Rewrite the following expression using the properties of rational exponents. Be sure your answer is in simplest form
(2 • 6) 3/2

Answer:

A

Step-by-step explanation:

The recursive rule allows any term to be found by multiplying the previous term by the common ratio r

Here r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{20}{4}[/tex] = 5

Then

f(n) = 5 . f(n - 1) , for n ≥ 2 → A

Answer:

381/90

Step-by-step explanation:

x = 4.2333.... ----------(I)

Number of digit after decimal is 2 ( 4 , 3). So multiply both sides by of equation 100

100x = 423.333..... (II)

One digit (3) is repeating.So, multiply by both sides of equation (I) by 10

10x = 42.333....... -----(III)

Subtract Equation (III) from (II)

(II)     100x = 423.333......

(III)        10x =  42.333......  {Subtract}

         90x   = 381

                x = 381/90

Answer:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]

Step-by-step explanation:

[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]

Answer:

x is 30 degrees

Step-by-step explanation:

Answer:

3(13x-5)

Step-by-step explanation:

first step open your bracket,u have

=4x²+20x-3x-15-4x²+22x then collect like terms

=4x²-4x²+20x-3x+22x-15

=0x²+39x-15

=39x-15

further simplifying u have:

=3(13x-5)

Answer:

y - 5 = -1/6 (x - 4)

Step-by-step explanation:

y = 6x - 1          y = -1/6x + b

y - 5 = -1/6 (x - 4)

Answer:

69.3

Step-by-step explanation:

if you put it into 2D, you get a right triangle with leg lengths 62 (vertical height) and 31 (1/2 the base's length). Using Pythagorean's Theorem you get sqrt((62^2)+(31^2))= 69.318. Rounding to the nearest tenth you get 69.3

Answer:

see explanation

Step-by-step explanation:

Under a reflection in the x- axis

a point (x, y ) → (x, - y ) , then

A (4,  2 ) → A' (4, - 2 )

B (7, 0 ) → B' (7, 0 )

C (9, 3 ) → C' (9, - 3 )

A translation of a shift to the left of 3 units is a horizontal shift.

This means subtracting 3 fro the x- coordinate and leaving the y- coordinate

A' (4, - 2 ) → A'' (4 - 3, - 2 ) → A'' (1, - 2 )

B' (7, 0 ) → B'' (7 - 3, 0 ) → B'' (4, 0 )

C' (9, - 3 ) → C'' (9 - 3, - 3 ) → C'' (6, - 3 )

Answer:

(27xy +3)/5x^2 +6x

Step-by-step explanation:

((15xy^2 )/ x^2 + 5x + 6 ) × ((2x^2 + 7x + 3) / 5x^2y)

(3y ×(2x+ 7x + 3)) / 5x^2 +6x)

Answer:

c

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

We can see in the expression that there are 2 x² blocks, 4 -x blocks, and 3 -1 blocks. Therefore, we can write this as

2 * x² + 4 * (-x) + 3 * (-1) = 2x²-4x-3

Comparing this with each answer, we have

A: x²-2x-4 + x² + 2x-1 = 2x²-5. This is not correct

B: 3x²-7x+1-(x²-3x+4) = 3x²-7x+1 -x²+3x-4 = 2x²-4x-3. This seems correct but we can check the other answers to be sure

C: (2x+1)(x-3) = 2x²-6x+x-3 = 2x²-5x-3. This is incorrect

D: [tex]\frac{8x^{12} - 16x^7 - 12x^6}{4x^6} = 2x^6 - 4x - 3[/tex]. This is incorrect

Answer:

C. 2(x + 10)(x - 10)

Step-by-step explanation:

2x^2-200\\2(x^2-100)\\2(x+10)(x-10)

Answer:

58%

Step-by-step explanation:

10*5=50

7*3=21

21/50 chance to choose inside small rectangle

21/50*2 = 42/100 chance to choose inside small rectangle

100-42=58%

Answer:

45g

Step-by-step explanation:

The amount of salt left once the whole water is evaporated can be calculated as follows

= 12% × 375

= 12/100 × 375

= 0.12×375

= 45

Hence 45g of salt is left after the evaporation of water

Answer:

45g

Step-by-step explanation:

Answer:

The y intercept of f(x) is 8 and the equation of the horizontal asymptote is y = 0

Answered by GAUTHMATH

Answer:

Step-by-step explanation:

Mean of the data = sum of the data / number of frequencies:

Correct choice is d

Answer:

Total number in favour:

Probability:

Total number in against:

Probability:

Answer:

divide, 2x+9

Step-by-step explanation:

got it right

Answer:not a man but I think you should just relax and be yourself, high school isn’t scary at all. When you go in for orientation walk around the school and find your classes so you have a good map of where you need to go in your head already! Best of luck

