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1. How would you prove that circles are similar?
3.Find the center and the radius for the circle, given the equation:
x^2-14x+y^2+8y=16
Answers
we know that
All circles are similar. Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. In our attempt to prove all circles are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another
Part 2)
a) ∡BAD=128°-----------> by central angle
b) ∡BCD
The inscribed angle measures half of the arc it comprises.
so
∡BCD=128°/2----> 64°
c) ∡BED
The measure of the external angle is the semi difference of the arcs that it covers.
arc BCD=360°-128°=232°
∡BED=(1/2)*[232-128]-----> 52°
d) What is the relationship between BA and BE?
in the right triangle ABE
∡BEA=∡BED/2-----> 52°/2-----> 26°
tan (∡BEA)=BA/BE------> tan 26°=BA/BE----> BA/BE=0.4877
Part 3) Find the center and the radius for the circle, given the equation:
x²-14x+y²+8y=16
Group terms that contain the same variable
(x²-14x)+(y²+8y)=16
Complete the square twice. Remember to balance the equation by adding the same constants to each side.
(x²-14x+49)+(y²+8y+16)=16+49+16
Rewrite as perfect squares
(x-7)²+(y+4)²=81
(x-7)²+(y+4)²=9²
a) the center is the point (7,-4)
b) the radius is 9
Related Questions
HELP!! PLEASE, 19 POINTS!! The equation (X squared + Y squared - 6x + 4y = d) describes a circle.
1. Determine the Y-coordinate of the center of the circle. (Hint.... Complete the square)
2. The radius of the circle is 6 units. What is the value of "d" in the given equation?
Answers
x²-6x+y²+4y=d
Group terms that contain the same variable
(x²-6x)+(y²+4y)=d
Complete the square twice. Remember to balance the equation by adding the same constants to each side
(x²-6x+9)+(y²+4y+4)=d+9+4
Rewrite as perfect squares
(x-3)²+(y+2)²=d+13the center of a circle is (3,-2)
the radius r²=d+13---------> 6²=d+13---------> d=36-13------> d=23
the answer is
the Y-coordinate of the center of the circle is -2
d is equal to 23
For this case we have the following equation:
x ^ 2 + y ^ 2 - 6x + 4y = d
By completing squares we have:
x ^ 2 + y ^ 2 - 6x + 4y + (-6/2) ^ 2 + (4/2) ^ 2 = d + (-6/2) ^ 2 + (4/2) ^ 2
Rewriting we have:
x ^ 2 + y ^ 2 - 6x + 4y + (-3) ^ 2 + (2) ^ 2 = d + (-3) ^ 2 + (2) ^ 2
x ^ 2 + y ^ 2 - 6x + 4y + 9 + 4 = d + 9 + 4
(x ^ 2 - 6x + 9) + (y ^ 2 + 4y + 4) = d + 13
(x-3) ^ 2 + (y + 2) ^ 2 = d + 13
Answer:
The y coordinate of the center of the circle is:
y = -2
Part 2:
For the value of d we have:
d + 13 = 6
d = 6 - 13
d = -7
Answer:
The value of d is:
d = -7
When darcy's school bus travels at 30 miles per hour, it gets from her home to school in 12 minutes. what is the speed of darcy's bus if it makes the same trip in 18 minutes?
Answers
speed=distance/time------> distance=speed*time
step 1
find the distance with
speed=30 miles/hour-----> 30 miles/60 minutes-----> 0.5 miles/minute
time=12 minutes
distance=speed*time------> distance=0.5/12----> distance=6 miles
the distance from home to school is 6 miles
step 2
find the speed with
distance=6 miles
time=18 minutes
speed=6/18----> 0.33 miles/minute-----> *60----> 20 miles/hour
the answer is
20 miles/hour or 0.33 miles/minutes
The rectangular prism shown has a volume of 140 m3. This prism is enlarged using a scale factor of 2. What is the volume of the enlarged prism?
Answers
A color called “shocking pink” is made by mixing red paint with white paint. The ratio of red to white is 2 to 7. How much red paint should be mixed with 16 fl. oz of white paint?
Answers
Answer:
4.5 oz
Step-by-step explanation:
Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)
Answers
V = (4/3) πr ^ 3
Deriving we have:
V '= (3) (4/3) (π) (r ^ 2) (r')
Clearing r 'we have:
r '= V' / ((3) (4/3) (π) (r ^ 2))
Substituting values:
r '= 4 / ((3) (4/3) (π) ((24) ^ 2))
r '= 0.000552621 c / min
Then, the surface area is:
A = 4πr2
Deriving we have:
A '= 8πrr'
Substituting values:
A '= 8π (24) (0.000552621)
A '= 0.33 cm ^ 2 / min
Answer:
The surface area of the balloon is shrinking at:
A '= 0.33 cm ^ 2 / min
Write the quadratic function in vertex form: f(x) = 4x2 + 2x -5
A)f(x) = 4(x + 14)2 - 214B)f(x) = 4(x + 116)2 - 214C)f(x) = 4(x + 14)2 - 194D)f(x) = 4(x + 116)2 - 194
Answers
f(x) = 4x^2 + 2x - 5
= 4(x^2 + (2/4)x) - 5
= 4(x^2 + (1/2)x ) -5
= 4(x^2 + (1/2)x + 1/16 ) - 4/16 - 5
= 4(x+1/4) - 21/4 <= in vertex form
Here h= -1/4 and k = -21/4. The vertex is at (-1/4, -21/4)
Answer:its B
Step-by-step explanation:
f(x) = -4 (x + 1/4)² - 15/4
Find the exact values of cos (3pi/4radians) and sin (3pi/4 Radians)
Answers
cos (π-π/4) = -cosπ/4 = -1/√2
similarly sin3π/4=sin(π-π/4) = sin π/4 = 1/√2
If you are doing on apex the answer is √2/2
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 miles above sea level. The radius of the Earth is 3959 miles. What is the climber's distance to the horizon?
Answers
x² + r² = (r+h)²
x² + 3959² = (3959 + 3.7)²
x² = 3962.7² - 3959²
x = 171.2 miles
I hope this helps
Use the intercept form to find the equation of the line with the given intercepts. the intercept form of the equation of a line with intercepts (a, 0) and (0,
b.is
Answers
b-0
m = -------- = -b/a
0-a
Then y-0 = (-b/a)(x-a), or y = (-b/a)(x-a) (answer)
What is the equation of a circle whose center is (4 6) and whose radius is 4 cm?
Answers
The h part in with the x is your x coordinate and the k part in with the y is your y coordinate. The r stands for the radius but be careful you have to square it.
so:
(x-(4))^2 +(y-(6)^2 = 16
I like to add the parenthesis around the "plugged in" numbers to help me remember negatives if I have any.
Last Monday, Luis's mother gave birth to twins and named them Ashley and Umaima. When they were first born, Ashley weighed 2.82.8 2.8 2, point, 8 kilograms , and Umaima weighed 2.52.5 2.5 2, point, 5 kilograms and was 4949 49 49 centimeters tall. How much did the babies weigh in total?
Answers
Ashley weighed 2.8 kilograms at birth.
Umaima weighed 2.5 kilograms at birth.
Umaima being 49 centimeters tall has nothing to do with the question, since the question asks for weight only.
Add their weights together.
[tex]2.8 + 2.5 = 5.3[/tex]
The twins weighed 5.3 kilograms together.
True or False: A rectangular equation that is not a function may be a function in the polar coordinate system
Answers
The given statement is true.
The given statement is a rectangular equation that is not a function that may be a function in the polar coordinate system.
What is a rectangular equation?A rectangular equation or an equation in rectangular form is an equation composed of variables like x and y which can be graphed on a regular Cartesian plane.
Polar equations indeed can describe graphs as functions, even when the equations in the rectangular coordinate system are not one of the functions. Polar equations can be graphed accurately using hands by using the Polar Coordinate System.
Therefore, the given statement is true.
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for v=4i-8j, find unit vector u in the direction of v
a. u= 1/3i - 2/3j
b. i-j
c. sqrt3/3 i - 2 sqrt3/3 j
d. sqrt5/5 i - 2 sqrt5/5 j
Answers
u = v / lvl
The module of v is:
lvl = root ((4) ^ 2 + (-8) ^ 2)
lvl = root (16 + 64)
lvl = root (80)
lvl = 4 * root (5)
Substituting:
u = 4i-8j / (4 * root (5))
Rewriting:
u = i-2j / root (5)
u = root (5) / 5 i - 2 * root (5) / 5 j
Answer:
The unit vector in the direction of v is:
d. sqrt5 / 5 i - 2 sqrt5 / 5 j
In a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. The spades and the clubs are black and the hearts and the diamonds are red.
If two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?
