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Pani-rosa [81]
3 years ago
6

How to find the minimum value of an expression

Mathematics
1 answer:
miv72 [106K]3 years ago
3 0
f(x)=9x²+24x+1
f(x)=(3x)²+ 2×3x× 4 + 1
= (3x)²+2×3x×4 +16 -16 +1
=. ( 3x+4)² -15. -------(1)
then (3x+4)² ≥0
least value of (3x+4)² is 0
putting in equation 1
= 0-15 =-15
- 15 is the least value
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Solve the inequality for w.<br><br> 20 ≥ - 4w<br><br> Simplify your answer as much as possible.
Oksanka [162]

Answer:

w\geq-5

Step-by-step explanation:

-4w\leq20

4w\geq-20

w\geq-5

8 0
3 years ago
Find the equation of the linethe line passes through the points (5,2) and (-4,-4)
almond37 [142]

Answer:

y =  \frac{2}{3}x -  \frac{4}{3}

Step-by-step explanation:

first find the slope using the above points then use the slope formula to calculate the slope

m =  \frac{y2 - y1}{x2 - x1}  \\  \frac{2 - -  4}{5 -  - 4}  =  \frac{2 + 4}{5 + 4}  =  \frac{6}{9}  =  \frac{2}{3}

substitute ⅔ for m and one of the above points into the y-intercept form of the equation for a line and solve for b

y = mx + b \\ 2 =  \frac{2}{3} (5)  + b \\ 2 =  \frac{10}{3}  + b \\ 2 -  \frac{10}{3}  = b \\  \frac{6}{3}  -  \frac{10}{3}  = b \\ b =  -  \frac{4}{3}

substitute the slope and the value for b into the equation to get the answer

y =   \frac{2}{3} x -  \frac{4}{3}

4 0
3 years ago
Rafael has a bag of marbles, there are 5 green marbles, 6 red marbles, and 4
yulyashka [42]

The probability of getting red marble from the consider withdrawal of a marble is 0.107 approximately.

<h3>How to calculate the probability of an event?</h3>

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as

P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Given that:

The bag contains:

  • 5 green marbles,
  • 6 red marbles,
  • 45 white marbles.
  • Rafael draws one marble at random

Since he draws one marbel, thus, only one colored marble would come out.

Let we suppose we've to find P(red marble coming out).

Then, if we take:

E = event of Rafael drawing a red marble,

then E can be done in 6 ways as there are 6 red marbles to choose from.

Also, withdrawal of 1 marble (of any color) can be done in (5+6+45 = 56) 56 ways.

Thus, we get:

P(E) = P(\text{Choosing a red marble}) = \dfrac{6}{56} = \dfrac{3}{28} \approx 0.107

Thus, the probability of getting red marble from the consider withdrawal of a marble is 0.107 approximately.

Learn more about probability here:

brainly.com/question/1210781

#SPJ1

3 0
2 years ago
Lan make 60 cakes. he gives 1/4 of the cakes to Helen. he gives 20 of the 60 cakes to sue. what fraction of the 60 cakes does he
weqwewe [10]

Answer:

5/12

Step-by-step explanation:

1/4 of the cakes is 60 divided by 4 which is 15. That goes to Helen

20 go to Sue

so far, he has given away 35 cakes out of the 60

he is left with 25 cakes

that is 25/60 which can be simplified to 5/12

4 0
3 years ago
Read 2 more answers
Use long division to find the quotient below.<br> (x2 + 3x - 18) + (x-3)
Vanyuwa [196]

Answer:

6x-21

Step-by-step explanation:

6 0
3 years ago
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