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3 years ago

13

How do you solve this equation with substitution, I was absent for school today and wasn’t able to learn the subject please help

.

1 answer:

Alenkasestr [34]3 years ago

3 0

Answer:

X=1 Y=6

Step-by-step explanation:

6x=-4x+10

10x=10

x=1

6×1=6

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Prove that H c G is a normal subgroup if and only if every left coset is a right coset, i.e., aH = Ha for all a e G

Kaylis [27]

$\Rightarrow$

Suppose first that $H\subset G$ is a normal subgroup. Then by definition we must have for all $a\in H$ , $xax^{-1} \in H$ for every $x\in G$ . Let $a\in G$ and choose $(ab)\in aH$ ( $b\in H$ ). By hypothesis we have $aba^{-1} =abbb^{-1}a^{-1}=(ab)b(ab)^{-1} \in H$ , i.e. $aba^{-1}=c$ for some $c\in H$ , thus $ab=ca \in Ha$ . So we have $aH\subset Ha$ . You can prove $Ha\subset aH$ in the same way.

$\Leftarrow$

Suppose $aH=Ha$ for all $a\in G$ . Let $h\in H$ , we have to prove $aha^{-1} \in H$ for every $a\in G$ . So, let $a\in G$ . We have that $ha^{-1} =a^{-1}h'$ for some $h'\in H$ (by the hypothesis). hence we have $aha^{-1}=h' \in H$ . Because $a$ was chosen arbitrarily we have the desired .

5 0

3 years ago

Vector u has initial point at (3, 9) and terminal point at (–7, 5). Vector v has initial point at (1, –4) and terminal point at

spin [16.1K]

Answer:

⟨-5, -1⟩

Step-by-step explanation:

Vector:

A vector is given by its endpoint subtracted by its initial point.

Vector u has initial point at (3, 9) and terminal point at (–7, 5)

Then

$u = (-7, 5) - (3,9) = (-7 - 3, 5 - 9) = (-10,-4)$

Vector v has initial point at (1, –4) and terminal point at (6, –1).

Then

$v = (6,-1) - (1,-4) = (6-1,-1-(-4)) = (5,3)$

What is u + v in component form?

$u + v = (-10,-4) + (5,3) = (-10+5,-4+3) = (-5,-1)$

⟨-5, -1⟩ is the answer.

3 0

3 years ago

Evaluate : -80 - (-15) =

frosja888 [35]

Answer:

-65

Step-by-step explanation:

-80 - -15

Two minuses become plus

= -80+15

Subtract and keep the sign of the higher number

= -(80-15)

= -65

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3 years ago

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The perimeter of a rectangle can be found using the formula P = 4 s .<br><br><br> True or False

Minchanka [31]

Answer:

${ \underline{ \sf{true}}}$

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3 years ago

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skelet666 [1.2K]

Answer:

D

Step-by-step explanation:

$x = 5 - 2y \\ y = 3(5 - 2y) - 8 \\ y = 15 - 6y - 8 \\ y = 7 - 6y \\ 7y = 7 \\ y = 1$

$x = 5 - 2y \\ x = 5 - 2 = 3 \\$

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