-1/8
-1/2
-2/3
-3/4
Answers
Factor the polynomial:
–x3 – 3x2 – 4x
A. –x(x2 + 3x + 4)
B. –x(–x2 – 3x – 4)
C. –x(x2 + 3x – 4x)
D. x(x2 + 3x + 4
Answers
Answer:
D. [tex]-x(x^2+3x+4)[/tex]
Step-by-step explanation:
[tex]-x^3-3x^2-4x = -(x^3+3x^2+4x)= -x(x^2+3x+4)[/tex]
The football team is running a jackpot in which the prize will start at $2500 for the first game, and then increase $500 each game if there is no winner. If there are no winners, find the value of the jackpot at the end of their 16-game season.
Answers
The value of the jackpot at the end of the 16-game season will be $10,000.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
The jackpot prize starts at $2500 for the first game and increases by $500 for each game if there is no winner.
For the second game,
The prize will be $2500 + $500 = $3000.
For the third game,
The prize will be $3000 + $500 = $3500.
Continuing in this pattern, the prize for the 16th game will be:
$2500 + ($500 × 15)
= $2500 + $7500
= $10000
Therefore,
The value of the jackpot at the end of the 16-game season will be $10,000.
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Rewrite with only sin x and cos x.
sin 2x - cos 2x
Select one:
a. 2 sin2x - 2 sin x cos x + 1
b. 2 sin x
c. 2 sin2x + 2 sin x cos x - 1
Answers
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y)^6 are _____.
Answers
x ^ 6 + 6x ^ 5y + 15x ^ 4y ^ 2 + 20x ^ 3y ^ 3 + 15x ^ 2y ^ 4 + 6xy ^ 5 + y ^ 6
Therefore, the coefficients of the expansion are given by:
1, 6, 15, 20, 15, 6, 1
Answer:
The coefficients corresponding to k = 0, 1, 2, ..., 6 in the expansion of (x + y) ^ 6 are 1, 6, 15, 20, 15, 6, 1
Answer:
1, 6, 15, 20, 15, 6, 1
Step-by-step explanation:
A recipe for cake calls for 5.25 deciliters of milk. How many liters of milk are needed for the cake?
Answers
Divide 5.25 by 10 to find how many liters are needed.
5.25/10 = 0.525
0.525 liters of milk are needed for the cake.
Geo: Topic 3- Parallelograms 1pt A rhombus is a parallelogram with all four sides of equal length. One way to determine if a given parallelogram is a rhombus is to test whether its diagonals are perpendicular. The vertices of a parallelogram are M(−1,2), N(9,2), P(3,−6), and Q(−7,−6). Determine whether the parallelogram is a rhombus by checking to see if the diagonals are perpendicular. What is the slope of MP¯¯¯¯¯¯? What is the slope of NQ¯¯¯¯¯¯? Are diagonals MP¯¯¯¯¯¯ and NQ¯¯¯¯¯¯ perpendicular? Is the parallelogram a rhombus?
Answers
Factor the trinomial below.
9x2 + 6x + 1
A. (9x + 1)(x – 1)
B. (9x + 1)(x + 1)
C. (3x + 1)(3x + 1)
D. (3x + 1)(3x – 1)
Answers
9x² + 6x + 1
9x² + 3x + 3x + 1
3x(3x + 1) + 1(3x + 1)
(3x + 1)(3x + 1)
Find the average value have of the function h on the given interval. h(u) = (15 − 10u)−1, [−1, 1]
Answers
The average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
What is average value of the function?The average value of a function is given by the formula:
[tex]fav = \frac{1}{b - a} \int\limits^b_a f({x}) \, dx[/tex]
Now the given function is,
h(u) = (15 − 10u) − 1
or, h(u) = 15 − 10u − 1
or, h(u) = 14 − 10u
So, the average value on the given interval [−1, 1] is given as:
[tex]fav = \frac{1}{1 - (-1)} \int\limits^1_{-1} h({u}) \, du[/tex]
Thus, putting the value of h(u) we get,
[tex]fav = \frac{1}{(1 + 1)} \int\limits^1_{-1} (14 - 10u) \, du[/tex]
Thus integrating we get,
fav = (1/2) { [14u] - [10u²/2]
⇒ fav = (1/2) { [14u] - [5u²]
Applying the limits we get, -1 to 1,
⇒ fav = (1/2) { 14[-1 + 1] - [5{-1² + 1²}]
Solving we get,
⇒ fav = (1/2) { 14[0] - [5{1 + 1}]
⇒ fav = (1/2) {- [5{2}]
⇒ fav = -5
Thus, the average value have of the function h(u) = (15 − 10u)−1 on the given interval [−1, 1] is -5.
