If f(x) = (x - 3)/(x + 4), find f -1(x).

The run is 9x miles long, while the bike race is 22y miles long.

The distance between two points in mathematics is referred to as the distance. The distance formula, which is simply a derivation of the Pythagorean theorem, which is used to find the length of any one side of a right triangle when you know the lengths of the other two sides, can be used to calculate this distance.

Therefore,

d = vt

where:

d = distance (miles)

v = speed (mph)

t = time (hours)

Let  x = run time

Let  y = bike time

Total time:      x + y = 4

We can create an equation that represents the formula using these variables.

d total = d bike + d run

49 = 9x + 22y

The equation is then only expressed in terms of x or y. We're going to get it in terms of x.

49 = 9x +22(4 - x)

49 = 9x + 88 - 22x

-39 = -13x

3 = x

To determine the distance between each part, enter this value of x into the variables.

run distance = 9x

bike distance = 22(4 - x)

Let x be run time, y be the bicycle race time.

Total time

x+y = 4

Run distance R = 9x

Bicycle race distance  B = 22y

Total distance

9x + 22y = 49

Replace y in the second equation with 4 - x to solve this system.

You'll obtain

y = 1

x = 3

so

R = 9x = 27

B = 22y = 22

Hence, The run is 9x miles long, while the bike race is 22y miles long.

The complete question is:

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during

Suppose you have entered a 49?-mile biathlon that consists of a run and a bicycle race. During your? run, your average velocity is 9 miles per? hour, and during your bicycle? race, your average velocity is 22 miles per hour. You finish the race in 4 hours. What is the distance of the? run? What is the distance of the bicycle? race?

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Answer:

D. \( 3x + 1 \)

Step-by-step explanation:

Perimeter of Rectangle ABCD = \( 9x + 3 \)

Perimeter of Rectangle PQRS = \( 6x + 2 \)

Difference between perimeter of Rectangle ABCD and Perimeter of Rectangle PQRS:

\( (9x + 3) - (6x + 2) \)

Open Parentheses

\( 9x + 3 - 6x - 2 \)

Collect like terms

\( 9x - 6x + 3 - 2 \)

\( 3x + 1 \)

Answer:

24

Step-by-step explanation:

i dont know if its correct

Answer:

it's toooo complicated

The proportional relation between two variable with constant of proportionality equal to 5 is,

For x = 5,

(5,1) not lies on the line as for x = 5, the y is 25.

For x = 3,

The point (3,15) lies on the line.

For x = 10

Point (10,2) not lies on the line.

For x = 0,

The point (0,5) not lies on the line.

So point (3,15) lie on the line.

Answer:

1. 4

2.40

3. 28

4.11

5.12

6. 1

7. 1200

Step-by-step explanation:

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

a

Step-by-step explanation:

the formula of the equation is y=mx+n; and if m=1/2 and n=-1 then it's y=1/2x-1

Surface Area of rectangular pyramid is lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²].

The area of ​​a rectangular pyramid is equal to the sum of the areas of the sides and faces of the rectangular pyramid. A quadrilateral pyramid is a three-dimensional shape with only a rectangular base and triangles on either side of the base.

The area of ​​the base of the rectangle is calculated by multiplying the length of the rectangle by the width of the rectangle.

The area of ​​a rectangle with a pyramidal formula is determined by observing the width, length, and height of the base,

S.A. = lw + l√[(w ÷ 2)² + h²] + w√[(l ÷ 2)² + h²],

where l is the length of the bottom of the rectangle, w is the width of the bottom of the rectangle, and h is the height.

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Juan's location after 60 seconds, given the starting point and the number of seconds would be ( 18, 14 )

Every 15 seconds, Juan moves 4 yards east and 3 yards north. He is therefore moving along the grid in steps of (4 , 3 ).

After 60 seconds, Juan will have moved 4 times because 15 seconds in 60 seconds gives 4. This means he would have moved east by :

= 4 x 4

= 16 yards

And north by :

= 3 x 4

= 12 yards

His location would be:

= ( 2 + 16 , 2 + 12 )

= ( 18, 14 )

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The rest of the question is:

What will Juan's location be after 60 seconds?

The required coefficients are:4, -1, -11, and 7.

Coefficients refer to the numerical values that are assigned to variables in mathematical equations, models, or formulas. They indicate the relative importance or contribution of each variable in the equation. Coefficients are used to determine the relationship between variables and are often estimated through statistical analysis or optimization techniques.

In algebraic equations, coefficients are the numbers multiplied by variables. For example, in the equation 2x + 3y = 5, the coefficients are 2 and 3.

