What is the effect on the area of a rectangle if the dimensions are doubled?
1 answer:
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ANSWER
EXPLANATION
The given rectangle has area,
It was given to us that, the length of the rectangle is l=(x+8)
To find the width, we need to factor, the expression for the area.
We split the middle term to get,
We now factor by grouping;
We know that area of a rectangle is
Hence the width of the rectangle is,
EXPLANATION
The given rectangle has area,
It was given to us that, the length of the rectangle is l=(x+8)
To find the width, we need to factor, the expression for the area.
We split the middle term to get,
We now factor by grouping;
We know that area of a rectangle is
Hence the width of the rectangle is,
Answer:
Step-by-step explanation:
The scenario is represented in the attached photo. Triangle ABC is formed. AB represents her distance from her base camp. We would determine BC by applying the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and B is the angle corresponding to b. It becomes
AB² = AC² + BC² - 2(AC × BC)CosC
AB² = 42² + 28² - 2(42 × 28)Cos58
AB² = 1764 + 784 - 2(1176Cos58)
AB² = 2548 - 1246.37 = 1301.63
AB = √1301.63
AB = 36.08 km
To find the bearing, we would determine angle B by applying sine rule
AB/SinC = AC/SinB
36.08/Sin58 = 42/SinB
Cross multiplying, it becomes
36.08SinB = 42Sin58
SinB = 42Sin58/36.08 = 0.987
B = Sin^-1(0.987)
B = 81°
Therefore, her bearing from the base camp is
360 - 81 = 279°
Answer:
Vanessa records a total of <u>11</u> quiz scores
Moe records a total of <u>10</u> quiz scores
According to the data, Vanessa's mean score is 80
According to the data, Vanessa's median score is 85
The range of Moe's quiz score is 45
The interquartile range of Moe's quiz score is 16.25
Step-by-step explanation:
Vanessa's score is given in the dot plot
Moe's scores are; 75, 80, 90, 90, 95, 55, 100, 95, 85, 85
1) The number of quiz scores Vanessa records is given by the number of dots on the dot plot, n = 11 dots ≡ 11 quiz scores
2) The number of quiz scores Moe records is given by the number of data points, n = 10 data points ≡ 10 quiz scores
3) Vanessa's mean score = ∑x/n
∑x/n = (60 + 2× 65 + 75 + 4 × 85 + 2 × 90 +95)/11 = 80
Vanessa's mean score = 80
4) Vanessa's median score is the (11 + 1)/2 th score = Her 6th score = 85
Vanessa's median score = 85
5) The range of Moe's score = Her largest score - Her least score = 100 - 55 = 45
The range of Moe's score = 45
6) Sorting Moe's scores gives;
75, 80, 90, 90, 95, 55, 100, 95, 85, 85
55, 75, 80, 85, 85, 90, 90, 95, 95, 100
The first quartile, Q₁ = 11/4th score = 2.75th score = 75 + 0.75 × 5 = 78.75
The 3rd quartile, Q₃ = The 3/4×11 score = 8.25th score = 95 + 0.25 ×0 = 95
The interquartile range, I = Q₃ - Q₁ = 95 - 78.75 = 16.25
The interquartile range of Moe's quiz score = 16.25.