Can someone pleaseeee help and if you’re correct i’ll give brainliest

Answer:

[tex] \displaystyle \: \frac{5}{4} [/tex]

Step-by-step explanation:

we are given a expression

we are said to solve it using L'Hôpital's Rule

recall, L'Hôpital's Rule:

[tex] \displaystyle \lim _{x \to \: c}( \frac{f(x)}{g(x)} ) = \lim _{x \to \: c} \frac{f ^{'}(x) }{ {g}^{'}(x) } [/tex]

it is to say the ' means derivative

our given expression:

[tex]\displaystyle\lim_{ x\to 2}\frac{x^2+x-6}{x^2-4}[/tex]

let's apply L'Hôpital's Rule

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2+x-6)}{ \dfrac{d}{dx} (x^2-4)}[/tex]

some formulas of derivative

[tex] \displaystyle \: \frac{d}{dx} {x}^{n} = {nx}^{n - 1} [/tex]

[tex] \displaystyle \: \frac{d}{dx} {x}^{} = 1[/tex]

[tex] \displaystyle \: \frac{d}{dx} {c}^{} = 0[/tex]

[tex] \sf \displaystyle \: \frac{d}{dx} {f}^{} (x) + {g}^{}(x) = {f}^{'} (x) + {g}^{'}(x)[/tex]

use sum derivative formula to simplify:

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2)+ \dfrac{d}{dx} (x) + \dfrac{d}{dx}( -6)}{ \dfrac{d}{dx} (x^2) + \dfrac{d}{dx} (-4)}[/tex]

simplify using exponents using exponent derivative formula:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ \dfrac{d}{dx} (x) + \dfrac{d}{dx}( -6)}{ 2x + \dfrac{d}{dx} (-4)}[/tex]

use variable derivative formula to simplify variable:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ 1+ \dfrac{d}{dx}( -6)}{ 2x + \dfrac{d}{dx} (-4)}[/tex]

use constant derivative formula to simplify derivative:

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2x+ 1+ 0}{ 2x + 0}[/tex]

simplify addition:

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

since we are approaching x to 2

we can substitute 2 for x

[tex]\displaystyle\lim_{ x\to 2}\frac{ 2.2+ 1}{ 2.2 }[/tex]

simplify multiplication:

[tex]\displaystyle\frac{ 4+ 1}{ 4}[/tex]

simplify addition:

[tex] \displaystyle \: \frac{5}{4} [/tex]

hence,

[tex]\displaystyle\lim_{ x\to 2}\frac{ \dfrac{d}{dx} (x^2+x-6)}{ \dfrac{d}{dx} (x^2-4)} = \frac{5}{4} [/tex]

Answer:

5/4 is your answer hope it helps

Answer

238π yd^2

Step-by-step explanation:

here's your solution

=> height of cylinder = 10 yd

=> radius of cylinder = 7 yd

=> formula to calculate surface area = 2πr(h + r)

=> putting the value of height and radius in formula

=> SA = 2*22/7*7(10+7)

=>. SA = 2*22*17

=> SA = 748 yd.sq

hope it helps

Answer:

376.99 cm^3 or 120π cm^3

Step-by-step explanation:

The volume of a cone is 1/3(B*h) where B is the base area and h is height.

The base of a cone is a circle.

Area of a circle=πr^2

Area of the circle=π6^2

Area of the circle=36π

Plug it into the formula for the volume:

V=1/3(36π*10)

V=1/3(360π)

V=120π

V=376.99

If this helped please consider giving brainliest.

Answer:

you just multiply the values inside the parentheses. 11 x -4 x 12, so its -44 x 12, being -528

Step-by-step explanation:

Answer:

94

Step-by-step explanation:

because it all adds up to 180 (i want brainliest)

Answer:

total surface area = 79.8 cm^2

Step-by-step explanation: open up the prism into nets, and it has a base of 3 and height of 2.6. do 1/2 times 3 times 2.6=3.9*2=7.8.  Then do 3(3*8)=72. 72+7.8=79.8. I believe this is the answer to the best of my ability, hope this helps.

