In this diagram, radius AD = 5 mm, radius BD = 12 mm and chord
CD = 8 mm. Find the exact length of AB, in surd form.
Answers
Answer:
The exact length of AB is [tex]3 + 4\sqrt{10}[/tex] milimeters.
Step-by-step explanation:
Both triangles ACD and BCD are isosceles and triangles AEC, ADE, BDE and BCE are right-angled, where E is the point where line segments AB and CD meet each other. We can determine the exact length of AB by means of two horizontal right triangles (i.e. AEC, BCE) and the Pythagorean Theorem:
[tex]AB = \sqrt{AC^{2}-CE^{2}}+\sqrt{CB^{2}-CE^{2}}[/tex]
If we know that [tex]AD = AC[/tex], [tex]BC = BD[/tex], [tex]AC = 5\,mm[/tex], [tex]BC = 12\,mm[/tex] and [tex]CE = 4\,mm[/tex], then the exact length of AB is:
[tex]AB = \sqrt{(5\,mm)^{2}-(4\,mm)^{2}}+\sqrt{(12\,mm)^{2}-(4\,mm)^{2}}[/tex]
[tex]AB = 3 + 4\sqrt{10}\,[mm][/tex]
Related Questions
The value of a home is $899,000 and increasing in value at a rate of 1% per year. Use an exponential growth function to find the approximate value of the home in 12 years.
Answers
Answer:
$1012993.2
Step-by-step explanation:
Given data
Cost of home V= $899,000
Rate of increase= 1%
Time= 12 years
The exponential growth function is expressed as
A=V(1+r)^t
A=899000(1+0.01)^12
A= 899000(1.01)^12
A= 899000*1.1268
A=$1012993.2
Hence the cost of the home will be $1012993.2
PLSSS HELP ASAP I NEED HELP
Answers
Explanation:
The area of a circle is pi * radius squared. The diameter is 4 m, the radius is half the diameter so for the equation the radius is 2 m.
Pi times 2 is 6.28 (remember that pi is roughly 3.14), then square that sum of 6.28.
6.28^2= 39.4384
The answer is 39.44 but the answer must be rounded to the nearest tenth, 39.4384 is 39.4 rounded to the nearest tenth.
WHAT. Is. THIS. pls haaaaaaalp
Answers
Answer: 56
Step-by-step explanation:
I need the answer nowwwwww right nowwwwww
Answers
Answer:
160 cm i think
Step-by-step explanation:
Which statements are true about ABCD? Select all that apply.
Answers
Please awnser this for brainliest
Answers
Answer:
she will pay 25% of the cost
Step-by-step explanation:
Well .35 is 35%
35+40 = 75
100-75 = 25
25%
Write the fraction as a decimal and a percent. 13/9
Answers
Answer:
Decimal form = 1.44
Fraction form = 144/100
Hope this helps!
decimal: 1.4444444444444
6. Roberta started the year with $125 in a savings account. She has been adding money at a rate of $15 per week. Write an equation in the form y = mx + b that represents the total amount of money (y) in the account after x weeks.
Answers
Answer:
y=15x+125
Step-by-step explanation:
Hope this helps!
I need help with this!!!!!
Answers
Answer:
48
Step-by-step explanation:
Find the volume and surface area of a sphere with a radius of 6cm.
Answers
Surface Area=452.39
Find the area of a regular pentagon that is inscribed in a circle of radius 3. Round to the nearest whole number.
Answers
Answer:
The area of the pentagon is approximately 21 square units
Step-by-step explanation:
The radius of the circle in which the regular pentagon is inscribed, r = 3
The area of a pentagon, 'A', inscribed in a circle with radius, r is given as follows;
A = 5×(1/2) ×2×r·sin(32°)×r·cos(32°) = (5/2)×r²×sin(72°)
Therefore, the area of the pentagon, A = (5/2)×3²×sin(72°) ≈ 21.3987716166 ≈ 21
The area of the pentagon, A ≈ 21 square units.
A) En cada caja hay 5 caramelos. Si tengo 8 cajas ¿cuántos caramelos tengo? b) Romina tiene 9 pelotas y Lidia 4 veces más que ella. ¿Cuántas pelotas tiene Lidia?
