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Rina8888 [55]
2 years ago
14

The sum of three consecutive integers is -51 what is the value of the smallest number

Mathematics
1 answer:
zubka84 [21]2 years ago
8 0

Answer: Let's say the first number is x, the next one is x+1, and so on

Step-by-step explanation:

x + (x + 1) + (x + 2) = -51

x + x + 1 + x + 2 = -51

3x + 3 = -51

3x = -54

x = -18

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300 students in a high school freshman class are surveyed about what kinds of pets they have. Of the 300 students, 200 have a do
Ad libitum [116K]

Answer:

C) ½

Step-by-step explanation:

P(C and D) = 150/300

= ½

5 0
3 years ago
The Cartesian coordinates of a point are given. (a) (−5, 5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0
Alex73 [517]

Answer:

a)

(i) The coordinates of the point in polar form is (5√2 , 7π/4)

(ii) The coordinates of the point in polar form is (-5√2 , 3π/4)

b)

(i) The coordinates of the point in polar form is (6 , π/3)

(ii) The coordinates of the point in polar form is (-6 , 4π/3)

Step-by-step explanation:

* Lets study the meaning of polar form

- To convert from Cartesian Coordinates (x,y) to Polar Coordinates (r,θ):

1. r = √( x2 + y2 )

2. θ = tan^-1 (y/x)

- In Cartesian coordinates there is exactly one set of coordinates for any

 given point

- In polar coordinates there is literally an infinite number of coordinates

 for a given point

- Example:

- The following four points are all coordinates for the same point.

# (5 , π/3) ⇒ 1st quadrant

# (5 , −5π/3) ⇒ 4th quadrant

# (−5 , 4π/3) ⇒ 3rd quadrant

# (−5 , −2π/3) ⇒ 2nd quadrant

- So we can find the points in polar form by using these rules:

 [r , θ + 2πn] , [−r , θ + (2n + 1) π] , where n is any integer

 (more than 1 turn)

* Lets solve the problem

(a)

∵ The point in the Cartesian plane is (-5 , 5)

∵ r = √x² + y²

∴ r = √[(5)² + (-5)²] = √[25 + 25] = √50 = ±5√2

∵ Ф = tan^-1 (y/x)

∴ Ф = tan^-1 (5/-5) = tan^-1 (-1)

- Tan is negative in the second and fourth quadrant

∵ 0 ≤ Ф < 2π

∴ Ф = 2π - tan^-1(1) ⇒ in fourth quadrant r > 0

∴ Ф = 2π - π/4 = 7π/4

OR

∴ Ф = π - tan^-1(1) ⇒ in second quadrant r < 0

∴ Ф = π - π/4 = 3π/4

(i) ∵ r > 0

∴ r = 5√2

∴ Ф = 7π/4 ⇒ 4th quadrant

∴ The coordinates of the point in polar form is (5√2 , 7π/4)

(ii) r < 0

∴ r = -5√2

∵ Ф = 3π/4 ⇒ 2nd quadrant

∴ The coordinates of the point in polar form is (-5√2 , 3π/4)

(b)

∵ The point in the Cartesian plane is (3 , 3√3)

∵ r = √x² + y²

∴ r = √[(3)² + (3√3)²] = √[9 + 27] = √36 = ±6

∵ Ф = tan^-1 (y/x)

∴ Ф = tan^-1 (3√3/3) = tan^-1 (√3)

- Tan is positive in the first and third quadrant

∵ 0 ≤ Ф < 2π

∴ Ф = tan^-1 (√3) ⇒ in first quadrant r > 0

∴ Ф = π/3

OR

∴ Ф = π + tan^-1 (√3) ⇒ in third quadrant r < 0

∴ Ф = π + π/3 = 4π/3

(i) ∵ r > 0

∴ r = 6

∴ Ф = π/3 ⇒ 1st quadrant

∴ The coordinates of the point in polar form is (6 , π/3)

(ii) r < 0

∴ r = -6

∵ Ф = 4π/3 ⇒ 3rd quadrant

∴ The coordinates of the point in polar form is (-6 , 4π/3)

6 0
3 years ago
Which of these is a simplified form of the equation 7x + 4 = 5 + 3x + 1x?
Leviafan [203]

Answer:

Step-by-step explanation:

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6 0
3 years ago
Read 2 more answers
Huda purchased 200 beads for AED 48 to make necklace. if she needs to buy 25 more beads, how much will she pay if she is charged
Natasha_Volkova [10]
She would need to spend 6 more. To find this answer, you divide 48 by 200 to see how much each bead costs, and then you multiply that amount by 25.
3 0
2 years ago
How many solutions does the system have? <br> {2x+2y=8 <br> {3x+y=8 2x+2y=8 ​
umka2103 [35]

Answer:

Step-by-step explanation:

first we put them in y = mx + b form...then we compare the slopes and the y int's. In y = mx + b form, the slope is in the m position and the y int is in the b position.

2x + 2y = 8

2y = -2x + 8

y = -x + 4......slope here is -1 and y int is 4

3x + y = 8

y = -3x + 8.....slope here is -3 and y int is 8

This system has 1 solution <===

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

learn this...it helps

* if there are different slopes and different y int, then there is 1 solution

* if there are the same slopes and different y int, then there is no solutions because u have parallel lines

* if there are same slopes and same y int, there is infinite solutions because u have the same line

4 0
3 years ago
Read 2 more answers
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