Answer:
(x + 4)^2 + (y - 8)^2 = 81
or
(x + 4)^2 + (y - 8)^2 = 9^2 depending on how your teacher wants it written.
Step-by-step explanation:
The standard form for a circle is
(x + h)^2 + (y + k)^2 = r^2
r is the radius.
You are given the diameter
r = d/2
r = 18/2
r = 9
So you already have the right hand side of the equation
(x + h)^2 + (y + k)^2 = 9*2
(x + h)^2 + (y + k)^2 = 81
You basically have h and k as well. They come from the center point.
h = 4
k = - 8
So the equation of the circle (and the answer) is
(x + 4)^2 + (y - 8)^2 = 81
One question remains. Why do the x and y values change signs? If you know what the distance formula is, then what you are finding is the distance r of all points on the circle from the center of the circle.
It is the distance formula that is actually the formula for the circle.
Find each interior angles the following regular polygons in degrees and grades
(a) Triangle
(b) Quadrilateral (c) Pentagon (d) Hexagon
(e) Heptagon
(1) Octagon (g) Nonagon
(h) Decagon
polygons in degrees and grades
(a) 120° or 133.33 grades.
(b)135° or 150 grades.
(c) 144° or 160 grades.
(d) 150° or 166.67 grades.
(e) 154.29° or 171.43 grades.
(f) 157.5° or 175 grades.
(g) 160° or 177.78 grades.
(h) 162° or 180 grades.
Step-by-step explanation:
A regular polygon is a polygon that has all sides and all angles equal.
Each interior angle, k (measured in degrees), of a regular polygon is given by;
k = s ÷ n -----------(k)
Where;
s = sum of the interior angle of the polygon.
n = number of sides of the polygon
To get s, we use
s = (n - 2) x 180 [This is the formula to calculate the sum of the interior angles of a polygon]
Substituting s this into equation (i) gives
k = (n - 2) x 180 ÷ n
k = 180(n - 2) ÷ n -------------(ii)
(a) Triangle.
A triangle has n = 3 sides, therefore, each interior angle of a triangle is found by substituting n = 3 into equation (ii)
k = 180(3 - 1) ÷ 3
k = 180(2) ÷ 3
k = 180 x 2 ÷ 3
k = 360 ÷ 3
k = 120°
Convert to grade.
Remember that;
90° = 100 grades
∴ 120° = [tex]\frac{120 * 100}{90}[/tex] grades
⇒ 120° = 133.33 grades.
Therefore, each interior angles of a regular triangle is 120° or 133.33 grades.
(b) Quadrilateral.
A quadrilateral has n = 4 sides, therefore, each interior angle of a quadrilateral is found by substituting n = 4 into equation (ii)
k = 180(4 - 1) ÷ 4
k = 180(3) ÷ 4
k = 180 x 3 ÷ 4
k = 540 ÷ 4
k = 135°
Convert to grade.
Remember that;
90° = 100 grades
∴ 135° = [tex]\frac{135 * 100}{90}[/tex] grades
⇒ 135° = 150 grades.
Therefore, each interior angles of a regular quadrilateral is 135° or 150 grades.
(c) Pentagon
A pentagon has n = 5 sides, therefore, each interior angle of a pentagon is found by substituting n = 5 into equation (ii)
k = 180(5 - 1) ÷ 5
k = 180(4) ÷ 5
k = 180 x 4 ÷ 5
k = 720 ÷ 5
k = 144°
Convert to grade.
Remember that;
90° = 100 grades
∴ 144° = [tex]\frac{144 * 100}{90}[/tex] grades
⇒ 144° = 160 grades.
Therefore, each interior angles of a regular pentagon is 144° or 160 grades.
(d) Hexagon
A hexagon has n = 6 sides, therefore, each interior angle of a hexagon is found by substituting n = 6 into equation (ii)
k = 180(6 - 1) ÷ 6
k = 180(5) ÷ 6
k = 180 x 5 ÷ 6
k = 900 ÷ 6
k = 150°
Convert to grade.
Remember that;
90° = 100 grades
∴ 150° = [tex]\frac{150 * 100}{90}[/tex] grades
⇒ 150° = 166.67 grades.
Therefore, each interior angles of a regular hexagon is 150° or 166.67 grades.
