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pickupchik [31]
4 years ago
14

Which statement follows from the given theorem? Theorem: The diagonal of a parallelogram divides it into two congruent triangles

.
Mathematics
1 answer:
Ivenika [448]4 years ago
8 0

Answer:

SSS

Step-by-step explanation:

the dividing line would give the triangles the same length for one side, the side it divided, and then it says the triangles are congruent, meaning they are both the same triangle.

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X2 -5<br> ———<br> X-5<br><br> Is x-5 equal to the rational expression
ira [324]

Step-by-step explanation:

no it doesn't equal

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6 0
3 years ago
Find the equation of the tangent line to the curve when x has the given value.
Leviafan [203]

Answer:

14) The equation of the tangent line to the curve f(x)=-2-x^2 at x = -1 is y=2x-1

15) The rate of learning at the end of eight hours of instruction is w'(8) = 5 \frac{items}{hour}

Step-by-step explanation:

14) To find the equation of a tangent line to a curve at an indicated point you must:

1. Find the first derivative of f(x)

f(x)=-2-x^2\\\\\frac{d}{dx} f(x)=\frac{d}{dx}(-2-x^2)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dx} f(x)=\frac{d}{dx}\left(-2\right)-\frac{d}{dx}\left(x^2\right)\\\\f'(x)=-2x

2. Plug x value of the indicated point, x = -1, into f '(x) to find the slope at x.

f'(-1)=-2(-1)=2

3. Plug x value into f(x) to find the y coordinate of the tangent point

f(-1)=-2-(-1)^2=-3

4. Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line

y-y_1=m(x-x_1)\\y+3=2(x+1)\\y=2x-1

5. Graph your function and the equation of the tangent line to check the results.

15) To find the rate of learning at the end of eight hours of instruction you must:

1. Find the first derivative of f(x)

w(t)=15\sqrt[3]{t^2} \\\\\frac{d}{dt}w= \frac{d}{dt}(15\sqrt[3]{t^2})\\\\w'(t)=15\frac{d}{dt}\left(\sqrt[3]{t^2}\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\\\f=\sqrt[3]{u},\:\:u=\left(t^2\right)\\\\w'(t)=15\frac{d}{du}\left(\sqrt[3]{u}\right)\frac{d}{dt}\left(t^2\right)\\\\w'(t)=15\cdot \frac{1}{3u^{\frac{2}{3}}}\cdot \:2t\\\\\mathrm{Substitute\:back}\:u=\left(t^2\right)

w'(t)=15\cdot \frac{1}{3(t^2)^{\frac{2}{3}}}\cdot \:2t\\w'(t)=\frac{10t}{\left(t^2\right)^{\frac{2}{3}}}

2. Evaluate the derivative a t = 8

w'(t)=\frac{10t}{\left(t^2\right)^{\frac{2}{3}}}\\\\w'(8)=\frac{10\cdot 8}{\left(8^2\right)^{\frac{2}{3}}}\\\\=\frac{80}{\left(8^2\right)^{\frac{2}{3}}}\\\\\left(8^2\right)^{\frac{2}{3}}=16\\\\=\frac{80}{16}\\\\w'(8) = 5 \frac{items}{hour}

The rate of learning at the end of eight hours of instruction is w'(8) = 5 \frac{items}{hour}

7 0
4 years ago
A system of equations has infinitely many solutions. If zy - 4x = 6 is one of the equations, which could be the other equation?
NemiM [27]

Answer:

I am not fully sure but C

4 0
3 years ago
What is the are of this trapizoid?
WARRIOR [948]

Answer:

110in

Step-by-step explanation:

↪Areas related to trapeziods..Basically the Area of a trapezium is given by Area = 1/2 ( sum of the non -parallel sides ) × H ↪thus we get as ..Area = 1/2 ( 9 + 13) 10 =》 1/2 ( 22 ) 10 = 110 ↪thus the area is 110 in^2_________________________

7 0
4 years ago
Read 2 more answers
Six less than two thirds of a number is 18. Find the number
zhenek [66]
(2/3) x -6= 18
2x/3 = 18+6
2x/3 = 24
2x = 24•3
X= 24•3/2
X= 12•3
X= 36
4 0
3 years ago
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