Consider the function: f(x) = x^3 - x^2 - 6x Determine the instantaneous rate of change at:a) x= -1b) x= 4

Answer:

y= 11/19

Step-by-step explanation:

the expression for f(x) = x^2 - 7

The graph of a function f in mathematics is the collection of ordered pairs where  f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

g(x)=x²-3

given that ,

     graph of g is translated vertically downward by 4 units, it becomes the graph of a function f

we need to find f(x)

so to find f(x) we know that

g(x) = f(x) -k vertically down by k units

so ,

 f(x) = g(x) - 4 as given in the question  for finding the expression

f(x) = g(x) - 4

f(x)= x^2 - 3 -4

f(x)= x^2 - 7

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Given -

f(x) = -2/9x + 1/3

To Find -

Y-intercept =?

Step-by-Step Explanation -

We know that:

At y-intercept x = 0

So,

Put x = 0 in the given equation

f(x) = -2/9(0) + 1/3

f(x) = 1/3

Final Answer -

Option (c)

Y-intercept = 1/3

Answer:Smith left 54 in the garden

Step-by-step explanation: 10% of 60 is 6

90% of 60 is 54

Hope this helps

6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.

The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.

6. For a = 20, b = 99 using the Pythagoras Theorem we have:

x² = a² + b²

x² = 20² + 99²

x² = 9801

x = 99

7. For a = 60, b = 91 we have:

x² = 60² + 91²

x² = 10521

x ≈ 102.56

8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.

a = 20, b = 21, and c = 29

Here,

20² + 21² = 841

29² = 841

Hence, the triangle is right.

9. For a = 15, b = 19, and c = 24. We have:

15² + 19² = 556

24² = 576

The triangle is acute.

10. For a = 11, b = 23, and c = 26. We have:

11² + 23² = 650

26² = 676

The triangle is acute.

11. Using the Pythagoras Theorem we have:

x² = 53² - 45²

x² = 1044

x ≈ 32.28

The value of x is 32.28

12. x² = 41² - 9²

x² = 1600

x = 40

The value of x is 40.

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Answer:

Step-by-step explanation:

Answer:

Zach earns $10 and for the pair of boots Zach earns $15

Step-by-step explanation:

Let be x the number of pairs of shoes

Let be y the number of pairs of boots

Then we can establish the following system of equations with the data of the statement:

\(5x + 9y = 185 \\7x + 9y = 205\)

We subtract the second equation from the first equation to eliminate the variable y and solve for x, just like this:

\(7x+9y-5x-9y=205-185\\2x=20\\x=\frac{20}{2}\\x=10\)

For y replacing in the first equation the value of x and solving for y:

\(5.10 + 9y = 185\\9y=185-50\\y=\frac{135}{9}\\y=15\)

So for the pair of shoes Zach earns $10 and for the pair of boots Zach earns $15

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Answer:

  y = -2

Step-by-step explanation:

A horizontal line has an equation of the form ...

  y = constant

In order for the line to go through a point with a y-coordinate of -2, the constant must be -2.

  y = -2 . . . . horizontal line through (-5, -2)

The equations that have a true solution include the following:

8⋅72−12=22−2⋅3 fraction numerator 8 times 7 over denominator 2 end fraction minus 12 equals 22 minus 2 times 3.

48 ÷ 8 + 2³ = 5 + 3²

In this exercise, we have to determine the equations that are true and this would  be done by simplifying and evaluating each of the equations as follows:

(8 × 7)/2 - 12 = 22 - (2 × 3)

Opening the bracket on both sides of the equation, we have:

56/2 - 12 = 22 - 6

28 - 12 = 16

16 = 16 (True).

48 ÷ 8 + 2³ = 5 + 3²

Next, we would evaluate the exponents as follows:

48 ÷ 8 + 8 = 5 + 9

6 + 8 = 14

14 = 14 (True).

150/5² = 30 - 4² - 12

By evaluating the exponents, we have the following:

150/25 = 30 - 16 - 12

6 = 2 (False).

9² - 7² = 20 ÷ (7 - 2)

Opening the bracket, we have the following:

9² - 7² = 20 ÷ 5

By evaluating the exponents, we have the following:

81 - 49 = 4

32 = 4 (False).

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Answer:

graph

Step-by-step explanation:

Answer:

3.25 or 3 1/4

Step-by-step explanation:

Remove the parentheses first: 3/4 + (1/3 / 1/6) - (-1/2)

1/3 / 1/6 turns into 1/3 * 6

Reduce the numbers:

3/4 + (1/3 * 6) + 1/2

cross multiplication, 6 divided by 3 = 2.

So the new equation is 3/4 + 2 + 1/2

Then you calculate.

3/4 + 2 + 1/2 = 13/4

13/4 reduced is 3 1/4 or 3.25

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

The cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

To find the cost of one hosta and one geranium, we can set up a system of equations based on the given information.

Let's assume the cost of one hosta is represented by 'h' and the cost of one geranium is represented by 'g'.

From the information given, we can set up the following equations:

Eugene's spending:

18h + 6g = $150

Jessica's spending:

7h + 16g = $113

We can now solve this system of equations to find the values of 'h' and 'g'.

Multiplying the first equation by 2 and the second equation by 3 to eliminate 'g', we get:

36h + 12g = $300

21h + 48g = $339

Now, we can subtract the second equation from the first to eliminate 'h':

(36h + 12g) - (21h + 48g) = $300 - $339

36h - 21h + 12g - 48g = -$39

15h - 36g = -$39

Simplifying further, we have:

15h - 36g = -$39

Now we can solve this equation for 'h' and substitute the value back into any of the original equations to find 'g'.

Let's solve for 'h':

15h = 36g - $39

h = (36g - $39) / 15

Substituting this value of 'h' into Eugene's equation:

18[(36g - $39) / 15] + 6g = $150

(648g - $702) / 15 + 6g = $150

648g - $702 + 90g = $150 * 15

738g - $702 = $2250

738g = $2250 + $702

738g = $2952

g = $2952 / 738

g ≈ $4

Now, substituting the value of 'g' back into Eugene's equation:

18h + 6($4) = $150

18h + $24 = $150

18h = $150 - $24

18h = $126

h = $126 / 18

h ≈ $7

Therefore, the cost of one hosta is approximately $7 and the cost of one geranium is approximately $4.

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Answer:

Difference=£2.4

Step-by-step explanation:

Here in shop A

130 cm=£1.82

1 cm=£1.82/130

1 cm=0.014

Now

400 cm=0.014*400

=£5.6

Again, In shop B

235cm=£1.88

1 cm=£1.88/235

1 cm=£0.008

Now

400cm=0.008*400

=£3.2

Now,

Difference=£5.6-£3.2

=£2.4

Answer:

D. y = -2x

Step-by-step explanation:

slope = rise/run = 2/-1 = -2

y-intercept = (0,0)

y = mx + b

y = -2x + 0

y = -2x

Answer:

I suggest that you use Socratic to solve this.

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\huge\textbf{This equation requires us to do}\\\huge\textbf{distributive property.}\)

\(\huge\textbf{If you're unsure what the}\\\huge\textbf{distributive property formula is,}\\\huge\textbf{it is: }\)

\(\large\textbf{a(b + c)}\)

\(\large\textbf{= a(b) + a(c)}\)

\(\large\textbf{= ab + ac}\)

\(\huge\textbf{Now, that we have that information}\\\huge\textbf{out of the way, we can find the}\\\huge\textbf{result of your given equation.}\)

\(\huge\textbf{Your equation that you provided:}\)

\(\large\textbf{2(3x + 5)}\)

\(\large\textbf{= 2(3x) + 2(5)}\)

\(\large\textbf{= 6x + 10}\)

\(\huge\textbf{Do you see how interesting it was to}\\\huge\textbf{find the result to the question? }\huge\boxed{:)}\)

\(\huge\textbf{Anyway! Let's label our result since}\\\huge\textbf{we found it already while working it out.}\)

\(\huge\textbf{Thus, your answer should be: \boxed{\mathsf{6x + 10}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjo your day!}\)

Answer:

N/A

Step-by-step explanation:

This question is impossible to answer, as there is no total amount of tickets given or any number to go off of at all

Answer:

twice

Step-by-step explanation:

Answer:

19/20 , 1 1/4 , 1 4/5

Step-by-step explanation:

1.8 = 1 4/5 (fraction)

1.8 converts to 18/10. This can be simplified twice, firstly by making it 9/5 since both 18 and 10 are divisible by two, but can be simplified further to 1 4/5

1.25 = 1 1/4 (fraction)

1.25 converts to 125/100. This can be simplified to 5/4 or 1 1/4

0.95 = 19/20 (fraction)

0.95 converts to 95/100. This can be simplified to 19/20

Ascending Order (smallest to largest)

smallest - 19/20

middle - 1 1/4

largest - 1 4/5

I believe this is the right answer, but haven't done fractions in a while so may want to double check to make sure

(x • (y³)) - 32xyz²

Pull out like factors :

xy³ - 9xyz² = xy • (y² - 9z²)

Factoring: y² - 9z²

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A² - AB + BA - B² =

A² - AB + AB - B² =

A² - B²

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : 9 is the square of 3

Check : y² is the square of y¹

Check : z² is the square of z¹

Factorization is : (y + 3z) • (y - 3z)

Final result :

xy • (y + 3z) • (y - 3z)

No, this shape does not belong in a group of shapes that have more than one pair of perpendicular sides.

In order to determine if the shape belongs to a group of shapes with more than one pair of perpendicular sides, we need to examine the number of right angles in the shape.

A right angle is a 90-degree angle, and shapes with perpendicular sides have right angles at their intersections. By counting the number of right angles in the shape, we can determine if it has more than one pair of perpendicular sides.

If the shape has only one right angle, then it does not have more than one pair of perpendicular sides. But if it has two or more right angles, then it would belong to the group of shapes that have more than one pair of perpendicular sides.

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Answer:

2. ) {25}^{2x} - 1 = {125}^{3x} + 4

=> {25}^{2x} = {125}^{3x} + 4 +1

=> {(5)^(2)}^{2x} = {(5)^(3)}^{3x} + {5}^{1}

=> {5}^{4x} = {5}^{9x} + {5}^{1}

=> 4x = 9x + 1

=> 4x - 9x = 1

=> - 5x = 1

=> x = 1/-5

a ruler is not the best tool to use to measure the field of view on medium- and high-power lenses.

Using a ruler to measure the field of view on medium- and high-power lenses would be difficult and inaccurate. This is because the magnification of the lenses changes the field of view, so a ruler would not be able to measure the field of view accurately at different magnifications. Additionally, a ruler is too small to measure the field of view accurately since it is usually measured in degrees. Therefore, Using a ruler to measure the field of view on medium- and high-power lenses is difficult and inaccurate. This is because the magnification of the lenses changes the field of view, and a ruler is not designed to measure this change. A ruler is also too small to measure the field of view accurately since it is usually measured in degrees. Therefore, using a ruler is not the most reliable tool for measuring field of view on medium- and high-power lenses. Instead, it is better to use a protractor or other specialized tools to accurately measure the field of view. Additionally, it is important to remember that the field of view changes with magnification and should be checked at different magnifications to get the most accurate measurement.

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Step-by-step explanation:

= f (8) - f (-5)

= 3*8-2 -(3*-5-2)

= 22-(-15-2)

= 22+17

= 39

length=8 cm, width=6 cm, height=5 cm. (answer = 2.1 g/cm3)

The density of the block is of:

\(d = \frac{500}{lwh}\)

In which l, w and h are the dimensions of the rectangular block, in centimetres.

----------------------

\(d = \frac{m}{v}\)

\(v = lwh\)

\(d = \frac{m}{v}\)

\(d = \frac{500}{lwh}\)

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The length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

To find the length of the fence around the enclosure, we need to first find the perimeter of the rectangle and then subtract the combined length of the two gates from it.

Let's assume the length of the rectangle is 'l' and the width is 'w'.

From the given data, we know that each gate is 4 m wide.

Therefore, the width of the rectangle is:

Width = w + (4 m + 4 m) = w + 8 m

The perimeter of the rectangle is:

P = 2l + 2(w + 8 m) = 2l + 2w + 16 m

Now, we need to subtract the combined length of the two gates from the perimeter:

P - 2 × 4 m = 2l + 2w + 16 m - 8 m = 2l + 2w + 8 m

So, the length of the fence around the enclosure not including the gates is:2l + 2w + 8 m

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The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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