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Papessa [141]
3 years ago
12

Consider the function represented by the equation y – x – 4 = 0. What is the equation written in function notation, with x as th

e independent variable?
a f(x) = x + 4
b f(x) = –y + 4
c f(x) = –x – 4
d f(x) = y – 4
Mathematics
2 answers:
Yuliya22 [10]3 years ago
7 0
<span>y – x – 4 = 0
   +x           +x
y - 4 = x
   +4     +4
y = x +4

answer
</span><span>a f(x) = x + 4</span>
MrMuchimi3 years ago
3 0

we have

y-x-4=0

we know that

If x is the independent variable

then

isolate the variable y

Adds (x+4) both sides

y-x-4+(x+4)=0+(x+4)

y=x+4

Convert to function notation

Let

f(x)=y

f(x)=x+4

therefore

<u>the answer is the option A</u>

f(x)=x+4

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Aliun [14]

Answer:

See explanation

Step-by-step explanation:

Simplify left and right parts separately.

<u>Left part:</u>

\left(1+\dfrac{1}{\tan^2A}\right)\left(1+\dfrac{1}{\cot ^2A}\right)\\ \\=\left(1+\dfrac{1}{\frac{\sin^2A}{\cos^2A}}\right)\left(1+\dfrac{1}{\frac{\cos^2A}{\sin^2A}}\right)\\ \\=\left(1+\dfrac{\cos^2A}{\sin^2A}\right)\left(1+\dfrac{\sin^2A}{\cos^2A}\right)\\ \\=\dfrac{\sin^2A+\cos^2A}{\sin^2A}\cdot \dfrac{\cos^2A+\sin^A}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A}\cdot \dfrac{1}{\cos^2A}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

<u>Right part:</u>

\dfrac{1}{\sin^2A-\sin^4A}\\ \\=\dfrac{1}{\sin^2A(1-\sin^2A)}\\ \\=\dfrac{1}{\sin^2A\cos^2A}

Since simplified left and right parts are the same, then the equality is true.

3 0
3 years ago
The sum of a number and its square is 182. Find the number.
Mars2501 [29]

Answer:

13 and -14 satisfy this condition

Step-by-step explanation:

Let's represent that number as x

and the square of x is x^2

So,

x + x^2 = 182

Subtract 182 from both sides

x + x^2 - 182 = 182 - 182

x + x^2 - 182 = 0

rearrange the quadratic equation

x^2 + x -182 = 0

let's use the quadratic formula

\frac{-b+\sqrt{b^2-4ac} }{2a}       or      \frac{-b-\sqrt{b^2-4ac} }{2a}

a = 1, b = 1, c = -182

\frac{-1+\sqrt{1^2-4*1*(-182)} }{2*1}       or     \frac{-1-\sqrt{1^2-4*1*(-182)} }{2*1}

\frac{-1+\sqrt{1+728} }{2}      or         \frac{-1-\sqrt{1+728} }{2}

\frac{-1+\sqrt{729} }{2}            or    \frac{-1-\sqrt{729} }{2}

\frac{-1+{27} }{2}     or    \frac{-1-{27} }{2}

\frac{26}{2}     or    \frac{-28}{2}

13 or    - 14

Lets check

13 + 13^2 = 13 + 169

= 182

Also,

-14 + (-14^2) = -14 + 196

= 182

8 0
3 years ago
I'm really confused, can you please help me
Anika [276]

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Since DF is bisected, it means but in half. This means DU and UF are equal in length. We can set them equal to each other to find y.

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4 0
3 years ago
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