Which example illustrates the commutative property of addition for polynomials?

Step-by-step explanation:

Hi,

Let's describe it in listing method;

S= {8,16,24}.

Hope you got it...

To find the vertex, you need to find the axis of symmetry first.

In order to find the axis of symmetry we have to do -b/2a.

In our case, the b is -8 and the a is 1.

Plug it in.

-(-8)/2(1)

8/2 = 4

Our axis of symmetry is 4.

Now, we plug it into the equation to find the rest of the vertex.

y = 4^2 - 8(4) + 1

y = 16 - 32 + 1

y = -16 + 1

y = -15

Put it together.

Our vertex is (4,-15).

Answer:

[tex]\huge\boxed{f(x - 2) = x + 6}[/tex]

Step-by-step explanation:

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

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

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

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

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

f(x) = x + 8

shift the graph 2 units to the right

f(x - 2) = (x - 2) + 8 = x - 2 + 8 = x + 6

Answer:

use factoring x (see attachment)

-8 x 7 = -56

-8 + 7 = -1

(x - 8)(x + 7) = 0

x = 8, -7

hope this helps :)

Answer:

Step-by-step explanation:

diameter=2×5=10 cm

32/10=3.2≈3

128/10=12.8≈12

total number of squares=12×3=36

Answer:

a) 18

b) 20

c) 12

d) 12

Step-by-step explanation:

a) The triangle is half of the square, so you can find the area of the square(36) and divide by 2: so 18

b) There are 4 same sized blank triangles with area of 4 ( (2*4)/2 ) so 4 * 4 is 16. 16 is the blank area so the area of the shaded is 36 - 16: 20

c) There are 2 blank triangles which areas are 6, and 18, so you subtract those numbers from 36: 36 - (6+18) = 12

d) Another 2 same blank triangles with areas of 12 ( (6 *4)/2 )so you subtract them from 36 too: 36 - (12*2) = 36 - 24 = 12

Answer:

Hey there!

Equation of Line FG: [tex]y=\frac{1}{2} x+3.5[/tex], because the slope (rise over run) is 2 and we see that the y intercept is 3.5.

Equation to a Line Perpendicular to FG: [tex]y=-2x-3\\[/tex], because the equations of perpendicular lines have the same (but could also be different y-intercepts), and opposite reciprocal slopes.

Let me know if this helps :)

Answer:

C)

Step-by-step explanation:

f(-5,1) & G(9,8)

Slope of FG = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

                    = [tex]\frac{8-1}{9-[-5]}=\frac{7}{9+5}\\\\[/tex]

                     [tex]\frac{7}{14}\\\\=\frac{1}{2}[/tex]

Slope of line perpendicular to FG = -1/m = -1/(1/2) = -2

Equation of line in slope intercept form : y = mx + b

m = - 2

So, option c will be the equation of the line perpendicular to FG

Answer:

The airplane can fly up to 240 miles in a hour

Step-by-step explanation:

Cross multiply

(12)(60)=3x

720=3x

Divide 3 on both sides

x=240

There are 60 minutes in 1 hour.

60 ÷ 3 = 20

12 × 20 = 240

In one hour, the airplane could fly at 240 miles.

Answer:

1).

A. Reflection across the y axis.

2).

A. Clockwise rotation about point B and a translation 20 units down.

The sequence of transformation that can be performed on quadrilateral

ABCD to show that is congruent to GHIJ is a B. 90 degree counter

clockwise rotation about point A  followed by a B. Reflection across the y-

axis and a translation 20 units down

Reasons:

The coordinates of the point (x, y) following a rotation of 90°

counterclockwise is the point (-y, x)

Taking point A as the origin

The coordinates of point A = (15, 10)

Coordinates of the points B, relative to the point A = (0, 10)

Coordinates of the points C, relative to the point A = (5, 5)

Coordinates of the points D, relative to the point A = (5, -5)

The location of the image of point B, following a rotation about the point A, is therefore;

B'(-10 + 15, 0 + 10) = B'(5, 10), C'(-5 + 15, 5 + 10) = C'(10, 15), D'(5 + 15, 5 + 10) = D'(20, 15)

The coordinates of the image of the point (x, y), following a reflection

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

A'B'C'D' following a reflection across the y-axis are the point B''(-5, 10),

C''(-10, 15), D''(-20, 15) A''(-15, 10). The coordinates of the quadrilateral GHIJ

are; G(-15, -10), H(-5, -10), I(-10 - 5), J(-20, -5)

The x-coordinates of the quadrilaterals A''B''C''D'', and GHIJ are the same,

therefore, we translate A''B''C''D'', 20 units down to get;

B'''(-5, -10), C'''(-10, -5), D'''(-20, -5) A'''(-15, -10)

Coordinates of A'''(-15, -10) = G(-15, -10)

Coordinates of B'''(-5, -10) = H(-5, -10)

Coordinates of C'''(-10, -5) = I(-10 - 5)

Coordinates of D'''(-20, -5) = J(-20, -5)

Therefore;

The sequence of transformation that can be performed on quadrilateral

ABCD to show that is congruent to GHIJ is a;

Followed by a;

Learn more here:

https://brainly.com/question/1593448

Answer:

interquartile range=20.55

Step-by-step explanation:

5.6, 11.1, 19.2, 24.5, 33.3

median is  19.2

Q1=(5.6+11.1)/2=8.35

Q3=(24.5+33.3)/2=28.9

interquartile range= Q3-Q1=28.9-8.35=20.55

Answer

24 frames per second

Step-by-step explanation:

Total frames=86,400

Total time=1 hour

Find frame per second

1 hour= 60 minutes*60 seconds

1 hour=3600 seconds

Frame per second=Total frames/Total number of seconds

=86,400/3600

=24 frames per second

Answer:

ii) £120

iii) £2,400

a) 10 workers

c) 4 workers more to be employed.

Step-by-step explanation:

ii) To find the buying price we deduct 20% (percent) from the selling price of £150.

= 20/100 x 150

= £30 (Next we substract this value from the selling price of £150) = €150 - £30 = £120

iii) A 12% interest per annum Implies a 12 percent of the borrowed amount of 20,000, which is calculated as

12% or 12/100 x 20,000 = £2,400

a) Put simply, we create an equation for the problem.

4 men * 10 days = 40 man days.

X men * 4 days = 40 man days.

Let's substitute the equation:

(X/ 4) * (4/ 10) = 40 / 40

(X/4) * 0.4= 1 (collect like terms)

0.4 * x = 4

0.4x/0.4= 4/0.4

x = 10 workers.

(c) 4 extra workers to would need to be employed since we have six already available (10-6=4).

Answer:

Height of flagpole before it fell = 5.15 m

Step-by-step explanation:

Given:

Height of remain pole (p) = 1.7 m

Distance from base (b) = 3 m

Find:

Height of flagpole before it fell

Computation:

Using Pythagorean theorem

H = √ p² + b

Length of broken part = √ 1.7² + 3²

Length of broken part = √ 2.89 + 9

Length of broken part = √ 11.89

Length of broken part = 3.45 (Approx)

Height of flagpole before it fell = Length of broken part + Height of remain pole

Height of flagpole before it fell = 3.45 + 1.7

Height of flagpole before it fell = 5.15 m

Answer:

y=3x+5

Step-by-step explanation:

8% lower means the gauge is showing 92% of the original pressure

( 100% - 8% = 92%)

Divide the pressure the gauge is showing by 92%

33.58 / 0.92 = 36.5

The actual pressure is 36.5

Answer:

The correct option is;

It has no reflectional symmetry

Step-by-step explanation:

Reflectional symmetry is one such that a line can be drawn across a shape or figure and the shape or figure on either side of the line is the equivalent of the reflection image obtained from a mirror

Lines of reflectional symmetry can be found in squares, circles, and triangles

The characteristics of the object that has line of reflection symmetry remains the same across the line of symmetry

Two dimensional objects have lines of symmetry while three dimensional objects have planes of symmetry.

Answer:

             i) TRUE

             ii) TRUE

             iii) TRUE

Step-by-step explanation:

[tex](ab+bc)(ab-bc)+(bc+ca)(bc-ca)+(ca+ab)(ca-ab)=\\\\=\underline{(ab)^2}-(bc)^2\ \,+\ \,(bc)^2-(ca)^2\ \,+\ \,(ca)^2-\,\underline{(ab)^2}=\\\\=0+0+0=0[/tex]

[tex](a+b+c)(a^2+b^2+c^2-ab-bc-ca)=\\\\=a^3\,\underline{\,+ab^2}\ \underline{\underline{+\,ac^2}}\,-a^2b\ -\,abc\ \underline{\underline{\underline{-\,a^2c}}}+a^2b+b^3+bc^2\,\underline{-\,ab^2}\ \underline{\underline{\underline{ \underline{-\,b^2c}}}}\,-\,abc+\\{}\qquad\qquad\qquad\qquad\qquad\qquad \qquad\qquad \underline{\underline{ \underline{+\,a^2c}}}\ \underline{\underline{\underline{\underline{+\,b^2c}}}}+c^3\,-\,abc-bc^2\ \underline{\underline{-c^2a}}=[/tex]

[tex]=a^3\ \underline{-\,a^2b}\ \underline{\underline{-\,abc}}\ \underline{+\,a^2b}+b^3\ \underline{\underline{\underline{+\,bc^2}}}\ \underline{\underline{-\,abc}}+c^3\ \underline{\underline{-\,abc}}\ \underline{\underline{\underline{-\,bc^2}}}=\\\\=a^3+b^3+c^3-3abc[/tex]

[tex](p-q)(p^2+pq+q^2)=\\\\=p^3\ \underline{+\,p^2q}\ \underline{\underline{+\,pq^2}}\ \underline{-\,p^2q}\ \underline{\underline{-\,pq^2}}-q^3=\\\\=p^3-q^3[/tex]

Answer:  see proofs below

Step-by-step explanation:

7i)  (ab + bc)(ab - bc) = a²b² - ab²c + ab²c - b²c²  →  a²b² - b²c²

  + (bc + ca)(bc - ca) = b²c² - abc² +abc² - a²c²   →             b²c²  - a²c²

  + (ca + ab)(ca - ab) = a²c² - a²bc + a²bc - a²b²  →                      a²c² - a²b²

                                                                             =   a²b² +  0   +   0   - a²b²

                                                                             = 0

7ii) a(a² + b² + c² - ab - bc - ca) = a³ + ab² + ac²           - a²b - abc - a²c

  + b(a² + b² + c² - ab - bc - ca) = b³ - ab²          + bc² + a²b - abc           - b²c

  + c(a² + b² + c² - ab - bc - ca) = c³           - ac² - bc²           - abc  + a²c + b²c

                                 =  a³ + b³ + c³  + 0     + 0   + 0     + 0   - 3abc + 0   + 0

                                  = a³ + b³ + c³ - 3abc

7iii) p(p² + pq + q²) = p³ + p²q + pq²

    -q(p² + pq + q²) =     - p²q  -  pq² - q³

                              = p³   + 0    + 0    - q³

                              = p³ - q³

Answer:

1,296

Step-by-step explanation:

Answer:

1,296

Step-by-step explanation:

Well 6 to the 4th power is also,

6*6*6*6 which is 1,296.

Answer:

D

Step-by-step explanation:

Here, we are given the values of the areas of the two triangles and we want to find the sum of these areas

The sum can be found by adding the area of triangle A to the area of triangle B

That would be;

x^2 + x + x^2-3x = 2x^2 -2x

Answer:

d

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

In Set A, the minimum is 4 and the maximum is 7 without X which would make the range 7 - 4 = 3 but we want the range to be 4, therefore X has to be 4 + 4 = 8. Unfortunately, this would then make the range of Set B 8 - 1 = 7 so X has to be the smallest number in Set A which would be 7 - 4 = 3.

Answer:

Step-by-step explanation:

identitiy property

Answer:

VX = 8.8 in

Step-by-step explanation:

By applying Sine rule in the right triangle WXV,

Sin(∠W) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

             = [tex]\frac{\text{VX}}{\text{WX}}[/tex]

Sin(34)° = [tex]\frac{VX}{15}[/tex]

VX = 15.Sin(34)°

     = 8.8379

     ≈ 8.8 in.

Therefore, measure of side VX is 8.8 in.

Answer:

The answer to your question is -5

Step-by-step explanation:

Data

            [tex]\frac{3}{2}x - \frac{7}{2} = 5x + 14[/tex]

Process

1.- Subtract 5x in both sides

            [tex]\frac{3}{2} x - \frac{7}{2} - 5x = 5x -5x + 14[/tex]

2.- Simplify

           [tex]- \frac{7}{2} x - \frac{7}{2} = 14[/tex]

3.- Add 7/2 in both sides

           [tex]-\frac{7}{2} x = 14 + \frac{7}{2}[/tex]

4.- Simplify

           - [tex]\frac{7}{2} x = \frac{35}{2}[/tex]

5.- Solve for x

               x = [tex]\frac{35}{2} / - \frac{7}{2}[/tex]

6.- Simplify

               x = -5

Answer: x = -3.71

Step-by-step explanation:

3/2*-7/2=5x+14

-4.55=5x+14

Subtract 14

-18.55=5x

Divide by 5

x = -3.71

Hope it helps <3

Answer:

See below.

Step-by-step explanation:

The perimeter = 2*length + 2 * width.

As the ratio is 3:2 the fraction 3 / (3 +2)  is used to find the length:

The measure of the 2 lengths = 3/ (3+2)  * 60

= 3/5 * 60

= 36 cm

So the measure of the length = 18 cm

So the measure of  the width = (60 - 36) / 2

= 24/2

= 12 cm.

Answer:

D. so you don't confuse properties of the model with properties of the real thing.

2-Mathematical and computer models are similar because both involve using calculation to represent an object or system

3- Some models can illustrate a system. What does the term system refer to

A. a collection of interacting things

4-J.J. Thomson's Plum Pudding Model is an example of _____B. an analogy

5. An advantage of describing a cell as being like a factory is that it _____

A. makes cells easier to understand

6- C. cheaper and more complex

7-C. clearly explained where electrons were located in an atom

8-C. a physical model

9-B. can be easier to change

GOOD LUCK

Answer:

63.4°

Step-by-step explanation:

The following data were obtained from the question:

Opposite = 6 cm

Adjacent = 3 cm

Angle x =?

The value of angle x can be obtained as follow:

Tan x = Opposite/Adjacent

Tan x = 6/3

Tan x = 2

Take the inverse of Tan.

x = Tan¯¹ 2

x = 63.4°

Therefore, the value of angle x is 63.4°

Answer:

63.4°

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

You remove the brackets and round down to the nearest whole number which is three..

Edge 2020

~theLocoCoco

Answer:

a

Step-by-step explanation:

edge 2021

Answer:

B

Step-by-step explanation:

In an isosceles triangle, the altitude is the median so the altitude splits the base into two segments with lengths of 5. We notice that x is part of a right triangle with legs of 5 and 12, therefore, using the 5 - 12 - 13 Pythagorean Triple, x = 13.

Answer:

(B) 13

Step-by-step explanation:

This isosceles triangle is broken up into two parts, both are right triangles.

To find the length of a missing side in a right triangle, we use the Pythagorean Theorem - [tex]a^2+b^2=c^2[/tex]. where one of the legs is a, the other leg is b, and the hypotenuse is c.

We know that one of the legs is 12, and since the base of the triangle is 10, the leg of one of the right triangles is 5.

Let's solve.

[tex]5^2+12^2=c^2\\25+144=c^2\\169=c^2\\\\\sqrt{169} =c\\13=c[/tex]

So, c is 13, therefore the hypotenuse is 13, therefore x is 13.

Hope this helped!

Answer:

d

Step-by-step explanation: