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2 years ago

Part 1 state the domain and range of the given relation.

1 answer:

5 0

A relation is any set of ordered pairs, which can be thought of as (input, output).

A function is a relation in which NO two ordered pairs have the same first component and different second components.

The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.

The set of second components (y-coordinates) is the RANGE of the relation.

Part 1:
Domain: {-1, 1, 3, 6}
Range: {2, 2, 2, 2}

Part 2:
To determine whether the given relation represents a function, look at the given relation and ask yourself, “Does every first element (or input) correspond with EXACTLY ONE second element (or output)?”

Remember that a function can only take on 1 output for each input.

It helps to plot the points on the graph and perform the Vertical Line Test (VLT):

The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

As you can see in the attached screenshot, every vertical line drawn only has 1 point in it. This means that each x-value corresponds to exactly one y-value. The given relation passed the VLT. Therefore, the relation is a function.

Please mark my answers as the Brainliest if you find my explanation helpful :)

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Show work

nika2105 [10]

Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.

Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

There are three right triangles we can work with.

Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation $x^{2} + 48^{2} = z^{2}$

Triangle with sides 27, x and y. Here y is the hypotenuse so we get $27^{2} + x^{2} = y^{2}$

Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get $y^{2} + z^{2} = (27+48)^{2}$ . That is, $y^{2} + z^{2} = 5625$

We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation: $y^{2} + z^{2} = 5625$ and replace $z^{2}$ and $y^{2}$ using expressions that contain an expression in terms of x from the first two equations we came up with.

That gives us: $48^{2} + x^{2} + x^{2} + 27^{2} =5625$ which we solve for x as follows:

$2 x^{2} + 3033 =5625
2x^{2} =2592
 x^{2} =1296
x=36$

Now that we know x we can substitute 36 for x into the equation $48^{2} + x^{2} = z^{2}$ and solve for z as follows:
$48^{2} + 36^{2} = z^{2} 
2304+1296=z^{2} 
3600=z^{2} 
z=60$

This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.

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3 years ago

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If 3/4 of an inch of rain fell in 1/2 hour, explain how to get the unit rate

bearhunter [10]

Answer:

Search to find the detailed rainfall collections if you want more detailed rainfall intensity data. If all available is monthly average in mm, take the monthly average and divide by number of hours in that month. So if you had 300 mm in April, take 360 mm/(30 days * 24 hours) = 0.5 mm/hour average monthly intensity. so that's it

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2 years ago

What is 30,000 expressed in scientific notation?

OlgaM077 [116]

The answer is b. It is the only choice that equals the right answer. You could also write this as 3 * 10^4, which is equivalent to b.

6 0

3 years ago

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Chris and Becky are comparing mortgages. The mortgage is for $183,500. If they choose 30 years at 5%, their monthly payment will

soldi70 [24.7K]

Answer:

For 30 years at 5% = $354,625.2

For 20 years at 4.5% = $278,618.4

Step-by-step explanation:

The total payback for each payment is given by the monthly payment multiplied by the total number of months for the payment period (years).

1) For 30 years at 5%

Total number of months in 30 years = 30 x 12 = 360 months

Payback = $985.07 x 360 = $354,625.2

2) For 20 years at 4.5%

Total number of months in 20 years = 20 x 12 = 240 months

Payback = $1160.91 x 240 = $278,618.4

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3 years ago

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a store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for 27.93 and large bags cost 66.98.w

Nonamiya [84]

Answer

Find out the ratio of price to pound for each bag.

To prove

As given

A store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for $27.93 .

7 pound = $27.93

Now find out the cost for the 1 pound.

$1\ pound\ cost= \frac{27.93}{7}$

1 pound cost = $3.99

As given large bags cost $66.98.

Now find out pounds in the large bags.

Let us assume that the number of pounds in the large bags be x.

Than

3.99 × x = 66.98

$x = \frac{66.98}{3.99}$

x = 16.8 pounds (approx)

Now find out the ratio of price to pound for each bag.

As small bags weight = 7 pounds

Cost of the small bags = $27.93

$\frac{Price\ of\ small\ bag}{Cost\ of\ the\ small\ bags} = \frac{27.93}{7}$

As large bags weight = 16.8 pounds

Cost of the large bags = $66.98

$\frac{Price\ of\ large\ bag}{Cost\ of\ the\ large\ bags} = \frac{66.98}{16.8}$

Hence proved

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3 years ago