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loris [4]
3 years ago
9

Write 1/3 x^2 - 4x + 17 in vertex form

Mathematics
1 answer:
Svetradugi [14.3K]3 years ago
8 0

Answer:

f(x)=−4(x+ 41 ) 2 − 4 11

Explanation:

The given function is

f(x) = - 4 {x}^{2} - 2x - 3f(x)=−4x 2 −2x−3

To write the function is vertex form, we need to complete the square.

We first factor -4 to get:

f(x) = - 4 ({x}^{2} + \frac{1}{2} x) - 3f(x−4(x2 + 21 x)−3

Add and subtract the square of half the coefficient of x.

f(x) = - 4( {x}^{2} + \frac{1}{2} x + \frac{1}{16} ) - \frac{1}{4} - 3f(x)=−4(x 2 + 21 x+ 16 1 )− 41 −3

We factor the perfect square trinomial and simplify to get:

f(x) = - 4( {x + \frac{1}{4} )}^{2} - \frac{11}{4}f(x)=−4(x+ 41 ) 2 − 4 11

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Answer:

A and B are the answers on Edge.

Step-by-step explanation:

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3 years ago
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In a geometric series each term is 21% less than previous term what is the value of r for this geometric series
motikmotik
To get a number to decrease by 21% you multiply it by 0.79 (1-0.21)
r = 0.79
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3 years ago
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2x-4y=8 and 7x-3y=61 solve by substitution
Ratling [72]

Answer:

(10, 3)

Step-by-step explanation:

Solve by Substitution

2x − 4y = 8 and 7x − 3y = 61

Solve for x in the first equation.

x = 4 + 2y 7x − 3y = 61

Replace all occurrences of x with 4 + 2y in each e quation.

Replace all occurrences of x in 7x − 3y = 61 with 4 + 2y. 7 (4 + 2y) − 3y = 61

x = 4 + 2y

Simplify 7 (4 + 2y) − 3y.

28 + 11y = 61

x = 4 + 2y

Solve for y in the first equation.

Move all terms not containing y to the right side of the equation.

11y = 33

x = 4 + 2y

 Divide each term by 11 and simplify.

y = 3

x = 4 + 2y

 

Replace all occurrences of y with 3 in each equation.

Replace all occurrences of y in x = 4 + 2y with 3. x = 4 + 2 (3)

y = 3

Simplify 4 + 2 (3).

x = 10

y = 3

The solution to the system is the complete set of ordered pairs that are valid solutions.

(10, 3)

The result can be shown in multiple forms.

Point Form:

(10, 3)

Equation Form:

x = 10, y = 3

4 0
3 years ago
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2. Construct Arguments An ostrich runs 6 miles
Alekssandra [29.7K]

Answer:

<u>At a constant speed of 0.5 miles per minute, the ostrich can run 20 miles in 40 minutes. The unit rate is 0.5 miles per minute.</u>

Step-by-step explanation:

Distance run by the ostrich = 6 miles

Time the ostrich takes to run this distance = 12 minutes

Speed of the ostrich = Distance / Time

Speed of the ostrich = 6 miles / 12 minutes = 0.5 miles per minute

How far the  ostrich could run in 40 minutes?

If the ostrich run 0.5 miles per minute, this is the formula:

Speed of the ostrich * 40 minutes = Distance

0.5 miles/minute * 40 minutes = 20 miles (Minutes is simplified in the numerator and the denominator on the left side)

<u>At a constant speed of 0.5 miles per minute, the ostrich can run 20 miles in 40 minutes. The unit rate is 0.5 miles per minute.</u>

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At the end of the month mr copley has $1473.61 in is checking account his checkbook showed the following transaction if made mad
ycow [4]

Total balance in Mr. Copley at the end of the month = $1473.61.

Initial deposite =  $75 (not shown in his checkbook).

Let us assume his balance at the beginning of the month = x.

Total balance at the end of the month = The balance at the beginning of the month + total deposite.

$1473.61 = x + 75.

Subtracting 75 from both sides, we get

1473.61 -75 = x + 75 -75.

1398.61 = x.

Therefore, his balance at the beginning of the month was $1398.61.

7 0
3 years ago
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