Answer:
m<D = 105
Step-by-step explanation:
So, Triangle STU and DEF are similar triangles, because their corresponding side lengths have the same ratio.
For example FD can be multiplied by 2.5 to get SU, and EF can be multiplied by 2.5 to get TU, and ED can me multiplied by 2.5 to get 15.
Anyways, since the two triangles are similar, they have the same angle measures, meaning that angle D can be found by subtracting 46 and 25 from 180 degrees to find the missing angle, which is 105 degrees. I hope that helps.
The algebraic expression of the part A is 6+7x. And the verbal expression for 3*(n+8) is "the triple of the sum between the numbers n and 8".
<h3>
Linear Expression</h3>
A linear expression can be represented by a line. The standard form for this equation is: y=ax+b , for example, y=2x+7.
First, you should choose a variable for unknow number. Here, the variable will be x. Then, 7 times a number can be represented for 7x.
The word <em>more </em>will be represented for the add symbol (+). Thus,
the algebraic expression is 6+7x.
The expression 3*(n+8) can be represented for the sentence:
The triple of the sum between the numbers n and 8.
Learn more about the algebraic expression here:
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Answer: The central angle of the arc is 162 degrees.
Step-by-step explanation: The information available are as follows;
Circumference of the circle equals 10. Length of an arc equals 9/2. The circumference of a circle is given as;
Circumference = 2Pi x r
That means 2Pi x r = 10.
Also the length of an arc along the same circle is 9/2. Length of an arc is calculated as;
Length of arc = (X/360) x 2Pi x r
Where X is the central angle of the arc
That means;
9/2 = (X/360) x 2Pi x r
We can now substitute for the known values as follows
Length of an arc = (X/360) x 2Pi x r
9/2 = (X/360) x 10
9/2 = 10X/360
By cross multiplication we now have
(9 x 360)/(2 x 10) = X
3240/20 = X
162 = X
The angle at the center of the arc is 162 degrees.