Answers
Answer:
a) 40 caramelos
b) 13 bolas
Step-by-step explanation:
A) En cada caja hay 5 caramelos. Si tengo 8 cajas, ¿cuántos caramelos tengo?
1 caja = 5 caramelos
8 cajas = x
Multiplicar cruzada
x × 1 caja = 8 cajas × 5 caramelos
x = 8 cajas × 5 caramelos / 1 caja
x = 40 caramelos
b) Romina tiene 9 bolas y Lidia 4 veces más que ella. ¿Cuántas bolas tiene Lidia?
Romina = 9 bolas
Lidia = 4 bolas más que ella
Lidia = 9 bolas + 4 bolas
= 13 bolas
PLEASE HELP WILL MARK BRAINLIEST IF CORRECT!!Given the point (18, -10), apply the rule and tell the image after the translation as an ordered pair with no spaces.
(x,y) --> (x - 11, y - 9)
Answers
Answer:
(7,-19)
Step-by-step explanation:
Just took the final got it correct
please help! answer and step by step explanation needed
Answers
Answer:
Step-by-step explanation:
Due to the equation [tex]y = mx+c[/tex],
y = y
mx = [tex]\frac{2}{5}x[/tex]
c = -7
Hence, from 'mx',
m = 2/5
Hence, the slope is 2/5
Feel free to mark it as brainliest :D
Answer:
slope is
[tex] \frac{2}{5} [/tex]
Step-by-step explanation:
from the linear equation we consider the Cof of x is slope Y = a x ± b a is slope and b is intercept - y then 2/5 is slope and -7 is interceptThe temperature in Elmwood is 5°C. The temperature in Gainesville is 9°C cooler than the temperature in Elmwood. The temperature in Knowlton is 12°C warmer than the temperature in Elmwood. Which equation shows the temperature in °C in Knowlton?
Answers
Selton e Danton São irmãos e trabalham juntos, vendendo instrumentos musicais. Selton vendeu um total de 62 instrumentos este mês. Já Danton vendeu o quintuplobdoque o irmão vendeu., quantos instrumentos musicais Danton vendeu? Cálculo: Resposta:
Answers
Answer:
Danton vendeu 310 instrumentos musicais.
Step-by-step explanation:
Selton vendeu 62 instrumentos esse mês.
Danton:
Quintuplo do que seu irmão Selton, ou seja:
62*5 = 310.
Danton vendeu 310 instrumentos musicais.
Which expression is equivalent to (2x+3)(3x2−2x+5)?
Answers
Answer:
See the steps below:)
Step-by-step explanation:
Expression is equivalent to (2x+3)(3x²−2x+5) is 6x³+5x²+4x+15.
What are equivalent expressions ?An expression can be of many types numerical expressions, Algebraic expressions.We can also form these mathematical expressions from a given statement or by observing a real world scenario.
Equivalent expressions are same expressions in different forms.To check whether an expression is equivalent to another expression or not we just need to do some algebraic manipulations.Like distributing or taking common and other algebraic and arithmetic operations.
According to the given problem we have to write an expression which is equivalent to the expression (2x+3)(3x²-2x+5).
(2x+3)(3x²-2x+5)
= (2x+3)(3x²-2x+5)
=2x(3x²-2x+5)+3(3x²-2x+5) (now we will distribute)
=6x³-4x²+10x+9x²-6x+15
=6x³+5x²+4x+15.
Learn more about equivalent expressions here :
https://brainly.com/question/3644212
#SPJ6
For the function f(x) = -(x + 1)2 + 4, identify the vertex, domain, and range.
Answers
f ( x ) = - ( x + 1)^2 + 4
_____________________
Vertex = ( - 1 , 4 )
♡♡♡♡♡♡♡♡♡♡♡♡
Domain = R
♡♡♡♡♡♡♡♡♡♡♡♡
Range = ( - infinite , 4 ]
y=x^2+8x+10
what does X=
Answers
For this problem you will need to use the quadratic formula. [tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex] (the + and - are together. basically the plus is on top and the minus is on bottom. you should have seen it in your notes hopefully). a = 1, b = 8, and c = 10. from there you just plug everything in and solve.
A bag contains 8 apples and 6 oranges. You randomly draw a piece of fruit from the bag, eat it, and than randomly draw another. What is the probability you draw and eat an apple than draw an orange?
Answers
Answer:
[tex]probability \ of\ choosing\ apple\ first = \frac{8}{14}\\\\probability\ of\ choosing\ orange\ second = \frac{6}{13}\\\\probability \ of \ choosing \ apple \ and \then \ orange = \frac{8}{14} \times\frac{6}{13} = \frac{24}{91}[/tex]
The pilot in a helicopter tossed a life float down to a swimmer in the water. The height, h, of the float after time t seconds is represented by the equation h(t) = -16t2 - 3t + 55. Find the time it takes the float to reach the swimmer.
Answers
Answer:
1.95secs
Step-by-step explanation:
Given the height of the float expressed as h(t) = -16t2 - 3t + 55.
The floats reach the swimmer at h(t) = 0
Substitute
0 = -16t^2 - 3t + 55.
16t^2 + 3t - 55 = 0
Using the general formula;
t = -3±√3²-4(16)(-55)/2(16)
t = 3±√9+3520/32
t = 3±√3529/32
t = 3+59.41/32
t = 62.41/32
t = 1.95
Hence it will take 1.95secs
4. Explain what an imaginary number is and its relationship to complex numbers. Then give
an example of where complex numbers occur naturally in mathematics.
Answers
Answer:
564643
Step-by-step explanation:
Answer:
In the real number system, there is no solution to the equation x^2=-1x
2
=−1x, squared, equals, minus, 1. In this lesson, we will study a new number system in which the equation does have a solution.
The backbone of this new number system is the number iii, also known as the imaginary unit.
i^2=-1i
2
=−1i, squared, equals, minus, 1
\sqrt{-1}=i
−1
=isquare root of, minus, 1, end square root, equals, i
By taking multiples of this imaginary unit, we can create infinitely many more new numbers, like 3i3i3, i, i\sqrt{5}i
5
i, square root of, 5, end square root, and -12i−12iminus, 12, i. These are examples of imaginary numbers.
However, we can go even further than that and add real numbers and imaginary numbers, for example 2+7i2+7i2, plus, 7, i and 3-\sqrt{2}i3−
2
i3, minus, square root of, 2, end square root, i. These combinations are called complex numbers.
Defining complex numbers
A complex number is any number that can be written as \greenD{a}+\blueD{b}ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i, where iii is the imaginary unit and \greenD{a}astart color #1fab54, a, end color #1fab54 and \blueD{b}bstart color #11accd, b, end color #11accd are real numbers.
\begin{array}{ccc} \Large\greenD a&\Large+&\Large \blueD bi \\ \uparrow&&\uparrow\phantom{i} \\ \text{Real}&&\text{Imaginary} \\ \text{part}&&\text{part} \end{array}
a
↑
Real
part
+
bi
↑i
Imaginary
part
\greenD aastart color #1fab54, a, end color #1fab54 is called the \greenD{\text{real}}realstart color #1fab54, start text, r, e, a, l, end text, end color #1fab54 part of the number, and \blueD bbstart color #11accd, b, end color #11accd is called the \blueD{\text{imaginary}}imaginarystart color #11accd, start text, i, m, a, g, i, n, a, r, y, end text, end color #11accd part of the number.
The table below shows examples of complex numbers, with the real and imaginary parts identified. Some people find it easier to identify the real and imaginary parts if the number is written in standard form.
Complex Number Standard Form \greenD a+\blueD b ia+bistart color #1fab54, a, end color #1fab54, plus, start color #11accd, b, end color #11accd, i Description of parts
7i-27i−27, i, minus, 2 \greenD {-2}+\blueD 7i−2+7istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 7, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 77start color #11accd, 7, end color #11accd.
