In the given diagram, the length of diagonal IE is 30. The correct option is (2) 30
<h3>Calculating the length of a diagonal of a Rhombus </h3>
From the question, we are to determine the length of diagonal IE
From the given information,
/TG/ = 16
∴ /RG/ = 16÷2 = 8
NOTE: The diagonals of a rhombus bisect each other at right angles
Then,
/GE/² = /ER/² + /RG/² (<em>Pythagoras' theorem</em>)
From the given information, the perimeter of the rhombus is 68
Since all the sides of a rhombus are equal to one another,
Then,
/GE/ = 68÷4
/GE/ = 17
Thus,
17² = /ER/² + 8²
289 = /ER/² + 64
/ER/² = 289 - 64
/ER/² = 225
/ER/ = √225
/ER/ = 15
But,
/IE/ = 2 × /ER/
∴ /IE/ = 30
Hence, the length of diagonal IE is 30. The correct option is (2) 30
Learn more on Calculating length of a diagonal of a rhombus here: brainly.com/question/12354523
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A right triangle has 1 90 degree angle and the interior angles must add to 180.
3(x+8)+x+90=180
3x+24+x+90=180
4x+114=180
4x=66
x= 16.5
Plug this value in to find the last angle
16.5+90+x=180
106.5+x=180
x=73.5
Final answer: 73.5 degrees and 16.5 degrees
Answer:
116 and 64 degrees.
Step-by-step explanation:
Supplementary angles add up to 180 degrees so we can create the following equation and solve for x:
4x + 2x + 6 = 180
6x + 6 = 180
6x = 180 - 6 = 174
x = 174/6 = 29.
So the first angle is 4*29 = 116 degrees and the second is 2*29 + 6 = 64 degrees.
To confirm these results add them up: 116 + 64 = 180 degrees.
9514 1404 393
Answer:
1,953,125
Step-by-step explanation:
The first term is a1 = 5; the common ratio is r = -25/5 = -5. The generic term is ...
an = a1×r^(n-1)
an = 5×(-5)^(n-1)
So, the 9th term is ...
a9 = 5×(-5)^(9-1) = 1,953,125
Answer:
1. 169 2. 163 3. 54 4. 221 5. 6 6. 7 7. 11 8. 9
Step-by-step explanation:
Remember the Order of Operations:
Parentheses
Exponents
Multiplication
Division
Addition
Subtract
*But always solve from left to right so there can be times where you either have to do division before multiplication or subtraction before addition
1. 14 + <u>18 ÷ 2 </u>x 18 – 7
14+<u>9 x 18</u>-7
<u>14+162</u>-7
176-7
169
2. <u>15 x 10</u> + 12 ÷ 3 + 9
150+<u>12÷3</u>+9
<u>150+4</u>+9
154+9
163
3. <u>8 x 4</u> + 9 – 9 + 18
<u>36+9</u>-9+18
<u>45-9</u>+18
36+18
54
4. 2 - 1 +<u> 5 x 4 </u>x 11
2-1+<u>20x1</u>1
<u>2-1</u>+220
1+220
221
5. 60 – <u>9 x 8</u> ÷ 8 x 6
60-<u>72÷ 8</u> x 6
60-<u>9x6</u>
60-54
6
6. <u>(10 ÷ 5)</u>3 + 100 – 9 x 11
<u>(2)3</u>+100-9x11
6+100-<u>9x11</u>
<u>6+100</u>-99
106-99
7
7. <u>3 x 8</u> x 2 – 42 + 5
<u>24x2</u>-42+5
<u>48-42</u>+5
6+5
11
8. <u>14 ÷ 2</u> -1 + 3
<u>7-1</u>+3
6+3
9