find the sum of these polynomials (x^2+x+9)+(7x^2+5)​

Answer:

Area = 16

Step-by-step explanation:

The plan is to find the area of the large triangle (blue and white together) and subtract the white triangle's area.

Area of blue + white.

h = 8

b = 5 + 4

b = 9

Area = 1/2 * 8 * 9

Area = 1/2 * 72

Area = 36

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

Area of white.

h = 8

b = 5

Area = 1/2 * 8 * 5

Area = 20

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

Area of the shaded region (blue) = Area of both triangles - Area of the white

Shaded = 36 - 20

Shaded = 16

Answer:

D:  (9, 23)

Step-by-step explanation:

Substitute the given value, 9, for x in y = 3x - 4.  We get:

y = 3(9) - 4, or y = 23.  Thus, the solution is (9, 23) (Answer D)

D. (9, 23) is the required ordered pair.

Substitution method is a mathematical method in which we have to pick one variable from one equation and substitute it to another equation.

Given equations are,

y = 3x - 4  .....(1)  &  x = 9   .....(2)

By using substitution method,

We have to put the value of x of (2) in (1),

i.e. we have to put x = 9 in (1),

∴ y = (3×9) - 4

     = 27 - 4

     = 23

So, the required ordered pair is (9, 23)

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Answer:

The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ

The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ

The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ

Step-by-step explanation:

* Lets explain the relation between the sides and the angles in

 a triangle

- The types of the triangles according the length of its sides:

# Equilateral triangle; all its sides are equal in length and all the angles

  have measures 60°

# Isosceles triangle; tow sides equal in lengths and the 2 angles not

  included between them are equal in measures

# Scalene triangles; all sides are different in lengths and all angles

  are different in measures

- The types of the triangles according the measure of its angles:

# Acute triangle; its three angles are acute and the relation between

  its sides is the sum of the squares of the two shortest sides is

  greater than the square of the longest side

# Obtuse triangle; one angle is obtuse and the other 2 angles are

  acute and the relation between its sides is the sum of the squares

  of the two shortest sides is smaller than the square of the longest

  side

# Right triangle; one angle is right and he other 2 angles are

  acute and the relation between its sides is the sum of the squares

  of the two shortest sides is equal to the square of the longest side

- The distance between the points 9x1 , y1) and (x2 , y2) is

  [tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

* Lets solve the problem

# The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)

∵ [tex]AB=\sqrt{(3-2)^{2}+(2-0)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]

∵ [tex]BC=\sqrt{(5-3)^{2}+(1-2)^{2}}=\sqrt{4+1}=\sqrt{5}[/tex]

∵ [tex]AC=\sqrt{(5-2)^{2}+(1-0)^{2}}=\sqrt{9+1}=\sqrt{10}[/tex]

- Lets check the relation between the sides

∵ AB = BC = √5 ⇒ shortest sides

∵ AC = √10

∵ (AB)² + (BC)² = (√5)² + (√5)² = 5 + 5 = 10

∵ (AC)² = (√10)² = 10

∴ The sum of the squares of the shortest sides is equal to the square

  of the longest side

∴ Δ ABC is right triangle

∵ Δ ABC has two equal sides

∴ Δ ABC is isosceles right triangle

# The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1)

∵ [tex]AB=\sqrt{(-3--3)^{2}+(4-1)^{2}}=\sqrt{0+9}=3[/tex]

∵ [tex]BC=\sqrt{(-1--3)^{2}+(1-4)^{2}}=\sqrt{4+9}=\sqrt{13}[/tex]

∵ [tex]AC=\sqrt{(-1--3)^{2}+(1-1)^{2}}=\sqrt{4+0}=2[/tex]

- Lets check the relation between the sides

∵ AB = 3

∵ BC = √13 ⇒ longest sides

∵ AC = 2

∵ (AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13

∵ (BC)² = (√13)² = 13

∴ The sum of the squares of the shortest sides is equal to the square

  of the longest side

∴ Δ ABC is right triangle

∴ Δ ABC is right triangle

# The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)

∵ [tex]AB=\sqrt{(-4--5)^{2}+(4-2)^{2}}=\sqrt{1+4}=\sqrt{5}[/tex]

