8c + 2(6 - 3c) - 7
How do I simplify this pls help

The conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule,

The limit expression is given as:

[tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex]

The limit of the expression cannot be solved without l'hopital's rule, because a direct substitution of ∞ for x would result in the following expression ∞/∞

i.e.

[tex]\lim_{x \to \infty} \frac{6 (2^{\infty}) - 1}{5(\infty)^2+ 10} = \frac{\infty}{\infty}[/tex]

So, the best way is to apply the l'hopital's rule.

This is done as follows:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \lim_{x \to \infty} \frac{f'(x)}{g'(x)}[/tex]

When the numerator and the denominator are differentiated, we have:

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln(2)\cdot 2^{x + 1}}{10x}[/tex]

Further, differentiate

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{x + 1}}{10}[/tex]

Now, we can substitute [tex]\infty[/tex] for x

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{3\ln^2(2)\cdot 2^{\infty + 1}}{10}[/tex]

Evaluate the numerator

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \frac{\infty}{10}[/tex]

Evaluate the quotient

[tex]\lim_{x \to \infty} \frac{f(x)}{g(x)} = \infty[/tex]

Hence, the conclusion is that the expression [tex]\lim_{x \to \infty} \frac{6 (2^x) - 1}{5x^2+ 10}[/tex] cannot be solved  without the l'hopital's rule

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Answer:

B

Step-by-step explanation:

1+2+3+4+6+8+12+24=60

60/24=5/2

so,B is the answer

The sum of all the reciprocals of the factors of 24 is 5/2.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.

The reciprocals of all the factors of 24 are;

1/1, 1/2, 1/3, 1/4, 1/6, 1/8, 1/12, 1/24

The sum of all the factors of 24:

1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

Take LCM of the fractions:

1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

= (24 + 12 + 8 + 6 + 4 + 3 + 2 + 1) / 24

1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

= 60 / 24

Hence, the fraction:

1/1 + 1/2 + 1/3 + 1/4 + 1/6 + 1/8 + 1/12 + 1/24

= 5/2

Therefore, 5/2 is the sum of all the reciprocals of the factors of 24.

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Answer:

1

Step-by-step explanation:

(1-x)/x=0

or, 1-x=0

or, -x=-1

or, x=1

Answer:

F(x) = 0 when x=1

Step-by-step explanation:

We need the numerator to equal zero

1-x = 0

Add x to each side

1-x+x = 0+x

1 =x

The denominator cannot equal zero( The denominator does not equal zero when x =1)

F(x) = 0 when x=1

Answer:

-20940

Step-by-step explanation:

5 x 512 - 312 x 75 - 115

According to BODMAS ,

2575 - 23400 - 115

= -2090

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

[tex] \frac{7}{5} \times \frac{5}{12} - \frac{3}{12} \times \frac{7}{5} - \frac{1}{15} = \frac{7}{5} ( \frac{5}{12} - \frac{3}{12} ) - \frac{1}{15} = \frac{7}{5} \times \frac{1}{6} - \frac{1}{15} = \frac{7}{30} - \frac{2}{30} = \frac{5}{30} = \frac{1}{6} [/tex]

Answer:I’m not sure

Step-by-step explanation: try and use the scientific demos

Answer:

-1

Step-by-step explanation:

im pretty sure its right

sry if it not good luck!!

The required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

The formula for calculating the volume of the conical lid's is expressed as

[tex]V = \frac{1}{3} \pi r^2h[/tex] where:

r is the radius

h is the height

v is the volume

Given the following

r = x

If the conical lid’s height is 2 centimeters less than the radius, x, then;

h = x - 2

V = 25π cm³

Substitute the given values into the formula as shown:

[tex]25 \pi = \frac{1}{3} \pi x^2 (x-2)\\3(25) = x^2(x-2)\\Expand\\75=x^3-2x^2\\Swap\\x^3-2x^2 = 75\\Equate \ to \ zero\\x^3-2x^2 - 75 = 0[/tex]

Hence the required expression that can be used to find the radius of the conical lid's with a height 2 centimeters less than the radius, x, of its base  is x³-2x²-75 = 0

Answer: (3b+2)(b+2)

Step-by-step explanation:

Answer:

V = 7234.56 km^3

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

V = 4/3 (3.14) (12)^3

V = 7234.56 km^3

Answer:

7234, 56 km³

Step-by-step explanation:

π×R³×4/3=3.14×1728×4/3=7234, 56 km³

Answer:

6.8=6 8/5

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hope it help

Answer:

∠ T = 82°

Step-by-step explanation:

In a Isosceles trapezoid, any lower base angle is supplementary to any upper base angle , so

∠ T + ∠ P = 180°

∠ T + 98° = 180° ( subtract 98° from both sides )

∠ T = 82°

Answer:

Step-by-step explanation:

When we take an average of something, we have to add up all the data on the somethings and then divide by the number of somethings we have. Ed takes 5 tests, and we have scores for them; we also have his current average. What we don't know for sure are 2 of the 5 test scores, but we have enough to determine what they are.

If one test has a score of x, and the other test is 3 points less than that, the score on that last test is x - 3. Putting all of that together into an average problem:

[tex]\frac{87+85+87+x+(x-3)}{5}=90[/tex] and simplfiying a bit:

[tex]\frac{256+2x}{5}=90[/tex]. Multiply both sides by 5 to get

256 + 2x = 450; subtract 256 from both sides to get

2x = 194 and divide by 2:

x = 97

The one test score was a 97 and the other one, which was 3 less than that, was a 94.

Answer:

56

Step-by-step explanation:

Answer:

56 hours

Step-by-step explanation:

I divided 384 dollars by 3w hours and then was Sue made 12 an hour. Then I tried mukyiplong different times until I discovered 12×56=672. So, 56 hours

Answer: [tex]9\sqrt{2}[/tex]

Step-by-step explanation:

Use the Pythagorean Theorem:

[tex]9^{2} +9^{2} =x^{2}\\x=\sqrt{9^{2} +9^{2}} =\sqrt{2(9)^{2} } =9\sqrt{2}[/tex]

Answer:

n-32

Step-by-step explanation:

edmentum

Answer:

It's actually: None of these.

Think about it: In this case we have an inequality, of x ≤ 0.

This basically means, that x can be less than OR equal to 0.

But 0 is neither negative or positive, so we can eliminate the following answer choices:

- all positive integers

- all negative real numbers

- all positive real numbers

- all negative integers

And we are left with "None of these"

Let me know if this helps!

Option B is correct. None of these options is the right answer since zero is neither an integer nor a real number

Before we can decide which option is correct, first we must integers and real numbers are.

Given the set of numbers {x | x ≤ 0}. The set of numbers in the set will be all integers less than zero including zero (zero is not an integer)

Hence the set of numbers are not all negative integers since 0 is not a negative integer.

They are not all positive integers rather they are mostly negative integers

They are not all positive and negative real values because zero is not a real integer.

Hence we can conclude that None of the options is correct.

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Answer: Choice D. [tex]\angle A \cong \angle E[/tex]

Explanation: Since AB is parallel to ED, this means the alternate interior angles A and E are congruent as marked below.

Angle A is congruent to angle E by alternate interior angle theorem. Therefore, option D is the correct answer.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

Given that, triangle CAB is similar to triangle CED and AB is parallel to ED.

From the given figure, AB=7 miles, DC=16 ft, EC=12 ft and DE=21 ft.

Here, in figure,

∠A ≅ ∠E  (Alternate interior angles)

∠B ≅ ∠D  (Alternate interior angles)

∠ACB ≅ ∠DCE  (Vertically opposite angles are congruent)

Therefore, option D is the correct answer.

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Answer:

The latest time Ruth's family can start their tour in order to make it to dinner on time is 2:50 P.M

Step-by-step

Change:

7h10= 430 mins

1 hour and 25 minutes= 85 mins

2 hours and 5 mintues= 125 mins

- Total time Ruth wants to do before his dinner reservations:

85+ 125+ 50= 260 (mins)

- The latest time Ruth's family can start their tour in order to make it to dinner on time:

430- 260= 170 (mins)

Change: 170 mins= 2 hours and 50 minutes

Good luck!

Answer:

Yes, the ratio is still 5:4.

Step-by-step explanation:

If you have a class of 5 males and 4 females, both numbers can be multiplied to get an even bigger class but the same ratio.

For example:

5 x 5 = 25 males

4 x 5 = 20 females

The amount of males to females is 25:20 when simplified (divided by 5) gets you back to your ratio of 5:4. You also can't go under this because the two don't have a way to get simplified without going into decimals. And I don't think decimals are very good with the number of students.

Have a good day! :)

Answer:

circumference = 25.12 yards

area = 50.24 yards squared or yd^2

Step-by-step explanation:

circumference = pi * d

3.14 * 8 =

25.12

area = pi* r^2

r = 1/2 of d = 4

area = pi * 16

3.14 * 16 =

50.24

Answer:

Area: 50.24yds^2            Circumference: 25.12yds

Step-by-step explanation:

Area: The formula for area of a circle is a = πr^2.

The radius (r) of the circle is 4yds because it is half the length of the diameter. The equation would like like this:

A = (3.14)(4)^2

A = (3.14)(16)

A = 50.24yds

Circumference: The formula for circumference is 2πr. We already know all of the variables so we can plug them in.

C = 2(3.14)(4)

C = 25.12yds

Hope this helps

Using Pythagorean thereon

[tex]\\ \Large\sf\longmapsto P^2=H^2-B^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=9^2-6^2[/tex]

[tex]\\ \Large\sf\longmapsto P^2=81-36[/tex]

[tex]\\ \Large\sf\longmapsto P^2=45[/tex]

[tex]\\ \Large\sf\longmapsto P=\sqrt{45}[/tex]

[tex]\\ \Large\sf\longmapsto P=6.3ft[/tex]

Answer:

x= 2/2

Step-by-step explanation:

Answer I think the answer is 9 if you round off to the nearest ones,in this case you are rounding off to 9 which will still be 9 because 4 is less than 5.

I hope this helps

Step-by-step explanation:

First, a half plane can be defined as one side of a line, e.g. x < y-3.

1: True. A solution to two half planes is where the two half planes intersect. If they never intersect, then there literally cannot be a solution.

2: False. Take, for example, y=x and y=x+1. These two lines are parallel because in the equation y=mx+b, m represents the slope, and in these two lines, x is multiplied by 1, so both lines have the same slope and are therefore parallel. Then, take two boundary planes -- y > x and y>x+1. If we graph this out (see picture), the planes clearly intersect when y>x+1. The solution is where the planes intersect, so there is a solution area

Answer:

I believe the answer would be 48.6 milliliters

Step-by-step explanation:

54 * 0.9 = 48.6