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2 years ago

14

Is a graph of a slanted line a one-to-one function? Justify your answer.

1 answer:

kkurt [141]2 years ago

7 0

Answer:

Yes

Step-by-step explanation:

A slanted straight line is one-to-one: It passes the "horizontal ilne test." This means that any line drawn horizontally through the given line intersects that line only once. The significance of this is that the given line/function has an inverse. y = x is one-to-one and has the inverse y = x. y = 2x is one-to-one and has the inverse y = (1/2)x.

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In 1987, 522 comma 000 people worked in the air transportation industry. In 2003, the number was 480 comma 000. (a) Find a li

umka2103 [35]

Answer:

the linear equation is :

y= -2625x+5737875

and 440000 employees will be in year 2271

Step-by-step explanation:

in order to find the linerar equation let us first convert the given data into (x,y ) co-ordinates i.e

x1= 1987 y1= 522,000

and

x2= 2003, y2 = 480000

according to two point form:

$y-y1 = (y2-y1) \frac{x-x1}{x2-x1}$

In this example we have x1=1987 , y1=522000 , x2=2003 and y2=480000. So,

$y - 522000 = \frac{480000-522000}{2003-1987} (x-1987)\\y- 522000 = -2625(x-1987)\\y- 522000= -2625x+5215875\\\\y= -2625x+5737875$

now to find the year when there will be 440000 employs working , we simply put y= 440000 in the above derived equation

$440000= -2625x+ 5737875\\\\2526x = 5737875 -440000\\2526x = 5736555\\x= \frac{5736555}{2526} \\x= 2271$

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3 years ago

A 20 ft. ladder is used against a 15 ft. wall. What is the measure of the angle made by the ladder and the ground (nearest whole

Brrunno [24]

Step-by-step explanation:

Given that,

The length of a ladder, H = 20 feet

The height of the wall, h = 15 ft

We know that,

$\sin\theta=\dfrac{h}{H}$

h is perpendicular and H is hypotenuse

So,

$\sin\theta=\dfrac{15}{20}\\\\\theta=\sin^{-1}(\dfrac{15}{20})\\\\\theta=48.59^{\circ}$

Now using Pythagoras theoerm,

$b=\sqrt{H^2-h^2}\\\\b=\sqrt{20^2-15^2}\\\\b=13.2\ ft$

Hence, the angle made by the ladder and the ground is 48.59° and the ladder is 13.2 feet from the wall on the ground.

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2 years ago