In statistical models, such as linear regression, coefficients represent the slopes or weights assigned to the predictor variables. These coefficients indicate how much the response variable is expected to change for a unit change in the corresponding predictor variable, assuming all other variables are held constant.

We need to consider the polynomial:

(4mn^2n - 2mn + 6) + (6mn^2 - 1) - (mn^2 - 2 + 9mn)

To combine the like terms and find the coefficients of each term, we can write the polynomial in the following form:

4mn^2n - 2mn + 6 + 6mn^2 - 1 - mn^2 + 2 - 9mn

Taking the coefficients of the terms with "mn^2"4mn^2n - mn^2

Taking the coefficients of the terms with "mn"-2mn - 9mn = -11mn

Taking the coefficients of the constant terms6 + 2 - 1 = 7

Therefore, the required coefficients are:4, -1, -11, and 7.

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Answer:

QS is 12.1

Step-by-step explanation:

9 / sin 48 = QS / sin 90

QS = 9 / sin 48 = 12.1

Answer:

1. x² 2. x

Step-by-step explanation:

For these problems, there actually pretty easy. What you do is the numbers like x2 are x times 2. So like if x is 3, it would be equal to 6 because 3 times 2 is 6. Easy, right?

But this time, its asking you for GCF. It's more harder, but it will be easy after you understand it.

#1

So its organize the equation. So x2 gets simpifiled to x times 2. x*2 is double the amount. x + y and x - z. Take the x's that is 2 x's. So x2. Then y and z which are unknown has the value left. And 1 more thing. Since there is no operation, it turns in to times/multiply. Please don't ask why. Ask it in a new question. So you can cross them off and multiply x2 with y times z. The equation now is basically x2 y times z). y times z. Again, the numbers are unknown. So you need to count them as zero. Add 2 zero's together is 0. Add x2 to 0. Which is x2.

You can now do problem 2 by yourself after you read the explaination. Remember, your answer isn't always like this type of explaination. Some ones work, try this for all your problems related. See if it works.

Therefore, the GCF of x2(x + y)(x - z) is x2

The GCF of the expressions x²(x + y)(x - z)  and x(x - y)(x - z) is x(x - z).

An expression is combination of variables, numbers and operators.

The given expressions are x²(x + y)(x - z) and x(x - y)(x - z).

To find the GCF, we need to find the common factors that are present in both expressions.

We can see that both expressions have a factor of x and a factor of (x - z). So, the GCF is x(x - z).

Therefore, the GCF of x²(x + y)(x - z) and x(x - y)(x - z) is x(x - z).

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Both of you are correct because using either way can solve the equation for the value of x.

In the case of solving for x in  2/5 x = 14, the goal is to get rid of the fraction that is multiplying x on the left side. This can be done by either multiplying both sides of the equation by the inverse of 2 / 5 ( which is 5 / 2 ) or by dividing both sides by 2 / 5.

Doing either of these things would get rid of the 2 / 5 and give an answer to x as shown below :

Multiplying :

2/5 x = 14

5 / 2 x 2 / 5 x = 14 x 5 / 2

x = 35

Dividing :

2/5 x = 14

2 / 5 x / 2 / 5 = 14 / 2 / 5

x = 35

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The correct option D: the origin, has the symmetry of the volume of sphere for the graph of the function rule.

For the stated question.

The volume of the sphere is modeled by the power function with respect to the radius as;

V = f(r) = 4/3πr³

As, r is independent of any of the coordinate axis.

Thus, the function rule's graph, which describes the volume of the sphere, is symmetric with regard to the origin.

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A poll of 1556 registered voters nationwide indicated that 43% of those polled blamed oil companies the most for the recent increase in gasoline prices. Therefore, option A is correct: Since the P-value > alpha, we cannot conclude that the percentage of registered voters nationwide who blame oil companies the most for the recent increase in gasoline prices is at least 45%.

To determine whether this poll result supports the claim that at least 45% of registered voters blame oil companies the most for the recent increase in gasoline prices, we test the null hypothesis against the alternative hypothesis.

Test the claim that the percentage of registered voters nationwide who blame oil companies the most for the recent increase in gasoline prices is at least 45% using alpha = 0.01. Test statistic z = -1.59. P-Value = 0.94.

Since the P-value > alpha, we cannot conclude that the percentage of registered voters nationwide who blame oil companies the most for the recent increase in gasoline prices is at least 45%.

Therefore, option A is correct: Since the P-value > alpha, we cannot conclude that the percentage of registered voters nationwide who blame oil companies the most for the recent increase in gasoline prices is at least 45%.

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Answer:

Jenny spent $206.63 for fencing.

