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sattari [20]
3 years ago
12

How many elements does each of these sets have where a and b are distinct elements?

Mathematics
1 answer:
harina [27]3 years ago
3 0

Answer:

a) 8

b) 16

Step-by-step explanation:

a) We note that the first set contains three elements: a, b, and {a,b}.

The power set of {a, b, {a,b}} contains all possible elements of {a, b, {a,b}}.

For each element, we have 2 options: the element is either in the subset or the element is not in the subsets. The number of possible subsets is then equal to product the of the number of options for each element.

                                    P({a,b,{a,b}}) = 2 * 2 * 2 = 2 ^ 3 = 8

b) We note that the second set contains four elements: ?, a, {a} and {{a}}.

The power set of {?, a, {a}, {{a}}} contains all possible elements of {?, a, {a}, {{a}}}.

For each element, we have 2 options: the element is either in the subset or the element is not in the subsets. The number of possible subsets is then equal to product the of the number of options for each element.

                              P({?, a, {a}, {{a}}}) = 2 * 2 * 2 * 2 = 2 ^ 4 = 16

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\begin{aligned} &A = 7x^2-3x+10 \\\\ &B = -4x^2+6x-4 \end{aligned} ​ A=7x 2 −3x+10 B=−4x 2 +6x−4 ​ A-B=A−B=A, minus, B,
fgiga [73]

Answer:

<h2>A-B = 11x²-9x+14</h2>

Step-by-step explanation:

Given the polynomial functions A = 7x^2-3x+10 and B = -4x^2+6x-4, we are to find the value of A - B.

A-B =  7x²-3x+10 - ( -4x²+6x-4)

open the parenthesis

A-B = 7x²-3x+10 + 4x²-6x+4

collect the like terms

A-B  = 7x² + 4x²-3x-6x+10+4

A-B = 11x²-9x+14

<em>Hence the difference between both quadratic equation in standard form is 11x²-9x+14</em>

4 0
3 years ago
Describe the direction of the parabola and determine the y-intercept and zeros. f(x) = 3x^2 + 4x +16
miv72 [106K]
For y=ax²+bx+c
if a>0 then it opens up
if a<0 then it opens down

hmm, y intercept is where x=0
x intercept is where y=0


so

f(x)=3x²+4x+16
3>0 so opens up
y intercep
x=0
3(0)²+4(0)+16
16
y intercept is y=16

x intercept
0=f(x)=3x²+4x+16
there are no real solutions since the discriminant is negative
no x intercepts or no zeroes


so
opens up
y intercept of 16
no zeroes
8 0
3 years ago
Judy plans to serve cheese to guests at a dinner party. She estimates
Mkey [24]

Answer: la primers poor que lo digo

Step-by-step explanation:

8 0
3 years ago
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Población de alces. Se introducen cíen alces en una reserva zoológica, cada uno de un año de edad. El número N(t) de animales vi
frutty [35]

Answer:

El número de animales vivos después de 1, 5 y 10 años es 90, 60 y 35 respectivamente.

Step-by-step explanation:

Sabes que el número N(t) de animales vivos después de t años se predice mediante N(t) = 100*0.9^{t}

Para estimar el número de animales vivos después de, por ejemplo, 1 año debes simplemente reemplazar el tiempo t por el tiempo correspondiente, en este caso 1 año:

N(1) = 100*0.9^{1}

Resolviendo:

N(1) = 100*0.9^{1}= 100*0.9= 90

De manera similar, podes estimar el número de animales vivos después de 5 y 10 años. Esto es, reemplazas t por 5 años:

N(5) = 100*0.9^{5}= 100*0.59049= 59.049≅ 60

y t por 10 años:

N(10) = 100*0.9^{10}= 100*0.3487= 34.86 ≅ 35

<u><em>El número de animales vivos después de 1, 5 y 10 años es 90, 60 y 35 respectivamente.</em></u>

6 0
3 years ago
Please Help Me:!!!!!!!!!!
AleksandrR [38]

Answer:

  • reflection over the x-axis
  • translation down 8 units

Step-by-step explanation:

g(x) = -f(x) -8

The function is multiplied by -1, which reflects it over the x-axis. -8 is added to each function value, which translates it down 8 units.

The transformations are reflection over y=0 and translation down 8 units.

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The original flattened-S shaped curve is reversed top-to-bottom and is moved down. Attached is the original (red) and the transformed function (blue).

Because this is an odd function, reversing it top-to-bottom has the same appearance as reversing it left-to-right.

6 0
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