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3 years ago

Marina is heating a solution in her chemistry lab. The temperature of the

Mathematics

1 answer:

vodka [1.7K]3 years ago

4 0

Answer:

Don’t really have a step by step explanation, I guessed and got (4,32)

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What is the sum of the first eight terms of the geometric series 2 + 6 + 18 + 54 + … ?

UkoKoshka [18]

2+6+18+54+162+486+1458+4375=6561

you multiply the previous number by three to find the next value

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3 years ago

3.) Simplify the expression by combining like

Evgesh-ka [11]

$45s^2-19-s^2+16\\=45s^2-s^2-19+16\\=s^2(45-1)-19+16\\=44s^2+(-19+16)\\=44s^2-3$

Hope that helps and hope you get better!

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2 years ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

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3 years ago

Does anyone want to be my fortnite girlfreind

Cloud [144]

STAN AND STREAM VICTON ATEEZ AND TXT NOW

7 0

3 years ago

Read 2 more answers

Point m is the midpoint of ab¯¯¯¯¯ . am=3x+3, and ab=8x−6. what is the length of am¯¯¯¯¯¯ ?

LuckyWell [14K]

As given m is a midpoint of ab. So am is half of ab.

So we can write

$am = \frac{ab}{2}$

As given am = 3x+3 , ab = 8x - 6.

So $3x+3 = \frac{8x - 6}{2}$

$3x+3 = \frac{2(4x - 3)}{2}$

$3x+3 = 4x - 3$

$3+3 = 4x - 3x
$

$6 = x$

So x = 6.

So length of am = 3x+3 = 3*6 + 3 = 21

5 0

3 years ago