Can someone please help me with calculus , i am having so much trouble. Thank you! 12points

Answer:

[tex]g(x)= -3x^{2} +4x +5[/tex]

Step-by-step explanation:

Five more = Addition of 5

Opposite = (-)

3 times = Multiplication by 3

Square = To the power (exponent) of two

4 times the number = Multiplication by 4

The number = unknown number = x

This value is approximate

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

Work Shown:

[tex]\log_{10}(2) \approx 0.301\\\\\log_{10}(3) \approx 0.477\\\\\log_{10}(6) = \log_{10}(2*3)\\\\\log_{10}(6) = \log_{10}(2)+\log_{10}(3) \ \text{ see note below}\\\\\log_{10}(6) \approx 0.301 + 0.477\\\\\log_{10}(6) \approx 0.778\\\\[/tex]

Note: I used the rule that log(A*B) = log(A)+log(B) which works for any valid log base.

Step-by-step explanation:

Since the question has already been answered, I'd like to add something new, and explain why: [tex]log_b(a*c)=log_ba+log_bc[/tex]

So let's just say that:

[tex]x=log_ba[/tex] and that [tex]y=log_bc[/tex]

This means that: [tex]b^x=a[/tex] and that [tex]b^y=c[/tex].

So if we were to multiply the two, a and c. You get

[tex]a*c=b^{x+y}[/tex]

This is due to the exponent identity that: [tex]b^a*b^c=b^{a+c}[/tex]

So if you rewrite this in logarithmic form you get:

[tex]log_b{ac}=x+y[/tex]

and remember what x and y are equal to? that's right, it's the logarithms

so now you substitute the logarithms back in and get

[tex]log_b{ac} = log_ba+log_bc[/tex]

Answer:

our volume is 4500cm³

Step-by-step explanation:

note: the following will be assuming that this fish tank is rectangular, as most fish tanks are

To find the volume of a rectangular structure, we multiply :

length × width × height

here, we know our

length to be 12 cm

width to be 15 cm

and height/depth to be 25 cm

so, we can follow our volume formula (length × width × height) using these values

length × width × height = volume

12 × 15 × 25 = 4500

so, our volume is 4500cm³

(also called 4500cubic centimeters)

(we write volume as cubed--units³)

hope this helps! have a lovely day :)

The mean of the data about students size of Mr. Sirac classes is 24.

Given students size of each of Mr. Sirac'sclasses 21,20,22,23,24,25,26,28,27 and we have to find the mean of the data.

We know that mean is the basically sum of numbers divided by the number. It is also known as average.

Mean =∑X/n where n is number of values and ∑X is sum of all the values.

∑X=21+20+22+23+24+25+26+28+27

=216

n=9

Mean is calculated by dividing sum by n.

Mean =216/9

=24

Hence the mean of the data about students size of each of Mr. Sirac classes is 24.

Learn more about mean at https://brainly.com/question/1136789

#SPJ4

The product is equal to:

[tex]\frac{18}{25}(cos(165) + i*sin(165))[/tex]

Remember that we can write a complex number in polar form as:

[tex]R*e^{i*a} = R*(cos(a) + i*sin(a))[/tex]

Then the given product:

[tex]\frac{6}{5}*(cos(120) + i*sin(120))*\frac{3}{5}*(cos(45) + i*sin(45))[/tex]

can be rewritten to:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})[/tex]

Now is easier to solve the product:

[tex](\frac{6}{5}*e^{i*120})*(\frac{3}{5}*e^{i*45})\\\\= \frac{6}{5} *\frac{3}{5} *e^{i*(120 + 45)}\\\\= \frac{18}{25}*e^{i*165}\\\\= \frac{18}{25}(cos(165) + i*sin(165))[/tex]

If you want to learn more about complex numbers:

https://brainly.com/question/10662770

#SPJ1

Answer:

8

Step-by-step explanation:

12+4=16

16 divided by 2= 8

The number of tickets for adults is 210 and the number of tickets for children is 83.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of tickets for adults and y be the number of tickets for children.

