Option C:
x = 6 units
Solution:
QR = 7 units, RS = 5 units, UT = 4 units and ST = x
<em>If two secants intersect outside a circle, the product of the secant segment and its external segment s equal to the product of the other secant segment and its external segment.</em>
⇒ SR × SQ = ST × SU
⇒ 5 × (5 + 7) = x × (x + 4)
⇒ 5 × 12 = x² + 4x
⇒ 60 = x² + 4x
Subtract 60 from both sides.
⇒ 0 = x² + 4x - 60
Switch the sides.
⇒ x² + 4x - 60 = 0
Factor this expression, we get
(x - 6)(x + 10) = 0
x - 6 = 0, x + 10 = 0
x = 6, x = -10
Length cannot be in negative measures.
x = 6 units
Option C is the correct answer.
Answer:
They provide you with a graph that already has all the numbers and there is a data table. The data table lists all the numbers you have to plot onto the graph.
How to graph: The first number is 27, which is the vehicle weight in hundreds of lbs. On the graph, you can see that on the x-axis, it says weight (in hundreds of lbs). So first, look at the x-axis numbers and find somewhere between 25 and 30 and try to estimate where 27 would be.
Now look at the city MPG value that corresponds to 27, the weight value. It is 25. That's perfect because it is exactly the intervals the graph is in. So find 25 on the y-axis since the y-axis represents the city MPG. Now draw a straight line from the 25 on the y axis to the right. Then, draw a line from the 27 on the x axis straight up and where the two meet is the first point. Obviously, you don't need to make it that complicated if you don't need all the extra steps to understand but it is just in case you don't know how to graph the points.
Repeat for the rest of the points (make sure you use the correct corresponding points). Good luck on your test!
Step-by-step explanation:
We are given degree of the polynomial function = 3.
Because degree is 3, there should be three x-intercepts of the given graph of the polynomial.
We also given roots of the equation f(x)=0 are −2 , 0, and 3.
Therefore, x intercepts should be at:
(0,0), (-2,0) and (3,0).
<h3>In the given options third option shows x-intercepts at 0, -2 and 3.</h3><h3>Therefore, correct option is 3rd option.</h3>
The two triangles on the side are 18 in^2 and the square in the middle is 36 in^2. So in total, it has an area of 72 in^2
Given a table of historical demand for a product as follows:
![\begin{tabular} {|c|c|} &Demand\\[1ex] April&60\\ May&55\\ June&75\\July&60\\August&80\\September&75\\ \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%0A%7B%7Cc%7Cc%7C%7D%0A%20%26Demand%5C%5C%5B1ex%5D%0AApril%2660%5C%5C%0AMay%2655%5C%5C%0AJune%2675%5C%5CJuly%2660%5C%5CAugust%2680%5C%5CSeptember%2675%5C%5C%0A%5Cend%7Btabular%7D)
The linear regression equation is given by
where:
and
We calculate the required values using the following table, where
<span>April = 1, May = 2, and so on.
![\begin{tabular} {|c|c|c|c|} X &Y&X^2&XY\\[1ex] 1&60&1&60\\ 2&55&4&110\\ 3&75&9&225\\ 4&60&16&240\\ 5&80&25&400\\ 6&75&36&450\\[1ex] \Sigma X=21&\Sigma Y=405&\Sigma X^2=91&\Sigma XY=1,485 \end{tabular}](https://tex.z-dn.net/?f=%5Cbegin%7Btabular%7D%20%0A%7B%7Cc%7Cc%7Cc%7Cc%7C%7D%0AX%20%26Y%26X%5E2%26XY%5C%5C%5B1ex%5D%20%0A1%2660%261%2660%5C%5C%20%0A2%2655%264%26110%5C%5C%20%0A3%2675%269%26225%5C%5C%0A4%2660%2616%26240%5C%5C%0A5%2680%2625%26400%5C%5C%0A6%2675%2636%26450%5C%5C%5B1ex%5D%0A%5CSigma%20X%3D21%26%5CSigma%20Y%3D405%26%5CSigma%20X%5E2%3D91%26%5CSigma%20XY%3D1%2C485%20%0A%5Cend%7Btabular%7D)
Thus,
and
Therefore, the </span><span>trend line for the historical data is given by
</span>
