Let [tex]sin\beta =\frac{2\sqrt[]{2} }{5} \\[/tex] and [tex]\frac{\pi }{2} \leq\beta \leq \pi \\[/tex].
Determine the exact value of [tex]sin(\frac{\beta }{2} )[/tex]

The length and width of the rectangle are 18 in and 1 in, respectively.

There are different types of quadrilaterals, for example, square, rectangle, rhombus, trapezoid, and parallelogram.  Each type is defined accordingly to its length of sides and angles. For example, in a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

The area of a rectangle can be found for the formula : b*h, where b = base and h =height.

For this question, the length exceeds its width by 17 inches - L=W+17. Here, the length is the base and the width is the height. Thus,  from the value of area given, you can find the values of the length and width of the rectangle.

A=b*h

18=(W+17)*W

18=W²+17W

W²+17W-18=0

Solving this quadratic equation, you have:

[tex]w_{1,\:2}=\frac{-17\pm \sqrt{17^2-4\cdot \:1\cdot \left(-18\right)}}{2\cdot \:1}[/tex]

[tex]w_{1,\:2}=\frac{-17\pm \:19}{2\cdot \:1}[/tex]

w1=1 and w2= -18

For dimensions, only positive numbers must be used. Then, the width is equal to 1 inch.

As, the area (l*w) is 18 in², see.

18=l*w

18=l*1

l=18 in

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The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.

The net change in latitude of the helicopter can be evaluated as follows;

x = |-6.20° - 22.27°| = |-28.47°|

x = 28.47°

The net change in longitude of the helicopter can be evaluated similarly as follows;

y = |106.80° - 114.15°| = |-7.35°|

x= 7.35°

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Answer:

17√3

Step-by-step explanation:

In a 45-45-90 triangle, the hypotenuse is √3 times larger than the legs.

17*√3 = 17√3

Hello,

[tex] \frac{p(x)}{q(x)} = \frac{ {x}^{2} - x - 12}{x + 3} = \frac{(x - 4)(x + 3)}{x + 3} = x - 4[/tex]

Answer:

Step-by-step explanation:

The first step is the parenthesis

The equation is given as:

8(2x+4) = 2(1x+3)

Using PEMDAS, the first step is to open the brackets by multiplication.

So, we have:

16x + 32 = 2x + 6

Hence, the first step is the parenthesis

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Answer:

Step-by-step explanation:

5x = 140

= x = 140/5

= x = 28

Answer:

1. 3 terms; degree 5

2. 2 terms; degree 3

3. 9mn³ + 14mn²

4. 9a^4b^3

Step-by-step explanation:

Problems 1 - 2:

Each product of a number and variables is a term. The number may be 1, so it is not written. Also, a term may not have a variable.

The degree of a term is the sum of the exponents of all the variables of the term. A plain variable, such as x has an exponent of 1 which is not written but must be added to determine the degree.

The degree of the polynomial is the same as the degree of the term with the highest degree.

1.

3 terms

degree 5

2.

2 terms

degree 3

Problems 3 - 4:

Combine like terms. Like terms have the same variables and exponents.

3.

6mn³ - mn² + 3mn³ + 15mn² =

= 6mn³ + 3mn³ - mn² + 15mn²

= 9mn³ + 14mn²

4.

a^4b^3 + 8a^4b^3 =

= 1a^4b^3 + 8a^4b^3

= 9a^4b^3

Answer:

Step-by-step explanation:

hello:

here an solution

The equation of directrix is D. y=± 432/13.

Definition of hyperbola -

1. The vertex i at (0, 36) and a focus at (0, 39), then you have:

  a=36

a²=1296

2. The equation of directrix is:

y =  a² =c

c  =  39

y =  1296/39

y  =  432/13

Therefore, the answer is the option D, which is: D. y=± 432/13

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The complete question is -

A hyperbola centered at the origin has a vertex at (0, 36) and a focus at (0, 39)

Which are the equations of the directrices ?

A. x= ±12/13

B. y=±12/13

C. x=±432/13

D. y=± 432/13

Answer: Correct

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

For the value of y, substitute x = 28 into the equation.

2x + 3y = 194

2(28) + 3(y) = 194

56 + 3y = 194

3y = 194 - 56

3y = 138

dividing bothsides by 3

y = 46

Answer:

y = 46

Step-by-step explanation:

We want to find the value of y

2x+3y = 194

We are given the value of x

x=28

Substitute the value of x into the first equation

2(28)+3y = 194

56 + 3y = 194

Subtract 56 from each side

56+3y -56 = 194 -56

3y = 138

Divide each side by 3

3y/3 = 138/3

y =46

Answer: [tex]42x^3 y^2[/tex]

Step-by-step explanation:

[tex]A=(3xy)(14x^2 y)=42x^3 y^2[/tex]

Answer:

315

Step-by-step explanation:

-3ac7

-3x-3=9x5=45x7=315

❄ Hi there,

evaluate this expression by using substitution:

If

then

[tex]\sf{-3(-3)(5)}[/tex]

[tex]\sf{9\times5}[/tex]

[tex]\triangleright \ \sf{45}[/tex]

That's it!

❄

The value of a is -3 and the value of k is 10

A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic

The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).

The fixed point is called the focus

A fixed line is called a directrix

Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation

Here the equation y = a(x -2)^2 + k...........(1)

and two points A(1,7) and B(4, -2) is given

We need to find the value of a and k

Put A(1,7) in equation (1) , we get,

7 = a + k ,therefore k = 7 - a......(2)

Put B(4, -2) in equation (1), we get,

-2 = 4a + k........(3)

Put k= 7-a in (3)

-2 = 4a+7 -a

3a = -9

a= -3

From equation (2) , we get k = 7-(-3)= 10

Hence the value of k is 10 and the value of a is -3

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For the given points to lie on the parabola,

a = -3 and k = 10.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).

According to the question,

Equation of parabola : y = a[tex](x-2)^{2}[/tex] + k

Points A(1,7) and B(4,-2)

For the points to lie on the parabola,

7 = a[tex](1-2)^{2}[/tex]+k

7 = a + k

Similarly,

-2 = a[tex](4-2)^{2}[/tex] + k

-2 = 4a + k

On solving the two equations simultaneously, we get,

a = -3

k = 10

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The value of the expression ((-3)^4)^2 when simplified is 6561

Expressions are mathematical statements represented by numbers, arithmetic operations and variables

The expression is given as:

((-3)^4)^2

Start by expanding the inner bracket

((-3)^4)^2 = ((-3)*(-3)*(-3)*(-3))^2

Next, we evaluate the product (-3)*(-3)*(-3)*(-3)

This gives

((-3)^4)^2 = (81)^2

Next, expand the exponent

((-3)^4)^2 = (81) * 81

Next, we evaluate the product

This gives

((-3)^4)^2 = 6561

Hence, the value of the expression ((-3)^4)^2 when simplified is 6561

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[tex]3/ 5x^6*y^6[/tex] is the solution f the expression [tex](-9x^-1*y^-9) / (-15x^5*y^-3)[/tex]

Given expression:

(-9x^-1*y^-9) / (-15x^5*y^-3)

As we know, any number with negative power can be written in inverse form with positive power.

[tex]x^-a = 1/x^a[/tex]

Two number having same base their powers are added:

[tex]x^a + x^b = x^a+b[/tex]

[tex]= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)[/tex]

Hence the solution would be [tex]3 (5x^6 y^6)[/tex].

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Answer:

b

Step-by-step explanation:

Answer:

C, 24 units^2

Step-by-step explanation:

The formula for area of a parallelogram is base times height.

The height of the parallelogram is 4 units

The base of the parallelogram is 6 units

4 times 6 is 24

Hope this helps:)

Answer:

C. 24 units²

Step-by-step explanation:

To calculate the area of a parallelogram we use the following formula:

A = B*h (B: base, h: height)

The base of the parallelogram is 6 units and the height is 4 units

4*6 = 24 units but, the area is presented in square units so the answer is  24 units²

The equation of parabola becomes y = -2/25(x-3)^2 + 4.

According to the statement

we have given a graph and from this graph we have to find the equation of parabola in the general form.

So,

we know that the equation of parabola in general form is

y = a(x-h)^2 +k - (1)

From the graph we have:

a point on the graph is (x,y) = (-2,2)

the vertex of the graph is (h,k) = (3,4)

Now, substitute these values in the equation number (1)

Then

y = a(x-h)^2 +k

2 = a(-2-3)^2 +4

2 = a(-5)^2 +4

2 = a(25) +4

25a = -2

a = -2/25.

Now put a = -2/25 and (h,k) = (3,4) in the equation(1).

Then

the equation of parabola becomes y = -2/25(x-3)^2 + 4

So, The equation of parabola becomes y = -2/25(x-3)^2 + 4.

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Answer:

70 degrees = a

Step-by-step explanation:

Triangle= 180 degrees.

Therefore, since a and the unmarked angle are congruent since it is an isosceles triangle, we subtract 40 from 180, with a result of 140. With 140, we divide by 2 to find the degrees for both the unmarked angle and angle a, since they are congruent. 140/2 = 70, Angle A will equal to 70 degrees

Answer:

[tex]g(f(x))=25x^2-15x-7[/tex]

domain: (-∞,∞)

Step-by-step explanation:

g of f means plug the function f(x) in to x in the function g(x)

[tex]g(f(x))=5(5x^2-3x-2)+3\\g(f(x))=25x^2-15x-10+3\\g(f(x))=25x^2-15x-7[/tex]

since this is a parabola with no interval, the domain (the graph on the x-axis from left to right) is all real numbers or (-∞,∞)

Answer:

See below.

Step-by-step explanation:

The $2 charge is independent of the miles driven.  It cost $2 regardless of mileage.  The $0.20.half mile is the dependent variable.  The cost changes as a function of 1/2 miles driven.

The value of x is (d) 1

The angle ABC is given as:

∠ABC = 43x

The line AB touches the tangent line BC at point B.

However, the line AB is not a radius.

This means that:

∠ABC < 90

So, we have

43x < 90

Divide by 43

x < 2.09

From the list of options, the number less than 2.09 is 1

Hence, the value of x is (d) 1

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Answer:

The slope of the line segment CD is ( - [tex]\frac{8}{9}[/tex] )

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

Coordinates of the midpoint are

( [tex]\frac{x_{1} +x_{2} }{2}[/tex] , [tex]\frac{y_{1} +y_{2} }{2}[/tex] )

The slope of a line segment with coordinates of the ends

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

is m = [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

~~~~~~~~~~~~~

Point D is the midpoint of a segment AB

A ( 4 , 12 )

B ( - 6 , - 8 )

( [tex]\frac{-6+4}{2}[/tex] , [tex]\frac{-8+12}{2}[/tex] ) = ( - 1 , 2 )

D ( - 1 , 2 )

C ( 8 , - 6 )

[tex]m_{CD}[/tex] = [tex]\frac{-6-2}{8-(-1)}[/tex] = - [tex]\frac{8}{9}[/tex]

Answer:

See below

Step-by-step explanation:

Slope, m of given line = - 1/2

perpendicular slope is = -1/m = -1 / (-1/2) = +2

Point (6,9)  slope form of line

y -9 = 2(x-6)    expand and simplify

y - 9 = 2x -12

y = 2x -3

The function equality that represents the point where f(x) = g(x) is; A: f(0) = g(0) and f(2) = g(2)

From the question, the curved red line represents g(x) while the straight blue line represents f(x).

Now, the equality of functions f(x) = g(x)  is represented as a common function between their curves. Thus, we will just need to find a common point for both. This is;

f(x) has points (0, 4) and (2, 0).

g(x) has points (0,4) and (2,0).

It is pertinent to note that both functions have the same y-value for x=0 and x = 2. Thus, we can say that;

f(2) = g(2) and f(0) = g(0)

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Answer:

5

Step-by-step explanation

becasue 2x0=0 and 1x0=0

and when you add 5 to 0 you get five

Using it's concept, the standard deviation of the data-set is of 2.39.

The mean of the data-set in this problem is given by:

M = (6.5 + 11.2 + 13 + 6.3 + 7 + 8.8 + 7.4)/7 = 8.6.

Hence the standard deviation is:

[tex]S = \sqrt{\frac{(6.5-8.6)^2+(11.2-8.6)^2+(13-8.6)^2+(6.3-8.6)^2+(7-8.6)^2+(8.8-8.6)^2+(7.4-8.6)^2}{7}} = 2.39[/tex]

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The probability computed shows that there ia enough evidence to support the director's claim.

From the information given, the hospital director is told that 79% of the emergency room visitors are insured.

p = 0.79

q = 1 - 0.79 = 0.21

The computation of the z value is -1.91. This is a two tailed test.

The p-value will be:

= P(Z < -1.91)

= 0.0562 under the distribution table.

In this case, the p value is less than 0.10, therefore, we reject the null hypothesis.

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The length of the other parallel side is 3x

The given parameters are:

Midsegment= 2x

One parallel side = x

The midsegment is calculated as:

Midsegment = 0.5 * (sum of parallel sides)

So, we have

2x = 0.5 *(x + Other side)

Divide by 0.5

4x = x + Other side

Evaluate the like terms

Other side = 3x

Hence, the length of the other parallel side is 3x

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