Find the exact value of cos ( 285 ∘ ) .

The equation of the conic represents a circle with an area of 36π square units.

In this problem we find the equation of the conic in general form, on which we need to determine what kind of conic it represents. This can be done by finding the standard form of the equation by means of algebra properties, using a strategy known as completing the square. The quadratic equation in general form is described by the quadratic equations of the form:

A · x² + B · y² + C · x + D · y + E · x · y + F = 0

Now we proceed to find the standard form of the equation. First, write the equation in standard form:

x² + y² - 3 · x + 6 · y = 7 · x + 2

x² + y² - 10 · x + 6 · y - 2 = 0

Second, complete the square:

(x² - 10 · x + 25) + (y² + 6 · y + 9) = 2 + 25 + 9

(x - 5)² + (y + 3)² = 36

The standard form of the quadratic equation indicates the equation of a circle with a diameter of 12 units and a center at (h, k) = (5, - 3). The area of the circle is calculated below:

A = 0.25π · D²

Where D is the diameter of the circle, in units.

A = 0.25π · 12²

A = 36π

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Answer:

I'm not sure exactly me myself

Answer:

Step-by-step explanation:

The sum of exterior angles in a quadrilateral is always 360 degrees.

So, 2x+x+4x+3x=10x=360

Soling for x, we get x=36 degrees.

15 pieces will there be.

 .5 is the same as  1/2, while 7.5 is the same as 7 1/2. To determine how many strips may be cut, use the following expression:

.5x = 7.5

This is due to the fact that the ribbon length that has to be cut is .5 feet, and we are attempting to determine how many pieces of that length might be cut from a roll of ribbon that is 7.5 feet long.

Divide both sides by 2.5 to separate the variable, and that's all there is to it.

7.5/.5 is 15.

x = 15.

Eli is able to slice a ribbon into three pieces that are each .5 feet long.

The complete question is: The red strips that are  1/2 feet long. The roll of ribbon is 7 1/2 feet long. Which expression could be one of the steps in determining how many strips can be cut?

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Answer:

D

Step-by-step explanation:

as a negative exponent always means 1/..., D is the correct answer.

9^-4 = 1/(9^4)

that is the precise definition of a negative exponent.

Answer:69.69

Step-by-step explanation:

FIrst add the sides then subtract the top and then mutilpy it by 2

Answer: True.

Step-by-step explanation:

        First, a right angle will always be equal to 90 degrees.

        Next, bisecting an angle means cutting it into two parts.

        Since the resulting two angles will always be less than 90 degrees, they will always be acute angles. The answer to this question is true.

For 10.75 years I'll receive an amount of $1,193 for an annuity of $12,083.

Simple interest is often a predetermined percentage of the principle amount borrowed or lent paid or received over a specific time period.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

A principle of $12,083 with 6.1% interest rate becomes $(12,083×1.061)

= $12,820.063.

∴ The no. of years the annuity provides you with payments of $1,193 is

= (12,820.063/1193).

= 10.75 years Or 10 years 9 months.

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Answer:

6.2 ft

Step-by-step explanation:

a² + b² = c²

a² + 5² = 8²

a² = 64 - 25

a² = 39

a = √39

a = 6.2

Answer: 6.2 ft

The slope intercept form is y= ( -3/2 ) x + 7/2

What is slope ?

A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x).

(x1,y1)= (3. -1) and (x2,y2)= (5, -4)

slope intercept form:

y=mx+b , m=slope, b = constant

m= (y2-y1) /( x2-x1) = (-4-(-1)) / ( 5-3) =  -3/2

line equation:

y-y1=m(x-x1)

Substitute the values

y-(-1)=( -3/2 ) (x-3)

y+1=( -3/2 ) x + 9/2

y= ( -3/2 ) x + 9/2 - 1

y= ( -3/2 ) x + 7/2

Thus, the slope intercept form is y= ( -3/2 ) x + 7/2

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Answer:

-3x + y = -39

Step-by-step explanation:

If it is perpendicular to y=-1/3x+2, then the slope is positive 3. If it passes through (9, -12), then we can set up our equation:

y+12 / x-9 = 3. Simplifying, we have:

y=3x-39, which in standard form is:

-3x+y= -39

Hope this helps!

Equation of the line passes through (10,2) and is perpendicular to the line y = 2x is given by  y = -x / 2 + 7.

As given in the question,

Given equation of the line :

y = 2x

Line passes through the point (x₁ , y₁ ) = (10, 2)

Standard form of slope intercept form

y = mx + c

'm' is the slope

slope of the given line 'm₁' = 2

let 'm₂' be the slope of the required line

Multiplication of the Slope of two perpendicular lines is given by :

m₁ × m₂ = -1

⇒2 × m₂ = -1

⇒m₂ = -1/2

Equation of the line perpendicular to the given line and passes through

(x₁ , y₁ ) = (10, 2)

y - y₁ = m₂ ( x - x₁ )

⇒ y - 2 = (-1/2) ( x - 10 )

⇒ y = -x / 2 + 7

Therefore, the required equation of the line in slope intercept form is given by  y = -x / 2 + 7 .

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The solution is Option A.

The mean of the actual weights of the samples is 1.002

What is Mean?

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the observations be represented as M

Now , the value of mean M is calculated as

The number of samples be = 10

The weight of the samples can be given from set A

The value of set A is

Set A = { 1.01 , 1.03 , 0.98 , 0.99 , 1.01 , 1.02 , 0.98 , 1.05 , 0.97 , 0.98 }

The sum of the values of weights of set A is S

Sum S = 1.01 + 1.03 + 0.98 + 0.99 + 1.01 + 1.02 + 0.98 + 1.05 + 0.97 + 0.98

Sum of weights S = 10.02

Now , the mean of the weights is given by

Mean = Sum of Values / Number of Values

Mean = Sum of weights / Number of samples

Substituting the values in the equation , we get

Mean = 10.02 / 10

Mean M = 1.002

Therefore , the value of M is 1.002

Hence , The mean of the actual weights of the samples is 1.002

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Using rule of volume integral , The answer of y=x, y-=0 and x=6 is [tex]216 \pi[/tex].

The process of combining smaller parts into a single, cohesive whole is known as integration.

A volume integral is a specific instance of multiple integrals and is used to denote an integral across a 3-dimensional domain in mathematics, notably multivariable calculus. In physics, volume integrals are crucial for many applications, such as calculating flux densities.

area covered by y=x y=0 and x=6 is [tex]\frac {1}{2} * 6 * 6[/tex]

=18 [tex]unit^{2}[/tex]

Perimeter covered by revolving the area about x-axis, y-axis , x=6 and x=9 is [tex]2*\pi *6[/tex]

=[tex]12 \pi[/tex]

Volume = [tex]18 * 12 \pi[/tex]

=[tex]216 \pi unit ^{3}[/tex]

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Answer:

the correct answer is 144

Step-by-step explanation:

Hence, the measure of each interior angle is 144∘.

hope this helps

Answer:

Step-by-step explanation:

each exterior angle=360/n=360/10=36°

each interior angle=180-36=144°

The value of the given composite function f(g(x)) at x = -1 is that f(g(-1)) will be 6.2.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function f(x) and g(x) are linear functions.

Take (-6,6) and (-1,5)

The equation will be as follows,

f(x) - 6 = (5 - 6)/(-1 + 6)(x + 6)

f(x) - 6 = -x/5 - 6/5

f(x) = -x/5 - 6/5 + 6

f(x) = -x/5 + (- 6 + 30)/5

f(x) = -x/5 + 24/5

Take (-6,-12) and (-1,-7)

g(x) + 12 = (-7 + 12)/(-1 + 6)(x + 6)

g(x) + 12 = x + 6

g(x) = x - 6

Now, f(g(x)) = -(x - 6)/5 + 24/5

f(g(-1)) = -(-1 - 6)/5 + 24/5

f(g(-1)) = 7/5 + 24/5 = 6.2

Hence "At x = -1, the value of the composite function f(g(x)) is that f(g(-1)) will be equal to 6.2.".

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We can say that the view in which one or more faces of the object are not perpendicular to the rest of the faces, but are inclined projections, are the auxiliary views.

Initially, we must know that the views of an object or body are orthogonal projections associated with it.

In this sense, auxiliary views are a type of view that are characterized by arising from a change in projection plane, they are usually used when highly complex parts or objects must be represented.

¡Hope this helped!

The number that must be added to complete the square in the expression is 0.9².

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

x² + 1.8x

The complete square is given as,

(a + b)² = a² + 2ab + b²

Now,

x² + 2 x 0.9(x) + 0.9²

(x + 0.9)²

Thus,

0.9² completes the square in the expression.

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We can say that the given Quadrilateral is Parallelogram

What is Parallelogram?

A parallelogram is a quadrilateral with two parallel sides (and therefore opposite angles equal). A rhombus is a quadrilateral with equal sides, while a rectangle is a parallelogram with all right angles.

Solution:

Since, the given Quadrilateral has all the opposite angles equal

and we do not know weather the opposite sides are equal or not it is closest to assume that the given Quadrilateral is Parallelogram

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Answer:

Step-by-step explanation:

180 = x + 50 +50

180 = x + 100

x + 100 = 180

x = 80

80 is the value of x.

Answer: x

Step-by-step explanation:

-3x-7+4x+7

than because the 7's cancel each other out it would become

-3x+4x which would be equal to x

The answer to this Question based on circles is 9

What is circle?

A circle is a two-dimensional geometric shape defined by a set of points equidistant from its center. It is the set of all points in a plane that are the same distance from a given point, called the center. A circle is a special type of ellipse, and all circles are similar. It is one of the most fundamental shapes in geometry, and is used in art, architecture, engineering, and many other disciplines. The circumference of a circle is the length of its perimeter, which is determined by its radius. A circle's area is the space enclosed by its circumference, and is equal to the value of pi multiplied by the square of the radius.

In the given Circle
Lets us denotes the 2 chords by AB and CD and let their intersecting point be E
Then from property of intersecting chords in circle we can write
(AE)(BE) = (CE)(DE)
4x = 36
x = 9

Hence proved

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Answer:

5x + 15

Step-by-step explanation:

5(x + 3) ← multiply each term in the parenthesis by 5

= 5x + 15

"5x+15" is an expression equivalent to "5(x+3)".

If we expand this factorization, the resulting expression is equivalent to the original expression. This is how you expand it:

[tex]5(x+3)[/tex]

Check the attached image.

[tex](5)(x)+(5)(3)=\\ \\5x+15[/tex]

3. Conclude.

5x+15 is an expression equivalent to 5(x+3).

The option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

In the given question, the triangles below are similar.

So, we have to state the reason and write the similarity statement.

ΔQRS≈

(a) Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT.

(b) Similar to due SAS and a scale factor of 0.29. Triangle QRS is similar to triangle TUV.

(c) Similar due to AA. Triangle QRS is similar to triangle VUT.

(d) Similar due to SSS and a scale factor of $0.29$. Triangle QRS is similar to triangle VUT.

As we know that, the ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor.

Since the both triangle area similar so using the SSS theorem;

Triangle QRS congruence to triangle VUT.

QR/VU = RS/UT = SQ/TV

So QR/VU = 56/16; RS/UT = 70/20; SQ/TV = 98/28

QR/VU = RS/UT = SQ/TV = 3.5

Hence, ΔQRS≈ΔVUT using the SSS theorem with the scale factor of 3.5. So the option 1 "Similar due to SSS and a scale factor of 3.5. Triangle QRS is similar to triangle VUT." is correct.

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The amount invested in the account that pays 1.5% interest is $584,285.71.

The amount invested in the account that pays 8.5% interest is $155,714.29.

The system of equations that represent the information in the question is:

x + y = 740,000 equation 1

0.015x + 0.085y = 22,000 equation 2

Where:

In order to determine the values, the elimination method would be used.

Multiply equation 1 by 0.015

0.015x + 0.015y = 11,100 equation 3

Subtract equation 3 from equation 2

0.070y = 10,900

Divide both sides of the equation by 0.070

y = 10,900 / 0.07

y = 155,714.29

Subtract 155,714.29  from $740,000

x = 740,000 - 155,714.29

x = 584,285.71

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If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.

One kind of proportionality relationship is the direct proportion. When two values are in direct proportion, one value rises when the other rises and vice versa when one value falls. A proportionate relationship is represented by the symbol. When one of the variables is a multiple of the other, there is a direct proportion between the two. For instance, 1 cm equals 10 mm. The multiplier for converting cm to mm is always 10. Petrol prices and foreign exchange rates are determined using a direct proportion.

Given,

We know that y fluctuates in direct proportion to x and z.

We are aware that the form of the equation y = kx for two quantities that are directly proportional is, where k is the proportionality constant.

Because y directly varies as x and z, our equation would be y = kxz

Additionally, it is stated that and y = 4, x = 6 and z = 1. Let's define the proportionality constant as follows:

4 = k × 6 × 1

4 = k ×6

k = 2/3

y = 2/3 × x ×z

Substituting value of x by k = 2/3 , x = 7 and z = 4

y = 2/3 × 7 × 4

y = 56/3

If y varies directly as x and z, and y=4 when x=6 and z=1, then value of y will be 56/3 when x=7 and z=4.

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Using the corresponding angle theorem, the value of y is 36 degree.

In the given question, b||c.

We have to find the value of y.

Given: b||c

Find: Value of y

Let x be the value of side angle of (2y+34) degree.

So, using the corresponding angle theorem

x = 74 degree

As we know that the sum of straight line is 180 degree.

So 2y+34+x = 180

Now putting the value of x

2y+34+74=180

After simplifying

2y+108=180

Subtract 108 on both side, we get

2y=72

Divide by 2 on both side, we get

y=36

Hence, the value of y is 36 degree.

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The equation of the line in slope-intercept form is y = 3x - 11.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

We know slope(m) = (y₂ - y₁)/(x₂ - x₁).

∴ Slope(m) = (- 5 + 8)/(1 - 0) = 3.

So, y = mx + b can be written as - 5 = 3(2) + b ⇒ b = - 11.

So, The required line is y = 3x - 11.

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