Which expressions are equivalent to the one below? Check all that apply.
4^3•4x

Answer:

Bob has 18 more miles to go

Step-by-step explanation:

90 ÷ 83 1/3 • 100 = 108

108 - 90 = 18

18 miles

power of a quotient

edge 2021

The law used to simplify the expression is quotient of powers.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,

3¹⁰ / 3⁴

For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.

By the definition we have the property of the power quotient of the same base set:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

So, using the same,

3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶

Thus, to simplify the expression we must use the property of the power quotient of the same base.

Hence, the law used to simplify the expression is quotient of powers.

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Answer:

The answer is below

Step-by-step explanation:

We have a vector with a magnitude of 50 miles and a direction of 240 °.

To draw it, the first thing is to make a Cartesian plane, the first thing is to know in which quadrant it would be, 240 ° is in the third quadrant (180 ° - 270 °), that is, it would be 30 ° (270 ° - 240 °) with respect to to the y axis negative.

Knowing this angle, we calculate the value of x and y, knowing that the magnitude of the vector is 50 miles, that is, this value would be the hypotenuse.

The value on the x-axis can be calculated using the sine of the angle, like this:

sin 30 ° = x / 50

x = sin 30 ° * 50

x = 25, how is the third quadrant would be -25

Now to calculate the value on the y-axis it would be by means of Pythagoras and it would be:

y ^ 2 = 50 ^ 2 - 25 ^ 2

y ^ 2 = 1875

y = 43.3, -43.3 because it must be located in the fourth quadrant

Which means that to draw the vector that we are asked to do, we must draw a point from origin (0,0) to (-25, -43.3).

Then I leave a sketch of what it would be:

Question

Points A, B and C are all on the

circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°

Work out the size of angle x

Answer:

62°

Step-by-step explanation:

To solve for the above question, we would be using circle theorems.

Step 1

Angle OBD = 90° This is because a radius and a tangent meet at 90°

Step 2

The sum of Angles in a triangle = 180°

180° = Angle OBD + Angle BDO + Angle BOD

180° = 90° + 31° + Angle BOD

Angle BOD = 180° - (90° + 31°)

= 180° - 121°

Angle BOD = 59°

Step 3

Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°

Step 4

The sum of angles of a straight line = 180°

Angle BOD, Angle AOD and Angle x are angles on a straight line

Hence,

180° = Angle BOD + Angle AOD + Angle x

180° = 59° + 59° + x

x = 180° - ( 59 + 59)°

x = 180° - 118°

x = 62°

Therefore Angle x = 62°

Step-by-step explanation:

We khow the sum and the product of the zeroes of this quadratic polynomial

Here is a trick :

when we khow the sum S and the product P ofvtwo numbers we can find them by solving :

x²-Sx+p=0

here S= -8 and P=12

so:

x²+8x+12=0

Let Δ be the discrminant of this equation: a= 1 , b= 8 and c=12

Δ= 8²-4*12 =16

the zeros are:

(-8-4)/2= -6

(-8+4)/2 = -2

verify:

-6+(-2)= -8

-2*(-6)= 12

now the polynomial quadratic is:

(x+6)(x+2)

Answer:

The length of the missing segment is 24

Step-by-step explanation:

Given

The figure above

Required

Determine the missing segment

Let the missing segment be represented with x

Given that, there exist parallel lines between the two triangles;

The relationship between the sides of the triangles is as follows;

[tex]\frac{15}{x} = \frac{15+5}{8+x}[/tex]

[tex]\frac{15}{x} = \frac{20}{8+x}[/tex]

Cross Multiply

[tex]15 * (8 + x) = 20 * x[/tex]

Open bracket

[tex]15*8 + 15 * x = 20 * x[/tex]

[tex]120 + 15x = 20x[/tex]

Subtract 15x from both sides

[tex]120 + 15x -15x= 20x-15x[/tex]

[tex]120 = 20x-15x[/tex]

[tex]120 = 5x[/tex]

Divide both sides by 5

[tex]\frac{120}{5} = \frac{5x}{5}[/tex]

[tex]\frac{120}{5} = x[/tex]

[tex]24 = x[/tex]

[tex]x = 24[/tex]

Hence, the length of the missing segment is 24

Answer:

The type of sampling method used is:

Step-by-step explanation:

A simple random sampling is a method where the pollster, in this case, the company, from a finite or infinite population (the costumers in the database) takes a representative sampling (in this case 100 costumers) to apply the survey and obtain data that can be used to deduce the way of thinking of all the costumers, though to actually identify this way of thinking, the sampling must be proportional to the size of the population, on the contrary, the data obtained won't be useful to reveal the real level of the satisfaction (In this case securely the database is 10,000 costumers or less, then the sampling is at least the 1% of the population). Another characteristic is all the people in the population should have the same opportunity to be part of the sampling, this is identified in the paragraph where says that the selection was random.

Answer:

B. simple random sampling

Step-by-step explanation:

right on edge

Answer:

Approximately 55 students

Step-by-step explanation:

13% of 420 is 54.6 which you can then round up to 55

Hope this helped!

Answer:

55 students

Step-by-step explanation:

Take the percent and multiply by the number of students

13% * 420

.13 * 420

54.6

Rounding up

55 students

Answer:

area = 25.12

Step-by-step explanation:

area of circle = pi(r)^2

area = 3.14 (4)^2 /2

area = 3.14 (16) / 2

area = 50.24 / 2

area = 25.12

Answer:

A = 78.9568350285

Step-by-step explanation:

A = TTr^2/2

A = TT4^2/2

A = 12.5663706^2/2

A = 157.913670057/2

A = 78.9568350285

The required transformation is to rotate 270 degrees counterclockwise, then shift 3 units down. Option B is correct.

Transform the coordinate plane's shapes by translating, rotating, or reflecting them. In the 19th century, Felix Klein introduced transformational geometry, a novel perspective on geometry.

Here,
In the graph, triangle ABC is transformed into triangle A'B'C' by a combination of rotation and translation. First, the triangle is rotated 270 degrees counterclockwise around the origin. Then, the resulting triangle is shifted 3 units down.

Thus, the required transformation is to rotate 270 degrees counterclockwise, then shift 3 units down. Option B is correct.

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Answer:

Step-by-step explanation:

x=✓25*9

x=✓5^2*3^2

x=5*3

x=15

Answer:

No it’s not a translation

Step-by-step explanation:

No it’s not a translation because a translation is when you are just moving a shape not resizing or rotating the shape.

Answer:

a) he would have 27500 won

b) changbin and han would have 70 lightsticks

Step-by-step explanation:

a)

multiply 45 rings by 500 won to get the total expense

45 x 500 = 22500

then subtract 22500 won from 50000 to get the amount left after the purchase

50000 - 22500 = 27500

this results in 27500 won total

b)

subtract 75 from 145 to get the amount left

145 - 75 = 70

Answer:

Hyunjin has 27,500 left.

Changbin & Han have 70 lightsticks left.

Step-by-step explanation:

A) 45 × 500 = 22500      50,000 - 22500 = 27500

B) 145 - 75 = 70

Answer:

y=5x+6

Step-by-step explanation:

Please see attached

Answer:

  21h miles

Step-by-step explanation:

The appropriate relation is ...

  distance = speed · time

__

We are given that ...

  biking time = h

  walking time = 2h

  running time = (1/4)(2h) = h/2

The total distance traveled is ...

  total distance = biking distance + walking distance + running distance

     = (10)(h) +(3)(2h) +(10)(h/2)

     = 10h + 6h + 5h

  total distance = 21h . . . miles

Answer:

21h miles

Step-by-step explanation:

The appropriate relation is ...

 distance = speed · time

__

We are given that ...

 biking time = h

 walking time = 2h

 running time = (1/4)(2h) = h/2

The total distance traveled is ...

 total distance = biking distance + walking distance + running distance

    = (10)(h) +(3)(2h) +(10)(h/2)

    = 10h + 6h + 5h

 total distance = 21h . . . miles:

Answer:

x = 18

Step-by-step explanation:

We can use Alternate Exterior Angles Theorem to find the angle above x. It would equal 94°. We then use Supplementary Angles to find x:

5x - 4 + 94 = 180

5x + 90 = 180

5x = 90

x = 18

Answer:

I am in 6th, doing 7th grade math, but can get up to 12th grade math lol.

x = 18

Step-by-step explanation:

First step: 5x - 4 + 94 = 180

Second step: 5x + 90 = 180

Last step: 5x = 90

So, therefore, your correct answer is: x = 18

Answer:

the answer is y+3=1/4x+4

Answer:

The answer is (a+c) + 7

Since addition is associative a + ( C + 7) can also be written as (a+c) + 7

Hope this helps you

Answer:

(a+c)+7

Step-by-step explanation: This method is called associative property.

On addition changing the order brings no change to the answer. For example:- 2+3=3+2. but don't confuse this with multiplication. For example, if the question was a(c+7), then you are supposed to multiply c, + and 7 by a.

Hope it would help :)

Answer:

B. Is the Answer 100 m²

Step-by-step explanation:

The ratio of the two solid is 729/125  

The ratio of the surface area = (729/125)^(2/3)=81/25  

Surface area = 25 * 324 / 81 = 100 m²

Answer:

86.82%

Step-by-step explanation:

A nautical mile = 6,174 feet.

Statute mile =5,360 feet

The percentage of a statute mile to a nautical mile is calculated as:

5360/6174 × 100

= 0.8681567865 × 100

= 86.81567865%

Approximately to the nearest hundredth = 86.82%

Therefore, the percent of a statute mile that is a nautical mile rounded to the nearest hundredth is 86.82%

Answer:

Step-by-step explanation

1.  8/9, 9/9, 10/9

2.  1/64, 1/128, 1/256

3.  -39, -48, -57

Answer

8/9,1,1 1/9

1/64, 1/128, 1/256

Step-by-step explanation:

the second sequence you just add1\9 each time then the other one you just double the denominator.

Answer:

12.6 hp

Step-by-step explanation:

output of motor = 85.4% of input of motor.

Given that motor delivers 10.75 hp, it means output of motor is 10.75hp

Using both the given conditions

10.75 = 85.4% of input of motor

=> 10.75 = 85.4/100  * input of motor

=> input of motor = 10.75*100/85.4 = 1075/85.5 hp = 12.57 hp.

Input of motor rounded to 1 decimal place = 12.6 hp

Answer:

The blue point will be at (4, 3)

Step-by-step explanation:

Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.

Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.

Answer:

the answer is b= -x+11

Answer:b

Step-by-step explanation:

Answer:

[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]

Step-by-step explanation:

Given

[tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex]

Required

Find the equivalent

To find the equivalent of the given expression; we have to apply laws of indices;

As a law;

[tex]a^{-m} = \frac{1}{a^m}[/tex]

So; the expression [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] becomes

[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}}*\frac{1}{z^2}[/tex]

This is further simplified to

[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}} * z^2}[/tex]

[tex]x^{\frac{1}{2}}*\frac{1}{y^{\frac{1}{4}}z^2}[/tex]

Combine to form a single fraction

[tex]\frac{x^{\frac{1}{2}}*1}{y^{\frac{1}{4}}z^2}[/tex]

Multiply numerator

[tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]

The expression can not be further simplified

Hence [tex]x^{\frac{1}{2}}y^{-\frac{1}{4}}z^{-2}[/tex] is equivalent to [tex]\frac{x^{\frac{1}{2}}}{y^{\frac{1}{4}}z^2}[/tex]

Answer:

c

Step-by-step explanation:

x has a exponent of -1 after multiplying 1/2 and -2, so x has to be in the denominator of the answer no matter what.

Hope this helped other than the guy above lol

Step-by-step explanation:

1. Population Area: this can be defined as a group of similar species

                                  inhabiting/ co-existing in a defined location or space

2. Urban population: urban areas are often more developed areas with                                                                   greater population than rural environments

                                   it's the people living in cities.

3. Population density: this  is a measurement of population per unit area..

Answer:

666.70 at the end of every six months.

Step-by-step explanation:

At the end of  every six months deposit amount is 666.70

Compound interest is the interest paid on both principal and interest, compounded at regular intervals.

Formula of compound interest :

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

where,

A = final amount

P = initial principal

n = time in years

r = rate per annum

According to the question

Final Amount needed for a special vacation (A) = ​$4000

Time in years needed to collect Amount (n) =  3 years

Rate per compounded semiannually (r) = 4.5​%

Substituting values in formula for six months

Now time (n) = 3 * 6 = 18 years

using formula of compound interest

[tex]A = P(1+\frac{r}{100} )^{n}[/tex]

[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]

[tex]4000 = P(1.045 )^{18}[/tex]

now,

P = 666.70

Hence, at the end of  every six months deposit amount is 666.70

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Answer:

mean =sum of all data values

total number of data

13+91+44+68+54+16+88+74

8

448

8

=56

therefore the mean is 56

Answer: 51

Step-by-step explanation:

Answer:

Permuation; 210 possibilites

Step-by-step explanation:

With permutations we care about the order of the elements, whereas with combinations we don’t. For this question order matters, because you have two different positions you want to fill (captain, and co-captain).

This would be written as 15p2

To find the number of possibilities we want to use the permuation equation.

(,)=!(−)!

P=permutation

n= the set or population (15 soccer players)

r= subset (1 captain and 1 co-captain, total of 2)

(,)=(15,2)

=15!(15−2)!

= 210

If u are confused about !(factorial) in the equation here is a quick explanation

Many calculators have a factorial key (look for the ! symbol). This function of the calculator will automate the multiplications, but if you do not have a calculator that can compute factorials you just have to go like this

1! = 1

2! = 2 x 1 = 2

3! = 3 x 2 x 1 = 6

4! = 4 x 3 x 2 x 1 = 24

5! = 5 x 4 x 3 x 2 x 1 = 120

6! = 6 x 5 x 4 x 3 x 2 x 1 = 720

7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040

8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 40320

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362880

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3628800

etc

Hope this helps!!

The number of possibilities in choosing captain and co-captain are 210 ways.

Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.

Given that, a team of 15 soccer players needs to choose a captain and a co-captain.

Number of captains can be choose from 15 players.

Number of co-captains can be choose from 15-1=14 players.

So, the number of possibilities= 15×14

= 210 ways

Therefore, the number of possibilities in choosing captain and co-captain are 210 ways.

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