Answer:
Step 1 : First, solve one linear equation for y in terms of x .
Step 2 : Then substitute that expression for y in the other linear equation.
Step 3 : Solve this, and you have the x -coordinate of the intersection.
Step 4 : Then plug in x to either equation to find the corresponding y -coordinate.
Step-by-step explanation:
For exponential functions
y=ab^x,
where
a is the scale vertical stretch factor,
b is the base, and
x the exponent (also independent variable)
It is a know fact that if the scale factor (1/2 or 2 in the answer choices) is positive, the graph is increasing if the base (3 or 1/3) is greater than 1.
This means that the base cannot be equal to 1/3. This eliminates choices 3 and 4.
Next, for a base greater than 1 (3>1), and the scale factor positive, it is a dilation (image gets bigger) if the scale factor is greater than 1. This eliminates the first choice where a=2.
This leaves us with the second choice where a=1/2, b=3, which is a shrink of the given exponential base function.
<span><span>2<span><span>(x+3)</span>2</span>+1</span><span>2<span><span>(x+3)</span>2</span>+1</span></span>Reorder the right side of the equation to match the vertex form of a parabola.<span><span>y=2<span><span>(x+3)</span>2</span>+1</span><span>y=2<span><span>(x+3)</span>2</span>+1</span></span>Use the vertex form, <span><span>y=a<span><span>(x−h)</span>2</span>+k</span><span>y=a<span><span>(x-h)</span>2</span>+k</span></span>, to determine the values of <span>aa</span>, <span>hh</span>, and <span>kk</span>.<span><span>a=2</span><span>a=2</span></span><span><span>h=−3</span><span>h=-3</span></span><span><span>k=1</span><span>k=1</span></span>Find the vertex <span><span>(h,k)</span><span>(h,k)</span></span>.<span>(−3,1<span>) ...................................</span></span>
The secant tangent theorem states that the distance from (y to the tangent point x) squared = the external segment * length of the secant.
Put in plane English
YX^2 = YV * YZ
YV = 9
YZ = 9 + 19 = 28
YX^2 = 28 * 9
yX^2 = 252
YX = sqrt(252)
YX = 15.87
