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Zolol [24]
3 years ago
6

Consider the statement : Congruent triangles are always similar. Which of the following statements is an example of the statemen

t above? Select all that apply.
angles are the same, but sides are proportional to eachother.
Sides are the same size.
A dilation of a scale factor #1
Corresponding angles and corresponding sides are congruent.
A dilation of a scale factor of 1.
Mathematics
1 answer:
swat323 years ago
4 0

Answer:

Yes, the congruent triangles are always similar. The following statements are applicable

1) Angles are the same, but sides are proportional to eachother.

2) Sides are the same size.

3)Corresponding angles and corresponding sides are congruent.

Step-by-step explanation:

Yes, they are similar.

For two triangles to be similar, it is sufficient if two angles of one triangle are equal to two angles of the other triangle. Note that if two angles of one are equal to two angles of the other triangle, the third angles of the two triangles too will be equal.

If two triangles are congruent then all corresponding sides as well as corresponding angles of one triangle are equal to those of other triangles. This can happen in four cases

1)- when all sides of triangles are equal,

2) - if one side and two angles of one are equal to one side and two angles of other triangle.

3) - if two sides and included angle of one triangle are equal to two sides and included angle of other triangle

4)- if in two right angled triangles, one side and hypotenuse of one triangle are equal to one side and hypotenuse of other triangle.

Observe that for triangles to be similar, we just need all angles to be equal. But for triangles to be congruent, angles as well as sides should be equal.

Hence, while congruent triangles are similar, similar triangles may not be congruent ( but the converse is not true) .

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3 years ago
The velocity function of a car is given by v(t) = -3t2 + 18t + 9 m/s. Find the acceleration of the car three seconds before it c
Tpy6a [65]

The acceleration of the car three seconds before it comes to a stop is  -2.76 m/s² (Letter B).

<h3>Derivative</h3>

Derivative indicates the rate of change of a function with respect to a variable. Thus, when you derivate the position function, you find the velocity function. And, when you derivate the velocity function, you find the acceleration function.

In other words, the velocity function represents the first derivative of the position, meanwhile, the acceleration function represents the second derivative of the position.

For derivating an equation, you should apply the rule: (\frac{d}{dx} ) (x^n ) = nx^{n-1}. Example: x²= 2x

The car stops when the velocity is equal to zero. Thus, v(t) = -3t² + 18t + 9 =0. Therefore, you  should solve this quadratic function:

Δ=b²-4ac=18^2-4\left(-3\right)\cdot \:9=324+12*9=324+108=432

t_{1,\:2}=\frac{-18\pm \sqrt{432}}{2\left(-3\right)}\\ \\ t_{1,\:2}=\frac{-18\pm \sqrt{432}}{-6}

t_1=\frac{-18+12\sqrt{3}}{-6}=3-2\sqrt{3}

t_2=\frac{-18-12\sqrt{3}}{-6}=3+2\sqrt{3}

Like <em>t </em>is a positive number, you should use t_2. Thus, the value of t that you should apply to find the acceleration of the car three seconds before it comes to a stop is 2\sqrt{3}.

The acceleration can be found from the derivative of the velocity function. See below.

a(t)= -6t+18 , for t=2\sqrt{3}

a(t)= -6*2\sqrt{3}t+18

a(t)= -12\sqrt{3}t+18

a(t)=-2.76

Read more about the derivative here:

brainly.com/question/29257155

#SPJ1

8 0
1 year ago
Please help on this math problem!!!
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The formula circumference is

c = 2\pi \: r

r is radius

radius in this situation is 6

so your equation would be c=2π6

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Blurry picture, need a better one
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