4-3i4−3i4, minus, 3, i \greenD 4 + (\blueD{-3})i4+(−3)istart color #1fab54, 4, end color #1fab54, plus, left parenthesis, start color #11accd, minus, 3, end color #11accd, right parenthesis, i The real part is \greenD{4}4start color #1fab54, 4, end color #1fab54 and the imaginary part is \blueD{-3}−3start color #11accd, minus, 3, end color #11accd
9i9i9, i \greenD 0+\blueD9i0+9istart color #1fab54, 0, end color #1fab54, plus, start color #11accd, 9, end color #11accd, i The real part is \greenD{0}0start color #1fab54, 0, end color #1fab54 and the imaginary part is \blueD 99start color #11accd, 9, end color #11accd
-2−2minus, 2 \greenD {-2}+\blueD0i−2+0istart color #1fab54, minus, 2, end color #1fab54, plus, start color #11accd, 0, end color #11accd, i The real part is \greenD{-2}−2start color #1fab54, minus, 2, end color #1fab54 and the imaginary part is \blueD 00start color #11accd, 0, end color #11accd
Step-by-step explanation:
plz brian list and allways happy to help.
What is the answer to the math question attached
Answers
Answer:
OK so this may or may not help u ...
this can be taken as the straight line with equation
y = mx + c
here f(x) is taken to be y
the attached pic is the graph of this function
so I think the value of x before it explodes would be 18.875
as in 18.875 seconds the rocket has reached its maximum height ( from 0 to 302)and x represents the time
the time before it explodes = 18.875and f(x) represents height so we see that the highest possible value of f(x) from the graph is 302
the height at which it explodes would be = 302What is the area of a square if the base is 4.25ft and the height is 4.25 ft?
Answers
Answer:
18.0625 ft²
Step-by-step explanation:
4.25 × 4.25
18.0625 ft²
PLEASE HELP ITS DUE SOON!!!!
Answers
Answer:
x=4
Step-by-step explanation:
4x+7=23
4x=23-7
4x=16
x=16÷4
x=4
Answer:
4
Step-by-step explanation:
4 x 4 + 7 = 23
What is the probability of drawing a red marble?
2/5
45%
1/3
9/11
Answers
Answer:
45%
Step-by-step explanation:
Counting the marbles, there are 5 green, 6 blue and 9 red.
Which means the odds of drawing a red to a non red are 11:9
In fraction form that would be 9 marbles out of 20 are red. 9/20
Since the fraction cannot be simplified, we can go to decimal form.
9/20=.45
.45=45%
The answer is 45%.
Answer:
45%
Step-by-step explanation:
Total = 20
Red = 9
9/20 = 0.45
Therefore 45 % is the correct option :))
SOMEONE PLSSSSS HELP MEEEE PLSSSS
Answers
Answer:
the answer is c !
Step-by-step explanation:
Answer:
Step-by-step explanation:
Find the distance from point A(2,-1) to the line y=-x+4
Answers
9514 1404 393
Answer:
(3/2)√2 ≈ 2.1213 units
Step-by-step explanation:
The distance d from point (x, y) to line ax+by+c = 0 is given by ...
d = |ax +by +c|/√(a^2 +b^2)
We can write the equation of the line as ...
x + y -4 = 0
so the distance is ...
d = |x + y - 4|/√(1^2 +1^2)
For point (x, y) = (2, -1), the distance is ...
d = |2 +(-1) -4|/√2 = 3/√2 = (3√2)/2
The distance from A(2, -1) to the line y = -x +4 is (3√2)/2 units.
The graph of quadratic function is shown on the grid.
Which of these best represents the domain of f?
A.
[tex]y \geqslant 5.5[/tex]
B.
All real numbers
C.
All real numbers less than -3 or greater than 2
D.
[tex] - 3 \leqslant x \leqslant 2[/tex]
Answers
please help due soon!!! will mark brainlyist if right
Answers
Step 1: Find the slant height
10^2 + 28^2 = c^2
884 = c^2
c = [tex]\sqrt{884}[/tex]
Step 2: Find the lateral area
LA = pi * radius * slant height
LA = pi * 10 * [tex]\sqrt{884}[/tex]
LA (rounded to the nearest tenth) = 297.3pi in^2
Step 3: Find the area of the base circle
A = pi * r^2
A = pi * 10^2
A = 100pi in^2
Step 4: Add the areas together
SA = 297.3pi + 100pi
SA = 397.3pi in^2
Hope this helps!! :)