Answer:
Step-by-step explanation:
since it starts at 62 and finishes at 150 u can find out that the increase in temp is 150F and since it increases by 8 every minute u can come to find that the increase in temp (150) divided by the amount it increases 8 is 18.75 which is the amount of minutes it took
Let
x--------> the border’s length
y--------> the border’s width
P--------> perimeter of the border
we know that
x=5+y------> equation 1
P=2*[x+y]-----> P=2x+2y
P <=180 ft
(2x+2y) <= 180-------> equation 2
substitute the equation 1 in equation 2
2*[5+y]+2y <= 180
10+2y+2y <= 180
4y <= 180-10
4y <=170
y <=42.5 ft
so
the maximum value of the width is 42.5 ft
for y=42.5 ft
x=42.5+5------> x=47.5 ft
the answer is
the width of the border is less than or equal to 42.5 ft
Answer:
1. 9 < s < 17
2. 5 < MN < 19
3. AD > BD
Step-by-step explanation:
1. The triangle inequality tells you the sum of any two sides of a triangle must exceed the length of the other side. (Some versions say, "must be not less than ..." rather than "must exceed.") In practice, this means two things:
- the sum of the shortest two sides is greater than the length of the longest side
- the length of any side lies between the sum and the difference of the other two sides
Here, we can use the latter fact to write the desired inequality. The difference of the given sides is 13 -4 = 9; their sum is 13 +4 = 17. The third side must lie between 9 and 17. If that side length is designated "s", then ...
9 < s < 17
(If you don't mind a "triangle" that looks like a line segment, you can use ≤ instead of <.)
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2. Same as (1) using different numbers.
12 -7 < MN < 12 +7
5 < MN < 19
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3. Side CD is congruent to itself, and side CA is shown congruent to side CB. This means the requirements of the Hinge Theorem are met. That theorem tells you the longer side is opposite the greater angle:
AD > BD
Answer:
x = 8/√3
Step-by-step explanation:
We solve that above question using the trigonometric function of sin
Sin theta = Opposite/Hypotenuse
Theta = 60°
Opposite = 4
Hypotenuse = x
Hence,
Sin 60 = 4/x
Cross Multiply
sin 60 × x = 4
x= 4/sin 60
in rational form
sin 60 = √3/2
Hence, x = 4/ √3/2
= 4 ÷ √3/2
= 4 × 2/√3
= 8/√3
