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2 years ago

Find the equation of the axis of symmetry of the following parabola algebraically.

Mathematics

1 answer:

Sonja [21]2 years ago

4 0

Answer:

x = 1

Step-by-step explanation:

y = 2x² − 4x − 14

y = 2 (x² − 2x) − 14

y = 2 (x² − 2x + 1) − 14 − 2(1)

y = 2 (x − 1)² − 16

The vertex of the parabola is at (1, -16). So the equation of the line of symmetry is x = 1.

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Find the area of each sector shown (the shaded section)

mihalych1998 [28]

Answer:

The area of the sector (shaded section) is 29.51 $m^{2}$ .

Step-by-step explanation:

Area of a sector = (θ ÷ 360) $\pi$ $r^{2}$

where θ is the central angle of the sector, and r is the radius of the circle.

From the diagram give, diameter of the circle is 26 m. So that;

r = $\frac{diameter}{2}$

= $\frac{26}{2}$ = 13 m

θ = 360 - (180 + 160)

= 360 - 340

= $20^{o}$

Thus,

area of the given sector = $\frac{20}{360}$ x $\frac{22}{7}$ x $(13)^{2}$

= $\frac{20}{360}$ x x $\frac{22}{7}$ x 169

= 29.5079

The area of the sector (shaded section) is 29.51 $m^{2}$ .

4 0

2 years ago

Drag an answer to each box to complete this paragraph proof.

kramer

1.substitution property

4 0

2 years ago

If 2^n + 1 is an odd prime for some integer n, prove that n is a power of 2. (H

vovikov84 [41]

Step-by-step explanation:

We will prove by contradiction. Assume that $2^n + 1$ is an odd prime but n is not a power of 2. Then, there exists an odd prime number p such that $p\mid n$ . Then, for some integer $k\geq 1$ ,

$n=p\times k.$

Therefore

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p.$

Here we will use the formula for the sum of odd powers, which states that, for $a,b\in \mathbb{R}$ and an odd positive number $n$ ,

$a^n+b^n=(a+b)(a^{n-1}-a^{n-2}b+a^{n-3}b^2-...+b^{n-1})$

Applying this formula in 1) we obtain that

$2^n + 1=2^{p\times k} + 1=(2^{k})^p + 1^p=(2^k+1)(2^{k(p-1)}-2^{k(p-2)}+...-2^{k}+1)$ .

Then, as $2^k+1>1$ we have that $2^n+1$ is not a prime number, which is a contradiction.

In conclusion, if $2^n+1$ is an odd prime, then n must be a power of 2.

4 0

2 years ago

If C=(a,b,x,y) and D=(m,n,o,p) then c union d is

Ilya [14]

Step-by-step explanation:

here,

C={ a,b,x,y}

D ={ m,n,o,p}

now,

C union D ={a,b,x,y} union {m,n,o,p}

= {a,b,x,y,m,n,o,p}

therefore C union D ={ a,b,x,y,m,n,o,p}

hope u get it...

5 0

3 years ago

Help me out here on this.............

WITCHER [35]

Answer:

You don NOT use (10 x 10) x 2

Step-by-step explanation:

You do not use it becuase its the only one that doesnt equal 100. hope this helps :)

6 0

2 years ago