Find all solutions in the interval [0, 2π).

4 sin2 x - 4 sin x + 1 = 0

Answer:

p - 2

Step-by-step explanation:

"2 less than a number" would be n - 2.  "Less than" implies subtraction.  We are subtracting 2 from the unknown number n.

Answer:

p-2

Step-by-step explanation:

To simplify the expression −4(−11+4n)−3(−2n+9), you distribute the multiplication and then combine like terms to get the equivalent expression +17−10n.

The student has asked to simplify the expression −4(−11+4n)−3(−2n+9). To simplify this expression, we need to distribute the numbers outside the parentheses across the terms inside the parentheses. We'll do this step by step.

Now combine like terms:

So, the simplified equivalent expression is +17−10n.

the simplified and equivalent expression is 17 - 10n.

We need to simplify the expression:

[tex]-4(-11+4n)-3(-2n+9)[/tex]

To do this we need to open the brackets which gives us:

[tex]-4(-11+4n)-3(-2n+9) = 44 -16n + 6n -27[/tex]

Now we can solve the expression as follows:

[tex]-4(-11+4n)-3(-2n+9) = (44 - 27) + (-16n + 6n)\\\\ -4(-11+4n)-3(-2n+9) =17 - 10n[/tex]

So, the simplified and equivalent expression is 17 - 10n.

Answer:

[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}=2\sqrt{6}+4[/tex]

Step-by-step explanation:

We have the expression:

[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex]

To simplify the expression multiply by the conjugate of the denominator.

The denominator is

[tex]\sqrt{3}-\sqrt{2}[/tex]

Then its conjugate is:

[tex]\sqrt{3}+\sqrt{2}[/tex]

Then:

[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}*\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\\\\=\frac{2\sqrt{2}\sqrt{3}+2\sqrt{2}\sqrt{2}}{(\sqrt{3})^2-(\sqrt{2})^2}\\\\\frac{2\sqrt{6}+4}{3-2}}\\\\= \frac{2\sqrt{6}+4}{1}}=2\sqrt{6}+4[/tex]

Answer:

[tex]4+2\sqrt{6}[/tex]

Step-by-step explanation:

Given expression is [tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex].

Now we need to simplify this. So multiply and divide by conjugate of denominator.

[tex]\frac{2\sqrt{2}}{\sqrt{3}-\sqrt{2}}[/tex]

[tex]=\frac{2\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)}[/tex]

[tex]=\frac{2\sqrt{2}}{\left(\sqrt{3}-\sqrt{2}\right)}\cdot\frac{\left(\sqrt{3}+\sqrt{2}\right)}{\left(\sqrt{3}+\sqrt{2}\right)}[/tex]

[tex]=\frac{2\sqrt{6}+2\sqrt{4}}{\left(\sqrt{3}\right)^2-\left(\sqrt{2}\right)^2}[/tex]

[tex]=\frac{2\sqrt{6}+2\cdot2}{3-2}[/tex]

[tex]=\frac{2\sqrt{6}+4}{1}[/tex]

[tex]=2\sqrt{6}+4[/tex]

[tex]=4+2\sqrt{6}[/tex]

Hence final answer is [tex]4+2\sqrt{6}[/tex].

Answer:

x = 8.5

L = 17

W = 6.5

Step-by-step explanation:

P = 2*(L + W)

W = x - 2

L = 2x

P = 47

47 = 2 * (2x + x - 2)

47 = 2 * (3x - 2)          Remove the brackets.

47 = 6x - 4                 Add 4 to both sides.

47 + 4 = 6x - 4+4       Combine

51 = 6x                       Divide by 6

6x/6=51/6                  Combine

x = 8 3/6 or 8.5

x = 8.5

========

L = 2*x

L = 2*8.5

L = 17

=====

W = x - 2

W = 8.5 - 2

W = 6.5

Answer:

x=8.5, length is 17, and width is 6.5

Step-by-step explanation:

To solve for x, you would add the two sides together, getting x-2+2x+3x-2. Now, you would multiply this figure by two, because you only have half of the perimeter as of now. (3x-2)*2+6x-4. Now, because the perimeter is 47, you have this equation

6x-4=47

Add four to both sides

6x=51

Divide by 6

x=51/6=8.5

Now, you would plug this into both of the other sides of the rectangle.

The length, or the longest side, measures 2x

2*8.5=17

The width, or the shorter side, measures x-2

8.5-2=6.5

Hope this helped

The answer is : 270 seats

Multiply 18*15

18*15

=270

Answer: 270 seats

Answer:

Answer

3.0/5

8

1cm = 50

2 cm = 50 x 2

3cm = 50 x 3

and the inverse:50m = 50/50 = 1cm

100m = 100/50 = 2cm

150m = 150/50 = 3cm

381m = 381/

The height in centimeters of Micah's model given the scale of the drawing is 7.62cm

A scale drawing is a reduced form in terms of dimensions of an original image / building / object

Scale of the drawing = original dimensions / dimensions of the scale drawing

The height of the model = 381 / 50 = 7,62cm

To learn more about scale drawings, please check: https://brainly.com/question/26388230

Answer:

It will look like a graph with a slope of 4 and a y intercept of -8

Step-by-step explanation:

Just rearrange the variables

Answer:

Step-by-step explanation:

If the question mentions a graph, you'll need to share that graph.

Here's one good procedure for graphing -4x + y = 8:

Find the y-intercept:  Let x = 0 and solve for y.  We get (0, 8).  Plot this.

Find the x-int.  Let y = 0 and solve for x.  We get (-2, 0).  Plot this.

Then draw a straight line through these two points.

31-3x+19x-5=90

26+16x=90

-26 -26

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

16x= 64

16x/16= 64/16

x=4

m <R=19 (4)-5= 71.

Answer:

Step-by-step explanation:

90=(31-3x)+(19x-5)

90=31-3x+19x-590=19x-3x+31-5

90=16x+26

90-26=17x

64=4x

x=4

m∠R=19(4)-5

m∠R=76-5

m∠R=71

Answer:

[tex]Y=(X-7)/2[/tex]

Step-by-step explanation:

we have

[tex]X=2t+3[/tex] -----> equation A

[tex]Y=t-2[/tex] -----> [tex]t=Y+2[/tex] -----> equation B

Substitute equation B in equation A

[tex]X=2(Y+2)+3[/tex]

[tex]X=2Y+4+3[/tex]

[tex]X=2Y+7[/tex]

solve for Y

[tex]2Y=X-7[/tex]

[tex]Y=(X-7)/2[/tex]

2* radius* pie

Step-by-step explanation:

first you times 2 by the radius, then you times that answer by 3.14.

hoped this helped a little

The Value of Pi is actually an infinite number and cannot be calculated. It is not a real number. Usually many just shorten Pi to the decimal 3.14, which it is most commonly used as since there is no exact decimal of Pi.

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081284811174502841027019385211055596446229489549303819644288109756659334461284756482337867831652712019091456485669234603486104543266482133936072602491412737245870066063155881748815209209628292540917153643678925903600113305305488204665213841469519415116094330572703657595919530921861173819326117931051185480744623799627495673518857527248912279381830119491298336733624406566430860213949463952247371907021798609437027705392171762931767523846748184676694051320005681271452635608277857713427577896091736371787214684409012249534301465495853710507922796892589235420199561121290219608640344181598136297747713099605187072113499999983729780499510597317328160963185950244594553469083026425223082533446850352619311881710100031378387528865875332083814206171776691473035982534904287554687311595628638823537875937519577818577805321712268066130019278766111959092164201989380952572010654858632788659361533818279682303019520353018529689957736225994138912497217752834791315155748572424541506959508295331168617278558890750983817546374649393192550604009277016711390098488240128583616035637076601047101819429555961989467678374494482553797747268471040475346462080466842590694912933136770289891521047521620569660240580381501935112533824300355876402474964732639141992726042699227967823547816360093417216412199245863150302861829745557067498385054945885869269956909272107975093029553211653449872027559602364806654991198818347977535663698074265425278625518184175746728909777727938000816470600161452491921732172147723501414419735685481613611573525521334757418494684385233239073941433345477624168625189835694855620992192221842725502542568876717904946016534668049886272327917860857843838279679766814541009538837863609506800642251252051173929848960841284886269456042419652850222106611863067442786220391949450471237137869609563643719172874677646575739624138908658326459958133904780275900994657640789512694683983525957098258226205224894077267194782684826014769909026401363944374553050682034962524517493996514314298091906592509372216964615157098583874105978859597729754989301617539284681382686838689427741559918559252459539594310499725246808459872736446958486538367362226260991246080512438843904512441365497627807977156914359977001296160894416948685558484063534220722258284886481584560285060168427394522674676788952521385225499546667278239864565961163548862305774564980355936345681743241125150760694794510965960940252288797108931456691368672287489405601015033086179286809208747609178249385890097149096759852613655497818931297848216829989487226588048575640142704775551323796414515237462343645428584447952658678210511413547357395231134271661021359695362314429524849371871101457654035902799344037420073105785390621983874478084784896833214457138687519435064302184531910484810053706146806749192781911979399520614196634287544406437451237181921799983910159195618146751426912397489409071864942319615679452080951465502252316038819301420937621378559566389377870830390697920773467221825625996615014215030680384477345492026054146659252014974428507325186660021324340881907104863317346496514539057962685610055081066587969981635747363840525714591028970641401109712062804390397595156771577004203378699360072305587631763594218731251471205329281918261861258673215791984148488291644706095752706957220917567116722910981690915280173506712748583222871835209353965725121083579151369882091444210067510334671103141267111369908658516398315019701651511685171437657618351556508849099898599823873455283316355076479185358932261854896321329330898570642046752590709154814165498594616371802709819943099244889575712828905923233260972997120844335732654893823911932597463667305836041428138830320382490375898524374417029132765618093773444030707469211201913020330380197621101100449293215160842444859637669838952286847831235526582131449576857262433441893039686426243410773226978028073189154411010446823252716201052652272111660396

