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3 years ago

Find the domain and range

Mathematics

1 answer:

LiRa [457]3 years ago

6 0

Answer:

Domain: x = all reals

Range: y is less than or equal to -4

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Find four consecutive even integers such that seven times the first exceeds their sum by 18.

Ganezh [65]

Answer:

10, 12, 14, 16

Step-by-step explanation:

Given: Four consecutive even integers such that seven times the first exceeds their sum by 18.

Lets assume the first number be "x".

As it is even integers

∴ Second consecutive number will be $(x+2)$

Third consecutive number will be $(x+4)$

Fourth consecutive number will be $(x+6)$

Now, as given seven times the first exceeds their sum by 18.

∴ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

solving the equation to find the number.

⇒ $[x+(x+2)+(x+4)+(x+6)]+18 = 7x$

Opening parenthesis

$x+x+2+x+4+x+6+18 = 7x$

⇒ $4x+30= 7x$

subtracting both side by 4x

⇒ $30= 3x$

Dividing both side by 3

∴ x= 10.

Hence, subtituting the value x to find four consecutive even integers.

First number is 10

Second consecutive number will be $(10+2)$ = 12

Third consecutive number will be $(10+4)$ = 14

Fourth consecutive number will be $(10+6)$ = 16

∴ Four consecutive even integers are 10,12,14,16.

8 0

3 years ago

A ship leaves port and travels due west for 30 knots, then changes course to S 30° W and travels 50 more knots. Find the bearing

leva [86]

Answer:

232°

Step-by-step explanation:

There are a couple of ways to find the desired direction. Perhaps the most straightforward is to add up the coordinates of the travel vectors.

30∠270° +50∠210° = 30(cos(270°), sin(270°)) +50(cos(210°), sin(210°))

= (0, -30) +(-43.301, -25) = (-43.301, -55)

Then the angle from port is ...

arctan(-55/-43.301) ≈ 231.79° . . . . . . . 3rd quadrant angle

The bearing of the ship from port is about 232°.

_____

Comment on the problem statement

The term "knot" is conventionally used to indicate a measure of speed (nautical mile per hour), not distance. It is derived from the use of a knotted rope to estimate speed. Knots on the rope were typically 47 ft 3 inches apart. As a measure of distance 30 knots is about 1417.5 feet.

5 0

3 years ago

Solve each equation by substitution: y = 6x - 17 y= -4x +23

NISA [10]

Answer:

$y = 6x - 17 \\ y = - 4x + 23 \\ then \\ 6 x - 17 = - 4x + 23 \\ 10x = 40 \\ x = 4 \\ y = 7$

7 0

3 years ago

4 over 5 in standard form

postnew [5]

Answer:0.8

Step-by-step explanation:

it is basically 10 times 8 to the power of -1

7 0

3 years ago

The “prize” discovery at the Nansen Crater was olivine. What valuable information did NASA learn from this sample?

Ghella [55]

Answer:

1. One valuable information NASA learnt from the sample of olivine is that some parts of Mars had been dry over a long period of time.

2. The two materials are:

i. Oxygen supply.

ii. Air temperature and pressure regulation.

Step-by-step explanation:

NASA went on a research mission on mars and observed the Nansen crater, and discovered the olivine in the crater. It was learnt from the sample of olivine that parts of Mars had been dry over a long period of time.

2. The Personal Life Support System is a part of the suit used by astronauts to create an artificial habitat condition for their body system. This suit contains some materials that preserve their lives in space. The major materials in the suit are; oxygen (for breathing purpose) and air temperature and pressure regulation.

3 0

3 years ago