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2 years ago

Which is NOT an example of the commutative property of addition?

Mathematics

1 answer:

sp2606 [1]2 years ago

3 0

Answer:

x - 13 = 13 - x

Step-by-step explanation:

The commutative property of addition is a+b=b+a

The third equation is the only one not following the rule. It states that a-b=b-a, whoich is not true.

For exaple, 2-1 is not equal to 1-2.

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The equation y 4.9t 2 3.5t 2.4 relates the height y in meters to the elapsed time t in seconds for a ball thrown downward at 3.5

tamaranim1 [39]

Answer:

$t \approx 0.43\,s$

Step-by-step explanation:

The vertical displacement function is $y(t) = -4.9\cdot t^{2}-3.5\cdot t + 2.4$ , where $y(t)$ is measured in meters and $t$ in seconds. Ball hits the ground when $y(t) = 0$ . That is:

$-4.9\cdot t^{2}-3.5\cdot t + 2.4 = 0$

Whose roots can be found by using the General Formula for Second-Order Polynomials:

$t_{1,2} = \frac{3.5\pm \sqrt{(-3.5)^{2}-4\cdot (-4.9)\cdot (2.4)} }{2\cdot (-4.9)}$

Solutions of this polynomial are:

$t_{1} \approx 0.43\,s,t_{2} \approx -1.14\,s$

Only the first root is physically consistent.

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3 years ago

Need some help please

denis23 [38]

The median of this problem is 84

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2 years ago

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Factor 15y2 + 10y − 40.

Vaselesa [24]

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2 years ago

Allison drew a triangle with 2 congruent sides and one obtuse angle. Which term accurately describe the triangle. Select all tha

Digiron [165]

Answer: B. Isoceles

Step-by-step explanation:

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3 years ago

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let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

$5^2+12^2=h^2$

Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

To calculate the sine and cosine of the sum

$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

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1 year ago