Find total number of solutions of [x]^2= x + 2 {x}, where (.) and {.} denotes the greatest integer
function and fractional part.

Answer:

Step-by-step explanation:

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Answer:

2×10⁵ is the same as 200,000 and 3×10⁴ is the same as 30000 so this simply means you have to multiply the 2 figures and give the answer in standard form

200,000×30000

6000000000

which will be written as

6×10⁹

I hope this helps

Answer:

b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex]

Step-by-step explanation:

Given

6b² + 12b - 14 = 0 ( add 14 to both sides )

6b² + 12b = 14

To complete the square the coefficient of the b² term must be 1

Factor out 6 from the 2 terms on the left side

6(b² + 2b) = 14

To complete the square

add/subtract ( half the coefficient of the b- term)² to b² + 2b

6(b² + 2(1)b + 1 - 1) = 14

6(b + 1)² + 6(- 1) = 14

6(b + 1)² - 6 = 14 ( add 6 to both sides )

6(b + 1)² = 20 ( divide both sides by 6 )

(b + 1)² = [tex]\frac{20}{6}[/tex] = [tex]\frac{10}{3}[/tex] ( take the square root of both sides )

b + 1 = ± [tex]\sqrt{\frac{10}{3} }[/tex] ( subtract 1 from both sides )

b = - 1 ± [tex]\sqrt{\frac{10}{3} }[/tex] ← exact solution

Answer:

x = -1 ± √(10/3) = (-3 ± √30)/3

Step-by-step explanation:

Steps to complete this process:

ax² + bx + c = 0

=> (ax² + bx + c)/a = 0/a

=> x² + (b/a)x + (c/a) = 0

=> x² + 2x(b/2a) + (c/a) = 0

Now it seems somewhat like a square (x² + 2x(b/2a), in order to complete:

=> x² + 2(b/2a) + (b/2a)² + (c/a) = (b/2a)²

=> (x + b/2a)² + (c/a) = b²/4a²

=> (x + b/2a)² = (b² - 4ac)/4a²

So on & you can derive quadratic formula.

In the given question:

=> 6b² + 12b - 14 = 0

=> (6b² + 12b - 14)/6 = 0/6

=> b² + 2b - 7/3 = 0

=> b² + 2(1)b + 1² - (7/3) = 1²

=> (b + 1)² - (7/3) = 1

=> (b + 1)² = 10/3 or 30/9

=> b + 1 = ±√(30/9)

=> b = -1 ± √(30)/3

=> b = (-3 ± √30)/3

*this is the rationalized form(rational-denominator), exact answer:

=> (b + 1)² - (7/3) = 1

=> (b + 1) = ± √(10/3)

=> b = -1 ± √(10/3)

You can take LCM, and even rationalize it to (-3 ± √30)/3.

Step-by-step explanation:

maybe I am wrong sorry for that but try to understand it

have a great day

Answer:

6+10×4=40+6=46 number

Answer:

(a)Seven-tenth=

7divde by 10 =0.7

(b) 4 tenth

4 divide by 10=.4

(c) 2 ones

2 multiply by1 =2

Answer:

Option A.

Step-by-step explanation:

An absolute value function can be written in two ways, as the absolute value sign does not allow negative values.

[tex]|x-5|=x-5[/tex]

or

[tex]|x-5|=-(x-5)=-x+5[/tex]

The only options with these equations are A. and D.

D. can be eliminated as the inequalities given for the piecewise function do not match f(x)

To see it visually, you can try graphing it on a calculator or internet graphing service.

4x + 4 = 14 + 14

4x + 4 = 28

4x = 24

x = 6

Verification : 3×6 - 4 = 14

4×6+4 = 28

.........

Answer:

(0,2)

Step-by-step explanation:

Hi there!

[tex]f(x) = 2*3^x[/tex]

The y-intercept of any function occurs when x=0.

To find the y-intercept, solve for f(0):

[tex]f(0) = 2*3^0\\f(0) = 2*1\\f(0) = 2[/tex]

Therefore, the y-intercept is 2 and occurs at (0,2).

I hope this helps!

[tex]\\ \rm\Rrightarrow sin\Theta=\dfrac{Perpendicular}{Hypotenuse}[/tex]

[tex]\\ \rm\Rrightarrow sinF=\dfrac{GE}{FG}[/tex]

[tex]\\ \rm\Rrightarrow sinF=\dfrac{a}{c}[/tex]

Step-by-step explanation:

[tex]thank \: you[/tex]

Answer:

(x−2)2+(y+1)2=100

Explanation:

the standard form of the equation of a circle is  

2 2 ( x − a ) 2 + ( y − b ) 2 = r 2 2 2  where  ( a , b )  are the coordinates of the center and r is  the radius  to find the center we require the  midpoint of the  2 given points  center  = [ 1 2 ( − 4+ 8 ) , 1 2 ( 7 − 9 ) ]  center = ( 2 , − 1 )  the radius is the distance from the center to either of  the 2 given points  calculate the radius using the  distance formula ∙  d = √ ( x2 − x 1 ) 2 + ( y 2 − y 1 ) 2  let  ( x 1 , y 1) = ( 2 , -1 )  and  ( x 2 , y 2 ) = ( − 4 , 7 ) r = √ = √ ( − 4 − 2 ) 2 + ( 7 + 1 ) 2 = √ 36 + 64 = 10 ⇒ ( x − 2 ) 2 + ( y − ( − 1 ) ) 2 = 10 2 ⇒ ( x − 2 )2 + ( y + 1 ) 2 = 100 ←  equation of circle

Answer:

7.2 cm

Step-by-step explanation:

The adjacent interior angles of a rhombus must be supplementary.

Let ABCD be the rhombus whose area is 40 cm².

Let the diagonals AC and BD intersect at O.

If s is the side, one-half diagonal = s× sin(25) and the other is s× sin(65) = s × cos(25)

Area of a rhombus = ½× (a×b)²× sin(ø)]

side length, a = b

Area of rhombus = ½× s² × sin(25)cos(25)

40 cm² = ½ × s² × sin(25)cos(25)

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)]

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°

sin(a)cos(b) = 2[sin(x+y)+sin(x-y)] Since x = y = 25°sin(a)cos(b) = 2[sin(x+y)]

》40 cm² = ½ × s² × 2sin(50)

》40 cm² = s² × sin(50)

[tex] {s}^{2} = \frac{40}{ \sin(50) } \\ s = \sqrt{ \frac{40}{ \sin(50) } } [/tex]

s = 7.2260841106 cm

Therefore, the length of the side of a rhombus, s is 7.2 cm

Answer: Box A is the first 2

Box C is the 3 option

Step-by-step explanation:

Answer:

84%

Step-by-step explanation:

you cross multiply 42/50 by 2 and then u get 84/100

Answer:

24

Step-by-step explanation:

3    9

8    

9 times 8

divided by 3 = denominator

9x8÷3=24

Answer:

[tex]\frac{9}{24}[/tex]

Step-by-step explanation:

Skills needed: Identify numerator, Multiplying to change fraction

1) First, we need to know what the numerator is. The numerator is the upper number of the fraction, which is separated by the fraction bar FROM the denominator (the bottom part of the fraction).

2) What we need to do here is rewrite the fraction [tex]\frac{3}{8}[/tex] so that the numerator is 9. Let's look at it in another way:

[tex]\frac{3}{8} * \frac{x}{x} = \frac{9}{z}[/tex] (The reason it is [tex]\frac{x}{x}[/tex] is because we want to multiply the original fraction/ratio by 1 so that we do not change it).

3) Now we know that [tex]3 * x=9[/tex], and if we divide both sides by 3, we get:

[tex]x=3[/tex].

This means it would be:

[tex]\frac{3}{8} * \frac{3}{3} = \frac{9}{z}[/tex]

Now we need to find [tex]z[/tex]. [tex]z=8*3 = 24[/tex]. [tex]z=24[/tex].

The numerator of our fraction would be 9, and the denominator is 24, making our answer: [tex]\frac{9}{24}[/tex].

Hope you understood and have a nice day!! :D (If you have any questions, please comment, and I can try to help!)

Answer:

2

Step-by-step explanation:

The example of speed and time is a basic and appropriate example of inversely proportional. As the speed increases, the time to complete your trip will decrease

Answer:

[tex]5x + \frac{1}{3} (3x + 6) > 14 \\ lcm = 3 \\ \\ (3 \times 5x) + 3 \times \frac{1}{3} (3x + 6) > 14 \times 3 \\ \\ 15x + 3x + 6 > 42 \\ 18x + 6 > 42 \\ 18x > 42 - 6 \\ 18x > 36 \\ x > 2[/tex]

Answer is below

x > 2

How I did it

What I first did was divide 3x + 6 by 3 because when you multiply by 1/3 it's basically just dividing by 3.

5x+x+2>14

Simplify

6x+2>14

Subtract 2 on both sides

6x>12

Since you want to get x by itself you divide both sides by 6, singling out x

x>2

Hope this helps!

Answer:

Cheetah

Step-by-step explanation:

American Antelope's speed = 94980 meters per hour

                                            = 59 miles per hour

The Cheetah is faster than the American Antelope

Answer:

TR = 23

Step-by-step explanation:

first we have to find TS, so we subtract 16 from 4 to get 12. then we can add 12 and 11 to get TR

Answer:

Step-by-step explanation:

[tex]\tt{ \green{P} \orange{s} \red{y} \blue{x} \pink{c} \purple{h} \green{i} e}[/tex]

Answer:22

Step-by-step explanation:

4*(2) + (6) +12 - 2*(2)=

8 +6 +12 -4=

14 +8= 22

Answer: 22

Step-by-step explanation:

Step-by-step explanation:

all steps are done in the picture

Answer:

1/36

Step-by-step explanation:

6^-2

~Use negative exponent rule [ a^-b = 1/a^b ]

1/6^2

1/36

Best of Luck!

Answer:

[tex]\huge\boxed{\sf \frac{1}{36}}[/tex]

Step-by-step explanation:

[tex]\displaystyle = 6^{-2}\\\\We \ know \ that\ a^{-b} = \frac{1}{a^b} \\\\= \frac{1}{6^2} \\\\= \frac{1}{36} \\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

t = 10

Step-by-step explanation:

z^t ⋅ z^5 = z^15

We know that a^b*a^c = a^(b+c)

z^(t+5) = z^15

Since the bases are the same, the exponents are the same

t+5 = 15

t = 15-5

t = 10

Answer:

√17

Step-by-step explanation:

Since it's a square, the area will simply be the side length squared. Therefore, we can take the square root of 17 to get the exact length. Since 17 is a prime number, it cannot be simplified any further.

Answer:

x = 74.89

Step-by-step explanation:

Because this is a right triangle we can use trigonometric ratios to solve for x

Remember the three main trig ratios are sine, cosine and tangent

Where

Sine = Opposite over Hypotenuse

Cosine = Adjacent over Hypotenuse

and Tangent = Opposite over Adjacent

In order to use trig ratios we must have a known angle that is not a right angle.

We are given ∠J which has a measure of 27°

We are also given ∠J's opposite side length. ( has a length of 34 )

and "x" is the hypotenuse.

When dealing with opposite and hypotenuse we use Sine

SineФ = Opposite over Hypotenuse

Ф = 27, opposite = 34 and hypotenuse = x

Sin(27)  = 34/x

solve for x

Multiply both side by x

sin(27) x = 34

divide both sides by sin (27)

x = 34 / sin (27)

simplify

x = 74.89 ( rounded to the nearest hundredth )

and we are done!

Answer:

The answer is 74.89

Step-by-step explanation:

Well it gives you 2 angles and one side length using the formula Called SAS you can find the missing lengths and side x = 74.891 while the other side equals 66.729. Hope this helps

Answer:

A

Step-by-step explanation:

We are given the function:

[tex]f(x) = x^2 - 4x[/tex]

And we want to find:

[tex]\displaystyle f(2b^2)[/tex]

Substitute:

[tex]\displaystyle f(2b^2) =(2b^2)^2 -4(2b^2)[/tex]

And evaluate:

[tex]\displaystyle \begin{aligned} f(2b^2) &=(2b^2)^2 -4(2b^2) \\ &=(4b^4) +(-8b^2) \\ &= 4b^4 - 8b^2 \end{aligned}[/tex]

In conclusion, our answer is A.