2. Triangles B and C have been built by dilating Triangle A. A A B C a. Find the center of dilation. b. Triangle B is a dilation of A with approximately what scale factor? c. Triangle A is a dilation of B with approximately what scale factor? d. Triangle B is a dilation of C with approximately what scale factor?​

In elementary algebra, the binomial expansion defines the algebraic expansion of powers of a binomial. The binomial equation be 27x² - 300 exists 3(3x + 10)(3x - 10).

In elementary algebra, the binomial theorem (or binomial expansion) defines the algebraic expansion of powers of a binomial. According to the theorem, it exists possible to extend the polynomial  [tex]$(x+y)^n$[/tex] into a sum involving terms of the form [tex]$a x^b y^c$[/tex], where the exponents b and c exists nonnegative integers with b + c = n, and the coefficient a of each term exists a specific positive integer depending on n and b.

Let the binomial equation be 27x² - 300

Factor out common term 3:

[tex]$\quad 3\left(9 x^2-100\right)$[/tex] [tex]$=3\left(9 x^2-100\right)$[/tex]

simplifying the above equation, we get

Factor [tex]$9 x^2-100: (3 x+10)(3 x-10)$[/tex]

= 3(3x + 10)(3x - 10)

If 3(3x - b)(3x + b) then we get

= 3(3x + 10)(3x - 10)

b = 10

The value of b = 10.

Therefore, the correct answer is option a. 10.

To learn more about binomial equation refer to:

https://brainly.com/question/9325204

#SPJ9

Answer:

79.

Step-by-step explanation:

Replace the x by -5 and simplify:

f(-5) = 3(-5)^2 + (-5) + 9

       = 75 - 5 + 9

       =  79.

The value of f(-5) will be 79.

Step-by-step explanation:

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s) is called a polynomial.

The following table gives special names given to polynomials of low orders.

polynomial order polynomial name

2                         quadratic polynomial

3                         cubic polynomial

4                        quartic

5                         quintic

6                         sextic

Here, the given polynomial: f(x) = 3x² + x + 9

by putting value of x = -5

[tex]3*(-5)^{2} + (-5) + 9[/tex]

after putting we get,

[tex]75 - 5 + 9[/tex]

On solving the above numerical we get,

[tex]79[/tex].

So our final answer would be 79 on putting x = -5 in the given polynomial : f(x) = 3x² + x + 9

To learn more about polynomials, visit :

https://brainly.com/question/11536910?referrer=searchResults

The complete table when Noah is running a marathon at a constant speed of 6 miles per hour is mentioned below:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

The running speed of Noah is 6 mph.

The formula for distance is given as:

D = v × t

Where D is the distance, v is the speed and t is the time.

Now,

When t = 1 hour,

D = 6 × 1 = 6 miles

When t = 1/2hour,

D = 6 × 1/2 = 3 miles

When t = [tex]1\frac{1}{3}[/tex] hour,

D = 6 × [tex]1\frac{1}{3}[/tex] = 6 × 4/3 = 8 miles

When t = [tex]1\frac{1}{2}[/tex] hour,

D = 6 × [tex]1\frac{1}{2}[/tex] = 6 × 3/2 = 9 miles

When t = 9 hours,

D = 6 × 9 = 54 miles

When t = [tex]4\frac{1}{2}[/tex] hour,

D = 6 × [tex]4\frac{1}{2}[/tex] = 6 × 9/2 = 27 miles

Therefore, the table will be:

Time                 Distance

 1                           6

 1/2                        3

 [tex]1\frac{1}{3}[/tex]                         8

 [tex]1\frac{1}{2}[/tex]                         9

  9                        54

 [tex]4\frac{1}{2}[/tex]                        27

Learn more about speed here:

brainly.com/question/13943409

#SPJ1

Firstly, we will need to try the following options one after the other in order to ascertain our answer

The first option

To find the distance between two points

Distance = Higher number - Lower number

-3 - 20

= - 23

This is very wrong because it has a negative sign

The second option

7 - (-16)

In mathematics, - x - = +

7 + 16

7 + 16 = 23

The answer is OPTION B

Cost of the TV before sale £350

We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Discount is the term used to describe a rebate or an offer made to clients on the listed price of goods. Let's examine the connections between these concepts.

Given,

Sale% = 20%

The cost of TV after the sale = £280

Finding the original price:

                   100% - 20% = 80%

So 80% is the price £280

We have to find the 20% which has been less

Or, £280 = 0.80 x T

Let the original price be T,

                               280 = 0.80 x T

                               280/0.80 = T

                                      350 = T

Hence, the original price of the TV was £350.

To learn more about Discount click on the link

https://brainly.com/question/24304697

#SPJ9

The graph of each equation is attached below each showing the point of intersection to the y-axis.

To solve this question, we have to use a graphing calculator to plot the coordinates as well as show the point of intersection.

A line graph is a graphical representation of information that changes over a period of time. It is a chart made by joining points using line segments.

The graph of equation is attached below.

Learn more on graph of a straight line here;

https://brainly.com/question/14323743

#SPJ1

Answer: y=-2x+8

Step-by-step explanation: Write a table of values where for every x y goes down 2 to find the y intercept (0,8) so it would be 8. The slope is -2 and that is all you need to write the equation.

Answer:

y-intercept= (0,0)

Step-by-step explanation:

4x+5y=0

4(0)+5y=0

5y/5=0/5

y=0

4x+5(0)=0

4x/4=0/4

x=0

same for x-intercept (0,0)

According to the central limit theorem for sums, if you keep taking sums from bigger and bigger samples, the sums will eventually form their own normal distribution (the sampling distribution), which will become more similar to a normal distribution as the sample size grows.

To learn more about Normal distribution refer to:

brainly.com/question/4079902

#SPJ4

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=4 \end{cases}\implies S=180(4-2)\implies S=360 \\\\[-0.35em] ~\dotfill\\\\ 360 ~~ = ~~ (7x+19)+(15x-1)+(4x-3)+(12x+3) \\\\\\ 360~~ = ~~38x+18\implies 342=38x\implies \cfrac{342}{38}=x\implies \boxed{9=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle C}{15x-1}\implies 15(9)-1\implies 135-1\implies \stackrel{\measuredangle C}{\text{\LARGE 134}}[/tex]

Answer:

u hv to do middle terms ig

[tex]\cfrac{13u^3 y^2 - 32u^2 y}{-4u^3 y^2}\implies \cfrac{13u^3 y^2}{-4u^3 y^2}-\cfrac{32u^2 y}{-4u^3 y^2}\implies -\cfrac{13}{4}+\cfrac{8}{uy}[/tex]

Answer:

-6

Step-by-step explanation:

by using -6 any value of x would make the equation true resulting in infinitly many solutions

Answer:

x = 6

Step-by-step explanation:

8x + 7x = 90

15x = 90

x = 6

The area of a parallelogram is:

a = bh

The base, b, of the parallelogram is 14.

The issue with this particular figure? We need the perpendicular height. We are given the side width, but that cannot be used in the final equation. So, we employ the Pythagorean Theorem.

We know that in the right triangle, a = 4, and c = 8.

a^2 + b^2 = c^2
4^2 + b^2 = 8^2
16 + b^2 = 64
16 - 16 + b^2 = 64 - 16
b^2 = 48
√b^2 = √48
b ≈ 6.93

So, b in this right triangle is equal to h in the parallelogram. So:

a ≈ 14(6.93)
a ≈ 97.02

The equivalent expression of 8(x+3)−14(20x−56)​ is - 272x + 808.

Two algebraic expressions are equivalent, when the two expressions have the same value when we plug in the same value(s) for the variable(s).

In other words, two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Therefore, the equivalent expression of 8(x+3)−14(20x−56)​ can be found as follows;

8(x+3) − 14(20x−56)​

open the parenthesis

8x + 24 -  280x + 784

combine the like terms

8x + 24 -  280x + 784

8x -  280x + 24 + 784

Therefore, the equivalent expression is as follows:

- 272x + 808

learn more on equivalent expression here: https://brainly.com/question/27950681

#SPJ1

The percentage of squirrels that have a weight between 3 and 5 pounds is; 95.017%

To learn more about percentage from the given link :

https://brainly.com/question/2155156

#SPJ4

Answer:$19.575

Solution

135/100of $14.50

=$19.575

or 35/100 of $14.50

=$5.075

$14.50+5.075

=$19.575

After calculating basic arithmetic we have come to find that, 1523 boxes of crayons are produced in each hour if crayons manufactory produces 36,552 crayons in an hour.

Arithmetic ((arithmós) 'number', 'art, craft') is a fundamental branch of mathematics that focuses on the properties of traditional operations on numbers such as addition, subtraction, multiplication, division, exponentiation, and root extraction.

Giuseppe Peano, an Italian mathematician, formalized arithmetic in the nineteenth century with his Peano axioms,[disputed - discuss], which are still very important in the field of mathematical logic today.

The prehistory of arithmetic is limited to a few artifacts that may indicate the concept of addition and subtraction, the best-known of which is the Ishango bone from central Africa, which dates from somewhere between 20,000 and 18,000 BC, though its interpretation is disputed.

We have given that

crayon manufactory produces 36,552 per hours

Each box contain 24 crayons

No. of boxes manufactured in 1 hour = 36,552/24

                                                              = 1523

Thus, 1523 boxes of crayons are produced in each hour if Crayons manufactory produces 36,552 crayons in an hour.

Learn more about arithmetic

https://brainly.com/question/6561461

#SPJ9

The value of the car in very nice condition is $5177.

From the information, a car that originally cost $3,668 in 1955 is valued today at $62,125 if in excellent condition, which is 12 times as much as a car in very nice condition.

Let the value of the nice condition car be x

Therefore, the expression will be;

= (12 × x) = 62125

12x = 62125

Divide

x = 62125 / 12

x = 5177

The value is $5177.

Learn more about car on:

brainly.com/question/25749514

#SPJ1

Answer:

1.9

Step-by-step explanation:

The surface age. The surface age is the amount of time that has passed between the start of a surface's or interface's creation and the observation or measurement. A continuous probability distribution called a normal distribution has values distributed symmetrically, primarily in an area around the mean.

To learn more about Normal distribution refer to:

https://brainly.com/question/4079902

#SPJ4

Number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162

The numbers are 8, 9 and 0

Combination is the one of the method to show the number of arrangements the from collection of objects or numbers

Here we have to form 5 digits numbers using the digits 8,9 and 0

The ten thousand's place can be only filled with 8 or 9, we cant fill the digit 0 on the ten thousands place,

In remaining places we can fill all three digits

Therefore the number of combination = 2 × 3 × 3 × 3 × 3

= 162

Hence, number of 5 digit numbers can be formed using the digits 8, 9 and 0 is 162

Learn more about combination here

brainly.com/question/28720645

#SPJ1

Answer:

|0.525| > |−0.067|

Step-by-step explanation:

Simplifying then comparing both terms |0.525| and |−0.067|, 0.525 is greater than 0.067, which means that the first term is greater than the second term.

The vertices of the image are the points J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3), respectively.

Triangles are created by three non-colinear points called vertices and the location of the image of the triangle is found by using a reflection around a line parallel to the x-axis for every point of the figure. This operation is described by the following expression:

P'(x, y) = P(x, y) - 2 · [P(x, y) - (p, k)]

Where:

If we know that J(x, y) = (3, - 5), K(x, y) = (4, - 1), L(x, y) = (0, - 3) and k = - 3, then the coordinates of the vertices of the image of the triangle are:

J'(x, y) = (3, - 5) - 2 · [(3, - 5) - (3, - 3)]

J'(x, y) = (3, - 5) - 2 · (0, - 2)

J'(x, y) = (3, - 5) + (0, 4)

J'(x, y) = (3, - 1)

K'(x, y) = (4, - 1) - 2 · [(4, - 1) - (4, - 3)]

K'(x, y) = (4, - 1) - 2 · (0, 2)

K'(x, y) = (4, - 1) + (0, - 4)

K'(x, y) = (4, - 5)

L'(x, y) = (0, - 3) - 2 · [(0, - 3) - (0, - 3)]

L'(x, y) = (0, - 3) - 2 · (0, 0)

L'(x, y) = (0, - 3) + (0, 0)

L'(x, y) = (0, - 3)

The vertices of the image of the triangle are J'(x, y) = (3, - 1), K'(x, y) = (4, - 5) and L'(x, y) = (0, - 3).

To learn more on reflections: https://brainly.com/question/17983440

#SPJ1

The graph of an inequality is a region in the Cartesian plane. To know which line is the limit of the graphical region, the inequalities are as if they were equations, that is, graph the following lines:

To do this, first clear y in each of the equations:

First equation

Second equation

Now, give x values ​​that are within the domain of each equation and replace them in each equation to find its corresponding value in y:

First equation

Second equation

Now, with the points found you can graph the lines that are the limit of the inequalities. So, you have

Finally, it only remains to paint the regions, taking into account the symbols of the inequalities

In the case of the first inequality, you can see that y "is less than" the rest of the terms, and in the second inequality, you can see that y "is greater than" the rest of the terms.

Therefore, the graph of the given system of inequalities is

Answer:

[tex]5x^{2} +12x-7[/tex]

Step-by-step explanation:

We're given : x+y+z = 4
x = -2y
z = -3y

So, we replace x = -2y and z = -3y in the original equation.

-> -2y + y + -3y = 4
-> -4y = 4
-> y = -1

Now we have the value of y, we substitute it into x and z
x = -2y = -2(-1) = 2
z = -3(-1) = 3