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2 years ago

Two supplementary angles have measures of 9x degrees and 3x degrees. What is the measure of the longer angle?

Mathematics

1 answer:

strojnjashka [21]2 years ago

5 0

9x+3x=180 by def. of supplementary
12x=180
12/12x=180/12
x=15

9x=9(15)=135°

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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

2 years ago

PLEASE HELP!!! GEOMETRY QUESTION

maria [59]

Answer:

Step-by-step explanation:

2y + 100 +6x-10=180(in a cyclic quadrilateral opposite angles are supplementary)

2y+6x+90 =180

2y + 6x = 90

dividing each side by 2

y+3x = 45 ........1

7x+1+2y+74 =180 ( same reason)

7x + 2y =105 ............2

multiplying 1 by 2

2y +6x =90........ 3

subtracting 3 from 2

7x+2y-2y-6x = 105-90

x = 15

substituting x=15 in 1

y+45 =45

y= 0

please mark me as the brainliest

7 0

2 years ago

Does anyone know this?!??

kondor19780726 [428]

Indeed!

This is a quadratic equation, and there are several ways to factor this. I will try to explain the way I do it and try to make sense of it.

2x^2-x-15 - Original Equation

Now set up an X(as I cannot draw very well in brainly it will look bad)

1 -3

\ /

/ \

2 5

This might all look very confusing so let me explain it.

First on the left side of the x, 1*2=2 which is the coefficient of the x^2 term.

The right side, -3*5=-15 which is the constant term.

What I did in the graph thing was to find 2 such pairs that line up in the graph in a way that the opposite corners multiplied and added together would = -1.

Such as the way I lined up the graph.

1*5(one of the diagonals) + 2*-3(the second diagonals)=5-6=-1 the coefficient of the middle term.

As long as you find 2 such pairs you got the answer, just write it from left it right then top to bottom.

The first ( ) would be (1x-3), the second ( ) would be (2x+5)

Now we can always switch the ( ) as in this problem we can write the answer as (x-3)(2x+5) or switch it around as (2x+5)(x-3).

Therefore the answer A is the correct answer.

**If you have any questions about my explanation, simply ask me in the comment section and I will come answer. (I know my explanation here isn't the most clear so you probably will ask questions and please don't just put the answer in and be done with it, actually try to understand my explanation it will help with further questions like this.)

6 0

2 years ago

Find the value of the trig function indicated

Lera25 [3.4K]

Answer:

$\cos(\theta)=\frac{4}{5}$

Step-by-step explanation:

Step 1:

Let us find the missing side. We know this is a right triangle, so we can use the pythagorean thereom to find the last side. Let us set 12 as variable a, 20 as variable c, and the unknown side as variable b.

$a^2+b^2=c^2\\12^2_b^2=20^2\\b^2=400-144\\b^2=256\\b=\pm16$

We do know that a length can never be negative, so the side b would be 16.

Step 2:

According to SOHCAHTOA, cosine is utilizes the adjacent and hypotenuse of the given angle theta. Let us write the equation:

$\cos(\theta)=\frac{adjacent}{hypotenuse} \\\\\cos(\theta)=\frac{16}{20} \\\\\cos(\theta)=\frac{4}{5}$

I hope this helps! Let me know if you have any questions :)

6 0

2 years ago

X^3 = 125 over 27 CAN I PLEASE GET HELP

agasfer [191]

X^3= (125/27)

To find the answer, find the cube root of both sides
x= ∛(125/27)

∛(125/27)= (∛125)/(∛27) = 5/3

Final answer: 5/3

3 0

2 years ago

Read 2 more answers