Evaluate cos^2 (n/12)

Answer:

Factoring

Step-by-step explanation:

We have the function [tex]x ^ 2 + 5x-6 = 0[/tex]

To factor this expression we must look for two numbers a and b that when adding them give as a result 5 and multiplying them give as a result -6

Then the factorization will have the form

[tex](x + a)(x + b)[/tex]

You can verify that:

[tex]a = 6\\b = -1\\6(- 1) = -6\\6 -1 = 5[/tex]

So:

[tex]x ^ 2 + 5x-6 = (x + 6)(x-1) = 0[/tex]

So:

The solutions are:

[tex]x = -6\\x = 1[/tex]

this coming off the top of my head but it's either C or A

Answer:

5m^5-m^3-3

Step-by-step explanation:

What you do is you have to distribute the negative sign into the equation.

-m^5-2m^3+4m-6. Next, you will either add or subtract from the other equation.

6m^5-m^5=5m^5.

m^3-2m^3=-m^3.

-4m+4m=0m or you don't put anything.

3-6=-3. Then you put it all together to get.

5m^5-m^3-3 as your answer.

Answer:

m∠CAO=8º

m∠SAC=82º

Step-by-step explanation:

We know that m∠OAS is 90º because it is a radius to a tangent. This will be useful later.

OA=OB because they are both radii. If we draw a line from A to B, this makes an isosceles triangle ABO with a vertex angle of 32 because of the central angle theorem. This means that m∠OAB and m∠OBA are both 74º.

Isosceles triangle CAB is also formed with the construction of AB. Using the inscribed angle theorem, we can find ACB, which is 16º. Solve for the other angles and you get 82º. To find m∠CAO, subtract m∠OAB from m∠CAB, and this returns 8.

To find m∠SAC, subtract m∠CAO from m∠OAS, which is 90º-8º, and you get 82º.

Answer:

1

Step-by-step explanation:

common denominator is 12

6 11/12 - (2 3/12 + 3 8/12)

6 11/12 - 5 11/12

1

Answer:

a. x = 13

b. x = 7

c. x = 24

d. x = Undefined

Step-by-step explanation:

Since all the bases are the same the power it is raised by is equivalent to the sum's power.

In mathematical terms

.

.

x^a + x^b = x^a+b

So all we have to do is add up the exponents and make them equivalent to each other.

For the last question, it is impossible since the powers added cannot ever be equal to each other.

9+x can never equal 4+x so it is undefined.

Answer:

0.14

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Consider the trinomial [tex]3x^2+10x-8.[/tex]

We can rewrite it as

[tex]3x^2+10x-8=3x^2+12x-2x-8.[/tex]

Now group first two terms and last two terms:

[tex](3x^2+12x)+(-2x-8).[/tex]

The common factor in first two terms is [tex]3x[/tex] and the common factor in last two terms is [tex]-2.[/tex] Use the distributive property for both groups of terms:

[tex]3x^2+12x=3x(x+4),\\ \\(-2x-8)=-2(x+4),[/tex]

so

[tex](3x^2+12x)+(-2x-8)=3x(x+4)-2(x+4).[/tex]

Now you can see that [tex](x+4)[/tex] is a common factor, thus

[tex]3x(x+4)-2(x+4)=(x+4)(3x-2)=(3x-2)(x+4).[/tex]

Since the trinomial can be represented as a product of binomials, this trinomial is not prime.

Answer:

1. 105°

2. 85°

3. 80°

4. 148°

5. 116°

6. 82°

7. 135°

8. x = 7

9. x = 2

10. x = 1

11. x = 10

Step-by-step explanation:

1. Arc WZ = Arc XY

Arc WZ = 105° Therefore Arc XY = 105°

2. Arc SR = Arc TU

Arc SR = 85° Therefore Arc TU = 85°

3. Arc PQ = Arc QR

Arc PQR = 40° + 40°

Arc PQR = 80°

4. Arc RT = 64°

x = (360° - 64°)/2

x = 296°/2

x = 148°

5. x = 116°

If the chords are congruent to each other, then the arcs are also congruent to each other.

