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sladkih [1.3K]
3 years ago
7

PLLZZ HELP ME OUT WITH THIS!!!!

Mathematics
2 answers:
Anna007 [38]3 years ago
5 0

Answer:

for 1. -30 - 12 = -42

Step-by-step explanation:

Andrei [34K]3 years ago
4 0
She is at -30 feet then dives down 12 more

30+12=42
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Quadrilateral PEST has vertices (-1, -5), (8, 2), (11, 13), and (2, 6), respectively. Classify the quadrilateral as a square, rh
Alchen [17]

Answer:

The figure PEST is a rhombus

Step-by-step explanation:

* Lets talk about the difference between all these shapes

- At first to prove the shape is a parallelogram you must have one

 of these conditions

# Each two opposite sides are parallel OR

# Each two opposite sides are equal in length OR

# Its two diagonals bisect each other

- After that to prove the parallelogram is:

* A rectangle you must have one of these conditions

# Two adjacent sides are perpendicular to each other OR

# Its two diagonals are equal in length

* A rhombus you must have one of these conditions

# Two adjacent sides are equal in length OR

# Its two diagonals perpendicular to each other OR

# Its diagonals bisect its vertices angles

* A square you must have two of these conditions

# Its diagonals are equal and perpendicular OR

# Two adjacent sides are equal and perpendicular

* Now lets solve the problem

∵ The vertices of the quadrilateral PEST are

   P (-1 , -5) , E (8 , 2) , S (11 , 13) , T (2 , 6)

- Lets find the slope from each two points using this rule :

 m = (y2 - y1)/(x2 - x1), where m is the slope and (x1 , y1) , (x2 , y2)

 are two points on the line

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ m of PE = (2 - -5)/(8 - -1) = 7/9

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ m of ES = (13 - 2)/(11 - 8) = 11/3  

- Let (x1 , y1) is (11 , 13) and (x2 , y2) is (2 , 6)

∴ m of ST = (6 - 13)/(2 - 11) = -7/-9 = 7/9

- Let (x1 , y1) is (2 , 6) and (x2 , y2) is (-1 , -5)

∴ m of TP = (-5 - 6)/(-1 - 2) = -11/-3 = 11/3

∵ m PE = m ST = 7/9

∴ PE // ST ⇒ opposite sides

∵ m ES = m TP = 11/3

∴ ES // TP ⇒ opposite sides

- Each two opposite sides are parallel

∴ PEST is a parallelogram

- Lets check if the parallelogram can be rectangle or rhombus or

 square by one of the condition above

∵ If two line perpendicular , then the product of their slops = -1

- Lets check the slopes of two adjacent sides (PE an ES)

∵ m PE = 7/9

∵ m ES = 11/3

∵ m PE × m ES = 7/9 × 11/3 = 77/27 ≠ -1

∴ PE and ES are not perpendicular

∴ PEST not a rectangle or a square (the sides of the rectangle and

  the square are perpendicular to each other)

- Now lets check the length of two adjacent side by using the rule

 of distance between two points (x1 , y1) and (x2 , y2)

 d = √[(x2 - x1)² + (y2 - y1)²]

- Let (x1 , y1) is (-1 , -5) and (x2 , y2) is (8 , 2)

∴ PE = √[(8 - -1)² + (2 - -5)²] = √[9² + 7²] = √[81 + 49] = √130 units

- Let (x1 , y1) is (8 , 2) and (x2 , y2) is (11 , 13)

∴ ES = √[(11 - 8)² + (13 - 2)²] = √[3² + 11²] = √[9 + 121] = √130 units

∴ PE = ES ⇒ two adjacent sides in parallelogram

∴ The four sides are equal

* The figure PEST is a rhombus

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Find the unknown side length
ohaa [14]
You use the formula a² +b² =c²
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3 years ago
tandard automobile license plates in a country display 1 numbers, followed by 2 letters, followed by 4 numbers. How many differe
kolbaska11 [484]

Answer:

39,917,124

Step-by-step explanation:

In order to solve this problem we must start by drawing a diagram of what the licence plates look like. (See Attached picture).

Now, each box in the picture will represent one digit of the plate. Some must be numbers and some must be letters. We know we have 9 posibilities for theh numbered boxes (1-9) and we have 26 possibilities for the boxes that are to contain letters. Repetitions allowed. So the possible character for each box is as follows:

box 1 = 1 to 9 = 9

box 2 = A to Z = 26

box 3 = A to Z = 26

box 4 = 1 to 9 = 9

box 5 = 1 to 9 = 9

box 6 = 1 to 9 = 9

box 7 = 1 to 9 = 9

so the total number of licence plates can be found by multiplying the possibilities for each box in the plate so we get:

# of plates = (9)(26)(26)(9)(9)(9)(9)

which can be simplified to:

plates= 9^{5}26^{2}=39,917,124

8 0
3 years ago
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