Answer:
c
Step-by-step explanation:
Using Pascal's triangle, the expansion, although EXTREMELY lengthy, will help you find the 7th term. I am going to type out the expansion only up til the 7th term (although there are actually 10 terms because we are raised to the power of 9). If you would like to learn how to use Pascal's Triangle for binomial expansion, you will need to visit a good website that explains it because it's just too difficult to do it via this website.
The expasion is as follows (up to the 7th term):
[tex]1(3c)^{9} +9(3c)^{8}(2d)^{1} +36(3c)^{7}(2d)^{2} +84(3c)^6(2d)^3+126(3c)^5(2d)^4+126(3c)^4(2d)^5+84(3c)^3(2d)^6[/tex]
That last term is the 7th term. You find out its value by multiplying all the numbers together and adding on the c^3d^6. Again those come from Pascal's triangle, and it's one of the coolest math things ever. I encourage you to take the time to explore how it works.
Will mark as brainliest!!
Lorenz wants to build a bigger flower box for his home. The current box has dimensions of 18“ x 12“ x 36“. What happens to the volume of the box if you double each dimension
Answer:
The answer is 62208
Step-by-step explanation:
The reason is because 18*2=36 12*2=24 and 36*2=72
36*24*72=62208
Can I get brainliest
Give coordinates X(3,-4) and Y(-3,-4), midpoint D of XY is?
A. D(-4,0)
B. D(-3,4)
C. D(3,-4)
D. D(0,-4)
Answer:
[tex]\large\boxed{D.\ D(0,\ -4)}[/tex]
Step-by-step explanation:
The formula of a midpoint of the segment"
[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points X(3, -4) and Y(-3 -4).
Substitute:
[tex]x=\dfrac{3+(-3)}{2}=\dfrac{0}{2}=0\\\\y=\dfrac{-4+(-4)}{2}=\dfrac{-8}{2}=-4[/tex]
What is the degree of the polynomial p(x) = [tex]17x^{4}-12x^3+51x^2-137x+2[/tex]
The degree of a polynomial is the highest exponent.
The highest exponent in this equation is 17x^4
The degree is 4.
Please help me out please
Answer:
110.9 sq ft
Step-by-step explanation:
split the equilateral triangle into two right triangles. use pythagorean theorem to discover that the height is about 13.86 ft. use the area formula, A= (1/2)bh
A=(1/2)(8)(13.86)= 110.9
Answer:
A = 64√2 ft² = approx. 90.5 ft²
Step-by-step explanation:
Because this is an equilateral triangle, the interior angles are also equal and are 60° each. We'll use the area-of-a-triangle formula, A = (1/2)(b)(h), to find the area of this particular triangle. We see from the diagram that the base is 16 ft.
Drawing an imaginary line representing the height of this triangle, and letting h represent this height, we get
sin 60° = opp / hyp = h / (16 ft) = 1/√2, so that
h 1
----- = -----
16 √2 16
and so √2*h = 16, and h = -------
√2
1 16 16
Then the area of this blue triangle is A = (1/2)(b)(h) = ---- * ----- * -------
2 1 √2
128 128√2
or A = ------- = ------------ = 64√2 ft² = approx. 90.5 ft²
√2 2
PLEASE HELP ASAP 60 PTS + BRAINLIEST TO RIGHT/BEST ANSWER
Answer:
x(x-3)(x+2)
Step-by-step explanation:
x^3-x^2-6x
First subsitute out x:
x(x^2-x-6)
Find the multiples of the x's:
x(x-3)(x+2)
Answer:
x(x-3)(x+2)
Step-by-step explanation:
x^3-x^2-6x
First subsitute out x:
x(x^2-x-6)
Find the multiples of the x's:
x(x-3)(x+2)
Step-by-step explanation:
What is the value of x? Enter your answer in the box
x = 180° - 67° - 52°
x = 61°
So, the value of x is 61°
The ordered pair (-2,-1) is a solution to which of the following equations?
The equation that has (-2, -1) as a solution is, C. 4x - y = -7.
How to Find the Ordered Pair That is a Solution to an Equation?To determine if an ordered pair is a solution to an equation, plug in the values of the coordinates of the pair into the equation to check if it will make it true
If it makes it true, it is a solution, otherwise, it is not if it does not make the equation true.
Given the ordered pair, (-2, -1) substitute the values to check which will be true:
-4(-2) - (-1) = 7
9 = 7 [not true].
4x + y = -7
4(-2) + (-1) = -7
-9 = -7 [not true]
4x - y = -7
4(-2) - (-1) = -7
-7 = -7
Therefore, the equation is: C. 4x - y = -7.
Learn more about the solution of an equation on:
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Complete Question:
The ordered pair (-2,-1) is a solution to which
of the following equations?
A.-4x - y = 7
B. 4x+y=-7
C. 4x - y = -7
D. -4x + y = -7
please help, i suck at these but i think its 3/6
Answer:
it is 1/6 because there is 6 colors and the probability of getting 3 which is 1 number is 1 out of 6
Step-by-step explanation:
Please answer this correctly
Answer:
The missing number is 8
Step-by-step explanation:
Hope this helps (3
it will be 297,088 as the answer
K-12 Algebra 2. PLEASE HELP! 25 points
For a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork.
A) Give an example of a question she could ask on her survey
B) How could Sofie select a simple random sample of students to take her survey?
C) she gives out 80 surveys but receives only 32 completed surveys. What are the sample and population for Sofies research?
D) of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. If sofie uses only the completed surveys, what conclusion could she make about the percent of all high school students who use social media while doing schoolwork?
DO NOT ANSWER IF YOU DO NOT KNOW. I WILL REPORT YOUR ANSWER!!!!’
Answer:
A. how much of the students time is spent on social media during school hours.
B. By using some kind of selection technique Like Having students draw number from a hat, who ever have the specific numbers will take her survey.
C. The population for Sofies research would be a rate of 5/2. For every 5 people who take the survey only 2 turned it in.
D. She would conclude that 1 out of every 2 or 50 percent of students use social media while doing school work.
Step-by-step explanation:
The percent of all high school students who use social media while doing schoolwork, if Sofie uses only the completed surveys, is 50%.
What is random sample?Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.
For a research project, students are asked to study how often students at an online high school look at social media while doing schoolwork.
A) Example of a question she could ask on her survey-Sofie can use the question as, how many times a student look at social media while doing schoolwork?
B) The way, Sofie select a simple random sample of students to take her survey-Sofie can use a simple random sampling technique to select a simple random sample of students to take her survey.
C) Sample and population for Sofie's research-
As Sofie gives out 80 surveys but receives only 32 completed surveys. Thus, the sample is data of 32 completed surveys and the population is total 80 surveys.
D) Percent of all high school students who use social media while doing schoolwork-Of the 32 students who completed surveys, 16 said they use social media while doing schoolwork. Thus, the percentage is,
[tex]P=\dfrac{16}{32}\times100\\P=50\%[/tex]
Hence, the percent of all high school students who use social media while doing schoolwork if Sofie uses only the completed surveys, is 50%.
Learn more about the random sample here;
https://brainly.com/question/17831271
A rectangle has length (x+4) cm and width (x-3) cm. Its area is 30 square centimeters. Write a quadratic equation and solve it to find the length of the rectangle.
(x+4)(x-3)=30
x^2 +x -12 =30
x^2 +x =42
x^2 +x -42 =0
(i solved it by factorising: _x^2 × -42)
x^2 -6x +7x -42 =0
x(x-6) +7(x-6) 0
(x-6)(x+7)=0
x=6; x=-7
since it's a length, x can't be a negative number, so it must be 6
What does it mean when a scatter plot has a good or bad fit? And how can you tell if it has a good or bad fit?
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A scatter plot has a good fit when data points cluster near the line of best fit and show a clear positive or negative correlation, suggesting a strong relationship between variables. A bad fit is characterized by scattered data points with no apparent pattern and large residuals between the points and the line, indicating a weak or no correlation.
When a scatter plot has a good fit, it means that the line of best fit accurately represents the trend in the data. This line minimizes the distances, or residuals, between itself and all the points on the graph. You can tell if a scatter plot has a good fit if the data points form a pattern that closely follows the line of best fit, indicating that the variables have a strong correlation. Conversely, a bad fit is evident when the data points are widely scattered and do not follow a distinct pattern, suggesting a weak or no correlation between the variables.
Signs of a Good Fit in Scatter Plots
Data points cluster near the line of best fit.Residuals (distances between data points and the line) are generally small.The pattern is either a clear positive or negative correlation.Signs of a Bad Fit in Scatter Plots
Data points are spread out with no discernible trend.Residuals are large, indicating significant variance from the line.No apparent correlation, positive or negative, is observable.Whether the X and Y variables in a scatter plot are good candidates for linear regression depends on the aforementioned signs. If there is a clear positive or negative correlation and data points approximate a linear trend, they are good candidates for linear regression.
Thom's restaurant bill is $45, and he leaves a 20 percent tip. What is the total cost for Thom's meal?
Multiply the price before the tip by .20
[tex]45 * .20 = 9[/tex]
Add 9 to the total:
[tex]45 + 9 = $54[/tex]
So, the total cost for Thom's meal is $54
The total cost for Thom's meal is $54.
What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a standard measurement.
Given
Thom's restaurant bill is $45
20 percent tip = 20 % of 45 = 20/100*45 = 9
Total cost = Thom's restaurant bill + 20 percent tip
= 45+ 9 = 54
Therefore, The total cost for Thom's meal is $54.
To know more about percentages refer to :
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15pts awarded and brainliest will be chosen!!!!!
The ideal length of a particular metal rod is 30.5 cm. The measured length may vary from the ideal length by at most 0.015 cm. What is the range of acceptable lengths for the rod?
Answer: OPTION B
Step-by-step explanation:
Let be "x" the acceptable lengths for the rod.
You know that the ideal length of the metal rod is 30.5 centimeters and the measured length may vary from the ideal length by at most 0.015 centimeters.
Therefore, knowing this, you can say that the acceptable lengths must be:
[tex]30.5cm-0.015cm\leq x\\\\30.485\leq x[/tex]
[tex]x \leq 30.5cm+0.015cm\\\\x\leq 30.515[/tex]
Therefore, the range of acceptable lengths for the rod is the following:
[tex]30.485\leq x\leq 30.515[/tex]
This range matches with the one shown in the option B.
Find the number of positive three-digit integers whose digits are among 9, 8, 7, 5, 3, and 1.
18
216
729
Answer:
216
Step-by-step explanation:
Each of the three digit positions can have any of 6 values, so there are ...
6^3 = 216
possible numbers that can be formed.
Why is (6, –2) not a solution to the system of equations given below?
{2x-3y=18
5x=3y=3
A.
It satisfies the top equation but not the bottom equation.
B.
It satisfies the bottom equation but not the top equation.
C.
It doesn’t satisfy either the top or the bottom equations.
D.
It satisfies both the top and the bottom equations.
ANSWER
A.
It satisfies the top equation but not the bottom equation.
EXPLANATION
The given equations are;
2x-3y=18
5x+3y=3
When we substitute x=6 and y=-2 into the top equation we get,
2(6)-3(-2)=18
12+6=18
18=18
This is true. Hence the point satisfy the top equation.
But when we substitute x=6 and y=-2 into the bottom equation we get,
5(6)+3(-2)=3
30-6=3
24=3
Hence the bottom equation is not satisfied.
The first choice is correct.
Suppose the function g(x) = 7x + 6 is translated down 9 units to become a new function, h(x). What's the equation of the new function?
Answer:
g(x)=7x-3
Step-by-step explanation:
the y axis becomes -3 because 6-9=-3
A weather forecast predicts a 25% probability of thunderstorms for tomorrow and a 10% probability of thunderstorms and hail. What is the probability that there is hail tomorrow given that there are thunderstorms?
Answer:
[tex]P(B | A)=0.4=40\%[/tex]
Step-by-step explanation:
Call A to the event in which there are electrical storms.
Call B the event in which there is hail.
Then, by definition.
The Probability of B given A is:
[tex]P(B | A)=\frac{P(B\ and\ A)}{P(A)}[/tex]
We know that:
[tex]P(B\ and\ A)= 10\%=0.1\\\\P(A) = 25\%=0.25[/tex]
Therefore
[tex]P(B | A)=\frac{0.1}{0.25}[/tex]
[tex]P(B | A)=0.4=40\%[/tex]
The conditional probability of hail given thunderstorms is calculated using the formula P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). Given the probabilities of 10% for thunderstorms with hail and 25% for thunderstorms, the result is a 40% probability of hail when thunderstorms are present.
Explanation:The student is asking to find the conditional probability of hail occurring, given that thunderstorms are already happening. This is a probability question that involves understanding and applying the concept of conditional probability.
The probability of thunderstorms is given as 25% (or 0.25 in decimal form), and the probability of thunderstorms with hail is given as 10% (or 0.10 in decimal form). To find the probability of hail given thunderstorms, you use the formula for conditional probability which is P(Hail | Thunderstorms) = P(Thunderstorms and Hail) / P(Thunderstorms). The 'given' part is represented by the condition after the vertical bar '|', and the numerator is the probability of both thunderstorms and hail occurring.
Substituting the given values into the formula, we get P(Hail | Thunderstorms) = 0.10 / 0.25 = 0.40 or 40%. Therefore, if thunderstorms are occurring, there is a 40% probability that there is also hail.
PLS HELP!!!!
Drag a statement or reason to each box to complete this proof.
If x−24=2, then x=10.
Statement Reason
1. x−24=2 Given
2. 4(x−24)=4∙2 ?
3. ? Simplifying
4. x−2+2=8+2
5. ? ?
______________________________________________________________
simplifying multiplication property of equality
addition property of equality x=10 x-2=8
Answer:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
Step-by-step explanation:
* Lets explain how to solve the problem
- The equation is [tex]\frac{x-2}{4}=2[/tex]
- The value of x is 10
- We want to a statement reason to each step to complete the proof
* Lets write each step with statement reason
1. [tex]\frac{x-2}{4}=2[/tex] ⇒ Given
2. [tex]4(\frac{x-2}{4})=4*2[/tex] ⇒ simplifying multiplication property of equality
3. x - 2 = 8 ⇒ Simplifying
4. x - 2 + 2 = 8 + 2
5. x = 10 ⇒ addition property of equality
- In step 2 we multiply both sides by 4 to cancel the denominator of
the left hand side (simplifying multiplication property of equality)
- Then we simplify the two sides to get (x - 2 = 8)
- Then we add two to both sides to cancel -2 in the left hand side
- Then after adding we find (x = 10) , (addition property of equality)
* The answer is:
2. simplifying multiplication property of equality
3. x - 2 = 8
5. x = 10 , addition property of equality
What is the formula for the sum of the interior angles of a polygon
Answer:
Sum of the interior angles = (n-2) x 180°
where
n is the number of sides of the polygon
Step-by-step explanation:
The formula for the sum of the interior angles of a polygon is:
[tex]sum=(n-2)*180[/tex]
where
[tex]sum[/tex] is the sum of the interior angle of the polygon
[tex]n[/tex] is the number of polygons
Let's check the formula using an example:
We want to find the sum of the interior angles of a square, we know that a square has 4 sides, so [tex]n=4[/tex].
Replacing values
[tex]sum=(4-2)*180[/tex]
[tex]sum=(2)*180[/tex]
[tex]sum=360[/tex]
We can apply the same procedure to any convex polygon with n sides.
Answer:
The fomula for the sum of the interior angles of a polygon is:Sum of the interior angles = (n - 2) × 180°.
Where n is the number of sides of the polygon.
Explanation:
The formula (n - 2) × 180° is valid for any convex polygon.
A convex polygon is one whose interior angles (every interior angle) measure less than 180°.
You can prove and remember that formula following this reasoning:
If you pick one vertex of the polygon you can build (n - 2) diagonals, and so split the figure into n - 2 triangles.Since, the sum of the interior angles of any trianle is 180°, the sum of the total angles is (n - 2) × 180°. And this is the formula for the sum of the interior angles of a polygon.For example, for a pentagon, a polygon with 5 sides, you can can draw 5 - 2 = 3 diagonals from one vertex, and so obtain 3 triangles. Then the sum of the interior angles shall be (n - 2) × 180° = (5 - 2) × 180° = 3 × 180° = 540°.
Tax returns filled manually have a 20% chance of containing errors while tax returns filled electronically have a .05% chance of containing the same if 2.7 million tax returns are filed each way how many more erroneous manually filed returns will there be than erroneous electronically filed returns
Answer:
538,650
Step-by-step explanation:
We must first find how many errors there will be if filed manually and if filed electronically
Manually: 2,700,000*20% or 2,700,000*.2
Answer: 540,000 errors
Electronically: 2,700,000*.05% or 2,700,000*.0005
Answer: 1,350 errors
We must then find the difference; 540,000-1,350=538,650
Answer:
538,650.
Step-by-step explanation:
Number of erroneous manual returns = 20% of 2.7 million
= 0.20 * 2,700,00 = 540,000.
Number for electronically returned = 2,700,000 * 0.0005 = 1350.
Difference = 540,00 - 1350 = 538,650.
Which is an equation of the circle with a radius of 9 units and center at
(–4, 2)?
A.
(x − 9)2 + (y + 4)2 = 4
B.
(x − 4)2 + (y + 2)2 = 81
C.
(x + 4)2 + (y − 2)2 = 81
D.
(x − 2)2 + (y + 4)2 = 81
We want (x - h)^2 + (y - k)^2 = r^2.
This circle is not centered at the origin.
The point we want is in the form
(h, k).
We are given that h = -4 and k = 2.
We also know that the radius is 9.
Let r = 9 leading to (9)^2 or 81.
We know substitute in the form given above for circles not centered at the origin.
(x - (-4)^2 + (y - 2)^2 = 81
(x + 4)^2 + (y - 2)^2 = 81
Answer: Choice C
Please help me out with this
Answer:
x = 17
Step-by-step explanation:
For the parallelogram to be a rhombus then then the diagonal must bisect the given angle, thus
3x - 11 = x + 23 ( subtract x from both sides )
2x - 11 = 23 ( add 1 to both sides )
2x = 34 ( divide both sides by 2 )
x = 17
A thirty year old man is considering buying a one-year life insurance policy for $500 with a coverage of $150,000. The probability of his living through the year is 0.994. Based ONLY on this information, should the man buy the policy?
Answer:
The man should not buy the policy.
Step-by-step explanation:
A life insurance policy is a contract that pays a sum assured to a policy holder upon death, either immediately or at the end of year of death. The policy holder pays a premium amount in advance to cater for the future benefits (sum assured).
In the scenario presented, the man is 30 years old with a probability of 0.994 of survival with respect to mortality. The high probability of being alive through the year implies that the man is very unlikely to die and thus the probability of receiving the coverage amount is too minimal
Answer: The expected value is $400, so the man should buy the insurance policy.
Step-by-step explanation:
(150,000-500)(.006)-500(.994)=400
What is the equation of a parabola with (4,6) as its focus and y = 2 as its directrix
Answer:
The equation of the parabola is (x - 4)² = 8(y - 4)
Step-by-step explanation:
* Lets revise the equation of a parabola
- If the equation is in the form (x − h)² = 4p(y − k), then:
• Use the given equation to identify h and k for the vertex, (h , k)
• Use the value of h to determine the axis of symmetry, x = h
• Use h , k and p to find the coordinates of the focus, (h , k + p)
• Use k and p to find the equation of the directrix, y = k − p
* Now lets solve the problem
∵ The directrix is y = 2
∴ The equation is (x - h)² = 4p(y - k)
∴ The focus is (h , k + p)
∵ The focus is (4 , 6)
∴ h = 4
∵ k + p = 6 ⇒ (1)
∵ The directrix is y = k - p
∴ k - p = 2 ⇒ (2)
* Add (1) and(2) to find k
∴ 2k = 8 ⇒ ÷ 2 for both sides
∴ k = 4
* Substitute the value of k in (1) to find p
∵ 4 + p = 6 ⇒ subtract 4 from both sides
∴ p = 2
* Now lets write the equation
∴ (x - 4)² = 4(2)(y - 4) ⇒ simplify
∴ (x - 4)² = 8(y - 4)
* The equation of the parabola is (x - 4)² = 8(y - 4)
Generalize the pattern by finding the nth term. 6, 10, 14, 18, 22, ... options: A. 4n B. 4n + 2 C. 4n + 10 D. 6n + 4
ANSWER
B.
[tex] 4n + 2[/tex]
EXPLANATION
The given pattern is:
6, 10, 14, 18, 22, ...
The first term if the pattern is a=6.
The common difference among the terms is
[tex]d = 10 - 6 = 4[/tex]
The general pattern can be found using the formula:
[tex]f(n)=a+d(n-1)[/tex]
We substitute the values to get,
[tex]f(n)=6+4(n-1)[/tex]
Expand to get;
[tex]f(n)=6+4n-4[/tex]
[tex]f(n) = 4n + 2[/tex]
The correct answer is B.
Tom opened a lemonade stand to earn money to buy a new bike for $200. He sells a cup of lemonade for $1.00. On the first day he sold 8 cups of lemonade, on the second day he sold 16 cups and on the third day he sol 32 cups. If Tom keeps selling cups of lemonade this way on what day will he have a total of $200.
1 - 8
2 - 16
3 - 32
x - +200
Each lemonade has a profit of $1, so the number of cups of lemonade he sells is the same as the amount of dollars he has. You just need to add each previous day's total to the next day's, doubling the amount of cups from the previous day's for each new day.
4 - (32 x 2 = ) 64
8 + 16 + 32 + 64 = 120. We need at least $80 dollars more, so we continue.
5 - (64 x 2 = ) 128
120 + 128 = $248.00 That's more than enough, so Tom will have enough money for his bike after the fifth day of selling lemonade.
Pleeeeeeeeease help!!!!!!!
Answer:
x = 11
Step-by-step explanation:
If a radius bisects a chord ( as in the lower chord )then it is perpendicular to the chord.
Thus both chords are equidistant from the centre ( both 12 ) and are therefore congruent.
Hence x = 11
Help with this question, please!! I don't understand!
Answer:
(0, 1)
Step-by-step explanation:
all of the points are the same number away: 2√5
Answer:
(0, 1)
Step-by-step explanation:
A, B, and C are points on a circle. You are being asked to find the center of the circle. You can do that any of several ways.
I find it useful to plot the points on a graph. Doing so reveals that AB is perpendicular to BC, so ABC is a right triangle, and the center you want is the midpoint of the hypotenuse (AC).
(A+C)/2 = ((2, -3) +(-2, 5))/2 = (2-2, -3+5)/2 = (0, 1) . . . . . coordinates of center
___
From a construction point of view, the center of the circle is the point of intersection of the perpendicular bisectors of the chords. In the attached, we have used a geometry program to draw the perpendicular bisectors of AB and BC. They meet at (0, 1).
___
From an algebra point of view, the points on the circle with center (h, k) and radius r satisfy the equation ...
(x -h)^2 +(y -k)^2 = r^2
Filling in the point values, you get three equations in the three unknowns (h, k, r):
(2-h)^2 +(-3-k)^2 = r^2(4-h)^2 +(3-k)^2 = r^2(-2-h)^2 +(5-k)^2 = r^2Finding the difference between any two pairs of these will result in two linear equations in h and k, so are easily solved.
First - second: (4 -4h +h^2) +(9 +6k +k^2) -(16 -8h +h^2) -(9 -6k +k^2) = r^2 -r^2
-12 +4h +12k = 0 . . . simplify
h +3k = 3 . . . . . . . . . put in standard form
Second -third: (16 -8h +h^2) +(9 -6k +k^2) -(4 +4h +h^2) -(25 -10k +k^2) = r^2 -r^2
-4 -12h +4k = 0 . . . . simplify
3h -k = -1 . . . . . . . . . put in standard form
Now, we can add 3 times the second of these equations to the first to find h:
(h +3k) +3(3h -k) = (3) +3(-1)
10h = 0
h = 0
Then either of the equations can be used to find k = 1.
The center is (h, k) = (0, 1).
Please help me out please
Answer:
x = 30°
Step-by-step explanation:
x° is the other acute angle of the right triangle with 60° as the acute angle at the center of the circle. (The tangent line makes a right angle with the radius at the point of tangency.)