Modeling Real-World Scenarios with Sine and Cosine Functions
The table below shows the illuminated percentage of the moon on a lunar cycle of 28 days. The relationship can be described using a cosine function.

Answer:

Half a mile is 2640 feet.

Answer:

sorry wanted pionts

Step-by-step explanation:

umm sorry

Answer: :Given : points G and I have coordinates (6,4) and (3,2)

To Find : Use  Pythagorean theorem  to calculate the straight line distance between points G and I

Solution:

points G and I have coordinates (6,4) and (3,2)

Draw a line parallel to y axis passing through G

Draw a line parallel to x axis passing through I

Intersection point K ( 6 , 2)

IK = 6 - 3 = 3

GK = 4 -2  = 2

ΔIKG right angled triangle

Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.  

GI² = IK² + GK²

=>  GI²  = 3² + 2²

=>  GI²  = 13

=> GI = √13

using distance formula

G (6,4) and I (3,2)

= √(6 - 3)² + (4 - 2)²

= √3² + 2²

= √9 + 4

= √13

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13. In Fig. 16.10, BCDE is a rectangle , ED = 3.88 cm,AD= 10 cm ...

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Answer:

68.75

Step-by-step explanation:

75 divided by 12 is 6.25 so you subtract 6.25 from 75 and get your answer.

i hope this helps.

Answer: I believe it is 38 degrees?

Answer:  $4x4x

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

To know if a table is a function or not, we have to see if 1 input only has 1 output.

Looking at the table each input only has 1 output, so it is a function.

With the help of percentage increase information, we conclude that,  Americans spent approximately $1,141.31 on summer vacation in 2014.

What is percenatge increase?

Percentage increase is a measure of how much a value has increased in comparison to the original value, expressed as a percentage.

To find what Americans spent in 2014, we need to use the percentage increase and the 2015 amount.

Let X be the amount spent in 2014.

We know that the increase from 2014 to 2015 is 3.4%, which can be expressed as:

3.4% = 0.034 (as a decimal)

We also know that the amount spent in 2015 is $1,180.

Using this information, we can set up an equation:

X + 0.034X = 1180

Simplifying the left side:

1.034X = 1180

Dividing both sides by 1.034:

X = 1141.31

So Americans spent approximately $1,141.31 on summer vacation in 2014.

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The evaluation of sample rational polynomial expressions in Unit 3 of the Study guide are presented as follows;

x/(x + 5) - 2/(x - 3) = (x² - 5·x - 10)/(x² - 2·x + 15)

(5·x - 3)/(4·x) - 1/(6·x)

Rational polynomials are polynomials, that are quotients of polynomials.

f(x) = P(x)/Q(x)

A possible rational expression from Unit 3 lesson 5, Adding and subtracting rational expressions is presented as follows;

x/(x + 5) - 2/(x - 3)

The multiplication of the denominators indicates that we get;

x/(x + 5) - 2/(x - 3) = (x·(x - 3) - 2·(x + 5))/((x + 5)·(x - 3))

(x·(x - 3) - 2·(x + 5))/((x + 5)·(x - 3)) = (x² - 5·x - 10)/(x² + 2·x - 15)

Therefore;

x/(x + 5) - 2/(x - 3) = (x² - 5·x - 10)/(x² + 2·x - 15)

A second equation from the Study guide is presented as follows;

(5·x - 3)/(4·x) - 1/(6.x)

Multiplying the denominator to obtain a common multiple, and multiplying the numerator by the factor of the common denominator obtained, we get;

(5·x - 3)/(4·x) - 1/(6.x) = (5·x × (6·x) - 3 × (4·x))/((4·x)·(6.x))

(5·x × (6·x) - 3 × (4·x))/((4·x)·(6.x)) = (30·x² - 12·x)/(24·x²)

(30·x² - 12·x)/(24·x²) = (5·x - 2) × x × 6/(6 × 4·x²)

(5·x - 2) × x × 6/(6 × 4·x²) = (5·x - 2)/(4·x)

(5·x - 3)/(4·x) - 1/(6.x) = (5·x - 2)/(4·x)

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Answer:

\(\sf 872\)

Step-by-step explanation:

Parentheses

\(9 + 3 = 12\)

\(=20^2\cdot \:2+6\cdot \:12\)

Exponents

\(20^2=400\)

\(=400\cdot \:2+6\cdot \:12\)

M/D(Multiply/Div.)

\(6\cdot \:12 = 72\)

\(=800+72\)

A/S(Add/Sub.)

\(800+72=872\)

\(\sf Thus,\\= 872\)

To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.

In this case, we are to determine the probability of selecting two even numbers. This can be solved as follows:There are six even numbers: {2, 4, 6, 8, 10, 12}.We can use the concept of conditional probability since the first event affects the probability of the second event. This can be expressed as follows:

In this case, P(A) represents the probability of selecting an even number, and P(B|A) represents the probability of selecting an even number given that the first card selected was even. P(A) = 6/12 = 1/2 (there are six even numbers and twelve cards in total)P(B|A) = 5/11 (there are five even numbers left in the box after the first even number is selected, and eleven cards are left in total).

The probability of selecting two even numbers can be found by multiplying these probabilities: P(A) x P(B|A) = (1/2) x (5/11) = 5/22Therefore, the probability of selecting two even numbers is 5/22.Answer: 5/22

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Answer:

-2 , 0 , 2

Step-by-step explanation:

HOPE THIS HELPS

PLZZ MARK BRAINLIEST

Answer:

the box after 4 is 2, 0, -2

Step-by-step explanation:

-2,0,2,4,6,8

It's counting down by two's  

Answer:

\(\displaystyle -2\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

a = 4

b = 8

f(4) = -1

f(8) = -9

Step 2: Find Average Rate

Answer:

Its b + 5

Step-by-step explanation:

if b is blue flowers, and 5 more green than blue, it means 5 more than blue. Getting b+5!!!

Answer:

b+5

Step-by-step explanation:

If she has b amount of flowers and 5 more yellow flowers than blue flowers, you add 5 flowers to the blue flowers and you get the yellow flowers.

Since we do not know the exact amount of blue flowers, we add 5 to b.

b+5

Answer:

The right triangle has sides of approximately 7.86 cm, 24 cm, and 24.88 cm, and angles of 90°, 72°, and 18°.

Answer:

A=18 degrees
a=7.80cm

C=24.54cm

Step-by-step explanation:

The required inequality is;

To solve the inequality, we have,

This implies that Juan can only afford 2 days' rent under his budget.

Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:B

Step-by-step explanation:

Answer:

3/4,

12/16,

18/24,

24/32

30/40

...So on, So on...

Step-by-step explanation:

Any fraction that you multiply by the same number on the bottom and on top.

So, multiply by two, what you do to the top do to the bottom. = 12/16

Multiply by three = 18/24

So on, so on.

Or you can reduce, 6/8 divide by 2 = 3/4.

I'm gonna give you 5 equivalent equations. I also taught you how to do it!

Answer:

The area of Alison's pizza would be 30 in.

Answer:

Perimeter = 69.4 cm

Area = 299.92 square cm

Step-by-step explanation:

Given:

length of rectangle (l) = 18.4 cm

Width of rectangle (w) = 16.3 cm

a) Perimeter of rectangle

    = 2( l + w)

    = 2 ( 18.4+16.3)

     = 2 * 34.7

     = 69.4 cm

b) Area of rectangle = lw = 18.4*16.3 = 299.92 square cm

Answer:

Proof

18 ( 1 + 1/2) = 27  rectangles

18 + 9 = 27

Same as

17 + 7 + 3 = 27

As 17 x 1.5 = 28

Step-by-step explanation:

18 squares means 18 + all the sequences of sets of numbers shown to show different size rectangles not different rotations of such rectangles.

Sequence set of numbers also is matched with the lowest factors of 18 being 3

We could also say prime factors but left over is 3 and 3^2 = (3 x 1) (3 x 1) so it would be 3, 1  and 2 just the same.

We get 18 + (16 + 1) + (14 + 1) (10= 2 x 5) + (8 = 2 x 4)  + ( 6 = 2x 3)  in example and see everything is shown in rows of 1, 2, 3  that so happen to be the lowest 3 factors of 18.  We know 3 is the lowest  number in 3 x 6 being is the highest factor before 18 so the link would be that 3 x 2 =  2^3+1 = 16 and proves we cannot go higher than 16 row for 2.    

Rows of one  = (2) + (2+1) +(3+1) + (4+1) + (5+1) + (6+1) + (7+1) + (8+1) + (9+1) +(10+1) = (11+1) +(12+1) + (13+1) + (14+1) + (15+1) + (16+ 1) + (17+ 1) = 17

Rows of two (2 x 3 ) + (2 x 4) + (2 x 5) + ( 2 x 6 ) +( 2x 7) + (2x8 ) + (2 x9)

=  6, 8, 9, 10. 12, 14, 16, 18    

= 7

Rows of three (3 x 4 ) (3 x 5)  (3 x 6)

= 12  + 15 + 18

= 3

Rows of 4  is already been shown

Therefore;

17 + 7 + 3 = 27

= 7 x 3 our rows of 2's and 3's = 27 - 17 and decreases our pattern at scale 17: 7 : 3

27 / 18 = 1.5  so we have learnt rectangles for numbers 18 and under are scale factored at 1.5

18( 1 + 1/2) = 27

18 + 9 = 27

17 x 1.5 = 27  rectangles

With 18 squares, you can make two rectangles: one with dimensions 2 × 9 and another with dimensions 3 × 6.To determine how many rectangles can be formed using 18 squares, we need to understand the relationship between rectangles and squares, as well as the concept of factors.

A rectangle can be made using squares if the number of squares can be arranged to form both the length and width of the rectangle. Since a rectangle has two pairs of equal sides, we need to find pairs of factors of 18 (the number of squares) that can be multiplied together to get 18.

The factors of 18 are: 1, 2, 3, 6, 9, 18.

Now, let's look at the pairs of factors that can be multiplied to get 18:

1 × 18 = 18 (not a rectangle, but still counts as a pair)

2 × 9 = 18

3 × 6 = 18

So, there are two pairs of factors that can be used to create rectangles using 18 squares: 2 × 9 and 3 × 6.

Steps:1. Pair of Factors: When we say "pair of factors," we mean two numbers that are multiplied together to get a certain product. For example, in the case of 2 × 9, 2 and 9 are factors, and when multiplied, they give 18.

2.Rectangle Formation: To form a rectangle using squares, we need to find pairs of factors where one factor can represent the length and the other factor can represent the width. For instance, with the pair 2 × 9, you could arrange 2 squares along the length and 9 squares along the width to create a rectangle.

3.Counting Rectangles: When you ask how many rectangles can be formed using 18 squares, you're essentially asking how many pairs of factors can be used to create rectangles. In this case, there are two such pairs: 2 × 9 and 3 × 6. Each pair corresponds to a unique rectangle.

So, with 18 squares, you can make two rectangles: one with dimensions 2 × 9 and another with dimensions 3 × 6.

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Based on the data recorded by Anna on Saturday, we can estimate the number of people expected to visit The Youth Wing on Sunday.

Let's calculate the proportion of visitors to The Youth Wing compared to the total number of visitors on Saturday:

\(\displaystyle \text{Proportion} = \frac{\text{Visitors to The Youth Wing on Saturday}}{\text{Total visitors on Saturday}} = \frac{382}{382 + 461 + 355}\)

Next, we'll apply this proportion to the total number of visitors on Sunday to estimate the number of people expected to go to The Youth Wing:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times \text{Total visitors on Sunday}\)

Now, let's substitute the values into the equation and calculate the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355}\)

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \text{Proportion} \times 800\)

Calculating the proportion:

\(\displaystyle \text{Proportion} = \frac{382}{382 + 461 + 355} = \frac{382}{1198}\)

Calculating the estimated number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} = \frac{382}{1198} \times 800\)

Simplifying the equation:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx \frac{382 \times 800}{1198}\)

Now, let's calculate the approximate number of visitors to The Youth Wing on Sunday:

\(\displaystyle \text{Expected visitors to The Youth Wing on Sunday} \approx 254\)

Therefore, based on the data recorded on Saturday, we can estimate that around 254 people should be expected to go to The Youth Wing on Sunday.

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The measure of the central angle is 0.75 radians

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The area of a figure is the amount of space it occupies in its two dimensional state.

The length of an arc with an angle of Ф is given by:

Length of arc = (Ф/360) * (π * diameter)

The diameter is 16 cm and intercepted arc length is 6 cm, hence:

Length of arc = (Ф/360) * (π * diameter)

6 = (Ф/360) * (π * 16)

Ф = 42.97°

Ф = 42.97° * π/180 = 0.75 radian

The measure of the central angle is 0.75 radians

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The expression that represents the area of the cement walkway is   11 ( 12 + 32x)

The formula for area of a rectangular prism is given as;

Area = 2 ( wl + hw + h )

Where;

Now, let's substitute into the formula for area;

Area = 2 {3(22) + 5x(3) + 22(5x) }

expand the bracket

Area = 2 { 66 + 15x + 110x }

collect like terms

Area = 2{66 + 176x}

Area = 132 + 352x

Area = 11 ( 12 + 32x)

Thus, the expression that represents the area of the cement walkway is   11 ( 12 + 32x)

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Answer: x = 36, y = 10, and z = -25

Step-by-step explanation:

99 and -3z +6 are same side interior angles, so they sum to 180 degrees.

99 -3z + 6 = 180

-3z = 75

z = -25

Opposite angles of a parallelogram are congruent

2x + 9 = -3x + 6

2x + 9 = 75 + 6

2x = 81 - 9

2x = 72

x = 36

9y + 9 = 99

9y = 90

y = 10

According to definition of parallelogram

\(\\ \rm\hookrightarrow 2x+9+99=180\)

\(\\ \rm\hookrightarrow 2x+108=180\)

\(\\ \rm\hookrightarrow 2x=72\)

\(\\ \rm\hookrightarrow x=36\)

And

And