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LiRa [457]
3 years ago
5

If f(x) = (x + 3)(x − 3), complete the square and determine the minimum or maximum value of the function.

Mathematics
1 answer:
Westkost [7]3 years ago
3 0

Answer:

Minimum of -9

Step-by-step explanation:

f(x) = (x + 3)(x − 3)

Distribute:

f(x) = x² − 9

In vertex form:

f(x) = 1 (x − 0)² − 9

The leading coefficient is positive, so this is an upwards parabola, meaning the vertex is a minimum.  The vertex is at (0, -9).  So the minimum of the function is -9.

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By what percent will a fraction change if its numerator is decreased by 20% and its denominator is decreased by 60%?
Vedmedyk [2.9K]

Answer:

The fraction will increase by 100%

Step-by-step explanation:

Say the fraction is x/y. The question is telling us to decrease x by 20% (i.e. 0.8x) and to decrease y by 60% (i.e. 0.4y):

= \frac{0.8x}{0.4y}\\= 2 (\frac {x}{y})

You can see that by applying these changes, the new fraction is actually double the old fraction (i.e. will increase by 100%).

6 0
3 years ago
Read 2 more answers
3. (03.06)
lisabon 2012 [21]

Answer:

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5 0
3 years ago
What is the largest whole number that will round up or down to 500 if we're rounding to the nearest hundred?
mojhsa [17]

Answer:

549

Step-by-step explanation:

The next larger whole number, 550, will round up to 600.

The largest whole number that rounds to 500 is 549 when rounding to hundreds.

6 0
3 years ago
When an object is thrown upwards with a speed of 64 ft/sec, its height above the ground is given by the function h(t)=−16t2+64t
Svet_ta [14]

Answer:

The object will reach its highest point 0.5 seconds after it has been thrown.

Step-by-step explanation:

The object reaches its maximum height when velocity is equal to zero, the velocity is the derivative of function height. That is:

v(t) = \frac{d}{dt}h(t) (1)

Where v(t) is the velocity of the object at time t, in feet per seconds.

If we know that h(t) =-16\cdot t^{2}+64\cdot t and v(t) = 0\,\frac{ft}{s}, then the time when object reaches its highest point is:

v(t) = -32\cdot t+64

-32\cdot t + 64 = 0

t = 0.5\,s

The object will reach its highest point 0.5 seconds after it has been thrown.

3 0
3 years ago
If the measure of DEF is 65 what is the measure of DE. PLEASE HELP FAST
Wittaler [7]

EF is tangent to the circle we'll assume; otherwise there's no progress.


Call the center C. ECD is isosceles, formed from two radii and the chord.


Angle CED is complementary to DEF


CED = 90 - 65 = 25 degrees


CDE is congruent, isosceles triangle and all that: CDE=25


That leaves DCE=180-25-25=130 degrees


That's the measure of arc DE as well:


Answer: 130 degrees, choice A




8 0
3 years ago
Read 2 more answers
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