Answer:
The length of a rectangle is 5 m less than three times the width. If the perimeter is 86 m, what are the dimensions or the rectangle? ... If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same ... The perimeter of a rectangle is 99 ft, and the length is twice the width.
Step-by-step explanation:
The area of the shaded region is 3x^2 + 6x
<h3>How to determine the area of the shaded region?</h3>
The given parameters are:
- Top side of the shaded rectangle = 2x + 7.
- Left side of the shaded rectangle = 2x.
- Top side of the unshaded rectangle = x + 8.
- Left side of the unshaded rectangle = x.
The area of the shaded region is calculated as:
Shaded region area = (Top side of the shaded rectangle * Left side of the shaded rectangle) - (Top side of the unshaded rectangle * Left side of the unshaded rectangle)
Substitute the known values in the above equation
Shaded region area = (2x + 7) * (2x) - (x + 8) * (x)
Evaluate the products
Shaded region area = (4x^2 + 14x) - (x^2 + 8x)
Open the bracket
Shaded region area = 4x^2 + 14x - x^2 - 8x
Collect the like terms
Shaded region area = 4x^2 - x^2 + 14x - 8x
Evaluate the like terms
Shaded region area = 3x^2 + 6x
Hence, the area of the shaded region is 3x^2 + 6x
Read more about areas at:
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Answer:
Step-by-step explanation:
Congruent triangles:
We can prove AZ ≅ BX using A S A congruent.
Statement Reason
∠X ≅ ∠Z Given
XY ≅ ZY Given
∠Y ≅ ∠Y Reflexive property
ΔXYB ≅ ΔZYA Angle Side Angle congruent
AZ ≅ BX CPCT {Corresponding Parts of Congruent Triangle}
Hence proved
Answer:
The percentage of people that scored less than Calvin is 38.21 %
Step-by-step explanation:
In this question, we are concerned with calculating the percentage of exam scores lesser than what Calvin scores.
To calculate this, we first need to calculate the standard score or the z-score of Calvin result.
Mathematically;
z = (x - mean)/SD
from the question, x = 78, mean = 81 and SD = 10
Substituting this, we have
z = (78 -81)/10 = -3/10 = -0.3
So we proceed to calculate the probability.
P(x < 78) or P(z < -0.3)
We make use of the standard table to get this probability
P(z< - 0.3) = 0.38209
In percentage, this is same as 38.209% or more simply 38.21%
Composite because it can go into 2 and other numbers
