Translating mathematical statements in english into logical expressions. info about consider the following statements in english. write a logical expression with the same meaning. the domain is the set of all real numbers. (a) there is a number whose cube is equal to 2. (b) the square of every number is at least 0. (c) there is a number that is equal to its square. (d) every number is less than or equal to its square.

See below

Step-by-step explanation:

(a) There is a number whose cube is equal to 2.

(b) The square of every number is at least 0.

(c) There is a number that is equal to its square.

(d) Every number is less than or equal to its square.

(By the way, this last statement is not true when 0 < x < 1)

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct