In 2017, the library was able to record 4907 borrow books. By December of the same year, the library has 6 times its January record. The library’s December record is ?

The value of sin(x/2)= √(1-√11/6)/2

The value of cos(x/2)=√(1+√11/6)/2

The value of tan(x/2) = 5/6/(√(1+√11/6)

In trigonometry, the half-angle formula is used to determine the exact values of the trigonometric ratios of angles such as 15° (half of the standard angle 30°), 22.5° (half of the standard angle 45 and so on. If θ is an angle, then the half angle is represented by θ/2.

In trigonometry, sin( x/2)= √(1-cosx)/2

cos( x/2)= √(1+cosx)/2

tan( x/2)=sinx/1+cosx

if sin (x) = 5/6

this means that 5 is the opposite and 6 is the hypotenuse, then the adjascent is

a= √(6^2-5^2)

a= √36-25

a= √11

therefore if cos x= √11/6

sin(x/2)= √(1-√11/6)/2

cos(x/2)= √(1+√11/6)/2

tan(x/2)=5/6/(√(1+√11/6)

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The value of the unknown angle x would be 43 degrees.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We have been given a right-angle triangle with a perpendicular side of 6 units and a hypotenuse of 10 units.

The unknown angle is x which needs to find.

Therefore, applying trigonometry;

Sin x = perpendicular/hypotenuse

Sin x = 6/10

Sin x = 3/5

Sin x = 0.6

x = Sin inverse (0.6)

x = 43 degrees.

Hence, the value of the unknown angle x would be 43 degrees.

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Answer:

Below

Step-by-step explanation:

4  3/10   * 3 =   43/10 * 3 = 129 / 10 =  12 9/10 miles

Inverse of the function is -2+x

What do you mean by inverse function?

A function that returns the initial value for which a function has produced an output is known as an inverse function. If f(x) is a function that produces the value y, then [tex]f^{-1}(y)[/tex] the inverse function of y, will provide the value x.

The function's inverse, represented by ,  [tex]f^{-1}[/tex] returns the original value that was used to create the output (x).

Given function is  y = x² + 4x + 4

To find the inverse function, we need to express x as a function of y:

Substitue y=x

⇒ x = [tex]y^{2}+4y+4[/tex]

Substract x from the above equation we get,

[tex]y^{2}+4y+4[/tex] - x = 0

Solve the above equation using quadratic formula we get,

y = [tex]\frac{-4+\sqrt{16-4(4-x)} }{2}[/tex]   [tex]=\frac{-4+\sqrt{16-16+4x} }{2}[/tex]  = [tex]\frac{-4+2x}{2}=-2+x[/tex]

Similarly, y = -2-x

Therefore, [tex]f^{-1}=[/tex] -2+x , -2-x

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Answer:

y-2

Step-by-step explanation:

Step-by-step explanation:

what is the problem to solve ?

I assume we need to calculate the area of the whole figure ?

in any case, we have a problem :

a rhombus is a tilted square, a special parallelogram, as it has 4 equal sides.

that would mean all 4 sides of that central rhombus are 5 in.

that would make both triangles equilateral triangles (all 3 sides are equally long : 5 in).

but in order for a right-angled triangle to have the Hypotenuse = 5 in and the height (= left leg) = 4 in, that must make the right leg

5² = 4² + leg²

25 = 16 + leg²

9 = leg²

leg = 3 in

and so, the baseline of the large triangle 2×3 = 6 in.

and not 5 in, which must be the top and base line of the rhombus.

so, the whole problem definition is wrong.

the only solution when accepting the given lengths, is that the triangle sides are NOT a straight extension of the rhombus sides.

the triangle side is the Hypotenuse of the smaller internal right-angled triangle

side² = 4² + (5/2)² = 16 + 6.25 = 22.25

side = 4.716990566... in

anyway, the area of each of the large triangles is

baseline×height / 2 = 5×4/2 = 10 in²

we have 2 triangles = 2×10 = 20 in²

the area of the rhombus is

baseline×height = 5×4 = 20 in²

please note that the area of a rhombus is also

diagonal1 × diagonal2 / 2

but that applies only, when we have the lengths of the diagonals. both approaches give the same result, of course.

so, the whole area is

20 + 20 = 40 in²

The difference in the cost of all 30 pens between two shops is,

£1.05

Given, Eve is going to buy 30 pens from either shop A or shop B.

Shop A: pack of 10 pens for £2

Shop B: pack of 5 for £1.10 buy 1 pack and get 1 half price.

So, the cost of 30 pens from the shop A is,

as, a pack of 10 pens is of £2

1 pen = 2/10

30 pens = £6

Now, the cost of 30 pens from the shop B is,

as, a pack of 5 for £1.10

1 pen = 1.10/5 = £0.22

also buy 1 and get 1 at half price.

So, 2 pens = 0.22 + 0.11 = £0.33

Therefore, 30 pens = £4.95

So, the cost of 30 pens from shop A is £6 and from shop B is £4.95.

Hence, the difference in the cost of all 30 pens between two shops is,

£1.05

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The roots of the equation x³ + 2x² + 36x + 72 = 0 are ( -2 , -6i , +6i )

What is Factorizing?

Brackets should be expanded in the following ways:

For an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

Let the equation be x³ + 2x² + 36x = -72

Adding 72 on both sides , we get

x³ + 2x² + 36x + 72 = 0

Now , on simplifying we get

Take the common factor x² in first two terms and 36 in last two terms

So ,

x² ( x + 2 ) + 36 ( x + 2 ) = 0

Now , taking ( x + 2 ) as common factor , we get

( x² + 36 ) ( x + 2 ) = 0

So , for the equation to be 0 , either ( x + 2 ) = 0 or ( x² + 36 ) =0

And , we can find the solutions to the equation as

x + 2 = 0

Subtracting 2 on both sides , we get

x = -2

So , one solution is -2

Now ,

( x² + 36 ) =0

Subtracting 36 on both sides , we get

x² = -36

x = √ ( -36 )

x = ± 6i

So , we got two more solutions as -6i and +6i

Hence , the roots of the equation are -2 , -6i and +6i

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The pairs of numbers given, (1, 2) is not a solution.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

y= 2x+1 /3

Now, First value of x = 0

y= 2(0)+1 /3

y= 1/3

i.e., (0, 1/3)

and, Second value of x = 1

y= 2(1)+1 /3

y= 5/3

i.e., (1, 5/3)

and, Third value of x = 4

y= 2(4)+1 /3

y= 9/3

y=3

i.e., (4, 3)

Hence, from the pairs of numbers given, (1, 2) is not a solution.

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The value of tan 30° after using trigonometric ratio  is  [tex]\frac{1}{\sqrt{3} }[/tex] .

What is trigonometric ratio?

 There are six trigonometric ratios used in trigonometry: sine, cosine, tangent, secant, and cotangent. The abbreviations for these ratios are sin, cos, tan, sec, cosec(or csc), and cot. Look at the below-displayed right-angled triangle. Any two of the three sides of a right-angled triangle can be compared in terms of their relative angles using trigonometric ratios.

Here the given

=> tan30°

Now ,Tan 30 degrees in radians is written as

=>tan (30° × π/180°)

=> [tex]\frac{1}{\sqrt{3} }[/tex]

Therefore the value of tan30° is  [tex]\frac{1}{\sqrt{3} }[/tex] .

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Answer:

2

Step-by-step explanation:

6w is a term

7x is a term

Answer: The answer to this question would be: 5 days

In this question, there are two kinds of rent pricing and you are asked to find the number of days when both of them will charge the same price.

From the description, you can get an equation of each price which would look like this(x=number of day rent):

cost1= 110 + 46x

cost2= 70 + 54x

Then, the days when the price same would be:

cost1 = cost2

110 + 46x= 70+54x

110-70= 54x - 46x

40= 8x

x=5

Step-by-step explanation:

Answer:

It is not a solution

Step-by-step explanation:

put in (-9,-5) in for x and y

9(-9)+4(-5)=10

-81-20=10

-101=10

This is false so (-9,-5) is not a solution to the equation 9x+4y=10

The solution set is X ∈{1, -7}

The set of values that satisfy a given set of equations or inequalities is known as a solution set. For example, the solution set for a set of polynomials over a ring is the subset on which the polynomials all vanish (evaluate to 0).

Given that 3(x+3) – 12 = 0

We have to find the solution set

3(x+3) – 12 = 0

3(x+3) = 12

X+3 = ±4

X + 3 = 4 or x + 3 = -4

X = 1 or x = -7

X ∈{1, -7}

Therefore the solution set is X ∈{1, -7}

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Answer:

-3/22

Step-by-step explanation:

Hope this helps!

Answer: [tex]-\frac{3}{22}[/tex]

Step-by-step explanation:

To find the product, multiply the two fractions:

[tex]-\frac{2}{11} *\frac{3}{4} =-\frac{2*3}{11*4} =-\frac{6}{44} =-\frac{3}{22}[/tex]

Every second, 44 megabytes of files will be transferred to her hard drive.

The size of the files on her external hard drive in megabytes is given F, where F = 38 + 6t and t is the time in seconds since the transfer began.

The function is below

F = 38 + 6t   ....(i)

To determine the number of megabytes of files transferred to her hard drive every second

Substitute the value of t = 1 in the equation (i), and solve for F

F = 38 + 6(1)

F = 38 + 6

F = 44

So the number of megabytes of files = 44

Therefore, every second, 44 megabytes of files will be transferred to her hard drive.

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The fraction of person that represents a degree is 1/4

A Π chart is a type of representation used in showing data representing the parts sometimes in degrees.

Π charts are made in circle and use the features of circle

Considering the problem at hand, the total number of workers in the office is 90

The total angle of a circle is 360

if 90 person is equivalent to 360 then one person would be

1 person = 360 / 90

1 person = 4 degrees

therefore 1 degree will be 1/4 person

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Answer:x^4+6

Step-by-step explanation:

you must combined both x squared to get x^4 and then add the opposite of -4 Which is +4  and what you do to one side you must do to the other therefore you add the 2 to it as well. in conclusion you get x^4+6. hope this helps:)

The simplified form of the expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex] after evaluating is equal to [tex]\sqrt[3]{2}[/tex]

What are Powers?

Steps to Combine and Simplify Exponents

The three basic rules of exponents used to combine the exponents and simplify the expression are as follows:

Here, we have to simplify and evaluate the given expression using the rules of exponents.

We have the given expression, [tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }[/tex]  -------(4)

Using the exponents rules, [tex](a^{m})^{n} =a^{m \times n}[/tex] and [tex](a \times b)^{m}=a^{m} \times b^{m}[/tex] in the above expression, we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3} } \times 3^{\frac{2}{3} } \times 2^{3 \times \frac{1}{3} } }{2^{\frac{2}{3} } \times 2^{\frac{2}{3} } \times 3^{\frac{2}{3} }}[/tex]

Simplifying further using (1) and (2), we get (4) as,

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = \frac{2^{\frac{2}{3}}}{2^{\frac{2}{3}+\frac{2}{3} }} \times \frac{3^{\frac{2}{3} } }{3^{\frac{2}{3} }} \times 2^{1} \\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =\frac{2^{\frac{2}{3}}}{2^{\frac{4}{3} }} \times 2^{\frac{2}{3}-\frac{2}{3} } \times 2\\\implies \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{\frac{2}{3}-\frac{4}{3} } \times 2^{0} \times 2[/tex]

