finding which number supports the idea that the rational numbers are dense in the real numbers?

a. a fraction between ĉ and 3
b. an integer between -11 and -10
c. a whole number between 1 and 2
d. a terminating decimal between -3.14 and -3.15
o

Tom is making a punch that contains 80% cranberry juice and the rest ginger ale. the punch has 2 liters of ginger ale. part a: write an equation using one variable that can be used to find the total number of liters of cranberry juice and ginger ale in the punch. define the variable used in the equation and solve the equation. hint: 0.8x represents the number of liters of cranberry juice in the punch. (5 points) part b: how many liters of cranberry juice are present in the punch? show your work.

In trapezoid efgh, m∠hef=(4x2+16)∘ and m∠gfe=(5x2+12)∘. find the value of x so that efgh is isosceles.

Raj encoded a secret phrase using matrix multiplication. using a = 1, b = 2, c = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. the matrix representing the encoded text is . what is the secret phrase? determine the location of spaces after you decode the text. yummy is the corn the tomato is red the corn is yummy red is the tomato