PLS HELP ILL GIVE BRAINLIEST

ANSWER

See explanation

EXPLANATION

The point (3,-6) is the fourth quadrant.

In this quadrant only the cosine ratio and the secant ratio are positive.

The remaining four trigonometric ratios are negative.

The diagram is shown in the attachment.

We use the Pythagoras Theorem to find the hypotenuse, h.

[tex] {h}^{2} = {6}^{2} + {3}^{2} [/tex]

[tex] {h}^{2} = 36 + 9[/tex]

[tex] {h}^{2} = 45[/tex]

[tex]h = \sqrt{45} [/tex]

[tex]h = 3 \sqrt{5} [/tex]

[tex] \sin( \theta) = - \frac{opp}{hyp} [/tex]

[tex]\sin( \theta) = - \frac{6}{3 \sqrt{5} } [/tex]

[tex]\sin( \theta) = - \frac{2 \sqrt{5} }{ 5 } [/tex]

[tex]\sin( \theta) = - \frac{2}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{adj}{hyp} [/tex]

[tex]\ cos(\theta) = \frac{3}{3 \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{1}{ \sqrt{5} } [/tex]

[tex]\ cos(\theta) = \frac{ \sqrt{5} }{5} [/tex]

[tex]\tan(\theta)= - \frac{opp}{hyp} [/tex]

[tex]\tan(\theta)= - \frac{6}{3} = - 2[/tex]

[tex]\csc(\theta)= - \frac{hyp}{opp} [/tex]

[tex]\csc(\theta)= - \frac{3 \sqrt{5} }{6} = - \frac{\sqrt{5} }{2} [/tex]

[tex] \sec( \theta) = \frac{hyp}{adj} [/tex]

[tex]\sec( \theta) = \frac{3 \sqrt{5} }{3} = \sqrt{5} [/tex]

[tex]\cot( \theta) = - \frac{adj}{opp} [/tex]

[tex]\cot( \theta) = - \frac{3}{6} = - \frac{1}{2}[/tex]

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]

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:

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.

I think it's B

[tex] - 11 \geqslant n + 0 \\ 1. \: - 11 \geqslant n \\ 2. \: n \leqslant - 11 \\ \\ - 11 \geqslant n \\ 1. \: n \leqslant - 11[/tex]

Answer:

The answer is B. Identity property of Addition

Step-by-step explanation:

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]

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:

(4, -3)

Step-by-step explanation:

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is changed to the opposite sign.

The reflection of the point (x, y) across the x-axis is the point (x, -y).

The reflected point across the x-axis of the original point (4,3) would have the coordinates (4, -3), where the x-coordinate remains the same and the y-coordinate changes sign. Hence correct option b.

When a point is reflected across the x-axis, the y-coordinate changes sign, but the x-coordinate remains the same. The reflection of the point across the x-axis means that the x-coordinate (4) does not change, but the y-coordinate (3) becomes its opposite (-3). Thus, the new coordinates of the reflected point are (4, -3).

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

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.

Complete the square on the right side of the equation

2(x-2)^2+1

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:

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.

Answer:

QC=16 this is correct on usa testprep

Step-by-step explanation:

The centroid of a triangle is the point of concurrency of the median lines of

the triangle.

The length of segment [tex]\overline{QC}[/tex] is C) 16

Reasons:

The given parameters are;

Point C = The centroid of ΔPQR

[tex]\overline{CZ}[/tex] = 8

Required:

The length of  segment QC

Solution;

Given that point C is the centroid of the triangle ΔPQR, we have;

[tex]\overline{QC} = \dfrac{2}{3} \times \overline{QZ}[/tex]

[tex]\overline{CZ}= \dfrac{1}{3} \times \overline{QZ}[/tex]

Therefore;

[tex]\overline{CZ}= \dfrac{1}{2} \times \overline{QC}[/tex]

[tex]\overline{QC} = 2 \times \overline{CZ}[/tex]

[tex]\overline{QC} = 2 \times 8 = 16[/tex]

Learn more here:

https://brainly.com/question/1747484

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:

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 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.

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:

b 93

Step-by-step explanation:

Answer:

Step-by-step explanation:

Alright, lets gets started.

The dimensions of the given triangle is 24 , 52 and 17.

The another triangle is given congruent to this triangle.

It means the dimensions of another triangle will also be 24, 52 and 17.

So the perimeter will be addition of these sides.

Hence the perimeter will be = [tex]24+52+17[/tex]

Hence the perimeter will be = 93 feet   :    Answer

Hope it will help :)

Answer:

Retailer

Step-by-step explanation:

A retailer buys goods from the manufactures and wholesalers and then sell these products directly to the consumers or users.In the supply chain retailers are the ones who connect with the customers to obtain information on goods and servicers delivered.

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]

the answer is 2yx^3/(2y^2)^3

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:

Answer:

It extends the time of the collision

Step-by-step explanation:

The correct option is : It extends the time of the collision.

The padding helmets have cushions inside it that moves inwards when a ball hits the helmets.

When the collision occurs, the time will increase and less force will be exerted on helmet that is why the impact of the collision will be less.

Answer:

A. It extends the time of the collision.

Step-by-step explanation:

the picture

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.

Step-by-step explanation:

[tex]\text{If}\ 10+\dfrac{6}{2}+3=10+3+3=16\\\\\text{If}\ \dfrac{10+6}{2+3}=\dfrac{16}{5}[/tex]

To simplify 10+6/2+3, we first perform the division operation (6 ÷ 2 = 3), and then carry out the addition operations in order (10 + 3 + 3), giving us a final result of 16.

To simplify 10+6/2+3, we have to follow the order of operations as guided by the mnemonic PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). In the given expression, there are no parenthesis, exponents, so we proceed by carrying out division and then addition.

Step 1: Perform the division operation 6 ÷ 2 = 3.

Step 2: Simplify the expression by performing the addition operations in the order from left to right. So, 10 + 3 (from division) + 3= 16.

Therefore, the simplified form of the original expression is 16.

https://brainly.com/question/15840745

#SPJ3

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:

https://brainly.com/question/15242961

#SPJ6

Answer:

The Numerator is 6x + 4y - 3z

Step-by-step explanation:

Step  1  :

           z

Simplify   —

           4

Equation at the end of step  1  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  2  :

           y

Simplify   —

           3

Equation at the end of step  2  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  3  :

           x

Simplify   —

           2

Equation at the end of step  3  :

  x    y     z

 (— +  —) -  —

  2    3     4

Step  4  :

Calculating the Least Common Multiple :

4.1    Find the Least Common Multiple  

     The left denominator is :       2  

     The right denominator is :       3  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 0 1

3 0 1 1

Product of all  

Prime Factors  2 3 6

     Least Common Multiple:  

     6  

Calculating Multipliers :

4.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 3

  Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)2   and  (y2+y)/(y+1)3  are equivalent as well.  

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

  L. Mult. • L. Num.      x • 3

  ——————————————————  =   —————

        L.C.M               6  

  R. Mult. • R. Num.      y • 2

  ——————————————————  =   —————

        L.C.M               6  

Adding fractions that have a common denominator :

4.4       Adding up the two equivalent fractions  

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • 3 + y • 2     3x + 2y

—————————————  =  ———————

      6              6    

Equation at the end of step  4  :

 (3x + 2y)    z

 ————————— -  —

     6        4

Step  5  :

Calculating the Least Common Multiple :

5.1    Find the Least Common Multiple  

     The left denominator is :       6  

     The right denominator is :       4  

       Number of times each prime factor

       appears in the factorization of:

Prime  

Factor   Left  

Denominator   Right  

Denominator   L.C.M = Max  

{Left,Right}  

2 1 2 2

3 1 0 1

Product of all  

Prime Factors  6 4 12

     Least Common Multiple:  

     12  

Calculating Multipliers :

5.2    Calculate multipliers for the two fractions  

   Denote the Least Common Multiple by  L.C.M  

   Denote the Left Multiplier by  Left_M  

   Denote the Right Multiplier by  Right_M  

   Denote the Left Deniminator by  L_Deno  

   Denote the Right Multiplier by  R_Deno  

  Left_M = L.C.M / L_Deno = 2

  Right_M = L.C.M / R_Deno = 3

Making Equivalent Fractions :

5.3      Rewrite the two fractions into equivalent fractions

  L. Mult. • L. Num.      (3x+2y) • 2

  ——————————————————  =   ———————————

        L.C.M                 12      

  R. Mult. • R. Num.      z • 3

  ——————————————————  =   —————

        L.C.M              12  

Adding fractions that have a common denominator :

5.4       Adding up the two equivalent fractions  

(3x+2y) • 2 - (z • 3)     6x + 4y - 3z

—————————————————————  =  ————————————

         12                    12      

Final result :

 6x + 4y - 3z

 ————————————

      12    

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]

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)