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3 years ago

1.5+ (-6)

Mathematics

1 answer:

I am Lyosha [343]3 years ago

8 0

1. -1
2. -2
3. -12
4. 7
5. -4

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What is the vertex of the graph of the function f(x) = x2 − 4x?

Vsevolod [243]

Answer:

(2, -4).

Step-by-step explanation:

x^2 - 4x

= (x - 2)^2 - 4.

So the vertex is at

(2, -4).

6 0

3 years ago

Read 2 more answers

List all possible rational roots. Then use synthetic division to confirm which rational roots exist:

Kisachek [45]

Answer:

$\boxed{(1) \, x = \, \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10; (2) \, x = -2}$

Step-by-step explanation:

2x³+ 6x² - x - 10 = 0

(1) Possible roots

The Rational Roots Theorem states that, if a polynomial has any rational roots, they will have the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

$\text{Possible rational root} = \dfrac{ p }{ q } = \dfrac{\text{factor of constant term}}{\text{factor of leading coefficient}}$

In your function, the constant term is -10 and the leading coefficient is 2, so

$\text{Possible root} = \dfrac{\text{factor of 10}}{\text{factor of 2}}$

Factors of 10 = ±1, ±2, ±5, ±10

Factors of 2 = ±1, ±2

$\text{Possible roots are } \large \boxed{\mathbf{x = \pm \dfrac{1}{2}, \pm 1, \pm2, \pm \dfrac{5}{2}, \pm 5, \pm 10}}$

(2) Synthetic division

Rather than work through all 12 possibilities, I will do one that works.

$\begin{array}{r|rrrr}-2 & 2 & 6 & -1 & -10\\& & -4& -4 & 10\\& 2 & 2& -5 & 0\\\end{array}$

So, x = -2 is a root, and the quotient is 2x² + 2x - 5.

(3) Check for other rational roots

2x² + 2x - 5 = 0

D = b² - 4ac =2²- 4(2)(-5) = 4 + 40 = 44

√44 = 2√11, which is irrational.

Since irrational roots come in pairs, the cubic equation has two real, irrational roots and one rational root at x = -2.

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4 years ago

What is a polygon? Giving brainliest

Charra [1.4K]

Step-by-step explanation:

a polygon is a plane figure that is described by finite number of line segments....

hope it helps

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3 years ago

An alloy that is 30% silver is mixed with 200 g of a

Alecsey [184]

Answer:

The answer is $466\frac{2}{3}\,g$

Step-by-step explanation:

Let,

Amount of alloy with 30% silver = x g

Given,

Amount of alloy with 10% silver = 200 g

So, Total Amount of alloy with 24% silver = (x+200) g

Now,

$x*0.30+200*0.10=(x+200)*0.24\\=>0.30x+20=0.24x+48\\=>0.06x=28\\x=466\frac{2}{3}\,g=466.67\,g$

Hope you have understood this....

pls mark my answer as the brainliest

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3 years ago

Arc Length and Radians question- please help! Will mark brainliest! Is 20pts!

Dmitry_Shevchenko [17]

Answer:

$\frac{2\pi}{5}$

Step-by-step explanation:

To convert from degrees to radians you multiply by $\frac{\pi}{180}$

$\frac{72 \pi}{180} = \frac{2 \pi }{5}$

7 0

3 years ago