(e) Heptagon
A heptagon has n = 7 sides, therefore, each interior angle of a heptagon is found by substituting n = 7 into equation (ii)
k = 180(7 - 1) ÷ 7
k = 180(6) ÷ 7
k = 180 x 6 ÷ 7
k = 1080 ÷ 7
k = 154.29°
Convert to grade.
Remember that;
90° = 100 grades
∴ 154.29° = [tex]\frac{154.29 * 100}{90}[/tex] grades
⇒ 154.29° = 171.43 grades.
Therefore, each interior angles of a regular heptagon is 154.29° or 171.43 grades.
(f) Octagon
An octagon has n = 8 sides, therefore, each interior angle of a octagon is found by substituting n = 8 into equation (ii)
k = 180(8 - 1) ÷ 8
k = 180(7) ÷ 8
k = 180 x 7 ÷ 8
k = 1260 ÷ 8
k = 157.5°
Convert to grade.
Remember that;
90° = 100 grades
∴ 157.5° = [tex]\frac{157.5 * 100}{90}[/tex] grades
⇒ 157.5° = 175 grades.
Therefore, each interior angles of a regular octagon is 157.5° or 175 grades.
(g) Nonagon
A nonagon has n = 9 sides, therefore, each interior angle of a nonagon is found by substituting n = 9 into equation (ii)
k = 180(9 - 1) ÷ 9
k = 180(8) ÷ 9
k = 180 x 8 ÷ 9
k = 1440 ÷ 9
k = 160°
Convert to grade.
Remember that;
90° = 100 grades
∴ 160° = [tex]\frac{160 * 100}{90}[/tex] grades
⇒ 160° = 177.78 grades.
Therefore, each interior angles of a regular nonagon is 160° or 177.78 grades.
(h) Decagon
A decagon has n = 10 sides, therefore, each interior angle of a decagon is found by substituting n = 10 into equation (ii)
k = 180(10 - 1) ÷ 10
k = 180(9) ÷ 10
k = 180 x 9 ÷ 10
k = 1620 ÷ 10
k = 162°
Convert to grade.
Remember that;
90° = 100 grades
∴ 162° = [tex]\frac{162 * 100}{90}[/tex] grades
⇒ 162° = 180 grades.
Therefore, each interior angles of a regular decagon is 162° or 180 grades.
pls answer! Dylan spots an airplane on radar that is currently approaching in a straight line, and
that will fly directly overhead. The plane maintains a constant altitude of 6400 feet.
Dylan initially measures an angle of elevation of 16° to the plane at point A. At some
later time, he measures an angle of elevation of 36° to the plane at point B. Find the
distance the plane traveled from point A to point B. Round your answer to the
nearest foot if necessary.
Answer:
13510 ft
Step-by-step explanation:
I have attached a triangle diagram to depict this situation.
From the diagram, we see that distance between A and B is denoted by x.
Now, from trigonometric ratios in this type of triangle, let's first find y.
6400/y = tan 36
y = 6400/tan 36
y = 8808.84 ft
Now, we can find x from;
6400/(8808.84 + x) = tan 16
6400/tan 16 = 8808.84 + x
22319.452 = 8808.84 + x
x = 22319.452 - 8808.84
x ≈ 13510 ft
The distance the plane traveled from point A to point B is 13510 ft
Calculation of the distance:Here we assume the distance between A and B should be x.
Now the y value should be
[tex]6400\div y = tan 36\\\\y = 6400\div tan 36[/tex]
y = 8808.84 ft
Now, we can find x
[tex]6400\div (8808.84 + x) = tan\ 16\\\\6400\div tan\ 16 = 8808.84 + x[/tex]
22319.452 = 8808.84 + x
x = 22319.452 - 8808.84
x ≈ 13510 ft
Learn more about distance here: https://brainly.com/question/785292
The graph of y=h(x) is a line segment joining the points (1, -5) and (9,1).
Drag the endpoints of the segment below to graph y = h-'(x).
Answer:
[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]
Step-by-step explanation:
Given
Graph h:
[tex](x_1,y_1) = (1,-5)[/tex]
[tex](x_2,y_2) = (9,1)[/tex]
Required
Plot [tex]h^{-1}(x)[/tex]
First, calculate h(x)
Calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1--5}{9-1}[/tex]
[tex]m = \frac{6}{8}[/tex]
[tex]m = \frac{3}{4}[/tex]
The equation is:
[tex]y = m(x - x_1) + y_1[/tex]
So, we have:
[tex]y = \frac{3}{4}(x - 1) -5[/tex]
[tex]y = \frac{3}{4}x - \frac{3}{4} -5[/tex]
[tex]y = \frac{3}{4}x + \frac{-3 - 20}{4}[/tex]
[tex]y = \frac{3}{4}x - \frac{23}{4}[/tex]
Next, calculate [tex]h^{-1}(x)[/tex]
Swap y and x
[tex]x = \frac{3}{4}y - \frac{23}{4}[/tex]
Solve for y
[tex]\frac{3}{4}y = x + \frac{23}{4}[/tex]
Multiply through by 4
[tex]3y = 4x + 23[/tex]
Divide through by 3
[tex]y = \frac{4}{3}x + \frac{23}{3}[/tex]
Replace y with [tex]h^{-1}(x)[/tex]
[tex]h^{-1}(x) = \frac{4}{3}x + \frac{23}{3}[/tex]
See attachment for graph
What is the value of a?
A. 12
B. 15
C. 17.25
D. 21.25
Answer:
the answer is a.12
i think
Answer:
17.25
Step-by-step explanation:
i am a number beetween 20 and 30 who is divisible by 2 4 and 7. I am an even number as well who am I?
Answer:
28
Step-by-step explanation:
28/2=14
28/4=7
28/7=4
28 is an even number
Step-by-step explanation:
28 is the answer
28 is a number between 20 and 30
and divisible by
28/2=14
28/4=7
28/7=4
1. What term means "per hundred"?
A base B. percent
C. percentage
D.rate
2. Which of the following is correct?
A. 33% = 0.33 B. 33% = 03.3
C.33% = 33
D. 33% = 3.03
3. 45% of the grade 5 pupils are girls. Express 45% as decimals.
A. 0.045 B. 0.45
C. 4.5
D. 45.0
4. In the statement 35% of 600 = 210. Which is the percentage?
A. 35%
B. 600
C.210
D. none
5. Which does not belong?
A. 21%
B. 21/100 C. 21:100 D. 21
6. Which element of percent represent part of the whole?
A. base B. percent C. percentage D.rate
7. In a survey on the choice of pizza, 900 out of 1500 people preferred brand A to B.
What percent preferred A? What is the missing element?
A. base B. percent
C. percentage D. rate
8. What is the missing element in the problem, "A big theater has 1400 seats. During a
concert, it is 95% full. How many seats were taken?"
A. base B. percent
C. percentage
D. rate
9. Which element of percent represents the whole?
A. base B. percent
C. percentage D.rate
10. How many is 75% of a class?
A. 1/3 B. 1/2 C.3/4 D. 5/6
Answer:
1. B
2. B
3. B
4. A
5. D
6. A
7. C
8. D
9. A
10. C
Which of these would be the opposite of a progressive tax?
Answer:
b
Step-by-step explanation:
(2+5i)+(-3-4i) what is the answer to this question?
Answer:
-1+i
Step-by-step explanation:
(2+5i)+(-3-4i)
=(2-3)+i(5-4)
=-1+i
Answer:
[tex]−1+i[/tex]
Step-by-step explanation:
[tex](2+5i)+(−3−4i)[/tex]
[tex]2+5i−3−4i[/tex]
[tex]−1+5i−4i[/tex]
[tex]−1+i[/tex]
Hope it is helpful.....Hamburger Heaven is having a lunch special where customers buy one -pound cheeseburger and get one free. If they set aside pounds of meat, how many -pound cheeseburgers can they make?
Answer:
hey um how many pounds of meat do we know that yet?
Answer:
49 hamburgers
Please quickly need this before 30 mimutes
Answer:
x = 4.48
Step-by-step explanation:
read the picture
Plz help i need a correct answer asap
Determine where the function is increasing, decreasing, and constant.
Answer:
X y better because it has X and Y is no no
A rope with a length of 3.5 meters is tied from a stake in the ground to
the top of a tent. It forms a 17 degree angle with the ground. How tall
is the tent?
