What is the frequency of the function f(x)?
f (x) = 3 cos (TX) – 2
Express the answer in fraction form.

There are two: -4 and -5/2

Steps

0 = (2x - 5)(x + 4) | FOIL (distribution)

2x = 5 | zero product rule

x = 5/2 <<<

x = -4 <<< | zero product rule again.

Answer:

Step-by-step explanation:

The question is asking for a system of equations, which make explanations easy. :)

Define the variables. Setting [tex]x[/tex] to the number of clubhouse seats sold and [tex]y[/tex] to the number of grandstand seats sold will be sufficient. The "let statement[s]" will be:

The number of equations shall be no less than the number of variables for the solution to be unique. There are two variables. It will take at least two equations to find a unique solution.

Everyone at the race need a seat. The number clubhouse seats plus the number of grandstand seats shall be the same as the number people at the race. There were 36,000 people. Therefore the first equation shall be:

[tex]x + y = 36000[/tex].

Every clubhouse seat will add $12.00 to the receipt. [tex]x[/tex] clubhouse seats will add $[tex]12\;x[/tex] to the receipt. Similarly, [tex]y[/tex] grandstand seats will add $[tex]5\;y[/tex] to the receipt. The two values shall add up to $250,000.

Drop the dollar sign to get the second equation:

[tex]12\;x +5\;y =250000[/tex].

Hence the system:

[tex]\displaystyle \left\{\begin{aligned}& x + y = 36000 && \textcircled{\raisebox{-0.9pt}1}\\ & 12\;x + 5\;y = 250000 && \textcircled{\raisebox{-0.9pt}2}\end{aligned} \phantom{\small credit for the raisebox hack: tex[dot]stackexchange[dot]com/questions/7032/good-way-to-make-textcircled-numbers}[/tex].

Solve this system.

The first non-zero coefficient in equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is already one. That's the coefficient for [tex]x[/tex]. Use multiples of equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get rid of [tex]x[/tex] in other equations (equation [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] in this case.)

[tex]-12[/tex] times equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] is

[tex]-12 \;x - 12\;y = -432000[/tex].

Add [tex]-12\times \textcircled{\raisebox{-0.9pt}1}[/tex] to [tex]\textcircled{\raisebox{-0.9pt}2}[/tex] to get:

[tex]0\;x + -7\;y = -182000[/tex].

Divide both sides by -7 to get:

[tex]y = 26000[/tex].

Add -1 times this equation to equation [tex]\textcircled{\raisebox{-0.9pt}1}[/tex] to get:

[tex]x = 10000[/tex].

That is:

[tex]\displaystyle \left\{\begin{aligned}&x = 10000\\&y = 26000\end{aligned}[/tex].

In other words,

Answer:

The third quartile is:

[tex]Q_3=29[/tex]

Step-by-step explanation:

First organize the data from lowest to highest

4, 5, 10, 12, 14, 16, 18, 20, 21, 21, 22, 22, 24, 26, 29, 29, 33, 34, 43, 44

Notice that we have a quantity of n = 20 data

Use the following formula to calculate the third quartile [tex]Q_3[/tex]

For a set of n data organized in the form:

[tex]x_1, x_2, x_3, ..., x_n[/tex]

The third quartile is  [tex]Q_3[/tex]:

[tex]Q_3=x_{\frac{3}{4}(n+1)}[/tex]

With n=20

[tex]Q_3=x_{\frac{3}{4}(20+1)}[/tex]

[tex]Q_3=x_{15.75}[/tex]

The third quartile is between [tex]x_{15}=29[/tex] and [tex]x_{16}=29[/tex]

Then

[tex]Q_3 =x_{15} + 0.75*(x_{16}- x_{15})[/tex]

[tex]Q_3 =29 + 0.75*(29- 29)\\\\Q_3 =29[/tex]

Answer:

29

Step-by-step explanation:

Answer:

4860 in ^3

Step-by-step explanation:

First we find the volume of the tank

V = l*w*h

V = 30*12*15

V = 5400 in ^3

It is 90% full so we multiply by 90 %

5400 * 90%

5400 * .90

4860 in ^3

Answer:

B

Step-by-step explanation:

Ratio of sides = a : b , then

Ratio of volumes = a³ : b³

Here the ratio of volumes = 27 : 729, hence

Ratio of sides = [tex]\sqrt[3]{27}[/tex] : [tex]\sqrt[3]{729}[/tex] = 3 : 9

Ratio of sides = 3 : 9 = 1 : 3 ← in simplest form

Hence sides of larger cube are 3 times sides of smaller cube → B

Answer:

The approximate value of angle theta is [tex]57.8\°[/tex]

Step-by-step explanation:

we have that

[tex]cos(\theta)=8/15[/tex]

so

using a calculator

[tex]\theta=arccos(8/15)=57.8\°[/tex]

Answer:

for plato or edmentum its option A 50 degrees

Step-by-step explanation:

Answer:

[tex]15x+60\leq 100[/tex]

Step-by-step explanation:

Let

x -----> the number of hours that the painter works

we know that

The inequality that represented this situation is equal to

[tex]15x+60\leq 100[/tex]

solve for x

Subtract 60 both sides

[tex]15x\leq 100-60[/tex]

[tex]15x\leq 40[/tex]

Divide by 15 both sides

[tex]x\leq 40/15[/tex]

[tex]x\leq 2.67\ hours[/tex]

The maximum number of hours is 2

[tex](f+g)(x)=-x^2+6x-1+3x^2-4x-1=2x^2+2x-2[/tex]

Answer: [tex](f+g)(x)=2x^2+2x-2[/tex]

Step-by-step explanation:

Given the function f(x), which is:

[tex]f(x)=-x^2 +6x-1[/tex]

And the function g(x), which is:

[tex]g(x) =3x^2-4x-1[/tex]

You can observe that [tex](f+g)(x)[/tex] indicates that you need to add the functions, then you know that:

[tex](f+g) (x)=(-x^2+6 x-1)+(3x^2-4x-1)[/tex]

Finally, to simplify it you must addthe like terms. Therefore, you get that  [tex](f+g)(x)[/tex] is:

[tex](f+g)(x)=-x^2+6 x-1+3x^2-4x-1[/tex]

[tex](f+g)(x)=2x^2+2x-2[/tex]

Answer:

0.75 mile(s) per minute

n-6=0.75(t-8)

hope this helps!!

Step-by-step explanation:

Answer:

0.75 miles per minute

Equation: n - 6 = 0.75(t - 8)

Step-by-step explanation:

took the test and got it right

Step-by-step answer:

Given:

5% annual interest (APR)

compounded daily

Principal = 500

Solution:

Since it is compounded daily, we first calculate the

daily rate =  5% / 365 = 0.05/365

After one year,

future value

= 500 ( 1 + 0.05/365)^365

= 525.634 (to the tenth of a cent)

note: sometimes a year is considered to be rounded to 360 days, or 366 days for a leap year, but there is practically no difference in the results for this problem.

Final answer:

To calculate the future value of a $500 deposit with a 5% annual interest rate compounded daily for one year, we use the compound interest formula. The resulting amount is approximately $525.64.

Explanation:

To calculate the value of a $500 deposit in a credit union that pays 5% annual interest compounded daily, we will use the formula for compound interest:

A = P(1 + (r/n))^(nt)

Where:

A = the amount of money accumulated after n years, including interest.

P = the principal amount (the initial amount of money).

r = the annual interest rate (decimal).

n = the number of times that interest is compounded per year.

t = the time the money is invested or borrowed for, in years.

Using the given information:

P = $500

r = 5% or 0.05 (as a decimal)

n = 365 (since the interest is compounded daily)

t = 1 year

Substituting the values into the formula:

A = 500(1 + (0.05/365))^(365*1)

After calculating, we get:

A ≈ $525.64

Therefore, the value of the $500 deposit at the end of one year with daily compounding at a 5% annual interest rate is approximately $525.64.

Answer:

25% Increase

Step-by-step explanation:

[(350 - 280) / 280] × 100% = 0.25 × 100% = 25%

Let x represent Ravi's current age.

Now, Ravi's age fifteen years from now is effectively Ravi's age plus fifteen, therefor we can write this as x + 15.

Four times Ravi's present age is four multiplied by his present age, therefor we can write this as 4x.

If Ravi's age fifteen years from now is equal to four times his present age, then:

x + 15 = 4x

Now all we have to do is solve for x to find Ravi's present age:

x + 15 = 4x

15 = 3x (Subtract x from both sides)

5 = x (Divide both sides by 3)

Therefor, Ravi's present age is 5 years.

Answer:

Step-by-step explanation:

This is impossible to figure out because 0 = 0x, as defined by the Zero Property of Multiplication. I apologize.

Answer:

The surface area increases by 4 times

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared

Let

z -----> the scale factor

x ----> the surface area of the new rectangular prism

y ---> the surface area of the original rectangular prism

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=2[/tex] ----> because is doubled

[tex]y=254\ in^{2}[/tex]

substitute and solve for x

[tex]2^{2}=\frac{x}{254}[/tex]

[tex]x=(4)254=1,016\ in^{2}[/tex] ----> surface area increases by 4 times.

Answer:

The surface area increases by four times.

Step-by-step explanation:

The word "climbing" has 8 letters, so there are [tex]8![/tex] permutations of all the letters.

Nevertheless, the letters are not unique: there are 2 I's. This means that, if we start from a given word and we exchange the positions of the two I's, we'd still get the same word. So, we have to divide the number of possible permutations by [tex]2![/tex], because for any given permutation there are two identical words, given by the interchange of the I's.

So, the number of possible words is

[tex]\dfrac{8!}{2!} = \dfrac{8\times7\times6\times5\times4\times3\times2}{2}=8\times7\times6\times5\times4\times3=40320[/tex]

Answer:

C

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

here m = [tex]\frac{1}{2}[/tex] and (a, b) = (5, 1), so

y - 1 = [tex]\frac{1}{2}[/tex](x - 5)

The equation that represents a line that passes through (5, 1) and has a slope of 1/2 is; C: y - 1 = ¹/₂(x - 5)

The formula for equation of a line in point- slope form is expressed as;

y - b = m(x - a)

where;

m is the slope of line

(a, b) is a coordinate point on the line

In this question, we are given;

m = 1/2  and (a, b) = (5, 1)

Thus equation of the line is;

y - 1 = ¹/₂(x - 5)

Read more about Equation of Line at; https://brainly.com/question/13763238

Answer:

It's minimum value

and the value is :(1 , -2)

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 3x² - 6x + 1

To express in vertex form

f(x) = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Use the method of completing the square

The coefficient of the x² must be 1, so factor out 3

f(x) = 3(x² - 2x) + 1

add/subtract ( half the coefficient of the x- term )² to x² - 2x

f(x) = 3(x² + 2(- 1)x + 1 - 1) + 1

     = 3(x - 1)² - 3 + 1

     = 3(x - 1)² - 2 ← in vertex form

with vertex = (1, - 2)

To determine if vertex is a max/ min

• If a > 0 then minimum

• If a < 0 then maximum

here a = 3 > 0 ⇒ minimum at (1, - 2)

The minimum value is the y- coordinate of the vertex, that is

minimum value = - 2

Answer:

A' = (- 5, - 1)

Step-by-step explanation:

The coordinates of point A = (- 6, 2)

Under the translation (x + 1, y - 3)

Add 1 to the x- coordinate of A and subtract 3 from the y- coordinate of A

A' = (- 6 + 1, 2 - 3) → A' = (- 5, - 1)

Based on the fact that there are  4 points which are given below, we have to move the trapezoid to the points of A will be (x+1, y-3). The coordinates of A be A(-6,2) =>A'(-5, -1)

A trapezoid is regarded as a  quadrilateral that has only one pair of opposite sides that are said to be parallel.

The points on the graph are:

A(-6,2) =>A'(-5, -1)

B(-5,4) =>B'( -4,1)

C(-2,4)=> C'(-1,1)

D( 1,2) => D'(2,-1)

It is made up of a right angles (called right trapezoid), and it can also contain a congruent sides (isosceles). Note that in the above, the only way the trapezoid  can fit into the translation movement (Point A)is if it is moved to the points of (x+1, y-3) on the graph.

The coordinates of A be A(-6,2) =>A'(-5, -1).

Find out more information about trapezoid here

brainly.com/question/1410008

#SPJ2

Answer:

-0.41 radians

Step-by-step explanation

(Credit goes to calculista)

let

A---> the angle

if sin A=-0.4

then 

A=sin-1(-0.4)

using a calculator

A=-23.578°----> the angle A belong to the IV quadrant

convert to radians

if pi radians--]----> 180°

x--------> -23.578°

x=-23.578*pi/180----> x=-0.41 radians

Read more on Brainly.com - https://brainly.com/question/9675799#readmore

Answer:

C. –0.41

Step-by-step explanation:

Answer:

Option B: 49 square units.

Step-by-step explanation:

The irregular polygon consists of a rhombus a square.

Area of rhombus = 0.5*(product of diagonals).

Area of square = length * length = l^2.

The diagonals of the rhombus measure 8 units and 6 units respectively. The diagram shows the length of half of the diagonals, so doubling both the lengths gives us the required lengths. The side of the square measures 5 units. Substituting all the information in the formula:

Total Area = Area of rhombus + Area of square.

Total Area = 0.5*8*6 + 5^2.

Total Area = 24 + 25

Total Area = 49 square units.

Therefore, Option B is the correct answer!!!

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}10x+2y=64&\text{multiply both sides by 2}\\3x-4y=-36\end{array}\right\\\underline{+\left\{\begin{array}{ccc}20x+4y=128\\3x-4y=-36\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=92\qquad\text{divide both sides by 2}\\.\qquad x=4\\\\\text{put the value of x to the first equation:}\\\\10(4)+2y=64\\40+2y=64\qquad\text{subtract 40 from both sides}\\2y=24\qquad\text{divide both sides by 2}\\y=12[/tex]

Answer:

Step-by-step explanation:

The pentagon RSTYZ is a regular polygon. Therefore all angles are congruent.

If m∠RST = 108°, then m∠STY = 108°.

We have the equation:

m∠UTY + m∠STY + m∠STU = 360°.

Substitute m∠STY = 108° and m∠UTY = 115°.

115° + 108° + m∠STU = 360°

223° + m∠STU = 360°          subtract 223° from both sides

m∠STU = 137°

Answer:

I(x) = 12x² + 8x + 5

Step-by-step explanation:

* Lets talk about the solution

- P(x) is a quadratic function represented graphically by a parabola

- The general form of the quadratic function is f(x) = ax² + bx + c,

  where a is the coefficient of x² and b is the coefficient of x and c is

  the y-intercept

- To find I(x) from P(x) change each x in P by 2x

∵ P(x) is dilated to I(x) by change x by 2x

∵ I(x) = P(2x)

∵ P(x) = 3x² + 4x + 5

∴ I(x) = 3(2x)² + 4(2x) + 5 ⇒ simplify

∵ (2x)² = (2)² × (x)² = 4 × x² = 4x²

∵ 4(2x) = 8x

∴ I(x) = 3(4x²) + 8x + 5

∵ 3(4x²) = 12x²

∴ I(x) = 12x² + 8x + 5

Answer:

x = 2.

Step-by-step explanation:

8(4-x) = 7x + 2​

32 - 8x = 7x + 2

32 - 2 =  7x + 8x

15x = 30

x =2.

Answer:

The answer should be A.

Answer: The Answer is A.) AG=6

Step-by-step explanation:

ANSWER

(C) y

EXPLANATION

We have two equations:

The first one is

[tex]x + y = z...(1)[/tex]

The second equation is

[tex]y - z = x...(2)[/tex]

Let us make z the subject of this second equation:

[tex] \implies \: -x +y = z...(3)[/tex]

We now add equation (1) and (3) to get:

[tex](-x + x) + (y + y) = z + z[/tex]

We simplify to get:

[tex]0+2y= 2z[/tex]

[tex]2y= 2z[/tex]

Divide throu by 2.

[tex] \frac{2y}{2} = \frac{2z}{2} [/tex]

[tex]y= z[/tex]

[tex] \therefore \: z = y[/tex]

The correct answer is C

Answer:

[tex]x=19[/tex]

Step-by-step explanation:

We have the following equation

[tex]3(x+6)=5(x-4)[/tex]

Notice that in this equation the variable that we want to find is x.

Then the equation for the variable x must be solved

After applying the distributive property and simplifying the equation Maria obtained the following result

[tex]19=x[/tex]

This is the same as:

[tex]x=19[/tex]

That means that the value of x for which equality is met is [tex]x = 19[/tex]. Therefore the solution of the equation is [tex]x = 19[/tex]

Answer:

When Harold wrote his equation, the point he used was (7,0).

Step-by-step explanation:

we know that

The equation of a line into point slope form is equal to

[tex]y-y1=m(x-x1)[/tex]

where

(x1,y1) is the point

m is the slope

In this problem we have

[tex]y=3(x-7)[/tex]

therefore

the point is (x1,y1)=(7,0)

the slope is m=3

Answer:

The correct options are B, C and D.

Step-by-step explanation:

It is given that the figure is a Japanese art of paper folding. It means the figure have many lines of symmetry (i.e., AK, IO, CM and NF).

From the figure it is clear that HV is larger than GW, so segment HV and GW are not pairs of congruent segments.

Therefore option A is incorrect.

[tex]\overline{IJ}\cong \overline{LM}[/tex]        (AK is line of symmetry)

[tex]\overline{AB}\cong \overline{AP}[/tex]        (AK is line of symmetry)

[tex]\overline{BC}\cong \overline{PO}[/tex]        (AK is line of symmetry)

Therefore the correct options are B, C and D.

From the figure it is clear that PO is smaller than ON, so segment HV and GW are not pairs of congruent segments.

Therefore option E is incorrect.