Prove the following

Hi

Your question would be better with  "  Could you help me please ? " at the end. Quite sure your mum told you that some time in the past.

I will show you how to solve but you will do the calculus. Math is all about rules, methods and training.  If you dont practice, you will never progress.

rule  :  you must know by heart your remarkable identities.

Here we have  :   ( 4x-3)² - (2x+5)² = 0

It 's of the  form  A² -B² =  ( A+B) ( A-B)  

here A is  :   4x-3   and  B is  2x+5  

Now let's apply rule  :   ( 4x-3)² - (2x+5)² =  ( (4x-3) +( 2x+5) )  ( (4x-3) - (2x+5)

                                                                  =    ( 4x-3 +2x+5 )  ( 4x-3 -2x-5 )

                                                                  =     ( 6x +2)  ( 2x-8)  

so :  ( 4x-3)² - (2x+5)² =  ( 6x +2)  ( 2x-8)  

so  ( 4x-3)² - (2x+5)²  = 0   means  :  ( 6x +2)  ( 2x-8)    = 0

Rule A*B = 0 if A = 0  or B = 0

A  is  6x+2     and B = 2x-8

So I let you now work  :  

You have to solve :   6x+2 = 0

and   2x-8 = 0

Solutions of this two calculus will be the solutions of  ( 4x-3)² - (2x+5)²  = 0  

Have fun !                                    

Answer:

B

Step-by-step explanation:

Looking at the graph, we can see that g(x) is a compressed version of f(x) in the x direction but stretched in the y direction. We know that it is compressed because the values of g(x) are inside of f(x) in the x direction, and that it is streched because the values of g(x) are higher than the values of f(x) in the y direction.

Next, we want to figure out how much g(x) is a compression/stretch of x.

In the y direction, at x=1, y=1. At x=3, y=9. The ratio between the y values is 9/1 = 9, so in the y direction, the graph is streched by 9.

A stretch in the y direction can be represented by kf(x), with k representing how much the graph is stretched. In our example, k=9, so we have

kf(x) = 9f(x) = 9(x²) = 9x². This is equal to (3x)² = 9x², or B

In the x direction,  at x=1, y=1. At x=3, y=9. The ratio between the x values is 3/1 = 3, so in the x direction, the graph is compressed by 3.

f(kx) represents a compression by a factor of k in the x direction, and k =3 here, so we have

f(kx) = f(3x) = (3x)² = 9x² = B

Answer:

total surface area of cube is 6 * area of one side

therefore area of one side is given 64cm^2

thickness is also given 5cm .

TSA is 64*5 = 320cm^2

hope it is helpful

Answer:

288 cm²

Step-by-step explanation:

The square base has an area of 64 cm².

That means the sides of the square base measure 8 cm.

The perimeter of the base is P = 4 * 8 cm = 32 cm.

The lateral area is Ph = 32 cm * 5 cm = 160 cm².

The two bases are congruent, and their combined area is 2 * 64 cm² = 128 cm².

The total surface area equals the sum of the lateral area and the area of the bases.

SA = 160 cm² + 128 cm²

SA = 288 cm²

Answer:

[tex] - 786 + - 923 = - 923 + - 786 \\ - 786 - 923 = - 923 - 786 \\ - 1709 = - 1709 \\ thank \: you[/tex]

To find the slope of a line, we can use the following formula:

[tex] \displaystyle \large{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]

m-term stands for slope or gradient. The formula is useful whenever you want to find a slope of two points.

Let these be the following:

[tex] \displaystyle \large{(x_1,y_1) = (0, - 11)} \\ \displaystyle \large{(x_2,y_2) = (8, - 8)}[/tex]

Substitute the points in formula:

[tex] \displaystyle \large{m = \frac{ - 8 -( - 11)}{ 8 - 0} }[/tex]

Negative multiply negative always come out as positive.

[tex] \displaystyle \large{m = \frac{ - 8 + 11}{ 8 - 0} } \\ \displaystyle \large{m = \frac{ 3}{ 8 } } \\ [/tex]

Since m stands for slope, we can say that:

[tex] \displaystyle \large \boxed{ \tt{slope = \frac{3}{8} }}[/tex]

Answer:

Step-by-step explanation:

(x₁  ,y₁) = (0,-11)     & (x₂ , y₂) =   (8,-8)

Slope = [tex]\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\[/tex]

          [tex]=\dfrac{-8-[-11]}{8-0}\\\\=\dfrac{-8+11}{8}\\\\=\dfrac{3}{8}[/tex]

Answer:

[tex]f(x) = {3}^{x} \\ f(x +1) = {3}^{(x + 1)} \\ f(x) + f(x + 1) \\ = {3}^{x} + {3}^{(x + 1)} \\ = {(1 \times 3}^{x} ) +( 3 \times {3}^{x} ) \\ By \: taking \: {3}^{x} \: common, \: we \: get \\ (1 + 3) \times {3}^{x} \\ = 4 \times {3}^{x} \\ = 4f(x)[/tex]

Answer:

semoga jawapan ini dapat membantu

Answer:

-60,-11,-3,5.5,11,31

Answer:

the value of cos 30degree is √3\2 ....

Answer:

B

Step-by-step explanation:

This is a linear function that continues both ways infinitely.

Answer:

B

Step-by-step explanation:

The domain of the function is all real numbers.

Answer:

Hello again!  The answer to this one is C

Step-by-step explanation:

As I said before, a fraction is out of 100, like a percent.  Divide 100 by the denominator (in this case, 4).  This gives you 75%.  However, to convert this into a decimal, we need to multiply it by 0.01.  This gives you 0.75.

Answer:

.75

Step-by-step explanation:

there are more that one way to represent numbers..

Roman numerals are quite obsolete, but fractions, decimals and percent's

are the ones that you mainly learn about in a math class...

numbers of one type can be converted to any other...

in this case you want to convert a FRACTION 3/4 to change to a DECIMAL version.... NOTE: at the end I will also show the PERCENT VERSION...

the fraction to decimal conversion is done by "LONG DIVISION"

   __.75__

4 | 3.0

    2.8

    -----

       20

       20

        ---

        0

Note  as a percent it is 75%

Answer:

2πr

Step-by-step explanation:

the Circumference of great circle =

2×π×r or 2πr

Answer:

15.07352941

Step-by-step explanation:

in short 15.07

Answer:

(8-w)-10

so -w-2

if w is a variable... sorry this answer is just for reference

Step-by-step explanation:

Answer:

4w + 6

Step-by-step explanation:

Let width = w

Length = w + 3

Perimeter = 2*length + 2* width

                = 2(w +3) + 2w           {Use distributive property}

                = 2w + 2*3 + 2w

                =  2w + 6 + 2w              {Combine like terms}

                = 4w + 6

Answer: 17

Step-by-step explanation:

since there are two minuses, you change them to a plus and add, ending up with 5+12 to get 17

Answer:

29° C

Step-by-step explanation:

-17(-12)

=29

Hope this helps

Answer:

29C

Step-by-step explanation:

Above zero temperature = +17C

Below zero temperature = -12C

Difference= 17 - (-12C)

                 = 17 + 12 C

                 =29C

Hi ;-)

[tex]3w+6w-19=-91\\\\3w+6w=-91+19\\\\9w=-72 \ \ /:9\\\\\huge\boxed{x=-8}[/tex]

Answer:

Step-by-step explanation:

Given:

Isolate w, add 19 to both sides:

Simplify both sides:

Divide both sides by 9:

Answer:

n = 7

Step-by-step explanation:

-2(-6n-3)-8=82,

12n + 6 - 8 = 82,

12n -2 = 82,

12n = 84,

n = 7

Answer:

n=7

Step-by-step explanation:

-2(-6n-3)-8=82

Add 8 to both sides

-2(-6n-3)-8+8=82+8

Simplify

-2(-6n-3)=90

Divided both sides by -2

-2(-6 -3) = 90

2 -2

Simply

-6n-3=-45

Add 3 to both sides

-6n-3+3=-45+3

Divided both side by -6

-6n = -42

-6. -6

Simply

n=7

Answer:

no

Step-by-step explanation:

x - 6 = -18

x = -18 + 6

x = -12 ← the end

Answer: B)

[tex]\boxed{\underline{\bf \: ANSWER}}[/tex]

[tex] \sf \: x - 6 = - 18 [/tex]

Add 6 to both sides.

[tex] \sf \: x=-18+6 [/tex]

Add -18 and 6 to get -12.

[tex] \boxed{\underline{ \bf \: x=-12 }}[/tex]

=> The correct answer will be Option B - x = - 12

_______

Hope it helps.

╰☆☆RainbowSalt2222☆☆╮

Answer:

1000

[tex]1000 \sqrt{6} [/tex]

Step-by-step explanation:

Given: Dimensions of each triangular piece used in umbrella.

Reasoning: By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and

s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2

We know that umbrella is made of 10 triangular pieces of cloth of two different colours.

Let us calculate the area of one triangle.

For each triangle, a = b = 50 cm, c = 20 cm

Semi Perimeter

s = (a + b + c)/2

= (50 + 50 + 20)/2

= 120/2

= 60 cm

By using Heron’s formula,

Area of triangle = √s(s - a)(s - b)(s - c)

= √s(s - a)(s - b)(s - c)

= √60(60 - 50)(60 - 50)(60 - 20)

= √60 × 10 × 10 × 40

= 200√6 cm2

Therefore,

Area of 10 triangular pieces = 10 × 200√6 cm2 = 2000√6 cm2

Hence, cloth required for each colour = (Total area of the cloth)/2

= (2000√6)/2

= 1000√6 cm2

Thus, 1000√6 cm2 cloth of each colour is required for the umbrella

Answer:

[tex] \sqrt{24} = 4.9[/tex]

[tex] \sqrt{102} = 10.1[/tex]

positive integers = x

4.9 < x < 10.1

x = 5, 6, 7, 8, 9, 10

sum = 5 + 6 + 7 + 8 + 9 + 10

= 45

Answer:

2

Step-by-step explanation:

Answer:

HJ = 17

IK = 30

Step-by-step explanation:

to find HI :

GH : 2

HI : ?

IJ : 12

GI : 7

HI = GI - GH

HI = 7- 2

HI = 5

HI + IJ = HJ

5 + 12 = HJ

17 = HJ

To find IK

IJ = ?

JK = 12

KL = ?

IL = 49

JL = 31

To find IK we need to find KL and IJ

KL = JL - JK

KL = 31 - 12

KL = 19

IJ = IL - (JK + KL)

IJ = 49 - 31

IJ = 18

IK = IJ + JK

IK = 18 + 12

IK = 30

Answer:

Step-by-step explanation:

300÷6x²÷3.14=2.6539278131634819533

Answer:

3

Step-by-step explanation:

7b + 2 = 23

Subtract 2 from both sides,

=> 7b = 21

=> b = 21/7

=> b = 3