Answer:
3/2
Step-by-step explanation:
y = mx + b
-6 = -3/2(5/1) + b
-12/2 = -15/2 + b
b = 3/2
Answer:
To find the domains you must graph this equation and find the x-coordinates of the points plotted. That's the domain.
Remember, if two points have the same x-coordinate then do not repeat the number when stating the domain. Domain also always must be written in the least to greatest order. Domains must be written with {} enclosing them.
So if the x-coordinates were 4,5,6,4,7,5
You would write the domain as {4,5,6,7}
Answer: 1106.13 (2 decimal places)
Step-by-step explanation:
To work out the area of this composite shape you would have to put the two semi circles together to form a circle and work out the area of the circle (they have provided the radius which is 11in), then work out the area of the rectangle separately.
The formula for the area of a circle is πr^2 (pi x radius squared).
So when you put the numbers in the formula the area is πx11^2=380.1327111
Then to work out the area of the rectangle you would do base x height.
The height of the rectangle is the same as the diameter of the circle (the diameter is double the radius of a circle) which is 22in.
To find the area of the rectangle you do 22x33=726
So then to find the area of the whole shape you would have to add the area of the circle and the rectangle together.
726+380.1327111=1106.13 (2 decimal places).
Answer:
x = 5
Step-by-step explanation:
The equality of bases property says powers of the same base will be equal if and only if the powers are equal. This property is used to solve exponential equations.
<h3>Application</h3>
![\dfrac{(2)^x}{2}=16\qquad\text{copy of the original equation}\\\\2\times\dfrac{(2)^x}{2}=2\times16\qquad\text{multiply by 2 to isolate the base}\\\\2^x=32\qquad\text{simplify}\\\\2^x=2^5\qquad\text{rewrite the constant as a power of 2}\\\\\boxed{x=5}\qquad\text{use the Equality of Bases Property}](https://tex.z-dn.net/?f=%5Cdfrac%7B%282%29%5Ex%7D%7B2%7D%3D16%5Cqquad%5Ctext%7Bcopy%20of%20the%20original%20equation%7D%5C%5C%5C%5C2%5Ctimes%5Cdfrac%7B%282%29%5Ex%7D%7B2%7D%3D2%5Ctimes16%5Cqquad%5Ctext%7Bmultiply%20by%202%20to%20isolate%20the%20base%7D%5C%5C%5C%5C2%5Ex%3D32%5Cqquad%5Ctext%7Bsimplify%7D%5C%5C%5C%5C2%5Ex%3D2%5E5%5Cqquad%5Ctext%7Brewrite%20the%20constant%20as%20a%20power%20of%202%7D%5C%5C%5C%5C%5Cboxed%7Bx%3D5%7D%5Cqquad%5Ctext%7Buse%20the%20Equality%20of%20Bases%20Property%7D)
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<em>Additional comment</em>
Equating the exponents is fully equivalent to taking the logarithm of both sides of the equation, to that base.
![\log_2(2^x)=\log_2(2^5)\ \Longrightarrow\ x=5](https://tex.z-dn.net/?f=%5Clog_2%282%5Ex%29%3D%5Clog_2%282%5E5%29%5C%20%5CLongrightarrow%5C%20x%3D5)