Answer:

c gsudhdbxjxjsjsbhxidhsv susb

Answer:

x=  10 −  129  i−1   ≈−0.1−1.135781669i

Step-by-step explanation:

(10x^2+3) - (-2x-10) = 10x^2+2x+13

Answer:

30

Step-by-step explanation:

took the test

Answer:

24

Step-by-step explanation:

6 x 4 = 24

Answer:

57.5

Step-by-step explanation:

(180-65)/2

Answer:

Dividing decimals +×÷=

Answer:

To multiply decimals, first multiply as if there is no decimal. Next, count the number of digits after the decimal in each factor. Finally, put the same number of digits behind the decimal in the product.

Answer:

X=reference angle, 8=opposite side, and 11 is the hypoteneuse

Answer:

independent

Step-by-step explanation:

f(x+3) means that when x is x + 3, what is y? X is always the input or the independent variable while y is dependant on y.

Answer: -30x^2 -12x + 24

Step-by-step explanation:

Answer:

p+p+p = 1/2 or 3p=1/2

Step-by-step explanation:

Answer:

x = 11.8

Step-by-step explanation:

hypotenuse = 12

1 leg = 10 - 8 = 2

Formula:

a² + b² = c²

a² + 2² = 12²

a² + 4 = 144

a² = 144 - 4

a² = 140

[tex]\sqrt{a^2} =\sqrt{140}[/tex]

a = 11.8

Answer:

x = 11.8

Step-by-step explanation:

hypotenuse = 12

1 leg = 10 - 8 = 2

Formula:

a² + b² = c²

a² + 2² = 12²

a² + 4 = 144

a² = 144 - 4

a² = 140

Answer:

Step-by-step explanation:

You need to give all the fractions a common denominator so you can compare the numerators.

The least common multiple of 5, 8, 16, 4, 3 is 240.

⅖ = 96/240

⅞ = 210/240

15/16 = 225/240

¾ = 180/240

⅜ = 90/240

⅓ = 80/240

The only numerator between 96 and 210 is 180.

180/240 = ¾

⅖ < ¾ < ⅞

Answer:

0,375

Step-by-step explanation:

Answer:

0.375

Step-by-step explanation:

Answer:

Dependent variable: total distance (d)

Independent variable: number of hours (h)

Equation: d = 6h

Step-by-step explanation:

In this case given, the dependent variable, total distance (d), is dependent on the independent variable, number of hours (h). This is because, a change in the value of h leads to the change in the value of d. In order words, total distance (d) is a function of the number of hours (h).

Therefore:

Dependent variable: total distance (d)

Independent variable: number of hours (h)

Rate: 6 miles/hr

Equation: d = 6h

Answer:

Step-by-step explanation:

Answer:

Mean- 5

median- 4

Mode- 2

Answer: 20 months

explanation: You subtract 8 from 28 since 8 is the amount he had before he joined. He also said he planned on reading 1 book per month after joining the club. You want to subtract the 8 since it isn't relevant to the book club books read.

Answer:

No

Step-by-step explanation:

For this triangle to be a right triangle the following has to happen:

a^2 + b^2 = c^2

a=3, b=9, c= 12

3^2+9^2 does not equal 12^2

9+81 = 90        12^2 = 144

90 does not equal 144 so is not a right triangle

Answer:

see explanation

Step-by-step explanation:

Using converse of Pythagoras' identity

If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.

longest side = 12 , then 12² = 144

3² + 9² = 9 + 81 = 90 ≠ 144

Thus the triangle is not right.

Answer:

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

Step-by-step explanation:

Given

See attachment

Required

The fraction of yellow

From the attached image:

[tex]Yellow = 5[/tex]

[tex]Total = 30[/tex]

So, the fraction is:

[tex]Fracton = \frac{Yellow}{Total}[/tex]

[tex]Fracton = \frac{5}{30}[/tex]

Divide by 5/5

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

Answer: 4/5

Step-by-step explanation: