Three students were scheduled to give book reports in 1 hour.


After the first report, 2/3 hour remained (HINT: this means the first persons' report was 1/3 of an hour)


The next report took 1/6 hour. What fraction remained?

The value of the function (f/g)(x) when f(x) = 4x^5 - x and g(x) = x^3 – 2 is

(f/g)(x) = (4x⁵- x)/(x³- 2)

Functions - It is defined as expressions, rules or laws that explains the relationship between two variables.

These variables are

It is important to note that composite functions are determined when the output of a given function is used as the input of another or different variable.

Given the functions;

f(x) = 4x^5 - x

and

g(x) = x^3 – 2

(f/g)(x) = f (x) / g(x)

(4x⁵- x)/(x³- 2)

The value of the function (f/g)(x) when f(x) = 4x^5 - x and g(x) = x^3 – 2 is

(f/g)(x) = (4x⁵- x)/(x³- 2)

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Answer:

The height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.

Step-by-step explanation:

Given:

To Find:

Formula used:

Let the height of each pole be H metres.

Also, let's assume that distance of the point from one pole (as shown in figure) be x m.

According to question, we have

tan60° = H/(80-x)

H = (80-x)√3.... (1)

Also, tan30° = H/x

H = x/√3... (2)

Putting value of eq(2) in eq(1), we get

x/√3 = (80-x)√3

x = 3(80-x)

x = 240 - 3x

4x = 240

x = 60 m

Putting value of x in eq(2), we get

H = 60/√3 = 20√3 m

So, the height of pole is 20√3 m each and distance of pole from the point on road is 60 m and 20 m respectively.

Answer:

Height of Pole: 20√3 m

Distance Of Point From Poles: 20m and 60m

Step-by-step explanation:

The attached graph may help you understand my explanation better

The two poles are Ab and CD and are 80m apart

O is the point between them

The angle of elevation from O to A is 60°

The angle of elevation from O to D is 30°

Since the two poles are given to be of equal height,

AB = CD

In ΔAOB using the law of tangents

tan 60° = AB/BO

tan 60° = √3 and AB = x

So we get

√3 = x/BO

Multiplying both sides by BO we get

√3 · BO = x

or BO = x/√3

Looking at ΔCOD

tan 30° = DC/OC

tan 30° = 1/√3

1/√3 = x/OC

OC · ( 1/√3) = x

OC = x ÷ 1/√3

= x · √3/1

OC = √3x

We also know that BO + OC = 80

Plugging this information with values computed gives us

x/√3 + √3x = 80

Multiply by √3 on both sides

(x/√3) · √3 +  (√3x) √3 = 80√3

(x/√3) · √3 = x since the √3 terms cancel out

(√3x) √3 = 3x

So we get

(x/√3) · √3 +  (√3x) √3 = 80√3

=>
x + 3x = 80√3

4x = 80√3

x = (80√3)/4

x =20√ 3

So the height of each pole = 20√ 3 m ≈ 34.64 m

The distance OC can be found from the previous equation
OC = √3x

=> OC = √3 x 20√3 = 20 x 3 =  60m

Since BO + OC = 80 m

BO = 80 - 60 = 20 m

Answer:
Height of each pole = 20√3 m

The point is located 20 m from one pole and 60 m from the other pole

[tex] - 6(4 - t) = 12t \\ - 6(4) - 6( - t) = 12t \\ - 24 +6 t = 12t \\ 6t - 12t = 24 \\ - 6t = 24 \\ \frac{ - 6t}{ - 6} = \frac{24}{ - 6} \\ t = - 4[/tex]

ATTACHED IS THE SOLUTION

The new value of gold was $1859 per ounce.

How to calculate profit amount?

Finding profit is simple using this formula: Total Revenue - Total Expenses = Profit.

Price in which Melissa bought gold per ounce = $1,430

Given that, Melissa sell it when the gold price is 30% more than when she purchased it.

Price in which Melissa sell gold per ounce =  $ 1,430 + 1,430×30%

                                                                      =  $ 1,430 + 1,430×[tex]\frac{30}{100}[/tex]

                                                                      =  $ 1,430 + 429

                                                                      =  $ 1,859

Hence, the new value of gold was $1859 per ounce.

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Answer:

Step-by-step explanation:

5?

Answer:

1. AM = 10

2. x = 21;

   AM = 14

Step-by-step explanation:

5x = 3x + 4

-3x   -3x

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

2x = 4

÷2   ÷2

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

x = 2

AM = 5x

5(2) = 10

AM = 10

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

|-------------x--------------|

*----|----*----|----*----|----*

A         H        M        S

            |---7---|

(assuming AH = HM = MS)

7 + 7 +7 = x

21 = x

AM = 14

I hope this helps!

Answer:

[tex] \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]

Step-by-step explanation:

[tex] {14}^{ - 1} = \frac{1}{14} [/tex]

[tex] {b}^{ - 2} = \frac{1}{ {b}^{2} } [/tex]

[tex] \frac{ {14}^{ - 1} {a}^{3} {b}^{ - 2} }{ {c}^{4} } = \frac{ {a}^{3} }{14 {b}^{2} {c}^{4} } [/tex]

Answer:

Step-by-step explanation:

As you see the picture the number is 1.249

step 1

As you know before decimal the digits are said to be ones,tens, hundred so on and starts from left to right.

But after decimal it goes right to left and they are said ones,tenth,hundredth

step 2

so here it says 1 decimal place means ones means one digit after dot or point so its 2

The number rounded off to 1 decimal place is 1.2

Rounding is a process to estimate a particular number in a context. To round a number look at the next digit in the right place, if the digit is less than 5, round down and if the digit is 5 or more than 5, round up. Rounding decimals refer to the rounding of decimal numbers to a certain degree of accuracy.

Given here, the number is 1.249 and thus the number rounded upto 2 decimal place is 1.25 and further rounding up the number to one decimal place we get 1.2

Hence, the number rounded upto one decimal place is 1.2

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The equation or tape diagram could be used to represent the context if x represents the number of miles in the taxi ride is A. 29.95 - 1.2 / 1.25 = x

From the information, Houa took a taxi from her house to the airport and the taxi company charged a pick-up fee of $1.20 plus $1.25 per mile. The total fare was $29.95,

Let the number of miles be represented by x.

Therefore, the information will be illustrated by:

1.20 + 1.25(x) = 29.95

1.20 + 1.25x = 29.25

Make x the subject

1.25x = 29.25 - 1.20

x = 29.25 - 1.20 / 1.25

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Answer: 0.004

Step-by-step explanation:

Answer:

1.1(x + 9)

Step-by-step explanation:

1.1x + 9.9 ← factor out 1.1 from each term

= 1.1(x + 9)

Answer:  x=12-3y

Step-by-step explanation:

Answer:

0.73855.

Step-by-step explanation:

log √30

log 30^1/2

= 1/2 log 30

30 = 2 * 3 * 5

= 3 * 10

So, log 30

= log (3*10) = log 3 + log 10

= 0.4771 + 1

= 1.4771

and log √30

= 1/2 log 30

= 1/2 * 1.4771

= 0.73855

Answer:

Five dollars?

Step-by-step explanation:

I don’t fully understand the question, so apologies if I am incorrect!

Answer:

61

Step-by-step explanation:

100+380+6(54)=804

804-500=304

304/5=60.8

Round answer to 61 because 60 is too little and will not meet the budget

Answer: 65.97

Step-by-step explanation:

Sin(0)=-7/10

To get the right triangle's known sides, use the sine definition. Each value's sign is determined by the quadrant.

sin(0)=opposite/hypotenuse

Find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.

Adjacent=√hypotenuse²−opposite²

Change the equation's known values with new ones.

Adjacent=√(10)²−(7)²

Inside the radical, simplify.

Raise10the strength of2.

Adjacent=√100−(7)²

Raise−7the strength of2.

Adjacent=√100-49

Multiply −1 by 49.

Adjacent=√100−49

Subtract49 from 100.

Adjacent=√51

Find the cosine value.

Find the value of using the cosine definition.

cos(0).

cos(0)=adj/hyp

Replace with the known values.

cos(0)=√51/10.

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To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.

The value of cos(0) exists √51/10.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.

To get the right triangle's known sides, use the sine definition. The quadrant determines each value's sign.

sin(0) = opposite/hypotenuse

To find the triangle formed by the unit circle's neighboring side. Use the Pythagorean theorem to determine the remaining side since the hypotenuse and opposite sides are known.

Adjacent = √hypotenuse² − opposite²

substitute the values in the above equation, we get

Adjacent = √(10)² − (7)²

Adjacent = √100 - 49

simplifying the above equation, we get

Adjacent = √51

To find the cosine value.

cos(0) = adjacent/hypotenuse

Replace with the known values.

cos(0) = √51/10.

Therefore, the value of cos(0) = √51/10.

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Answer:

Find the probability of pulling a red card out of a standard deck of cards

Step-by-step explanation:

So, the probability of drawing a red-faced card is 6 out of 52 cards. Thus, the probability of drawing a red face card from a deck of cards is 6/52 = 3/26.

A standard deck of playing card consists 52 cards.

Cards is splitted into 4 suit i.e. Hearts, Spades, Diamond and Clubs.

Each suits consists of 13 cards - the Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, King and Queen.

Hearts & Diamond are red cards and Spades and Clubs are black cards.

Probably = Number of favourable/Possible outcomes/ Total outcomes.

Probability of pulling a red card = 26/ 52 = 0.5

Thus, probability of pulling a red card is 0.5.

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Answer:

a = -2

b = -3

c = 2

Step-by-step explanation:

a*b = 6     {The product of a and b is 6]

a*c = -4     [The product of a and c is -4]

b*c = -6     [The product of b and c is -6]

-  Rearrange:

 1)   a*c = -4 to a = (-4/c)

 2)  b*c = -6 to b = (-6/c)

Now substitute:

a*b = 6

(-4/c)*(-6/c) = 6

(24/c^2) = 6

c^2 = (24/6)

c^2 = 4

c = 2

use this value of c to find a and b:

a = (-4/c)

a = (-4/2)

a = -2

b = (-6/c)

b = (-6/2)

b = -3

Perimeter of polygon is 96 inches

Area is 192 square inch.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given,

Perimeter = sum of all sides

Perimeter = 8 + 10 + 10 + 18 + 12 +12 +8+ 10 + 10+8 + 10

Perimeter = 86

Perimeter of polygon is 96 inches

Area = Triangle ABC + Rectangle BCED + Triangle DEF

Area = [tex]\frac{1}{2}[/tex] × 12× 8 + 12×8 + [tex]\frac{1}{2}[/tex] ×12 × 8

Area = 192

Area is 192 square inch.

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The statement is true. Multiplication is commutative, which means that the order of multiplication does not affect the result.

The statement "0 x 5 = 5 x 0" is true because of the commutative property of multiplication. In multiplication, the order of factors does not change the result.

When we multiply 0 by 5, it equals 0 since anything multiplied by 0 is 0. Similarly, when we multiply 5 by 0, the result is still 0. Both expressions are equal to 0, confirming the commutative property.

In summary, 0 x 5 and 5 x 0 are interchangeable and yield the same result, proving the truth of the statement based on the fundamental property of multiplication.

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An element of a line known as a line segment joins two places that are thought of as line's ends. Point C is on line segment BD, Given CD = 2 and BC = 8, the length BD is 10.

A line segment in geometry is a section of a straight line that is enclosed by two clearly defined end points and contains all of points on the line that lie inside those endpoints. The Euclidean distance between the two ends of a line segment determines its length. Half-open line segments contain exactly one of endpoints, while closed line segments have both of the endpoints. Open the line segments do not contain either of the endpoints. A line drawn above the symbols for the two endpoints is frequently used in geometry to indicate a line segment.

An element of a line known as a line segment joins two places that are thought of as line's ends. It is possible to measure the separation between two places. Given that line segments have a defined length, they can form the sides of any polygon.

Point C is on line segment BD.

CD+BC=2+8=10

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Answer:�

�

=

BC=

15

15

Step-by-step explanation:

Answer:

A is translation because it's being moved to the right to get a'b'

b is reflection because you would reflect over the x-axis \

C is rotation

Picture A represents the translation, the picture represents the reflection, and picture C represents the rotation.

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

It is given that:

The lines are shown in the picture.

As we know from the definition of the geometric transformation, geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

From the picture,

Picture A, which is being moved to the right to obtain A'B', serves as a representation of the translation.

Because you would reflect over the x-axis, Picture A represents reflection.

Image A illustrates rotation.

Thus, picture A represents the translation, the picture represents the reflection, and picture C represents the rotation.

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The value of z in this convex polygon is equal to 66°

A polygon can be defined as a two-dimensional geometric shape that comprises straight line segments and a finite number of sides.

Note: The number of sides (n) of a pentagon is 5.

In Geometry, the sum of all the interior angles of a polygon with "n" sides is given by this formula:

Interior angle = 180 × (n - 2)

Interior angle = 180 × (5 - 2)

Interior angle = 180 × 3

Interior angle = 540°.

Now, we can determine the value of z as follows:

(180° - 2z) + (180° - z) + 130° + 108° + 140° = 540°

3z - 378° = 540° - 360°

3z = 378° - 180°

3z = 198°

z = 198°/3

z = 66°

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Answer:

They are 6 sunsets

Step-by-step explanation:

the sets are

(abc),(abd),(ade),(acd),(ace),(ade)

The value which the four digit number is divisible by 5 is 608

What is Divisibility?

By looking at the digits of an integer, a divisibility rule can be used to quickly and conveniently determine if it can be divided by a specific number.

The given four-digit number is divisible by 5:

3040

To find the value from which the four digit number is divisible by 5

3040 ÷ 5

= 3040/5

= 608

Hence, The value of the be so that this four-digit number is divisible by 5 is 608

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The value of x in the triangle is 46.40° .

The angle of a triangle can be found using sine rule.

Therefore, applying sine rule,

a / sin A = b / sin B = c / sin C

Hence,

5 / sin x = 6.9  / sin 88°

cross multiply

5 sin 88° = 6.9 sin x

5 × 0.99939082701 = 6.9 sin x

4.9969541351 = 6.9 sin x

divide both sides by 6.9

sin x = 4.9969541351  / 6.9

sin x = 0.72419625146

x = sin⁻¹ 0.72419625146

x = 46.4020264383

Therefore,

x = 46.40°

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The true statement about the expressions is (d) None of these

Polynomial expressions are mathematical statements that are represented by variables, coefficients and operators

From the list of options, the given parameters are

(a) 2 − √6 + 2 (b) 52 − 3 + 1 (c)√1

For an expression to be a polynomial, the expression must have variables, coefficients and operators

None of the given expressions have variables, coefficients and operators.

This means that the expressions are not polynomial

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