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3 years ago

Please help! f(x)=x^2. What is g(x)

Mathematics

1 answer:

lorasvet [3.4K]3 years ago

4 0

Answer:

Step-by-step explanation:

The standard form for a parabola is ax^2+bx+c. In this equation, b=0 and c=0. For g(x), you would plug in your y-value that was given (which is 4) and you would plug in your x-value that that given (which is 1). Use PEMDAS. The correct answer is the one that is true.

A. g(x) = (4x)^2

4 = (4(1))^2

4 = 16. (not true)

B. g(x) = 1/4 x^2

4 = 1/4 (1)^2

4 = 1/4 (not true)

C. g(x) = 16x^2

4 = 16(1)^2

4 = 16 (not true)

D. g(x) = 4x^2

4 = 4(1)^2

4 = 4. (true --> correct answer)

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3 years ago

Solve the inequality for x. Show each step of the solution.10x > 2(8x – 3) – 18

Luden [163]

Answer: x<4

Given the inequality:

$10x>2(8x-3)-18$

We want to solve the inequality for x.

First, distribute the bracket on the right side of the inequality.

$\begin{gathered} 10x>2(8x)-2(3)-18 \\ 10x>16x-6-18 \\ 10x>16x-24 \end{gathered}$

Next, subtract 10x from both sides of the inequality.

$\begin{gathered} 10x-10x>16x-10x-24 \\ 0>6x-24 \end{gathered}$

Add 24 to both sides of the inequality.

$\begin{gathered} 0+24>6x-24+24 \\ 24>6x \end{gathered}$

Divide both sides of the inequality by 6.

$\begin{gathered} \frac{24}{6}>\frac{6x}{6} \\ 4>x \\ \implies x$

The solution to the inequality is x<4.

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1 year ago

<img src="https://tex.z-dn.net/?f=%5Cfrac%7B%5Csec%5Cleft%28x%5Cright%29%7D%7B%5Ccos%5Cleft%28x%5Cright%29%7D-%5Cfrac%7B%5Csin%5

DanielleElmas [232]

Answer:

Step-by-step explanation:

First, convert all the secants and cosecants to cosine and sine, respectively. Recall that $csc(x)=1/sin(x)$ and $sec(x)=1/cos(x)$ .

Thus:

$\frac{sec(x)}{cos(x)} -\frac{sin(x)}{csc(x)cos^2(x)}$

$=\frac{\frac{1}{cos(x)} }{cos(x)} -\frac{sin(x)}{\frac{1}{sin(x)}cos^2(x) }$

Let's do the first part first: (Recall how to divide fractions)

$\frac{\frac{1}{cos(x)} }{cos(x)}=\frac{1}{cos(x)} \cdot \frac{1}{cos(x)}=\frac{1}{cos^2(x)}$

For the second term:

$\frac{sin(x)}{\frac{cos^2(x)}{sin(x)} } =\frac{sin(x)}{1} \cdot\frac{sin(x)}{cos^2(x)}=\frac{sin^2(x)}{cos^2(x)}$

So, all together: (same denominator; combine terms)

$\frac{1}{cos^2(x)}-\frac{sin^2(x)}{cos^2(x)}=\frac{1-sin^2(x)}{cos^2(x)}$

Note the numerator; it can be derived from the Pythagorean Identity:

$sin^2(x)+cos^2(x)=1; cos^2(x)=1-sin^2(x)$

Thus, we can substitute the numerator:

$\frac{1-sin^2(x)}{cos^2(x)}=\frac{cos^2(x)}{cos^2(x)}=1$

Everything simplifies to 1.

7 0

3 years ago