8) Simplify.
5(3x – 3) + 4(6x - 12)

The trigonometry identity sin(x + y) = sinx cosy + cosx siny.

sin(x + y) is one of the identities in trigonometry for compound angles.

The angle (x + y) represents the compound angles.

sin(x + y) = sinx cosy + cosx siny

To prove sin(x + y) = sinx cosy + cosx siny

Consider OX as a rotating line anti-clockwise. Let angle XOY = a

the making of an acute angle b the rotation in the same direction is

angleYOZ = b , angle XOZ = a + b

From triangle PTR,

∠TPR = 90 - ∠PRT , ∠ROX = a

From the right-angled triangle PQO

sin(a + b) = PQ/OP

= (PT + TQ) / OP

= PT/OP + TQ/OP

= PT/PR × PR/OP + RS/OR × OR/OP

= cos (∠TPR ) sinb + sina cosb

= sina cosb + cosa sinb

if we replace a=x and b=y

Therefore, sin(x + y) = sinx cosy + cosx siny.

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The inequalities x≤2 or x<5 are unequal expressions

The common points of both inequalities are {.......0,1,2}

Inequalities are expressions that have unequal values

Number lines are lines that are used to represent numbers and expressions at regular intervals

The inequalities are given as;

x≤2 or x<5

This means that:

x is less than or equal to 2

And

x is less than 5

So, we have:

x≤2 = {.......0,1,2}

x<5 = {.......0,1,2,3,4}

The common points of both inequalities are:

x≤2 or x<5 = {.......0,1,2}

See attachment for the number line

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Answer:

See below ↓

Step-by-step explanation:

Given side lengths :

This question can be solved in two ways :

Case 1

Case 2

Hope it helps~

As x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

Given function is:

[tex]f(x) = \frac{2x}{1-x^{2} }[/tex]

A function f(x) is a rule which relates two variables where x and y are independent and dependent variables.

Divide the numerator and denominator of the given function by x.

[tex]f(x) = \frac{2}{\frac{1}{x} -x}[/tex]

[tex]\lim_{x \to \infty} f(x) \\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x}[/tex]

As we know that as x approaches the infinity 1/x approaches 0.

So, [tex]\\\\\lim_{x \to \infty} \frac{2}{\frac{1}{x} -x} = \lim_{x \to \infty} \frac{2}{-x}[/tex]

[tex]\lim_{x \to \infty} \frac{-2}{x} =0[/tex]

Therefore, as x tends to infinity the function [tex]f(x) = \frac{2x}{1-x^{2} }[/tex] approaches zero.

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Answer: 40 degrees

Step-by-step explanation:

Answer:

4.5^5

Step-by-step explanation:

Answer:

(4.5)^5

Step-by-step explanation:

Answer:

800m

Step-by-step explanation:

If 100cm is equivalent to a meter (1 Meter). 8 Meters would be equivalent to 8 Meters multiplied by 100cm and divided by a meter (1 Meter)

Answer:

x^2+9x+14

Step-by-step explanation:

x×(x+7)+2×(x+7)

x^2+7x+2x +14

x^2+9x+14

Answer:

66(2/3) %

Step-by-step explanation:

There are 30 possible outcomes because there are 30 cold drinks.

 The Probability of orange flavored  20/30   = 2/3 = 0.6666....

66.6666....%= 66(2/3) %

To find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.

A box plot consists of a rectangular box, a vertical line that divides the box, and two whiskers extending from the box.

The box plots being referred to in the question are missing, however, the diagram attached shows how to determine the values you will need in solving the question.

The median is represented by the vertical line that divides the rectangular box.

The range = max value - min value.

The interquartile range = the range of the rectangular box = Q3 - Q1.

In summary, to find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.

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Answer:

the interest would be $5,400 after 15 years

Answer:

cars value decreases in value exponentially

Step-by-step explanation:

cant really read it but say that the cars value decreases in value exponentially and compare that to however the other cars decrease in value over time

Answer:

  b.  √3

Step-by-step explanation:

Given a point on the unit circle that represents the position of the terminal ray of an angle, the tangent of that angle is the ratio of the y-coordinate to the x-coordinate.

  tan(4π/3) = y/x = (-√3/2)/(-1/2) = √3/1

  tan(4π/3) = √3

_____

Additional comment

A calculator can confirm this for you.

Answer:

f(4) = 13

Step-by-step explanation:

f(4) = 2(4)+5
f(4) = 13

Answer:

13

Step-by-step explanation:

f ( x ) = 2x + 5

To find : f ( 4 )

f ( 4 ) = f ( x )

Here,

x = 4

So,

f ( 4 ) = 2 ( 4 ) + 5

        = 2*4 + 5

        = 8 + 5

f ( 4 ) = 13

Answer:

Step-by-step explanation:

[tex]\frac{180(n-2)}{n}[/tex] degrees, where n is the number of sides

The measure of an interior angle inside a regular polygon is given by;

[tex]\rm S = (n -2) \times 180[/tex].

An interior angle of a polygon is an angle formed inside the two adjacent sides of a polygon. Or, we can say that the angle measures at the interior part of a polygon are called the interior angle of a polygon.

An Interior Angle is an angle inside a shape.

As per the angle sum theorem, the sum of all the three interior angles of a triangle is 180°.

Multiplying two less than the number of sides times 180° gives us the sum of the interior angles in any polygon.

The measure of an interior angle inside a regular polygon is determined by the following formula;

[tex]\rm S = (n -2) \times 180[/tex]

S = sum of interior angles and n = number of sides of the polygon.

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Answer:

398

Step-by-step explanation:

3582 / 9 = 398

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, reflection and dilation.

Given the points A(2, 3), B(–1, –4), and C(2, –2), the translation 1 unit left and 4 units down gives:

A'(1, -1), B'(-2, -8) and C'(1, -6)

The translation of points A(2, 3), B(–1, –4), and C(2, –2), 1 unit left and 4 units down gives A'(1, -1), B'(-2, -8) and C'(1, -6)

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Answer:Its -3.5

Step-by-step explanation:

Answer:

C or D Both basically

Step-by-step explanation:I read them

Answer:

1. (a. 8 b. 3 d. 6,6,12 e. 3,3,9) 2. (a. 2,3 b. 4,5 c. 6,6,2,3 d. 5,3,5) 3. (a.2/3 b.1/3 c.2/3 f.1/2 g.7/8 h.4/5)

Step-by-step explanation:

OK this is quite simple. Just multiply the top and bottom, otherwise known as the numerators and denominators, by whatever is next to it. In this case, 1a is [tex]\frac{2*4}{5*4}[/tex].

That would result in [tex]\frac{8}{20}[/tex]

Hey there!

In order to multiply fractions, we should multiply the numerator of the 1st fraction by the numerator of the 2nd fraction.

Same with denominators.

Let's multiply these fractions.

2/5=2*4/5*4=8/20

2/3=2*6/3*6=12/18

1/4=1*3/4*3=3/12

3/4=3*3/4*3=9/12

now divide:

10/15=10:5/15:5=2/3

12/18=12:6/18:6=2/3

12/15=12:3/15:3=4/5

15/25=15:5/25:5=3/5

Now, simplify the following fractions:

4/6

divide the top & bottom by 2:

2/3

next:

5/10

divide the top & bottom by 5:

1/2

next

5/15

divide the top & bottom by 5:

1/3

next:

12/18

divide the top & bottom. by 6

2/3

next

5/10

divide the top & bottom by 5

1/2

next

14/16

divide the top & bottom by 2

7/8

and then last but not least

28/35

divide the top & bottom by 7

4/5

And we're done!

Hope everything is clear.

Let me know if you have any questions!

#LearningDoesn'tEnd

:-)

Answer:

15

Step-by-step explanation:

Okay, so we know that Base*Length=Area, so we just have to divide the area by the base, so the formula here is Area/Base=Length.

That would get us 120/8=Length,

and if we just divide 120 by 8 we get 15, so the length is 15

The equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

The area of the rectangle is the product of its length and its breadth.

As it is given that the length of the rectangular frame is (2x+10), while the width of the rectangular frame is (2x+6). Also, it is mentioned that the area of the rectangular frame is 140 in².

Now we know the area is the product of length and breadth, therefore,

[tex]\rm \text{Area of rectangle} = length \times breadth[/tex]

[tex]140 = (2x+10)(2x+6)\\\\140 = 4x^2 + 12x + 20x + 60\\\\0=-140+4x^2 + 12x + 20x + 60\\\\4x^2 + 32 x -80=0[/tex]

Hence, the equation to solve for the width of a rectangular frame that has a total area of 140 square inches is 4x²+32x-80=0.

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Answer:

A.)  4x2 + 32x − 80 = 0

Step-by-step explanation:

Just took the test

Equation of a Circle: (x - h)^2 + (y - k)^2 = r^2

---Center = (h, k)

---Radius = r (this value will need to be squared in the final answer)

Center = (-3, -6)

---h = -3

---k = -6

Radius = 4

Equation: (x + 3)^2 + (y + 6)^2 = 16

Correct Answer: A

Hope this helps!

Answer:

<1 and <2

Step-by-step explanation:

Complementary angles are two angles which their measure add up to 90 degrees.

There are only one angle pair that meet this requirement:

angle 2 and angle 1

We are given a cylinder and a cone of same volume i.e

[tex] \longrightarrow[/tex] Volume of cone = Volume of cylinder

And also the diameter of the cylinder is given 4 inches

[tex] \longrightarrow[/tex] Radius = [tex]\sf \dfrac{Diameter}{2}[/tex]

[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{4}{2}[/tex]

[tex] \longrightarrow[/tex] Radius = 2 inches

The height of cylinder is 3 inches. And the diameter of the cone is 6 inches

[tex] \longrightarrow[/tex] Radius = [tex]\sf\dfrac{Diameter}{2} [/tex]

[tex] \longrightarrow[/tex] Radius = [tex] \sf\dfrac{6}{2}[/tex]

[tex] \longrightarrow[/tex] Radius = 3 inches

First, let us recall the Formulas of volume of cylinder and cone:

[tex] \quad\longrightarrow\quad \sf {Cone = \dfrac{1}{3}\pi r^2 h }[/tex]

[tex] \quad\longrightarrow\quad \sf {Cylinder = \pi r^2 h }[/tex]

Now, we know that the volume of cone is equal to the volume of cylinder

[tex] \implies\quad \sf{\dfrac{1}{3}\pi r^2 h = \pi r^2 h }[/tex]

On putting the values:

[tex] :\implies\quad \sf{\dfrac{1}{3}\pi \times 3^2 \times h = \pi \times 2^2 \times 3 }[/tex]

[tex] :\implies\quad \sf{\dfrac{1}{\cancel{3}}\times 3.14 \times\cancel{ 9 }\times h = 3.14 \times 4 \times 3 }[/tex]

[tex] :\implies\quad \sf{3.14 \times 3 \times h = 3.14 \times 12 }[/tex]

[tex]: \implies\quad \sf{ h = \dfrac{ \cancel{3.14} \times 12 }{ \cancel{3.14} \times 3} }[/tex]

[tex] :\implies\quad \sf{ h =\cancel{ \dfrac{12}{3}}}[/tex]

[tex] :\implies\quad \underline{\underline{\pmb{\sf{h = 4 inches }}} }[/tex]

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ~Hence the height of the cone is 4 inches.

The roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

The factor of a polynomial is the terms in linear form, which are, when multiplied together, give the original polynomial equation as a result.\

To find the roots of a polynomial, equate these factors of a polynomial to zero.

The given polynomial equation is,

[tex]x^4+x^2=4x^3-12x+12[/tex]

Take all the terms left side of the equation,

[tex]x^4+x^2-4x^3+12x-12=0\\x^4-4x^3+x^2+12x-12=0[/tex]

The factor form of the polynomial on solving the above equation, we get,

[tex](x-2)(x-2)(x-1.73)(x+1.73)=0[/tex]

Equate all the factors to zero, to find the roots. The roots we get are,

[tex]2,2,1.73,-1.73[/tex]

Hence, the roots of the provided polynomial equation of 4 degree are 2,2,1.73,-1.73.

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Answer:

–1.73, 1.73, 2

Step-by-step explanation:

Answer:

height: 125m; distance: 500m

Step-by-step explanation:

x = 250

f(x) = x − 0.002x2

f(x) = 250 − 0.002(250 )2

= 250 − 0.002(62,500)

= 250 − 125

= 125

250 times 2 = 500

[tex]\\ \rm\rightarrowtail y=x-0.002x^2[/tex]

So

[tex]\\ \rm\rightarrowtail y=250-0.002(250)^2[/tex]

[tex]\\ \rm\rightarrowtail y=250-0.002(62500)[/tex]

[tex]\\ \rm\rightarrowtail y=250-125[/tex]

[tex]\\ \rm\rightarrowtail y=125m[/tex]

Distance:-

Answer:

20 - 2n

n = a number