Answer:
We are given a equation as:
5log(x+3)=5
We are asked to find a graph that is used to solve the above equation.
We can write the given equation as:
we will divide both side of the equation by 5 to obtain:
log(x+3)=1
Now we have to determine which graph represents the function:
y=log(x+3)
since we know that when x=-2.
y=log(-2+3)=log(1)=0
Hence, the graph should pass through (-2,0).
Hence, the graph that satisfies this is attached to the answer.
Step-by-step explanation:
Answer:
y = 13*( -x/9 + 1/5)
Step-by-step explanation:
Given:
- The curve has an equation as follows:
Find:
a. Verify that the given point (2,2) lies on the curve.
b. Determine an equation of the line tangent to the curve at the given point.
Solution:
- To verify whether the point lies on the given curve we will substitute the coordinates of the point into the equation as follows:
44 = 5*(2)^2 + 3*(2)(2) + 3*(2)^2
44 = 20 + 12 + 12
44 = 44 ......Hence proven.
- The equation of the line tangent to the curve is expressed as a linear function as follows:
y = m*x + C
Where, m is the gradient of the line.
C is the y-intercept.
m = Δy / Δx = dy/dx
- We will take the derivative of the given curve with respect to x as follows:
- Evaluate y' at the point (2,2) we get:
y' = - ( 10(2) + 3(2) ) / ( 3(2) + 6(2) )
y' = - ( 26 ) / (18)
y'= m = - 13/9
- To evaluate C, we will use the point (2,2) for linear expression above with m as follows:
y = -13*x/9 + C
2 =-13*(2)/9 + C
C = 13 / 5
- The equation of the tangent is as follows:
y = 13*( -x/9 + 1/5)
Answer:
and
Step-by-step explanation:
The area of a rectangle is which factors through GCF, by finding the greatest common monomial factor between the two.
The length and width of the rectangle are and
.