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grigory [225]
3 years ago
13

Determine whether the following equation defines y as a function of x.

Mathematics
1 answer:
Aleks04 [339]3 years ago
3 0

Answer:

The equation can define y as a function of x and it also can define x as a function of y.

Step-by-step explanation:

A relation is a function if and only if each value in the domain is mapped into only one value in the range.

So, if we have:

f(x₀) = A

and, for the same input x₀:

f(x₀) = B

Then this is not a function, because it is mapping the element x₀ into two different outputs.

Now we want to see it:

x + y = 27

defines y as a function of x.

if we isolate y, we get:

y = f(x) = 27 - x

Now, this is a linear equation, so for each value of x we will find an unique correspondent value of y, so yes, this is a function.

Now we also want to check if:

x +  y = 27

defines x as a function of y.

So now we need to isolate x to get:

x = f(y) = 27 - y

Again, this is a linear equation, there are no values of y such that f(y) has two different values. Then this is a function.

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Can somebody help me extra points<br> Complete the statement below about the two figures.
Katena32 [7]

Answer:

NOT CONGRUENT - DIFFERENT

Step-by-step explanation:

For triangles to be congruent the angles have to be the same, in other words, any transformation would work, but a completely different triangle would not.

6 0
2 years ago
A regular hexagon is circumscribed about a circle with a radius of 6. Find the area of the shaded region shown. Give the exact a
Alecsey [184]

Answer:

19.58 unit²

Step-by-step explanation:

To find the area of the shaded region, we use the formula:

A_{shaded}=A_{circle} - A_{hexagon}\\\\

As we know that,

A_{circle} = \pi r^2 = \pi 6^2

           =36πunit²

   

Next is to split up the hexagon into 6 regular triangles.

A_{hexagon} = 6. A_{triangle}

               =6 x \frac{1}{2} bh

the base is equal to the radius i.e 6 as the triangles are regular.The height can be represented by taking one of the triangles and drawing a line down the middle.

So, the newly formed triangle is a 30°-60°90° right triangle.

(see figure 1 in attachment)

Here, a= 6/2=> 3

h= a√3 => 3√3

Substituting the required values in the formula of area of hexagon, we get

A_{hexagon}= 6.\frac{1}{2}.6.3\sqrt{3} => 54√3unit²

A_{shaded}=A_{circle} - A_{hexagon}\\\\

           =36π-54√3

            = 19.58 unit²  

4 0
3 years ago
Carry out the calculation: (1.43) + (3.11) × (1.5) what is the answer rounded to the correct number of significant figures?
SashulF [63]
<span>Begin with 3.11 x 1.5, which equals 4.665. Then add 1.43. The answer is thus 6.095.</span>
6 0
3 years ago
Read 2 more answers
Miranda has 5/8 of a yard of ribbon. if she used 1/3 of it to make a hair bow, how much ribbon would she have left. PLEASE HELP
bezimeni [28]

Answer: 5/12

Step-by-step explanation:

Step 1

Whenever you have something OF  something, you just mulltiply.

1/3 of  5/8=  

1/3x5/8

5/24

She used 5/24, and started with 5/8

5/8-5/24= 5/12  left

8 0
1 year ago
Read 2 more answers
The answer is 4 right??
Step2247 [10]
Yes, you are correct. The answer to your problem is indeed 4.
7 0
3 years ago
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