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2 years ago

Write the function f(x) = |-4x+36| As a piecewise-defines function.

Mathematics

1 answer:

REY [17]2 years ago

6 0

Answer:

Option (A)

Step-by-step explanation:

The given absolute function is,

f(x) = |-4x + 36|

If the given function f(x) ≥ 0,

(-4x + 36) ≥ 0

4x ≤ 36

x ≤ 9

If the given function f(x) < 0,

(-4x + 36) < 0

4x > 36

x > 9

Therefore, piecewise function that defines the absolute function will be,

f(x) = 4x - 36 if x ≤ 9

-4x + 36 if x > 9

Option (A) will be the correct option.

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2x + 3 > 13 x= 0 is this true? O True O False

omeli [17]

False.

Replace x with 0 and solve:

2(0) + 3 = 0+ 3 = 3

3 is not greater than 13 so the answer is false.

5 0

1 year ago

PLEASE HELP!!!!!

Ne4ueva [31]

Answer:

Equation: $30=2(x-2)+2(2x+3)$

$x:\frac{14}{3}$

Step-by-step explanation:

By definition, the perimeter of a figure can be calculated by adding the lenghts of its sides.

Knowing this, you can write the following equation:

$P=2(x-2)+2(2x+3)$ [Equation 1]

According to the data given in the exercise, the perimeter in feet of the fighter is:

$P=30$

Therefore, you can substitute this values into [Equation 1]:

$30=2(x-2)+2(2x+3)$

Finally, you must solve for "x" in order to find its value. This is:

$30=6x+2\\\\30-2=6x\\\\\frac{28}{6}=x\\\\x=\frac{14}{3}$

3 0

2 years ago

What is f(g(x)) for x > 5?

mel-nik [20]

Answer:

$\large\boxed{B.\ 4x^2-41x+105}$

Step-by-step explanation:

$f(x)=4x-\sqrt{x}\\\\g(x)=(x-5)^2\\\\f(g(x))\to\text{put}\ x=(x-5)^2\ \text{to}\ f(x):\\\\f(g(x))=f\bigg((x-5)^2\bigg)=4(x-5)^2-\sqrt{(x-5)^2}\\\\\text{use}\\(a-b)^2=a^2-2ab+b^2\\\sqrt{x^2}=|x|\\\\f(g(x)=4(x^2-2(x)(5)+5^2)-|x-5|\\\\x>5,\ \text{therefore}\ x-5>0\to|x-5|=x-5\\\\f(g(x))=4(x^2-10x+25)-(x-5)\\\\\text{use the distributive property:}\ a(b+c)=ab+ac\\\\f(g(x))=(4)(x^2)+(4)(-10x)+(4)(25)-x-(-5)\\\\f(g(x))=4x^2-40x+100-x+5\\\\\text{combine like terms}\\\\f(g(x))=4x^2+(-40x-x)+(100+5)\\\\f(g(x))=4x^2-41x+105$