For all real numbers a and b, if ab=0, then a=0 or b=0. True or false?
2 answers:
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Answer:
Step-by-step explanation:
The question lacks the required diagram. Find the diagram attached below;
According to the first triangle, taking 30° as the reference angle, the opposite side of the triangle will be 5 and the adjacent will be the unknown side "b"
According to SOH, CAH, TOA;
tanθ = opposite/adjacent (using TOA)
Given;
θ = 30°, opposite = 5 and adjacent = b
tan30° = 5/b
b = 5/tan30°
b = 5/(1/√3)
b = 5*√3/1
b = 5√3
According to the 45° triangle, the opposite side of the triangle will be d and the hypotenuse will be 7
Using SOH;
sinθ = opposite/hypotenuse
Given;
θ = 45°, opposite = d and adjacent = 7
sin45° = d/7
d = 7sin45°
d = 7(1/√2)
d = 7/√2
Rationalize 7/√2
= 7/√2*√2/√2
=7√2/2
Hence the value of d is 7√2/2
Answer:
On the circle
Step-by-step explanation:
Because all of the points on a circle are equidistant from the center, if a circle has a radius of 10 then all of the points are 10 units from the center. Using the Pythagorean Theorem, you know that the distance from (4,0) to (-2,8) is:
, meaning that it is on the circle. Hope this helps!
Step-by-step explanation:
We get two equations here. One for the area and one for the perimeter. The area gives us x×y=50. The perimeter, if we have a rectangle, x+y+x+y=30=2x+2y. For this to work we need to make a simple expression for x or y. Let's go with x here. 2x+2y=30 so x=15-y. if we fill that in the other equation we get (15-y)×y=50 (see picture). y=5 or y=10. If we fill in x×5=50 we get x=10 and vice versa. So the dimensions are 5 centimeters by 10 centimeters