Step-by-step explanation:

$13.55 x 15.25ft =$206.6375

Answer:

-5.5 and 0.4 (first option in your list)

Step-by-step explanation:

Please see attached image where we have graphed the expression \(y=6x^2+31x\\\)  and the expression \(y=12\)  and looked for the two points of intersection of the parabola (representing the first expression) with the horizontal line (second expression)

From the graphing we extract that one solution for "x" is approximately -5.5, and the other one around 0.36, which can be rounded to one decimal to: 0.4. then the closest solution is that one shown as the first option in your list.

The net operating income using variable costing for the upcoming year is $327,000.

Sales:

13,000 units sold × $65 per unit = $845,000

Variable Costs:

Direct materials + Direct labor + Variable manufacturing overhead per unit manufactured:

13,000 units manufactured × $31 per unit = $403,000

Variable operating expenses:

13,000 units sold × $2 per unit = $26,000

Total Variable Costs:

$403,000 + $26,000 = $429,000

Contribution Margin:

Sales - Total Variable Costs:

$845,000 - $429,000 = $416,000

Operating Expenses:

Fixed operating expenses for the year: $89,000

Net Operating Income:

Contribution Margin - Operating Expenses:

$416,000 - $89,000 = $327,000

The net operating income using variable costing for the upcoming year is $327,000.

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Answer:

60 but im to surw

Step-by-step explanation:

All i remember is that you have to do A=lwh so it would have to be 4x2x7.5=60

Answer:

X=11 trust me on my mom

Answer:

100,000 x $15 = 1.5 million US$

It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

To solve this problem, we can use the concept of "work rates."

Let's find out how much work Fran and Denise can do individually in one hour.

If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).

Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).

When they work together, their work rates are additive.

So, their combined work rate would be:

\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)

\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)

\(=\frac{7}{24} room/hour\)

This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.

To determine the total time required for them to paint the entire room, we can invert their combined work rate:

\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)

Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.

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Answer:38%

Hope this helps

Answer:

the answer will be 0.314

The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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Using the mean concept, the expression that gives the average of the low and high temperatures is:

(-3 + 8)/2.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.

In this problem, the two observations are -3 and 8, hence their average is given by:

(-3 + 8)/2.

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the two planes will be at the same altitude of approximately 5675.48 feet after 49.45 seconds.

A plane is a flat two-dimensional surface that extends infinitely in all directions. In geometry, a plane is defined as a surface that is completely flat and has no thickness. It is often represented as a coordinate system with two perpendicular axes, usually labeled as the x-axis and y-axis.

Assuming that the two planes maintain their rates of ascent, we can use the following equations to determine when the planes will be at the same altitude:

altitude of plane A = 4000 + 33.5t

altitude of plane B = 3146 + 50.75t

where t represents time in seconds.

To find the time at which the two planes will be at the same altitude, we can set the two equations equal to each other and solve for t:

4000 + 33.5t = 3146 + 50.75tSubtracting 3146 from both sides, we get:

854 + 33.5t = 50.75t

Subtracting 33.5t from both sides, we get:

854 = 17.25t

Dividing both sides by 17.25, we get:

t = 49.45 seconds

Therefore, it will take approximately 49.45 seconds for the two planes to be at the same altitude. To find the altitude at which they will meet, we can substitute this value of t into either equation. Using the equation for plane A, we get:

altitude of plane A = 4000 + 33.5(49.45) = 5645.08 feet

Using the equation for plane B, we get:

altitude of plane B = 3146 + 50.75(49.45) = 5675.48 feet

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Answer:

  17 bars

Step-by-step explanation:

Peter wants to compute the maximum number of bars he can load safely if the load limit of 1200 kg and the bar weight of 60 kg are each rounded to the number of significant digits those numbers have.

The error in a rounded number is assumed to be as much as half of the least significant digit of the number.

Peter's load limit may actually be as low as ...

  1200 kg - (1/2)(100 kg) = 1150 kg . . . . . . . 1200 is rounded to nearest 100

Peter's bar weight might be as high as ...

  60 kg + (1/2)(10 kg) = 65 kg . . . . . . . . . . . 60 is rounded to nearest 10

If Peter has maximum-weight bars and does not want to exceed the minimum his load limit might be, the number of bars he can load is ...

  (1150 kg) / (65 kg/bar) ≈ 17.7 bars

The greatest number of bars Peter can load safely is 17.

Answer:

three

Step-by-step explanation:

stem. is the tens place and the leaf is the. ones place

so you want to find 68 so you look in the stem column and look for six

in the row there are 6 numbers which mean:

60, 61, 67, 68, 68, 68

as you can see there is three 68 there for the answer ths 3

The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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