O GRAPHS AND FUNCTIONSFinding values and intervals where the graph of a functioning is..

The imaginary number 'i" can be written in another form below:

Whenever we have the root of a negative number, we use the imaginary number 'i' to write it in an easier form.

For example:

Therefore:

1) We have here a right triangle, so we can use the Pythagorean Theorem to find the adjacent leg. Note that the hypotenuse is leg opposite to the right angle. In this case, a=4.

a²=b²+c²

4²=b²+3²

16=b²+9

16-9=b²

b=√7

2) Let's find the trigonometric functions. The first one is the sine (θ), which relates the opposite side and the hypotenuse:

2.2)Moving on, we can deal with the tangent of theta, relating the opposite side over the adjacent, for this one we have to rationalize it:

Finally, let's find the reciprocal function of the cosine function by setting this as the reciprocal of the cosine, and then calculating it:

Let t be the time in hours it takes a block of ice to melt at T degrees.

Since both variables have an inverse relation, we can say that:

Where alpha is a constant value.

Since we know that a block of ice melts in 2.5 hours when the temperature is 54 degrees, we can plug in such data and find alpha as following:

Therefore, our expression would be:

For T = 45,

We can conclude that it would take 3 hours for the block of ice to melt.

4) [tex]m\angle XWY=m\angle HGY[/tex] (definition of congruent angles)

5) [tex]\angle HGY \cong \angle GTU[/tex] (corresponding angles theorem)

6) [tex]m\angle HGY=m\angle GTU[/tex] (definition of congruent angles)

7) [tex]\angle GTU[/tex] and [tex]\angle UTR[/tex] are supplementary (linear pair)

8) [tex]m\angle GTU+m\angle UTR=180^{\circ}[/tex] (definition of supplementary angles)

9) [tex]m\angle HGY+m\angle UTR=180^{\circ}[/tex] (substitution)

10) [tex]m\angle RTU+m\angle XWY=180^{\circ}[/tex] (substitution)

The price elasticity of the demand function as a function of p is C. E(p)= p/200-p

It should be noted that the price elasticity of demand simply means the ratio of the percentage change in quantity demanded to the percentage change in price.

In this case, the function is given as:

q = D(p) = 600-3p

Differentiate with respect to p

D'(p) = 3

The elasticity of demand will be:

= (P / 600 - 3p) × (-3)

= P / (200 - P)

In conclusion, the correct option is C.

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A premise or premiss is a true or false statement that helps form the body of an argument, By law of syllogism the statement is true. Your cat will chase mice.

A premise or premiss is a true or false statement that helps form the body of an argument, which logically leads to a true or false conclusion.

If the following two statements are true: (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

If you have a cat, then it will chase mice.

is the given statement.

Let p is you have a cat

q is chase mice.

r is cat will chase mice.

iby the law of syllogism Your cat will chase mice. because  (1) If p , then q . (2) If q , then r . Then we can derive a third true statement: (3) If p , then r .

Hence by law of syllogism the statement "if you have a cat, then it will chase mice" is true.

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As given by the question

There are given that the college charges a reservation fee of $46.

Now,

According to the question, the inequality is:

Then,

To solve the above inequality, collect the constant terms on the right side

So,

Hence, the room could be rented for up to 9 hours less than the stated amount.

Answer:

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

Step-by-step explanation:

[tex] \frac{3}{94} = 0.31 \\ \\ \frac{1}{3} = 0.33[/tex]

To factor this expression we need to find two numbers which sum is 4 and the product is -21.

Now, 21 has only 2 factors (besides 1 and 21), 7 and 3, se we need to write them in a way such that they sum 4, so

we see that 7-3=4 and 7(-3)=-21, so the factorization is correct.

Answer:

x = 64

Step-by-step explanation:

to find x add make an equation to solve for x. the equation is 90+90+44+2x+8=360. after solving for x, x will equal 64.

The mixed fraction 11 [tex]\frac{7}{16}[/tex] - 4[tex]\frac{7}{12}[/tex]  is equivalent to the fraction to 6 41/48

An equation shows the relationship between two or more numbers and variables.The mixed fraction 11 7/16 is equivalent to the fraction (11 * 16 + 7)/16 = 183/16

The mixed fraction 4 7/12 is equivalent to the fraction (4 * 12 + 7)/12 = 55/12

Substituting:= 18 [tex]\frac{3}{16}[/tex] - 5 [tex]\frac{5}{12}[/tex]

Simplifying:= 329/48

= 6 41/48

11 [tex]\frac{7}{16}[/tex] - 4 [tex]\frac{7}{12}[/tex] is equal to 6 [tex]\frac{41}{48}[/tex]

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The ratio of time spent studying math to studying English is 7:2.

According to the question,

We have the following information:

One spends 1 hour a week to study English and 3.5 hours to study math.

Now, we know that the ratio can be simply understood as the division.

So, we will divide the number of hours devoted to math by the number of hours devoted to English.

Ratio of time spent studying math to studying English = 3.5/1

Ratio of time spent studying math to studying English = 35/10

(Now, we will convert this fraction into the simplest form by dividing both the numerator and denominator of the fraction by 5.)

Ratio of time spent studying math to studying English = 7/2

Ratio of time spent studying math to studying English = 7:2

Hence, the ratio of time spent studying math to studying English is 7:2.

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Length has 5 cubes

width has 3 cubes

height has 7 cubes

Volume = length x width x height

5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2

D; Both statements are correct

Here, we want to check the correct statement

Basically from the diagram, it is confirmed that what we have is a 30-60-90 triangle

Now, for a 30-60-90 degrees triangle, the side lengths are in a particular ratio

From the diagram, MO faces the right angle and thus, it is the longest side and the hypotenuse

Now, let us take a look at the ratio of the sides in both submissions

For a 30-60-90 degrees triangle, the ratio of the sides is;

Hence, one side must be twice the length of the other

From Kellie's statement we can see MO is twice NO

From Eddie's statement, we can also see that MO is twice NO

Lastly, we can also see in both that dividing MN by NO yields the root of 3 in both statemets which confirms the existence of the theoretical ratio

So the conclusion here is that;

Both students are correct

Answer: Per rock or pound?

10. |x - 4| - 4 = 1/2x

⇒ Multiplying by 2,

2 |x - 4| - 8 = x

So, x - 4 = (x + 8)/2

             = -(x + 8)/2

When,

x - 4 = (x + 8)/2

2x - 8 = x + 8 (Multiplying by 2)

2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)

x = 16

When,

x - 4 = - (x + 8)/2

2x - 8 = -x - 8 (Multiplying by 2)

2x + x = -8 + 8 (Adding 8 and x to both sides)

3x = 0

x = 0

Hence, the solution is x = 16 and x = 0.

13. (3/4)x = 2x - 10

⇒ Subtract 2x from both sides.

-5x/4 = -10

Multiply both sides by 4/(-5).

(-5x/4)×4/(-5) = -10 × 4/(-5).

x = 8 is the solution of the equation.

15. x² - 7x - 8 > 0

⇒ Solve the quadratic equation by splitting the middle term,

x² - 8x + x - 8 > 0

x(x - 8) + 1(x -8) > 0

(x + 1)(x- 8) > 0

-1 and 8 are the critical points of the inequality.

x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.

16. x - 5 > - 2x + 4

⇒ Adding 2x to both sides.

3x - 5 > 4

Adding 5 to both sides.

3x > 9

Divide both sides by 3.

x > 3 is the required solution represented by blue shade region in the graph.

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We need to graph the following inequality:

First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:

Now, notice that:

represents a line containing all points with coordinates (x,y) such that y=-4x.

The solution to the inequality includes those points, and also the points for which y is greater than -4x.

Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:

Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:

Given:

The z-score for 90 percent is 1.64.

To find the 90 percent confidence interval,

Answer: The 90 % confidence interval is ( 20.3906 , 22.4094 )

Answer:

x = 10/a; restrictions a ± 0

Answer:

=============================

Given expression

Solve it for x in steps below:

Answer:

0.58333333333

Answer:

45 times

Step-by-step explanation:

it is 45 times because it can land on blue or green 5 out of 8 times so u do 72 divided by 8 and u get 9 so I do 9 times 5 and u get 45

Answer:

2/3

Step-by-step explanation:

If 4 were late, then 8 were on time.

8/12  Divide the top and bottom by 4

2/3

Answer:

-72

Step-by-step explanation:

Answer:

Step-by-step explanation:

12x-6 = 90 because opposite angles are equal if intercepted in parallel lines

12x=96

x= 8

Rajan must climb down 25 ft to return to the bottom of the climbing wall

Height climbed from the bottom of the wall = 15ft

Height: The measurement of an object's height from the base to the top is known as height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Additional height climbed = 10ft

Total height climbed = 25ft

He should climb down the distance, as climbing up will further move him away from the bottom of the wall

Distance to climb down to the bottom of the wall = 25ft

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The distance between the parallel lines measured in the y direction is 3 units.

given data

y = - 3x + 4

y = - 3x + 1

let line 1 be y = - 3x + 4 and line two be y = -3x + 1

Analyzing the two lines show that the slope is equal hence parallel

slope = -3

The y intercept of the line or just the intercept is what varied

The difference between these two pints represents the distance between them measured in the y direction.

The difference is solved as

4 - 1 = 3 units

The distance is 3 units

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1. The value of f(2) = 0 and g(2) = 0

2. The value of k is 9

A function can simply be described as a law, rule, theorem or expression that explains the relationship between two terms.

These terms are known as;

Given the functions;

To prove that f(2) = g(2)

Substitute the value of x as 2 in the functions, we have;

f(2) = 2^2 - 2(2)

expand the bracket

f(2) = 4 - 4

f(2) = 0

Then for g(2), we have;

g(2) = 2 - 2

g(2) = 0

Then, f(2) = g(2) = 0

If g(k) = 7

Then, we have;

k - 2 = 7

collect like terms to determine the value of k

k = 7 + 2

k = 9

Hence, the value is 9

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Answer:

(a) 73.1 cm (b) 120 cm

Step-by-step explanation:

Step-by-step explanation:

Part (a)

73.1 cm                 [It remains the same as it is already given in cms]

Part (b)  

To convert 0.0012km to cm we multiply x 100000

=> 0.0012 x 100000

=> 120 cm