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Kisachek [45]
2 years ago
13

A banner is made of a square and a semicircle. The square has side lengths of 26 inches. One side of the square is also the diam

eter of the semicircle. What is the total area of the banner? Use 3.14 for pi (please show work)
Mathematics
1 answer:
Anna007 [38]2 years ago
7 0
Your answer is 891.33
26*26 = 626 (area of the square)
26 / 2 = 13 ( radius of the semecircle )
13*13 = 169
169 * 3.14 = 530.66
530.66 / 2 = 265.33 ( area of the semecircle)
265+626 = 891.33
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The function g is defined as g(x)=5x² – 3.<br> Find g(x+1).
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Answer:

<em>5x² + 10x + 2 </em>

Step-by-step explanation:

g(x + 1) = 5(x + 1)² - 3 = 5( x² + 2x + 1 ) - 3 = <em>5x² + 10x + 2</em>

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3 years ago
Explain how to determine the zeros of f(x)= (x+3)(x-2)(x-6)
Deffense [45]

Answer:

The zeros of f(x)  are -3, 2 , 6

Step-by-step explanation:

f(x) is a polynomial of degree 3.

If the polynomial is not factorized we will either factorize to find the zero or use trial and error method.

Since the f(x) in the question is in the factorized form. we will have to equate each factor to zero.

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2 years ago
Please help me i don’t understand this question at all.
Maru [420]

9514 1404 393

Answer:

  D.

Step-by-step explanation:

The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)

When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.

The only reasonable choice is D.

__

Your calculator can check this for you.

  √12/(√3 +3) ≈ 3.4641/(1.7321 +3)

  = 3.4641/4.7321 ≈ 0.7321 = -1 +√3

__

If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.

  \displaystyle\frac{\sqrt{12}}{\sqrt{3}+3}=\frac{\sqrt{12}}{(\sqrt{3}+3)}\cdot\frac{(\sqrt{3}-3)}{(\sqrt{3}-3)}=\frac{\sqrt{36}-3\sqrt{12}}{3-9}\\\\=\frac{6-3\cdot2\sqrt{3}}{-6}=\boxed{-1+\sqrt{3}}

_____

<em>Additional comment</em>

We "rationalize the denominator" in this way to take advantage of the relation ...

  (a -b)(a +b) = a² -b²

Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.

We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).

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