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3 years ago

The temperature is 60°F. The temperature will decrease by 3°F each hour. Let

Mathematics

1 answer:

ohaa [14]3 years ago

6 0

Answer:

approximately 9 hours

Step-by-step explanation:

Just take three out of 60 untill you reach the closest thing to 32

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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

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<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

4 years ago

Read 2 more answers

A red ballon starts at 7 meters off the ground and rises at 3 meters per second. A ballon starts at 12 meters off the ground and

GrogVix [38]

Let x be the no. of seconds it takes for the balloons to be at the same height.
7+3x = 12+2x
Deduct both sides by 2x.
7+x = 12
Deduct both sides by 7.
x = 5
Ans: It will take 5 seconds for the balloons to be at the same height.

4 0

3 years ago

The cost of a car rental is twenty-five dollars a day plus ten cents a mile. What is the total cost, in dollars, if the car is r

Fudgin [204]

Answer:

The total cost is D) $141

Step-by-step explanation:

To solve we can use the equation: $y=25d+0.10m$

d= number of days m= number of miles

We know both of these values so we can plug them in and solve.

y= 25(3) + 0.10(660)

y= 75 + 66

y = 141

4 0

3 years ago

WRITE Math Explain how percents, fractions, and

sineoko [7]

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4 0

4 years ago

Convert the measurement as indicated. 5.2 mi to feet

FrozenT [24]

It would be 27,456 feet

7 0

3 years ago

Read 2 more answers