Which value must be added to the expression x2 + x to make it a perfect-square trinomial? a. 1/4b. 1/2c. 1d. 4

x²+x given, we have to make it a perfect square.

To make it a perfect square first we have to check the x term. We have to check co-efficient of x. Here only x given, that means there is 1 with it. As x means 1*x which is also x. So, co-efficient of x is 1 here.

We will have to divide co-efficient of x by 2 and have to add the square with the expression to make it a perfect square.

As co-efficient of x is 1, so 1 divided by 2 is 1/2.

We are adding the square of 1/2 with the expression.

x²+x+(1/2)²

We know that (a+b)² = a²+2ab+b²

So here x²+2×(x)×(1/2)+(1/2)² = (x+1/2)², as 2×(x)×(1/2) = x

So by adding (1/2)² with it, we are getting a perfect square here.

(1/2)² =1/4

So, we have to add 1/4 with this expression to make it a perfect square.

the inequality is:

250c+180g≥950

step-by-step explanation:

let c denotes the number of days in a week   miyoko worked as a cryptographer.

and g denotes the number of days in a week she works as a geologist.

now we are given that she earns $250 for every day she works as a cryptographer,and earns $180 for every day she works as a geologist.

now miyoko's goal is to earn more than $950 this week.

hence, the inequality could be represented as:

250c+180g≥950