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LekaFEV [45]
3 years ago
10

Help with Algebra Questions

Mathematics
1 answer:
kap26 [50]3 years ago
7 0
Here is a quadratic equation x^2 + 5x = 14
x^2 + 5x - 14 = 0 - Subtract 14 from both sides
(x + 7)(x - 2) = 0 - Factor
x + 7 = 0      x - 2 = 0  - Set each factor equal to 0
x = -7           x = 2  - solve each piece

If the constant is easy to find factors of then use the factoring method
If the constant is difficult and you have a graphing calculator, then graph
If no graphing calculator then use the quadratic formula
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You have 480 grams of a radioactive kind of samarium. If its half-life is 90 years,
lisov135 [29]

Answer:

120 grams will be left after 180 years.

Step-by-step explanation:

A radioactive half-life refers to the amount of time it takes for half of the original isotope to decay and its given by

                                             N(t)=N_0(\frac{1}{2})^\frac{t}{t_{1/2}}

where,

N(t) = quantity of the substance remaining

N_0 = initial quantity of the substance

t = time elapsed

t_{1/2} = half life of the substance

From the information given we know that:

  • The initial quantity is 480 g,
  • The half-life is 90 years,
  • 180 years is the time elapsed.

And we want to find how much will be left. For this we use the above formula.

N(t)=480\left(\frac{1}{2}\right)^{\frac{180}{90}}\\\\N(t)=480\left(\frac{1}{2}\right)^2\\\\N(t)=480\cdot \frac{1}{2^2}=120

120 grams will be left after 180 years.

3 0
3 years ago
Given that cos θ = –12∕13 and θ is in quadrant III, find csc θ.
Trava [24]

Answer:

A

Step-by-step explanation:

We are given:

\displaystyle \cos(\theta)=-\frac{12}{13},\,\theta\in\text{QIII}

Since cosine is the ratio of the adjacent side over the hypotenuse, this means that the opposite side is (we can ignore negatives for now):

o=\sqrt{13^2-12^2}=\sqrt{25}=5

So, the opposite side is 5, the adjacent side is 12, and the hypotenuse is 13.

And since θ is in QIII, sine/cosecant is negative, cosine/secant is negative, and tangent/cotangent is positive.

Cosecant is given by the hypotenuse over the opposite side. Thus:

\displaystyle \csc(\theta)=\frac{13}{5}

Since θ is in QIII, cosecant must be negative:

\displaystyle \csc(\theta)=-\frac{13}{5}

Our answer is A.

7 0
3 years ago
Read 2 more answers
Kiley can complete 3 math problems in 1 1/4 hours. How many can she complete in one hour
Sergio [31]
3/(5/4) = x/1
x = 12/5 = 2.4 Problems/h
7 0
4 years ago
Read 2 more answers
A machine stamps 3600 metal parts in 12 minutes. Find the unit rate in parts per minute.
Studentka2010 [4]

Answer:

300

Step-by-step explanation:

you just divide the number of parts by minutes. In this case, 3600/12=300. There's your answer

5 0
3 years ago
Sue buys a certain brand of cereal that costs $12 per box. Sue changes to a super-saving brand of the same size. The equation sh
masya89 [10]
A) To buy one box of the new cereal it will be y=8*1 so 8$. 12-8= 4. So the original brand is 4$ more.

B) 4*4=16$
3 0
3 years ago
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