The function f(x) = (x − 4)(x − 2) is shown. What is the range of the function? all real numbers less than or equal to 3 all real numbers less than or equal to −1 all real numbers greater than or equal to 3 all real numbers greater than or equal to −1

Answer:

dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

Step-by-step explanation:

* Lets revise some rules for the derivative

- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

- The derivative of u/v = (vu'-uv')/v²

- The derivative of the constant is 0

* Lets solve the problem

∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]

- Let u = 4x³ - 7 and v = 3x^5 + 1

∵ u = 4x³ - 7

∴ u' = 4(3)x^(3-1) - 0 = 12x²

∵ v = 3x^5 + 1

∴ v' = 3(5)x^(5-1) + 0 = 15x^4

∵ The derivative of u/v = (vu' - uv')/v²

∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]

∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]

- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the

 same bracket in the 2nd fraction

∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

Answer:

-a (14 +a) =0

Step-by-step explanation:

-14a-a^2=0

Factor out  -a

-a (14 +a) =0

Using the zero product property

-a =0   14+a =0

a =0   a = -14

Replace x with the binomial a - 2.

f(a - 2) = [3(a - 2) + 5]/(a- 2)

f(a - 2) = [3a - 6 + 5]/(a - 2)

f(a - 2) = [3a - 1]/(a - 2)

f(a - 2) = (3a - 1)/(a - 2)

Done.

[tex]\text{Hey there!}[/tex]

[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]

[tex]\text{Percentages (\%) usually run out of 100}[/tex]

[tex]\text{First, put the numbers set to multiply from each other.}[/tex]

[tex]\text{7\%}\times\text{14.50}[/tex]

[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]

[tex]\dfrac{7\%}{100}[/tex]

[tex]\dfrac{7\%}{100}=0.07[/tex]

[tex]\text{Next, solve for your answer.}[/tex]

[tex]\text{0.07}\times\text{14.50 = ?}[/tex]

[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]

[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C

Step-by-step explanation:

To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)

g(7) = (2 × 7) - 5 = 14 - 5 = 9, then

f(9) = 3(9)² - 4 = 243 - 4 = 239 → C

Option C is correct.

Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]

We have to find  [tex]f(g(7))[/tex].

             [tex]g(7)=2*7-5=14-5=9[/tex]

So that,  [tex]f(g(7))=f(9)[/tex]

           [tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]

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Answer:

-3

Step-by-step explanation:

Answer:

The slope of the line is [tex]m=-3[/tex]

Step-by-step explanation:

For a linear equation of the form

[tex]y = mx + b[/tex]

the slope of the line is the constant m

in this case we have the equation

[tex]y + 1 = -3x[/tex]

Solving for y we have:

[tex]y = -3x -1[/tex]

Then [tex]m = -3[/tex]

The slope of the line is -3

See the attached picture:

Answer:

5

Step-by-step explanation:

When you given input of "x" into a floor function  y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"

For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.

So, if we put 5.7 into this function, the floor function would give "5" as the output.

Thus value of y would be 5

Answer:

5

Step-by-step explanation:

Answer: 45°

Step-by-step explanation:

Because AB and CD are parallel, angle x must be congruent with its corresponding angle.

Answer:

Step-by-step explanation:

The dominant term of this function is x^4.  The graph of x^4 starts in Quadrant II and continues in Quadrant I.

If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV.  This is the end behavior for f(x)=-x^4+5x^3-3.

Find  the cost of the chair and desk by multiplying the total amount pent by the 70%

Chair and desk = 900 x 0.70 = $60

Subtract that cost from the total spent:

900 - 630 = $270 was spent on the other three items.

Subtract the cost of the bookshelf:

270 - 50 = 220

The two tables cost 220.

For the price of one table divide that cost by 2:

220/2 = 110

One table cost $110.

The cost of each table is $110.

Given that

There are five items i.e. chair, bookshelf, 2 tables, and a desk.

The total amount incurred for these 5 items should be $900.

And, the chair + desk = 70% of total.

The cost of the bookshelf is $50.

Since 70% of total = chair + desk

That means

Chair + desk = 0.70 of $900 = $630

So the other items cost should be

= $900 - $630

= $270

And, the cost of bookshelf is $50

So, the two tables cost should be

= $270 - $50

= $220

So for one it should be

= $220 ÷ 2

= $110

Therefore we can conclude that the cost of each table is $110.

Learn more about the cost here: brainly.com/question/5282141

Answer:

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Step-by-step explanation:

If Marcel has $8.25 and is only playing $0.25 games, then the equation will be given by:  8.25 - 0.25X.

If Floyd has $9.75 and is only playing $0.75 games, then the equation will be given by:  9.75 - 0.75X.

If we want to find the number of games after which Marcel and Floyd will have the same amount of money remaining, we need to solve the system of equations:

Equation: 8.25 - 0.25X = 9.75 - 0.75X

Step 1: -1.50 - 0.25X = - 0.75X

Step 2: -1.50 = - 0.50X

Step 3: x=3

The mistake is that from Step 1 to Step 2, Jorge did not add 0.25 correctly to both sides.

Answer: Option B

From Step 1 to Step 2, Jorge did not add 0.25x correctly to both sides.

Step-by-step explanation:

To solve this problem, let's consider the initial equation that Jorge had.

[tex]8.25-0.25x=9.75-0.75x[/tex]

Subtract 9.75 on both sides of equality

[tex]8.25-9.75-0.25x=9.75-9.75-0.75x[/tex]

[tex]-1.50-0.25x=-0.75x[/tex]

Add 0.25x on both sides of equality

[tex]-1.50-0.25x+0.25x=-0.75x+0.25x[/tex]

[tex]-1.50=-0.50x[/tex]

[tex]x=3[/tex]

You can see then that Jorge's error was adding [tex]-0.75x + 0.25x[/tex]

When this sum is correctly done, the result is [tex]-0.50x[/tex]

The answer is the option B.

Answer:

y = 4.125x + 496.25

Step-by-step explanation:

Set the data up as points. Then deal with the points.

Givens

(30,620)

(70,785)

y2 = 785

y1 = 620

x2 = 70

x1 = 30

Formula

Slope = (y2 - y1) / (x2 - x1)

Solution

Slope = (785 - 620)/(70 - 30)

Slope = 165 / 40

Slope = 4.125

===================

Now you need the y intercept. Either one of the two given points will give you that.

y = 620

x = 30

m = 4.125

y = mx + b

620 = 4.125*30 + b

620 = 123.75 + b

620 - 123.75 + b

b = 496.25

the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

First, we calculate the slope (m):

m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125

Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):

620 = 4.125(30) + b

b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25

So the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

Answer:

y+3 = -7/5(x+2)

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (4--3)/(-7--2)

  = (4+3)/(-7+2)

  =7/-5

  = -7/5

The point slope form is y-y1 = m(x-x1)

y--3 = -7/5(x--2)

y+3 = -7/5(x+2)

We could use the second set of points

y-4 = -7/5(x--7)

y-4 =-7/5(x+7)

Answer:

m=4

Step-by-step explanation:

3-(-1)/-1-(-2)=3+1/-1+2=4/1

Answer:

4

Step-by-step explanation:

Slope formula:

     ↓

[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]

[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]

[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]

Therefore, the slope is 4.

4 is the correct answer.

I hope this helps you, and have a wonderful day!

Step-by-step explanation:

Use Pythagorean theorem:

c² = a² + b²

Here, c = 42 and a = 31.

42² = 31² + b²

b = √803

b ≈ 28.3

Answer:

The resulting equation is

x^2/4+16x^2/9=1

Step-by-step explanation:

The given equations are:

3y=12x   eq(1)

x^2/4+y^2/9=1    eq(2)

We need to isolate variable y in equation 1

Divide both sides of the equation with 3

3y/3 = 12x/3

y = 4x

Now, substitute the value of y=4x in second equation

x^2/4+y^2/9=1

x^2/4 + (4x)^2/9 = 1

The resulting equation is

x^2/4+16x^2/9=1

Answer:

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Step-by-step explanation:

Given system of equations,

[tex]3y=12x-----(1)[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]

As per statement,

Isolating the variable y in the first equation,

[tex]y=\frac{12}{3}x=4[/tex]

Now, substituting into the second equation,

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Which is the resulting equation,

Simplifying the equation,

[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]

[tex]\frac{9x^2+64x^2}{36}=1[/tex]

[tex]73x^2=36[/tex]

Answer:

The correct answer is R(2, 4)

Step-by-step explanation:

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad ~\hspace{10em}slope = m\implies 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-1=4[x-(-2)]\implies y-1=4(x+2) \\\\\\ y-1 = 4x+8\implies y=4x+9[/tex]

Answer:

5

Step-by-step explanation:

1. Find the Mean

(2+8+10+16)/4=9

2.For each number, subtract the Mean and square the result.

(2-9)^2=49

(8-9)^2=1

(10-9)^2=1

(16-9)^2=49

3. Find the Mean of those squared differences.

(49+1+1+49)/4=25

4.Take the square root of that and this is what you want.

square root of 25 = 5

If the value of the mean is 9. Then the mean absolute deviation will be 4.

It is the average distance between each data point and the mean.

The MAD is given as

[tex]\rm MAD = \dfrac{\Sigma _{i = 1}^n|x_i - \mu|}{n}[/tex]

The data set is given below.

2,8,10,16

Then the mean will be

μ = (2 + 8 + 10 + 16) / 4

μ = 36 / 4

μ = 9

Then the mean absolute deviation will be

MAD = (|2 - 9| + |8 - 9| + |10 - 9| + |16 - 9|) / 4

MAD = (7 + 1 + 1 + 7) / 4

MAD = 16 / 4

MAD = 4

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For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]

We replace:

[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]

Thus, the distance between the two points is 25 units.

Answer:

25

Answer:

The distance is 25 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)

Distance = √[(x2 - x1)² + (y2 - y1)²]

= √[(21 - -3)² + (11 - 4)²]

= √[(21 +3)² + (11 - 4)²]

= √[24² + 7²]

 = √(576 + 49)

 = √625

 =25

Therefore the distance is 25 units

Answer for A. (-8,-2)

answer for B. (4,-7)

Answer:

C

Step-by-step explanation:

Since the angles at the centre subtended by the congruent arcs WX and YZ

Then ∠YOZ = ∠WOX = 103° → C

The measure of the angle YOZ is b°.  Option c is correct.

In a circle arc WX and YZ are congruent. Than angle YOZ is to be determine.

Arc is defined as the circular curve or part of circle. Arc = angle * radius.

Here, arc WX = arc YZ
If arc is equal in a circle than angle sub tainted by this arc to center are also equal.
angle YOZ = angle WOX = 103°

Thus, the measure of the angle YOZ is 103°.

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Answer:

D

Step-by-step explanation:

The first and last sequence have a common difference in them. The first having d = 4 and the second having d = 7.

The second and third have a common ratio instead and are geometric sequences. The second has r = 2, and the third having r = (-3)

Answer:

12 days

Step-by-step explanation:

Sally has  pet snail that fell into a well.

Depth of the well = 16 feet

Snail climbs up 5 feet but each night it slides back down 4 feet.

So the snail climbs up per day = 5 feet - 4 feet = 1 feet.

Number of days snail took to reach at 11 feet = 11 × 1 = 11 feet

Remaining distance to cover by the snail = 16 - 11 = 5 feet

Number of days to cover remaining 5 feet to reach the top of the well = 1 day

Therefore, snail will take 12 days to reach the top of the well.

Final answer:

The snail climbs up 5 feet and slides back 4 feet each day in a 16-foot deep well. With a net gain of 1 foot per day, the snail will escape on the 16th day after reaching the top without sliding back.

Explanation:

Sally's pet snail finds itself in a classic mathematical problem often associated with algebra and arithmetic sequences. The snail is attempting to escape a 16-foot deep well by climbing up 5 feet during the day and sliding back 4 feet each night. To determine how many days it will take for the snail to get out, we need to calculate the net progress made by the snail each day and then examine how this applies on the final day of the snail's ascent.

Each day, the snail makes a net gain of 1 foot (5 feet up during the day minus 4 feet down at night). After 15 days, the snail would have climbed 15 feet during the day. On the 16th day, the snail climbs up 5 feet and reaches the top of the well, coming out without sliding back down since it already reached the goal during daylight. Therefore, it will take the snail a total of 16 days to escape the well.

Answer:

n² + 3

Step-by-step explanation:

It's a quadratic sequence, so it follows the form:

y = ax² + bx + c

We're given five points that satisfy the equation.  (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28).  Picking any three points, we can form a system of equations.

If we pick (1, 4), (2, 7), and (4, 19):

4 = a(1)² + b(1) + c

7 = a(2)² + b(2) + c

19 = a(4)² + b(4) + c

4 = a + b + c

7 = 4a + 2b + c

19 = 16a + 4b + c

Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.

y = x² + 3

So the nth term of the sequence is n² + 3.

Answer:

a(n) = a(n-1) + (2n - 1)

Step-by-step explanation:

Start by analyzing the pattern:

7 is 3 more than 4;

12 is 5 more than 7;

19 is 7 more than 12, and so on.  

Each step is an odd number and is 2 greater than the previous step.

a(2) = 7 = 4 + step = 4 + 3 = 7

a(3) = 12 = 7 + step = 7 + 5 = 12

a(4) =                      12 + 7  = 19

a(5) =                       19 + 9 = 28

and so on.  

Looking at a(2), we see that the step is 2+1, or 3;

Looking at a(3), we see that the step is 2(3) - 1, or 5;

Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.

Looking at a(n), we see that the step is 2n - 1.

Thus, a(n) = a(n-1) + (2n - 1)

Answer:

The length of the missing side of the triangle is represented by the equation:

  (6a + 2b - 5) - (2a - 3b) - (a - 3)

= 6a + 2b - 5 - 2a + 3b - a + 3

= 3a + 5b - 2

Answer:

1. 50 cm

2. 550 mm

3. 5000 mm

4. 5000 cm

5. 5000 m

Step-by-step explanation:

We can convert all the measures in same unit to arrange them one by one.

5000 cm:

As there are 10 millimeters in 1 cm,

5000 cm = 5000*10mm

=> 50000 mm

5000 meters:

As there are 100 cms in one meter

5000 m = 5000*100 cm

=> 500000 cm

Now to convert in millimeter

500000*10= 5000000 mm

50 cm:

50*10 = 500 mm

Then there is 550 mm and 5000 mm

So, the order from least to greatest is:

1. 500 mm which is equivalent of 50 cm

2. 550 mm

3. 5000 mm

4. 50000 mm which was equivalent of 5000 cm

5. 5000000 mm which was equivalent of 5000 m ..

Final answer:

To compare the given measurements, we converted each one to millimeters (mm) using a conversion table, then arranged them in ascending order: 50 cm (500 mm), 550 mm, 5,000 mm, 5,000 cm (50,000 mm), and 5,000 m (50,000,000 mm).

Explanation:

To determine which of the given measures is the smallest and which is the largest, we need to convert each measure to the same unit for comparison. Using the ratio conversion table, we will convert all measures to millimeters (mm).

Now we arrange the measures in order from least to greatest:

Answer:

[tex]x^{5}[/tex]

Step-by-step explanation:

We simply add the exponents together. This depicts the exponent product rule, which states that when multiplying together two values with the same base (x) but different exponents, we can solve the answer by adding together the exponents with the base staying the same.

Explanation / Proof:

[tex]2^{2} * 2^{3} = 4 * 8 = 32\\\\2^{2} * 2^{3} = 2^{5} = 2*2*2*2*2 = 32[/tex]

As you can see, adding together the exponents will give the same answer. Therefore, the answer is [tex]x^{5}[/tex].