The equation line passing through a point is understood to be parallel to the x-axis. In this case, the equation should be expressed as y = b where b is any number. Since y = 14 in the point (1,14), the equation of horizontal line passing through this point is y = 14.

3 0

3 years ago

Read 2 more answers

Which statements accurately describe the function f(x) = 3(16)^3/4 ?

photoshop1234 [79]

Answer:

3rd and 5th options

Step-by-step explanation:

For f(x) = 3(16)^(3x/4):

There is no initial value, because exponents can be any real number (positive or negative), so #1 is false

Because exponents can be any real number (positive or negative), #2 is false

A positive number to the power of anything will always be positive, and not equal to 0, so #3 is true

The simplified value of this is 3((16)^(3/4) )^x = 3(2^3)^x = 3(8)^x, so #4 is false, but #5 is true.

4 0

3 years ago

Y+1 y+8 y+2 y+7

kipiarov [429]

$\dfrac{y+1}{y+2}+\dfrac{y+8}{y+9}=\dfrac{y+2}{y+3}+\dfrac{y+7}{y+8}$

Write all fractions in terms of a common denominator:

$\dfrac{y+1}{y+2}=\dfrac{(y+1)(y+9)(y+3)(y+8)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+8}{y+9}=\dfrac{(y+8)^2(y+2)(y+3)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+2}{y+3}=\dfrac{(y+2)^2(y+9)(y+8)}{(y+2)(y+9)(y+3)(y+8)}$

$\dfrac{y+7}{y+8}=\dfrac{(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}$

Then move all fractions to one side and simplify the numerator:

$\dfrac{(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)}{(y+2)(y+9)(y+3)(y+8)}=0$

The numerator dictates when the fraction reduces to 0. The denominator can never be 0, so we know that <em>y</em> cannot take any of the values -2, -9, -3, nor -8.

So the equation reduces to

$(y+1)(y+9)(y+3)(y+8)+(y+8)^2(y+2)(y+3)-(y+2)^2(y+9)(y+8)-(y+7)(y+2)(y+9)(y+3)=0$