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given,

m || n

So,

35° = y° [Alternate interior angles]

And,

y° + x° = 180° [Since linear pair]

=> x + 35 = 180

=> x = 180 - 35

=> x = 145°

Hence,

x = 145°, y = 35°

Answer:

x = 145

y = 35

Step-by-step explanation:

35 and y are alternate interior angles and alternate interior angles are equal when the lines are parallel

35 = y

x+y = 180 because x and y form a straight line

x+35 = 180

x = 180-35

x = 145

Answer:

14.3

Step-by-step explanation:

sin73 = opposite/hypotenuse = x/15

x = 15sin73 = 14.344571 = 14.3

Answer:

1) The total displacement vector is ((16 + √2)/2, -(6+11·√2)/2)

2) The number of miles they'd have to walk is approximately 13.856 miles

Step-by-step explanation:

1) The distance, direction, and location of the path of the walk the person takes,  are listed as follows;

Start location, (0, 0)

6 miles East walk to location, (6, 0)

6 miles Southeast to location, (6 + 3·√2, -3·√2)

3 miles South to location, (6 + 3·√2, -3·√2 - 3)

5 miles Southwest to location, (6 + 3·√2 - 2.5·√2, -3·√2 - 3 - 2.5·√2)

2 miles East to location, (6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2)

(6 + 3·√2 - 2.5·√2 + 2, -3·√2 - 3 - 2.5·√2) = ((16 + √2)/2, -(6+11·√2)/2)

Therefore the destination coordinates is ((16 + √2)/2, -(6+11·√2)/2)

The total displacement vector, [tex]\underset{d}{\rightarrow}[/tex] = ((16 + √2)/2, -(6+11·√2)/2)

d =  (16 + √2)/2)·i - (6+11·√2)/2)·j

2) If the person walked straight home, the number of miles they'd have to walk, [tex]\left | \underset{d}{\rightarrow} \right |[/tex], is given as follows;

[tex]\left | \underset{d}{\rightarrow} \right | = \sqrt{\left(\dfrac{16 +\sqrt{2} }{2} \right)^2 + \left(-\dfrac{6 + 11 \cdot \sqrt{2} }{2} \right)^2 } = \sqrt{134 + 41 \cdot \sqrt{2} }[/tex]

Therefore;

If the person walked straight home, the number of miles they'd have to walk [tex]\left | \underset{d}{\rightarrow} \right | \approx 13.856 \ miles[/tex]

Answer:

D

Step-by-step explanation:

Using the Cosine rule to find AC

AC² = BC² + AB² - (2 × BC × AB × cosB )

      = 18² + 12² - ( 2 × 18 × 12 × cos75° )

      = 324 + 144 - 432cos75°

      = 468 - 111.8

      = 356.2 ( take the square root of both sides )

AC = [tex]\sqrt{356.2}[/tex] ≈ 18.9

-----------------------------------------

Using the Sine rule to find ∠ A

[tex]\frac{18}{sinA}[/tex] = [tex]\frac{18.9}{sin75}[/tex] ( cross- multiply )

18.9 sinA = 18 sin75° ( divide both sides by 18.9 )

sinA = [tex]\frac{18sin75}{18.9}[/tex] , then

∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{18sin75}{18.9}[/tex] ) ≈ 66.9°

Answer:

[tex]{ \tt{x = \sqrt{ {10}^{2} - {8}^{2} } }} \\ { \tt{x = \sqrt{36} }} \\ { \tt{x = 6}}[/tex]

Answer:

X = 6

Step-by-step explanation:

This is a right angled triangle. Thus, pythagoras theorem will be best for its solution.

Hypotenuse squared = height squared + base squared

SH² = H² + B²

10² = x² + 8²

100 = x² + 64

10 – 64 = x² + 64 – 64 (grouped like terms)

36 = x²

Root of both sides

Therefore x = 6

Step-by-step explanation:

Hope you understand through the steps on the attachment, if not kindly reach out

Answer:

Step-by-step explanation:

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero. If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.

Answer:

m=4

Step-by-step explanation:

m = y2 - y1/x2 - x1

(y2=8, y1=0, x2= 2, x1=0)

m = y2 -y1/x2 - x1

= 8 - 0/2 - 0

= 8/2

=4

Answer:

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.

Standard deviation 4 minutes.

This means that [tex]\sigma = 4[/tex]

A sample of 25 wait times is randomly selected.

This means that [tex]n = 25[/tex]

What is the standard deviation of the sampling distribution of the sample wait times?

[tex]s = \frac{4}{\sqrt{25}} = 0.8[/tex]

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.

Answer:

D

Step-by-step explanation:

[tex]8x \sqrt{2} - 4 \sqrt{2} [/tex]