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UkoKoshka [18]
3 years ago
7

He breakdown of a sample of a chemical compound is represented by the function p(t) 300(0.5)t , where p(t) represents the number

of milligrams of the substance and t represents the time, in years. in the function p(t), explain what 0.5 and 300 represent
Mathematics
1 answer:
Inessa05 [86]3 years ago
8 0
300 represents the initial amount of the substance, the amount present at t=0.

0.5 is the fraction of substance remaining at the end of each year. The fact that this number is 1/2 indicates the half-life of the substance is 1 year.
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Without drawing the graph of the equation answer the question. How many points does the given equation have in common with the x
Alexandra [31]

Answer:

There are two points common with the x-axis

The vertex is under the x-axis by 24 units at x = 6

Step-by-step explanation:

* For the quadratic equation y = ax² + bx + c

- The roots of the equation are the intersection point between

  the equation and the x-axis ⇒ y = 0

- To find these roots we factorize the equation into two factors

  and equate each factor with zero

- The graph of the quadratic equation is called parabola,

 the parabola has vertex point. If the vertex point is (h , k)

∴ h = -b/2a, where b is the coefficient of x and is the coefficient of x²

∴ k = y where x = h

* Lets solve the problem

∵ y = x² - 12x + 12

- The formula to find the values of x when y = 0 is

 x=\frac{-b+\sqrt{b^{2}-4ac}}{2a},x=\frac{-b-\sqrt{b^{2}-4ac}}{2a}

∵ a = 1 , b = -12 , c = 12

∴ x=\frac{-(-12)+\sqrt{(-12)^{2}-4(1)(12)}}{2(1)}=\frac{12+\sqrt{144-48}}{2}

∴ x=\frac{12+\sqrt{96}}{2}=\frac{12+4\sqrt{6}}{2}=6+2\sqrt{6}

∴ The two roots are 6 + 2√6 and 6 - 2√6

* There are two points common with the x-axis

* Lets calculate the vertex

∵ h = -b/2a

∵ b = -12 and a = 1

∴ h =-(-12)/2(1) = 12/2 = 6

∴ k = (6²) - 12(6) + 12 = 36 - 72 + 12 = -24

∴ The vertex is (6 , -24)

* That means the vertex is under the x-axis by 24 units at x = 6

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^DEF and ^RSQ are shown in the diagram below
lakkis [162]

Answer:

53.3 degrees

Step-by-step explanation:

∆DEF and ∆RSQ are similar. We know this, because the ratio of their corresponding sides are equal. That is:

DE corresponds to RS

EF corresponds to SQ

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Also <D corresponds to <R, <E corresponds to <S, and <F corresponds to <Q.

The ratio of their corresponding sides = DE/RS = 6/3 = 2

EG/SQ = 8/4 = 2

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Since the ratio of their corresponding sides are equal, it means ∆DEF and ∆RSQ are similar.

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Since <F corresponds to <Q, therefore,

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Answer:

See Below

Step-by-step explanation

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You have the answer

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