Identify the special name for ∠3 and ∠10

Quadrilateral PQRS is circumscribed about a circle. Line PQ is tangent to the circle at A, line QR at B, line RS at C, and line

yuradex [85]

The sum of the angles of a quadrilateral is 360 degrees. So P+Q+R is 206, 360 - 206 = 154 degrees, the measure of angle S.

The four triangles, AQB, BRC, CSD, and DPA are all isosceles. So angle QBA = angle BAQ, etc. We find QBA = (180-24)/2 or 78 degrees.

RBC = (180-114)/2 = 33 degrees.

180 - (78 + 33) is the measure of angle B: 69 degrees.

The student should be able to see how to calculate the missing information from this.

6 0

3 years ago

In 2009, Zane paid $9,540 in federal income tax. In 2010, he paid 10% less. How much did Zane pay in 2010?

Dominik [7]

Answer: $940

Step-by-step explanation:

You multiply the 9540 by .10 because 10% turns into .10 and then when you multiply that which is.... 9540x.10= 954

4 0

4 years ago

Read 2 more answers

Can someone plz help me it’s due at 11:30 plz help!!!

arsen [322]

Well it is b I’m 80% sure

4 0

3 years ago

Put the numbers in ascending order.5–√, 2, −135,−2, −94

scoundrel [369]

Answer:

√5, 2, −13/5,−2, −9/4

Step-by-step explanation:

You basically just Calculate all of the numbers and order them from greatest to least, that's it.

7 0

3 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

3 years ago