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3 years ago

Find the measure of the numbered angles for the parallelogram for number one!

Mathematics

1 answer:

omeli [17]3 years ago

8 0

Consecutive angles of a parallelogram are supplementary, therefore:

Angle 3 + 110° = 180°

Subtract 110° from both sides of the equation

Angle 3 + 110° – 110° = 180° – 110°

Angle 3 = 70°

Opposite angles of a parallelogram are congruent, therefore:

Angle 2 = 110°

Angle 1 = Angle 3

Since Angle 3 = 70°

Angle 1 = 70°

Summarily,

Angle 1 = 70°

Angle 2 = 110°

Angle 3 = 70°

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Find a number that is 15 more than 4 times its opposite

svetlana [45]

X - the number

$x=4\cdot(-x)+15\\
x=-4x+15\\
x+4x=15\\
5x=15\\
x=3$

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3 years ago

Abbey's class is made up of 21 students--11 girls and 10 boys. What is the ratio of girls to boys?

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Answer:

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Read 2 more answers

Someone buys 6 cakes for 8$ each he sells them for ten each then he got 8 more and selled them for 10$ how much money does he ha

trapecia [35]

Answer: $28

Step-by-step explanation:

The person bought 6 cakes for $8 which reduces his money by:

= 6 * 8

= -$48

He then sells them for $10 each so the money made was:

= 10 * 6

= $60

He then buys 8 more for the same price which will reduce his money by:

= 8 * 8

= -$64

He sells these 8 for $10 so the money made was:

= 8 * 10

= $80

Total money left is therefore:

= 60 + 80 - 48 - 64

= $28

4 0

2 years ago

(a)5%)Let fx, y) = x^4 + y^4 - 4xy + 1. and classify each critical point Find all critical points of fx,y) as a local minimum, l

lara31 [8.8K]

$f(x,y)=x^4+y^4-4xy+1$

has critical points wherever the partial derivatives vanish:

$f_x=4x^3-4y=0\implies x^3=y$

$f_y=4y^3-4x=0\implies y^3=x$

Then

$x^3=y\implies x^9=x\implies x(x^8-1)=0\implies x=0\text{ or }x=\pm1$

If $x=0$ , then $y=0$ ; critical point at (0, 0)
If $x=1$ , then $y=1$ ; critical point at (1, 1)
If $x=-1$ , then $y=-1$ ; critical point at (-1, -1)

$f(x,y)$ has Hessian matrix

$H(x,y)=\begin{bmatrix}12x^2&-4\\-4&12y^2\end{bmatrix}$

with determinant

$\det H(x,y)=144x^2y^2-16$

At (0, 0), the Hessian determinant is -16, which indicates a saddle point.
At (1, 1), the determinant is 128, and $f_{xx}(1,1)=12$ , which indicates a local minimum.
At (-1, -1), the determinant is again 128, and $f_{xx}(-1,-1)=12$ , which indicates another local minimum.