The equivalent ratios are A and D.
Here's an explanation:
When you look at D, you see that 12 is a multiple of 6, and 16 is a multiple of 8. So you know that it looks like they're equivalent. Then you test it out, 12/2=6. 16/2=8. so 12:16 = 6:8. Eyeballing it first can save time sometimes.
Using the slope line formula,
The slope of line y = mx is 1.0315.
We have given that,
parabola equation is y = 5x - 3x²
line passing through origin is in the form of y = mx
==> mx = 5x - 3x²
==> 3x²+ mx - 5x = 0
==> 3x² + x(m -5) = 0
==> x(3x + (m -5)) = 0
==> x = 0 , x = (5 -m)/3
The total area of the bounded region is then the integral of 5x - 3x² from x = 0 to x = (5-m)/3
Area under y = 5x - 3x2 and y = mx is (125/54)/2 = 125/108
==> [0 to (5 -m)/3] ∫(5x - 3x²-mx )dx = 125/108
==> [0 to (5 -m)/3]∫( (5 - m)x - 3x2 )dx = 125/108
==> [0 to (5 -m)/3] ((5 - m)x²/2 - x³ )= 125/108
==> (5 - m)[(5 -m)/3]²/2 - ((5 -m)/3)³ = 125/108
==> (5 -m)³/18 - (5 -m)³/27 = 125/108
==> (5 -m)³/54 = 125/108
==> (5 -m)³ = 125/2
==> (5 -m) = 3.9685
==> m = 5 - 3.9685
==> m = 1.0315
Hence slope of line = 1.0315
To learn more about slope of line , refer:
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The measure of angles are 137.5 degrees and 42.5 degrees
Solution:
Given that two angles are supplementary
Let "a" be the one of supplementary angle
Let "b" be the other supplementary angle
Given that measure of one angle is 10 degree more than three times the other
measure of one angle = 10 + three times the other angle
a = 10 + 3b ---- eqn 1
We know that,
Two Angles are Supplementary when they add up to 180 degrees.
a + b = 180 ---- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "b"</u></em>
Substitute eqn 1 in eqn 2
10 + 3b + b = 180
10 + 4b = 180
4b = 170
<h3>b = 42.5</h3>
From eqn 1,
a = 10 + 3(42.5)
a = 10 + 127.5 = 137.5
<h3>a = 137.5</h3>
Thus the measure of angles are 137.5 degrees and 42.5 degrees
I think that the length of DE is 4. you can add 0.5 to each side of BC in order to find the length of EF since EF starts 0.5 before BC does and therefore also ends 0.5 after BC since the circle is symmetrical.
Answer:
Step-by-step explanation:
