Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each radical expression to the corresponding expression in rational exponent form.

Answer:

Important: 3

6

looks like a fraction, but it is actually an improper fraction.

There is an infinity number of equivalent fractions to 3

6

.

To find an equivalent fraction to 3

6

, or to any other fraction, you just need to multiply (or divide, if the fraction is not yet reduced), both the numerator and the denominator of the given fraction by any non-zero natural number. For example:

By dividing the original fraction by 3, we get:

3 ÷ 3

6 ÷ 3

= 1

2

By multiplying the original fraction by 2, we get:

3 × 2

6 × 2

= 6

12

Step-by-step explanation:

Answer:

nth term = n(n + 2)

Step-by-step explanation:

Note that the first number in each parentheses is the sequence number n of the term. This  value of n is then multiplied by (n + 2) - for example 3 x 5

( 3 x (3+2)).

So the nth term = n(n + 2).

This is an example of a Quadratic Sequence.

Answer:

The correct answer is B.

Step-by-step explanation:

Pay per month depends on hours of training, so hours of training is the domain, and pay per month is the range.

Answer:

Step-by-step explanation:

8

Answer:

63

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

The equation of the tangent to the curve at the point corresponding to the given value of the parameter will be x + y = c.

The curves are given below.

x = t⁵ + 1 and y = t⁶ + t

Then differentiate the functions with respect to t, then we have

[tex]\rm \dfrac{dx}{dt} = 5t^4\\[/tex]   ...1

and

[tex]\rm \dfrac{dy}{dt} = 6t^5 + 1[/tex]   ...2

Divide equation 2 by equation 1, then we have

[tex]\rm \dfrac{\dfrac{dy}{dt} }{\dfrac{dx}{dt} } = \dfrac{dy}{dx} = \dfrac{6t^5 + 1}{5t^4}[/tex]

Then the slope of the equation at t = −1, then we have

dy/dx = [6(-1)⁵ + 1]/[5(-1)⁴]

dy/dx = (-6+1)/5

dy/dx = -5/5

dy/dx = -1

Then the equation of the tangent line will be

y = -x + c

x + y = c

Where c is a constant.

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Answer: 24.15

Step-by-step explanation:

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the objects. The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The polar coordinate of the coordinate (1, -3) are,

r = √(x² + y²) = √[(1)²+(-3)²] = √10

θ = tan⁻¹(-3/1) = -71.565 = 288.435

Hence, The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

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[tex]\text{L.H.S}\\\\\sec x - \tan x \sin x\\\\\\=\dfrac{1}{\cos x}- \dfrac{\sin x }{ \cos x } \cdot \sin x\\\\\\=\dfrac 1{\cos x} - \dfrac{\sin^2 x}{\cos x}\\\\\\=\dfrac{1- \sin^2 x}{\cos x}\\\\\\=\dfrac{\cos^2 x}{\cos x}~~~~~~~~~~~~~;[\sin^2 x + \cos^2 x = 1]\\\\\\=\cos x\\\\\\=\text{R.H.S}\\\\\text{Since both sides are equal, the given equation is an identity.}[/tex]

80 * 25 /100 = 20 .........

Answer:

20

Step-by-step explanation:

25% of 80

to turn 25% into a decimal, 25 / 100 = 0.25  

multiply 80 by 0.25, 80 x 0.25 = 20

The data value that is an outlier in the data for boxes of cookies is: E. 56.

The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.

Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:

First Quartile (Q1) = 15.5

Third Quartile (Q3) = 22.5

Interquartile Range (IQR) = 22.5 - 15.5 = 7

Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5

Q3 + 1.5 × IQR = 33

None of the values are lower than 5.

However, the only value that is greater than 33 is 56.

The outlier in the data is: E. 56.

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The angle the longer chain makes with the ceiling is 38.5°

The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle

The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that

a/sinA = b/sinB = c/sinC

Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.

So, a/sinA = b/sinB  where

Making A subject of the formula, we have

A = sin⁻¹(asinB/b)

So, substituting the values of the variables into the equation, we have

A = sin⁻¹(asinB/b)

A = sin⁻¹(46 cm × sin60/64 cm)

A = sin⁻¹(46 cm × 0.8660/64 cm)

A = sin⁻¹(39.84 cm/64 cm)

A = sin⁻¹(0.6225)

A = 38.49°

A ≅ 38.5°

So, the angle the longer chain makes with the ceiling is 38.5°

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Answer:

$301

Step-by-step explanation:

 Charge for 1 hour = $ 72

To find the cost for 3 hours, multiply hourly rate ($72) by 3

Charge for 3 hours = 72 * 3  = $ 216

Now, to find the total cost, add the charge for 3 hours and the fixed rate.

Total cost = fixed rate + charge for 3 hours

                = 85 + 216

                = $ 301

Answer:

x = 19/2 or 9.5

Step-by-step explanation:

Hello!

We can distribute the parenthesis and solve.

Move all x terms to one side and integer terms to the other

Answer:

y=-x+6

Step-by-step explanation:

Start by graphing y=-x+5.  Then mark the point (2,4) for easier reference.  A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.

Step-by-step explanation:

2×length + 2×width = 45

length = 4×width

now, we are using the second equation (a variable identity) in the first equation

2×4×width + 2×width = 45

8×width + 2×width = 45

10×width = 45

width = 45/10 = 4.5 in

length = 4×width = 4×4.5 = 18 in

the area of the rectangle is

length × width = 18 × 4.5 = 81 in²

Answer:

(1) 1 and 7

Step-by-step explanation:

Hello!

We can solve by isolating the variable.

There are two solutions, 1 and 7.

The answer is option 1: x = 7, x = 1.

Answer:

[tex]\sf M=\left(-\dfrac{1}{2},0\right)[/tex]

Step-by-step explanation:

Let (x₁, y₁) = Point A = (-2, 1)

Let (x₂, y₂) = Point B = (1, -1)

[tex]\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)[/tex]

The equation that must be true about the rotation is that m∠EAE ' = m∠FAF.

Rotation is a type of transformation in which the shape of the original object is preserved and the angle of rotation is constant for all the parts of the body.

In this case, ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F, m∠EAE ' = m∠FAF.

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Answer:

hope you can understand

The number of books Alisha did not sell after making a profit of £490 is 45 books

How to find how many book she sell base on the profit?

She buys 200 books costing £3 each.

Therefore,

cost = 3 × 200 = £600

Hence,

She sells 2/5 of the books at £8 each.

total amount = 2 / 5 of 200 × 8

total amount = 80 × 8

total amount = £640

Alisha then reduces the price of the remaining books by a quarter.

She then sells some of the remaining books.

Therefore,

the remaining book = 120

She sold some of the remaining books.

profit = selling price - cost price

490  = selling price - 600

selling price = 490 + 600

selling price = £1090

Therefore,

the cost of the remaining book she sold = 1090 - 640 = £450

Hence,

let

x = number of book sold

6(x) = 450

x = 450 / 6

x = 75

The number book she did not sell = 120 - 75 = 45

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Answer: Choice A

The two characteristics here are:

The graph of choice B is [tex]y \le 2x-3[/tex] since we have a solid line and shading below the solid line. This time points on the boundary are part of the solution set.

A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two variables, with the resulting points showing any association (correlation) between the data set.

A line of best fit is also referred to as a trendline and it can be defined as a statistical (analytical) tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any correlation between a data.

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that an equation for the line of best fit is given by:

y = 22.214x + 291.27

Since the slope of the equation for the line of best fit is positive, the paid advertisement is responsible for the restaurant's increase in pizza sales during the first quarter.

Next, we would predict the restaurant's sales for the Monday of the 20th week as follows:

y = 22.214x + 291.27

y = 22.214(20) + 291.27

y = 444.28 + 291.27

y = $735.55.

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Answer:

Step-by-step explanation:

angle c

The angle of the triangle with the greatest measure is ∠A

A triangle is a polygon with three sides and three angles.

Analysis:

For the triangle, ABC the angle facing the side with the greatest measure is the angle with the greatest measure. From the given information side BC is the side with the greatest measure and the angle facing it is ∠A.

In conclusion, the angle with the greatest measure is ∠A

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When we try to compute gamma, for this problem, the value of gamma is 1

To answer the question, we need to know what time dilation is.

Time dilation is a phenomenon in special relativity in which there is an elongation of time due to the motion of an object.

Now, the time is given by t = γt₀ where

Since we need to compute gamma when the speed of the automobile moving past you is 30 m/s.

Given that

Substiting these into γ, we have

γ = 1/√[1 - (v/c)²]

γ = 1/√[1 - (30 m/s/3 × 10⁸ m/s)²]

γ = 1/√[1 - (1/1 × 10⁷)²]

γ = 1/√[1 - (1 × 10⁻⁷)²]

γ = 1/√[1 - (1 × 10⁻¹⁴)]

γ = 1/√[1 - 0.00000000000001]

γ = 1/√0.99999999999999

γ = 1/1

γ = 1

So, when we try to compute gamma, the value of gamma is 1

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The slope of the line is [tex]\frac{6-0}{0-6}=-1[/tex]. so in point-slope form, the equation of the line is [tex]y=-x+6[/tex].

In standard form, this is [tex]\boxed{x+y=6}[/tex]

Answer:

6 hours 30 minutes

Step-by-step explanation:

10 subtract 4 is 6

55 subtract 25 is 30

Answer:

[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

Triangle ABC is similar to triangle DEC, because all angles in one triangle are equal to angles in the other triangle.

That means that corresponding sides have the same ratio. Side AB and side DE are corresponding sides. Since there are no unknowns we can calculate the ratio (scale factor).

Since we are looking for scale factor of triangle DEC to triangle ABC, we put side AB (which is in triangle ABC) in the numerator.

[tex]\text{scale factor} = \frac{\text{AB}}{\text{DE}} = \frac{6}{21} = \frac{2}{7}[/tex]

I've marked corresponding sides and angles in the attached picture.

Rounded to the nearest whole number, the standard deviation of the data is 29.

The following notations and formulas will be used in these calculations:

Mean = (sum of the values) / n

Variance = ((Σ(x - mean)^2) / (n - 1)

Standard deviation = Variance^0.5

Where:

n = number of values = 4

x = each value

Therefore, we have:

Mean = (65 + 75 + 100 + 130) / 4 = 92.50

Variance = ((65-92.5-)^2 + (75-92.50)^2 + (100-92.50)^2 + (130-92.50)^2) / (4-1) =  2,525 / 3 = 841.666666666667

Standard deviation = Variance^0.50 = 841.666666666667^0.5 = 29.011491975882

Rounding to the nearest whole number, we have:

Standard deviation = 29

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Answer:

The answer is C. 100

Step-by-step explanation:

We need radius

Let that be r

Answer:

12 feet

Step-by-step explanation:

It asks how many feet away from the sprinkler can water be spread. Therefore, in this scenario, we require the radius.

Area of a circle :

Area (circle) = πr²

Solving :

⇒ 452.16 = 3.14 × r²

⇒ r² = 452.16 ÷ 3.14

⇒ r = √144

⇒ r = 12 feet