zero and negative exponentswrite in simplest form without zero or negative exponents

Apply trigonometric functions:

Cos a = adjacent side / hypotenuse

Where:

a = angle = 59°

adjacent side = 34

Hypotenuse = x

Replacing:

Cos 59 = 34 / x

Solve for x:

x = 34 / cos 59

x = 66

Answer:

The 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.

Explanation:

If the numbers are consecutive even numbers, it means that the next number will be 2 more than the previous one.

Let the 1st number be x, then other 2 consective numbers will be x + 2 and x + 4.

We're told that the sum of the 3 consecutive even numbers is equal to 186, our equation can then be written as shown below;

Let's go ahead and collect like terms and solve for x;

So our 1st number is 60.

Let's go ahead and find the other 2 numbers;

1st number: x + 2 = 60 + 2 = 62

2nd number: x + 4 = 60 + 4 = 64

So the 3 consecutive even numbers are 60, 62 and 64 and the value of the greatest is 64.

lets remember how to find the equation of a parallel line

two lines are parallel if they don"t intersect, that means they slopes are the same

y=-2x+3

slope as we see is m=-2

the other line has to pass through point (5,4)

y-y1=m(x-x1)

y-4=-2(x-5)

we solve the equation

y= 4-2x+10

y= -2x+14

i will send you a picture

green line is y=-2x+14

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Work Shown:

A = he eats pizza

B = he drinks cola

P(A) = 0.40

P(B) = 0.60

P(A and B) = 0.30

Then apply the conditional probability formula.

P(A given B) = P(A and B)/P(B)

P(A given B) = 0.30/0.60

P(A given B) = 0.5 exactly

P(A given B) = 50%

If we know for certain he drinks cola, then there's a 50% chance of him eating pizza.

`Answer:

h(x) = -x^2/2 - 4x + 32

Explanation:

The standard form of a quadratic equation is expresssed as

ax^2 + bx+c

Writing the given equation h(x)= -1/2 (x+4)^2 +10 in stabdard form will give;

h(x)= -1/2 (x+4)^2 +10

h(x)= -1/2 (x^2+8x+16)+40

h(x)= -x^2/2 - 4x - 8 + 40

h(x) = -x^2/2 - 4x + 32

Hence the equation in standard form is expressed as h(x) = -x^2/2 - 4x + 32

Answer: 7040

Step-by-step explanation:

1
352

x20

——-

000
7040

+
———

7040

Given:-

Cost of blouse is $27.50

Cost of sweater is $34.99

To find the cost if laura bought :-

So since laura bought one blouse and two sweaters, we get

So the cost is $97.48 and she bought the cloths of her summer needs.

Answer:

I think its done this way. But I don't know if the answer is correct.

From the problem, we have 3.25% to convert into fraction.

Note that percentage a% can be written as a/100

So 3.25% will be :

From here, we can multiply the numerator and the denominator by 100 to make 3.25 a whole number.

Next step is to simplify the fraction by getting the factors of the numerator and the denominator.

325 = 25 x 13

10000 = 25 x 400

Rewriting it again :

Cancel the common factor (25)

The answer is 13/400

We can solve these values using the next triangle:

First, we need to label the sides using the angle of 30 degrees.

- The largest side is always the hypotenuse, h = 1.

- The opposite side is opposite to the angle, opp = 1/2.

- The adjacent side is between the angle of 30 degrees and the right angle,

adj = √3/2.

Now, we can solve the trigonometric expressions:

For sin:

sin θ = opposite side / hypotenuse

sin 30 = (1/2) / 1

sin 30 = 1/2

For cos:

cos θ = adjacent side / hypotenuse

cos 30 = (√3/2)/1

cos 30 =√3/2

For tan:

tan θ = opposite side / adjacent side

tan 30 =(1/2) / (√3/2)

Simplify the fractions:

tan 30 = 1/√3

By the 65-95-99.7 rule,

By symmetry,

In our case,

Therefore,

Hence, 2.5 % of the values lie below 8

To find the factors of a number, we can look for factors to divide it by subsequently.

It is easier to start with lower factors.

Let's start by "2".

Since "54" is even, it is divisable by "2":

So "2" is one of the factors.

Now, we have got 27. It is not even anymore, but it is divisable by "3":

So "3" is another factor.

Now we have got "9" and it is also divisable by "3":

So there is another "3" factor.

And since we have got now another "3", we know it is divisable by "3":

Now we have got to "1", so we found all the prime factors:

Now,, we need to combine them to find all possible combinations.

We will start from low to high.

"1" is always a factor.

There is "2" there, so it is also a factor.

Then we have "3" as another factor.

There is no need to combine "1" with another factor, so we will start b combining 2 and 3:

So, "6" is another factor.

We can combine 3 with 3:

"9" is another factor.

Now we start combining three of them:

So, "18" and "27" are factors.

And now we combine 4 of them, but this is get us back to "54" which is the last factor.

So, the factors of 54 are: 1, 2, 3, 6, 9, 18, 27, 54.

Answer:

Step-by-step explanation:

1 × 54 = 54, (1, 54) is a pair factor of 54.

2 × 27 = 54, (2, 27) is a pair factor of 54

3 × 18 = 54, (3, 18) is a pair factor of 54

6 × 9 = 54, (6, 9) is a pair factor of 54

Therefore, the positive pair factors are (1, 54), (2, 27),(3, 18) and (6, 9).

We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:

In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this:

The given function can be represented f(x) and g(x) as below

What are functions?

