what is the value of tan 30?

Answer:

2/sqrt6 = sqrt6/3

3/sqrt54 = sqrt6/6

2/sqrt6 + 3/sqrt54

= sqrt6/2

Step-by-step explanation:

Simplifying when there are radicals involved usually means "rationalizing".

Rationalizing means getting rid of the square root on the bottom of a fraction.

See image.

The statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.

We are given;

h(x) = -x^3 - 9x^2 + 4x + 96

The function is a cubic function.

Since the leading coefficient is negative the graph start from second quadrant.

So, the graph must be positive in the second quadrant.

Let us check the option D;

The graph is positive on the intervals (- ∞ , - 8) and (- 4, 3).

The graph is positive in the second quadrant. So, (- ∞ , - 8) satisfy.

Let's choose any point between -4 to 3 and substitute in the given equation.

Put x = -1 in the given equation;

h(x) = -(-1)^3 - 9(-1)^2 + 4(-1) + 96 = 1 - 9 - 4 + 96 = 84

So, h(x) is positive.

So, option D is correct.

Thus, the statement which is true about the graph representing function h is the graph is positive on the intervals (- ∞, - 8) and (- 4, 3). Option D is correct.

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The solution after the multiplication of 0.01 x 4066.61 is 40.6661

Multiplication

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. And the word multiply means the repeated addition of groups of equal sizes.

Given,

Here we have the operation 0.01 x 4066.61

Now we have to perform the multiplication operation in it.

While we looking into the given operation, we have identified that there are  4 total decimal places in both numbers.

First, we have to ignore the decimal places and complete the multiplication as if operating on two integers.

The the calculation for the multiplication is shown in the following image.

Now, we have to rewrite the product with 4 total decimal places.

Then we get the answer is 40.6661

Therefore, 0.01 × 4066.61 = 40.6661

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Answer:

a=3

Step-by-step explanation:

To find a, you plug the known numbers into the given equation (coordinates). f(x) is the same as the y-coordinate.

With that, you get:

5=a(-1)^2+2

Then you solve for a

3=a(-1)^2

3=a(1)

3=a

Answer: The answer is -4

If you use the chips to help illustrate your point, here's a good way to explain it:

Let's say that there are five -1 chips and one +1 chip. In order to use chips, you would have to subtract the chips from each other. Put a -1 chip and a +1 chip together and then take them away (as to subtract them). This would leave you with four -1 chips, thus giving you your answer.

Hope this helps!

Answer:

when two different signs are in numbers if +or_ you I'll substruct or +or+ you I'll added ok

y=4/5x-2/5 is the equation used to plot the graph.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given equation is 4x−5y=1

Four times of x minus five times of y equal to one

4x−5y=1

Let us write this equation in slope intercept form

-5y=1-4x

5y=-2+4x

y=-2/5+4/5x

y=4/5x-2/5

x       0         1        2         3

y       -2/5    2/5    6/5     10/5

y       -0.4     0.4     1.2     2

by using these points we plot the graph.

Hence y=4/5x-2/5 is the equation used to plot the graph.

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The Total Distance is 51 yards.

Coordinates are a pair of integers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane. The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical).

Given:

As, A and B have same x- coordinate

AB = | (y- coordinate of A) - (y- coordinate of B)|

     = |5 - (-2)|

     = 7

and, B and C have same y- coordinate

AB = | (x- coordinate of B) - (x- coordinate of A)|

     = |3 - (-7)|

     = 10

Then, Total distance= 7+ 10= 17

and, Total distance in yards = 17 x 3= 51 yards

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Answer: 9

Step-by-step explanation:

The ratio of two outputs for any two input values that are 2 units apart is

27

Ratio refers to fractions of two numbers say a and b written in the form

a / b

The problem involves dividing the output for the larger x-value by the output or the smaller x-value

choosing output for x = 3 and x = 6, the two values are 2 units apart

the outputs are y = 27 and y = 729 respectively

taking the ratios

= 729 / 27

dividing gives the lowest term of the fraction

= 27 / 1

= 27

Hence dividing the output values for x = 3 and x = 6 is 27

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The equation that will be used to illustrate the information regarding the total cost is C = 50 + 75h.

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Initial fee = 50

Amount charged by hour = 75

Number of hours = h

The total cost will be:

= Initial fee + Amount for each hour

= 50 + 75(h)

= 50 + 75h

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The speed of the raft was 2.86 km/hr.

Speed is defined as the rate of change of position of an object in any direction.

Given that, a patrol boat with speed of 12 km/hr caught a raft after travelling for 20 km and patrol boat left the dock after 5 hours and 20 minutes the raft left,

The time taken by the patrol boat to catch the raft is;

t = 20/15 = 5/3 hours

5/3 hours = 1 hour 40 minutes

Thus, it took 1 hour 40 minutes for the patrol boat to catch the raft

Thus, the raft was travelling for 5 hours 20 minutes plus 1 hour 40 minutes which 7 hours,

The speed of raft = 20/7 = 2.86 km/hr

Hence, The speed of the raft was 2.86 km/hr.

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The three consecutive odd intergers are 3,5 and 7

What do you mean by algebraic expression ?

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.

An algebraic expression can be a combination of variables and constants. Any multiplied value that is prefixed to a variable is a factor.

Let the three consecutive odd integers are x, x+2 and x+ 4

Here x is the smallest odd integer and x+4 is the largest odd integer

According to the question:

3(x +4) = 7x

3x + 12 = 7x

7x - 3x = 12

4x = 12

x = 12/4

x = 3  

Three consecutive odd integers become:

x = 3

x + 2 = 3 +2 = 5

x + 4 = 3 + 4 = 7

Hence, the three consecutive odd intergers are 3,5 and 7

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Answer: 2

x = 2

[tex]x^{2}[/tex] = 4

[tex]2^{2}[/tex] = 4

4 = 4

Answer: 8 books

Step-by-step explanation:

First, she has 40 books.

1) Then she fills 4/5 of it. 4/5 of 40 is 32.

2) (4/5) x (40) = 32.

3) 40 - 32 = 8

4) So she needs to add 8 books.

Hope this helps :)

Answer:

The answer is 6.5

Step-by-step explanation:

The equation is y=3x-1. Plug in 2.5 as the value for x and solve.

3×2.5=7.5

7.5-1=6.5

Through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.

It is given to us that -

Each carton of food will feed 11 people

Each carton of clothing will help 4 people

Each 20-cubic-foot box of food weighs 40 pounds

Each 5-cubic-foot box of clothing weighs 20 pounds

The total weight per carrier cannot exceed 23,000 pounds

The total volume must be no more than 9000 cubic feet

We have to find out the number of cartons of food and clothing should be sent with each plane shipment to maximize the number of people who can be helped.

Let us say that -

The number of cartons of food = x

The number of cartons of clothing = y

According to the given information, the constraints on weight and size can be represented as -

Constraints on weight:

[tex]40x+20y\leq 23000\\= > 20y\leq 23000-40x\\= > 20y\leq -40x+23000\\= > y\leq -2x+1150[/tex]------ (1)

Constraints on size:

[tex]20x+5y\leq 9000\\= > 5y\leq 9000-20x\\= > 5y\leq -20x+9000\\= > y\leq -4x+1800[/tex]----- (2)

We also know that

[tex]x\geq 0[/tex] and [tex]y\geq 0[/tex]

The equation for the help that will be provided with each carton of food and clothing can be represented as -

[tex]11x+4y[/tex] ---- (3)

From equation (1), for weight graph, we have

[tex]y\leq -2x+1150[/tex]

For [tex]x=0[/tex], [tex]y\leq 1150[/tex]

For [tex]y=0, x\leq 575[/tex]

From equation (2), for size graph, we have

[tex]y\leq -4x+1800[/tex]

For [tex]x=0, y\leq 1800[/tex]

For [tex]y=0, x\leq 450[/tex]

For (0,1150), the equation (3) becomes

[tex]11x+4y[/tex]

[tex]= 11*0+4*1150\\= 4600[/tex]

For (360, 550), the equation (3) becomes

[tex]11x+4y\\= 11*360 + 4*550\\= 6160[/tex]

For (450,0), the equation (3) becomes

[tex]11x+4y\\= 11*450 + 4*0\\= 4950[/tex]

Thus, through linear programming, we find out that the number of cartons of food is 360 cartons and the number of cartons of clothing is 550 cartons.

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The length and width of the rectangular plot that will maximize the area are 50 feet and 25 feet respectively.

The vertex (maximum) of this equation is equal to 1,250 square feet.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = lw

Where:

Since one side of this rectangular plot along the river does not require fencing, the perimeter equation is given by:

P = 2(l + w)

100 = 2w + l      

Making length the subject of formula, we have:

l = 100 - 2w

Therefore, the area of this rectangular plot would now be:

A = (100 - 2w)w

A = 100w - 2w²

Next, we would take the first derivative and equate to zero in order to obtain the maximum area:

dA/dw = 100 - 4w

0 = 100 - 4w

4w = 100

Width, w = 25 feet.

For the length of this rectangular plot, we have:

Length, l = 100 - 2w

Length, l = 100 - 2(50)

Length, l = 50 feet.

Now, we can find the vertex (maximum) of this equation is given by:

Maximum area = 50 × 25

Maximum area = 1,250 square feet.

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According to the concept of polynomial division, the equivalent expression is option (a). x+7 + 26/(x-3)

Polynomial division

Polynomial division refers the process of dividing one polynomial with another.

Given,

Here we have the expression (x² + 4x + 5) / x - 3.

Now, we have to find the equivalent polynomial expression when x - 3 is not equal to 3.

In order to find the equivalent expression, we have to do the following steps:

1. Divide the first term of the dividend by the first term of the divisor

2. Write down the calculated result x in the upper part of the table.

3. Multiply it by the divisor

4. Subtract this result from the dividend

Repeat this 4 steps until no further division.

This process is illustrated below.

According to this process, the equivalent fraction for the given fraction is

x + 7 + 26/(x - 3)

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The slope of the line, 8x + 3y = 8 – 2x, is -10/3

From the question, we are to determine the slope of the given equation.

The given equation is

8x + 3y = 8 – 2x

To determine the slope of the line, we will express the equation in the general form of the slope-intercept form of the equation a line.

The general form of the slope-intercept form of a line is

y = mx + b

Where m is the slope

and b is the y-intercept

Expressing the equation in the slope-intercept form of a line

8x + 3y = 8 - 2x

Subtract 8x from both sides of the equation

8x - 8x + 3y = 8 - 2x - 8x

3y = 8 - 10x

3y = -10x + 8

Divide through by 3

3y/3 = -10x/3 + 8/3

Y = -10/3 x + 8/3

By comparison,

m = -10/3

Hence, the slope is -10/3

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The translated function is g(x)= 8x+0

What is Function?

A relation between a collection of inputs and outputs is known as a function. A function is an association between inputs in which each input is connected to precisely one output. A domain,  range exists for every function.

An example of a rule is a function, which produces one output for a single input.

Given:

f(x)= 8x - 10

Now,  translation 10 units up

Thus, g(x)= f(x) + 10

g(x)=  8x - 10+ 10

Hence, g(x)= 8x+0

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Each of the equations should be matched with the value of x that makes them true as follows:

x = 2; x + 2x + 3 = 9, 5(x + 3) = 25, and 4x − (2x + 1) = 3.

x = 3; 2(2x − 3) = 6, 5x - 2x - 4 = 5, and 5x − (3x − 1) = 7.

In order to determine which x-values are true solutions based on the given equations, we would have to test each of the values of x by substituting them into the equations as follows;

When x = 2, we have:

2(2x − 3) = 6

4x − 6 = 6

4(2) - 6 = 6

8 - 6 = 6

2 = 6 (False).

When x = 3, we have:

2(2x − 3) = 6

4x − 6 = 6

4(3) - 6 = 6

12 - 6 = 6

6 = 6 (True).

When x = 2, we have:

5x - 2x - 4 = 5

3x - 4 = 5

3(2) - 4 = 5

6 - 4 = 5

1 = 5 (False).

When x = 3, we have:

5x - 2x - 4 = 5

3x - 4 = 5

3(3) - 4 = 5

9 - 4 = 5

5 = 5 (True).

When x = 2, we have:

x + 2x + 3 = 9

3x + 3 = 9

3(2) + 3 = 12

9 = 12 (False).

When x = 3, we have:

x + 2x + 3 = 9

3x + 3 = 9

3(3) + 3 = 12

12 = 12 (True).

5(x + 3) = 25

5x + 15 = 25

5x = 25 - 15

5x = 10

x = 2 (True).

4x − (2x + 1) = 3

4x - 2x - 1 = 3

2x = 3 + 1

2x = 4

x = 2 (True).

