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2 years ago

8

Determine the number of roots, using the most efficient method possible.

1 answer:

Dmitry [639]2 years ago

7 0

Answer:

2 roots in every case, not all are real.

Step-by-step explanation:

All of these equations are quadratic equations (degree 2). Every quadratic has two roots. They may be identical (looks like 1 root), and they may be complex (zero real roots), but there are always 2 of them.

a) the y-value of the vertex is negative and the parabola opens downward (leading coefficient -5), so there are no real zeros and both roots are complex.

b) each binomial factor contributes a root. Both roots are real.

c) the discriminant is positive, (3²-4·2·1=1), so both roots are real.

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The sale price of a laptop bag is $35.00. This is 80% of the original price.

Marrrta [24]

Answer:

43.75 was the original price of the laptop bag

Step-by-step explanation:

according to question

X of 80% = 35

X x 80/100 = 35

X = (35x 100)/80

X = 43.75 dollars

8 0

2 years ago

Please help me with this question

san4es73 [151]

Step-by-step explanation:

Given: $f'(x) = x^2e^{2x^3}$ and $f(0) = 0$

We can solve for f(x) by writing

$\displaystyle f(x) = \int f'(x)dx=\int x^2e^{2x^3}dx$

Let $u = 2x^3$

$\:\:\:\:du=6x^2dx$

Then

$\displaystyle f(x) = \int x^2e^{2x^3}dx = \dfrac{1}{6}\int e^u du$

$\displaystyle \:\:\:\:\:\:\:=\frac{1}{6}e^{2x^3} + k$

We know that f(0) = 0 so we can find the value for k:

$f(0) = \frac{1}{6}(1) + k \Rightarrow k = -\frac{1}{6}$

Therefore,

$\displaystyle f(x) = \frac{1}{6} \left(e^{2x^3} - 1 \right)$

5 0

2 years ago

The number of gallons of water,y, in a swimming pool is modeled by the equation y=7.5x+500,where x represents the time in minute

podryga [215]

Y = 7.5*200 +500
y = 1500 +500
y = 2000

2000 gallons are in the pool 200 minutes after the pump is turned on.

5 0

2 years ago

50 points Quick answer, thank you.

PIT_PIT [208]

Lines R and S are parallel.

this seems like a geometry question and I’m in Algebra so I probably shouldn’t even try to answer this.

6 0

2 years ago

Read 2 more answers

Max has a drawer full of green and red socks. He has three times times as many red socks subtracted from four times as many gree

monitta

Answer:

There are 42 red colour socks and 44 green color socks

Step-by-step explanation:

Let there are r red socks and g green socks.

ATQ,

He has three times times as many red socks subtracted from four times as many green socks which he believes is 50 socks.

4g-3r=50 ....(1)

Half the number of green socks plus one-third of the number of red socks is 36.

$\dfrac{g}{2}+\dfrac{r}{3}=36\\\\3g+2r=216\ .....(2)$

Multiply equation (1) by 2 and equation (2) by 3.

8g-6r = 100 ....(3)

9g +6r = 648 ....(4)

Add equation (3) and (4)

8g-6r + 9g +6r = 100+648

17g = 748

g = 44

Put the value of g in equation (1).

4(44)-3r=50

176-3r = 50

176-50 = 3r

r = 42

Hence, there are 42 red colour socks and 44 green color socks.

7 0

2 years ago