∵ [tex]BC=\sqrt{(-2--4)^{2}+(2-4)^{2} }=\sqrt{4+4}=\sqrt{8}[/tex]

∵ [tex]AC=\sqrt{(-2--5)^{2}+(2-2)^{2}}=\sqrt{9+0}=3[/tex]

- Lets check the relation between the sides

∵ AB = √5

∵ BC = √8

∵ AC = 3 ⇒ longest sides

∵ (AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13

∵ (AC)² = (3)² = 9

∴ The sum of the squares of the shortest sides is greater than the

   square of the longest side

∴ Δ ABC is acute triangle

∵ Δ ABC has three different sides in lengths

∴ Δ ABC is acute scalene triangle

# The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)

∵ [tex]AB=\sqrt{(-2--4)^{2}+(4-2)^{2}}=\sqrt{4+4}=\sqrt{8}[/tex]

∵ [tex]BC=\sqrt{(-1--2)^{2}+(4-4)^{2} }=\sqrt{1+0}=1[/tex]

∵ [tex]AC=\sqrt{(-1--4)^{2}+(4-2)^{2}}=\sqrt{9+4}=\sqrt{13}[/tex]

- Lets check the relation between the sides

∵ AB = √8

∵ BC = 1

∵ AC = √13 ⇒ longest sides

∵ (AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9

∵ (AC)² = (√13)² = 13

∴ The sum of the squares of the shortest sides is smaller than the

   square of the longest side

∴ Δ ABC is obtuse triangle

∵ Δ ABC has three different sides in lengths

∴ Δ ABC is obtuse scalene triangle

Where the above is given,
The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1) is isosceles right Δ

The triangle with vertices A (-3 , 1) , B (-3 , 4) , C (-1 , 1) is right Δ

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2) is acute scalene Δ

The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4) is obtuse scalene Δ

Here is the definition of all the Triangles according to their respective sides:

Triangle classification based on angle measurement:

To determined the kind of triangles we are given from the above information, we use the distance formula:

The distance from (x₁, y₁) and (x₂, y₂)

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

The triangle with vertices A (2 , 0) , B (3 , 2) , C (5 , 1)

AB  [tex]= \sqrt{(-3- -3)^2 + (4 - 1)^2[/tex]

= √(0+9)

= 3

BC [tex]= \sqrt{(-1- -3)^2 + (1 - 4)^2[/tex]

= √(4+9)

= √13

AC  [tex]= \sqrt{(-1- -3)^2 + (1 - 1)^2[/tex]

AC = √(4+0)

= 2

- Lets evaluate the relation between the respective sides

AB = 3

BC = √13 ⇒ longest sides

AC = 2

(AB)² + (AC)² = (3)² + (2)² = 9 + 4 = 13

(BC)² = (√13)² = 13

The sum of the squares of the shortest sides is equal to the square of the longest side

Δ ABC is right triangle

Δ ABC is right triangle

The triangle with vertices A (-5 , 2) , B (-4 , 4) , C (-2 , 2)
AB = √[(-4- -5)² + (4-2)²]

= √(1+4)

= √5

BC = √[(-2- -1)² +(2-4)²

= √(4+4)

= √8

AC = √[(-2- -5)² +(2-2)²
=  √(9+0)

= 3

Checking the relation between the sides we know that

AB = √5

BC = √8

AC = 3 ⇒ longest sides

(AB)² + (BC)² = (√5)² + (√8)² = 5 + 8 = 13

(AC)² = (3)² = 9

Hence, the sum of the squares of the shortest sides is greater than the square of the longest side

Δ ABC is acute triangle

Δ ABC has three different sides in lengths

Δ ABC is acute scalene triangle



The triangle with vertices A (-4 , 2) , B (-2 , 4) , C (-1 , 4)

AB = √[(-2- -4)² + (4-2)²]
= √(4+4)
= √8

BC = √[(-1- -2)² + (4-4)²]
= √(1+0)
= 1

AC = √[(-1- -4)² + (4-2)²]

= √(9+4)
= √13


Thus, - checking the relation between the sides

AB = √8

BC = 1

AC = √13 ⇒ longest sides

(AB)² + (BC)² = (√8)² + (1)² = 8 + 1 = 9

(AC)² = (√13)² = 13

The sum of the squares of the shortest sides is smaller than the square of the longest side

Δ ABC is obtuse triangle

Δ ABC has three different sides in lengths

Δ ABC is obtuse scalene triangle


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Answer:

The correct answer is third option

1/√3

Step-by-step explanation:

From the figure we can see a right angled triangle ABC.

Right angled at C.

AB = 10

AC = 5

BC = 5√3

Points to remember

Tan θ = Opposite side/Adjacent side

To find the value of tan(B)

Tan B =  Opposite side/Adjacent side

 = AC/BC

 = 5/5√3

 = 1/√3

Therefore the value of tan(B) =  1/√3

Answer:

Option C is correct.

Step-by-step explanation:

tan (B) = Perpendicular / Base

For angle B:

Perpendicular = 5

Base = 5√3

tan (B) = Perpendicular / Base

tan (B) = 5/5√3

tan (B) = 1/√3

So, Option C is correct.

Answer:

The required expression is f = 3+6t

Step-by-step explanation:

Let t represent number of tens

Let f represent number of fives

So, the expression for number of fives can be formed by using:

The number of fives is 3 more than six times the number of tens.

f = 3+6t

So, the required expression is f = 3+6t

[tex]\bf \begin{cases} 3x+6y=21\\ \cline{1-1} -8x+y=63\\ \boxed{y}=63+8x \end{cases}~\hspace{7em}\stackrel{\textit{substituting on the 1st equation}}{3x+6\left( \boxed{63+8x} \right)}=21[/tex]

[tex]\bf 3x+378+48x=21\implies 51x+378=21\implies 51x=-357 \\\\\\ x=\cfrac{-357}{51}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=63+8x\implies }y=63+8(-7)\implies y=63-56\implies \blacktriangleright y=7 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-7,7)~\hfill[/tex]

According to Side Angle Side theorem the correct option is d)

[tex]\rm \dfrac{AC}{GI}=\dfrac{BC}{HI}[/tex]

According to SAS theorem:

From the given triangles we can see that,

[tex]\rm \dfrac{AC}{BC}=\dfrac{GI}{HI}[/tex]      ----       (according to SAS theorem)

Therefore, the correct option is D).

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Answer:

D !!!!!

Step-by-step explanation:

According to Side Angle Side theorem the correct option is d

AC / GI = BC / HI

-edge did the test

For this case we must find the quotient of the following expression:

[tex]\frac {2196} {12}[/tex]

According to the attached figure, we must build a quotient that, when multiplied by the divisor, cancels the terms of the dividend, until we reach the remainder. In this case the division is exact and the quotient is 183.

Answer:

See attached image

Answer:

(x+2) + x + (x+4) = 2(1/2) + 2(x+3)

Step-by-step explanation:

They are equal to each other and the rectangle has 2x more perimeter

The triangle would be divided in half from that rectangle.

Sorry If this is confusing I am not very good at explaining things.

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^2

where h and k is the center point and r is the radius.

Using the center point and radius given the equation becomes:

(x-4)^2 + (y+3)^2 = 3^2 or (x-4)^2 + (y+3)^2 = 9

Answer:

(x+16)^2=20^2+x^2

Step-by-step explanation:

Given there was no bending of the tree, the Pitagorean Theory would help finding the value of the trees hight.

x^2+32x+16^2=400+x^2

32x=(20-16)×(20+16)

x=144/32

x=4m and 50cm

Answer:

Step-by-step explanation:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

(x₁, y₁) - point on a line

We have the slope m = -5, and the point (2, 6).

Substitute:

[tex]y-6=-5(x-2)[/tex]

The slope-intercept form of an equation of a line:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

Convert:

[tex]y-6=-5(x-2)[/tex]           use the distributive property a(b + c) = ab + ac

[tex]y-6=-5x+(-5)(-2)[/tex]

[tex]y-6=-5x+10[/tex]            add 6 to both sides

[tex]y=-5x+16[/tex]

The standard form of an equation of a line:

[tex]Ax+By=C[/tex]

Convert:

[tex]y=-5x+16[/tex]            add 5x to both sides

[tex]5x+y=16[/tex]

Answer:

46°

Step-by-step explanation:

BE is the bisector so abe is the same as ebc

2x+20=4x-6

26=2x

13=x

so now plug x back into abe to find its measure

2(13)+20

26+20

46

The answer is 46°.

