Consider the functions f(x)=4x+15 and g(x)=x^2-x+6. at what positive integer value of x does the quadratic function, g(x), begin to exceed the linear function, f(x)?

At x=7

Step-by-step explanation:

Let's evaluate!!

When x = 6

f(6) = 4*6 + 15 = 24 + 15 = 39

g(6) = 6² - 6 + 6 = 36

When x = 7

f(7) = 4*7 + 15 = 28 + 15 = 43

g(7) = 7² - 7 + 6 = 48

Check!! When x=7, g(x) excees f(x).

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt