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Type the correct answer in each box. Consider this expression.

romanna [79]

Answer:

The expression is equivalent to $-4\cdot x^{2}+3\cdot x -5$ .

Step-by-step explanation:

In this exercise we must transform $-4\cdot x^{2}+2\cdot x -5\cdot (1+x)$ into its standard form, that is a polynomial of the form:

$y = a\cdot x^{2} + b\cdot x + c$ (1)

Where:

$y$ - Dependent variable.

$x$ - Independent variable.

$a$ , $b$ , $c$ - Coefficients.

Let $y = -4\cdot x^{2}+2\cdot x -5\cdot (1+x)$ , now we proceed to convert it into its standard form:

1) $-4\cdot x^{2}+2\cdot x -5\cdot (1+x)$ Given

2) $(-4)\cdot x^{2}+2\cdot x + (-5)\cdot (1+x)$ $(-a)\cdot b = -a\cdot b$

3) $(-4)\cdot x^{2}+2\cdot x +(-5)\cdot 1 +(-5)\cdot x$ Distributive property

4) $(-4)\cdot x^{2}+[5+(-2)]\cdot x -5$ $(-a)\cdot b = -a\cdot b$ /Commutative and distributive properties

5) $-4\cdot x^{2}+3\cdot x -5$ $(-a)\cdot b = -a\cdot b$ /Definition of subtraction/Result

The expression is equivalent to $-4\cdot x^{2}+3\cdot x -5$ .

6 0

3 years ago

4/5(2x+5)−4=1<br> 4/5 is a fraction

muminat

Answer:

x = $\frac{5}{8}$

3 0

3 years ago

Read 2 more answers

If x=5,y=4, and h=5, then what is the area of the parallelogram .

WITCHER [35]

20 is the area as long as y is the measure of the base

3 0

3 years ago

Roulette is a very popular game in many American casinos. In roulette, a ball spins on a circular wheel that is divided into 38

ludmilkaskok [199]

Answer:

a. P(AUB) = 0.74

b. P(A∩C) = 0.24

c. P(BUC) = 0.71

d. P(Bc) = 0.55

e. P(A∩B∩C) = 0.11

Step-by-step explanation:

n(U) = Total number of elements in the set = number of elements in the universal set = 38

A: (Outcome is an odd number (00 and 0 are considered neither odd nor even)]

An odd number referred to any integer, that is not a fraction, which is not possible to be divided exactly by 2. Therefore, we have:

A: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35

B: 2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35

C: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18

a. Calculate the probability of AUB

AUB picks not more than one each of the elements in both A and B without repetition. Therefore, we have:

AUB = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 33, 35

n(AUB) = number of elements in AUB = 28

P(AUB) = probability of AUB = n(AUB) / n(U) = 28 / 38 = 0.736842105263158 = 0.74

b. Calculate the probability of A ∩ C

A∩C picks only the elements that are common to both A and C. Therefore, we have:

A∩C: 1, 3, 5, 7, 9, 11, 13, 15, 17

n(A∩C) = number of elements in A∩C = 9

P(A∩C) = probability of A∩C = n(A∩C) / n(U) = 9 / 38 = 0.236842105263158 = 0.24

c. Calculate the probability of BUC

BUC picks not more than one each of the elements in both B and C without repetition. Therefore, we have:

BUC: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35

n(BUC) = number of elements in BUC = 27

P(BUC) = probability of A∩C = n(BUC) / n(U) = 27 / 38 = 0.710526315789474 = 0.71

d. Calculate the probability of Bc

Bc indicates B component it represents all the elements in the universal set excluding the elements in B. Therefore, we have:

Bc: 00, 0, 1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36

n(Bc) = number of elements in Bc = 20

P(Bc) = probability of Bc = n(Bc) / n(U) = 20 / 38 = 0.526315789473684 = 0.55

e. Calculate the probability of A∩B∩C

A∩B∩C picks only the elements that are common to A, B and C. Therefore, we have:

A∩B∩C: 11, 13, 15, 17

n(Bc) = number of elements in A∩B∩C = 4

P(A∩B∩C) = probability of A∩B∩C = n(A∩B∩C) / n(U) = 4 / 38 = 0.105263157894737 = 0.11

Note: All the answers are rounded to 2 decimal places.

7 0

3 years ago

What expressions is equivalent to -3 3/7 + 2 5/7

bonufazy [111]

Answer:

-5/7

Step-by-step explanation:

-3 3/7 + 2 5/7

-3 - 3/7 + 2 + 5/7

-3 + 2 + 5/7 - 3/7

-1 + 2/7

-5/7

5 0

3 years ago