Pi is 3.14, and is an irrational number, meaning that it does not end and has no repetition of numbers in a row.

The area of the circle is calculated by multiplying pi by the radius.

3.14 * 10 = 314.16.

To round it to the nearest tenth, you must know whether the second decimal number is greater or less than 5. If it is 5 or greater, you round the first decimal up 1. If it is 4 or less, then you just remove the second decimal and keep the first one.

In this case, the answer would be approximately 314.2 because 6 is greater than 5, so you round up the 1 to a 2.

Answer:

7

Let's solve your equation step-by-step.

5x−7+2−2x=−26

Step 1: Simplify both sides of the equation.

5x−7+2−2x=−26

5x+−7+2+−2x=−26

(5x+−2x)+(−7+2)=−26(Combine Like Terms)

3x+−5=−26

3x−5=−26

Step 2: Add 5 to both sides.

3x−5+5=−26+5

3x=−21

Step 3: Divide both sides by 3.

3x

3

=

−21

3

x=−7

Answer:

x=−7

Answer:

the solution is x = -7

Step-by-step explanation:

Collect terms:

x(5 -2) +(-7 +2) = -26

3x -5 = -26

Add 5 to get the variable term by itself:

3x = -21

Divide by the coefficient of the variable:

x = -7

____

The answer to, "what is it?" is that it is a linear equation in x. After you collect terms, it is what is referred to as a "two-step" linear equation, because it takes two steps to solve it: add 5, divide by 3.

Answer:

Part 1) The system of equations that represent this situation is

[tex]12x+6y=180[/tex] and [tex]x=2y[/tex]

Part 2) The number of hardcover books sold was [tex]12[/tex] and the number of paperback books sold was [tex]6[/tex]

Step-by-step explanation:

Part 1) What is the system of equations that represents this situation?

Let

x---->  number of hardcover books sold

y----> number of paperback books sold

we know that

The system of equations that represent this situation is equal to

[tex]12x+6y=180[/tex] -----> equation A

[tex]x=2y[/tex] -----> equation B

Part 2) What is the solution to the system and what does it represent in the context of this situation?

Substitute equation B in equation A and solve for y

[tex]12(2y)+6y=180[/tex]

[tex]24y+6y=180[/tex]

[tex]30y=180[/tex]

[tex]y=6[/tex]

Find the value of x

[tex]x=2y[/tex]

[tex]x=2(6)=12[/tex]

The solution of the system of equations is the point (12,6)

That means

The number of hardcover books sold was [tex]12[/tex]

The number of paperback books sold was [tex]6[/tex]

Answer:

The volume of the cylinder is 63π or 197.9 units³

Step-by-step explanation:

* Lets revise how to find the volume of any cylinder

- The volume of the regular solid = area of the base × its height

- The cylinder has two circular bases

- The area of the circle = πr²

∴ The volume of the cylinder = πr² × its height

* Now lets take the dimensions of the cylinder from the problem

- The height of the cylinder is 7 units

- The radius of the cylinder is 3 units

∵ The volume of the cylinder = πr² × its height

∴ The volume = π × 3² × 7 = 63π = 197.9 units³

* The volume of the cylinder is 63π or 197.9 units³

Answer:

The volume of cylinder =197.82 units²

Step-by-step explanation:

Formula:-

Volume of cylinder =  πr²h

Where r - Radius of cylinder and

h - Height of cylinder

To find the volume of cylinder

Here r = 3 units and h = 7 units

Volume = πr²h

 = 3.14  * 3² * 7

 = 3.14 * 9 * 7

 = 197.82 units²

Therefore the volume of cylinder =197.82 units²

Answer:

Alex walks more miles

Step-by-step explanation:

Answer:

Jenna walks more miles per day

Step-by-step explanation:

i got this answer by doing 12 divided by 5 = 2.4 and 7 divided by 3 = 2.33333333333  and 2.4 is more that 2.33333333333  so Jenna walked futher,

i hope that this answer helped you, pls give me good votes if it did, because im new here and trying to get points.

ANSWER

[tex]3{a}^{4 } [/tex]

EXPLANATION

The cube root of

[tex]27 {a}^{12} [/tex]

is

[tex] \sqrt[3]{27 {a}^{12} } [/tex]

This is the same as:

[tex](27 {a}^{12} )^{ \frac{1}{3} } [/tex]

[tex]( {3}^{3} ({a}^{4})^{3} )^{ \frac{1}{3} } [/tex]

[tex] = (3{a}^{4} )^{3 \times \frac{1}{3} } [/tex]

[tex] = 3{a}^{4 } [/tex]

Complete the square on the right side of the equation

2(x-2)^2+1

Answer:

3,500

Step-by-step explanation:

70% is equal to 0.70.

When you need to find a percent of a population, you multiply the decimal form to the population.

Therefore, with 70% of 5000, you multuiply 5000 by 0.70 which will give you 3500.

3,500 students would select roller coasters as their favorite ride.

The answer to this question would be 3,500 students.

Answer:

Domain: [tex]n\ge1[/tex]

Step-by-step explanation:

For a geometric sequence, the n-th term is given by:

[tex]a_n=a_1r^{n-1}[/tex]

From the question, [tex]a_1=1[/tex] and [tex]r=6[/tex].

Hence the explicit formula for the sequence is:

[tex]a_n=6^{n-1}[/tex], where [tex]n\ge1[/tex]

Therefore the domain is natural numbers or positive integers.

Answer:

[tex]d(P,D)= \sqrt{41}\\d(P,D)=6.40312[/tex]

Step-by-step explanation:

We need to find the distance between the points P=(-2,3) and D(2,-2)

The formula used to find distance between points is:

[tex]d(P,D)= \sqrt{(x2-x1)^2 + (y2-y1)^2)}[/tex]

Here, x2 =2 and x1 = -2,  y2=-2 and y1= 3

Putting values in formula

[tex]d(P,D)= \sqrt{(2-(-2))^2 + (-2-3)^2}\\d(P,D)= \sqrt{(2+2)^2 + (-2-3)^2}\\d(P,D)= \sqrt{(4)^2 + (-5)^2}\\d(P,D)= \sqrt{16 + 25}\\d(P,D)= \sqrt{41}\\d(P,D)=6.40312[/tex]

Answer:

4 inches.

Step-by-step explanation:

Convert 10ft in to inches

10 ft = 120 inches

So, 10ft/30inches =120inches/30 inches

120÷30=4

The requried, 10 ft / 30 inches simplified is 4

To simplify the expression 10 ft / 30 inches, we need to convert the units to a common format. We can convert both feet and inches to inches to make the division easier.

1 foot is equal to 12 inches. So, 10 feet can be written as 10 * 12 = 120 inches.

Now we have 120 inches / 30 inches, which simplifies to:

120 inches / 30 inches = 4.

Therefore, 10 ft / 30 inches simplified is 4.

Learn more about simplification here:

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Answer:

1/4 would be your answer

Step-by-step explanation:

There are four other pieces (I think)

Answer:

Option A.  [tex]\frac{1}{16}[/tex]

Step-by-step explanation:

Two boxes contains the following pieces of chalk of the same size.

Red = 2

Yellow = 1

Green = 4

White = 3

Blue = 2

Each box contains = 2 + 1 + 4 + 3 + 2  = 12 pieces of chalk of the same size.

There are total pieces of chalks are 12 and white chalks are 3 in each box.

If one piece of chalk will be randomly selected from each box.

The probability of first box that piece will be white = [tex]P_{1}=\frac{3}{12}[/tex]

The probability of second box =  [tex]P_{2}=\frac{3}{12}[/tex]

Therefore,  P =  [tex]p_{1}[/tex] × [tex]p_{2}[/tex]

                   P = [tex]\frac{3}{12}[/tex] × [tex]\frac{3}{12}[/tex]

                   P = [tex]\frac{1}{4}[/tex] ×  [tex]\frac{1}{4}[/tex]

                   P = [tex]\frac{1}{16}[/tex]

The probability that both pieces will be white is  [tex]\frac{1}{16}[/tex] .

the sales tax is close to 217.94

Answer:17.9955

Step-by-step explanation:

199.95 * 0.09 = 17.9955

when ever you want to work out a % just multiple it by the % in decimal ie 10% = 0.1, 100% = 1.0, 9% =0.09

OR

if you want to work out what 9% is added on top of the price to total 199.95 you can you this

A1= gross amount

B1 = tax percentage

(A1/(100+B1)*100) = 183.440367 before the tax is added so the total tax at 9% = 16.509633

Answer:

120

Step-by-step explanation:

We need the formula of combination:

nCr = [tex]\frac{n!}{(n-r)!*r!}[/tex]

Also we need to understand "factorial" notation, which is the "!" mark. For example, 5! means 5 * 4 * 3 * 2 * 1, and

4! would mean 4 * 3 * 2 * 1

Now we can find out 16C14 by plugging it into the formula and doing the steps shown below:

[tex]nCr=\frac{n!}{(n-r)!*r!}\\16C14=\frac{16!}{(16-14)!*14!}\\=\frac{16!}{2!*14!}\\=\frac{16*15*14!}{(2*1)*14!}\\=\frac{16*15}{2}\\=120[/tex]

Answer:

A. 4/7

Step-by-step explanation:

If Susie has a bag with 9 hairpins, 7 pencils, 2 snacks, and 4 books, the ratio of books to pencils is 4/7 or 4:7.

4 books.

7 pencils.

You could combine the 4 and 7 getting, 4/7 or 4:7

Even though, there are more numbers, the question only asked for the ratio of books to pencils.

Answer:

(x + 3)(x + 7)

Step-by-step explanation:

Given

x² + 10x + 21

Consider the factors of the constant term (+ 21) which sum to give the coefficient of the x- term (+ 10)

The factors are + 3 and + 7, since

3 × 7 = 21 and 3 + 7 = 10, hence

x² + 10x + 21 = (x + 3)(x + 7)

A linear equation is an equation in which each term has at max one degree. The correct option is B.

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on the cartesian plane with axes of those variables, give a straight line.

The total deposit and rent collected by an apartment manager for one resident are given by the equation t = 350 + 700m, where m is the number of months the resident has lived there. Since the equation is in the form of a linear equation it can be concluded that the model is linear.

Comparing the equation with a linear equation,

t = 350 + 700m

y = C + mx

The slope of the equation is 700, while the y-intercept is 300.

Hence, the correct option is B.

Learn more about Linear Equations:

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Answer:

The answer is A. F(x)=(X+3)^4

Step-by-step explanation:

1. Whenever the function is in parenthesis, the symbol does the opposite then it usually does. So for (X+3)^4, the + in the parenthesis shifts the graph to the left instead of right.

2. Also, when in parenthesis, function shifts horizontally, not vertically. So answers B and C would shift the graph up and down, instead of left or right.

Please feel free to ask me if you have more questions or concerns with this problem!

Answer:

Step-by-step explanation:

f(x) + n - shift the graph n unit up

f(x) - n - shift the graph n unit down

f(x + n) - shift the graph n unit to the left

f(x - n) - shift the graph n unit to the right

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

F(x) ← G(x) shifted 3 units to the left

F(x) = G(x + 3) → F(x) = (x+3)⁴

The hypotenuse of the triangle would be the diameter of the semi circle.

Using the Pythagorean theorem you can find that.

8^2 + 6^2 = x^2

64 +36 = x^2

100 = x^2

x = √100

x = 10

The diameter is 10, now find the circumference.

Circumference = diameter x PI = 10 x 3.14 = 31.4

Since it is a semi circle, the circumference would be 1/2 of that.

31.4 / 2 = 15.7

The perimeter would be 8 + 6 + 15.7 = 29.7

Answer:

20 Meters

Step-by-step explanation:

5 Sides a Pentagon has - with a length at 4 meters per side you have a perimeter of 20 meters.