A=43°
B=82°
c=28
1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)
2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°
2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3
2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
b=28 sin 82° / sin 55°
Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8
Answer: Option B) C=55°, b=33.8, a=23.3
Full question:
In a basketball game, Elena scores twice as many points as Tyler. Tyler scores four points fewer than Noah, and Noah scores three times as many points as Mai. If Mai scores 5 points, how many points did Elena score? Explain your reasoning
Answer and explanation:
We start from known to unknown. We know that Mai scored 5 points and so we work from here.
Since Mai scored 5 points and Noah scored three times as many points then Noah's score = 3×5= 15 points
Since Tyler scored four points less than Noah, Noah's score= 15-4= 11 points
Finally Elena's score is twice that of Tyler hence Elena's score =2×11= 22 points
Answer:
450 ounces
Step-by-step explanation:
We know that the cost of the mixture 
must be the cost of the everyday moisturizing lotion 
plus the cost of the self-tanning lotion 
, which means 
.
The cost of any substance will be the cost per ounce of the substance (c), multiplied by the number of ounces (n), which means C=nc, so we have from the previous formula that we have:
But we also know that the number of ounces of the mixture must be the sum of the number of ounces of the everyday moisturizing lotion with the number of ounces of the self-tanning lotion, so we have
We want to calculate the number of ounces of the self-tanning lotion (
), so we solve for that variable:
And substitute our values in this formula, to get:
Answer:
x≥ -4/55, x≤−89
Step-by-step explanation:
Step 1: Subtract 1 from both sides.
−110x+1−1≤9−1
−110x≤8
Step 2: Divide both sides by -110.
−110x/-110≤8/-110
x≥ -4/55
