evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5

For large enough x, exponential functions like 2ˣ will always dominate a polynomial of any degree. This is to say the denominator will always be larger than the numerator (again, for sufficiently large x). So the limit in this case would be 0. (I'll leave a link in comments to a variety of answers regarding this detail.)

But if you've been introduced to L'Hopital's rule: we have

[tex]\displaystyle \lim_{x\to\infty}\frac{5x^3+10}{6\times2^x-1} = \lim_{x\to\infty}\frac{15x^2}{6\ln(2)\times2^x} = \lim_{x\to\infty}\frac{30x}{6\ln^2(2)\times2^x} = \lim_{x\to\infty}\frac{30}{6\ln^3(2)\times2^x} = \frac1\infty = 0[/tex]

9514 1404 393

Answer:

  7.56 cm

Step-by-step explanation:

The volume is given by the formula ...

  V = 1/3b²h . . . . where b is the base edge length, and h is the height.

Here we have V = 144 cm³, and b = h. Filling in these values and solving for h, we get ...

  144 cm³ = 1/3h³

  432 cm³ = h³

  h = ∛432 cm ≈ 7.55953 cm

The height of the pyramid is about 7.56 cm.

Answer:

[tex]7.56cm[/tex]

Step-by-step explanation:

Given that,

base length = Height

so,

[tex]volume = \frac{1}{3} {b}^{2} h \\ [/tex]

We can also write this as( according to this question)

[tex]v = \frac{1}{3} \times {b}^{2} \times b \\ v = \frac{ {b}^{3} }{3} [/tex]

let's solve

[tex]v = \frac{ {b}^{3} }{3} \\ 144 = \frac{ {b}^{3} }{3} \\ 144 \times 3 = {b}^{3} \\43 2 = {b}^{3} \\ \sqrt[3]{432} = b \\ b = 7.55[/tex]

[tex]base = height = 7.55cm \\ [/tex]

= 7.56cm

Answer:

where is the rest of the question??

Step-by-step explanation:

Answer:

x=21

Step-by-step explanation:

45=2x+3

Subtract 3 from both sides of the equation.

42=2x

Divide 2 from both sides of the equation.

21=x

Hope this helps!

Answer:

x=21°

Step-by-step explanation:

Angle A = Angle B

Angle A = 45°

2x+3 =45°

To work out what x is, you would have to do inverse operations.

45-3=42°

2x=42°

42÷2=21° (We divide by 2 because, in algebra, whenever a number is next to a letter, it means times, so then we have to do the opposite and divide).

So, x=21°

Hope this helps :)

Answer:

The answer is 12

Step-by-step explanation:

You see its because.

Answer:

?=12

Step-by-step explanation:

Using the Thalès's theorem:

[tex]\dfrac{6}{6+4}=\dfrac{?}{20} \\\\?*10=6*20\ (cross\ products)\\\\?=\dfrac{6*20}{10} \ dividing\ by\ 10\\\\?=12[/tex]

Answer:

[tex](x-4)^2+(y)^2=9[/tex]

Step-by-step explanation:

The general format for the equation of a circle is the following:

[tex](x-n)^2+(y-m)^2=a[/tex]

This circle will have a radius of ([tex]\sqrt{a}[/tex]), moreover, this circle will have its center at point [tex](n,m)[/tex]. Please note that its center is shifted (n) units to the right of the origin, and (m) units up. Apply this knowledge to the given problem.

The circle in the given problem has its center at (4, 0). Therefore the following can be stated,

[tex]n=4\\\\m =0[/tex]

Since one knows the center of the circle is at (4, 0), and (the circle has (4, 3) on its circumference, the distance between the coordinates will produce the radius of the circle. The following formula can be used to find the distance between two points on a number line,

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

Where ([tex](x_1,y_1)[/tex]) and ([tex](x_2,y_2)[/tex]) are the points one is trying to find the distance between. Substitute the given points into the formula and solve for the distance between them.

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

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

Simplify,

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

[tex]D=\sqrt{(0)^2+(3)^2}[/tex]

[tex]D=\sqrt{0+9}[/tex]

[tex]D=\sqrt{9}[/tex]

[tex]D=3[/tex]

The parameter (a) is equal to ([tex]D^2[/tex]) are per the format of the equation, thus one must do the following to find the value of (a):

[tex]a = D^2[/tex]

[tex]a=3^3[/tex]

[tex]a = 9[/tex]

Substitute all of the information into the general formula for the equation of a circle, then simplify,

[tex](x-n)^2+(y-m)^2=a[/tex]

[tex](x-4)^2+(y-0)^2=9[/tex]

[tex](x-4)^2+(y)^2=9[/tex]

Let the cost of a lamp = x

6 lamps would cost 6x

He bought 3 lamps at 3x plus Thad 950 left.

3 lamps plus the 950

Would be the same amount as 6 lamps:

Set up an equation and solve for x:

3x + 950 = 6x

Subtract 3x from both sides:

950 = 3x

Divide both sides by 3:

X = 316.67

Each lamp was $316.67

Multiply the price of a lamp by 6:

316.67 x 6 = 1900

He had $1900

Answer: $1900

Step-by-step explanation:

Mr Lim had enough money to buy 6 similar lamps. However he only bought 3 such lamps. That means he had only spent half of his money (6-3=3).

So, if he take money remaining with him = x = $950

Amount of money he first had = 2x =$950×2 = $1900

Answer:

11

Step-by-step explanation:

On a fair six-sided die, there is a [tex]\frac{1}{6}[/tex] chance of rolling each number. Therefore, for each of the rolls, the number 6 has a [tex]\frac{1}{6}[/tex] chance of being rolled. This can be read as for every 6 rolls, one 6 should appear.

Since the die is being rolled 66 times, we have the following proportion:

[tex]\frac{1}{6}=\frac{x}{66}[/tex], where [tex]x[/tex] is the theoretical number of times a roll of "6" occurs.

Multiply both sides by 66:

[tex]x=\frac{1}{6}\cdot 66=\boxed{11}[/tex]

Answer:

8

Step-by-step explanation:

(16^3/2)^1/2

We know a^b^c = a^(b*c)

16 ^(3/2*1/2)

16 ^3/4

Rewriting 16 as 2^4

2^4^3/4

2^(4*3/4)

2^3

8

Answer:

The answer is 7.5

Answer:

Step-by-step explanation:

let the height of the room(h) = x

Length(l) = 3*x = 3x

length = 2 * breadth

breadth(b) = length /2 = 3x/2

Cost of whitewashing the 4  walls = ₹ 7200

Area of 4 walls = 7200 ÷ 50 = 144 m²   ------(I)

Area of walls = 2lh + 2bh

                      = 2*3x*x + 2  *[tex]\frac{3x}{2}[/tex] * x

                       = 6x² + 3x²

                        = 9x²

9x² = 144    {From (I)}

x²  = 144/9

x²  = 16

x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]

x = 4 m

height = 4 m

length = 3*4 = 12m

Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]

Area of floor = l*b

                    = 12 * 6

                    = 72 m²

Cost of carpeting the floor = 72 * 325 = ₹ 23400

Step-by-step explanation:

[tex]cd + db = a \\ b(c + d) = a \\ \frac{b(c + a)}{a + b} \\ b = \frac{a}{c + d} [/tex]

Answer:

The other answer is correct

Step-by-step explanation:

Answer:

A. 45%

Step-by-step explanation:

34/75=45 = 45%

Answer:

6 questions

Step-by-step explanation:

Take the total number of questions and divide by the number of days

150/28

5.357142858

You would need to round up to make sure that the packet is completed in time

6 questions

Answer:

-2/5

Step-by-step explanation:

Well, a y-intercept is a the point on a graph where the x value equals 0, because the point sits exactly on the y-axis. In this case, the y-intercept would be (0, -9).

Answer:

(0,-9)

Step-by-step explanation:

The y intercept is where the graph crosses the y axis ( where x =0)

The y intercept is

-9

(0,-9)

Answer:

a = 50

b = 50

c = 80

d = 50

e = 130

Step-by-step explanation:

e = 180 - (25 + 25)   {Angle sum property & It is an isosceles triangle}

    = 180 - 50 = 130

a +e = 180  {Linear pair}

a + 130 = 180

a = 180 - 130

a = 50

d =a   {Vertically opposite angles}

d = 50

c = 180 -(50+ 50 )     {Angle sum property & It is an isosceles triangle}

c = 180 -100

c = 80

a+b + c = 180  {Straight angles}

50 + b + 80 = 180

  b + 130 = 180

          b = 180 - 130

          b = 50

Answer:

62

Step-by-step explanation:

Of means multiply and is means equals

.03 * n = 1.86

Divide each side by .03

.03n/.03 = 1.86/.03

n =62

Answer:

27, 18

Step-by-step explanation:

Here's why

Answer:

2.6

Step-by-step explanation:

We'll use the Pythagoras theorem to solve this, which states that in a right angle triangle:

h^2 = a^2 + b^2

4^2 = 3^2 +b^2

16= 9 +b^2

16-9= b^2

7= b^2

(take square root in both sides)

b= 2.65

round to nearest 10th = 2.6

answer by Gauthmath

Answer:

Missing side is 2.6

3^2 + x^2 = 4^2

9 + x^2 = 16

-9            -9

x^2 = 7

([tex]\sqrt{x}[/tex])^2 = [tex]\sqrt{7}[/tex]

x = 7

Find the approximation o the square root of 7 in fractions then carry out the long division.

Or

Approx. is 2 3/5 which equals 2 6/10 which equals 2.6

Answer:

Step-by-step explanation:

-2a(a - d) + 2a(2a - 3d)

(-2a * a) + (-d * -2a) + (2a * 2a) + (2a * -3d)

-2a^2 + 2ad + 4a^2 - 6ad

(4a^2 - 2a^2) + (2ad - 6ad)

2a^2 - 4ad

---The above expression is simplified, though not fully. The below expression is fully simplified.

2a(a - 2d)

Hope this helps!

Answer:

C. 30

Step-by-step explanation:

We have a list of names that need to be sorted in a specific order. For this, we will use a permutation. This can be found on a scientific calculator, however, I'll be using the equation.

[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]

n = total number of objects

r = number of objects selected

In this instance, n will equal 6 since we have 6 different names to choose from and r will equal 2 since we are picking two names. Enter the values into the equation and evaluate.

[tex]_6P_2=\frac{6!}{(6-2)!}=30[/tex]

Therefore, there are 30 possible two-part names.

Answer:

Nicholas can order up to 3 toppings.

Step-by-step explanation:

Solve for the tip:

15% of the total cost = 15% × $7.50

Convert percentage into a decimal:

0.15 × 7.50 = 1.125

Variable x = number of toppings

Set up an equation:

7.50 + 1.125 + 1.25x = 13

Combine like terms:

8.625 + 1.25x = 13

1.25x = 4.375

x = 3.5

Since it is impossible to order "half" of a topping (0.5), Nicholas can only order up to 3 toppings.

Answer:

Mr Mohapi is selling cheaper chairs

Step-by-step explanation:

Find the cost per chair from both prices by dividing the total price by the number of chairs:

22500/500

= 45

9600/200

= 48

So, Mr Mohapi is selling at a price of $45 per chair and Mr Shuma is selling at a price of $48 per chair.

Since 45 is smaller than 48, Mr Mohapi's chairs are a better deal.

Mr Mohapi is selling cheaper chairs.

Answer:

Part A: A = 8

B = 20

C = 28

D = 35  

E = 37

F = 72

G = 43

H = 57

I = 200

Part B: 18.5%

Part C:

D = People who do not like Orange Juice

B = People who do not like Apple Juice

I use the values of B and D because these are the values that represent dislike for that juice, and also because adding them together creates a value for not liking either juice.

D = 35

B = 20

So there is a greater dislike for Orange Juice.

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

APR means annual percentage rate.

To convert the daily rate to an APR, multiply the daily rate by the number of days in a year

365 days = 1 year

0.02192% x 365 = 8.0008%

To round off to the nearest percent, look at the first number after the decimal, if it is less than 5, add zero to the units term, If it is equal or greater than 5, add 1 to the units term.

The tenth digit is 0, so the number would be rounded off to 8%

Answer:

Option B is the right answer.

Step-by-step explanation:

x ^2 -7x+12 = (x-4)(x-3)

so, if we put x=3 or 4 than it will be undefined. hope u understand.