6. x = 82°

If the chords are congruent to each other, then the arcs are also congruent to each other.

7. Arc BC = 90°

x = (360° - 90°)/2

x = 270°/2

x = 135°

8. 2x + 4 = 18

2x = 18 - 4

[tex]\dfrac{2x}{2}=\dfrac{14}{2}[/tex]

x = 7

9. 2x + 1 = 5x - 5

2x - 5x = -5 - 1

[tex]\dfrac{-3x}{-3} = \dfrac{-6}{-6}[/tex]

x = 2

10. 3x + 16 = 12x + 7

3x - 12x = 7 - 16

[tex]\dfrac{-9x}{-9}=\dfrac{-9}{-9}[/tex]

x = 1

11.  3x - 11 = x + 9

3x - x = 9 + 11

[tex]\dfrac{2x}{2}=\dfrac{20}{2}[/tex]

x = 10

The answer is:

There are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.

We can solve this problem creating a system of equations. Let's make the two equations that will help us to solve the problem.

From the statement we know that a solution of 70 liters of a 40% is needed, and there are two differents solutions available, of 30% and 60% and we need to use them to make 70 liters of a  40% solution, so:

So:

[tex]30(Percent)SolutionVolume=X\\60(Percent)SolutionVolume=Y[/tex]

If both solutions will make a 70 liters solution, so the first equation will be:

[tex]x+y=70L[/tex]

Let's work with real numbers converting the percent values into real numbers by dividing it into 100, so:

[tex]30(Percent)=\frac{30}{100}=0.3\\\\40(Percent)=\frac{40}{100}=0.4\\\\60(Percent)=\frac{60}{100}=0.6[/tex]

Then, we know that both solutions will make 70 liters of a 40% solution, so the second equation will be:

[tex]0.30x+0.60y=0.4*70[/tex]

Therefore, from the first equation we have:

[tex]x=70-y[/tex]

Then, substituting x into the second equation to find y, we have:

[tex]0.30(70-y)+0.60y=28\\21-0.30y+0.60y=28\\0.3y=28-21\\y=\frac{7}{0.3}=23.33[/tex]

Hence, substituting y into the first equation to find x, we have:

[tex]x=70-y=70-23.33=46.67[/tex]

So, there are needed 46.67 liters of the 30% solution and 23.33 liters of the 60% solution in order to make 70 liters of a 40% solution.

Have a nice day!

Final answer:

To prepare 70 liters of a 40% alcohol solution, a scientist should mix equal amounts of the 30% and 60% alcohol solutions that are available. In this case, the scientist would need to mix 35 liters of the 30% solution with 35 liters of the 60% solution.

Explanation:

To solve the problem, we need to set up a system of equations based on the volumes and concentrations of the alcohol solutions. Let's define x as the volume in liters of the 30% alcohol solution and y as the volume in liters of the 60% alcohol solution.

First, we know that the total volume of the two solutions must add up to 70 liters:

x + y = 70

Second, we also know that the total amount of pure alcohol in the final 40% solution must be 40% of 70 liters. We can express the amount of pure alcohol in the 30% solution as 0.30x and in the 60% solution as 0.60y. The equation representing the alcohol concentration is:

0.30x + 0.60y = 0.40 × 70

Next, we solve these equations simultaneously to find the values of x and y.

Therefore, the scientist needs 35 liters of the 30% alcohol solution and 35 liters of the 60% alcohol solution to make a 40% solution.

I absolutely love these.

Your answer would be A since "h" is how many hours has pass and "J" is your jogging.

A + B = C.

Your "A" is the number of jogs you have, "B" is "h", and your "C" is "j".

Hopefully this helps!

Answer:

A) is what you are kooking for Bro

Step-by-step explanation:

Good day to you!

The question involves understanding exponential growth in Mathematics. The cost of concert tickets is increasing by 8% each day, as calculated using the given prices for two successive days.

The student's question pertains to exponential growth, a concept in Mathematics. Here, the increase in the cost of tickets is an example of exponential growth, where the growth rate is proportional to the current value. You can determine the daily percentage increase by using the formula for exponential growth:[tex](today's cost / yesterday's cost) ^ (^1^ /^ n^u^m^b^e^r^ o^f^ d^a^y^s^ b^e^t^w^e^e^n ^t^h^e^ d^a^t^e^s^) - 1.[/tex]

Here, the cost of the concert was $150 yesterday, and today it is $162. Insert these amounts into the formula, and we get [tex](162 / 150) ^ (^1^ /^ 1^) - 1[/tex]= 0.08 or 8%. Therefore, the ticket prices increase by 8% daily.

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To determine the daily percent increase in the price of concert tickets, use the exponential growth formula. The tickets increased from $150 to $162 in one day, resulting in a calculated daily percent increase of 8%.

The student asked: Tickets for a concert have been in incredibly high demand, and as the date for the concert draws closer, the price of tickets increases exponentially.

A pair of concert tickets cost $150 yesterday, and today is $162. As you complete the parts below, assume that each day's percent increase from the day before is the same.

To find the daily per cent increase, we assume an exponential growth model where ticket prices grow by a constant percentage each day.

Let's denote yesterday's price as P₀ = 150 and today's price as P₁ = 162.

Step-by-Step Explanation:

Define the exponential growth formula: P₁ = P₀ * (1 + r), where r is the daily rate of increase.

→ Substitute the known values into the formula: 162 = 150 * (1 + r).

→ Solve for the rate r: Divide both sides of the equation by 150 to isolate (1 + r).162 / 150 = (1 + r), simplifying to 1.08 = 1 + r.

→ Subtract 1 from both sides to solve for r: r = 0.08.

→ Convert the rate to a percentage: r = 0.08 * 100

                                                          = 8%.

Therefore, the daily percent increase in the price of the concert tickets is 8%.

The answer is to your question is 7:35.

Answer:

7:35 AM or PM

Step-by-step explanation:

depends on what time of day it is AM is daytime and PM is nightime. Ithink I deserver brainliest compared to the other answer. Up to you though.

Answer:

Step-by-step explanation:

So what you do is

1 cup = 8 fluid ounces

(Don’t use that)

So you is

“Since 1 cup= 8 fluid ounces, what you do is multiply by 2. 8 times 2 is 16 , 3 times 8 is 24. 24+16 is 40” there’s your answer

The equation that shows the relation between the cups of sparkling water (s) and apple juice (j) mixed by Jada is 2s = j, meaning that the quantity of apple juice is always twice the quantity of sparkling water.

In the question provided, we're given that Jada makes her sparkling juice by mixing 2 cups of sparkling water and 3 cups of apple juice. Let's define s as the number of cups of sparkling water, and j as the number of cups of apple juice. Given this, the equation that shows how s and j are related is 2s = j. This equation expresses that the quantity of apple juice (j) is always twice the quantity of sparkling water (s).

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Answer:

A

Step-by-step explanation:

Remark

Just as a guess, the answer should be A or B. It's always a good idea to estimate an answer so that if you get something really far away, you know it is incorrect.

Equation

Set up a proportion for the problem

26/30 is the basic ratio of the home fans wearing the right color

x/45000 is the ratio of those in the entire stadium.

Solution

26/30 = x / 45000                 Cross multiply

30x = 26 * 45000                  Simplify the right

30x = 1170000                        Divide by 30

30x/30 = 1170000/30    

x = 39000 And that is A

Answer:

30 , 45 , 51 , 39

Step-by-step explanation:

You just add up the numbers until you get 165

Number of beads of each color in Yasmin's bag is:

  Red--   30

  Brown--  45

 Orange-- 51

Yellow--  39

The record of experiment are as follows:

Color                    Red            Brown       Orange  Yellow

Number of Beads     10           15              17      13

Total number of beads recorded=10+15+17+13=55 beads

Also, the Probability of Red bead is=10/55

Probability of Brown bead is=15/55

Probability of Orange bead is=17/55

Probability of Yellow bead is=13/55

Number of red beads in Yasmin's bag are:

[tex]\dfrac{10}{55}\times 165=30[/tex]

Number of brown beads in Yasmin's bag are:

[tex]\dfrac{15}{55}\times 165=45[/tex]

Number of orange beads in Yasmin's bag are:

[tex]\dfrac{17}{55}\times 165=51[/tex]

Number of yellow beads in Yasmin's bag are:

[tex]\dfrac{13}{55}\times 165=39[/tex]

Answer:

pie equals 3.14159265359 but it's always rounded to just 3.14 so you don't have to write all of those numbers.

Pie equals 22/7

Pi (π) is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159.

It is represented by the Greek letter "π" .

It is the circumference of any circle, divided by its diameter.

Answer:

7/39 = 17.94%

Step-by-step explanation:

Town          Students     Relative Frequency

Wilmette   12 boys + 7 girls = 19 19/39 = 48.72%

Glencoe    9 girls + 4 boys = 13 13/39 = 33.33%

Kenilworth  2 boys + 5 girls = 7  7/39 = 17.94%

Total         39 students         39/39 = 100%

Another approach to solve probability is the Relative Frequency. A frequency is the number of times an event occurs. To solve for the relative frequency, it’s the ratio of the frequency of an event to the total outcomes. From the question, it is clear that for each town, it was subdivided into boys and girls but the word students represent the combined number of boys and girls for a particular town. so finding the probability that a student called at random to answer a question is from kenilworth is simply the ratio of students from kenilworth over the total number of students in the class.  

Answer:

172 cm^2

Step-by-step explanation:

Since it is a rectangular prism, you would have 6 sides, with two of them being the same. Each side is the values but multiplied by each other. So 7x2, 8x2, and 7x8. If you add them up it would be 14+16+56= 86, but that is only 3 sides, so you need to multiply 86 by 2, thus 172.

The maximum occurs at x = -b/2a

Using f(x) = ax^2 +bx +c

Replace a and b in the equation.

a = 2

b = 8

Now you have x = -8 / 2(2)

x = -8 / 4

x = -2

The maximum is -2

Answer:

C is the correct answer.

Step-by-step explanation:

Look at the X values for each coordinate pair. If an X value is represented twice with different Y values, it is not a function. If no X value is repeated, or it is repeated but has the same Y value, then it is a function. A has two values for x = 1, B has two values for x = -3, D has two values for x = 7, but C does not, so it is the correct answer.

Answer:

[tex]x=\frac{\pi}{2}[/tex]  and  [tex]x=\frac{3\pi}{2}[/tex]

Step-by-step explanation:

We need to solve the 2 equations to figure out the x-values (intersecting points).

Note: The identity  [tex]cos^{2}x=\frac{1}{2}+\frac{1}{2}cos(2x)[/tex]

[tex]cos(2x)=cos^{2}(x)-1\\cos(2x)=(\frac{1}{2}+\frac{1}{2}cos(2x))-1\\cos(2x)=\frac{1}{2}cos(2x)-\frac{1}{2}\\\frac{1}{2}cos(2x)=-\frac{1}{2}\\cos(2x)=-1\\2x=cos^{-1}(-1)\\2x=\pi, 3\pi\\x=\frac{\pi}{2}, \frac{3\pi}{2}[/tex]

So they intersect at  [tex]x=\frac{\pi}{2}, \frac{3\pi}{2}[/tex]

Answer:

x=pi/2 and x=3pi/2

Step-by-step explanation:

Answer: s, v, w, & x = 13      y = 20        z = 20 + 13√3

Step-by-step explanation:

First, you need to understand the side lengths of each special triangle in the drawing.

A 45°- 45°- 90° triangle has corresponding sides of a - a - a√2

A 30°- 60°- 90° triangle has corresponding sides of b - b√3 - 2b

The hypotenuse of the 45-45-90 triangle is 13√2, so its legs are 13.

So A F = 13 → s = 13 and w = 13

     FB = 13 → x = 13

     EC = 13 → v = 13

Since the x-value of C is 20, then the x-value of E is also 20 → y = 20

ED is opposite of the 60° angle of the 30-60-90 triangle so ED is EC√3.  Since EC = 13, then ED = 13√3.

AE + ED = AD

20 + 13√3 = AD → z = 20 + 13√3

Answer:

WEDNESDAY: 45 planted.

THURSDAY: 22 Harvested.

Step-by-step explanation:

Based on the information given in the problem, Maeve plants 5 trees for every 2 tree she harvests. Then the ratio can be expressed as following:

[tex]5:2[/tex] or [tex]\frac{5}{2}[/tex]

Then, you can complete the values in the table as you can see below:

WEDNESDAY

[tex]\frac{5}{2}=\frac{planted}{18}\\\\planted=\frac{18*5}{2}\\\\planted=45[/tex]

THURDAY

[tex]\frac{5}{2}=\frac{55}{harvested}\\\\(harvested)(\frac{5}{2})=55\\\\harvested=\frac{55*2}{5}\\\\harvested=22[/tex]

Answer:

Wed --------45---------

Thu ---------22-----------

Frank has 88 oranges at his stand, found by setting up an equation based on the ratio of apples to oranges (6:4) and the total count of fruit (220) and solving for x.

We need to find out the total number of oranges at Frank's fruit stand given that there are 220 fruits in total and the ratio of apples to oranges is 6:4. To do this, let's denote the total number of apples as 6x and the total number of oranges as 4x. The reason behind this is to maintain the ratio of 6 to 4 (or 3 to 2 when simplified). Since the total amount of apples and oranges is 220, we can set up the equation:

6x + 4x = 220

Combining like terms, we get:

10x = 220

Dividing both sides by 10 yields:

x = 22

Now that we have the value of x, we can find the number of oranges (which is 4x) by multiplying 4 by 22:

4x = 4 * 22 = 88

Therefore, Frank has 88 oranges at his fruit stand.

Answer:

C=s+4

Step-by-step explanation:

Hope this helps!

Answer:

884yd²

Step-by-step explanation:

Given in the question a pyramid with a square base

Slant height = 20

length of side of square = 18

To calculate base area

base area of pyramid = l²

                                   = 324 yd²

To calculate the one face of pyramid

area of one face  = 1/2 (height) x (base)

                            = 1/2 (20)(14)

                            = 140

Plug values in the formula

Area of the figure = 324 + 4(140)

                              = 884 yd²

Answer:

Total surface area = 1044 yd²

Step-by-step explanation:

From the figure we can see a square pyramid.

Base = 18 yd

Slant height = 20 yd

To find the Base area

Total surface area = Base area + (4* area of one lateral face)

Base area = Base² = 18² = 324 yd²

To find the lateral surface area

Area of one face = bh/2

b = base = 18 yd

h = Slant height = 20 yd

Area = bh/2 = (18 * 20)/2 = 180 yd²

Lateral surface area = 4 * 180 = 720 yd²

To find the total surface area

Total surface area = 324 + 720 = 1044 yd²

Answer:

2x^3 +3x^2 + 12x - 8

Step-by-step explanation:

(x^2- 4x + 8)(2x-1)

we expand the notation by using (2x-1)

2x(x^2 - 4x + 8) -1(x^2- 4x +8)

= 2x^3 -8x^2 +16x -x^2 + 4x -8

collect like terms

2^3 - 8x^2 - x^2 +16x + 4x -8

2x^3 + 7x^2 + 20x - 8