Answer:
Perimeter = 42 cm.
Step-by-step explanation:
The 2 legs are equal in length as it is an isosceles trapezoid.
Area of trapezoid = (h/2)(a + b) where a and b are the parallel bases.
So
(5/2) (a + b) = 45
a + b = 45 * 2/5 = 18 cm.
We are given that the length of a leg (L) is 2/3 * sum of the bases, so:
L = 2/3(a + b)
= 2/3 * 18
= 12 cm.
The perimeter = a + b + 2L
= 18 * 2*12
= 42 cm.
Answer:
Step-by-step explanation:
X=4
The correct answer is: [C]: " m∠H = 91 ° " .
_______________________________________________
Explanation:
_______________________________________________
Note:
_______________________________________________
m∠F + m∠G = 90 ;
{since 2 complementary angles, by definition, add up to 90°.}.
m∠G + m∠H = 180 ;
{since 2 supplementary angles, by definition, add up to 180°.}
____________________________________________________
We are asked to find the smallest value of the " m∠H "
(among the given answer choices):
____________________________________________________
Note:
____________________________________________________
m∠G = 180 − m∠H ;
m∠H = 180 − m∠G ;
m∠F = 90 − m∠G ;
m∠G = 90 − m∠F ;
m∠G = 180 − m∠H ;
m∠H = 180 − m∠G .
__________________________________________________
The question is:
"What is the smallest value of " m∠H "; in whole number, among the answer choices given?" ;
__________________________________________________
Note: Consider each of the answer choices given:
______________________________________________________
Choice: [A]: " m∠H = 1 " ;
{Note, This value is SMALLEST value among ALL the answer choices.}.
If " m∠H = 1" ; then " m∠G = 179 ", since: " m∠G + m∠H = 180".
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 179" ;
then m∠F would have to equal a "negative number" to get:
" m∠F + m∠G = 90 " ;
So, "Choice [A]: " m∠H = 1 " ; is incorrect.
________________________________________________
Choice [B]: " m∠H = 89 " ;
If "m∠H = 89" ; then "m∠G = 91", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 89 = m∠G ;
→ "m∠G = 91" .}.
Then, could "m∠F + m∠G = 90" ?? NO! Because, if "m∠G = 91" ; then "m∠F " would have to equal a "negative number" to get: "m∠F + m∠G = 90" ;
So; "Choice: [B]: "m∠H = 89" ; is incorrect.
_______________________________________________________
Choice [C]: " m∠H = 91 " ;
If "m∠H = 91" ; then "m∠G = 89", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 91 = m∠G ; → "m∠G = 89" .}.
Then, could "m∠F + m∠G = 90" ?? YES! Because, if "m∠G = 89" ; then
"m∠F" COULD equal "1" ; and in such a case; "m∠F + m∠G = 1 + 89 = 90."
So; Choice: [C]: " m∠H = 91 " ; is a possible correct answer.
______________________________________________________
Let us try the last answer choice:
______________________________________________________
Choice [D]: " m∠H = 179 " ;
If "m∠H = 179" ; then "m∠G = 1", since: "m∠G + m∠H = 180".
{Note: "180 − m∠H = m∠G " ; → "180 − 179 = m∠G ; → "m∠G = 1" .}.
Then, would "m∠F + m∠G = 90" ?? Yes! Because, if "m∠G = 1" ; then "m∠F" would equal "89";
{Note: "m∠F + m∠G = 89 + 1 = 90 " .
{Note: "90 − m∠G = m∠F " ; → "90 − 1 = m∠F " ;
→ m∠F = 89° . }.
→ So; "Choice: [D]: " m∠H = 179 " ; is a possible correct answer.
_______________________________________________
Note: The question asks:
_______________________________________________
"What is the smallest possible measure of "angle H" {" m∠H "} ?
_______________________________________________
The 2 (TWO) possible correct answers are:
_______________________________________________
Choice [C]: " m∠H "= 91 " ;
and Choice [D]: " m∠H = 179 " .
_______________________________________________
The smallest possible " m∠H" is:
_______________________________________________
Answer choice: [C]: " m∠H = 91° " .
_______________________________________________
Answer:
6 were not playing games
Step-by-step explanation:
9514 1404 393
Answer:
18
Step-by-step explanation:
There are two areas where the circles P and C overlap. One is labeled "4" and the other is labeled "3x". The sum of these two values is the number of people who like Pop and Classical music, 13.
4 + 3x = 13
3x = 9 . . . . . subtract 4
x = 3 . . . . . . divide by 3
__
We are asked to find the number of people who like two types only. The three regions where only two circles overlap are labeled x, 3x, and 6. The answer to the question is the sum of these values.
like 2 types only: x +3x +6 = 4x +6 = 4(3) +6 = 18
18 students like two types of music only.