From the problem:

x + y = 293

25.50x + 8y = 6019

After solving with the substitution method:

[tex]\rm 25.5\left(293-y\right)+8y=6019[/tex]

y = 83

x = 210

Thus, the number of tickets for adults is 210 and the number of tickets for children is 83.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ1

Answer:

4² + b² = 12²

16 + b² = 144

b² = 144 - 16

b² = 128

b = √128

b = 11.3 feet

Step-by-step explanation:

Answer:

0.36ml

Step-by-step explanation:

Note: micrograms = [tex]10^{-6} g[/tex]

Given the concentration,

[tex]500*10^{-6} g = 1ml\\1*10^{-6}g =\frac{1}{500} ml\\180*10^{-6} g=(\frac{1}{500} *180)ml\\180micrograms = 0.36ml[/tex]

The graph which has the same end behaviour as the function given; f(x) = (10x³+x² +3)/(2x²+1) is; a linear graph whose slope is 5.

The function given can further be simplified by means of polynomial division in which case;

although not a perfect division; the quotient of the division is; (5x-0.5) and evidently, the function which would have the same end behaviour as the given function is a linear function whose slope is 5.

Read more on graph of functions;

https://brainly.com/question/4025726

#SPJ1

A) A parallelogram has 4 sides.

B) The opposite angles of parallelogram are congruent.

C) [tex]\angle A \cong \angle C, \angle B \cong \angle D\\\\\implies m\angle C=115^{\circ}, m\angle D=65^{\circ}[/tex]

Based on the conditional statement given, the truth value can be found to be T T → T.

The truth value can be found by using the Boolean Table which is shown as:

p        q        p → q

T         T        T

T         F        F

F         T        T

F         F        T

From the table, we can then see that if both p and q are true, then p → q is true as well.

We will then have a truth value of T T → T.

Find out more on truth value for conditional statements at https://brainly.com/question/2770634.

#SPJ1

The total number of possible fivey sequences are; 6

We are told we are dealing with a fivey sequence which means that all the terms of the sequence must be positive integers and they must add up to 5.

Now, the possible numbers that can be used are;

1, 2 and 3.

If we start with 3, number of possible sequences is; 1

If we start with1, number of possible sequences is; 3 ways

If we start with 2, number of possible sequences is; 2 ways

Thus;

Total number of fivey sequences is 1 + 2 + 3 = 6 possible sequences

Read more about Sequence at; https://brainly.com/question/13612968

#SPJ1

Answer:The answer is 27.04

Step-by-step explanation:

The solution is in the attached

By using the table, we see that the correct options are:

a) f(2) = 7

b) f(x) = 3 when x = 8.

c) f⁻¹(7) = 2

d) f⁻¹(x) = 8 when x = 3.

Here we have a table of x and f(x).

First, we want to find f(2). To get that, we need to go to the row where we have x = 2.

In that same row we can see that f(x) = 7.

Then f(2) = 7.

Then it says:

"if f(x) = 3, then x = ?"

This time we do the opposite. We find the row where f(x) = 3, and then we see the value of x in that row.

In the second row (counting from the bottom) we can see that when x = 8, f(x) = 3.

Then:

"if f(x) = 3, x = 8"

Then we want to get the inverse of f(x) evaluated in 7.

Here we use the rule:

[tex]f(x) = y\\f^{-1}(y) = x[/tex]

Then

[tex]f(2) = 7\\f^{-1}(7) = 2[/tex]

The answer here is 2.

Finally:

"if the inverse evaluated in x si 8, then what is the value of x"

Similar to before, we know that when we evaluate f(x) in 8, the outcome is 3.

Then when we evaluate the inverse in 3, the outcome is 8.

So here we must have x = 3.

If you want to learn more about inverse functions:

https://brainly.com/question/14391067

#SPJ1

1) Between the years 2003 and 2009, 768 students joined the school.

2) It took 6 years for the population to grow from 1219 students to 1987 students.

3) The average population growth per year is 128 students per year.

P = 128 students per year

4) The population of students in the year 2000 was a total of 835 students.

5) 1219 + (p3) = 1987

6) 1987 + (p3) = 2371

P3 = 384

The slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

Given that:

3x -2y ≥ 12

First we write the inequality in slope intercept form y = mx + b.

