Please answer with show work. Trigonometry!

⇒The line passes through the points (3,0) and (1,-3) I will use them to find the gradient of the line. Note this information is from the graph.

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{-3-0}{1-3} \\m=\frac{3}{-2} \\m=-\frac{3}{2}[/tex]

You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.

17/28 of all the letters are X's.

Answer:

Acute angle

OLN angle

Step-by-step explanation:

In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].

What is an equation?

A movie ticket cost $4.25 in 1990.

The inflation rate is about 3.5%

Rate increased ,r=100%+3.5%=103.5%=1.035

equation generated is,

y=4.25[(1.035)^x]

Solving the equation for each year, we get the following data:

Tabulating the data

Year         cost

1990         4.25

1991          ....

....              ....

1998          5.5964~ 5.6

In the year 1998, the will be greater than $5.50.

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Answer:

a) ∠13

b) ∠13

c) ∠2

Step-by-step explanation:

a) ∠ 8  + ∠13 = 180°  

Co - interior angles are supplementary, when m // l

b) ∠5 ≅ ∠13

If m // l, the corresponding angles are congruent.

c) ∠5 + ∠2 = 180°

∠5 and ∠2 are co interior angles and they are supplementary if a // b.

a) 10 percent people arrive before 7 am.

b) 64 percent of the people arrive after 7:59 am.

Here, we are given the following data-

Time                                No. of people

before 7 am                           15

7am to 7:59 am                     39

8am to 8:59 am                    75

9am to 9:59 am                    21

a) the number of people who arrive at the office before 7am = 15

The total number of people in the office = 150

Thus, the percentage of people surveyed who arrived before 7 am = (15/150)*100

= (1/10)*100

= 10

Thus, 10% people arrive before 7 am.

b) The number of people who arrive after 7:59 am = 75 + 21

= 96

Thus, the percentage of people surveyed who arrived after 7:59 am =

(96/150)*100

= (0.64)*100

= 64

Thus, 64 percent of the people arrive after 7:59 am.

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Answer:

it's a chemical change.

Step-by-step explanation:

a raw egg is converted into a hard boiled one by chemical changes happening inside it. Its also an irreversible change

Accurate Whole numbers .

What is accurate whole number?

Accuracy is defined by the number of significant digits while precision is identified by the location of the last significant digit. For instance the number 1234 is more accurate than 0.123 because 1234 had more significant digits.

What does function mean?

Each element of x is given exactly one element of y via a function from a set x to a set y. The sets x and y are collectively referred to as the function's domain and codomain, respectively.

The following details must to be taken into account:

The term "whole number" refers to a number that is free of fractions and decimals.

It calculated the number of household online devices in relation to the number of occupants.

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Answer:

Step-by-step explanation:

2x+3

x=3divides2

Answer:

x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex]8^{x}[/tex] = 2

[tex]2^3)^{x}[/tex] = 2 , that is

[tex]2^{3x}[/tex] = [tex]2^{1}[/tex]

since the bases on both sides are equal, both 2, then equate the exponents

3x = 1 ( divide both sides by 3 )

x = [tex]\frac{1}{3}[/tex]

The equation of the linear function is: 3x + y = 1.

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y - y₁ = m(x - x₁), where m is the slope and c is the y-intercept.

Given, the line passes through the points (-2, 7) and (2, -5).
Now, using the formula established in the literature, we get:
Slope = m = (y₂ - y₁)/(x₂ - x₁) = (-5 - 7)/(2 - (-2)) = -12/4 = -3
Equation of the linear function: y - 7 = (-3)(x - (-2)) ⇒ y - 7 = (-3)(x + 2)
⇒ y - 7 = -3x - 6 ⇒ 3x + y = 1
Thus, the equation of the linear function is: 3x + y = 1.

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Answer:

A = 135 cm²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 9 , b₁ = 19 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 9 × (19 + 11) = 4.5 × 30 = 135 cm²

Answer: Hi this would be the arrow that goes to the left and the dot on the right, so something like ← and dot. Hope this helps, I know this is confusing but try your best.

Step-by-step explanation:

Answer:

After solving the inequality, we get:

[tex]x\leq -10[/tex]

With the plotted inequality given.

Step-by-step explanation:

Step 1: Manipulate and solve the inequality

The inequality is given as:

[tex]\frac{1}{2}x+8\leq 3[/tex]

Make [tex]x[/tex] the subject of the inequality to solve it:

[tex]\frac{1}{2}x+8\leq 3\\\\\text{Subtract 8 from both sides of the equation:}\\\frac{1}{2}x+8-8\leq 3-8\\\\\text{Simplify:}\\\frac{1}{2}x\leq -5\\\\\text{Multiply by 2 on both sides of the inequality:}\\2\times \frac{1}{2}x\leq -5\times 2\\\\\text{Simplify:}\\x\leq-10[/tex]

Step 2: Plot the inequality

After solving the inequality, we get:

[tex]x\leq -10[/tex]

Which means that [tex]x[/tex] consists of all values that are equal to and less than [tex]-10[/tex].

On a number line, when the inequality includes the value, it is denoted by a closed circle.

With all this information, let's plot the number line:

A) The type of function that can be used to describe the value of the investment after a fixed number of years using option 1 and option 2 are respectively; Linear Function and Exponential function.

B) One function for each option to describe the value of the investment f(n), in dollars, after n years.;

Option 1; f(n) = n + 100

Option 2; f(n) = n + 100x

C) The amount from option 1 after 20 years would be 3000 and the amount from option 2 after 20 years would be 4900

A) For option 1, the linear function can be used to describe the value of the investment after a fixed number of years. This reason is that, in option one, the amount increases by a fixed amount every year.

For option 2, the exponential function can be used to describe the value of the investment after a fixed number of years. The reason is that, in option 2, the amount increase is higher than the previous year.

B) For option 1, the function is;

f(n) = n + 100

For option 2, the function is;

f(n) = n + 100x

C) After 20 years, the amount from option 1 would be 3000 and the amount from option 2 would be 4900. Thus, there is a difference of 1900.

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Answer:

6cm by 1.5cm

18cm by 4.5cm

80cm by 20cm

Step-by-step explanation:

The inverse and domain of the function are y = x²-9 and all real numbers.

A function's inverse is a function that reverses the action of a function, such as g(x). If and only if g(x) is bijective, then the inverse of g(x) exists, and if it exist.

If the function f(x)=√x + 9, find the inverse;

y = √x+9

x = √y+9

x² = y+9
y = x²-9

The domain of the inverse function will exist on all real numbers.
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The value of the function f(0) = 1, obtained from the graph.

For the given question;

The graph for the function is given.

For finding the value of function f(0), simply see the value of y with respect to x = 0.

f(0) = 1, taken from graph.

Thus, the value of function f(0) is found as 1.

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A unit rate means a rate for one of something.

The number of boxes packed in 18 hours is 216 boxes.

A unit rate means a rate for one of something.

We write this as a ratio with a denominator of one. 

We have,

From the graph, we see that,

In 5 hours, there are 60 boxes packed.

This can be written as:

5 hours = 60 boxes

Similarly,

1 hour = 12 boxes

3 hours = 36 boxes

The number of boxes packed in 18 hours:

1 hour = 12 boxes

Multiply both sides by 18.

18 hours = 18 x 12 boxes

18 hours = 216 boxes

Thus,

The number of boxes packed in 18 hours is 216 boxes.

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a. The line equation is given by:

Where m is the slope of the line and b is the y intercep.

In this case y is the number of active pilots and x is the year.

In order to obtain the line equation of the function, you use the information about a pair of years in the given table, in order to calculate the slope of the line. You can select whichever two years with its number of active pilots.

For example, for years 1980 and 1990, you have that the pilots were 182,097 and 149,666 respectively.

To calculate the slope of the line, you use the following formula:

Then, the slope of the line is negative.

If you consider the zero point of the year axis, as the year 1980, the y intercept of the function will the value of the active pilots in that years, which is 182,097.

Finally, the line equation is:

b. For the year 2003, you have that x is:

x = 2003 - 1980 =23

You replace this value of x into the linear equation:

The number of active pilots for 2003 is 107,506

MK = 50

to get from 13 to 53

times 1 plus 40

10 times 1 plus 40 =50

Answer:

1.265 x 10-10

Step-by-step explanation:

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=17

Step-by-step explanation:

Answer:

The stadium’s seating options will include premium seats (boxes closest to the action), medium-priced seats, and budget-friendly bleachers. Your design calls for 4,500 upper-deck premium seats and 7,500 lower-deck premium seats. The team’s policy is to have a 3:2 ratio of premium seats to bleacher seats. How many bleacher seats will the stadium include?

Answer: 8,000 bleacher seats. 4,500 + 7,500 premium seats = 12,000. 12,000/x = 3/2. x = 8,000.

Answer:

y = 3x - 1

Step-by-step explanation:

In order for lines to be parallel, they must have the same slope.

The slope of y = 3x - 8 is 3.

Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:

y − y₁ = m(x − x₁)

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

y + 7 = 3(x + 2)

Distribute 3 and isolate y:

y + 7 = 3x + 6

y = 3x - 1

Answer:

x=8

Step-by-step explanation:

83+(12x+1)=180

It equal to 180 because the line measures to 180.

Then write out the equation and solve.

Answer:

20002

Step-by-step explanation:

100*20=2000

2000*10=20000

20000+2=20002

The correct answer is options A and E.

f(x) = 6x + 4

f(1) = 6(1) + 4 = 10

f(2) = 6(2) + 4 = 16

f(3) = 6(3) + 4 = 22

Clearly, options A and E are the same sequences.

The car will catch up the cyclist 3 hours after it starts moving.

The cyclist travels at 9 miles per hour, and travels for 4 hours before the car starts moving, so the equation for the position of the cyclist as a function of time, t, is:

C(t) = 9*4 + 9*t = 36 + 9*t

And the car moves at 21 miles per hour, then the position is:

P(t) = 21*t

The car will catch the cyclist when:

C(t) = P(t), this gives:

36 + 9*t = 21*t

36 = 21*t - 9*t = 12*t

36/12 = t

3 = t

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