Solve this problem using estimation.

A secant and a tangent to a circle intersect in a 42-degree angle. The two arcs of the circle intercepted by the secant and the

Amanda [17]

Answer:

The measure of the third arc is $150\°$

Step-by-step explanation:

step 1

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

in this problem

Let

x----> the greater arc of the circle intercepted by the secant and the tangent

y----> the smaller arc of the circle intercepted by the secant and the tangent

$42\°=\frac{1}{2}(x-y)$

$84\°=(x-y)$ ----> equation A

$\frac{x}{y}=\frac{7}{3}$

$x=\frac{7}{3}y$ -----> equation B

Substitute equation B in equation A and solve for y

$84\°=(\frac{7}{3}y-y)$

$84\°=(\frac{4}{3}y)$

$y=3*84\°/4=63\°$

Find the value of x

$x=\frac{7}{3}(63\°)=147\°$

step 2

Find the measure of the third arc

Let

z------> the measure of the third arc

we know that

$x+y+z=360\°$ -----> complete circle

substitute the values and solve for z

$147\°+63\°+z=360\°$

$z=360\°-(147\°+63\°)=150\°$

3 0

2 years ago

Find the midpoint of the segment with the following endpoints. (2,9) and (8,1)

vazorg [7]

Answer:

$\displaystyle (5,5)$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Left to Right

Algebra I

Coordinates (x, y)
Midpoint Formula: $\displaystyle (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Step-by-step explanation:

Step 1: Define

Point (2, 9)

Point (8, 1)

Step 2: Identify

(2, 9) → x₁ = 2, y₁ = 9

(8, 1) → x₂ = 8, y₂ = 1

Step 3: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint

Substitute in points [Midpoint Formula]: $\displaystyle (\frac{2+8}{2},\frac{9+1}{2})$
[Fractions] Add: $\displaystyle (\frac{10}{2},\frac{10}{2})$
[Fractions] Divide: $\displaystyle (5,5)$

7 0

2 years ago

Graphing Exponential Functions In Exercise, sketch the graph of the function.

denis23 [38]

Answer:

The graph of the function $f(x) = (1/2)^2x + 4$ is attached as image below.

Analysis:

We have two intersection points in the graph

The function $f(x) = (1/2)^2x + 4$ intersects the y-axis at points (0,4)

The function $f(x) = (1/2)^2x + 4$ intersects the x-axis at points (-16,0)

f(x) is positive for x>-`16

f(x) is negative for x<-`16

5 0

2 years ago

What percentage is 15 out of 17?

Ket [755]

88.23%

Simply plug 15/17 into you calculator

and it will give you a decimal, in this case it should be .88235294...

simply move the decimal back to placements and you should have

88.235294... thats still a lot of numbers so just reduce it to 2 places after the decimal and add a percent sign

88.23%

and your done :) this works for any similar problems

I hope this helps

8 0

2 years ago

Read 2 more answers

Which of the following statements does not describe the structure of an atom? (3 points)

Vikentia [17]

Answer: letter D. Most of the mass of an atom comes from elctron cloud

Step-by-step explanation: your welcome and have a good day

6 0

2 years ago

Read 2 more answers