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2 years ago

F(x)=4x^2+2x-6.find the range of function f(x).

Mathematics

1 answer:

Triss [41]2 years ago

4 0

Answer:

y ≥ 6.25

Step-by-step explanation:

f(x)=4x²+2x-6

positive (4) leading coefficient, curve is left up and right up

x coordinate of vertex: x = - b/2a = - 2/2*4 = - 1/4 (-0.25)

y = 4*(-1/4)² + 2*(-1/4) - 6 = -6 1/4 (-6.25) ... extreme

range: y ≥ - 6.25 [-6.25,∞)

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(-3,2) and ( 2,-13) slope intercept equation

Georgia [21]

Given:

The points are (-3, 2) and (2, -13).

To find:

Slope-intercept form of the equation.

Solution:

Here $x_1=-3, y_1=2, x_2=2, y_2=-13$ .

Slope of the line:

$$m=\frac{y_2-y_1}{x_2-x_1}$

$$m=\frac{-13-2}{2-(-3)}$

$$m=\frac{-15}{5}$

m = -3

Using point-slope formula:

$y-y_1=m(x-x_1)$

$y-2=-3(x-(-3))$

$y-2=-3(x+3)$

$y-2=-3x-9$

Add 2 on both sides.

$y-2+2=-3x-9+2$

$y=-3x-7$

Slope-intercept form of the equation is y = -3x - 7.

8 0

3 years ago

three tanks are capable of holding 108 litres, 168 litres and 180 litres of milk. determine the capacity of the greatest vessel

SpyIntel [72]

A vessel of 7,560 liters

Step-by-step explanation:

This means finding the Least Common Multiple for;

108 168 180

We begin by finding the multiples of each number;

Multiples of 108:

108, 216, 324, 432, 540, 648, 756, 864, 972, 1080, 1188, 1296, 1404, 1512, 1620, 1728, 1836, 1944, 2052, 2160, 2268, 2376, 2484, 2592, 2700, 2808, 2916, 3024, 3132, 3240, 3348, 3456, 3564, 3672, 3780, 3888, 3996, 4104, 4212, 4320, 4428, 4536, 4644, 4752, 4860, 4968, 5076, 5184, 5292, 5400, 5508, 5616, 5724, 5832, 5940, 6048, 6156, 6264, 6372, 6480, 6588, 6696, 6804, 6912, 7020, 7128, 7236, 7344, 7452, 7560, 7668, 7776

Multiples of 168:

168, 336, 504, 672, 840, 1008, 1176, 1344, 1512, 1680, 1848, 2016, 2184, 2352, 2520, 2688, 2856, 3024, 3192, 3360, 3528, 3696, 3864, 4032, 4200, 4368, 4536, 4704, 4872, 5040, 5208, 5376, 5544, 5712, 5880, 6048, 6216, 6384, 6552, 6720, 6888, 7056, 7224, 7392, 7560, 7728, 7896

Multiples of 180:

180, 360, 540, 720, 900, 1080, 1260, 1440, 1620, 1800, 1980, 2160, 2340, 2520, 2700, 2880, 3060, 3240, 3420, 3600, 3780, 3960, 4140, 4320, 4500, 4680, 4860, 5040, 5220, 5400, 5580, 5760, 5940, 6120, 6300, 6480, 6660, 6840, 7020, 7200, 7380, 7560, 7740, 7920

The Least Common Multiple for the 3 number is;

= 7560

Therefore a vessel of 7,560 liters fills each one of them an exact number of times with no remainder.

Learn More:

For more on Least Common Multiple check out;

brainly.com/question/11978021

#LearnWithBrainly

5 0

3 years ago

Is (4, 1) a solution to this system of inequalities? x ≥ 4 x + 7y ≤ 11

Naya [18.7K]

Yess!!!!!!!!!!!!!!!!!!!!

6 0

3 years ago

Read 2 more answers

Hi I’ll appreciate it if you help me!

dexar [7]

The answer would be 30in.
Reasoning: if the two figures are proportional, you would set it up in a proportion. It would be 36/x=12/10. Then cross multiply, so it would be 12x and 36(10). Afterwords you’ll have 12x=360, then divide both sides by 12 and you’ll end up with 30.

4 0

3 years ago

Ocdjiowfhva; brbnhgdn

kotegsom [21]

Answer:

yup i guess

Step-by-step explanayuption:

7 0

3 years ago