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Paladinen [302]
3 years ago
11

Which expressions are equivalent to 12r - 5?

Mathematics
1 answer:
melamori03 [73]3 years ago
6 0

Answer:

Any real number can substitute for <em>r</em>, because there is not equal sign. As for expressions equivalent to 12r - 5, here are some:

3(4)<em>r</em> - 5

(6 + 6)<em>r</em> - (2^2 + 1)

(24 * 1/2)<em>r </em>+ (-5)

The point is, there are countless expressions to represent 12r - 5

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Find an equation in standard form of the parabola passing through these points: (0,-6),(-1,-12),(3,0)
Elan Coil [88]
One form of the equation of a parabola is
y = ax² + bx + c

The curve passes through (0,-6), (-1,-12) and (3,0). Therefore
c = - 6                       (1)
a - b + c = -12            (2)
9a + 3b + c = 0         (3)

Substitute (1) into (2) and into (3).
a - b -6 = -12
a - b = -6                  (4)
9a + 3b - 6 = 0
9a + 3b = 6              (5)

Substitute a = b - 6 from (4) into (5).
9(b - 6) + 3b = 6
12b - 54 = 6
12b = 60
b = 5
a = b - 6 = -1

The equation is
y = -x² + 5x - 6 

Let us use completing the square to write the equation in standard form for a parabola.
y = -[x² - 5x] - 6
   = -[ (x - 2.5)² - 2.5²] - 6
   = -(x - 2.5)² + 6.25 - 6

y = -(x - 2.5)² + 0.25
This is the standdard form of the equation for the parabola.
The vertex us at (2.5, 0.25).
The axis of symmetry is x = 2.5
Because the leading coefficient is -1 (negative), the curve opens downward.
The graph is shown below.

Answer: y = -(x - 2.5)² + 0.25

3 0
3 years ago
If f(x)=4x+10, find f(2)
Genrish500 [490]

Answer:

18

Step-by-step explanation:

f(2)=4x+10

f=(4)(2)+10

f=8+10

f=18

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What is the distance between the points (–3, 5) and (2, –6)?
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the answer is C.12.1 units
4 0
3 years ago
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The sale price of an item is $160 after a 20% off discount. What was the original price of the item?
bulgar [2K]

Answer:

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Step-by-step explanation:

160/80 is 2. 2 times 100 is 200

6 0
3 years ago
Do anyone know please and thank u
Varvara68 [4.7K]

Answer:

The correct answer is A

6 0
3 years ago
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