Trigonometry question
Given the following function, choose the graph with the two possible angles with the domain 0[tex]\leq[/tex]0[tex]\leq[/tex]360 degrees.

1. sin0 = -2/3

2. sec0 = 2/1

3. tan0 = 4/5

4. csc0 = -3/2

5. cos0 = -3/5

Question 10

Lines a and b by the converse of the consecutive interior angles theorem

Question 11

Lines e and f by the converse of the alternate interior angles theorem

Answer:

SSS

Step-by-step explanation:

We know the length of DE and JK are the same because as shown in the diagram, they are both equal to 15 cm. While we know that EF and KL are congruent because it is shown that both sides are 8 cm long. Even though we are not sure of the exact lengths of FD or LJ, we are aware that they are the same length sue to the ticks found on both sides on the triangles, indicating that they are both the same length.

The Solution:

Given the graph of f(x), we are required to determine whether the degree of the function is ODD or EVEN, and also to determine whether the function itself is ODD.

An odd function is defined as a function that has f(–x) = –f(x) for any value of x. The opposite input gives the opposite output.

From the given graph of f(x), the function f(x) is ODD.

The degree of the function f(x) is odd since the f(x) itself is odd.

Answer:

Step-by-step explanation:

solve for x

2x+14=-21-5

2x+14=-26

subtract 14 from both sides

2x+(14-14)=-14-26

2x=-14-26

2x=-40

divide both sides of 2x = -40 by 2

[tex]\frac{2x}{2} =\frac{-40}{2}[/tex]

2/2=1

x=[tex]\frac{-40}{2}[/tex]

x= -20

The speed of the tennis ball is 6.2 metres per seconds.

Speed is measured as the ratio of distance to the time in which the distance was covered.

Therefore, speed can be represented mathematically as follows;

speed = distance / time

Hence, the table tennis travels 12.4 metres south in 2 seconds.

The speed of the tennis can be computed as follows:

distance = 12. 4 metres

time = 2 seconds

Therefore,

speed = 12.4 / 2

speed = 6.2 meters per seconds.

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If Katie and her best friend Liam play tennis every Saturday morning. When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds. Then the speed of tennis ball is 6.2 m/s

Speed is the time rate at which an object is moving along a path, while velocity is the rate and direction of an object's movement.

Given that,

Katie and her best friend Liam play tennis every Saturday morning.

When Katie serves the ball to Liam, it travels 12.4 meters south in 2 seconds.

The speed of the tennis can be found by using formula

speed=distance/time

distance = 12. 4 metres

time = 2 seconds

Now speed=12.4/2

speed=6.2

Hence speed of the tennis ball is 6.2m/s

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Answer:

x = 11,2 inchs

Step-by-step explanation:

I infer that the units are in inches.

8-3 = 5

Then:

By the Pythagorean Teorem:

x² = 10² + 5²

x² = 100 + 25

x² = 125

√x² = √125

x = 11.18

to the nearest tenth:

x = 11.2 inches

Answer:

[tex]x = 4 \pm \sqrt7[/tex]

Step-by-step explanation:

Hello!

Standard form of a Quadratic: [tex]ax^2 + bx + c= 0[/tex]

Given the Equation: [tex]x^2 -8x+9=0[/tex]

Quadratic Formula: [tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\[/tex]

Solve by substituting the values into the Quadratic Formula.

The solution to the quadratic is [tex]x = 4 \pm \sqrt7[/tex].

For the given tables, we have that:

a. The grids are given at the end of the answer.

b. The functions are classified as follows: f(x) exponential, g(x) linear.

c. When x increases by one unit from left to right, we have that:

d. The functions are equal for a value between 1 and 2, as at x = 1 g(x) is greater while at x = 2 f(x) is greater.

The difference between exponential and linear functions is in the rate of change, as:

Hence the functions are classified as follows:

We have one exponential and one linear function, so it is quite difficult to solve an equation to verify where they are equal. We have that:

This means that at one point between x = 1 and x = 2, they intersected, that is, they had the same function values.

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Answer: y = 15

Step-by-step explanation:

Combine multiplied terms into a single fraction

-6 = -2y/5

Then, multiply both sides by 5 to get:

-30 = -2y

Last, you divide both sides by -2 to get:

15 = y or y = 15

Hope this helps!

Draw of a modelled object

Answer:

1/x to the -8 power simplified would be x^8

Step-by-step explanation:

When there is a negative exponent you put the fraction under 1

[tex]\frac{1}{\frac{1}{x^{8} } }[/tex]  and its the same as x^8

The simplified expression is [tex]x^8[/tex].

Exponent is the power of the variable or constant to which it is raised.

The expression 1 over x is denoted by 1/x.

The exponent of the obtained expression will be -8. So, the expression will be [tex](\frac{1}{x})^{-8}=\frac{1}{x^{-8}}[/tex].

The exponents of the denominator change from negative to positive when they move from denominator to numerator.

[tex]\frac{1}{x^{-8}}=x^8[/tex]

Thus, the simplified expression will be x raised to the power 8.

