The sum of two numbers is thirty seven. using x to represent the larger of two numbers, translate “the difference between nine more than twice the larger number and the sum of the smaller number and three” into a variable expression

Two numbers = 37

Larger number is x, so the smaller number is 37 - x:

x + (37 - x) = 37

“The difference” is subtraction, so we are subtracting the smaller and larger number.

“Nine more than twice the larger number” looks like 9 + 2x, and “the sum of the smaller number and three” looks like (37 - x) + 3. Because this is subtraction, we would write (9 + 2x) - (37 - x) + 3. First, distribute the negative sign:

-(37 - x) = -37 + x

We then simplify:

9 + 2x - 37 + x + 3 (subtract 3)

9 + 2x - 34 + x

-25 + 2x + x (subtract 8 and 34 then add 2x and x)

-25 + 3x

m a t h w a y. c o m

step-by-step explanation:

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in and ;

, as these are radii of our given circle.

therefore, by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

now let us substitute x=17 in the expression for the length of be.

therefore, length of be will be 27 units and option c is the correct choice.