Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
where m is the slope and b is the y-intercept (the value of y when x is equal to 0)
<u>1) Determine the slope (m)</u>
where two points that the line passes through are 
and 
We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.
Plug these points into the equation
Therefore, the slope of the line is 3. Plug this into
<u>2) Determine the y-intercept (b)</u>
The y-intercept is given; it is 4. Plug this back into
I hope this helps!
The answer is 15.50 your welcome
Answer:
A = √29
Step-by-step explanation:
The short of it is that ...
A² = 2² + 5² = 29
A = √29
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<u>Amplitude</u>
If you expand the second form using the sum-of-angles formula, you get ...
Asin(ωt +φ) = Asin(ωt)cos(φ) +Acos(ωt)sin(φ)
Comparing this to the first form, you find ...
c₂ = 2 = Acos(φ)
c₁ = 5 = Asin(φ)
The Pythagorean identity can be invoked to simplify the sum of squares:
(Asin(φ))² + (Acos(φ))² = A²(sin(φ)² +cos(φ)²) = A²·1 = A²
In terms of c₁ and c₂, this is ...
(c₁)² +(c₂)² = A²
A = √((c₁)² +(c₂)²) . . . . . . . formula for amplitude
_____
<u>Phase Shift</u>
We know that tan(φ) = sin(φ)/cos(φ) = (Asin(φ))/(Acos(φ)) = 5/2, so ...
φ = arctan(c₁/c₂) . . . . . . . formula for phase shift*
φ = arctan(5/2) ≈ 1.19029 radians
___
* remember that c₁ is the coefficient of the cosine term, and c₂ is the coefficient of the sine term.
Answer:
There is no way of simplification by multiplying/dividing
Step-by-step explanation:
Answer:
55 cents.
Step-by-step explanation:
First, we start off with a half dollar (50 cents), and add a quarter (25 cents). 50 + 25 = 75. Next we take two dimes (each dime being 10 cents). 10 + 10 is 20, so we have twenty cents in dimes. It says to subtract the 2 dimes from our current number 75 minus 20 is 55. Therefore, we have 55 cents left. (If needed, that is 1 half dollar and 1 nickel.)
Hope this helps! :D
