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aliina [53]
2 years ago
12

[*Please Help me with this Question, Thank you & Please!*]

Mathematics
1 answer:
Aliun [14]2 years ago
3 0

Answer:

x=3

Step-by-step explanation:

Since both triangles are similiar, this means they can have different sized sides, but they are just scaled versions of each other. This also means that no matter what sides they have, their angles are going to be the exact same

Knowing this, it helps to draw them out side by side so you can match them up easier. Both of them have a 90 degree angle, and more specifically they are 45-45-90 triangles (45-45-90 is a special right triangle). You can point this out since they give us a 90 degree angle and two angles that are congruent in the same triangle. In order for that to work, they HAVE to be 45-45-90

With this, we can find out what x equals. Since the two angles markings line up with the two side angles in the other triangle, we know that they are equal to each other.

we can use the equation 15x = 45, since 45 is what the side angle should equal.

now, we just divide 45 by 15, and we should get 3

so x = 3!

I hope this helps :)

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A prism is dilated by a factor of 1.5. How many times larger is the volume of the resulting prism than the volume of the origina
Temka [501]

Answer:

The answer is 3.375

r = (1.5)^3

= 3.375

4 0
2 years ago
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A single-elimination basketball tournament starts with 64 teams. The teams compete in pairings until there is 1 winner. Which re
notka56 [123]

Answer:

a(n-1)(0.5)

Step-by-step explanation:

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3 years ago
can someone show me how to find the general solution of the differential equations? really need to know how to do it for the upc
mariarad [96]
The first equation is linear:

x\dfrac{\mathrm dy}{\mathrm dx}-y=x^2\sin x

Divide through by x^2 to get

\dfrac1x\dfrac{\mathrm dy}{\mathrm dx}-\dfrac1{x^2}y=\sin x

and notice that the left hand side can be consolidated as a derivative of a product. After doing so, you can integrate both sides and solve for y.

\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1xy\right]=\sin x
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\implies y=-x\cos x+Cx

- - -

The second equation is also linear:

x^2y'+x(x+2)y=e^x

Multiply both sides by e^x to get

x^2e^xy'+x(x+2)e^xy=e^{2x}

and recall that (x^2e^x)'=2xe^x+x^2e^x=x(x+2)e^x, so we can write

(x^2e^xy)'=e^{2x}
\implies x^2e^xy=\displaystyle\int e^{2x}\,\mathrm dx=\frac12e^{2x}+C
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- - -

Yet another linear ODE:

\cos x\dfrac{\mathrm dy}{\mathrm dx}+\sin x\,y=1

Divide through by \cos^2x, giving

\dfrac1{\cos x}\dfrac{\mathrm dy}{\mathrm dx}+\dfrac{\sin x}{\cos^2x}y=\dfrac1{\cos^2x}
\sec x\dfrac{\mathrm dy}{\mathrm dx}+\sec x\tan x\,y=\sec^2x
\dfrac{\mathrm d}{\mathrm dx}[\sec x\,y]=\sec^2x
\implies\sec x\,y=\displaystyle\int\sec^2x\,\mathrm dx=\tan x+C
\implies y=\cos x\tan x+C\cos x
y=\sin x+C\cos x

- - -

In case the steps where we multiply or divide through by a certain factor weren't clear enough, those steps follow from the procedure for finding an integrating factor. We start with the linear equation

a(x)y'(x)+b(x)y(x)=c(x)

then rewrite it as

y'(x)=\dfrac{b(x)}{a(x)}y(x)=\dfrac{c(x)}{a(x)}\iff y'(x)+P(x)y(x)=Q(x)

The integrating factor is a function \mu(x) such that

\mu(x)y'(x)+\mu(x)P(x)y(x)=(\mu(x)y(x))'

which requires that

\mu(x)P(x)=\mu'(x)

This is a separable ODE, so solving for \mu we have

\mu(x)P(x)=\dfrac{\mathrm d\mu(x)}{\mathrm dx}\iff\dfrac{\mathrm d\mu(x)}{\mu(x)}=P(x)\,\mathrm dx
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\implies\mu(x)=\exp\left(\displaystyle\int P(x)\,\mathrm dx\right)

and so on.
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3 years ago
Which method correctly solves the equation using the distributive property? Negative 0. 2 (x minus 4) = negative 1. 7 Negative 0
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The method which is used to solve the provided equation using the distributive property is,

\rm x = 4 + 8.5 = 12.5

<h3>What is distributive property?</h3>

The distributive property is to make something easier to do or understand and to make something less complicated.

The given expression is \rm - 0.2(x-4) = -1.7.

The expression can be written as

\rm 0.2(x-4) = 1.7

Divide both sides by 0.2

\rm x-4 = \dfrac{1.7}{0.2} = 8.5

Add 4 both sides, we have

\rm x = 4 + 8.5 = 12.5

Thus, the value of x is 12.5.

More about the distributive property link is given below.

brainly.com/question/13130806

4 0
2 years ago
The equation v=√2.5 represents the maximum velocity that a car can travel safely on a unbanked curve when v is the maximum veloc
Sergeeva-Olga [200]

Answer:

41.1 feet to the nearest tenth.

Step-by-step explanation:

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At 65 mph the radius of the turn r

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= 41.1 feet.

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2 years ago
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