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Jet001 [13]
3 years ago
12

What is the solution to the inequality -4x<8

Mathematics
1 answer:
Ivahew [28]3 years ago
6 0

Answer:

x>-2

Step-by-step explanation:

because it is divided by -4.

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Derive the equation of the parabola with a focus at (2, −1) and a directrix of y = −one half.
yKpoI14uk [10]
Basically, the parabola has to have all points that are equidistant from the focus and the directrix, the directrix being a horizontal line, and the focus being a point given. To derive an equation from this you need to use the distance formula which I'm guessing you already know because you're already in precalc.
The gist of it is that we have a random point on the parabola (x,y), and the point (x,y) will be equidistant from both the focus and the directrix. If we use the distance formula, you get something like this:
\sqrt{(y-(- \frac{1}{2} ))^2} = \sqrt{(x-2)^2+(y-(-1)^2}
The square root of y-(-1/2) coming from the directrix, and the righthand side of the equal sign being derived from the focus.
All you need to do is simplify now!
<span>(y+\frac{1}{2})^2 = (x-2)^2+(y+1)^2 \\\ y^2+y+ \frac{1}{4} = x^2-4x+4 + y^2+2y+1 \\\ -y-\frac{3}{4} = x^2-4x+4 \\\ -y-\frac{3}{4} = (x-2)^2 \\\ -y = (x-2)^2+\frac{3}{4} \\\ y = -(x-2)^2-\frac{3}{4}
</span>
Hope I helped! 
3 0
3 years ago
Read 2 more answers
There are some Chicken and rabbits in a cage. There are 20 heads and 62 feet in total, the question is: how many chicken and rab
horsena [70]

Answer:There are 72 heads (chicken and rabbit) and 200 legs. How many chickens and rabbits are present totally?

Step-by-step explanation

There are 72 heads (chicken and rabbit) and 200 legs. How many chickens and rabbits are present totally?

Legs of a chicken = 2

Legs of a rabbit = 4

Total heads = 72

Total legs= 200

Let's assume that each of them has minimum 2 legs.

So 72*2 = 144 legs

Remaining legs: 200-144= 56

These remaining legs belong to rabbit because rabbit has 4 legs each.

2*Rabbits= 56

Rabbits= 56/2 = 28

Out of 72, 28 are rabbits. So there are 72-28= 44 chicken.

5 0
2 years ago
Brain if correct help pls
zheka24 [161]

Step-by-step explanation:

<u>Complete the operation, find the quotient and match with correct option:</u>

  • 44.1/4.9 = 9
  • 32.8/8.2 = 4
  • 43.2/3.6 = 12
  • 161.2/5.2 = 31
  • 93.6/7.2 = 13
3 0
2 years ago
Read 2 more answers
Margaret makes bracelets and sells them to tourists. the function s(t) approximates how many bracelets margaret makes per hour.
Fantom [35]

The units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

To define the unit of the composite function s(w(h)), we first need to find the units of the functions s(t) and w(h).

The function s(t)  represents the number of bangles per hour, so its unit will be bangles over an hour.

The function w(h) represents the hours per week spent on making the bracelets, so its unit will be hours over a week.

Now, we can define the unit of the composite function s(w(h)).

To find the unit of the composite function we follow these steps:-

s(w(h)),

= s(hours over a week) {replacing the function w(h) by its units},

= (bangles over an hour(hours over a week)) {replacing the function s(t) with its units},

= bangles over a week {Simplifying}.

Thus, the units for the composite function s(w(h)) is <u>bracelets over a week</u> when the function s(t) approximates how many bangles Margaret makes per hour and the function w(h) represents how many hours per week Margaret spends making the bracelets.

Learn more about the units of a composite function at

brainly.com/question/15056566

#SPJ4

4 0
2 years ago
Determine whether the improper integral converges or diverges, and find the value of each that converges.
Rus_ich [418]

Answer:

Diverges

Step-by-step explanation:

We can solve this by using integral by parts:

Let

u=lnx            dv=(1/x)dx

du=(1/x)dx    v=lnx

\int\limits {lnx/x} \, dx = (lnx)^2-\int\limits {lnx/x} \, dx

We can add

\int\limits {lnx/x} \, dx to both sides

\int\limits{lnx/x} \, dx = (1/2)\cdot{(lnx)^2}

We can evaluate the limit between 2 and infinity.

If x tends to infinity the limit will be infinity and therefore the integral diverges to ∞

6 0
2 years ago
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