A function from X to Y is an assign of each constituent of Y to each variable of X. The set X is known as the function's scope, while the set Y is known as the function's image domain. The notation f: XY denotes a function, its domain, and its codomain, and the value of a function f at an element x of X, indicated by f(x), is known as the image of x under f, or the value of f applied to the argument x. When defining a function, the domains and codomain are not often explicitly specified, and without performing some (complicated) calculation, one may only know that perhaps the domain is included in a larger package.

The functions are

(a) f(x) = 3x+2 and g(x) = |x|

so, H(x) = f(g(x)) = |3x+2|

(b)  f(x) = 5x+4 and g(x) = √√√√x

so, H(x) = f(g(x)) = √√√√5x+4

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Answer: I am pretty sure you can only have one.

Step-by-step explanation:

Given:

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.

Required:

To write an inequality to find the three numbers and to solve the inequality.

Explanation:

(a)

Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.

(b)

We will have the following:

First:

Since we have that sides a & c have the same length by theorem angles A & C are equal, so the following is true:

so, angles A & C have a measure of 77.5°.

*Second: We determine the measurement f the segment b, that is:

So we will have that the measurements are:

A = 77.5°

b = 10.8

C = 77.5°

[Option B]

Given:

Adding a negativen number is the same as subtracting that number, so:

Since both denominators (bottom number ) are equal we can subtract the numerators ( top numbers)

Answer:

The position of the scuba diver is 23 1/60 feet.

From the information, the scuba diver descended 19 5/12 feet blow sea level and then he descended another 3 3/5 feet.

The position of the diver will be. the addition of the fraction for descending. This will be:

= 19 5/12 + 3 3/5

= 19 25/60 + 3 36/60

= 22 61/60

= 23 1/60

Note that your information is incomplete as the question was answered based on information given.

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The time needed to look over the resumes depends on how many papers is the resume

But it is convenient to have a speed looking on each one

so, the answe will be 50 seconds

Step 1:

Cost of large cup = $5

Step 2:

Number of large David orders = 10 cups

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

Jon order 4 fewer large cups

Therefore,

Jon order = 6 cups

Step 3:

A good plan to find the amount Jon spent is to find the number of large cups Jon orders from the number of large cups David orders.

The amount Jon spent on coffee = 6 x $5 = $30

The weight of the granite pyramid in tons is 1350 tons.

A pyramid is a three-dimensional shape.

The granite pyramid is 50 feet high and has a square base of 30 feet on a side.

Granit weighs 180 pounds per cubic foot.

Therefore, the weight in tons of the pyramid can be calculated as follows;

Hence,

volume of the granite pyramid = 1 / 3 b² h

Therefore,

volume of the granite pyramid = 1 / 3 × 30² × 50

volume of the granite pyramid = 45000 / 3

volume of the granite pyramid = 15000 ft³

Hence,

1 ft³ = 180 pounds

15000 ft³ = ?

weight = 2700000 pounds

1 pounds = 0.0005 tons

2700000 pounds = ?

Therefore,

weight of the pyramid granite in tons = 1350 tons

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Answer:

27 cubic feet

Explanation:

The volume of a cube with side length L is given by

Now in our case, L = 3 ft; therefore, the volume is

which simplifies to give

which is our answer!

Hence, the volume of the cube with the side length of 3 cm is 27 cubic cm.

Exponential growth (EG):

2001 = 0.3

2008 = 11

2013 = ?

a = initial amount = 0.3

b= growth factor = ?

t = period = 7

n = 11

b = 1.67

Solving the number of keylogging programs that will be reported in 2013:

Given that the triangles are similar, we can express a proportion between their sides. DE and XY are corresponding sides. EF and YZ are corresponding sides. Let's define the following proportion.

Now, we solve for x

Solution

- The event is "73% of nineteen year old males are at least 166 pounds"

- The complement of this event is the set of all 19 year old males not in the event described above.

- These set of 19 year olds, must represent the remaining 27% of the population.

- Also, they would weigh less than 166 pounds.

- Thus, the complement of the event is:

"27% of nineteen year old males weigh less than 166 pounds"

Answer:

72

Explanation:

To choose a number between 49 and 95 that is a multiple of 3, 8, and 12, the first step is to find the lowest common multiple of the three numbers.

Begin by expressing them as a product of their prime factors:

Next, we find multiples of the L.C.M in between 49 and 95.

The only number that she could choose is 72.

First, we need to calculate the total earned during the three days, so we need to sum 20.56, 32.90, and 20.78 as:

So, the total earned is 74.24, then half of 74.24 is calculated as:

If he spends the half, he has left the half. Therefore, he has left 37.12

Answer: 37.12

The most appropriate choice for equation of line in slope intercept form will be given by-

y = 2x - 8 is the required equation of line

What is equation of line in slope intercept form?

The most general form of equation of line in slope intercept form is given by y = mx + c

Where m is the slope of the line and c is the y intercept of the line.

Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.

If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by

m = [tex]tan \theta[/tex]

The distance from the origin to the point where the line cuts the x axis is the x intercept of the line

The distance from the origin to the point where the line cuts the y axis is the y intercept of the line

Here,

The given equation of line is y= 2x +3

Slope of this line = 2

Slope of the line parallel to this line = 2

The line passes through (-2, -12)

Equation of the required line = y - (-12) = 2(x - (-2))

                                                = y + 12 = 2x + 4

                                                = y = 2x + 4 - 12

                                                = y = 2x - 8

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