if the edge of the circle lies four units directly up from the x-axis what is the length of BC? What is the distance from B to D?
Answers
By using what we know about circles and distance between points, we will see that:
BD = 18 units
BC = 16.97 units
What is the distance from B to D?
Remember that the distance between two points (x₁, y₁) and (x₂, y₂) is given by:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
The distance from B to D, will be equal to the distance from B to A, minus the radius of the circle.
Because we know that the center of the circle is at (8, 10), and the edge of the circle is 4 units above the x-axis, we can assume that the closest point on the circle to the x-axis is:
(8, 4)
Then the radius of the circle is given by the distance between these two points:
[tex]r = \sqrt{(8 - 8)^2 + (10 - 4)^2} = 6[/tex]
Now we need to find the distance between A and B.
A = (8, 10)
B = (0, 10 - 16*√2)
The distance between these points is:
[tex]d = \sqrt{(8 - 0)^2 + (10 - 10 + 16*\sqrt{2})^2 } \\\\d = \sqrt{(8)^2 + (16*\sqrt{2})^2 } = 24[/tex]
And the distance from B to D is the distance from B to A, minus the radius of the circle, so we have:
BD = BA - r = 24 - 6 = 18
The distance from B to D is 18 units.
To get the value of BC, we use the fact that this is a cathetus of a right triangle with a hypotenuse of 18 units, and where the other side AC measures 6 units, then we have:
BC^2 + 6^2 = 18^2
BC = √(18^2 - 6^2) = 16.97 units.
If you want to learn more about circles, you can read:
https://brainly.com/question/1559324
Related Questions
Q. A room measure 3m 55cm by 2m 25 cm. What is the perimeter of the room?
Ans. Given L=3m,55cm
B=2m,25cm
Perimeter = 2(l+b)
=2 (3m,55cm + 2m, 25cm)
3m 55cm
2m 25cm +
_____________
5m 80cm
______________
2×(5cm,80) 5×2=10 , 80×2=160
So 10m 160cm
but the answer is 11m 60 cm why and how to convert?
Answers
Answer:
100cm = 1m
Thus, one more step should be added to your working to arrive at the final answer:
Perimeter
= 10m 160cm
= 11m 60cm
This is because 160cm= 100cm +60cm, which is also equivalent to 1m 60cm.
Alternative working:
Convert all the units to cm first.
[tex]\boxed{1 \: m= 100 \: cm}[/tex]
Length
= 5m 55cm
= 300cm +55cm
= 355cm
Breadth
= 2m 25cm
= 200cm +25cm
= 225cm
Perimeter
= 2(length +breadth)
= 2(355 cm +225 cm)
= 2(580 cm)
= 1160 cm
= 11m 60cm
From the second last step to the last step, you could divide 1160 by 100 to find how many meters are there. You would get a quotient of 11 and a remainder of 60. Since this 60 cannot be changed into meters as a whole number, we can leave it as 11m 60cm. Otherwise, it is also correct to leave it as 1160cm or 11.6m unless otherwise stated.
However, 10m 160cm is not preferred since the conversion of cm to m is done partially, as the 160 cm can still be further simplified.
This hyperbola is centered at the origin. Find its equation.
Answers
Step-by-step explanation:
Use these equations.
Equation of a Hyperbola, centered at orgin
[tex] \frac{ {x}^{2} }{ {a}^{2} } - \frac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
where a is the major axis
B is the minor axis.
Since a and X are first, the x axis is the major.
This also means the x axis contains the vertices and foci as well.
The equation of vertices when x is major axis is
[tex](x ±a)[/tex]
Since the vertices are (±1,0), and the orgin is (0,0). The length of a is 1.
So a=1.
The equation of foci is
[tex](x±c)[/tex]
Where c is formed by
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
We know that c is 2 since the distance from the foci and center is 2. A is 1, so let find b.
[tex] {2}^{2} = {1}^{2} + {b}^{2} [/tex]
[tex]4 = 1 + {b}^{2} [/tex]
[tex]3 = {b}^{2} [/tex]
[tex] \sqrt{3} = {b}[/tex]
So our equation is
[tex] \frac{ {x}^{2} }{1 {}^{2} } - \frac{ {y}^{2} }{ (\sqrt{3}) {}^{2} } = 1[/tex]
[tex] \frac{ {x}^{2} }{1} - \frac{ {y}^{2} }{3} = 1[/tex]
Hi is 19,683 the answer?
Answers
Answer:
No
Step-by-step explanation:
the answer is 3.
3×3×3=27.
therefore the cube root of 27 is 3.
An architect’s drawing was drawn so the scale of 1/2 inch represented 6 feet. What was the actual height of a wall marked 4 1/2 inches high?
Answers
Ratio remains same
Let that be x4 -1/2=9/2[tex]\\ \rm{:}\dashrightarrow 1/2/6=9/2/x[/tex]
[tex]\\ \rm{:}\dashrightarrow x/2=27[/tex]
[tex]\\ \rm{:}\dashrightarrow x=54ft[/tex]
Find the solutions to x2 = 24.
O A. x = 6/4
O B. x = 14 16
O C. *= +62
D. X = +2.16
Answers
Answer:
b.× = 14 16
Step-by-step explanation:
#stay safe
hope it helps
Variables y and x have a proportional relationship, where y = 18 when x = 2.
What is the value of x when y = 36?
Enter your answer in the box.
x=
Answers
Answer:
x = 4
Step-by-step explanation:
If y = 36, that means the original y = 18 was multiplied by 2. So, we have to multiply x = 2 by 2 as well.
2 * 2 = 4, so x = 4
which fraction is closest to 1 a) 8/7 b) 9/11 b) 6/5 c) 1 whole 2/9
Answers
Step-by-step explanation:
a) 8/7
hope it helps u...
If f(x) = 5x + 6 and g(x) = x + 5, what is (fºg)(31)?
Answers
Here’s a step by step process
It takes 56 pounds of seed to completely plant an 8-acre field. How many acres can be planted per pound of seed?
Answers
Answer:
About 0.14 acres
Step-by-step explanation:
56 lb = 8 acres
1 lb = x
We can cross multiply:
(8 acres)(1 lb) = (56 lb)(x)
Solving for x:
x = 8 ÷ 56 ≈ 0.14 acres
Multiply: (x + 3) (x + 7) Simplify and write your answer in Standard Form.
Answers
Answer:
[tex](x + 3)(x + 7) \\ (x)(x) + (x)(7) + (3)(x) + (3)(7) \\ = {x}^{2} + 7x + 3x + 21 \\ = {x}^{2} + 10x + 21[/tex]
**Find all x - coordinates on the curve y = 2x ^ 3 - 3x ^ 2 - 12x + 20 where the tangent line is parallel to the x-axis.
Answers
Answer:
openup 1 em We want to find the points on the curve y=2x^3-3x^2-12x+20y where the tangent line is parallel to the xx-axis, which means that the slope=0
Jack rides in a motorboat against a river current for 36 km. Then he returns to his
starting point by floating down river on a raft. Tommy travels 9 hours less on the
motorboat than on the raft. Find the speed of the river current if the speed of the
motorboat in still water is 15 km/h.
Answers
The speed of the river current is 11.5 km/h.
What is speed?
Speed is the ratio of total distance travelled to total time taken. IT is given by:
Speed = distance / time
Let b represent the speed of the current and t represent the time, hence:
(15 + b)= 36/t
t = 36 / (15 + b)
Also:
(15 - b)= 36/(t + 9)
t = [36 - 9(15 - b)]/(15 - b)
Hence:
36 / (15 + b) = [36 - 9(15 - b)]/(15 - b)
b = 11.5 km/h
The speed of the river current is 11.5 km/h.
Find out more on speed at: https://brainly.com/question/4931057
RSM VERIFIED ANSWER
this answer was written by an RSM student, and has been confirmed by the portal
Answer:
3km/hr
not sure how to do it i just copied off my rsm teacher, but its right lol
also would rly appreciate brainliest but i know i didnt have an explaination. I would also really appreciate if other users would thank and rate this answer so people looking at a later date would know its reliable
Write a completely simplified rational expression that represents the exchange rate Salma will receive in dollars per euro. Explain how you came up with your expression.
Answers
The exchange rate that She will receive is an algebraic expression
The exchange rate that Salma will receive in dollars per euro is [tex]\frac{12x - 9}{4x -6}[/tex]
How to determine the exchange rateThe amount of dollars with Salma is given as:
[tex]Dollar = \frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}[/tex]
The amount of Euro she can buy is:
[tex]Euro = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]
Let the exchange rate be r.
So, we have:
[tex]Dollar * \frac 1r = Euro[/tex]
The equation becomes
[tex]\frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}* \frac 1r = \frac{2x^2 -x-3}{x^2 + 6x +5}[/tex]
Factorize the expressions
[tex]\frac{3(x + 2)(4x - 3)}{2(x + 5)(x +2)}* \frac 1r = \frac{(x +1)(2x -3)}{(x + 5)*x + 1)}[/tex]
Cancel out the common factors
[tex]\frac{3(4x - 3)}{2}* \frac 1r = \frac{(2x -3)}{1}[/tex]
Make r the subject
[tex]\frac 1r = \frac{2(2x -3)}{3(4x - 3)}[/tex]
Expand
[tex]\frac 1r = \frac{4x -6}{12x - 9}[/tex]
Make r the subject
[tex]r = \frac{12x - 9}{4x -6}[/tex]
Hence, the exchange rate is [tex]\frac{12x - 9}{4x -6}[/tex]
Read more about algebraic expressions at:
https://brainly.com/question/4344214
Correct answers only please put number with answer ex:(1.A, 2.B, 3.C etc.)
