together gives us:

-8P + 0C = -63

Simplifying gives us:

P = 63/8

This means that the cost for a pound of pistachios is $63/8 or $7.875.

Substitute the value of P to any of the two equations so we can have the value of C.

4(63/8) + 1C = 37

C = 11/2 = 5.5

Therefore, the cost of a pound of pistachios is $7.875 while the cost of a pound of cashews is $5.50.

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Step-by-step explanation:

Refer to pic...........

The measure of angle TYK is given as follows:

46º.

Two angles are defined as complementary if the sum of their measures is of 90º.

In this problem, we have that angle Y is an angle of 90º, which is then divided into two angles, given as follows:

Then 44 and TYK are complementary angles, and thus the measure of angle TYK is given as follows:

m < TYK + 44 = 90

m < TYK = 90 - 44

m < TYK = 46º.

(the angle addition postulate is also applied for the complementary angles in this problem, as the sum of the two smaller smaller angles combined is of 90º).

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To determine the values of r for which v is in the span of S, we need to find a scalar multiple of the vector in S that equals v.

In other words, we need to solve the equation:
v = c* S
where c is a scalar and S is the vector in the span. Plugging in the values for v and S, we get:
\[\left[\begin{array}{c}2 \\ r \\ -1\end{array}\right] = c*\left[\begin{array}{c}1 \\ 0 \\ -1\end{array}\right]\]
To solve for c, we can equate the corresponding entries of the two vectors:
2 = c*1
r = c*0
-1 = c*-1
From the first equation, we get c = 2. Plugging this value into the third equation, we get:
-1 = 2*-1
which simplifies to:
-1 = -2

This equation is not true, so there is no value of c that satisfies all three equations.
Therefore, there is no value of r for which v is in the span of S.
The vector v is not in the span of S for any value of r.

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The mean advertising spent for the automotive sector is $72,450 and for the department store sector is $67,650.

The standard deviation for the automotive sector is $10,808.16 and for the department store sector is $8,265.49.

The range of advertising spent for the automotive sector is $41,000 and for the department store sector is $30,800.

The interquartile range for the automotive sector is $14,250 and for the department store sector is $10,200.

Based on this sample and the answers to the previous questions, it can be seen that the automotive sector spends more on advertising on average than the department store sector. The automotive sector also has a larger standard deviation, indicating that there is more variation in the amount of advertising spent by companies in this sector.

The range of advertising spent for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the highest and lowest amounts spent on advertising in this sector.

The interquartile range for the automotive sector is also larger than that of the department store sector, indicating that there is a larger difference between the 25th and 75th percentiles of advertising spent in this sector.

Overall, these results suggest that there is more variation in the amount of advertising spent by companies in the automotive sector compared to the department store sector.

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Perimeter would not be used to solve the problem of determining the cost of replacing a linoleum floor with a wood floor. Perimeter is a measure of the boundary of a two dimensional shape, such as a square, rectangle, or triangle. This measure would not be useful in calculating the cost of replacing a floor, as the cost of the flooring materials will depend on the total area of the floor, rather than its perimeter.

Area is the measure of the two dimensional space of a shape, and would be the correct measure to use when calculating the cost of replacing a floor. Area is calculated by measuring the length and width of the floor, then multiplying them together. The cost of the flooring materials can then be calculated by multiplying the area of the floor by the cost of the materials per square foot. This would give an accurate figure for the total cost of the flooring materials.

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Answer:

Karla Saved for 15 months.

Step-by-step explanation:

Tom saved 60 each month if he saved for 8 months then he made $480. Karla saved 32 each month, each of them saved the same amount, 480 because 480 + 480 = 960. divide 480 by 32 and you'll get 15. therefore Karla saved her money for 15 months.

Hope this helps :)

So the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

In this problem, you are given a graph of a linear function. The graph shows two points on the line: (-2, 0) and (3, 5).

To find the slope of the line, we can use the formula:

slope = (change in y) / (change in x)

We can use the two points given to find the change in y and the change in x:

change in y = 5 - 0 = 5

change in x = 3 - (-2) = 5

Plugging these values into the formula, we get:

slope = 5/5 = 1

So the slope of the line is 1.

To find the y-intercept of the line, we can use one of the points on the line and the slope we just found. Let's use the point (-2, 0):

y - y1 = m(x - x1)

where (x1, y1) is the point (-2, 0) and m is the slope we just found:

y - 0 = 1(x - (-2))

y = x + 2

Therefore, the equation of the line in slope-intercept form is y = x + 2. The y-intercept is 2.

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After 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet

The depth of the water variations via- 3/ 4 foot each hour, this means that the depth decreases by employing 3/4 foot every hour.

Still, also after one hour of draining, the intensity of the water might be

If the primary depth of the water was five bases.

5-(3/4) = 41/4 ft

After hours, the depth might be

-(3/4) = 31/2 fr

After three hours

-(3/4) = 23/4 ft

After 4 hours

-(3/4) = 2 ft

After five hours

2-(3/4) = 11/4 bases

Thus, after 5 hours of draining, the depth of the water in Mara's swimming pool will be 11/4 feet

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Answer:

1. plot the point (6,5) and label it Mr. Snuffles

2. 26 treats were eaten in total (21 not counting Mr.Snuffles)

Step-by-step explanation for plotting the point:

On the bottom line (miles walked) go to the number six, then go up five until it is on the five line for the side line (number of treats) plot the point here and then label the point Mr.Snuffles.

plot the point (6,5)

21 treats were eaten in total

Step-by-step explanation:

On the X axis, go to the number six, then go up five until it is on the five line for the side line (number of treats) plot the point here and then label the point Mr. Snuffles.

The cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

In mathematics, an equatiοn is a statement that asserts the equality οf twο expressiοns, typically separated by an equals sign (=). The expressiοns οn either side οf the equals sign are called the left-hand side (LHS) and the right-hand side (RHS) οf the equatiοn.

Let's use variables tο represent the cοst οf each item. Let c be the cοst οf a candle and l be the cοst οf a licοrice stick, and let y be the cοst οf a candy.

Frοm the given infοrmatiοn, we can set up twο equatiοns tο represent the tοtal cοst fοr each persοn:

2c + l = 3.25 (Equatiοn 1)

y + 4l = 2.50 (Equatiοn 2)

We can then sοlve fοr each variable by using algebraic manipulatiοn.

Frοm Equatiοn 1, we can isοlate l by subtracting 2c frοm bοth sides:

l = 3.25 - 2c

We can substitute this expressiοn fοr l intο Equatiοn 2, and sοlve fοr y:

y + 4(3.25 - 2c) = 2.50

y + 13 - 8c = 2.50

y = 2.50 - 13 + 8c

y = 8c - 10.5

Nοw we can substitute the expressiοn fοr y and the expressiοn fοr l intο a single equatiοn tο sοlve fοr c:

2c + (8c - 10.5) = 3.25 + 2.5

10c - 10.5 = 5.75

10c = 16.25

c = 1.625

Sο a candle cοsts $1.625. We can use this value tο find the cοst οf a licοrice stick:

l = 3.25 - 2c

l = 3.25 - 2(1.625)

l = 0.975

Sο a licοrice stick cοsts $0.975. Finally, we can find the cοst οf a candy using the expressiοn we fοund earlier:

y = 8c - 10.5

y = 8(1.625) - 10.5

y = 2.5

Sο a candy cοsts $2.50.

Therefοre, the cοst fοr οne οf each item is:

Candle: $1.625

Licοrice stick: $0.975

Candy: $2.50

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Answer:

The discount on the skateboard is 12% of its original price, so the discounted price is:

Discounted price = $79.28 - 0.12($79.28) = $69.78

Now we need to calculate the sales tax on the discounted price. The sales tax rate is 8.25%, so the amount of sales tax is:

Sales tax = 0.0825($69.78) = $5.76

Adding the discounted price and the sales tax, we get the total cost of the skateboard:

Total cost = $69.78 + $5.76 = $75.54

Therefore, the total cost of the skateboard, including the discount and sales tax, is $75.54.

The present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

The present value of an annuity is calculated using the following formula:

PV = A[((1+i)n-1)/(i(1+i)n)]

where A = amount of each annuity payment, i = interest rate, and n = number of payments.

For this problem, A = $500, i = 6%, and n = 15 years.

Therefore, the present value of the annuity necessary to fund the withdrawal is:

PV = $500[((1+0.06)15-1)/(0.06(1+0.06)15)]

PV = $500[5.72982/0.105638]

PV = $5,354.82

Therefore, the present value PV of the annuity necessary to fund the withdrawal is $5,354.82, rounded to the nearest cent.

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Answer:

Let's first simplify the left-hand side and right-hand side of the inequality:

2 - 5(x + 1) = 2 - 5x - 5 = -5x - 3 3(x - 1) - 24 = 3x - 27

So the inequality becomes:

-5x - 3 ≥ 3x - 27

Now we can solve for x:

-5x - 3 ≥ 3x - 27 -8x ≥ -24 x ≤ 3

The solution set is all x-values less than or equal to 3. We can express this in interval notation as:

(-∞, 3]

The solution set in interval notation is (-∞, 4].

To solve the inequality 2 − 5(x + 1) ≥ 3(x − 1) − 24 and write the solution set in interval notation, we need to follow these steps:

Distribute the -5 and 3 on the left and right sides of the inequality, respectively:
2 - 5x - 5 ≥ 3x - 3 - 24

Simplify both sides of the inequality by combining like terms:
-3x - 3 ≥ 3x - 27

Add 3x to both sides of the inequality to isolate the variable on one side:
-3 ≥ 6x - 27

Add 27 to both sides of the inequality:
24 ≥ 6x

Divide both sides of the inequality by 6 to solve for x:
4 ≥ x

Write the solution set in interval notation. Since the inequality is "greater than or equal to," we use a closed bracket for the lower bound and an open bracket for the upper bound:
(-∞, 4]

Therefore, the solution set in interval notation is (-∞, 4].

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Answer:

Below

Step-by-step explanation:

9/5  X   4/1  X  1/6   =  ( 9 x 4 x 1)  / (5 x 1 x 6) = 36/30  = 1 6/30 = 1  1/5

Answer:

1 1/5

Step-by-step explanation:

Answer: 38.465 feet

Step-by-step explanation: The diameter (7 feet) divided by 2, equals 3.5. multiply 3.5 squared (12.25 feet) by pi (3.14) equals your answer of 38.465 feet.

The leading coefficient of f(x) is positive, which means that the graph will be pointing upwards on both ends. The graph is attached below.

Graphs are a not unusual place technique to visually illustrate relationships within side the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately within side the textual content and in much less space.

To sketch the graph of f(x) = x^4 - 3x^3 + x - 3, we can use the information gathered from analyzing the function:

Using this information, we can sketch the graph of f(x) as follows:

Putting all of this information together, we can sketch the graph of f(x) as shown below:

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The inequality's solution set can be described by inspection as x <= 8.

Inequality is the unequal treatment of people based on factors such as race, gender, class, or other social characteristics. It is often seen as unfair and can lead to social and economic disparities.

This is because the inequality (x-8)^(6)<=0 is asking when the quantity (x-8) raised to the 6th power is less than or equal to zero.

Since any number raised to an even power will always be positive or zero, the only way for this inequality to be true is when (x-8) is equal to zero. This occurs when x = 8. Therefore, the solution set is x <= 8.

To summarize, the inequality's solution set is:
x <= 8

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The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage. 

Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount. 

Solution according to the information given in the question :

Given, Principal(P) = $5,000

          Compounding frequency(n) = 4

          Time(in years)(T) = 5  

           Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5,000 × (1 + 6/4×100)⁵

             = 5,000 × (1 + 0.015)⁵

             = 5,000 × (1.015)⁵

             = 5000 ×1.077

             = $5286.42

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The simplified form of [tex](4x-3)(-5x^(2)+2x-4)[/tex] is: [tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

To multiply and simplify the given expression [tex](4x-3)(-5x^(2)+2x-4)[/tex], we can use the distributive property. This means we will multiply each term in the first parentheses by each term in the second parentheses and then combine like terms.

