A function is a relation in which each element in the input is mapped to how many elements in the output?

Kara and Lindsey both hike in separate directions from their campsite, with Kara hiking straight to the east and Lindsey hiking

xz_007 [3.2K]

Answer:

A. f(x)=x^2+x+0.25

Step-by-step explanation:

If x represents Lindsey's distance at 2:00 PM, then 2x represents Kara's distance at 2:00 PM because she walked twice as far as Lindsey. Then adding on the values we got for 2:30 PM, we get that Kara walked a distance of 2x+1 and Lindsey walked a distance of x+0.5 at the time of 2:30 PM. Now, we know that they have formed a right triangle because we are given the directions they walked in; east and north. This allows us to use a formula for the area of a right triangle: 1/2(L x W). Plugging in our values, we get...

1/2(2x+1)(x+0.5)

which simplifies to...

1/2(2x^2+2x+0.5)

which further simplifies to...

x^2+x+0.25

which is our answer.

4 0

2 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

3 years ago

Read 2 more answers

Solve for the value of z.

Yuki888 [10]

z=18

3z+4+2z-4+90=180

5z+4-4+90=180

5z+90=180

5z=90

z=18

4 0

2 years ago

Joe's new car travel 418 miles on 16 gallons of gas find the unit rate in miles per gallon show your work I will Mark brainiest

seraphim [82]

To find the unit rate, divide total miles by number of gallons:

418 miles / 16 gallons = 26.125 miles per gallon
Round the answer as needed.

5 0

2 years ago

Last year at a certain high school, there were 100 boys on the honor roll and 60 girls on the honor roll. This year, the number

defon

Answer:

last year 100 boys and 60 girls, for a total of 160.

this year, 120 boys and 75 girls, for a total of 195.

35 more than 160 is a 21.8% increase

4 0

2 years ago