Answers
Answer:
See below for answers and explanations
Step-by-step explanation:
Problem 1
Here, [tex]\frac{3}{4}v[/tex] tells us that the vector [tex]v[/tex] is impacted by a scale factor of [tex]\frac{3}{4}[/tex], so we are doing scalar multiplication basically for both components of the vector. This only impacts the magnitude of the vector and not its direction. If we were to assume that [tex]v=\langle4,8\rangle[/tex], then [tex]\frac{3}{4}v=\langle\frac{3}{4}(4),\frac{3}{4}(8)\rangle=\langle3,6\rangle[/tex]. Therefore, this matches vector [tex]u[/tex], so D is the correct answer
Problem 2
Cannot be able to read as the text is too small
Problem 3
Cannot be able to read as the text is too small
Problem 4
[tex]-7u=\langle-7(8),-7(-4)\rangle=\langle-56,28\rangle=-56i+28j[/tex], so A is correct. Remember to use scalar multiplication for each component.
Problem 5
[tex]r-s=\langle5-9,11-(-8)\rangle=\langle-4,19\rangle[/tex], so B is correct. Remember to subtract the horizontal and vertical components seperately.
PLS HELP 40PTS Select the inequality that models the problem.
The sum of two consecutive odd integers is at least 76. Find the least possible pair of integers.
n + n + 2 ≥ 76
n + n + 2 > 76
n + n + 1 > 76
n + n + 1 ≥ 76
Answers
Answer:
n + n + 2 ≥ 76Explanation:
To find odd numbers, we have to use n + n + 2
For example let the number be 1, the 1 + 2 = 3, 3 + 2 = 5.
Therefore, used: n + n + 2 expression and it should be equals or at least 76. so finally n + n + 2 ≥ 76 applies.
SOMEONE PLEASE ANSWER THIS I NEED HELP REALLY BADLY
Answers
Answer:
x=-1
Step-by-step explanation:
2x-5=-5x+2
7x=-7
x=-1
The quadrilateral shown is a rhombus. What is angle 4?
A; 28
B; 32
C; 58
D; 90
Answers
This is because 3 is congruent to 4.
Below is the graph of a trigonometric function. It has a maximum point at
(1/4pi,-2.2)
and a minimum
point at
(3/4pi,-8.5) what is the amplitude
Answers
Step-by-step explanation:
Amplitude is the distance between the center line of the function and the top or bottom of the function.
The amplitude is half the distance between the max and the min, so
Amplitude = 1/2(max - min)
Amplitude = 1/2(-2.2 -(-8.5))
So amplitude = 1/2(6.3)
= 3.15
how many solutions does "-4x" + 10 y = 6 2x - 5y = 8
Answers
Answer:
Infinitely many
Step-by-step explanation:
There are many solutions because 0=0.
help guys plsss i don't know this one ;( plsss i will wait
Answers
Answer:
1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
there are 4 cans of soup and 1 of them is tomato
you have a 1 out of 4 chance of picking tomato soup
Over 40 hours a person earns $1,000. How much money does she earn per hour?
Answers
40/1000 = 25 or $25 x 40 hours = $1,000
you have a credit card that has a balance of $3589.90 if you have a good credit rating how much must you pay at the end of the month to get the balance to acceptable debt ratio percentage?
Answers
Answer:
$1107.55
Step-by-step explanation:
3,589.90 x .0590/12 = $17.653,589.90 + 17.65 =3,607.553,607.55 - 2,500 = $1,107.55
BRAINLIEST?
Graph the line whose y-intercept is 9 and whose x-intercept is -2.
Answers
Answer:
y = 4.5x + 9, graphing done below.
Solving steps:
( -2 , 0 ), ( 0, 9)
slope:
[tex]\sf \frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\sf \frac{9-0}{0+2}[/tex]
[tex]\sf 4.5[/tex]
equation:
y - 9 = 4.5 ( x - 0 )
y = 4.5x + 9
note: point -2 on x axis and 9 on y axis, and keep the ruler on those two points and draw a straight linear line, ta-daa you are done.
help choose if you do i will give branlest to right answer
Answers
EGA and AGB aka the fourth option
Step-by-step explanation:
EGA and AGB create a 180 degree angle together
You purchase a car for $36,000. Five years later, the car is worth $28,500.
a. By how much is the car decreasing in value per year? (3 points)
Hint: Find the slope
Find the equation that would give the worth of the car for any given year. (4 points)
*y = mx +b
Answers
Answer:
36,000-28,500
=7,500 decrease per year
Nonsense will be reported!!
Answers
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
The required additional information required to prove the Triangles congruent are :
[tex]\qquad \sf \dashrightarrow \: 1. \: X V= FD[/tex]
The Triangles will be congruent by HL congruency.
[tex]\qquad \sf \dashrightarrow \: 2. \: MH = MI[/tex]
The Triangles are congruent by LL congruency.
[tex]\qquad \sf \dashrightarrow \: 3. \: \angle EDC = \angle VUC[/tex]
The Triangles are congruent by HA congruency.
[tex]\qquad \sf \dashrightarrow \: 4. \: \angle J = \angle C[/tex]
The Triangles are congruent by LA congruency.
Convert: 8 quarts = _____ pints
2 pints
4 pints
16 pints
32 pints
Answers
Answer:
C. 16 pints
Step-by-step explanation:
1 quart equals to 2 pints
Answer:
answer is 2 pints
Step-by-step explanation:
2 x 4 is 8
2^3 + 4m divided by 2 when m = 1.5
PLS HELP ME RN!!!
Answers
Answer:
14
Step-by-step explanation:
2^3 is 8. 8+4(1.5) is 8+6 is 14.
Answer:
Answer is 7 after simplifying and solving.Step-by-step explanation:
Equation that we have been provided with :
[tex]\boxed{ \tt {\dfrac{2 {}^{3} \: + \: 4m}{2}\: }} \: \red\bigstar[/tex]And the value of m is 1.5. So we would be simply substituting the value of m in the equation given above and divide it by 2 as per the demand of the question.
[tex]: \longmapsto \: \sf{\dfrac{2 {}^{3} \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{(2 \times 2 \times 2) \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{(4 \times 2) \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 4 \: (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 4 \: \times (1.5)}{2}\: }[/tex]
[tex]: \longmapsto \: \sf{\dfrac{8 \: + \: 6}{2}\: }[/tex]
[tex] : \longmapsto \: \sf{\dfrac{14}{2}\: }[/tex]
[tex]: \longmapsto \: \cancel{\sf{\dfrac{14}{2}\: }}[/tex]
[tex]: \longmapsto \: \red{\bf{7}}[/tex]
Consider the line y=−4x+2.
Find the equation of the line that is perpendicular to this line and passes through the point , (−3,5).
Find the equation of the line that is parallel to this line and passes through the point , (−3, 5).
equation of perpendicular line:
equation of parallel line:
Answers
Answer and step by step esplanation:
The perpendicular line has the slope opposite and inverse, in our case [tex]-4 \rightarrow +\frac14[/tex]
Line passing through the point will have then equation - using the point-slope form [tex]y-y_0=m(x-x_0)[/tex]
[tex]y-5=\frac14 (x-(-5))\\y-5=\frac14(x+5)[/tex]
The parallel line will have the same slope as the given line, in our case -4. Again with the point-slope equation:
[tex]y-5=-4(x-(-5)\\y-5=-4(x+5)[/tex]
Answer:
Perpendicular: y = 1/4x + 5 3/4
Parallel: y = -4x - 7
Step-by-step explanation:
Hello!
A perpendicular line would have a negative reciprocal slope, meaning you flip the sign of the slope, and the numerator and denominator.
Perpendicular LineGiven our equation: y = -4x + 2, we can find the perpendicular slope by finding the negative reciprocal:
-44 -> negative1/4 -> reciprocal (4/1 -> 1/4)So the perpendicular slope is 1/4.
We can now solve for the y-intercept by plugging in the x and y-value of the point into the equation y = 1/4x + b:
y = 1/4x + b; (-3,5)5 = 1/4(-3) + b5 = -3/4 + bb = 5 3/4.The y-intercept is 5 3/4, so the equation of the line would be y = 1/4x + 5 3/4.
_____________________
Parallel LineParallel lines have the same slope. So we can use -4 as our slope, and plug in the points to find the y-intercept.
y = -4x + b; (-3,5)5 = -4(-3) + b5 = 12 + b-7 = bSo the equation of the parallel line would be y = -4x - 7.
Consider the line y=5x-4
What is the slope of a line perpendicular to this line?
What is the slope of a line parallel to this line?
Answers
Answer:
slope of perpendicular line= -⅕
slope of parallel line= 5
Step-by-step explanation:
y= 5x -4
The equation is in the slope-intercept form, thus the slope is the coefficient of x.
Slope of given equation= 5
The product of the slopes of perpendicular lines is -1.
Let the slope of the perpendicular line be m.
m(5)= -1
[tex]m = - \frac{1}{5} [/tex]
Thus, the slope of the perpendicular line is -⅕.
Parallel lines have the same gradient.
Slope of parallel line= 5
What is slope-intercept form?
y= mx +c, where m is the slope and c is the y-interceptIn this form, the coefficient of y is 1, while all the other terms and constant is on the right hand side of the equation