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3 years ago

Determine the sum: (14abc2 + 12a2b + 16b2c) + (−3abc2 + 2b2c).

Mathematics

1 answer:

Alenkinab [10]3 years ago

4 0

The answer is 11abc^2 + 12a^2b + 18b^2c because:
14abc^2-3abc^2 is 11abc^2
12a^2b + 0 = 12a^2b
16b^2c +2b^2c = 18b^c

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3 years ago

The parabola with equation $y=ax^2+bx+c$ is graphed below:

Mashutka [201]

Answer:

$m-n=2$

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

$f(x)=a(x-h)^2+k$

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

$f(x)=a(x-2)^2-4$

Now, we need to determine a.

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$12=a(2)^2-4$

Add 4 to both sides:

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Square:

$16=4a$

Solve:

$a=4$

Thererfore, the value of a is 4.

So, our function is:

$f(x)=4(x-2)^2-4$

Now, let’s find our roots. Set the equation to 0 and solve for x:

$0=4(x-2)^2-4$

$4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1$

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3 years ago

Read 2 more answers

Note: Figure is not drawn to scale. If m1 + m2 = 134°, what is m3? A. 138° B. 49° C. 46° D. 136°

NemiM [27]

Answer:

Measure of angle 3: C (46 degrees)

Step-by-step explanation:

As there is no attachment, I will assume the question is in reference to a triangle. Knowing that a triangle contains 3 angles the answer can be retrieved through simple steps:

m∠1 + m∠2 + m∠3 = 180 degrees, by Sum of Angles in Triangle Theorem, <em>thus;</em>

Through substitution + algebra:

134 + m∠3 = 180,

m∠3 = 46 degrees

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