Practising
and Applying
1. Write each radial in simplified form.
a) √48
b) √ 1000

So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.

Here we want to get the limit:

[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1}[/tex]

First, we can try to evaluate directly in x = 2 and see if it does not generate any problem, we will get:

[tex]\lim_{x \to \ 2} \frac{x^2 + 3x + 1}{x^3 + x + 1} = \frac{2^2 + 3*2 + 1}{2^3 + 2 + 1} = 1[/tex]

So by direct evaluation we can see that the limit when x tends to 2 is equal to 1.

If you want to learn more about limits:

https://brainly.com/question/2264127

#SPJ1

Esta estrategia se puede aplicar sumando  15,75 + 0,25, –1,8 + –0,20, 3,5 + 12,5 y 2,62 + 7,38 antes de sumar el tercer número dado en cada caso.

La estrategia propuesta consiste en sumar dos números decimales que den como resultado un número entero antes de sumar el tercer número decima. Por ejemplo si teneos  1,4 + 0,6  + 1,2, se debe sumar primero 1,4 + 0,6 lo que es igual a 2 antes de sumar el 1,2.

Este estrategia es beneficiosa porque facilita sumar números decimales.

Aprenda más sobre números decimales en: https://brainly.com/question/24620232

#SPJ1

Answer: x^{3}(2x+9)

Step-by-step explanation:

Eliminate redundant parentheses:

(3x^{4}+3x^{3}+5x^{2})-1(x^{4}-6x^{3}+5x^{2})

3x^{4}+3x^{3}+5x^{2}-1(x^{4}-6x^{3}+5x^{2})

Distribute:

^{4}+3x^{3}+5x^{2}{-1(x^{4}-6x^{3}+5x^{2})}

3x^{4}+3x^{3}+5x^{2}

Combine like terms UNTIL YOU FIND ONE FACTOR

Answer:

5/12a + 1/3b

Step-by-step explanation:

2/3a + 1/6b + (-1/6a) + 3/18b + (-1/12a)

[2/3a + (-1/6a) + (-1/12a)] + [3/18b + 1/6b]

5/12a + 1/3b

Answer:

17 / 4

Step-by-step explanation:

To find the right sum, you need to....

Step #1: Find Δx

Step #2: Find [tex]x_k[/tex]

Step #3 Make the right-hand sum equation: ∑[tex]^n_{k=1}f(x_k)[/tex]Δx

Step #4: Solve the right-hand sum equation

Answer:

following the (x,y) coordinate system,

(0,4) ; (1,1) ; (2,-2)

Step-by-step explanation:

youre given the value of the x variable in the table, so all you need to do is substitute x and follow pedmas!! hope this helps<3

Answer:

Step-by-step explanation:

the graph is down below

The next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

From this, we can deduce that her next step is to use her ruler to join the given point to the point where the arcs intersect

Thus, the next step she should take is to use her ruler to join the given point to the point where the arcs intersect.

Learn more about construction here:

https://brainly.com/question/27164219

#SPJ1

Answer:

Step-by-step explanation:

true

Answer:

False because the account isn't full

The measure of the angle rst is [tex]105^{o}[/tex].

According to the theorem, a quadrilateral can be inscribed by a circle if and only if its opposing angles are supplementary. A quadrilateral that may be encircled by a circle is known as a cyclic quadrilateral.

The sum opposite angles of a quadrilateral is 180 degrees.

We can see that the angles rst and angle tqr are opposite angles of quadrilateral qrst, hence supplementary angles.

Therefore,

<RST + <TQR = 180

5x+15 + 4x+ 3 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162

x = 162/9

x = 18

Since <RST = 5x+15

<RST = 5(18) + 15

<RST = 90 + 15

<RST = 105degrees

Learn more about cyclic quadrilateral at: https://brainly.com/question/14352697

#SPJ4

Answer:

4c=12

c=3

Step-by-step explanation:

Since 4c's make up one 12, it is safe to assume that 4c=12. This results in c=3 once simplified.

Answer:

4c = 12.

Step-by-step explanation:

There are 4 of the same objects marked c.

Answer: D

Step-by-step explanation: a^2+b^2=c^2

so use y value for b2 and 6 square root 3 as a and check with it.

See my explanation in the pic

The sampling method used is classified as Systematic.