Solve for y

3x -2y ≥ 12

-2y ≥ 12 - 3x

Now, divide each term by -2

y ≤ -6 + 3x/2

We re-arrange

y ≤ (3/2)x - 6

Using the slope intercept form y = mx + b. we can see that;

m = 3/2

b = -6

Hence, the slope m = 3/2 and the y-intercept = ( 0, -6 ).

The graph is a solid line and shaded area below the boundary line since y is less than (3/2)x - 6.

Learn more about inequality here: https://brainly.com/question/13790048

#SPJ1

Answer:

4

Step-by-step explanation:

The common difference is found by subtracting the 2nd term from the 1st term. In this example we can say 11 is the 2nd term and 7 is the 1st term. 11 - 7 = 4.

Answer:

C

Step-by-step explanation:

it just is

Answer:

  B.  360 meters

Step-by-step explanation:

The triangles shown are similar, so their corresponding parts are proportional.

There are a couple of useful proportions here. We can equate the ratio of horizontal segments to the ratio of diagonal segments:

  (600 m)/(250 m) = ??/(150 m)

Or, we can equate the ratios of the diagonal segment to the corresponding horizontal segment:

  ??/(600 m) = (150 m)/(250 m)

Either way, when we multiply the equation by the denominator of ??, we get the result ...

  ?? = (600)(150/250) m = 360 m

The distance from F to G is 360 meters.

The equation of the line through the points is y = 3/5 + 1/5.

First, we find the Slope using the formula: m = y2 - y1/x2 - x1

You may choose any two points but I will use these two for no reason at all.)

Points: (3,2) and (8,5)

m = y2 - y1/x2 - x1

m = 5 - 2/8 - 3

m = 3/5

Now that we have the slope, we can now find the Slope-Intercept Form by using the Slope Form Formula. (need at least one point and slope.)

Formula: y - y1 = m(x - x1)

Point: (3,2)

y - y1 = m(x - x1)

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

y - 2 = 3/5x - 9/5

y - 2 = 3/5x - 9/5

y = 3/5x - 9/5 + 10/5 (2 can be is any fraction that consists of the numerator multiplied twice by the denominator, such as 2/1, 4/2, 8/4, etc.)

y = 3/5 + 1/5

To learn more about the equation of the line visit:

https://brainly.com/question/18831322

#SPJ1

Answer:

Step-by-step explanation:

This problem is similar to many others in which the sum of two quantities and their difference are given. The solution can be found easily when the equations for the relations are written in standard form.

Let s and h represent numbers of sodas and hot dogs sold, respectively. The given relations are ...

Adding the two equations eliminates one variable.

  (s +h) +(s -h) = (235) +(59)

  2s = 294 . . . . simplify

  s = 147 . . . . . .divide by 2

  h = 147 -59 = 88 . . . . h is 59 less

147 sodas and 88 hot dogs were sold.

__

Additional comment

The solution to a "sum and difference" problem is always the same. One of the numbers is half the sum of those given, and the other is half their difference. ((235-59)/2 = 88)

Answer:

Proof:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

Step-by-step explanation:

Analyze and ensure the answer is correct.

Answer:

Step-by-step:

By the inscribed angle theorem, we know that angle BAC is equal to angle DEC. By the second corollary to the inscribed angle theorem, we know that line segment AE is perpendicular to line segment AC. Therefore, line segment AE is tangent to circle C.

The equation solved for w is w = 6g - 40

The complete question is in the attached image

The equation is given as:

g = 1/6(w + 40)

Multiply both sides by 6

6g = w + 40

Subtract 40 from both sides

w = 6g - 40

Hence, the equation solved for w is w = 6g - 40

Read more about equations at:

https://brainly.com/question/12895249

#SPJ1

Answer:

Step-by-step explanation:

x=40

Answer:

here is

Step-by-step explanation:

5x-20=180

5x=180+20

=200

X=200/5

40

The range of the given relation is:   range = { 3, 9, 10}

Range is the out come of the event is know as y.

Here, the given relation:

               R = {(0,3), (8,9), (16,10)

Now, range = { 3, 9, 10}

Thus, the range of the given relation is: range = { 3, 9, 10}

Learn more about Range from:

https://brainly.com/question/15697193

#SPJ1

Answer:

35

Step-by-step explanation:

28 Orange Marbles divided by 4 Orange Marbles =

7

5 Blue Marbles for every 7 Orange Marbles =

35