What do rigid motions preserve

True or False: A trapezoid is a polygon that has two bases, each with a different length.

elixir [45]

……….Yes it is true that trapezoid is a polygon that has two bases

8 0

2 years ago

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Rewrite this as a simplified fraction;<br> 0.7...=?

d1i1m1o1n [39]

Answer:

0.7777..... is 7/9

Step-by-step explanation:

use the calculator to solve this q

8 0

2 years ago

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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.

3 0

2 years ago

Please can someone answer this question! Worth 15 points

Westkost [7]

The statements that aer true or not or whatever

hmm, let's try te sencnarios
remember the commutative property of multiplication
ab=ba
so

what if they are both negative?
well, the negatives would cancel to leave with positive
the oposite would be both positive resulting in a positive

if they are differnt signs then result is negative
oposite would be still different signs so still negative
true statment

8 0

3 years ago

At the start of the experiment substance is measured to be 70°C, and by the end of the experiment its temperature is measured as

11Alexandr11 [23.1K]

9514 1404 393

Answer:

-130 °C

Step-by-step explanation:

The change is found by subtracting the start temperature from the finish temperature. It is ....

-60 °C - 70 °C = -130 °C

3 0

2 years ago