First, we will distribute the 4x to each term in the second parentheses:
[tex]4x * (-5x^(2)) = -20x^(3)4x * (2x) = 8x^(2)4x * (-4) = -16x[/tex]

Next, we will distribute the -3 to each term in the second parentheses:
[tex]-3 * (-5x^(2)) = 15x^(2)-3 * (2x) = -6x-3 * (-4) = 12[/tex]

Now we will combine all of the terms:
[tex]-20x^(3) + 8x^(2) - 16x + 15x^(2) - 6x + 12[/tex]

Finally, we will combine like terms:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

So the simplified expression is:
[tex]-20x^(3) + 23x^(2) - 22x + 12[/tex]

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Nick is 36 years old now.

To solve the problem, we can use the following steps:

Step 1: Let Nick's age be x and Madelyn's age be y.

Step 2: We are given that Nick is 64 years younger than Madelyn, so we can write an equation: x = y - 64

Step 3: We are also given that 4 years ago, Madelyn's age was 3 times Nick's age, so we can write another equation: y - 4 = 3(x - 4)

Step 4: Substitute the first equation into the second equation to get: y - 4 = 3(y - 64 - 4)

Step 5: Simplify the equation to get: y - 4 = 3y - 204

Step 6: Solve for y to get: y = 100

Step 7: Substitute the value of y back into the first equation to get: x = 100 - 64 = 36

Therefore, Nick is 36 years old now.

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Answer: 48

Step-by-step explanation:

6 x 8 = 48

Step-by-step explanation:

Refer to pic...........

Answer:

To simplify this expression, we need to first evaluate the terms inside the square root:

(-1)² = 1

(-2 - (-1))² = (-2 + 1)² = (-1)² = 1

Now we can substitute these values and simplify the expression:

√(6 - (-1)² + (-2 - (-1))²)

= √(6 - 1 + 1)

= √6

Therefore, the simplified form of the expression is √6.

Answer:

To evaluate the expression √(6-(-1)² + (-2-(-1)²), we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

1. First, we need to evaluate the expressions inside the parentheses:

-1² = (-1) × (-1) = 1

-2-(-1)² = -2-1 = -3

2. Next, we substitute these values into the expression:

√(6-(-1)² + (-2-(-1)²)

= √(6-1 + (-2-1))

= √(5 - 3)

= √2

Therefore, the value of the expression √(6-(-1)² + (-2-(-1)²) is √2.

Step-by-step explanation:

wag na e delete ang bob0 nang mag dedelete nito

It is a vertical stretching by a factor of 2 followed by a vertical shift of 1 unit.

1- To transform f(x) in the given equations, the following transformations need to be done:

a) y = −0.5f(−0.5x) − 1 is a transformation by vertical stretching by a factor of 0.5, followed by a horizontal compression by a factor of 0.5, and then a vertical shift of 1 unit.

b) y = 2f(x − 5) + 4 is a transformation by horizontal shifting of 5 units to the left, followed by a vertical stretching by a factor of 2, and then a vertical shift of 4 units.

c) y = 3f (−2(x + 1)) is a transformation by horizontal shifting of 1 unit to the right, followed by a horizontal compression by a factor of 2, and then a vertical stretching by a factor of 3.

2- To transform f(x) = √x, it is a vertical stretching by a factor of 2 followed by a vertical shift of 1 unit.

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The r value is close to 0, it indicates that there is no correlation between the two variables.

The Pearson correlation coefficient (r value) is a measure of the strength of the linear relationship between two variables. It is calculated using the formula:

r = (sum of the products of the paired scores) / (square root of the sum of the squares of the first scores) * (square root of the sum of the squares of the second scores)

In this case, the two variables are traitanx and comanx2. To find the Pearson correlation between these two variables, we would need to calculate the sum of the products of the paired scores, the sum of the squares of the first scores, and the sum of the squares of the second scores. Then, we would plug these values into the formula and calculate the r value.

Without the actual data set, it is not possible to calculate the Pearson correlation between traitanx and comanx2. However, if the r value is close to 1, it indicates a strong positive correlation between the two variables. If the r value is close to -1, it indicates a strong negative correlation between the two variables. If the r value is close to 0, it indicates that there is no correlation between the two variables.

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