BE is the bisector so abe is the same as ebc

2x+20=4x-6

26=2x

13=x

So now plug x back into abe to find its measure

2(13)+20

26+20

46

Bisecting a line is cutting a line exactly in half. It may also be referred to as constructing a perpendicular bisector as the line you are drawing will be at a right angle to the original line. You will need a compass, pencil, and ruler.

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Answer:

2.3km in meters is 2300 Meters

Step-by-step explanation:

Multiply the length value by 1000

Answer:

x-intercept equals 3

y-intercept equals 9

Step-by-step explanation:

we have

[tex]3x+y=9[/tex]

step 1

Find the y-intercept

The y-intercept is the value of y when the value of x is equal to zero

so

For x=0

substitute in the equation and solve for y

[tex]3(0)+y=9[/tex]

[tex]y=9[/tex]

The y-intercept is the point (0,9)

step 2

Find the x-intercept

The x-intercept is the value of x when the value of y is equal to zero

so

For y=0

substitute in the equation and solve for x

[tex]3x+0=9[/tex]

[tex]x=3[/tex]

The x-intercept is the point (3,0)

therefore

x-intercept equals 3

y-intercept equals 9

Answer:

If want just the approximated solutions in the interval from 0 to 360:

199.47

340.53

90

270

If you want all the approximated solutions:

199.47+360k

340.53+360k

90+360k

270+360k

Step-by-step explanation:

2 cos(x)+3 sin(2x)=0

First step: Use double angle identity for sin(2x). That is, use, sin(2x)=2sin(x)cos(x).

2 cos(x)+3*2sin(x)cos(x)=0

2 cos(x)+ 6sin(x)cos(x)=0

Factor the 2cos(x) out, like so:

2cos(x)[ 1  + 3 sin(x)]=0

In order for this product to be zero, we must find when both factors are 0.

2cos(x)=0         or     1+3sin(x)=0

Let's do 2cos(x)=0 first.

2cos(x)=0

Divide both sides by 2:

 cos(x)=0

So the x-coordinate is 0 on the unit at x=90 deg  and x=270 deg (in the first rotation).

Let's do 1+3sin(x)=0.

1+3sin(x)=0

Subtract 1 on both sides:

  3sin(x)=-1

Divide both sides by 3:

   sin(x)=-1/3

Unfortunately this is not on the unit circle so I'm just going to take sin^-1 or arsin on both sides (this is the same thing sin^-1 or arsin).

   x=arcsin(-1/3)=-19.47 degrees

So that means -(-19.47)+180 is also a solution so 19.47+180=199.47 .

And that 360+-19.47 is another so 360+-19.47=340.53 .

So the solutions for [0,360] are

199.47

340.53

90

270

If you want all the solutions just add +360*k to each line where k is an integer.

Answer:

Step-by-step explanation:

Note. You should put the item you are trying to solve for in the numerator when using the sine law.

sin(x) / 15 = Sin 27 / 11

sin(x) = 15 * sin(27 / 11

sin(x) = 0.4539

sin(x) = 15 * 0.4539/11

sin(x)  = 6.809 / 11

sin(x) = 0.6191

x = sin-1(0.6191)

x = 38.3

Answer: its 38.2 :)

Step-by-step explanation:

Answer:

Answer choice 4

Step-by-step explanation:

Since alternate interior angles create congruent angles, angle 5 and 3 are congruent as well as 4 and 2, and since the only option that has these statements is answer choice 4, it is the correct answer.

Answer:

it is d

Step-by-step explanation:

Answer:

$835.20

Step-by-step explanation:

First you need to find out how many profit you had at first by multiplying 145 and $44.17.

So, 145*$44.17 = 6404.65

Then find out how much profit you had after it decreased by multiplying 145 and $38.41.

So, 145*$38.41 = 5569.45

Now to find how much profit you lost, you have to subtract $6,404.65 and $5,569.45.

$6,404.65 - $5,569.45 = $835.20

Answer:

your answer would be 6

Step-by-step explanation:

hope this helps

Answer:

y = - 6x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 6x + 2 ← is in this form with slope m = - 6

• Parallel lines have equal slopes, hence

y = - 6x + c ← is the partial equation of the parallel line.

To find c substitute (- 1, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y = - 6x - 4 ← equation of parallel line

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x+x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

From the graph we have the points (-3, -3) and (0, 3).

Calculate the slope:

[tex]m=\dfrac{3-(-3)}{0-(-3)}=\dfrac{6}{3}=2[/tex]

Put the value of the slope and the coordinates of the point (-3, -3) to the equation of a line:

[tex]y-(-3)=2(x-(-3))\\\\y+3=2(x+3)[/tex]

[tex]y=2x+3[/tex]

Answer: $3.75

Step-by-step explanation

(This may not be the way teachers see it)

So take the $1.50 and multiply it by two and you get $3 for four hours

Then you would take the $0.75 and add it to the $3 to get $3.75

(would it be 0.75 for 15 min?)

You are correct in selecting choice A as the answer.

You need the middle angles between the two pairs of given congruent sides, so that you can prove the triangles to be congruent through SAS. The vertical angle theorem is used in this case. Alternate interior angles only come from parallel lines, but we dont know if any of the lines are parallel. Even if we did know the lines were paralle, we still wouldn't use the alternate interior angle theorem.

The part that is necessary in Valerie's proof using SAS to prove ΔVWX ≅ ΔYZX  is prove that ∠VWX ≅ ∠YXZ by vertical angles.

The SAS(side angle side) theorem for congruent triangle states that If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

The side WX and XZ are congruent and VX and XZ are congruent . Then the included angles ∠VWX should be congruent to ∠YXZ. The both angles are vertically opposite angles. This can be represented with mathematical symbols below

WX≅XZ

VX ≅XZ

Therefore,

∠VWX ≅ ∠YXZ(vertically opposite angles)

Therefore, the necessary step in Valerie proof is Prove that ∠VWX ≅ ∠YXZ by vertical angles.

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Answer:

2/5, 8/20, 4/10,16/40

Step-by-step explanation:

40%

Percent means out of 100

40/100 = 4/10 = 2/5

Lets look at the choices

8/100 =4/50 =2/25  not equal

2/5  equal

8/20 = 4/10 =2/5 = equal

4/10 = 2/5 = equal

16/40 = 4/10 = 2/5 equal

Answer:

Second option.

Third option.

Fourth option.

Fifth option.

Step-by-step explanation:

In order to find equivalent fractions to 40%, you can:

- Write 40 as the numerator and 100 as the denominator and then reduce the fraction:

[tex]\frac{40}{100}=\frac{4}{10}=\frac{2}{5}[/tex]

- Multiply the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 2:

[tex]\frac{4*2}{10*2}=\frac{8}{20}[/tex]

- Multiply  the numerator and the denominator of the fraction [tex]\frac{4}{10}[/tex] by 4:

[tex]\frac{4*4}{10*4}=\frac{16}{40}[/tex]

The quadratic equation 12t^2 + 4t - 9 = 0 has a discriminant value of 448, which is greater than zero indicating two real solutions. These solutions are irrational given that the square root of the discriminant (448) is not a clean number, hence answer A. 2; irrational, is correct.

The quadratic equation in question is 12t² + 4t - 9 = 0. The discriminant (D) of a quadratic equation in the form at² + bt + c = 0 is defined as D = b² - 4ac. Use the values from your equation: a = 12, b = 4, and c = -9. Plugging these values into the formula gives D = 4² - 4*(12)*(-9) = 16 + 432 = 448.

The value of the discriminant determines the solutions of the quadratic equation. If D > 0, then there are two real solutions. If D = 0, then there's one real solution. If D < 0, then there are no real solutions. Here, we have that D = 448 which is greater than 0, hence, the quadratic equation has two real solutions.

The type of solutions depends on whether the square root of D is a rational or irrational number. The square root of 448 is not a clean number, meaning it's an irrational number. Therefore, the solutions are of an irrational type.

So, this quadratic equation has 2 solutions that are irrational meaning the correct answer is A. 2; irrational.

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The equation 12t^2+4t-9=0 has a. two irrational solutions.

To determine the number and type of solutions for the equation 12t^2+4t-9=0, we can use the discriminant formula.

The discriminant is found by calculating b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation.

In this case, a = 12, b = 4, and c = -9. Substituting these values into the discriminant formula, we get b^2 - 4ac = (4)^2 - 4(12)(-9) = 16 + 432 = 448.

Since the discriminant (448) is positive, this means that the quadratic equation has two real solutions. The nature of these solutions can be determined by the discriminant as well. If the discriminant is a perfect square, the solutions are rational. If the discriminant is not a perfect square, the solutions are irrational.

In our case, the discriminant (448) is not a perfect square, so the solutions to the equation 12t^2+4t-9=0 are two irrational solutions. Therefore, the correct answer is a. 2; irrational.

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An expression for the given statement is (x²/3)+4.

The given statement is 4 more than the quotient of x squared and 3.

We need to find an expression for the given statement.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be addition, subtraction, multiplication, or division.

The terms involved in an expression in math are:

Constant: A constant is a fixed numerical value.

Variable: A variable is a symbol that doesn't have a fixed value.

According to the question, we get (x²/3)+4.

Therefore, an expression for the given statement is (x²/3)+4.

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Answer:

it should be 3.3

Step-by-step explanation:

I did it with friend

Answer:

C) 3.3

Step-by-step explanation:

this is the correct answer on ed-genuity, hope this helps! :)

Step-by-step explanation:

For two points (x₁, y₁) and (x₂, y₂), the distance between them is:

d² = (x₁ − x₂)² + (y₁ − y₂)²

The order of points 1 and 2 don't matter.  You can switch it:

d² = (x₂ − x₁)² + (y₂ − y₁)²

This is basically the Pythagorean theorem for a coordinate system.

Let's do an example.  If you have points (1, 2) and (4, 6), then the distance between them is:

d² = (4 − 1)² + (6 − 2)²

d² = 3² + 4²

d² = 9 + 16

d² = 25

d = 5

If you have points with negative coordinates, remember that subtracting a negative is the same as adding a positive.

For example, the distance between (-1, -2) and (4, 10) is:

d² = (4 − (-1))² + (10 − (-2))²

d² = (4 + 1)² + (10 + 2)²

d² = 5² + 12²

d² = 25 + 144

d² = 169

d = 13

Answer:

x² - 16 ⇒ (x + 4)(x - 4)

(2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

(2x + 3y)² ⇒ 4x² + 12xy + 9y²

x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)

Step-by-step explanation:

* Lets explain how to solve the problem

# x² - 16

∵ x² - 16 is a difference of two squares

- Its factorization is two brackets with same terms and different

 middle signs

- To factorize it find the square root of each term

∵ √x² = x and √16 = 4

∴ The terms of each brackets are x and 4 and the bracket have

   different middle signs

∴ x² - 16 = (x + 4)(x - 4)

* x² - 16 ⇒ (x + 4)(x - 4)

# (2x + 1)³

- To solve the bracket we will separate (2x + 1)³ to (2x + 1)(2x + 1)²

∵ (2x + 1)² = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x² + 4x + 1

∴ (2x + 1)³ = (2x + 1)(4x² + 4x + 1)

∵ (2x + 1)(4x² + 4x + 1) = (2x)(4x²) + (2x)(4x) + (2x)(1) + (1)(4x²) + (1)(4x) + (1)(1)

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 8x² + 2x + 4x² + 4x + 1 ⇒ add like terms

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + (8x² + 4x²) + (2x + 4x) + 1

∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 12x² + 6x + 1

∴ (2x + 1)³ = 8x³ + 12x² + 6x + 1

* (2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1

# (2x + 3y)²

∵ (2x + 3y)² = (2x)(2x) + 2(2x)(3y) + (3y)(3y)

∴ (2x + 3y)² = 4x² + 12xy + 9y²

* (2x + 3y)² ⇒ 4x² + 12xy + 9y²

# x³ + 8y³

∵ x³ + 8y³ is the sum of two cubes

- Its factorization is binomial and trinomial

- The binomial is cub root the two terms

∵ ∛x³ = x and ∛8y³ = 2y

∴ The binomial is (x + 2y)

- We will make the trinomial from the binomial

- The first term is (x)² = x²

- The second term is (x)(2y) = 2xy with opposite sign of the middle

  sign in the binomial

- The third term is (2y)² = 4y²

∴ x³ + 8y³ = (x + 2y)(x² - 2xy + 4y²)

* x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)