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2 years ago

Determine if the function is one-to-one. A decreasing line intercepting the y axis at 0,4

Mathematics

2 answers:

PilotLPTM [1.2K]2 years ago

8 0

Answer:

Yes, it is a one-to-one function.

Step-by-step explanation:

If every element of the range of the function corresponds to exactly one element of the domain, then the function is called one-to-one.

A linear function is always a one-to-one function. It means all straight lines represent one-to-one function, except the vertical or horizontal lines.

It is given that a decreasing line intercepting the y axis at (0,4). We need to check whether it is a one-to-one function or not.

Since, all increasing or decreasing lines represent the one-to-one function, therefore the given function is also a one-to-one.

sesenic [268]2 years ago

3 0

Answer:

it is

Step-by-step explanation:

Any linear function is one-to-one. It passes both the horizontal and vertical line test. Every element of the range maps to exactly one element of the domain and vice versa.

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Find the equation of the line that contains the given point and has the given slope-

mylen [45]

Answer:

y-5 = -3x

y = -3x+5

Step-by-step explanation:

We can use the point slope form of the equation

y-y1 = m(x-x1) where m is the slope and (x1,y1) is a point on the line

y-5 = -3(x-0)

y-5 = -3x

We can change it to slope intercept form y= mx+b by adding 5 to each side

y-5+5 = -3x+5

y = -3x+5

3 0

2 years ago

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The length of a rectangle is 5 meters less than twice the width. If the area of the rectangle is 273 meters, find the dimensions

AleksandrR [38]

The length of the rectangle = 16 meters

The width of the rectangle = 10.5 meters

Step-by-step explanation:

Given that,

The Area of the rectangle is 273.

Step 1 :

Let, the width of the rectangle be 'x'

The length of the rectangle is 2x - 5

Step 2 :

Area of the rectangle = length $\times$ width

273 = (2x - 5) x

273 = 2x^2 - 5x

Step 3 :

The equation formed is 2x^2 - 5x -273 = 0

a= coefficient of x^2 = 2

b= coefficient of x = -5

c = constant = -273

Find the roots of the equation, to find the width.

Step 4 :

Find the roots using factorizing method,

ac = 2 $\times$ -273 = -546 and b= -5

Factorizing -546 as -26 $\times$ 21

The product of -26 $\times$ 21 = -546

The sum of -26 + 21 = -5

Step 5 :

The roots of the equation 2x^2 - 5x -273 = 0 are x= -26/2 and x= 21/2

The values of x are x= -13 and x= 10.5

Since the width cannot be a negative value, neglect x= -13

Step 6 :

Therefore,

The width of the rectangle = 10.5 meters

The length of the rectangle = 2x-5

= 2(10.5) - 5

= 21 - 5

length = 16 meters

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3 years ago

A 1.8-ounce jar cinnamon costs $4.05. What is the cost per ounce?

Paha777 [63]

$4.05/1.8 oz= $2.25 per oz

Final answer: $2.25 per oz

6 0

2 years ago

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Which equation represents the graphed function?

scoundrel [369]

Solution:

we have been asked to find

Which equation represents the graphed function?

As we can see in the graph, the line is passing through the point (2,0) and (0,-3).

As we know the equation of the passing through two points is given by the formula

$(y-y_1)=m(x-x_1)\\
\\
m=slope=\frac{y_2-y_1}{x_2-x_1}=\frac{-3-0}{0-2}=\frac{3}{2} \\$

So the equation of the line will be

$y-0=\frac{3}{2}(x-2)\\
\\
y= \frac{3}{2}x-3\\
\\$

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2 years ago

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Musichelp me out please

kenny6666 [7]

Answer:

right arrow

Step-by-step explanation:

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3 years ago