1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Gnoma [55]
2 years ago
14

Find the measure of /_ MFZ

Mathematics
1 answer:
marshall27 [118]2 years ago
7 0

Given:

MZ\cong PZ

m\angle MFZ=(x+9)^\circ

m\angle PFZ=(2x-1)^\circ

To find:

The measure of angle MFZ.

Solution:

In triangles MFZ and PFZ,

m\angle FMZ\cong \angle FPZ           (Right angle)

MZ\cong PZ           (Given)

FZ\cong FZ           (Common side)

\Delta MFZ\cong \Delta PFZ                  (HL congruent postulate)

\angle MFZ\cong \angle PFZ           (CPCTC)

m\angle MFZ=m\angle PFZ

x+9=2x-1

9+1=2x-x

10=x

The value of x is 10.

The measure of angle MFZ is:

m\angle MFZ=(x+9)^\circ

m\angle MFZ=(10+9)^\circ

m\angle MFZ=19^\circ

Therefore, the measure of angle MFZ is 19 degrees.

You might be interested in
Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and roots of 2-√6 , 2+ √6
horsena [70]

Answer:

x^{4} -18x^{3}+104x^{2} -172x-100

Step-by-step explanation:

The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:  

\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))(  x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\

7 0
3 years ago
Find the area of a regular hexagon with a radius of 6 in
s344n2d4d5 [400]
Hexagon is a total of 6 triangle
Let find area of one triangle the multiplying with 6
Area of a triangle is A=1/2bh
We know b=6 and h= (6(square root of 3))/2
A= 1/2x6x(6(square root of3))/2=9(square root of 3)
Where square root of 3= 1.732
Area of a triangle=9x1.732 =15.588
Area of Hexagon equals 6 area of triangle so
Area of Hexagon= 6x 15.588=93.53
4 0
3 years ago
The volume of a hemisphere is 144 pi. Find the radius and total surface area.
sineoko [7]
Formula of the Volume of a hemisphere:
V = \frac{2}{3}\pir³
144\pi = \frac{2}{3}\pir³
Multiply by 3 to cancel fraction in the right side
144\pi × 3 = 2\pi r³
432 \pi = 2\pir³
Divide by 2\pi on either sides to isolate r³
\frac{432 \pi }{2 \pi } = \frac{2 \pi }{2 \pi }r³
2\pi and 2 \pi cancel out
216 = r³
Take cube root to find the radius
\sqrt[3]{216} = \sqrt[3]{r^3}
6 = r
Radius is 6 units

The formula of the surface area of a hemisphere is:
S.A = 2\pir² + \pir²
       = 2\pi(6)² + \pi(6)²
       =2\pi × 36 + 36\pi
       = 72\pi + 36\pi
       = 108\pi units²  (in terms of \pi)
       ≈ 339.12 units²

Surface area = 108\pi units
8 0
3 years ago
Which function represents the dotted graph? :)
7nadin3 [17]

Answer:

The function is:

y = -|x -1|

4 0
2 years ago
Read 2 more answers
Given triangle MNK below, find sin M/ Cos K
meriva

Answer:

The Answer is A

Step-by-step explanation:

its A I got it right

8 0
2 years ago
Other questions:
  • 14-3(5t-12)=1-(20t+1)<br> How am I supposed to do this?
    8·1 answer
  • Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans
    7·1 answer
  • Convert these unlike fractions to equivalent like fractions and add them. You must use the LCD to get the answer correct. If pos
    10·1 answer
  • Which of the a-values satisfy the following inequality?<br> 7 + a &lt; 11
    10·2 answers
  • (2 + 3) + 4^2 x (5 − 3)=
    10·1 answer
  • Sam wrote exactly half of his land in his daughter's name and ⅓ of his land in his son's name. He donated the remaining 10 acres
    13·2 answers
  • Question 5
    5·2 answers
  • Tulsi and Gary are competing in a basketball free throw competition. Tulsi’s ratio of free throws made to free throws missed is
    5·2 answers
  • How many 0.3's would it take to make 3? Explain your reasoning. ​
    13·1 answer
  • Joe travelled 60 miles in 1 hour 30 minutes.<br>Work out Joe's average speed.​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!