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babunello [35]
3 years ago
11

According to the lecture, a valedictory speech should last approximately ________ minutes.

Mathematics
1 answer:
fiasKO [112]3 years ago
6 0
<span>According to the lecture, a valedictory speech should last approximately 15 minutes. </span>
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The maximum capacity of the school auditorium is 420 people. Write an inequality for the situation. Tell what type of numbers th
posledela
The number of people in the auditorium can be less than or equal to 420 so let p represent the number of people
The inequality is p≤420
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True or false a rectangle with four right angles is a square
iragen [17]
False a rectangle could never be a square
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Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = −1. (2 points)
umka2103 [35]

Focus of the parabola is (-5,5) and directrix is y = -1.

Let's assume a point (x,y) on parabola.

According to definition of parabola, the distance between point (x,y) and focus (-5,5) would be same as the distance between the point (x,y) and directrix y = -1.

\sqrt{(x+5)^2+(y-5)^2} = \sqrt{(y+1)^2} \\\\(x+5)^2+(y-5)^2=(y+1)^2 \\\\(x+5)^2 + y^2 - 10y +25 = y^2 +2y +1 \\\\(x+5)^2 =  -y^2 +10y -25 + y^2 +2y +1 \\\\(x+5)^2 = 12y -24 \\\\12y =  (x+5)^2  +24 \\\\ y = \frac{1}{12} (x+5)^2  +2

Hence, option D is correct, i.e. f(x) = one twelfth (x + 5)2 + 2.

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Help me ASAP please :( Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and wr
Alla [95]

Answer:

see explanation

Step-by-step explanation:

Using the laws of logarithms

• log x - log y = log(\frac{x}{y})

• log_{b} x = n ⇔ x = b^{n}

Hence

log_{x}( \frac{8x-3}{4} ) = 2, hence

\frac{8x-3}{4} = x² ( multiply both sides by 4 )

8x - 3 = 4x² ← rearrange into standard form

Subtract 8x - 3 from both sides

4x² - 8x  + 3 = 0 ← in standard form

(2x - 1)(2x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = \frac{1}{2}

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = \frac{3}{2}

4 0
2 years ago
What can you conclude about the distance from zero for both an integer and its opposite
lakkis [162]
One can be, they both have the same absolute value no matter what.
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