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3 years ago

Subtract the sum of a^2 − 2ab + b^2 and 2a^2 + 2ab + b^2 from the sum of a^2 − b^2 and a^2 + ab + 3b^2

Mathematics

1 answer:

solniwko [45]3 years ago

5 0

Answer:

-a^2 + ab

Step-by-step explanation:

(a^2 - 2ab +b^2) + (2a^2 + 2ab + b2) = 3a^2 + 2b^2

(a^2 - b^2) + (a^2 + ab + 3b^2) = 2a^2 + 2b^2 + ab

subtract the first part from the second part:

(2a^2 + 2b^2 + ab) - (3a^2 + 2b^2) = -a^2 + ab

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ziro4ka [17]

The answer is D. 10x-2y-6

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3 years ago

What is the multiplicative inverse of 5 in z11, z12, and z13? you can do a trial-and-error search using a calculator or a pc?

grin007 [14]

A multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m.

1. $Z_{11}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{4};$
$5\cdot 4=20=\overline{9};$
$5\cdot 5=25=\overline{3};$
$5\cdot 6=30=\overline{8};$
$5\cdot 7=35=\overline{2};$
$5\cdot 8=40=\overline{7};$
$5\cdot 9=45=\overline{1};$
$5\cdot 10=50=\overline{6}.$

The multiplicative inverse of 5 in $Z_{11}$ is 9.

2. $Z_{12}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{3};$
$5\cdot 4=20=\overline{8};$
$5\cdot 5=25=\overline{1};$
$5\cdot 6=30=\overline{6};$
$5\cdot 7=35=\overline{11};$
$5\cdot 8=40=\overline{4};$
$5\cdot 9=45=\overline{9};$
$5\cdot 10=50=\overline{2};$
$5\cdot 11=55=\overline{7}.$

The multiplicative inverse of 5 in $Z_{12}$ is 5.

3. $Z_{13}=\{\overline{0},\overline{1},\overline{2},\overline{3},\overline{4},\overline{5},\overline{6},\overline{7},\overline{8},\overline{9},\overline{10},\overline{11},\overline{12}\}.$

Check:

$5\cdot 0=\overline{0};$
$5\cdot 1=\overline{5};$
$5\cdot 2=\overline{10};$
$5\cdot 3=15=\overline{2};$
$5\cdot 4=20=\overline{7};$
$5\cdot 5=25=\overline{12};$
$5\cdot 6=30=\overline{4};$
$5\cdot 7=35=\overline{9};$
$5\cdot 8=40=\overline{1};$
$5\cdot 9=45=\overline{6};$
$5\cdot 10=50=\overline{11};$
$5\cdot 11=55=\overline{3};$
$5\cdot 12=60=\overline{8}.$

The multiplicative inverse of 5 in $Z_{13}$ is 8.

8 0

3 years ago

Napa and Newton are 24 miles apart. On a map, the two cities are 3 inches apart. What is the map scale?

Andreas93 [3]

Answer:

one inch on the map is 8 miles

Step-by-step explanation:

divide 24 by 3

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3 years ago

Which graph represents the function?

BlackZzzverrR [31]

Answer:

The last one.

Step-by-step explanation:

The solutions with the horizontal lines are wrong because then h(x) would be -1 and 1 respectively.

The subtlety is in the open or closed dot. x ≥ -1 means that -1 is included, which is drawn as a closed dot. x < -1 means that -1 is excluded, which is drawn as an open dot.

Hence the last graph is the correct one.

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3 years ago

Read 2 more answers

I really need help with these questions

Alona [7]

Answer:

£10.91

Step-by-step explanation:

72p is 1kg of potatoes

1kg of carrots is 62p

10kg of potatoes is £7.20 add 3 extra kg's

which is £2.16

add £2.16 with £7.20 = £9.36

2kg of carrots is £1.24 add an extra half of kg an you get £1.55

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3 years ago