Which of the following explains why Cosine 60 degrees = sine 30 degrees using the unit circle?

The answer is: The side opposite a 30° angle is the same as the side adjacent to a 60° angle in a right triangle. On a unit circle, the (sin) distance of a 30° angle is the same as the x (cos) distance of a 60° angle.

But I would really appreciate someone to explain this to me, thank you!

Answer:

3.98 cm

Step-by-step explanation:

V= πr²h

V= 200 cm³, r= 4 cm, h=?

h= V/(πr²)= 200/(3.14*4²)= 3.98 cm

Answer: divide both numbers

Step-by-step explanation:

20.95

Answer:

3 and 4

Step-by-step explanation:

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size so here reducing a photograph to half its dimensions and enlarging a photograph to double the dimensions is dilation.

=> For dilation, we use a certain scale factor

=> In the 3rd option, scale factor is 1/2

=> In the 4th option, scale factor is 2.

Answer:

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

ΔABC ≅ ΔEFD

This is because:

∠A ≅ ∠E (30°)

∠B ≅ ∠F (100°)

∠C ≅ ∠D (50°)

Answer:

Step-by-step explanation:

The formula for simple interest is prt = I, where p is the initial investment (our unknown in this case), r is the interest rate in decimal form, t is the time in years, and I is the interest earned. That is NOT the same as the amount of money in the account t years later.

For us,

p = ??,

r = .05,

t = 18, and

I = 225.

Filling in:

p(.05)(18) = 225 and

.9p = 225 so

p = 250

Answer:

The answer is $250.

Step-by-step explanation:

First, the money that his grandmother deposited is called the principal, P. Substitute the given values into the formula, interest equals principal times rate times time, and solve for P. Here, I is 225 dollars and t is 18 years.

Next, the percent given represents the interest rate, r, but first it must be changed to a decimal. To change it, move the decimal point 2 places to the left.

Now, multiply point 0, 5, and 18 to simplify the right side of the equation. The product is point nine.

Finally, divide both sides of the equation by .9 . The result is P equals $225 The principal, or original deposit, is $250.

Answer:

3, 12, 27 and 300

Step-by-step explanation:

Plug n as 1, 2, 3 and 10.

3(1)² = 3

3(2)² = 12

3(3)² = 27

3(10)² = 300

Answer:

ab = 2

Step-by-step explanation:

Given equations

ax² +ax + 2 = 0

x² + x + b = 0

root of both the equation

x= 1

then we can plug in x = 1 in both the equation

ax² +ax + 2 = 0                        x² + x + b = 0

a*1² +a*1 + 2 = 0                        1² + 1 + b = 0

a +a + 2 = 0                                 1 + 1 + b = 0

2a + 2 = 0                                    2 + b = 0

2a = -  2                                         b = -2

a = -2/2 = -1

Thus,

a = -1

b = -2

a*b = -1*-2 = 2

ab = 2

Hey there! :)

Answer:

x = -24.

Step-by-step explanation:

Plug in the values to find the value of 'k':

-3 = k(6)

Divide both sides by 6 to solve for 'k':

-3/6 = k

k = -1/2

Plug this into the equation to solve for the value of x when y= 12:

12 = -1/2(x)

Divide both sides by -1/2:

-24 = x

x = -24.

Answer:

x would be -24

Step-by-step explanation:

since k is a constant, we have to find out what k is from the equation

. -3=6(k) divide both sides by 6 to get that k is -0.5/-1/2.

then, solve for what x is when y is 12 by setting up the equation 12=(-0.5)x. this would result in x being -24

Answer:

h=5/2

Step-by-step explanation:

200h=180h+50

20h=50

Answer:

m<EAD=29°

m<CAB=119°

Solution,

< CAE+<EAD+90°=180°( angles on a straight line)

61+<EAD+90°=180°

<EAD=180-(90+61)

=180-151

=29°

<CAB+<FAB=180°( Linear pair)

<CAB+61°=180°

<CAB=180°-61°

<CAB=119°

hope this helps ..

Good luck on your assignment..

Answer:

2nd option.

Step-by-step explanation:

3(8 - 4x) < 6(x - 5)

24 - 12x < 6x - 30

-12x - 6x < -30 - 24

-18x < -54

x > 3

Answer:

2nd graph

Step-by-step explanation:

3(8 – 4x) < 6(x – 5)

Distribute

24 -12x < 6x -30

Add 12x to each side

24-12x+12x < 6x-30+12x

24 < 18x-30

Add 30 to each side

24+30 < 18x-30+30

54 <18x

Divide by 18

54/18 < 18x/18

3<x

Open circle at 3 and line going to the right

Answer:

see explanation

Step-by-step explanation:

∠ 1 and ∠ 2 are adjacent angles and supplementary, thus

∠ 2 = 180° - ∠ 1 = 180° - 110° = 70°

--------------------------------------------------

The chord- chord angle 3 is half the sum of the measures of the arcs intercepted by the angle and its vertical angle, thus

∠ 3 = [tex]\frac{1}{2}[/tex] (100 + 60)° = 0.5 × 160° = 80°

∠ 3 and ∠ 4 are adjacent angles and supplementary, thus

∠ 4 = 180° - 80° = 100°

Thus

Angle    Value

   1           110

   2            70

   3             80

   4            100

Answer:

(i) 12.25

(ii) 12.25.

Step-by-step explanation:

(1) cot^2 O = (7/2)^2 = 49/4

= 12.25.

(2) (1 - sin O) ( 1 + sin O)         1 - sin^2 O          cos^2 O

     ----------------------------  =     -------------   =       --------------

    (1 - cos O)(1 + cos O)         1 - cos^2 O         1 - cos^2 O

As cot O = 2/7, tan O = 1 /2/7 = 7/2.

Hypotenuse of the right  triangle = √( 2^2 + 7^2)

= √53

So cos O = 7/√53

Therefore  the original function = cos^2 O / (1 - cos^2 O)

= (7/√53)^2 / (1 -  (7/√53)^2 )

= 49/53 / 4/53

= 49/4.

Answer:

Step-by-step explanation:

Locate the 1 on the x axis. This is one hour worked. Go up vertically along x = 1 and you "land" on the red line very quickly. If you go straight across to the left, you are at 14 on the y-axis. The y-axis indicates the amount of money Leo earns tutoring. If he works one hour and earns $14 and this is a straight line (linear function with a constant slope), that means that for every hour he works he will earn $14. Locate the 2 on the x-axis and go up x = 2 til you hit the red line. Read it to the left and you "land" on the y-axis at $28. $28 divided by 2 hours of work is $14 per hour of tutoring. The first choice is the one you want.

Answer:

1) 38

2) 160

3) 40

Step-by-step explanation:

Answer:

23, 42, 12

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

0.5 is said as "five-tenths". This is because it is one place after the decimal. It would then become five-tenths, written as: 510. You would then simplify the fraction: 510=12

// have a great day //

Answer:

  C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y–axis and a dilation about the origin by a scale factor of 3/4

Answer:

c and something is not d

Step-by-step explanation:

Answer:

C. y < -1/5x + 1

Step-by-step explanation:

We can eliminate A and B because the inequality sign is incorrect. If we were to graph those, the shaded area would be above the line, not below. We are left with C and D. Notice in our given graph that the line is dotted, so solution on the line are not included. So our answer would be C. because the inequality sign is y is less than and not y is less than or equal to.

Answer:

Please see the attached picture...

Hope it helps...

Good luck on your assignment....

Answer:

The number Alexis thinks of first is 6.7.

Step-by-step explanation:

Let the number Alexis thinks of be x and the first answer he got be y.

Since he multiplies the number by x and divides the answer by 100, the equation is

10x = y

10x = [tex]\frac{y}{100}[/tex]

Then, he multiplies this answer, [tex]\frac{y}{100}[/tex], by 1000 and gets a final answer of 67. The equation is

[tex]\frac{y}{100}[/tex] × 1000 = 67

To find y, you divide 1000y by 100 which gives 10y.

i.e. [tex]\frac{1000y}{1000} = 67[/tex]

10y = 67

Divide both sides of the equation by the coefficient of y (which is 10)

[tex]\frac{10y}{10} = \frac{67}{10}[/tex]

y = 6.7

Substituting 6.7 for y in 10x = y

10x = 6.7

Divide both sides of the equation by the coefficient of x (which is 10)

[tex]\frac{10x}{10} = \frac{6.7}{10}[/tex]

x = 0.67

∴ The number Alexis thinks of first is 0.67.

Hope this helps!!! :))

Answer:

0.67

Step-by-step explanation:

Solution 1

We can work out the initial number by going backwards from the end:

67/1000= 0.067

0.067*100= 6.7

6.7/10= 0.67

Solution 2

(x*10/100)*1000= 67

x/10*1000= 67

100x= 67

x=67/100

x=0.67

None thats impossible. think about it

98+90= 180

its too high

no triangle

Answer:

None

Step-by-step explanation:

An obtuse angle means that the angle is larger than 90 degrees. Since the total interior angle measures in a triangle must add up to 180 degrees, you cannot have 2 angles more than 90 degrees. Hope this helps!

Answer:

$2466.55

Step-by-step explanation:

We use the formula for Compound Amount, the amount gotten after a particular time, to find the balance:

[tex]A = P(1 + r)^t[/tex]

where P = Principal = $700

r = rate = 6.5% = 0.065

t = time elapsed 20 years

Therefore:

[tex]A = 700(1 + 0.065)^{20}\\\\A = 700(1.065)^{20}\\[/tex]

A = $2466.55

The balance of the account will be $2466.55

Answer:

12.1 =x

Step-by-step explanation:

Since this is a right triangle, we can use  trig functions

cos theta = adj/ hyp

cos 30 = x/14

14 cos 30 = x

12.12435565 =x

12.1 =x

Answer:

C) [tex]n^3+4n^2+8n-16[/tex]

Step-by-step explanation:

[tex]2n^3+4n^2-7+(-n^3)+8n-9=\\n^3+4n^2-7+8n-9=\\n^3+4n^2+8n-9-7=\\n^3+4n^2+8n-16[/tex]

(Just combine like terms)

Only C) [tex]n^3+4n^2+8n-16[/tex] fits our answer.

Answer:

[tex] {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]

Option C is the right option

Solution,

[tex]2 {n}^{3} + 4 {n}^{2} - 7 + ( - {n}^{3} + 8n - 9) \\ = 2 {n}^{3} + 4 {n}^{2} - 7 - {n}^{3} + 8n - 9 \\ [/tex]

combine like terms

[tex]2 {n}^{3} - {n}^{3} + 4 {n}^{2} + 8n - 7 - 9 \\simplify \\ = {n}^{3} + 4 {n}^{2} + 8n - 16[/tex]

hope this helps...

Good luck on your assignment..

Answer:

f(-7)=224

Step-by-step explanation:

[tex]f(x) = 4x^2 -4x\\f(-7)= 4(-7)^2 - 4(-7)\\= 4(49) -+28\\=196+28\\f(-7) = 224[/tex]

Answer:

[tex](C) \dfrac{x+3}{x}[/tex]

Step-by-step explanation:

We want to determine an  equivalent expression to:

[tex]\dfrac{x}{x-3} \div \dfrac{x^2}{x^2-9}[/tex]

Step 1: Factorise [tex]x^2-9[/tex] using the difference of two squares.

[tex]x^2-9=x^2-3^2=(x-3)(x+3)[/tex]

Step 2: Change the division sign to multiplication

[tex]\dfrac{x}{x-3} \times \dfrac{(x-3)(x+3)}{x^2}[/tex]

Step 3: Cancel out common terms and simplify

[tex]= \dfrac{x+3}{x}[/tex]

The correct option is C.

The expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Given expression is,

                        [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}[/tex]

Use factorization,   [tex]x^{2} -9=(x-3)(x+3)[/tex]

Now simplify the given expression.

                       [tex]\frac{x}{x-3}\div\frac{x^{2} }{x^{2} -9}\\\\=\frac{x}{x-3}*\frac{(x-3)(x+3)}{x^{2} } \\\\=\frac{x+3}{x}[/tex]

Hence, the expression equivalent to given expression is [tex]\frac{x+3}{3}[/tex]

Learn more:

https://brainly.com/question/1280754

Answer:

480 in.^3

Step-by-step explanation:

volume of pyramid = (1/3) * (area of base) * height

Since this pyramid has a square for the base, the area of the base is

A = s^2, where s = length of the side of the square

volume = (1/3) * s^2 * h

volume = (1/3)(12 in.)^2 * (10 in.)

volume = (1/3)(144)(10) in.^3

volume = 480 in.^3

The volume of the square-based pyramid is 480 cubic inches as per the concept of the pyramid.

To find the volume of a square-based pyramid, we can use the formula:

Volume = (1/3) x base area x height.

In this case, the base of the pyramid is a square with a side length of 12 inches, and the height of the pyramid is 10 inches.

First, we calculate the base area of the pyramid, which is the area of the square base:

Base area = side length x side length

                = 12 in x 12 in

                = 144 square inches.

Now, we can substitute the values into the volume formula:

[tex]Volume = \frac{1}{3} \times 144 \times 10[/tex].

Multiplying these values, we get:

[tex]Volume = \frac{1}{3} \times1440 {in}^3[/tex]

Simplifying the expression, we have:

[tex]Volume = 480\ in^3[/tex].

To learn more about the pyramid;

https://brainly.com/question/17615619

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Answer:

[tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.

Step-by-step explanation:

We are given that in 1995, the USPS approximated that they handled  [tex]1.8 \times 10^{11}[/tex] pieces of mail and in 2010, the USPS reported that they handled [tex]1.7 \times 10^{11}[/tex]  pieces.

To find how many more pieces of mail were handled in 1995 than in 2010, we do subtraction of the pieces of mail that were handled in both the years.

Pieces of mail handled in 1995 = [tex]1.8 \times 10^{11}[/tex]

Pieces of mail handled in 2010 = [tex]1.7 \times 10^{11}[/tex]  

As it is clear that more pieces of mail were handled in 1995.

So, Pieces of mail handled in 1995 - Pieces of mail handled in 2010 = [tex](1.8 \times 10^{11}) -(1.7 \times 10^{11})[/tex]

=  [tex]10^{11} \times (1.8 -1.7)[/tex]

=  [tex]10^{11} \times 0.1[/tex] = [tex]1 \times 10^{10}[/tex]

Hence, [tex]1 \times 10^{10}[/tex] more pieces of mail were handled in 1995 than in 2010.