Samples may be classified as:

In this problem, every 4th element is taken, which is a systematic sample with k = 4.

More can be learned about sampling at https://brainly.com/question/25122507

#SPJ1

Answer:

22480.000

Step-by-step explanation:

Cost of 1km²=6000

So,

Cost of 4.08km²=6000x4.08

=22480.000

I don't know what nearest $100 means tho maybe nearest hundredth but I'm not sure.

The total cost nearest 100 is = $22500.

Modern mathematics heavily relies on the concept of area. The area is the quantity that shows the amount of space occupied by a two-dimensional figure or shape or planar lamina in the plane. Simply put, the area is the amount of cloth or other material with the specified thickness needed to build a model of the form or the quantity of paint required to cover the shape's surface in a single layer, or "coat," of paint.

Cost of 1km2 = 6000

So,

Cost of 4.08km2 = 6000 * 4.08

                              =  22480.000

Rounding off to 100;

Cost = 22500.00

Hence,

Total cost of the land nearest 100 is = $22500.

To know more about Area visit:

https://brainly.com/question/27683633

#SPJ4

Answer:

(x-y)(x-y)(x-y)= x²-yx+x²-yx-yx+y²-yx+y²

2x²-4yx+2y²

(y-x)(y-x)= y²-yx-yx+x²

y²-2yx+x²

-(y²-2yx+x²) = -y²+2yx-x²

2x²-4yx+2y²-y²+2yx-x²= x²-2yx+y²

or

(x−y−1)(x−y)² ≡ x³−x²+3xy²+2xy−y³−y²−3yx³

Answer:

Let m be the number of muffins.

a) 4m <= 30

b) m <= 7.5, so the maximum number of muffins to buy is 7.

c) $4 × 7 = $28, so $2 will be left over.

Answer:

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

Step-by-step explanation:

The new coordinates can be found using the transformation function for figures rotated 90° about the origin.

Rotation 90° (counterclockwise) about the origin can be described by ...

  (x, y) ⇒ (-y, x)

The end points of the diagonal that comes closest to the origin will be transformed to ...

  (2, 2) ⇒ (-2, 2)

  (-5, 6) ⇒ (-6, -5)

The other diagonal end points will be on the same horizontal and vertical lines as these.

  (2, 6) ⇒ (-6, 2)

  (-5, 2) ⇒ (-2, -5)

The solutions to the given quadratic equation are as follows:

x = 1.10, x = 10.9.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

For this problem, the equation in item D is:

-x² + 12x - 12 = 0

x² - 12x + 12 = 0

Hence the coefficients are:

a = 1, b = -12, c = 12.

Then the solutions to the equation are found as follows:

The solutions are:

x = 1.10, x = 10.9.

More can be learned about quadratic functions at https://brainly.com/question/24737967

#SPJ1

The option that can be used to support the idea that the set of polynomials is closed under multiplication is; Option C: (10x^(0.5) - 8)(5x^(0.5) + 4)

When multiplying polynomials, the variables' exponents are added, according to the rules of exponents. It is pertinent to note that the exponents in polynomials are whole numbers. The whole numbers are closed under addition, which guarantees that the new exponents will be whole numbers. Thus, we can also say that the polynomials are closed under multiplication.

Now, looking at the options, we can say that option C is the only polynomial that is closed under multiplication because its' variables and exponents will not change;

(10x^(0.5) - 8)(5x^(0.5) + 4)

The output will retain the same thing.

Read more about closure property at; https://brainly.com/question/19340450

#SPJ1

The total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

Elsa + 3(her friends) ≤ Total

145 + 3(110) ≤ x

145 + 330 < x

475 ≤ x

Therefore, the total amount spent by Elsa and her friends must not exceed RM 475; 475 ≤ x

Learn more about inequality:

https://brainly.com/question/11613554

#SPJ1

Answer:

The length of the diagonal of a rectangle is 10m

Step-by-step explanation:

There is a visual below,

The diagonal of a rectangle has formed 2 right triangles.

This diagonal is called hypotenuse side length of a triangle

To find the hypotenuse, we can use the Pythagorean Theorem

a² + b² = c²

we are given the length of a and b, where a = 6 and b = 8

(6)² + (8)² = c²

36 + 64 = c²

100 = c²

√100 = c

10 = c

Learn more about the Pythagorean Theorem here: https://brainly.com/question/343682

The expression, written as the sine of an angle is sin (7π/10)

From the question, we are to write the given expression as the sine or cosine of an angle.

The given expression is

sin(π/5)cos(π/2) + sin(π/2)cos(π/5)

Let A = π/5

and

B = π/2

Thus, we get

sinA cosB + sinB cosA

From the given information, we have that

sin(A ± B) = sinA cos B ± cosA sinB

∴ sin(A + B) = sinA cos B + cosA sinB

Now,

sinA cosB + sinB cosA = sinA cosB + cosA sin B

∴ sinA cosB + sinB cosA = sin (A + B)

Put A = π/5

and

B = π/2

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (π/5 + π/2)

sinπ/5 cosπ/2 + sinπ/2 cosπ/5 = sin (7π/10)

Hence, the expression, written as the sine of an angle is sin (7π/10)

Learn more on Trigonometry identities here: https://brainly.com/question/12994136

#SPJ1

The terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.

In this case, we have to expand a power binomial by means of the Pascal's triangle, which offers a useful and quick resource to expand expressions of this kind, now we proceed to present the result of this approach:

(3 · a + 4 · b)⁸ = 6 561 · a⁸ + 69 984 · a⁷ · b + 326 592 · a⁶ · b² + 870 912 · a⁵ · b³ + 1 451 520 · a⁴ · b⁴ + 1 548 288 · a³ · b⁵ + 1 032 192 · a² · b⁶ + 393 216 · a · b⁷ + 65 536 · b⁸

Such combinations of products between variables a and b are also supported by the theorem of the binomial. Finally, the terms b⁸, a⁶ · b², a⁴ · b⁴, a⁷ · b and a⁸ are part of the expansion of (3 · a + 4 · b)⁸.

To learn more on binomials: https://brainly.com/question/11379135

#SPJ1

The simplified form of the expression is given as 83x/56 -(97/105)

Alphabets are usually represented as unknown variables in a equation or expression.

Given the following expression shown below

6/7 x -2/3 + 3/5 + 5/8 x -6/7

Collect the like terms to have;

6/7 x+ 5/8 x  -2/3 + 3/5 -6/7

Simplify

48x+35x/56 - (70-63 + 90)/105

The final expression will be given as;

83x/56 -(97/105)

Hence the simplified form of the expression is given as 83x/56 -(97/105)

Learn more on expression simplification here: https://brainly.com/question/723406

#SPJ1

by breaking it down u can write it as

15p^-4/_20p^-12 * q^-6/q^-3

15/-20=-3/4

using law of indices we have

-3/4p^-4+12 * q^-6+3

-3/4p^8q^-3

the answer is the first own

Answer:

The answer is 3

Step-by-step explanation:

25% of 2.40 equals 0.6

so 3 will be the total price and he will get 0.6 profit.

William bought canned goods at 2.40 per can. he wants to increase the price per can so that he makes a 25% profit,  the selling price per can be, 3.00

The percentage is a mathematical term, which means a number or a ratio which is represented in fractions of 100. We use the '%' symbol to represent the percentage.

Formula for percentage;

Percentage = (present quantity/whole quantity)×100

Given that,

William bought canned goods at 2.40

He wants to increase the price per can so that he makes a 25% profit

The selling price per can be =?​

Percentage = Amount he wants to increase/previous amount×100

25 = x/2.40×100

x = 0.60

new selling price = 2.40+0.60

                             = 3.00

Therefore, The new selling price is 3.00 per can

To know more about Percentage check:

https://brainly.in/question/33820520

#SPJ2

Answer:

y = 3x + 4

Step-by-step explanation:

Substituting into point-slope form and converting to slope-intercept form,

[tex]y+5=3(x+3) \\ \\ y+5=3x+9 \\ \\ \boxed{y=3x+4}[/tex]

Answer:

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

Triangle with:

As per definition of midsegment, it is connecting the midpoints of two sides and its length is half the length of the opposite side of the triangle.

So we have:

Solve it for n:

Correct choice is D.

Answer:

2.72 / 16 x 28 = $4.76

Step-by-step explanation:

Since they give you $2.72 for 16 ounces you put in:

2.72 / 16 x 28 = $___

Then you just solve it to get $4.76:

2.72 / 16 = 0.17

0.17 x 28 = 4.76