. Cho biểu thức A = |3x -1| - (x -7)

a) Rút gọn A b) Tính A biết x= 3 ; x= 0; x= -2 c)Tìm x biết |A| = 8

[tex]\displaystyle f(x)=\sin(3x)\\\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3(x+h))-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{\sin(3x+3h)-\sin(3x)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{3x+3h+3x}{2}\right)\sin\left(\dfrac{3x+3h-3x}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{h}\\\\f'(x)=\lim_{h\to0}\dfrac{2\cos\left(\dfrac{6x+3h}{2}\right)\sin\left(\dfrac{3h}{2}\right)}{\dfrac{3h}{2}}\cdot\dfrac{3}{2}[/tex]

[tex]\displaystyle f'(x)=\lim_{h\to0}2\cos\left(\dfrac{6x+3h}{2}\right)\cdot\dfrac{3}{2}\\\\f'(x)=\lim_{h\to0}3\cos\left(\dfrac{6x+3h}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x+3\cdot 0}{2}\right)\\\\f'(x)=3\cos\left(\dfrac{6x}{2}\right)\\\\f'(x)=3\cos(3x)[/tex]

The derivative of sin 3x using first principles is; 3cos(3x)

We want to find the derivative of sin 3x using first principles.

Step 1;

f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin3(x + h)) - sin(3x)}{h}[/tex]

Step 2; Expand the bracket to get;

f'(x) = [tex]\lim_{h \to \ 0} \frac{(sin(3x + 3h)) - sin(3x)}{h}[/tex]

Step 3: According to trigonometric identities, we know that;

sin A - sin B = [tex]2cos\frac{A + B}{2} sin\frac{A - B}{2}[/tex]

Applying that to the answer in step 2 gives;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(3x + 3h + 3x)}{2}) sin\frac{(3x + 3h - 3x)}{2})}{h}[/tex]

Step 4; Simplify the brackets to obtain;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{h}[/tex]

Step 5; Rewrite the denominator to get;

f'(x) = [tex]\lim_{h \to \ 0} \frac{2(cos\frac{(6x + 3h)}{2}) sin\frac{(3h)}{2})}{\frac{3h}{2}*\frac{2}{3}}[/tex]

Step 6; Input the limit of 0 for h to get;

f'(x) = [tex]\frac{2(cos\frac{(6x)}{2}) sin\frac{(0)}{2})}{\frac{0}{2}*\frac{2}{3}}[/tex]

⇒ f'(x) = [tex]\frac{2(cos3x)}{2/3} \frac{ 0}{{0}}[/tex]

0/0 = 1. Thus;

f'(x) = 3cos(3x)

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Answer:

See Explanation

Step-by-step explanation:

Given

Students = 24

Musical Instrument and Sport = 6

Neither = 3

Sport = 14

Required

Complete the two-way frequency table

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------------------

Does not play a musical instrument -------------------------------------3-----------

Total ---------------------------------------------------- 14 ---------------------------------------

To solve this, we'll make use of the following naming rules

A represent students that plays musical instrument; A = 6

B represent students that do not play musical instrument

C represent students that plays sport

D represent students that do not play sport; D = 3

Considering the first column [Plays a sport] and taking note of the naming rules;

[tex]A + B = 14[/tex]

Substitute 6 for A

[tex]6 + B = 14[/tex]

Solve for B

[tex]B = 14 - 6[/tex]

[tex]B = 8[/tex]

Also, given that there are 24 students in the class and 14 of them play sport; this implies that 10 do not play sport

Considering the second column [Does not play a sport]

[tex]C + D = 10[/tex]

Substitute 3 for D

[tex]C + 3 = 10[/tex]

Solve for C

[tex]C = 10 - 3[/tex]

[tex]C = 7[/tex]

Hence, the complete table is:

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------7----------

Does not play a musical instrument ---------8--------------------------3---------

Total ---------------------------------------------------- 14 -----------------------10---------

Hi

as the triangle is rectangle   isoceles, then the  three side are  :  

x , x , 6  where 6 is the  hypotenuse.  

So using pythagoras theorem we know that  :    x²+x² = 6²

                                                                                2x² = 36

                                                                                  x² = 36/2

                                                                                  x² = 18

                                                                                   x = √18

Answer:

[tex] \boxed{12 \sqrt{2} }[/tex]

Step-by-step explanation:

Isosceles triangle are those triangle which have two equal sides.

Perpendicular ( p ) = 12 inches

Base ( b ) = 12 inches

Hypotenuse ( h ) = ?

Now,Using Pythagoras theorem,

[tex] \mathsf{ {h}^{2} = {p}^{2} + {b}^{2} }[/tex]

Plug the values

[tex] \mathsf{ {h}^{2} = {12}^{2} + {12}^{2} }[/tex]

Evaluate the power

[tex] \mathsf{ {h}^{2} = 144 + 144}[/tex]

Calculate the sum

[tex] \mathsf{ {h}^{2} = 288}[/tex]

Squaring on both sides

[tex] \mathsf{h = 12 \sqrt{2} }[/tex]

Hope I helped!

Best regards!

Answer:

[tex]\boxed{n=18}[/tex]

Step-by-step explanation:

[tex]\frac{n}{6} =\frac{9}{3}[/tex]

[tex]\sf Divide \ 9 \ by \ 3.[/tex]

[tex]\frac{n}{6} =3[/tex]

[tex]\sf Multiply \ both \ sides \ by \ 6.[/tex]

[tex]\frac{n}{6} \times 6 =3 \times 6[/tex]

[tex]n=18[/tex]

Answer:

n = 18

Step-by-step explanation:

n/6 = 9/3

Simplify the right side

n/6 = 3

Multiply each side by 6

n/6 *6 = 3*6

n = 18

Answer:

If the ladder is 9 m from the wall

cos theta = 9 / 20 = .45 and theta = 63.3  angle made with floor

So the angle made with the wall is 90 - 63.3 = 26.7

Answer:

x=17

Step-by-step explanation:

Product means multiply  is means equals

2x = 34

Divide each side by2

2x/2 = 34/2

x = 17

Step-by-step explanation:

let f(x)=y

y=7x-13

y+13=7x

y+13/7=x

f-1(x)=x+13/7

Answer:

62.8 cubic units

Step-by-step explanation:

Because, The formula of volume of cylinder is Volume = square of radius multiply by its height

The volume of the cylinder round to the nearest tenth is 62.8 cubic inches

The formula for calculating the volume of a cylinder is expressed as;

V = πr²h

where

r is the radius of the cylinder

h is the height of the cylinder

Given

radius = 2 units

height = 5 units

Substitute

V = (3.14)* 2² * 5
V = 3.14 * 20
V = 62.8 cubic inches

Hence the volume of the cylinder round to the nearest tenth is 62.8 cubic inches

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Answer:

x=-3

y=3

(-3-3i)(3+5i)

Step-by-step explanation:

[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]

and we have that must equal

6-24i

3x+5y=6

5x-3y=-24 and if we work it we found out that the solutions are

x=-3 and

y=3

Answer:

Option B, 187.5 cm³

Step-by-step explanation:

Volume of the triangular prism,

base area × height

= (10×7.5/2)×5

= 187.5 cm³

Answer:

1.0625

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

cause if 72 book were divided by 18 kids they would hav all gotten 4 books each

so a is the answer cause it gives youthe answer 4

Answer: a. 8/3 divided by 6/9

Step-by-step explanation: I got this question on my test

Answer:

A

Step-by-step explanation:

Answer:

Choice A is correct.

Step-by-step explanation:

72/9 basically means: 72➗9, which makes 8.

To check, you could also do 8✖️9=72.

To find the correct answer, you need to find the fraction that has the denominator of 1, because you cancel out 9 in the fraction.

The only choice that has the denominator of 1, is choice A, so choice A is correct.

Answer:

increasing

Step-by-step explanation:

a function is increasing when y increases as x increases

Since the graph goes up as x increases, the function f(x) is increases between -2 and -1

Answer:

Option C is correct

Step-by-step explanation:

[tex]y−6=−4(x+1) \\ [/tex]

[tex]y−6=−4x−4 \times 1[/tex]

[tex] y−6=−4x−4 [/tex]

[tex]y=−4x−4+6 [/tex]

[tex]y=−4x+2[/tex]

Answer:

T(H) = -3H + 50.

Step-by-step explanation:

The constant will be 50 degrees Celsius. The surface temperature at the location will not change. The temperature decreases by 3 degrees Celsius for every kilometer going up, so the slope will be -3 degrees.

You are trying to find the temperature on the planet, and you are changing the kilometers of altitude to find the temperature. The x-variable is your independent variable, which means that you will be changing the x-variable. So, H is your x-variable while T is your y-variable.

T = -3H + 50.

To graph, we can use the Math is Fun Function Grapher and Calculator. The graph is seen below.

Hope this helps!

Answer:

4.44

Step-by-step explanation:

The tangent of B is the relation of the opposite cathetus to the lying cathetus

tg B= AC/CB= 40/9= 4.44

The value of the tangent of angle B is 4.4.

In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.

Given that, a right triangle Δ ABC, the measure of ∠C = 90°, AC = 40, BA = 41, and CB = 9. We need to find the value of the tangent of ∠B,

So, here,

The opposite side = AC and the adjacent side = CB

So, tan B = AC / CB = 40/9 = 4.4

Hence, the value of the tangent of angle B is 4.4.

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Answer:

Hey There!! The question to this is: The circumference and the area of the circle are 6.28 yards and 3.14 yd² respectively. The Circumference: This is defined as the distance around a circle.

The circumference of a circle is

P = πd............................. Equation 1

Where p = circumference of the circle, d = diameter of the circle

Area: This is the region bounded by a plane surface.

The area of a circle is

A = πd²/4 .................................. Equation 2

Where A = area of the circle, π = pie = constant.

Given: d = 2 yd.

Constant: π = 3.14

Substituting these values into equation 1 and 2 respectively.

P = 3.14(2)

P = 6.28 yard.

P = 6.28 yd

and

A = 3.14(2)²/4

A = 3.14×4/4

A = 3.14 yd²

Thus the circumference and the area of the circle are 6.28 yards and 3.14 yd² respectively.

Hope This Helped!~ ♡

ItsNobody~ ☆

Answer:

1

Step-by-step explanation:

Anything real number (except 0) to the zeroth power would be 1.

Therefore, 12 to the zeroth power would also be 1.

[tex]12^0=1[/tex]

Answer:

As you know everynumber raised to 0 is always 1 even if its x or infinity so the answer will be 12^0 will be 1

Step-by-step explanation:

any and every number raised to 0 is 1

Answer:

Step-by-step explanation:

The figure above is a rectangle

Area of a rectangle = length × width

From the question

The total length of the rectangle = 3x

The total width of the rectangle = 4x + 5

So the area of the figure is

A = 3x( 4x + 5)

Expand

We have the final answer as

Hope this helps you

Consecutive years that saw the largest increase in median mode is C. 1998-1999.

Median is the the middle term when data are arranged in ascending or descending order when we have odd number of terms and median is sum of the mean of the middle term and the next term when we have even number of terms.

According to the figure and statement given a bar graph hows the median income for families in the United States from 1993 through 2000.

We have to determine which two years saw the largest increase in median income.

If we observe the graph carefully and go through options we can conclude that 1998-1999 has the largest increase in median income which is of 1500 dollars.

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Answer:

1) 120

2) E (Z) = 12 and Variance of Z = 90

a) 5 liters

Step-by-step explanation:

1. We can find this by suing combinations.

Here n= 10 and r= 3 so n C r

= 10 C 3= 120

2. E(X) = 8 and E(Y) = 3

Z = 2X - 3Y +5

E(Z ) = 2 E (X) - 3(E)(Y) +5   ( applying property for mean)

       = 2(8) - 3(3)+ 5 = 16+5-9= 21-9= 12

V(X) = 9 and V(Y) = 6.

V(Z) = E(Z )²-  V(X) *V(Y)   (applying property for Variance for two variables )

        = 144- 54= 90

3. 55 liters contain adulterated milk in 7: 4.

So it contains 4/ 11*55= 20 liters of water

But we want to make it a ratio of 7:6

the water will be 6/13 *55= 25.38 when rounded gives 25 liters of water

So 25- 20 = 5 liters must be added to make it a ratio of 7:6

Answer:

FV(n)=42,000(1.04)^n

Step-by-step explanation:

FV=PV(1+r/n)^nt

Where

FV=future value

PV=present value

r=interest rate

n=number of periods

t=time (years)

PV=42,000

r=4%=0.04

n=1

t=n

FV(n)=p(1+r/n)^nt

=42,000(1+0.04/1)^1*n

=420000(1+0.04)^n

=42,000(1.04)^n

FV(n)=42,000(1.04)^n

Answer:

42000(1-1.04^n/-0,04)

Step-by-step explanation:

Answer:

4) A

5) E

Step-by-step explanation:

#4

[tex]\frac{x}{y}=\frac{1}{10} * \frac{z}{y}[/tex]

[tex]\frac{x}{y} =\frac{1z}{10y}[/tex]

Cross multiply the equation and you get:

[tex]10xy=zy[/tex]

Since [tex]\frac{a}{b}=\frac{c}{d}[/tex]  is the same thing as [tex]ad=bc[/tex], you can change the equation into [tex]\frac{x}{z} =\frac{y}{10y}[/tex]

Cancel out the y on the top and bottom and you get 1/10

#5

[tex]\frac{2}{3} *\frac{x}{2} =5[/tex], simplify and you get [tex]\frac{x}{3} =5[/tex] so x=15

[tex]\frac{1}{5} * 3(x)[/tex] is equal to [tex]\frac{1}{5} *3(15)[/tex] after you plug in x, and that is equal to 9

Answer:

The choose C. 18

Step-by-step explanation:

UC —> 105+82=187 —> 96+22+51=169 —> 187–169=18

I hope I helped you^_^

Answer:

[tex]\huge\boxed{(4,1)}[/tex]

Step-by-step explanation:

The point is (-1,-4)

It is reflected over y = - x, So, the coordinate will be like: ( -y , -x )

So, when it is reflected over y = -x , it becomes (4,1)

When a point is reflected, it must be reflected over a line.

The image of (-1,-4) after a reflection over the line y=-x is (4,1).

The point is given as:

[tex]\mathbf{(x,y) = (-1,-4)}[/tex]

The rule of reflection over line y = -x is:

[tex]\mathbf{(x,y) \to (-y,-x)}[/tex]

So, we have:

[tex]\mathbf{(x,y) \to (-(-4),-(-1))}[/tex]

[tex]\mathbf{(x,y) \to (4,1)}[/tex]

Hence, the image of (-1,-4) is (4,1).

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