Do a proportion.
5/32= x/800
Cross multiply and divide
800 x 5= 4,000
4,000 divided by 32= 125
So answer is 125 students
Answer:
(a) 4
(b) 2√3
(c) 60°
(d) 120°
Step-by-step explanation:
(a) The relationship between tangents and secants is ...
CB^2 = CD·CA
Filling in the given values, we find ...
CB^2 = 2·(2+6) = 16
CB = √16 = 4
The length of BC is 4 units.
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(b) Triangle ABC is a right triangle, so the sides of it satisfy the Pythagorean theorem.
CA^2 = CB^2 +AB^2
8^2 = 16 +AB^2
AB = √48 = 4√3
The radius is half the length of AB, so the radius is 2√3.
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(c) The measure of angle C can be determined from the cosine relation:
cos(C) = CB/CA = 4/8 = 1/2
C = arccos(1/2) = 60°
The measure of angle C is 60°.
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(d) Arc AD is intercepted by angle ABD, which has the same measure as angle C. Hence the measure of arc AD is twice the measure of angle C.
The measure of arc AD is 120°.
The answer is 12 to the question
Hopes this helps you with your question!!
1. Given that the width of the rectangle is x, and the area of the rectangle may be represented by the equation x^2 + 5x = 300, we can solve this equation for the width (x) as such:
x^2 + 5x = 300
x^2 + 5x - 300 = 0 (Subtract 300 from both sides)
(x - 15)(x + 20) = 0 (Factorise x^2 + 5x - 300)
From this, we get: x = 15 or x = -20
Since the width must be a positive length (ie. more than 0), -20 would be an invalid answer in the given context and thus the width is given by x = 15.
2. If we know that the length is 5 inches more than the width, we simply need to add 5 to the width we found above to obtain the length:
Length = x + 5
Length = 15 + 5 = 20
Thus, the width of the rectangle is 15 inches and the length of the rectangle is 20 inches.
