All categories

3 years ago

For f(x)=4x+1 and g(x)=x^2-5 find (f-g)(x)

Mathematics

2 answers:

Marrrta [24]3 years ago

6 0

$f(x)=4x+1,\ g(x)=x^2-5\\\\(f-g)(x)=f(x)-g(x)\\\\\text{Therefore}\\\\(f-g)(x)=(4x+1)-(x^2-5)=4x+1-x^2+5=-x^2+4x+6$

almond37 [142]3 years ago

4 0

Answer:

x^2+4x-4

Step-by-step explanation:

This guy made me miss it so it gave me the answer

APEX

You might be interested in

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

4 0

2 years ago

There are 5 yellow marbles and 12 blue marbles in a bag. You randomly choose one of the marbles. What is the probability of choo

Anettt [7]

5 yellow marbles out of total of 17 marbles so 5/17

3 0

3 years ago

Read 2 more answers

Round 21,000 to the nearest 10,000

kolezko [41]

The answer will be 20,000

5 0

3 years ago

Read 2 more answers

Matt bought 8 pie molds at a cost of $0.67 per mold. He also bought 8 pre-

kupik [55]

Answer:

$5.36

Step-by-step explanation:

multiply 8 by .67

6 0

3 years ago

On a map, 1/4 inch between locations represents an actual distance of 2 miles between the locations. What is the actual distance

Fittoniya [83]

Answer:

12/17 miles

Step-by-step explanation:

Make the denominators equal -> 1/4 = 17/68, 3/34 = 6/68

17/68 inches represent 2 miles

The ratio between 17/68 and 6/68 is 17/68 : 6/68 = 17/6
So, the ratio between the distance should also be 17/6

-> 3/34 inches represent 2 : 17/6 = 12/17 (miles)

Hope it helps :)

3 0

2 years ago