Answer: 117.6° ; 32.4° .
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Explanation:
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Note: ALL triangles, by definition, have exactly 3 (THREE) sides and exactly 3 (THREE) angles.
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We are given the following:
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We have a triangle.
Angle 1: m∡1 = (8x) ;
Angle 2: m∡2 = (2x + 3) ;
Angle 3: m∡3 = 30.
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We are asked to find: "m∡1" and " m∡2" .
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Note: In ALL TRIANGLES, the measurements of all THREE (3) angles ALWAYS add up to 180 degrees.
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So, " m∡1 + m∡2 + m∡3 = 180 " .
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Let us substitute our given values for the measurements in EACH of
the THREE (3) angles — on the left-hand side of the equation; then solve for "x" ; then substitute that solved value for "x" into the given expressions for BOTH "m∡1" AND "m∡2" ; to find the values for " m∡1" AND " m∡2 " ; which are the values asked for in this very question ;
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m∡1 + m∡2 + m∡3 = 180 ;
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8x + (2x + 3) + 30 = 180 ;
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8x + 2x + 3 + 30 = 180 ;
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Combine the "like terms" on the 'left-hand side" of the equation; to simplify:
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+8x + 2x = +10x ;
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+3 + 30 = +33 ;
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Rewrite the entire equation, as:
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10x + 33 = 180 ;
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Now, subtract "33" from EACH SIDE of the equation:
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10x + 33 − 33 = 180 −<span> 33 ;
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to get:
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10x = 147 ;
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Now, divide EACH side of the equation by "10" ; to isolate "x" on ONE SIDE of the equation; and to solve for "x" :
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10x / 10 = 147 / 10 ;
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to get:
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x = 14.7 ;
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Now, given the following, we plug in our solved value, "14.7", for "x", into the expression given for "m</span>∡1" and "m∡2"; as follows:
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Angle 1: "(8x)" = 8*(14.7) = 117.6° ;
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Angle 2: "2x + 3" = 2*(14.7) + 3 = 29.4 + 3 = 32.4° ;
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These are the two answers; that is the 2 (TWO) values asked for in the question: 117.6° ; 32.4° .
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Do they make sense? That is, do the measurements of ALL 3 (THREE) angles; that is, our two solved measurements added together, and then added to the value of the third angle (given: "m</span>∡3 = 30°); all add up to 180° ?
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Let us check:
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m∡1 + m∡2 + m∡3 = 180 ;
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Plugging in our solved values for "m∡1" and "m∡2" ; and our given value: "30" — for "m∡3 — does the equation hold true?
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→ 117.6 + 32.4 + 30 = ? 180 ??
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→ 117.6 + 32.4 = 150 ; → 150 + 30 =? 180 ? Yes!
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Answer:
D,1
Step-by-step explanation:
In the attached file
Step-by-step explanation:
Consider a function
f
(
x
)
which is twice differentiable. The graph of such a function will be concave upwards in the intervals where the second derivative is positive and the graph will be concave downwards in the intervals where the second derivative is negative. To find these intervals we need to find the inflection points i.e. the x-values where the second derivative is 0.
Answer:
Tj should write 5.75 hours on her time card.
Step-by-step explanation:
We have been given, Tj worked for 5 hours and 45 minutes.
We will convert 45 minutes to hours by dividing 45 by 60 as one hour has 60 minutes.
=0.75 hours
Hence, Tj should write 5.75 hours on her time card.