Answer: Approximately 1.0233 meters
Round this however you need to
====================================================
Work Shown:
Refer to the drawing below.
sin(angle) = opposite/hypotenuse
sin(17) = x/3.5
3.5*sin(17) = x
x = 3.5*sin(17)
x = 1.02330096652958
x = 1.0233
Be sure that your calculator is in degree mode.
simplify 2p/3 ×5p/12
Answer:
After simplify answer will be :[tex]\frac{5p}{18}[/tex]
Step-by-step explanation:
Given data:
[tex]\frac{2p}{3} *\frac{5p}{12}[/tex]
Now,
[tex]\frac{10p}{36}[/tex]
Final answer would be :
[tex]\frac{10p}{36}=\frac{5p}{18}[/tex]
How many solutions does this linear system have?
y=-1/2x+4
x + 2y = 8
one solution: (8,0)
one solution: (0,8)
no solution
O infinite number of solutions
Answer:
no solution
Step-by-step explanation:
__________
There are ''infinite number of solutions'' does this linear system have.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Linear systems are,
⇒ y = -1/2x + 4 ... (i)
⇒ x + 2y = 8 .. (ii)
Now, From equation (ii);
⇒ x + 2y = 8
⇒ 2y = - x + 8
⇒ y = - 1/2x + 4
Which is same as equation (i).
Hence, There are infinite number of solutions does this linear system have.
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ7
Help help help help
answer: 116⁰
z⁰ for y⁰ because it's
equal
A student takes a true-false test consisting of 10 questions. Assuming the student guesses at each question, find the probability that the student gets a 60% on the test.
the perimeter of a rectangular painting is 304 CM. If the width of the paint is 63 cm what is the length
Answer:
The PERIMETER P is the distance around the rectangle.
Let's call the width of the rectangle W and the length of the rectangle L.
As you go around the edge there two equal lengths and two equal widths.
The formula for the perimeter of a rectangle is P=2*L+2*W.
P=2L%2B2W
Substitute 290 for P and 62 for the width.
290=2L%2B2%2862%29
Solve for L.
290=2L%2B2%2862%29
290=2L%2B124
290-124=2L
2L=166
L=83
The equation L=83 means that the length is 83 cm.
CHECK your work.
2(62)+2(83) = 124+166 = 290cm.
The length of the rectangle is 83cm.
What is the solution of |4 − y| = 1?
A. y = 3 or y = 5
B. y = −3 or y = −5
C. y = −3 or y = 5
D. y = 3 or y = −5
A is the answer.
Answer:
A
Step-by-step explanation:
|4 − y| = 1
drop absolute value lines
create two problems
4 - y = 1
and
4 - y = -1
solve for y
Two cards are drawn without replacement from a standard deck of 52 playing cards. What is the probability of choosing a king and then, without replacement, a face card? Express your answer as a fraction or a decimal number rounded to four decimal places
Answer:
0.0181 probability of choosing a king and then, without replacement, a face card.
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Probability of choosing a king:
There are four kings on a standard deck of 52 cards, so:
[tex]P(A) = \frac{4}{52} = \frac{1}{13}[/tex]
Probability of choosing a face card, considering the previous card was a king.
12 face cards out of 51. So
[tex]P(B|A) = \frac{12}{51}[/tex]
What is the probability of choosing a king and then, without replacement, a face card?
[tex]P(A \cap B) = P(A)P(B|A) = \frac{1}{13} \times \frac{12}{51} = \frac{1*12}{13*51} = 0.0181[/tex]
0.0181 probability of choosing a king and then, without replacement, a face card.
Use the method of least squares to solve the following problem.
Given the data set below, find the line of best fit? Then find the y-value for when x=7. Yes, there are supposed to be
two 6's.
Х
1
2
4
5
6
6
8
9
Y
14
10
12
8
9
6
3
4
If a triangle has side lengths a, b, and c, and if a^2 + b^2 = c^2, then the converse of the Pythagorean theorem says that the triangle is a(n)
A. equiangular triangle
B. scalene triangle
C. equilateral triangle
D. right triangle
Mr.flood records that 48% of his class do their homework on time. What decimal represents the percent of students who hand it late
Answer:
0.52
Step-by-step explanation:
100% - 48% = 52%
[tex]\frac{52}{100}[/tex]
0.52
Select the TRUE statement for completely random design.
a.)The experimental units are assigned randomly to exactly one control group and one treatment group.
b.)The experimental units are assigned randomly to one or more control groups and exactly one treatment group.
c.)The experimental units are assigned randomly to one or more control groups and one or more treatment groups.
d.)The experimental units are assigned randomly to exactly one control group and one or more treatment groups.
Answer:
d.)The experimental units are assigned randomly to exactly one control group and one or more treatment groups
Step-by-step explanation:
Completely randomized design can be regarded as a type of experimental design in which the experimental units are assigned randomly for different treatments. This experimental design is utilized in cases whereby experimental units are seen to be “uniform" this implies that no uncontrolled factor in the experiment. completely randomized designs are engaged in studying effects of one primary factor by ignoring other nuisance variables it perform comparison of values of a response variable taking into account of the different levels of that primary factor. It should be noted that in completely random design, the experimental units are assigned randomly to exactly one control group and one or more treatment groups
1 ÷ 7
pls help me
hi)
Answer:
7 lol
Step-by-step explanation:
self explanatory-
but you divide 1 by 7 you get 7
A retail brand plans to open its stores across all cities with a population of more than one million. To prepare for this, it refers to the past year's census done by the government.
Which statement accurately describes the type of data the retail brand is using?
A. The retail brand is relying on raw data because it has to ask for permission to use the census.
B. The retail brand is relying on available data because customers provide information to the census.
C. The census is an example of available data because the government provides it.
D. The census is an example of raw data because the government provides it.
Answer: C. The census is an example of available data because the government provides it.
Step-by-step explanation:
The statement that accurately describes the type of data the retail brand is using is that census is an example of available data because the government provides it.
Acensus is referred to as an official survey of a country's population which is done in order to know the number of people living there and to know the details of the people like their ages, gender etc.
Find the distance between the points ( 19,-5) and ( 11, 10).
Answer:
Let the given two points be A & B. Let A ( 19 , - 5 ) be ( x₁ , y₁ ) & B ( 11 , 10 ) be ( x₂ , y₂ ) Remember : The formula to find out the distance between any two points is [tex] \tt{ \sqrt{( x_{2} -x _{1}) ^{2} + (y _{2} - y_{1}) ^{2} }} [/tex] .[tex] \large{ \tt{✺ \: SOLUTION}} : [/tex]
[tex] \large{ \boxed{ \tt{AB = \sqrt{(x_{2} - x_{1} ) ^{2} + (y_{2} - y_{1}) ^{2} } }}}[/tex]
[tex] \large{ \tt{⟶ \sqrt{(11 - 19)^{2} + (10 - ( - 5) ^{2} } }}[/tex]
[tex] \large{ \tt{⟶ \sqrt{ {8}^{2} + {15}^{2} } }}[/tex]
[tex] \large{ \tt{⟶ \: \sqrt{64 + 225} }}[/tex]
[tex] \large{ \tt{⟶ \sqrt{289}}} [/tex]
[tex] \boxed{ \large{ \tt{⟶ \: 17 \: \text{units}}}}[/tex]
And we're done! Let me know if you have any questions regarding my answer :)▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁
A wet bicycle tire leaves a trace of water on the floor. The tire has a radius of 30 cm, and the bicycle wheel
makes 3 full rotations before stopping.
How long is the trace of water left on the floor?
Round your answer to the nearest cm.
Answer:
The trace of the water left on the floor is 566 cm.
Step-by-step explanation:
The bicycle wheel has a circular shape, therefore;
1 revolution is the same as the circumference of the wheel. So that 3 revolutions is the same as multiplying the circumference of the wheel by 3.
circumference = 2[tex]\pi[/tex]r
where r is the radius of the wheel (r = 30 cm).
Thus,
circumference = 2 x [tex]\frac{22}{7}[/tex] x 30
= [tex]\frac{1320}{7}[/tex]
circumference = 188.57 cm
3 revolutions = 3 x 188.57
= 565.71 cm
Therefore, the trace of the water left on the floor is 566 cm.
I need help with this fast
Answer:
1. positive
2. No
(for number 3, I'm not sure if my answer to it is going to be correct)
Step-by-step explanation:
1. the dots look like they are going up
2. there are no outlying dots that look unusual
What is the answer pls I need finals
Answer:
[tex]( - 2,1)[/tex]
Step-by-step explanation:
Hope it is helpful...