We know that, [tex]a^{0} =1[/tex]

So, further simplifying we get

[tex]\frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } =2^{-\frac{2}{3} } \times 1 \times 2\\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } } = 2^{-\frac{2}{3}+1 } \\\imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=2^{\frac{1}{3}}\\ \imples \frac{6^{\frac{2}{3} } \times 8^{\frac{1}{3} } }{12^{\frac{2}{3} } }=\sqrt[3]{2}[/tex]

Therefore, the simplied form of the given expression is [tex]\sqrt[3]{2}[/tex]

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The solution of linear programming problem is the maximum value is 2, x_1 = 1, x _2 =0.

What is linear programming problem?

The goal of the Linear Programming Problems (LPP) is to determine the best value for a given linear function. The ideal value may be either the highest or lowest value. The specified linear function is regarded as an objective function in this situation. The objective function may have a number of variables that must meet a set of linear inequalities known as linear constraints. These variables may also be subject to conditions. The following scenarios, such as manufacturing difficulties, diet problems, transportation challenges, allocation problems, and so on, can be solved optimally using the linear programming problems.

After first iteration,

Negative minimum Z_j-C_j is -2 and its column index is 1. So, the entering variable is x_1.

Minimum ratio is 1 and its row index is 2. So, the leaving basis variable is S_2.

∴ The pivot element is 2.

Entering =x_1, Departing =S_2, Key Element =2

After second iteration:

Since all Z_j-C_j≥0

Hence, optimal solution is arrived with value of variables as :

x_1=1,x_2=0

Max Z=2

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Step-by-step explanation:

g(x) = the original function at x-2.

just means it is the same function as the original function, just moved 2 units to the right.

just think about it :

e.g.

g(3) is the same as the originated function at x=1.

g(4) is the same as the original function at x=2.

...

so, everything that happened for the original function at x, happens now for g at x+2.

therefore, again, things move 2 units to the right (positive x direction) .

that means the vertex "moves" from

(-5, 6) to (-3, 6)

the vertex of g(x) = (-3, 6)

Answer:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Equation of a circle}\\\\$(x-a)^2+(y-b)^2=r^2$\\\\where:\\ \phantom{ww}$\bullet$ $(a, b)$ is the center. \\ \phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

The points that are a distance of 5 units from P(-8, 4) will be all the points on the circumference of a circle with center (-8, 4) and radius 5.

Substitute the center and radius into the formula to create an equation of the circle:

[tex]\implies (x+8)^2+(y-4)^2=25[/tex]

The y-value of any point on the x-axis is zero.

Therefore, to find the points on the x-axis that are 5 units from point P, substitute y = 0 into the equation of the circle and solve for x:

[tex]\implies (x+8)^2+(0-4)^2=25[/tex]

[tex]\implies (x+8)^2+(-4)^2=25[/tex]

[tex]\implies (x+8)^2+16=25[/tex]

[tex]\implies (x+8)^2+16-16=25-16[/tex]

[tex]\implies (x+8)^2=9[/tex]

[tex]\implies \sqrt{(x+8)^2}=\sqrt{9}[/tex]

[tex]\implies x+8=\pm3[/tex]

[tex]\implies x+8-8=\pm3-8[/tex]

[tex]\implies x=-8\pm3[/tex]

[tex]\implies x=-11, x=-5[/tex]

Therefore:

[tex](x,y)=\left(\; \boxed{-11,0}\; \right)\; \textsf{(smaller $x$-value)}[/tex]

[tex](x,y)=\left(\; \boxed{-5,0}\; \right)\; \textsf{(larger $x$-value)}[/tex]

Step-by-step explanation:

okok

Check the picture below.

Answer:

AAS

Step-by-step explanation:

let us say that angleDAB is 60 then angleADB is 30

due to the presence of line DB we can also say that angleDCB is 60 and angle CBD is 30