The measure of EF from the given diagram is 6 units
<h3>Secant secant theorem</h3>
The theorem states that if two secants are drawn from an external point to a circle, then the product of the measures of one secant's external parts is the same as the product of the other external part.
Mathematically according to the given figure;
4(4+2x) = 5(5+x)
Expand
16 + 8x = 25 + 5x
Collect the like terms
8x - 5x = 25 - 16
3x = 9
Divide both sides by 3
3x/3=. 9/3
x = 3
Find EF
EF = 2x
EF = 2(3) = 6
Hence the measure of EF from the given diagram is 6 units
Learn more on secant theorem here: brainly.com/question/10732273
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Answer:
Step-by-step explanation:
The relationship between the number of popcorn and drinks is linear relationshipThe responses are;(a) Please find attached the required graph created with MS Excel(b) From the graph, we have that as the number of bags of popcorn Judy buys increases, the number of drinks decreases linearlyReasons:The given parameter are;Amount Judy took with her to spend on popcorn and drinks = $30Price of each bag of popcorn = $5Price of each drink = Half the price of a bag of popcorn∴ The price of each drink = (a) Let X represent the number of bags of popcorn Judy buys and let Y represent the number of drinks she buys, we have;5·X + 2.5·Y = 302.5·Y = 30 - 5·XWhich gives;Y = 12 - 2·XUsing the above equation, the graph of popcorn and drinks bought by Judy is plotted with MS Excel and attached here(b) The data in the graph are presented as followsThe point corresponding to the y-intercept is the point that gives the maximum number of drinks Judy can buy if she does not buy popcorn is 12 drinks. The number of drinks she can buy reduces by 2 for each bag of popcorn she buys, such that she can buy 6 bags of popcorn and no drinks which is the x-intercept.
Answer:
Step-by-step explanation:
(Let the point where the altitude from 
intersects 
be called as point 
.) First, let's find the area of parallelogram 
. The area of a parallelogram is simply 
, where 
is the parallelogram's base and 
is the parallelogram's height. If we let and 
be the base and height respectively, since we are already given their lengths, we know that the area of parallelogram will be 
.
Now, how does this information matter, you might ask? Well, we can take either <em>or </em>
to be the base and either or 
to be the height. In this case, let's take the latter two options, as we are looking to find the length of .
Therefore, we know that the area of parallelogram can also be found by calculating 
. Since we know the values of the area and , we can write the following equation to solve for :
(Substitute 
and 
into the equation)
(Divide both sides of the equation by 
to get rid of 's coefficient)
(Simplify)
(Symmetric Property of Equality)
Hope this helps!
The formula for simple interest is <em>I</em> = <em>prt</em>, where <em>I</em> is the amount of interest, <em>p</em> is the principal borrowed, <em>r</em> is the interest rate written as a decimal number, and <em>t</em> is the amount of time in years. First we find the amount of interest. He borrowed $35000 but paid back $46375. That means he paid 46375-35000 = $11375 in interest. We can now substitute our information into our interest formula:
11375=35000(<em>r</em>)(5)
11375=35000(5)(<em>r</em>) ----- remember that multiplication is commutative
11375=175000<em>r</em>
Divide both sides by 175000 to cancel it:
11375/175000 = 175000<em>r</em>/175000
0.065 = <em>r</em>
To convert this to a percentage, we multiply by 100:
0.065(100) = 6.5%