5x − (3x − 1) = 7

5x - 3x + 1 = 7

2x = 7 - 1

2x = 6

x = 3 (True).

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Answer:

When a die is rolled, here it's Total possible outcome is= 6

and sample space is = 2 ( i.e. 1 & 2)

So. Probability of getting less than 3 =  26

=13

That's it.

Step-by-step explanation:

Adam earned $100.12 more interest than the Sophie

Consider Sophie

The principal amount = $3330

The interest rate = 7.4%

The time period = 5 years

Simple interest = PRT

Where P is the principal amount

R is the interest rate

T is the time period

Substitute the values in the equation

Simple interest = 3330× (7.4/100) × 5

= $1232.1

Consider Adam

The principal amount = $2795

The interest rate = 8.1%

The time period = 5 years

Simple interest = 2795 × (8.1/100) × 5

= $1131.98

The difference = 1232.1 - 1131.98

= $100.12

Hence, the Adam earned $100.12 more interest than the Sophie

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The number of cards that are needed to ensure that you have 12 cards of the same color is of:

43 cards.

The highest number of cards for which at least one color having 12 cards is not guaranteed is obtained as follows:

Hence the number is:

11 + 11 + 11 + 10 = 3 x 11 + 10 = 33 + 10 = 43 cards.

With the next card, that is, the 44th card, it will be ensured that at least one color will have 12 cards.

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The final cost of the necklace if the customer bought it on February 28th or March 1st is $96.05 or $113, respectively.

The final cost of the necklace purchased on February 28th includes the markup and excludes the promotional and coupon discounts, before adding the sales tax.

Similarly, the final cost of the necklace purchased on March 1st includes the markup and excludes the coupon discount, before adding the sales tax.

Cost price to the store = $75

Markup =55%

Marked-up selling price = $116.25 ($75 x 1.55)

February sales discount = 15%

Promotional price during February = $98.81 ($116.25 x 1 - 15%)

Discount coupon rate = 10%

Discounted price = $88.93 ($98.81 x 1 - 10%)

Sales tax = 8%

Final selling price = $96.05 ($88.93 x 1.08)

Cost price to the store = $75

Markup =55%

Marked-up selling price = $116.25 ($75 x 1.55)

Discount coupon rate = 10%

Discounted price = $104.63 ($116.25 x 1 - 10%)

Sales tax = 8%

Final selling price = $113 ($104.63 x 1.08)

Thus, the customer pays an additional $16.95 if they purchase the necklace on March 1st without the promotional discount, instead of February 28th.

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The total loss of yards is 10yards(-10yards)

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

There are positive integers e g 1,2,3,5,7,8,11,16 and negative integers -1,-2,-4, -22 e t c

The addition of a negative and positive integers of the same number will give 0 .i.e -5+(+5)=0

similarly -6+(+6)= 0

if the lost yards are represented by negative and the gained yards by positive then,

-5yards-9yards-8yards = -22yards

+12 yards is gained

therefore the total yards lost or gained is

-22+12= -10yards

since it is -10yards then the yards are lost yards.

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According to the concept of complex numbers, the solution function is (5 - 6i) (2 + 4i) = (34 + 8i)

Complex numbers:

Complex numbers means a combination of a real number and an imaginary number.

The standard form of complex number is,

a + ib

Where a complex number, where a,b are real numbers and i = √-1.

Given,

Here we have the following complex number expression

(_ + _i) (_ + _i) = 34 + 8i

Here we need find the value of the dashes and the number must lies between -9 to +9.

Let us consider a, b, c and d as the number presented in the dashes then it can be written as,

=> (a + bi) (c + di)

Now, we have to expand this expression then we get,

=> ac + adi + bci + bdi²

Combine the like terms,

=> (ac − bd) + (ad + bc)i

Now, we have to match the coefficients as,

30 < ac − bd < 80

We also know that,

=> ad + bc = 0

Now, we need to pick four integers between -9 and 9 such that these two equations are satisfied.  

We also know that

=> ac − bd = 34

=> ad + bc = 8

Therefore, it makes sense to assume b is negative.  

After some trial and error, one possible answer is a = 5, b = -6, c = 2, d = 4

Therefore, the expression is written as,

=> (5 - 6i) (2 + 4i) = (34 + 8i)

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