Find the value of f(2).
y = f(x)

Answer:

17 terms

Step-by-step explanation:

Let the number of terms be n which will add up to 425.

So, 425=(n/2)*(2+(n-1)*3). 850=n*(3n-1), n=17 or - 50/3 but n can't be negative, so the answer is n=17

Answer:

24 days

Step-by-step explanation:

Find LCM, or least common multiple

List out all the multiples of 3:

3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...

Now 8:

8, 16, 24, 32, 40, 48, 56, 63, 72, 80, 88...

LCM is 24, because they both hit 24 first.

If my answer is incorrect, pls correct me!

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-Chetan K

Explanation:

This is because 24 is the LCM (lowest common multiple) of 8 and 3.

We multiply the given values to get 8*3 = 24. This trick only works if the original two numbers have no common factors other than 1.

We can verify that 24 is indeed the LCM by listing out the multiples

We see that 24 is found in both lists and it's the smallest such item. The next common item would be 48, which is a multiple of 24. In other words, every 24 days, your two practices will line up on the same day.

Answer:

It should be 490000.0005

Step-by-step explanation:

4.9*10^5+.0005

10^5=100000

4.9*100000=490000

490000+.0005=490000.0005

Answer:

Step-by-step explanation:

[tex]10^{-5}=\frac{1}{10^{5}}=\frac{1}{100,000}=0.00001\\\\[/tex]

4.9* 10^-5 +0.0005 = 4.9 * 0.00001  + 0.0005

                               = 0.000049 + 0.0005

                              =  0.000549

Answer:

(4x + 5)²

4x² + 20x + 25

Step-by-step explanation:

Step 1: Factor 16x² + 40x + 25

(4x + __)(4x + __)

What multiplies to 25 and adds up to 40 with 4 multiplied as coefficient?

(4x + 5)(4x + 5) or (4x + 5)²

Step 2: Factor perfect square trinomial

36x² - 4x + 16 --> 4(9x² - x + 4) No

16x² - 8x + 36 --> 4(4x² - 2x + 9) No

25x² +9x + 4 --> 25x² + 9x + 4 No

4x² + 20x + 25 --> (2x + 5)(2x + 5) or (2x + 5)² Yes

Answer:

(4x + 5)(4x + 5).

4x^2 + 20x + 25.

Step-by-step explanation:

16x^2 + 40x + 25

= (4x + 5)(4x + 5)

= (4x + 5)^2.

36x^2 − 4x + 16: To be a perfect square trinomial, the factors would have to be (6x + 4) or (6x - 4). Since the value of b is only -4, this is NOT a perfect square trinomial.

16x^2 − 8x + 36: To be a perfect square, factors would have to be (4x + 6) or (4x - 6). Since the value of b is only -4, this is NOT a perfect square.

25x^2 + 9x + 4: To be a perfect square, factors have to be (5x + 2) or (5x - 2). Since b is positive, factors would be (5x + 2)(5x + 2) = 25x^2 + 20x + 4. 20x is not equal to 9x, so this is NOT a perfect square.

4x^2 + 20x + 25: Perfect square would have to have factors (2x + 5) or (2x - 5). b is positive, so factors are (2x + 5)(2x + 5) = 4x^2 + 10x + 10x + 25 = 4x^2 + 20x + 25. This IS a perfect square!

Hope this helps!

Answer:

47

Step-by-step explanation:

first of all simply the ones with powers and you will get 156-9*5-64 then multiply and you will get 156-45-64 simplify and the answer is 47

Answer:

x + 2(2x-4) = 10

Step-by-step explanation:

Here in this question, we want to select which is the correct answer if we substitute for the value of y in the second equation, using the first.

In the first, we have;

y = 2x -4

Now, let’s input this value of y into the second equation.

By direct substitution, what we have is the following;

x + 2y = 10

—-> x + 2(2x -4) = 10

Answer:

the equilibrium expected growth rate is 6.65%

Step by step Explanation:

We were given stock sold per share of $32.50

Dividend per share =$1.25

Required Return rate = 10.5%

Then we can calculate Percentage of Dividend for share as;

dividend of br. 1.25 per share at the end of the year (D1=br.1.25)

= 1.25×100= 125

Let the dividend percentage = y

stock sold per share × y= 125

125= 32.50y

y = 125/32.50

y= 3.85

y= 3.85*100%

Then the Dividend percentage = 3.85%

Growth rate=(required rate of return -Dividend percentage)

= 10.5 - 3.85 = 6.65

Therefore, the equilibrium expected growth rate is 6.65%

if you convert it all into one hour, Team B clearly worked at a faster pace.

Answer:

[tex]team \: a \: \\ 8in \: number \: with \: in \: 2 \: hours \\ so \: in \: 1 \: hour \: \frac{8}{2} = 4 \: in \: number \\ \\ team \: b \\ 5 \: in \: 1hour \\ so \: \: team \: b \: work \: in \: fast \\ thank \: you[/tex]

You would know that

[tex]\displaystyle\lim_{x\to\pm1}f(x)=1[/tex]

It follows from the sandwich/squeeze theorem: for instance,

[tex]x^4 \le f(x) \le x^2 \implies \displaystyle\lim_{x\to-1}x^4 \le \lim_{x\to-1}f(x) \le \lim_{x\to-1}x^2 \implies 1 \le \lim_{x\to-1}f(x) \le 1 \\\\ \implies \lim_{x\to-1}f(x)=1[/tex]

Answer: Yo-yo

Concept:

In order to find the Cost Per Toy, we need to do the operation Cost / Toy.

Solve:

Slinky = Cost / Toy = 9 / 5 = $1.8 per toy

Wind-up robot = Cost / Toy = 16 / 8 = $2 per toy

Yo-yo = Cost / Toy = 15 / 6 = $2.5 per toy

Emoji beach ball = Cost / Toy = 3 / 2 = $1.5 per toy

Hope this helps!! :)

Please let me know if you have any questions

Answer:

0.577

Step-by-step explanation:

inv. sin (0.5) = 30

tan (30) = 0.577

The value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Tan[tex](Sin^{-1}(1/2))[/tex]

[ Sin 30° = 1/2 ]

= Tan([tex]sin^{-1}sin30)[/tex])

= Tan 30°

= 0.58

Thus,

0.58 is the value of Tan[tex](Sin^{-1}(1/2))[/tex] is 0.58.

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Answer:

18 square centimeters

Step-by-step explanation:

Notice that if e is the midpoint of the side CB, and angle [tex]\angle x = 45^o[/tex], then this rectangle is in fact two squares of side 3 cm put together. therefore, side CD has a length of 6 cm, and as a result, the area of the figure is given by the product base times height = 6 x 3 = 18 [tex]cm^2[/tex]

Answer:

(B)  18

Step-by-step explanation:

The angle x is 45 degrees.  Since it is bisecting a 90 degree angle, the angle on the other side is 45 degrees.

90 - 45 = 45

Since AB is 3, DC is 3.  Since the right triangle DC is 45-90-45, the other side, CE, will also be 3.  Since CE is half of the side of the rectangle, multiply it by 2 to get 6.  The sides of the rectangle are 3 and 6.  Use the formula for area of a rectangle to solve.

A = lw

A = (6)(3)

A = 18

The answer is B.

Answer:

1.34%

Step-by-step explanation:

First of all subtract the 2 values

9.84−9.71=0.13

use this value and find the percentage from the original price which was 9.71

0.13

-------  ⋅100

9.71

percentage increase is

1.34%

Answer:

I think its average

Step-by-step explanation:

not sure:)

Answer: it is average

Step-by-step explanation: just done It

Answer:

1:55 pm

Step-by-step explanation:

So, you arrive at 4: 15 pm in Orlando after a 2 hr and 20 minute flight from Houston.  So, lets start with the easy part: let's subtract the 2 hrs part.  

2 hrs earlier from 4:15 pm is 2:15 pm.

Then, you have to subtract the 20 minutes.  Well, it's quite obvious that if you left at 2:00 pm, that would be a total of 2 hrs and 15 minutes.  Just subtract the 15 minutes from the 2:15 pm.  However, it's 20 minutes, not 15, so you have to still subtract that last five minutes.  

So, 2:00 pm minus 5 minutes would equal 1:55 pm.

Answer:

The simplified answer of the given equation is -57.

Step-by-step explanation:

For this problem, we are given values for our variables.

k = -1

n = -4

So, let's plug these numbers into our expression so we can easily solve it.

-(-1)² - (4(-1) - 6(-4)) + 9(-4)

Simplify your parentheses.

-(-1)² - (-4 + 24) - 36

-(-1)² - 20 - 36

Now, simplify your exponents.

-1 - 20 - 36

Combine -1 and -20.

-21 - 36

Now, subtract -21 from 36.

-57

Answer:

-18

)())()()()()()()( ;)

Answer:  see proof below

Step-by-step explanation:

Use the following when solving the proof...

Double Angle Identity: cos2A = 1 - 2sin²B

Pythagorean Identity: cos²A + sin²A = 1

note that A can be replaced with B

Proof from LHS → RHS

Given:                            cos²A + sin²A · cos2B

Double Angle Identity: cos²A + sin²A(1 - 2sin²B)

Distribute:                      cos²A + sin²A - 2sin²A·sin²B

Pythagorean Identity:                        1 - 2sin²A·sin²B

Pythagorean Identity:   cos²B + sin²B - 2sin²A·sin²B

Factor:                           cos²A + sin²B(1 - 2sin²A)

Double Angle Identity: cos²B + sin²B · cos2A

cos²B + sin²B · cos2A = cos²B + sin²B · cos2A  [tex]\checkmark[/tex]

Answer:

9/5 < m < 9/4

Step-by-step explanation:

The conditions are:

If we take a point like (-1,0)

Slope (m) = change in y ÷ change in x = [tex]\frac{0 - 9}{-1 - 4} = \frac{-9}{-5}[/tex] = 9/5

This point satisfies the conditions above since;

From the choices given;

we can say that:

m > 9/5 and m < 9/4

And can be expressed as;

9/5 < m < 9/4

Answer:

Initially 18,500 students

Every 1 year

increase by a factor 1.03

Step-by-step explanation:

The missing information is selected from the given options from the drop down menu. The correct answers are : Initially 18,500 students enroll at the university. Every 1 years the number of students who enroll at the university increases by a factor 1.03.

F(t) = 18,500 * (1.03)^t

Answer:

0.15(5,-1)

Step-by-step explanation:

[tex]\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}[/tex]  ⇒ [tex]\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)[/tex] ⇒  [tex]\frac{4}{26} (5,-1)[/tex]  ⇒  [tex]0.15(5,-1)[/tex]

The best approximation of the projection  IS ( 5,-1).

Vector A ,

                 (2,6) in terms of vectors is represented by = 2 i +6 j

Vector B,

                 (5,-1) in terms of vectors is represented by =5 i - 1 j

Projection of Vector A on Vector B

       [tex]\frac{(A . B)(B)}{IBI^{2} } \\[/tex] =  [tex]\frac{[(2i + 6j).(5i - j)]( 5i - j)}{\sqrt{5^{2} }+ (-1)^{2} }[/tex]

[tex]= \frac{(2)(5) +(6)(-1)}{\sqrt{5^{2} }+(-1)^{2} }[/tex]

= ( 5 ,-1 ) ⇒ 0.15 (5,-1)

Therefore, The best approximation of the projection  IS ( 5,-1) .

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Answer:

D) 972

Step-by-step explanation:

2160*9/20 = 19440/20

= 972

Answer:

s = 15 in (positive square root of 225)

Step-by-step explanation:

A = 225 in²

side of square mosaic is sq. root of 225 = 15 in

therefore the side (s) = 15 in

Answer:

Look at photo

Step-by-step explanation:

Answer:

perimeter = 24

Step-by-step explanation:

it´s a regular hexagon = 6 sides

perimeter = 6(4x) = 24x

Answer:

186,250 rs

Step-by-step explanation:

So

149m is the whole space

0.2m is one tile space

250 rs = 0.2 tiles (so 250=1)

so if there is

Answer:

y = x + 2

Step-by-step explanation:

Slope-Intercept Form: y = mx + b

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Step 1: Find slope m

m = (1 - 6)/(-1 - 4)

m = -5/-5

m = 1

y = x + b

Step 2: Find y-int b

y = x + b

1 = -1 + b

b = 2

Step 3: Rewrite equation

y = x + 2

Answer:

The quadratic formula: (-b+-sqrtb^2-4ac)/2a

Plugging in the values of a=1, b=9, and c=10, the roots of the equation are: -7.7 and -1.3.

So, the first option is correct.

Let me know if this helps!

Answer:

[tex]\frac{1}{256}[/tex]

Step-by-step explanation:

(¼)²=√x

√x=1/16

x=(1/16)²

x= 1/256

Answer:

Hello,

Step-by-step explanation:

Formula used (a+b)^2=a²+2ab+b²

[tex](12-9i)^2=3^2*(4-3i)^2\\\\=9*(16-9-24i)\\\\=9*(7-24i)\\\\=63-216i\\[/tex]