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astraxan [27]
3 years ago
11

The sum of the angle measures of any triangle is

Mathematics
1 answer:
romanna [79]3 years ago
3 0
Let's say that y is the unknown
180=2x+3+5x+1+y
180=7x+4+y
180-7x-4=y
176-7x=y=third angle
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Point M is the midpoint of AB¯¯¯¯¯¯¯¯. Find the length of AB¯¯¯¯¯¯¯¯.
alina1380 [7]

Answer:

AB = 142

Step-by-step explanation:

If M is the midpoint, then AM = MB

6x+5 = 7x -6

Subtract 6x from each side

6x-6x+5 = 7x-6x -6

5 = x-6

Add 6 to each side

5+6 = x-6+6

11=x

We want to find AB

AB = 6x+5+7x-6

AB = 13x -1

     = 13(11) -1

     =143-1

     = 142

6 0
3 years ago
Help with 30 please. thanks.​
Svet_ta [14]

Answer:

See Below.

Step-by-step explanation:

We have the equation:

\displaystyle  y = \left(3e^{2x}-4x+1\right)^{{}^1\! / \! {}_2}

And we want to show that:

\displaystyle y \frac{d^2y }{dx^2} + \left(\frac{dy}{dx}\right) ^2 = 6e^{2x}

Instead of differentiating directly, we can first square both sides:

\displaystyle y^2 = 3e^{2x} -4x + 1

We can find the first derivative through implicit differentiation:

\displaystyle 2y \frac{dy}{dx}  = 6e^{2x} -4

Hence:

\displaystyle \frac{dy}{dx} = \frac{3e^{2x} -2}{y}

And we can find the second derivative by using the quotient rule:

\displaystyle \begin{aligned}\frac{d^2y}{dx^2} & = \frac{(3e^{2x}-2)'(y)-(3e^{2x}-2)(y)'}{(y)^2}\\ \\ &= \frac{6ye^{2x}-\left(3e^{2x}-2\right)\left(\dfrac{dy}{dx}\right)}{y^2} \\ \\ &=\frac{6ye^{2x} -\left(3e^{2x} -2\right)\left(\dfrac{3e^{2x}-2}{y}\right)}{y^2}\\ \\ &=\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\end{aligned}

Substitute:

\displaystyle y\left(\frac{6y^2e^{2x}-\left(3e^{2x}-2\right)^2}{y^3}\right) + \left(\frac{3e^{2x}-2}{y}\right)^2 =6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}- \left(3e^{2x} -2\right)^2}{y^2} + \frac{\left(3e^{2x}-2\right)^2}{y^2}= 6e^{2x}

Combine fractions:

\displaystyle \frac{\left(6y^2e^{2x}-\left(3e^{2x} - 2\right)^2\right) +\left(\left(3e^{2x}-2\right)^2\right)}{y^2} = 6e^{2x}

Simplify:

\displaystyle \frac{6y^2e^{2x}}{y^2} = 6e^{2x}

Simplify:

6e^{2x} \stackrel{\checkmark}{=} 6e^{2x}

Q.E.D.

6 0
2 years ago
A wire was bent to make a triangular clothes hanger. If the lengths of the sides are 38 cm, 25 cm, 25 cm. Find the minimum lengt
erastovalidia [21]

Answer:

88cm

Step-by-step explanation:

38+25+25=88

6 0
2 years ago
Solve-3.5+4.2=?solve
cluponka [151]
7.7 the answer in 7.7 because 2+5 = 7 and 3+4= 11
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2 years ago
Read 2 more answers
1 3.1.5 Quiz: Comparing Functions
Burka [1]

Answer:

the statements are not written here .

7 0
2 years ago
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