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3 years ago

The sum of two numbers is 21 The second number is six times the first number

Mathematics

1 answer:

Snowcat [4.5K]3 years ago

5 0

Answer:

3+18=21

Step-by-step explanation:

first see the second number

let us assume as x & y

3+ (3×6)= 21

3+18=21

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Solve these equations. 1. -16 = v - 14 2. -2n = -22 3. 25 = b + 7

leonid [27]

1) -16 = v - 14

Add 14 to both sides.

v = -2

2) -2n = -22

Divide both sides by -2.

n = 11

3) 25 = b + 7

Subtract 7 from both sides.

b = 18

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3 years ago

Find a parabola with equation y = ax2 + bx + c that has slope 5 at x = 1, slope −11 at x = −1, and passes through the point (2,

azamat

By "slope" I assume you mean slope of the tangent line to the parabola.

For any given value of x, the slope of the tangent to the parabola is equal to the derivative of y :

$y=ax^2+bx+c\implies y'=2ax+b$

The slope at x = 1 is 5:

$2a+b=5$

The slope at x = -1 is -11:

$-2a+b=-11$

We can already solve for a and b :

$\begin{cases}2a+b=5\\-2a+b=-11\end{cases}\implies 2b=-6\implies b=-3$

$2a-3=5\implies 2a=8\implies a=4$

Finally, the parabola passes through the point (2, 18); that is, the quadratic takes on a value of 18 when x = 2:

$4a+2b+c=18\implies2(2a+b)+c=10+c=18\implies c=8$

So the parabola has equation

$\boxed{y=4x^2-3x+8}$

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3 years ago

For which of the following would similar triangles and trigonometry be useful for measuring?

Helen [10]

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Mice21 [21]

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