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Solution

We will draw a diagram to illustrate the information

Using the concept of SOHCAHTOA

We are given adjacent and we want to find opposite

Therefore, the answer is

Part A

start by naming the variables you will be using in the system of equation

x= number of two-point baskets

y= number of three-point baskets

since she did 23 baskets the first equation representing the number of baskets she made will be

the second equation will be for the points, taking into account that x is 2 points and y is 3 points and she made 53 points.

Part B

Since the equations are not in the slope-intercept form they will be more complicated to graph, which using substitution it will be faster to find the solution of the system.

However both methods could be used.

Part C

The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

Given,

A triangle ABC with vertices A(2,3) , B(4,-5), and C(-1,2)

To find the coordinates of the vertices of each figure after a reflection over the given axis.

Now, According to the question:

We should know that:

You should know that you can predict changes in coordinates after translations without a graph or anything like that.

(x, y) reflected over the x axis = (x, -y)

(x, y) reflected over the y axis = (-x, y)

(x, y) rotated 90 degrees around the origin = (y, -x)

(x, y) rotated 180 degrees around the origin = (-x, -y)

(x, y) rotated 270 degrees around the origin = (-x, y)

So here's our set of points.

A(2,3) , B(4,-5), and C(-1,2)

Here's those points reflected over the x axis.

A' (2, -3) B' (4, 5) and C' (-1, -2)

Hence, The coordinates of the vertices after the reflection over the x-axis are A' (2, -3) B' (4, 5) and C' (-1, -2)

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On solving using combinations (C) we get the answers for part a)the probability that you will be assigned none of the tasks that you want = 0.035% b) the Probability that I am assigned exactly 7 of the tasks that I want = 0.0427 c)The probability that I am assigned at least one of the tasks I want = 0.9996 d)Probability that I am assigned at least 7 of the tasks I want = 0.049

a) There are 27 tasks and 10 tasks I want to do. Thus there are 17 tasks I do not want to do. I am randomly assigned 12 tasks. The probability that I will be assigned none of the tasks that I want is p = 17C12 / 27C12 = 3. 55 * 10 ^ (-4) = 0.035 %

b) The probability that I am assigned exactly 7 of the tasks that I want

p = 10C7 * 17C5 / 27C12 =  0.0427  = 4.27%

c) The probability that I am assigned at least one of the tasks I want

p = 1 - 17C12 / 27C12    where 17C12 / 27C12 is the probability that I get assigned 0 tasks I want.

Thus, p = 1 - (7/19665) = 0.9996

d)Probability that I am assigned at least 7 of the tasks I want

p = (10C7*17C5+10C8*17C4 + 10C9*17C3 + 10C10*17C2) / 27C12

⇒ p = 17 / 345 = 0.049 = 4.9%

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The probability that their hospital stay is greater than 6 days is equal to 0.67724 and the probability that their hospital stay is from 5 to 6 days is equal to 0.108

Mean (μ) = 7.37

Standard deviation (σ) = 3

we need to calculate probability that their hospital stay is from 5 to 6 days i.e.

⇒ P(5 < X < 6) = P(X < 6)-P(X < 5)

Here we will use standard normal distribution where,

Z-score = (X -μ )/ σ = (6 - 7.37)/3 = -0.46

Z-score = (5 - 7.37)/3 = -0.79

from Z table we found p-value

⇒P(5<X<6) = P(X<6) - P(X<5) = 0.32276 - 0.21476 = 0.108

So there is 0.108 probability that their hospital stay is from 5 to 6 days.

we need to calculate probability that their hospital stay is greater than 6 days i.e.

We get: P(X > 6) = 1 − P(X < 6)

Here we will use standard normal distribution where,

Z-score = (X - μ)/σ = (6 - 7.37)/3 = -0.46

from Z table we found p-value

P(X > 6) = 1 - P(X<6) = 1 - 0.32276 = 0.67724

So there is 0.67724 probability that their hospital stay is greater than 6 days.

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The salesman used 460 order forms in total, when he used three types of order forms: a, b, c.

Given that,

A salesman used three types of order forms: a, b, c. he used 50 of form a. of form b he used four times as many as form a plus 1/2 as many as form c. he used as many of form c as form a plus 1/2 as many as form b

A = 50

B = 4A + 0.5C = 200+ 0.5C  .......... (i)

C =  A +  0.5B =  50 + 0.5 B  .......... (ii)

multiply (ii) with 2

B = 2C -50              .......... (iii)

B = 0.5C + 160        ...........(i)

subtract (i) from (iii)

0 = 1.5C -210

C = 420/3 = 140

put in (i)

B = 200 + 0.5(140) = 270

Total forms = A+B+C = 50 + 270 + 140 = 460

Therefore, he used 460 forms altogether.

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Explanation:

Anything perpendicular to Ax+By = C is of the form Bx-Ay = D

The given equation is x-y = -2 showing that A = 1, B = -1 and C = -2.

So Bx-Ay = D will update to -x-y = D

Plug in the coordinates of (-4,1) to find D.

-x-y = D

D = -x-y

D = -(-4)-1

D = 4-1

D = 3

We go from -x-y = D to -x - y = 3

Then multiply both sides by -1 to end up with x + y = -3

Answer:

769 and 858

Step-by-step explanation:

Every hour, the distance between the two planes increases by 2x + 89

2 hours = 4x + 178

3254 = 4x + 178

4x = 3076

x = 769

The function that represents the total charge for renting a truck for a certain number of hours is f(h) = 90 + 20h What is the value of the function for an input 5 represent : $190, which is the total charge in dollars for renting a truck for 5 hours.

Given data :

Charges = $90 + $20 per hour

Value = 5

Now let formulate an equation

f(h) = 90 + 20h

Where,

h = 5

So,

Total charge = 90+ 20 ×5

Total charge = 90 + 100

Total charge =190

Therefore  the correct option is B.

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623 / 7 = 89

Result = 89

A) A function rule for the total cost T, including the mandatory examination, for a dog to stay at the hotel for n days is; T = 25n + 15

B) The total cost to stay for 6 nights is; $165

C) No, 3 night does not cost half as much as the cost for 6 nights due to the addition mandatory cost of $15.

We are told that a pet hotel charges $25 per night to keep a dog. We are also told that there is a mandatory $15 examination fee when the dog arrives there.

A) If the number of nights spent is n, then the function rule here for the total cost  is;

T = 25n + 15

B) We are told that the number of nights is 6 nights. Thus, we will just plug in 6 for n into the total cost equation to get;

T(6) = 25(6) + 15

T(6) = $165

C) The cost of 3 nights would be;

T(3) = 25(3) + 15

T(3) = $90

This is more than half of the cost of 6 nights.

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Answer:

x < 5

Step-by-step explanation:

[tex]2x - 4 < 6[/tex]

[tex]2x < 10[/tex]

[tex]x < 5[/tex]

.........................................................

The dimensions are Width = 7 feets ; length = 20 feets

As given,

Meadow area is 140 square feet.

Height = W (smaller dimension and 2 sides)

Height = L (longer dimension and 1 side)

Fence yards equal 34 feet;

Hence,

L + W = 34

L + 2W = 34

L = 34 - 2W - - - (1)

Recall:

Area = L * W = 140

Substitute value of L

140 = (34 - 2W) * W

140 = 34W - 2W²

2W² - 34W + 140 = 0

W² - 17W + 70 = 0

W² - 10W - 7W + 70 = 0

W(W - 10) - 7(W - 10) = 0

(W - 10) = 0 or (W - 7) =0

W = 10 or W = 7

We choose the shorter width because length should be as long as possible:

W = 7

L + 2W = 34

L = 30 - 14

L = 20 feets

Therefore, The measurements are 7 feet wide and 20 feet long.

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Answer: b=13

Step-by-step explanation:

b=39/3

b=13

Answer:  its 13  

Step-by-step explanation

We need to know how to interpret a graph to solve the problem. (a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

(a) h is a function of t since the height of the projectile varies with time. The input values of the function is the time interval and the output values is the height of the projectile.

(b) The approximate height of the projectile after 0.5 second according to the graph is 20 feet and the height of the projectile after 1.25 second according to the graph is 30 feet.

(c)The domain of the function is [0,2.5] and the range of the function is [0,30].

(d) t is not a function of h.

Therefore a) h is a function of t. (b) Approximate  height of the projectile affter 0.5 second is 20 feet and after 1.25 seconds is 30 feet (c).The approximate domain is [0,2.5] and range is [0,30] (d) t is not a function of h.

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39,916,800 color combinations are possible

Here, we want to get the possible number of color combinations possible.

Since any number of colors can be chosen, there are no restrictions here

That means the number of possible color combinations will be;

11! = 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 39,916,800 color combinations

The following investments were done:

In this problem we must determine how much money from a $ 8,000 investment has been deposited in each account based on overall yield after a period of one year. In accordance with the statement, the person deposited the following quantities in each account:

Metal: x

Glass: 2 · x

Paper: 8,000 - 3 · x

And the yield function is equal to:

280 = x · (4 / 100) + 2 · x · (5 / 100) + (8,000 - 3 · x) · (2 / 100)

280 = 0.04 · x + 0.1 · x + 160 - 0.06 · x

120 =  0.08 · x

x = 1500

The person made an investment of $ 1,500 in the metal account, $ 3,000 in the glass account and $ 3,500 in the paper account.

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The picture is represented by the absolute value function g(x) = |x - 5| - 4. (Correct choice: A)

Absolute values are functions defined by the following piecewise function:

The function in the picture is the consequence of the following rigid transformations:

Now we proceed to obtain the image of f(x):

Horizontal translation

f'(x) = |x - 5|

Vertical translation

g(x) = |x - 5| - 4

The picture is represented by the function g(x) = |x - 5| - 4.

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[tex]0.744\div6[/tex]

Simplify:

[tex]\frac{0.744}{6}[/tex]

[tex]=0.124[/tex]

Answer:

Explanation:

• Loan Amount = $500

• Time = 2 weeks

• The amount paid pack = $520

We want to determine the simple interest rate.

First, find the amount paid as interest: