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3 years ago

10

Given: , ∠DAC ≅ ∠BCA Prove: ∆ADC ≅ ∆CBA Look at the proof. Name the postulate you would use to prove the two triangles are congr

uent. SAS Postulate SSS Postulate AAA Postulate

1 answer:

Zolol [24]3 years ago

6 0

Answer:

SAS Postulate

Step-by-step explanation:

The contributors to the proof are listed in the left column. They consist of a congruent Side, a congruent Angle, and a congruent Side. The SAS Postulate is an appropriate choice.

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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

From a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. In how many dif

Romashka [77]

Answer:

11,880 different ways.

Step-by-step explanation:

We have been given that from a pool of 12 candidates, the offices of president, vice-president, secretary, and treasurer will be filled. We are asked to find the number of ways in which the offices can be filled.

We will use permutations for solve our given problem.

$^nP_r=\frac{n!}{(n-r)!}$ , where,

n = Number of total items,

r = Items being chosen at a time.

For our given scenario $n=12$ and $r=4$ .

$^{12}P_4=\frac{12!}{(12-4)!}$

$^{12}P_4=\frac{12!}{8!}$

$^{12}P_4=\frac{12*11*10*9*8!}{8!}$

$^{12}P_4=12*11*10*9$

$^{12}P_4=11,880$

Therefore, offices can be filled in 11,880 different ways.

3 0

3 years ago

Find the general solution of the following ODE: y' + 1/t y = 3 cos(2t), t > 0.

Margarita [4]

Answer:

y = 3sin2t/2 - 3cos2t/4t + C/t

Step-by-step explanation:

The differential equation y' + 1/t y = 3 cos(2t) is a first order differential equation in the form y'+p(t)y = q(t) with integrating factor I = e^∫p(t)dt

Comparing the standard form with the given differential equation.

p(t) = 1/t and q(t) = 3cos(2t)

I = e^∫1/tdt

I = e^ln(t)

I = t

The general solution for first a first order DE is expressed as;

y×I = ∫q(t)Idt + C where I is the integrating factor and C is the constant of integration.

yt = ∫t(3cos2t)dt

yt = 3∫t(cos2t)dt ...... 1

Integrating ∫t(cos2t)dt using integration by part.

Let u = t, dv = cos2tdt

du/dt = 1; du = dt

v = ∫(cos2t)dt

v = sin2t/2

∫t(cos2t)dt = t(sin2t/2) + ∫(sin2t)/2dt

= tsin2t/2 - cos2t/4 ..... 2

Substituting equation 2 into 1

yt = 3(tsin2t/2 - cos2t/4) + C

Divide through by t

y = 3sin2t/2 - 3cos2t/4t + C/t

Hence the general solution to the ODE is y = 3sin2t/2 - 3cos2t/4t + C/t

3 0

3 years ago

Ratchpad<br> Which line of reflection maps point Q at (1, 2) to point Q at (-2,-1)?

allochka39001 [22]

Idk...................................

7 0

3 years ago

What is y=(x+5)(x+4) in standard form?

Helen [10]

It is already in standard form.

4 0

2 years ago