independent practice: tangents of circles
Find the value of x in each of the following:
(see picture)
Answers
Answer:
Step-by-step explanation:
9). "Tangent is perpendicular to the radius of a circle"
By applying Pythagoras theorem in the given triangle,
x² = 15² + 20²
x = √625 = 25
10). By applying Pythagoras theorem in the given triangle,
(r + x)² = r² + 15²
(8 + x)² = 8² + 225
8² + x² + 16x = 8² + 225
x² + 16x = 225
x² + 16x - 225 = 0
x² + 25x - 9x - 225 = 0
x(x + 25) - 9(x + 25) = 0
(x + 25)(x - 9) = 0
x = -25, 9
But x > 0
Therefore, x = 9 is the answer.
11). By the property of the tangents drawn to the circle from a point,
"Tangents drawn from a point lying outside the circle are equal in measure"
AC = BC
3x + 4 = 40
3x = 36
x = 12
12). By the same property used in question (11)
DE = DC = 4 units
BA = BC = 3 units
x = 4 + 3 = 7 units
Related Questions
The function V(x)=650(0.77)^x models the change in yearly value for Anya's cellphone. What was the original value of the cellphone? Does the function represent exponential growth or exponential decay?
Answers
Answer: ↓↓
Step-by-step explanation:
The original value of the cellphone is $650. The function represents an exponential decay because if it was exponential growth, the function would look like this:
[tex]V (x) = 650 (1.77)^{x}[/tex]
At a fundraiser, a school group charges $6 for tickets for a "grab bag." You choose one bill at random from a bag that contains 39 $1 bills, 19 $5 bills, 3 $10 bills, 7 $20 bills, and 3 $100 bills. Is it likely that you will win enough to pay for your ticket?
Answers
Answer:
no, the probability is only about 18%
Step-by-step explanation:
there are total of 71 bills of varying denominations in the bag
you need to select a bill that is $10 or more to cover your $6 expense; therefore, P($ ≥ 10) = 3 + 7 + 3 / 71 or 13 /71, about 18%
A method for solving 5(x - 2) = 10 is shown below. Which step shows
distributive property?
A. 5x+2=10
B.5x-2=10
C.5x+10=10
D.5x-10=10
Answers
Answer:
D
Step-by-step explanation:
On average, Carter can get ready in 25 minutes but, depending on the day, his time can vary from the average by 15 minutes.
Which absolute value equation can be used to calculate Carter's maximum and minimum time to get ready?
Let x represent the maximum and minimum time.
|x−15|=25
|x+15|=25
|x+25|=15
|x−25|=15
Answers
Answer:
x-25=15 or D
Step-by-step explanation:
I promise that is the answer
What is the slope of the line?
Answers
Answer:
y= -x-2
Step-by-step explanation:
Please help me solve this and please also show work so I can understand it BETTER PLEASEEE ITS DUE
Answers
Answer:
6. 8b²-5b-4
7. -3x²+9x-4
8. 3
9. 6a+15
Step-by-step explanation:
you will subtract/add the numbers with the same variables and exponent.
ex. (number 6) 7b²+ b²= 8b²
5b= 5b 8b²+5b-4
1-5= -4
(plus 5b because it didnt come out to a negative) if you have any questions, say in the comments and ill try my best to help
Line 1: 4x-6y= -6 Line 2: -3y=2x+5 Line 3: y= -3/2x-5 Are line 1 and 2: parallel, perpendicular, or neither? Are line 1 and 3: parallel, perpendicular, or neither? Are line 2 and 3: parallel, perpendicular, or neither?
Answers
Answer:
Line 1 and line 2 are neither parallel nor perpendicular
Line 1 and 3 are perpendicular to each other
Line 2 and line 3 are neither parallel nor perpendicular
Step-by-step explanation
Given the equations of the line
Line 1: 4x-6y= -6
Line 2: -3y=2x+5
Line 3: y= -3/2x-5
Before we can know which line is parallel or perpendicular to each other, we need to find their slope first
For line 1:
4x-6y= -6
Write in standard form y = mx+c
-6y = -4x - 6
Divide through by -6
-6y/-6 = -4x/-6 - 6/-6
y = 2/3 x + 1
The slope of line 1 is 2/3
For line 2:
-3y=2x+5
Divide through by -3
-3y/-3 =2x/-3 + 5/-3
y = -2/3 x - 5/3
The slope of this line is -2/3
For line 3:
y= -3/2x-5
this is already written in standard format. The slope of this line is -3/2
Note that for two lines to be parallel, they must have the same slope
For two lines to be perpendicular, the product of their slope must be -1
For line 1 and line2, we can see that their slope are not the same and the product is not -1, hence both lines are neither parallel nor perpendicular
For line 1 and line 3, we can see that their slope are not the same but the product of their slope is -1 (2/3 * -3/2 = -1), hence both lines are perpendicular.
For line 2 and line 3, we can see that their slope are not the same and the product is not -1, hence both lines are neither parallel nor perpendicular
Identifying the Rate of Change
Warm-Up
Which statements are correct? Check all that apply.
The graph shows the linear relationship between the
height of a plant (in centimeters) and the time in
weeks) that the plant has been growing.
The rate of change is 4.
The rate of change is 1.
24
y
20
The rate of change is 4.
16
Height (cm)
The plant grows 4 cm in 1 week.
o me plant grows 1 cm in 4 weeks.
12
Time (weeks)
Answers
Answer:
Data collected shows that the more you water, the larger your plant will grow. If you use the following Equation, y = 1/2x + 2 How tall will a plant be at 25 weeks if x is the number of weeks watered and y represents the height of the plant? Show your work.
Step-by-step explanation:
Solve. y −3 = 1 6 y =
Answers
Step-by-step explanation:
y - 3 = 16y original problem
y - 3 - y = 16y - y grouping variables
-3 = 15y Simplification
-3÷15 = 15y÷15 Isolating the variable
-1/5 = y the answer
I hope this helps!!!!!!
Which expression doe
11/15-1/6
Answers
Answer:
Exact Form:
17/30
Decimal Form:
0.56
Step-by-step explanation:
Answer:
0.56 i think
Step-by-step explanation:
PLEASE HELP!! WILL MARK BRAINLIEST!!!!
Answers
Answer:
Choice A (-18.75 or -75/4)
1.8 to 1 decimal place
Answers
Step-by-step explanation:
1.8
8 is 1 decimal place
1./8
8 > 5
1 change to 2
2.0
given f(x) = -3x - 1, solve for f(x)= -4
Answers
Answer:
its 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
x= -4
f(x)= -4
f(-4)= -3(-4) -1
=11
what information is necessary to prove two triangles are similar by SAS similarity thereom?
Answers
Answer:
two sides and an angle of the triangle should be equal
What is the measure of XYZ?
Answers
Which statements are true? Select all that apply.
A. m∠WZX = 34°
B. m∠WXY = 123°
C. m∠XYZ = 46°
D. m∠WPZ = 90°
Answers
Answer:
C. and D.
Step-by-step explanation:
C.) Angle sum property, as XY = ZY
12x+9y=-36 4x+3y=-12 graphed
Answers
Answer:
graph attached
Step-by-step explanation:
12x+9y=-36
(12x+9y)/3=-36/3
4x+3y=-12
2 functions has the same value, they are identical line
Work out the percentage change to 2 decimal places when a price of £8.95 is increased to £10.
Answers
Answer:
12% increase
Step-by-step explanation:
Divide the difference between the two prices by the original price:
1.05/8.95
= 0.12
So, the percent change is 12%
Convert 40.64 centimeters to inches.
1 Inch = 2.54 centimeters
PLS HELP!!!
Answers
please help me on this.
Answers
Answer:
here
Step-by-step explanation:
so most of the time it would land on brown only 5% of the time would it land on red and the other there is a 0% chance
15y+3=36
Y=?/?
It’s asking for y in a fraction
Answers
Answer:
y = 33 / 15 = 11 /5
Step-by-step explanation:
subtract 3 from both sides,
15y = 33
divide 15 from both sides
y = 33/15
simplify ( divide top and bottom by 3)
y = 11/5
pls help i’m not good at this lol
Answers
Answer:
You selected the right one, 12^5 :)
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why. 10 ÷ 5 and 5 ÷ 10
Answers
Answer:
no, its not equivalent
Step-by-step explanation:
10/5= 2
5/10=0.5
What is the equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1)?
A. O y=-3x+
B. O y = 2x - 3
CO y = 2x
DO y = 2x + 3
Answers
Answer:
The equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1) will be:
[tex]y=2x+3[/tex]
Hence, option D is true.
Step-by-step explanation:
We know that linear function can be represented using the slope-intercept formula
y = mx+b
where m is the slope and b is the y-intercept
Given the equation
y = 2x - 1
comparing with the slope-intercept form y = mx+b
Hence, the slope of the line y = 2x - 1 is: m = 2
We know that the parallel lines have the same slopes.
Thus, the slope of the equation of the line that is parallel to the linear graph of y = 2x - 1 will also be: 2
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values of the slope = 2 and the point (-1, 1)
[tex]y-1=2\left(x-\left(-1\right)\right)[/tex]
[tex]y-1=2\left(x+1\right)[/tex]
Add 1 to both sides
[tex]y-1+1=2\left(x+1\right)+1[/tex]
Simplify
[tex]y=2x+3[/tex]
Therefore, the equation of the line that is parallel to the linear graph of y = 2x - 1 and passes through the point (-1, 1) will be:
[tex]y=2x+3[/tex]
Hence, option D is true.
‼️‼️‼️ please help fast ‼️‼️‼️
Answers
Answer:
d
Step-by-step explanation:
Answer:
Step-by-step explanation:
i believe the answer is either A or D
6x-8y-x+3y please this is hard
Answers
6x-8y-x+3y
= (6x-x)+(-8y+3y)
= 5x+(-5y)
=5x-5y
Answer:
5x-5y
Step-by-step explanation:
Equation;
6x-8y-x+3y(Group like terms)
Which is going to be;
6x-x-8y+3y
Then you proceed to simplify;
5x-5y
This is the final answer
*
8. Determine the rate of change (slope) in the graph
Answers
Answer:
Step-by-step explanation:
2 calculate rise over run
-3p = -48
What does p equal
Answers
Answer:
p=16
Step-by-step explanation:
Answer:
16
Step-by-step explanation:
[tex] - 3p = - 48 \\ \\ p = \frac{ - 48}{ - 3} \\ \\ p = 16[/tex]
Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The length of A B is 8, the length of B C is 5, and the length of B D is 15.
What is the value of s
Answers
Answer:
17 units
Step-by-step explanation:
just took the quiz
Answer:
17 units.
Step-by-step explanation:
Hope it helps!!!
Mariah drank 2/3 cup of orange juice. A serving size of is 5/6 cup. What part of a serving did she drink?
Answers
Answer:
80% of a serving
Step-by-step explanation:
First, convert 2/3 into 6ths
2/3 = 4/6
She drank 4 of 5 6ths
This is 80% of a serving