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BlackZzzverrR [31]
3 years ago
7

Phyllis is going to take a 5-hour-17-minute flight from Orlando, Florida, to Las

Mathematics
1 answer:
Rainbow [258]3 years ago
6 0

Answer:

Step-by-step explanation:

ok...so she leaves Orlando at 11:05 am.....the flight takes 5 hr and 17 minutes..

11:05 am + 5 hrs = 4:05 pm.....4:05 + 17 minutes = 4:22 pm.

so she arrives at 4:22 pm eastern time....(orlando time)...but Las Vegas is pacific time

so if 12 pm eastern = 9 am pacific.....a difference of 3 hrs

so the local time in Las Vegas when her plane lands is :

4:22 pm - 3 hrs = 1:22 pm <===

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Help I will be marking brainliest!!!
Keith_Richards [23]
<h3>Answer:  A.  18*sqrt(3)</h3>

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

Explanation:

We'll need the tangent rule

tan(angle) = opposite/adjacent

tan(R) = TH/HR

tan(30) = TH/54

sqrt(3)/3 = TH/54 ... use the unit circle

54*sqrt(3)/3 = TH .... multiply both sides by 54

(54/3)*sqrt(3) = TH

18*sqrt(3) = TH

TH = 18*sqrt(3) which points to <u>choice A</u> as the final answer

----------------------

An alternative method:

Triangle THR is a 30-60-90 triangle.

Let x be the measure of side TH. This side is opposite the smallest angle R = 30, so we consider this the short leg.

The hypotenuse is twice as long as x, so TR = 2x. This only applies to 30-60-90 triangles.

Now use the pythagorean theorem

a^2 + b^2 = c^2

(TH)^2 + (HR)^2 = (TR)^2

(x)^2 + (54)^2 = (2x)^2

x^2 + 2916 = 4x^2

2916 = 4x^2 - x^2

3x^2 = 2916

x^2 = 2916/3

x^2 = 972

x = sqrt(972)

x = sqrt(324*3)

x = sqrt(324)*sqrt(3)

x = 18*sqrt(3) which is the length of TH.

A slightly similar idea is to use the fact that if y is the long leg and x is the short leg, then y = x*sqrt(3). Plug in y = 54 and isolate x and you should get x = 18*sqrt(3). Again, this trick only works for 30-60-90 triangles.

4 0
2 years ago
PROMPT:
pentagon [3]
For this answer let's pick the Fish Pond.

QUESTION: <span>What do you know? 
We know that the total area of the rectangular patio is 24 square feet. The rectangular fish pond that we want to build should have the length that is twice the width. We also need a 1-foot border around the pond.

The total area of the patio is represented by </span>2 x^{2} +6x+4 where x is the width of the fish pond.

QUESTION: What do you want to find out? 
We can answer this question by examining what we have been given (we have answered this in the previous question). Since we only have one variable in the equation and this is the width of the fish pond, then this is the only thing that we need to find out. The length will just follow after the width is solved. (Basically, we are concerned with the dimensions of our project.)

QUESTION: What kind of answer do you expect? 
Since we are only expecting to solve for the dimensions, then we should expect two numbers which would represent the width and the length. Through the polynomial, we can get the width of our project, then the length would just be twice our answer for the width.

1. To set our polynomial equation equal to the total area of our patio, we just write the equation on the left side and the total area of the patio on the right. We recall the equation that we gave in the first question above as well as the patio's area.

2x^{2} +6x+4=24

2. For this item, we just simply negate the constant term on the right side by subtracting the same number to both sides. Since our constant term is 24, we subtract 24 from the polynomial as well as the term on the right side.

2x^{2} +6x+4-24=24-24
2x^{2} +6x-20=0

3. In this item we are only tasked to find the GCF of the trinomial and factor it out of the left side of the equation. The GCF just means the common number or variable in all terms. Upon examining, we can see that the only common factor of the terms is 2 (since all terms are divisible by 2), thus this will be the GCF and we will factor this one out.

2(x^{2} +3x-10)=0

4. To factor the polynomial completely, we just figure out the possible factors of the quadratic equation. You can do this by trying out all factors of -10 that will have a sum of 3 (since -10 is the constant and 3 is the coefficient of x). Upon examining you should end up with:

2(x+5)(x-2)=0 (Notice that 5 and -2 are factors of -10 and their sum is 3).

5. The rule stated on this item just means that we can equate each individual factor to zero (except for the constant term) to find out the possible values of x. That means that we can solve for x by using the equations x+5=0 and x-2=0.

x+5=0
x=-5

x-2=0
x=2

6. For this item, we just do simple substitutions to the equation 2x^{2} +6x-20=0 to verify whether the values we got in question 5 is really a solution to the equation. The values of x that we got are -5 and 2 so we substitute these one at a time.

2(-5)^{2} +6(-5)-20=0
50-30-20=0
0=0

2(2)^{2} +6(2)-20=0
8+12-20=0
0=0

Both values of x make the left side equal to zero therefore both are solutions to the equation.

7. We can tell the dimensions of the project by looking at the values that we got for x, since we assumed x to be the width of our project. The fact that we got two values for x won't be a problem since one of these values is negative. There is no negative measurement/width so we can just ignore this negative value (-5). Thus, the width for our project would be 2 and the length would be twice this value which is 4.

Width = 2 feet
Length = 4 feet

8. For this item, we just illustrate the dimensions of our project and add a 1-foot border (as we are told initially). You can see this illustration in the picture I attached below. 

Since we have an extra 1 foot in every side, that means we need to add 2 feet to both the width and the length. Therefore, our width now is 4 while our length is 6.

Multiplying these numbers to verify the area, we get 24 square feet which is exactly the area of the patio.

6 0
3 years ago
Read 2 more answers
What is the percent increase of 24 to 32?
goblinko [34]

Answer:

8%???????????????????????

6 0
2 years ago
Read 2 more answers
10. Mark built a fence around his clubhouse. The perimeter of the fence is 80 feet. The
Svetlanka [38]

Answer:

if the clubhouse is 4 sided then the length would be 25 ft

Step-by-step explanation:

15x2=30

80-30=50

50/2=25

7 0
3 years ago
Read 2 more answers
Find a irrational number between 7.7 and 7.9 explain why it’s irrational
Alexeev081 [22]
7.77777777 repeating

Irrational numbers are:

Numbers that repeat 
7.7777777 repeats the number 7 after the decimal

Numbers that CANNOT be written as a simple fraction.
7.7777777 cannot be written as a fraction in simplest form.

Answer = 7.777777777 repeating

~Aamira~

Hope this helped :)
8 0
3 years ago
Read 2 more answers
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