A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee.

Dividing by 2, we have S/2=lw+lh+wh. After that, we subtract lh from both sides to get S/2-lh=lw+wh. Next, we divide both sides by w to get (S/2)/w=l+h. Next, we divide by S/2 to get 1/w=(l+h)/(S/2). Lastly, we multiply by w and divide by (l+h)/(S/2) to get w=(S/2)/(l+h)

7 0

2 years ago

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Please answerrrrr Thank you!!!!!!!!!!!!

dlinn [17]

The correct answers are:

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" (x − 13) ° = 53 ° " ;

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" x = 66 " ;

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" m∠2 = 55° " ;

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" m∠1 = 55° " .

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Step-by-step explanation:

Note: The following "given values/answers" within the attached image:

Specifically:

(x − 13)° = 72° ; and;

x = 85° ;

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are: "incorrect"—and are "arbitrarily assigned values"

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The values and expressions given in the attached image, however, are correct/do make sense; and we can use such data to solve the problem.

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Let's start by finding the measure of ∠2 ; that is: " m∠2 " :

To find m∠2:

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Note that: both: "∠2 " ; and the angle that measures "175" with the attached image:

→ both form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

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So: To solve for: "m∠2" :

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→ m∠2 = 180 − (125) = 55° ,

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Now; to solve for: " m∠1 " :

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Note that ∠1 and ∠2 are vertical angles: which means that they have equal measurements;

{since: vertical angles are congruent; which means that vertical angles are equal.} ;

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→ As such, m∠1 = m∠2 = 55 °.

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Now, take either ∠1 or ∠2 ; (each has the same "measurement"—"55° " ;

And combine with angle with the given measurement of 72° ;

And combine with the angle with the "given measurement of [the expression: ["x − 13"]° ;

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All three of these angles form a straight line—that is;

→ they are "supplementary angles" ;

→ which means they add up to "180° " ;

So, 55° + 72° + (x − 13)° = 180° ;

Let us solve for "x" ; and for "(x − 13)" ;

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55 + 72 = 127 ;

→ 127 + (x − 13) = 180 ;

Now, subtract "127" from each side of the equation:

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→ 127 + (x − 13) − 127 = 180 − 127 ;

to get:

" (x − 13) = 53 " ; → which is one of our answers;

Now, to solve for "x" ; we add "13" to Each Side of the equation;

to isolate "x" on one side of the equation; & to solve for "x" :

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x − 13 + 13 = 53 + 13 ;

to get:

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x = 66 ;

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So: The correct answers are:

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" (x − 13) ° = 53 ° " ;

→ Double check by substituting our value of "66" for "x" :

" (66 − 13) =? 53 ? Yes! ;

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" x = 66 " ;

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" m∠2 = 55° " ;

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" m∠1 = 55° " .

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Hope these answers—and explanations—are helpful!

Best wishes!

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3 0

2 years ago