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The sine of an angle 0 in the third quadrant is -0.5. So the value of cos∅ is -√(3)/2.

In the third quadrant, both sine and cosine are negative. We know that the sine of ∅ is -0.5, so we can use the Pythagorean identity to find the cosine of ∅:

sin²(∅) + cos²(∅) = 1

Substituting -0.5 for sin(∅), we get:

(-0.5)² + cos²(∅) = 1

Simplifying:

0.25 + cos²(∅) = 1

cos²(∅) = 1 - 0.25

cos²(∅) = 0.75

Taking the square root of both sides:

cos(∅) = ±√(0.75)

Since we're in the third quadrant where cosine is negative, we take the negative square root:

cos(∅) = -√(0.75)

Simplifying the square root:

cos(∅) = -√(3/4)

cos(∅) = -√(3)/2

Therefore, the value of cos(∅) is -√(3)/2.

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Answer:

A food manufacturer may use zero-rated goods in the manufacturing of a food product, but when the consumer buys the final product, it includes a VAT.

Step-by-step explanation:

The actual distance from A to the mid-point of BC is 42 m.

The actual distance from B to the mid-point of AC is 27 m.

A scale of 1 cm to 10 m can draw the triangular field ABC as follows:

        C

       / \

85 /   \ 90

    /      \

  A-------B

     30

Here, we draw AB as a horizontal line segment of length 9 cm (since AB is 90 m and the scale is 1 cm to 10 m), BC as a vertical line segment of length 3 cm (since BC is 30 m and the scale is 1 cm to 10 m) and AC as the hypotenuse of a right triangle with legs of length 8.5 cm and 9 cm (since AC is 85 m and AB is 90 m).

We can use a ruler to measure the actual distances from A to the mid-point of BC and from B to the mid-point of AC on the scale drawing.

The actual distance from A to the mid-point of BC, we first locate the mid-point of BC on the scale drawing is at a distance of 1.5 cm from B.

Then, we measure the distance from A to the mid-point of BC on the scale drawing is approximately 4.2 cm.

The scale of 1 cm to 10 m, we can convert this to the actual distance:

Actual distance = 4.2 cm × 10 m/cm

= 42 m

The actual distance from B to the mid-point of AC first locate the mid-point of AC on the scale drawing is at a distance of 4.25 cm from A.

Then, we measure the distance from B to the mid-point of AC on the scale drawing is approximately 2.7 cm.

Using the scale of 1 cm to 10 m, we can convert this to the actual distance:

Actual distance = 2.7 cm × 10 m/cm

= 27 m

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The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The equation of the conic in xy-coordinates when the axes are rotated through the given angle can be determined by using a rotation matrix. Given that the conic is represented by the equation:

x^2 - y^2 = 2y

And the rotation angle is θ = arccos(3/5), we can proceed as follows:

1. Rewrite the given equation in matrix form:

[x, y] * [1  0] * [x]  = [2y]

        [-1 0]   [y]      [0]

2. Define the rotation matrix using the given angle θ:

R(θ) = [cos(θ)  -sin(θ)]

          [sin(θ)   cos(θ)]

3. Apply the rotation matrix to the equation:

[x, y] * R(θ)^T * R(θ) * [x] = [2y]

        [1  0]     [-1 0]   [y]     [0]

[x, y] * R(θ)^T * [1  0] * R(θ) * [x] = [2y]

                              [-1 0]   [y]     [0]

[x, y] * [cos(θ) sin(θ)] * [1  0] * [cos(θ)  -sin(θ)] * [x] = [2y]

        [-sin(θ) cos(θ)]   [-1 0]     [sin(θ)   cos(θ)]   [y]     [0]

Simplifying the expression:

[x * cos(θ) + y * sin(θ)] * [x * cos(θ) - y * sin(θ)] - [x * sin(θ) - y * cos(θ)] * [x * sin(θ) + y * cos(θ)] = 2y

Expanding and rearranging terms:

x^2 * cos^2(θ) - y^2 * sin^2(θ) - x^2 * sin^2(θ) + y^2 * cos^2(θ) = 2y

Combining like terms:

x^2 * (cos^2(θ) - sin^2(θ)) + y^2 * (cos^2(θ) - sin^2(θ)) = 2y

Using the trigonometric identity cos^2(θ) - sin^2(θ) = cos(2θ):

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

The final equation of the given conic, after rotating the axes through the angle θ = arccos(3/5), is:

x^2 * cos(2θ) + y^2 * cos(2θ) = 2y

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The values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

The given quadratic equation is 2x² - 6x + 7 = 0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

When we compare the given quadratic equation with standard form we get the values of a , b and c

a=2

b=-6

c=7

Hence, the values of a is 2, b is -6 and c is 7 from the quadratic equation  2x² - 6x + 7 = 0

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Answer: 45T + 55S +102 + 96= Combined income

Step-by-step explanation:

Answer:

To generate a linear function model using average rates of change, we need to have two points on the line. Let's suppose we have two points (x1, y1) and (x2, y2) on the line, where x2 > x1. Then the slope of the line, m, can be calculated as:m = (y2 - y1) / (x2 - x1)This represents the average rate of change of y with respect to x between the two points.Once we have the slope, we can use the point-slope form of the equation of a line to write the equation of the line:y - y1 = m(x - x1)where (x1, y1) is one of the points on the line.To simplify this equation, we can rearrange it to slope-intercept form, y = mx + b, where b is the y-intercept. We can solve for b by plugging in the coordinates of one of the points on the line:y1 = mx1 + bb = y1 - mx1Once we have m and b, we can write the equation of the line in slope-intercept form:y = mx + bHere's an example: Suppose we have the two points (2, 5) and (4, 9). The slope of the line between these two points is:m = (y2 - y1) / (x2 - x1) = (9 - 5) / (4 - 2) = 2Using point-slope form, we can write the equation of the line as:y - 5 = 2(x - 2)Simplifying, we get:y = 2x + 1So the linear function model generated using average rates of change is y = 2x + 1.

Step-by-step explanation:

Answer:

a = 10

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

a² + 24² = 26²

a² + 576 = 676 ( subtract 576 from both sides )

a² = 100 ( take square root of both sides )

a = [tex]\sqrt{100}[/tex] = 10

Answer:

The distance from first base to third base is 127.3 ft,

Answer:

im pretty sure the slope would be 3 over 7 (3/7)

Step-by-step explanation:

The weight of the 0.8-meter piece is 19.6 kilograms.

We can use the ratio of length to weight to determine the weight of the 0.8-meter piece.

Let's call the weight of the 2.8-meter piece "W₁" and the weight of the 0.8-meter piece "W₂". Then we have:

W₁/2.8m = 24.5kg/1m

Solving for W₁, we get:

W₁ = (24.5kg/1m) x 2.8m = 68.6kg

Now we can use the same ratio to find W₂:

W₂/0.8m = 24.5kg/1m

Solving for W₂, we get:

W₂ = (24.5kg/1m) x 0.8m = 19.6kg

Therefore, the weight of the 0.8-meter piece is 19.6 kilograms.

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Answer:

Step-by-step explanation:

20=17+12+9 so the answer is 4982

The absolute value function y = |x| looks like a "V" shape, with the vertex at the origin and the arms going off to positive and negative infinity. To shrink this function vertically by a factor of 2/9, we can multiply the entire function by 2/9:

y = (2/9)|x|

This new function has the same "V" shape, but the y-values are only two-ninths as large as they would be for the original function at any given value of x. The vertex of the new function is still at the origin, and the arms still go off to positive and negative infinity.

The area of the given triangle, given the height and the type of triangle would be E. 16 cm ²

To find the area of an equilateral triangle when given just the height, the formula is:

= ( height ² x  √ 3 ) / 2

We are given a height of 4 cm.

The area of the triangle is therefore :

= ( height ² x  √ 3 ) / 2

= ( 4 cm ² x  √ 3 ) / 2

= ( 16 x  √ 3 ) / 2

=  27. 712 / 2

= 13. 85

The closest option is 16 cm ² so this is the answer.

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Answer:

Step-by-step explanation:

The equation to solve the problem is:

x + 550 = 750

Explanation:

The manager has already distributed $550, and the remaining amount to distribute is represented by the variable x. Adding the distributed amount to the remaining amount should equal the total amount of tips the manager has, which is $750. Therefore, the correct equation is x + 550 = 750.

The measures of angle 1 and angle 2 are 12.5 degrees

We have to find the measures of angle 1 and angle 2

The circle will have 360 degrees

The unknown arc length be taken as x

175+160+x=360

Add the like terms

335+x=360

Subtract 335 from both sides

x=360-335

x=25

So angle m∠1 = 1/2(25)

m∠1 is 12.5

m∠1 = m∠2 as both are equal.

m∠2 = 12.5 degrees

Hence, the measures of angle 1 and angle 2 are 12.5 degrees

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The measure of m∠BCA is equal to: C. 70°

In Mathematics and Geometry, a circle is a closed, two-dimensional curved geometric shape with no edges or corners.

Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis), and a full circle always has a measure of 360 degrees.

In this context, the sum of an angle around any point is equal to 360 degrees;

m∠(BOA) = 360 - 250

m∠(BOA) = 110°

Also, the sum of all the interior angles inscribed in this circle, CAOB = 360 degrees;

m∠BCA = 360 - (110 + 90 + 90)

m∠BCA = 70°

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The difference between the interquartile range of Matt's and Linda's remaining vacation days is 1.5.

The interquartile range will be calculated through the formula -

[tex] Q_{3}[/tex] = [tex] Q_{2}[/tex] - [tex] Q_{1}[/tex]

Firstly calculating [tex] Q_{3}[/tex] for Matt

[tex] Q_{2}[/tex] = (4+5)/2

[tex] Q_{2}[/tex] = 4.5

[tex] Q_{3}[/tex] = (8+12)/2

[tex] Q_{3}[/tex] = 10

Finding interquartile range now -

[tex] Q_{3}[/tex] = 10 - 4.5

[tex] Q_{3}[/tex] = 5.5

Now, performing calculation for Linda

[tex] Q_{2}[/tex] = (0+10)/2

[tex] Q_{2}[/tex] = 5

[tex] Q_{3}[/tex] = (11+13)/2

[tex] Q_{3}[/tex] = 12

Finding interquartile range now -

[tex] Q_{3}[/tex] = 12 - 5

[tex] Q_{3}[/tex] = 7

The difference between the interquartile range of Linda and Matt will be calculated as:

Difference = Interquartile range of Linda - Interquartile range of Matt (as we see Linda has greater interquartile range than Matt)

Difference = 7 - 5.5

Difference = 1.5

Hence, the difference between interquartile range of days is 1.5.

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The amount of liquid that the larger cup holds more than the smaller cup would be =3.14cm³

To calculate the volume of the cylindrical cups, the formula for volume of cylinder should be used an it is given below as follows;

Volume of cylinder = πr²h

For smaller cup;

radius = 4cm

height = 5cm

volume = 3.14×4×4×5

= 251.2cm²

For the larger cup;

radius = 3cm

height= 9cm

volume = 3.14×3×3×9

= 254.34

The difference between the two cups = 254.34 -251.2 = 3.14cm³

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Step-by-step explanation:

answer is 10 hope it's helps

The function of C(d) in the given inverse function is determined as C(d) = (d - 3)/10

option A.

The inverse of the given function is calculated by applying the principle of inverse of functions as follows;

let C(d) = 10d + 3

The inverse of the function is calculated as follows;

C = 10d + 3

make d the subject of the formula;

10d = C - 3

d = (C - 3)/10

Now replace, C with d;

C = (d - 3)/10

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Answer:

The rectangle is 7.9 meters by 2.9 meters.

Step-by-step explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

[tex]w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9[/tex]

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m

Answer:

[tex]y = (x-1)^2-9[/tex]

Step-by-step explanation:

The form of a quadratic equation is  [tex]y = a(x-h)^2+k[/tex]. Lets identify each change in words before switching to the formula:

Shifted 1 right

Shifted 9 down

No stretch horizontally

No stretch vertically.

Our equation will be [tex]y = (x-1)^2-9[/tex].

Answer:

[tex]\large {\mbox{R = 3.6}}[/tex]

Step-by-step explanation:

The formula for finding a magnitude of an earthquake on the Richter Scale is given as
[tex]R = \log\left(\dfrac{A}{A_0}\right)\\[/tex]

[tex]\rm{where}\\\textrm{A - measure of amplitude of quake wave}\\\textrm{$A_0$ = amplitude of smallest detectable wave}\\[/tex]

Given A = 0.3954 and A₀ = 0.0001, we can plug in these values into the R equation to get

[tex]R = \log\left(\dfrac{0.3954}{0.0001}\right)\\\\= \log(3954)\\\\= 3.597\\\\= 3.6\text { rounded to the nearest tenth}[/tex]

The solution for x  in the circle is:

x = 6

Tangent-tangent theorem states that "The measure of an angle formed by a two tangents drawn from a point outside the circle is one-half the difference of the intercepted arcs".

Using the above theorem. We can say:

5x + 17 = 1/2 * [(37x+5) - (23x-5)]

5x + 17 = 1/2 * [37x + 5 - 23x + 5]

5x + 17 = 1/2 * [14x + 10]

5x + 17 = 7x + 5

7x - 5x = 17 - 5

2x = 12

x = 12/2

x = 6

Therefore, the solution for x is 6.

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Complete Question

Check attached image

The length of BD is equal to 9 units.

In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).

Since C is the midpoint of line segment BD, we can logically deduce the following relationship:

Line segment BD = Line segment BC + Line segment CD

By substituting the given line segments into the equation above, we have the following:

Line segment BD = 4 + 5

Line segment BD = 9 units.

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Answer:

Step-by-step explanation:

There are many expressions that could have an answer of 14, but here’s one example:

(7 x 2) - 1 = 14

Let’s break it down step by step:

The first operation in this expression is multiplication. We multiply 7 by 2, which gives us 14.

7 x 2 = 14

The second operation in this expression is subtraction. We subtract 1 from the result of our multiplication, which gives us 14.

14 - 1 = 14

So, the final expression is (7 x 2) - 1 = 14, which has an answer of 14.

Keep in mind that there are many other expressions that could have an answer of 14 as well. This is just one example!

Answer:

(49÷7)2=14

(2×3.5)2=14

Step-by-step explanation:

I honestly don't know of this is exactly what our asking for but here are two equations that are equal to 14, hope this helps