Solve the inequality.
3x + 5
———- <4
2

x < [?]

Answer:

[tex]\displaystyle h'(x) = \cos (x) f'(\sin x)[2 + f(\sin x)]'''[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Derivative Rule [Basic Power Rule]:

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify.

[tex]\displaystyle h(x) = [2 + f(\sin x)]''[/tex]

Step 2: Differentiate

From here, if you would like, you can take the 3rd derivative of the last piece.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Answer:

the answer to this problem is D: 180 + w-z

Answer:

... ................................

Answer:

Step-by-step explanation:

It's a lot greater. If you take 0.4% of some number and the answer is 76, you better be starting with something that is very large. The formula will make the solution automatic.

Formula

Let the number be x

0.4% x = 76

0.4% = 0.4/100

0.4 / 100 * x = 76            Multiply both sides of the equation by 100

0.4x = 76*100                Combine the right.

0.4x = 7600                  Divide by 0.4

x = 7600/0.4

x = 19000                       Which is quite a bit larger than 76

Answer:

greater than 76

Step-by-step explanation:

hope it will help goodbye

Answer:

third option: log_2  1/3

Step-by-step explanation:

change of base formula:

log_b  a= (log_x a)/(log_x b)

(log 1/3)/(log 2)

apply reverse change of base formula

2 from log 2 becomes new base, and 1/3 becomes the other number

=log_2  1/3

The original logarithmic expression which when undergoes the change of base formula gives the expression ㏒ (1/3) / ㏒ (2) is third option ㏒₂ (1/3).

Given a logarithmic expression,

㏒ (1/3) / ㏒ (2)

This expression is the result of a logarithmic expression when undergoes change of base formula.

The change of base formula is as given below.

㏒ₐ (x) = ㏒ₙ (x) / ㏒ₙ (a)

Using the same formula here,

We have the expression ㏒ (1/3) / ㏒ (2).

Here x = 1/3 and a = 2

So, the required expression is,

㏒ₐ (x) = ㏒₂ (1/3)

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Answer:

[tex] \sqrt{8} [/tex]

Step-by-step explanation:

an

irrational number can only be written in the form with never ending,non-repeatinng digits after the decimal comma

Answer:

centre = (- 6, - 1 ) , radius = 5

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Given

x² + y² + 12x + 2y + 12= 0

Collect the x- terms and the y- terms together and subtract 12 from both sides

x² + 12x + y² + 2y = - 12

Using the method of completing the square

add ( half the coefficient of the x / y coefficients )² to both sides

x² + 2(6)x + 36 + y² + 2(1)y + 1 = - 12 + 36 + 1

(x + 6)² + (y + 1)² = 25 ← in standard form

with (h, k ) = - 6, - 1 ) as centre and r = [tex]\sqrt{25}[/tex] = 5

[tex]y = \frac{x}{2} [/tex]

[tex]2x + 2y = \sqrt{180} \\ = > 2x + 2( \frac{x}{2} ) = \sqrt{180} \\ = > 2x + x = \sqrt{2 \times 2 \times 3 \times 3 \times 5} \\ = > 3x = 2 \times 3\sqrt{5} \\ = > 3x = 6 \sqrt{5} \\ = > x = \frac{6 \sqrt{5} }{3} \\ = > x = 2 \sqrt{5} [/tex]

[tex]x.y \\ = x \times \frac{x}{2} \\ = \frac{ {x}^{2} }{2} \\ = \frac{ {(2 \sqrt{5} )}^{2} }{2} \\ = \frac{4 \times 5}{2} \\ = \frac{20}{2} \\ = 10[/tex]

Answer:

10

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

b

Step-by-step explanation:

Given

2x + 2y = [tex]\sqrt{180}[/tex] = [tex]\sqrt{36(5)}[/tex] = 6[tex]\sqrt{5}[/tex]

and y = [tex]\frac{x}{2}[/tex] , then

2x + (2 × [tex]\frac{x}{2}[/tex] ) = 6[tex]\sqrt{5}[/tex]

2x + x = 6[tex]\sqrt{5}[/tex]

3x = 6[tex]\sqrt{5}[/tex] ( divide both sides by 3 )

x = 2[tex]\sqrt{5}[/tex]

and y = [tex]\frac{2\sqrt{5} }{2}[/tex] = [tex]\sqrt{5}[/tex]

Then

xy = 2[tex]\sqrt{5}[/tex] × [tex]\sqrt{5}[/tex] = 2 × 5 = 10 → b

Answer:

27/31

Step-by-step explanation:

5pink : 1yellow

4yellow : 7blue

times the first ratio by 4 so that the yellows are equal (if that makes sense)  

20pink : 4yellow : 7blue = 31 buttons

so the total is 31 buttons alltogether

and the pink and blue buttons together = 27 buttons

so 27/31 is the probability the button is pink or blue

Step-by-step explanation:

Area of Semi Circle

The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius.

Answer:

x-490=t

Step-by-step explanation:

Marlee has x money

She deposited $60 meaning adding $60 to the bank

So x+60

THen Marlee need to withdraw $550 from her bank to rent

So the equation is now

x+60-550

60-550 is -490

Thus:

x-490

(I will represent (t) as the money she has left for the equation)

Thus the equation is

x-490=t

Hope this helps!

Answer:

I believe the answer is 47. Forgive me if I'm wrong

Answer:

53.

Step-by-step explanation:

DE = CD = 6 ( as triangle ACE is isosceles so AD is the perpendicular bisector of CE.

Therefore CE = 12.

AB + BC + AC = 41 (given perimeter of ABC)

AB + BC + AE + 12 =   perimeter of ABE.

But AE = AC   ( given), so

AB + BC + AC + 12 = perimeter of ABE

Now we know that AB + BC + AC = 41 , so

41+ 12 = perimeter of ABE.

Step-by-step explanation:

in that case we can imagine a diagonal line DB that splits the quadrilateral into 2 right-angled triangles: ADB and CDB.

the area of the quadrilateral is then the sum of the areas of the 2 triangles.

the area of a right-angled triangle is

leg1 × leg2 / 2

with the legs being the sides that enclose the 90 degree angle.

so, for ADB we get

AD × AB / 2 = 3 × 11 / 2 = 33/2 = 16.5

for CDB we get

BC × CD / 2 = 7 × 9 / 2 = 63/2 = 31.5

so, in total for the area of the quadrilateral we get

16.5 + 31.5 = 48

Answer:

X=[tex]\frac{36}{85}[/tex]

Step-by-step explanation:

-[tex]-\frac{7}{8}=-\frac{1}{6}-\frac{3}{10x}[/tex]

move the contants to the right hand side

[tex]-\frac{3}{10x}=-\frac{1}{6}+\frac{7}{8}[/tex]

Add the to terms on the right

[tex]-\frac{3}{10x}=\frac{17}{24}[/tex]

Cross multiply

72=170x

Swap sides of the equation

170x=72

Divide by 170 to both sides

x=[tex]\frac{36}{85}[/tex]

This is the simplest form.

The solution of the linear equation −7/8 = −1/6 − (3/10)x in the form of a mixed fraction number will be 2 ¹³/₃₆.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The linear equation is given below.

−7/8 = −1/6 − (3/10)x

Simplify the equation, then we have

−7/8 = −1/6 − (3/10)x

(3/10)x = −1/6 + 7/8

(3/10)x = 17/24

x = 85/36

x = 2 ¹³/₃₆

The arrangement of the direct condition −7/8 = −1/6 − (3/10)x as a blended part number will be 2 ¹³/₃₆.

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[tex]\dfrac 17 x^2 + 1 = \dfrac 37 x\\\\\implies x^2 +7 =3x~~~;[\text{Multiply both sides by 7}]\\\\\implies x^2 -3x +7 =0\\\\\text{Apply quadratic formula}~ x = \dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}.\\\\\text{In this case ,}~ a =1, b= -3 , c =7\\\\x = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(7}}{2(1)}\\\\\implies x= \dfrac{3 \pm \sqrt{-19}}{2}\\\\\implies x =\dfrac{ 3 \pm i\sqrt{19}}2\\\\\\\text{Smaller value of x } =\dfrac{ 3 -i\sqrt{19}}2\\\\\text{Larger value of x } =\dfrac{ 3 +i\sqrt{19}}2[/tex]

Answer: Hence, by ASA ( Angle side Angle) Rule of congruency two triangles;

Angle ADE = CDF Hence proved.

Step-by-step explanation:Diagram of two triangles are given such that side ED = FD and <AED = < CFD = 90

To Find: TO prove <ADE = <CDF

Solution; In figure ; we can see that <EDA and <FDC are vertically opposite angles and hence are equal.

=> <EDA = <FDC |Vertically opposite angles

<DEA = <CFD = 90 |Given

Also, ED = FD |Given

Hence, by ASA (Angle Side Angle)

Rule of congruency two triangles; <ADE = <CDF

Hence Proved.

5x = 10 + 3x

5x - 3x = 10

2x = 10

x = 5

To check

5(5) = 10 + 3(5)

25 = 10 + 15

25 = 25

Answer:

x = 5

Step-by-step explanation:

Number = x

5x = 10 + 3x  

2x = 10

x = 5

Answer:

1/15

Step-by-step explanation:

Answer:

Step-by-step explanation:

1/15

Answer:

0

Step-by-step explanation:

positive numbers are always bigger than negative numbers

Answer:

9x-5y=2======>9x-5y=2===>(+)7y=-28=>y=-4=>(1)3x-4(-4)=10=>x+16=20=>x=4

3x-4y=10(1)=>(×-3)-9x+12y=-30=>(+)

Answer:

5

Step-by-step explanation:

[tex]1\frac{7}{8}\div\frac{3}{8}[/tex]

[tex]=\frac{15}{8}\div \frac{3}{8}[/tex]

[tex]=\frac{15\times \:8}{8\times \:3}[/tex]

[tex]=\frac{15}{3}[/tex]

[tex]=5[/tex]

The quotient is 5.

[tex]\large\underline{\sf{Solution-}}[/tex]

[tex]\textsf{Given that:}\\[/tex]

[tex] \sf1 \dfrac{7}{8} \div \dfrac{3}{8} \\ [/tex]

[tex] \sf \longmapsto \: \dfrac{7 \times 8}{8} \div \frac{3}{8} \\ [/tex]

[tex] \sf \longmapsto \: \dfrac{15}{8} \div \dfrac{3}{8} \\ [/tex]

[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} }{ \dfrac{3}{8} } \\ [/tex]

[tex] \sf \longmapsto \: \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{ \dfrac{ \cancel \green3}{ \cancel \red8} \times \frac{ \cancel \red8}{ \cancel \green3} } \\ [/tex]

[tex]\sf \longmapsto \dfrac{ \dfrac{15}{8} \times \frac{8}{3} }{1} \\ [/tex]

[tex]\sf \longmapsto \: \dfrac{15}{ \cancel \red8} \times \dfrac{ \cancel \red8}{3} \\ [/tex]

[tex]\sf \longmapsto \: \dfrac{15}{3} \\ [/tex]

[tex]\sf\longmapsto \:\dfrac{15÷3}{3÷3}\\[/tex]

[tex]\sf\longmapsto \:\dfrac{5}{1}\\[/tex]

[tex]\sf\longmapsto \:\boxed{5} \: Answer.\\[/tex]

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Answer:

An improper fraction

Step-by-step explanation:

In improper fraction is when the numerator (top number) is greater than or equal to the denominator (bottom number)

The range would be needed to label the subjects correctly is 000-210.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

Given that a researcher is comparing the effectiveness of three devices.

There are 210 people who snore participating in the experiment

The researcher will randomly place the participants into three equally sized treatment groups suitable for comparison.

We need to find the range which would be needed to label the subjects correctly.

210 people are participating in experiment

We need to label subjects from 001 to 210

Since there is no value in using 000 to indicate someone.

Hence, 000–210 is the range would be needed to label the subjects correctly.

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Answer:

11m + 4n

Step-by-step explanation:

when two numbers with the same variable are added together or subtracted the result is just the numbers added or subtracted. So you can add 6m and 5m to get 11m. and you can subtract 3n from 7n to get 4n

11m + 4n

Answer:

(x+1)x(x+7)x(3x-4)

Step-by-step explanation:

[tex]\text{Given that,}\\\\ab = 8 ~ \text{and}~ a^2 +b^2 = 35\\\\\text{Now,}\\\\(a-b)^2 = a^2 +b^2 -2ab\\\\\implies (a-b)^2 =35 - 2 (8) \\\\\implies (a-b)^2 = 19\\\\\implies a-b = \pm\sqrt{19}\\\\\text{Case 1:}\\\\(a-b)^3 = (a-b)^2(a-b)\\\\\implies (a-b)^3 = 19 \left(\sqrt{19}\right)\\\\\text{Case 2:}\\\\(a-b)^3 = (a-b)^2(a-b)\\\\\implies (a-b)^3 = -19 \left(\sqrt{19}\right)[/tex]