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exactly 2/5 of the unversity students live off campus. Of those students, 3/10 of them live at home. what fraction of the univesity's students live at home? Reduce your answer to lowest terms
Answers
2/5 * 3/10
6/50
3/25 of the students live at home
Ron and kathy are ticket sellers at their class play. ron handles student tickets that sell for $2.00 each, and kathy handles adult tickets that sell for $4.50 each. if their total income for 364 tickets was $1,175.50, how many tickets did ron sell?
Answers
You can get this by setting up a system of equations and solving by substitution.
x + y = 364 (number of tickets)
2x + 4.5y = 1175.50 (Cost)
Before simplifying, how many terms are there in the expression -2x + 8 - 6y + 8x + 11?
Answers
Final answer:
The expression contains five terms before simplifying. We simplify by combining like terms to get a simplified result of 6x - 6y + 19 and then confirm the simplification by checking if the answer is reasonable.
Explanation:
The student has asked how many terms are in the expression -2x + 8 - 6y + 8x + 11 before simplifying. A term is a single mathematical expression that may consist of constants and/or variables, sometimes multiplied together but not added or subtracted to another term. In the given expression, there are a total of five terms: -2x, +8, -6y, +8x, and +11.
To simplify the algebra, we can combine like terms. Like terms are terms that contain the same variables to the same power. Here, -2x and +8x are like terms. When we combine them, we get 6x. The constants +8 and +11 are also like terms and can be added together to get +19. So, the simplified expression is 6x - 6y + 19.
Finally, we check our answer to ensure it is reasonable. Combining like terms -2x and +8x should result in +6x, and adding constants +8 and +11 should give us +19, which is our simplified result, confirming the reasonableness of our simplification.
What are the foci of the hyperbola with equation 5y^2-4x^2=20?
Answers
divide each term by 20
(5y^2)/20-(4x^2)/20=20/20
simplifying gives us:
y^2/4-x^2/5=1
This follows the standard form of the hyperbola
(y-k)²/a²-(x-h)²/b²=1
thus
a=2, b=√5 , k=0, h=0
Next we find c, the distance from the center to a focus.
√(a²+b²)
=√(2²+(√5)²)
=√(4+5)
=√9
=3
the focus of the hyperbola is found using formula:
(h.h+k)
substituting our values we get:
(0,3)
The second focus of the hyperbola can be found by subtracting c from k
(h,k-c)
substituting our values we obtain:
(0,-3)
Thus we have two foci
(0,3) and (0,-3)
Choose the best answer.
The most expensive type of life insurance is:
term insurance
whole-life insurance
endowment life insurance
limited-payment life insurance
Answers
Answer:
Endowment life insurance
Step-by-step explanation:
got it right on odyssey
YO!!!!!!WILL GIVE 100 POINTS!!!!!!!!!!!BRAIN!!!!!!!!!!!!
Answers
f (x) = ((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3
The roots are given by:
((x + 2) ^ 2) * (x-4) * (x + 1) ^ 3 = 0
x + 2 = 0
x = -2 (multiplicity 2)
x-4 = 0
x = 4 (multiplicity 1)
x + 1 = 0
x = -1 (multiplicity 3)
Answer:
option A
Answer:
Following function:
f (x) = {(x + 2)²} × (x-4) × (x + 1)³
The roots are given by:
{(x + 2)²} × (x-4) × (x + 1)³ = 0
x + 2 = 0
x = -2
x-4 = 0
x = 4
x + 1 = 0
x = -1
Answer:
option A
Step-by-step explanation:
What is the perimeter of rectangle that is 92 feet long and 46 feet wide?
Answers
The perimeter of a rectangle that is 92 feet long and 46 feet wide is calculated using the formula P = 2l + 2w, resulting in a perimeter of 276 feet.
Explanation:The question asks for the perimeter of a rectangle with specific dimensions. To calculate the perimeter of a rectangle, we use the formula P = 2l + 2w, where l is the length and w is the width of the rectangle. Given that the rectangle is 92 feet long and 46 feet wide, we substitute these values into the formula to get the perimeter: P = 2(92) + 2(46) = 184 + 92 = 276 feet.
Therefore, the perimeter of the rectangle is 276 feet.
which of the following parametric equations are equivalent to the polar equation r=3 cos theta
Answers
x = rcos (θ)
Where "r" is the radius
Likewise y = rsin (θ)
Therefore, in the expression r = 3cos (θ) one can write r as:
r = x / cos (θ)
So:
x / cos (θ) = 3cos (θ)
x = 3cos ^ 2 (θ)
The same for y ...
y = rsin (θ)
y = 3cos (θ) sin (θ).
Finally the correct answer is option 2.
x = 3cos ^ 2 (θ) y = 3cos (θ) sin (θ).
Answer:
B
Step-by-step explanation: