Step-by-step explanation:
Example 1:
a+c=b+c then a=b
First let the value of a and b be different (not equal)
a=5
b=7
c=10
a+c=b+c
5+10=7+10
15≠17
Example 2:
Let the value a and b be equal (the same)
a=5
b=5
c=10
a+c=b+c
5+10=5+10
15=15
So when,
a+c and b+c is equal, a and b are always equal.
Hope this helps ;) ❤❤❤
Answer:
a=b
Step-by-step explanation:
Reason:
a+c=b+c
a-b=c-c
c-c would be 0
if a-b=c-c=0
a-b=0
Only if a=b can a-b=0
You can also take it as:
b-a=c-c (a+c=b+c)
b-a=0=c-c
Therefore b=a
By the way even I am a BTS army
Please help me Tramserran mam...
Answer: see proof below
Step-by-step explanation:
Use the following when solving the proof...
Double Angle Identity: cos2A = 1 - 2sin²B
Pythagorean Identity: cos²A + sin²A = 1
note that A can be replaced with B
Proof from LHS → RHS
Given: cos²A + sin²A · cos2B
Double Angle Identity: cos²A + sin²A(1 - 2sin²B)
Distribute: cos²A + sin²A - 2sin²A·sin²B
Pythagorean Identity: 1 - 2sin²A·sin²B
Pythagorean Identity: cos²B + sin²B - 2sin²A·sin²B
Factor: cos²A + sin²B(1 - 2sin²A)
Double Angle Identity: cos²B + sin²B · cos2A
cos²B + sin²B · cos2A = cos²B + sin²B · cos2A [tex]\checkmark[/tex]
how many cars the baseball team needs to wash before it starts making a profit. The team spent $75 setting up the car wash, and they are charging $5 per car for a wa The first step in modeling this situation is to track how much money the baseball team will take in. Write an equation to represent the amount of money collected in dollars, y, in terms of the number of cars washed, x. Ignore the setup cost.
Answer:
y = 5x
Step-by-step explanation:
The revenue (y) is 5 dollars for each car washed. The number of cars washed is x, so the revenue equation is ...
y = 5x
_____
Additional comment
At the end of the exercise of writing revenue and cost and profit equations, you will find that the break-even number of cars is the ratio of fixed cost (start-up cost in this case) to the profit contribution of each car (per-car charge in this case). That is, it will take 75/5 = 15 cars to break even. Each additional car will contribute a positive profit.
Answer:
Equation INCLUDING the setup cost: y = 5x - 75
Equation EXCLUDING the setup cost: y = 5x
Step-by-step explanation:
It spent a total of $75 to set up the car wash.
It is charging $5 per car.
y = amount collected in $
x = number of cars washed
=> We can make an equation INCLUDING the setup cost and EXCLUDING the setup cost.
=> INCLUDING the setup cost.
=> y = 5x - 75
=> I subtracted 75 from 5x because they spent a total of $75 to set up the car wash.
=> I wrote 5x because they get $5 for each car so if they wash 10 cars they get 5 * 10 = $50.
An EXAMPLE from the above equation:
y = 5x -75
=> y = 5*14 - 75
=> y = 70 - 75
=> y = -5
=> This means that if they wash 14 cars, they still have a debt of 5 dollars.
An equation EXCLUDING the setup cost will look like:
=> y = 5x
I wrote this because, they didn't spend any money so they will get 5 dollars per car. How many cars they wash, the answer will be 'number of cars x 5'.
An EXAMPLE from the above equation is:
=> y = 5x
=> y = 5 * 14
=> y = $70
=> This means that if they wash 14 cars, they get $70.
A rectangle with sides 13 cm and 7 cm has the same diagonal as a square. What is the length of the side of the square. Give your answer as a surd.
Answer:
Step-by-step explanation:
The diagonal ^2= 13^2+7^2
=169+49=218
diagonal = V218
the lengh of the square=l
l^2+l^2= 218
2l^2=218
l^2= 218/2= 109
l= ✓109
which whole number has a factor that is the greatest prime factor between 1 and 30?
А. 1,593
B. 1,247
C. 1,311
D. 943
Answer:
B
Step-by-step explanation:
The greatest prime factor between 1 and 30 is 29. Remember that a prime number is a number whose only 2 factors is 1 and the number itself. To find out which number is a multiple of 29, all we have to do is divide it by 29, and if the quotient is a whole number then we have found our answer.
A: 1593 / 29 ≈ 54.93
B: 1247 / 29 = 43
We don't need to check C and D because we know that B is the answer.
1247 has the greatest prime factor between 1 and 30
The factor of a number that divides another number perfectly without leaving any remainder.
For example, the factors of 12 are 1,2,3,4,6 and 12
A prime factor is a number that a prime number
A prime number is a number that can be divided only by 1 and that number
Prime numbers between 1 and 30 are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29
The greatest prime factor between 1 and 30 is 29
To determine which number has the greatest prime factor, divide each of the numbers in the options by 29.
1593 / 29 = 54.9 (29 is not a prime factor of 1593)
1247/29 = 43 (29 is a prime factor of 1247)
1311 / 29 = 45.2 (29 is not a prime factor of 1311)
943 / 29 = 32.5 (29 is not a prime factor of 943)
To learn more about prime factors, please check: https://brainly.com/question/10371102?referrer=searchResults
Will someone please help me with this problem!! **It's multiple choice!
A = (-7,-6)
B = (8,-9)
Find the slope of line AB
m = (y2-y1)/(x2-x1)
m = (-9-(-6))/(8-(-7))
m = (-9+6)/(8+7)
m = -3/15
m = -1/5
The slope of line AB is -1/5.
Flip the fraction and the sign to go from -1/5 to +5/1 = 5. The perpendicular slope is 5.
Let m = 5.
Use the coordinates of point C (2,12) along with the perpendicular slope to get
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 12 = 5x - 10
y = 5x - 10+12
y = 5x + 2
Lastly, convert this to standard form
y = 5x + 2
5x+2 = y
5x+2-y = 0
5x-y = -2
Choice A is the closest match, but the -56 should be -2 instead. It seems like your teacher made a typo somewhere.
Answer:
5x - y = -2.
Step-by-step explanation:
The equation of this altitude line has a slope = -1/m where m is the slope of line AB . It will also pass through the point C.
The slope of line AB = (-9 - (-6)) / (8 - (-7))
= -3/15
= -1/5
So the slope of the required line = -1 / -1/5 = 5.
Using the point C and the point-slope form of a line:
y - y1 = m(x - x1)
y - 12 = 5(x - 2)
y - 5x = -10 + 12
y - 5x = 2
5x - y = -2.
The parentheses are around 270-54, the value is _______. When the parentheses are around 54÷9, the value is _______.
What is the answer? I'm having trouble with GoMath! I can't seem to figure it out.
Answer:
Im pretty sure they stay the same. But that might just be me
Please answer this question now
Answer:
420 cubic inches is the answer
Answer:
420 cubic inches
Step-by-step explanation:
Volume of rectangular pyramid
= 1/3*lbh
= 1/3 * 10*9*14
= 10*3*14
= 420 cubic inches
*LAST QUESTION, HURRY AND PLEASE ANSWER, WILL CHOOSE BRAINLIEST FOR DETAILS AND ANSWER* How many times larger is the rectangular prism than the cube?
Answer:
The rectangular prism is 30 times larger than the cube.
Step-by-step explanation:
The Cube has a length of 2, a width of 2, and a height of 2.
Volume = length times width times height or V=lwh
2 x 2 x 2= 8
The Rectangular prism has a length of 10, a width of 6, and a height of 4.
10 x 6 x 4= 240
240 divided by eight is 30.
Answer:
30 times larger than the cube.
Step-by-step explanation:
Convert the following:
22 tons is equivalent to
kilograms
Answer:
19958.1
step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
whats the factored form of 6x 2 - 8x - 8 = 0
Answer:
2(x -2)² = 0
Step-by-step explanation:
2(x² - 4x - 4) = 0
2(x -2)² = 0
x = 2
Answer:
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]
Step-by-step explanation:
[tex]6x^2-8x-8=0[/tex]
The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]
First, divide both sides by 2
[tex]3x^2-4x-4=0[/tex]
Now, it is about thinking. From the equation, we will get something in the format: [tex](ax-b)(cx+d)[/tex]
Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]
From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:
[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]
Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.
[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]
Therefore,
[tex](3x-2)(x+2)=3x^2-4x-4[/tex]
But we are not ready yet!
This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
Factor 8(9) + 18
8(9+18)
9(8+2)
18(4+1)
18(1+4)
[tex]8(9)+18[/tex]
$=8\cdot9+2\cdot9$
$=(8+2)\cdot9$
convert degree into Radian that is 18 degree 12'
Answer:
[tex]\frac{\pi }{10}[/tex] radians
Step-by-step explanation:
To convert degrees into radians, multiply the degrees with [tex]\frac{\pi}{180}[/tex].
If you have 18 degrees:
[tex]18*\frac{\pi}{180} = \frac{\pi }{10}[/tex]
HELP IM BEING TIMED!!
Answer:
Value of x is 8
Step-by-step explanation:
Given:
[tex]\sqrt{\frac{896z^{15}}{225z^6} }=\frac{xz^4}{15} \sqrt{14z}\\\\Computation: \\\\From\ squaring\ both\ side\\\\ {\frac{896z^{15}}{225z^6} }=\frac{x^2z^8}{225} ({14z})\\\\896z^9=14x^2z^9\\\\896=14x^2\\\\64=x^2\\\\x = 8[/tex]
So, Value of x is 8
1. Which expression is equivalent to (-2)(a + 6)?
Answer:
please mark my answer brainliest
Step-by-step explanation:
- 2a -12
Priya, Han, and Mai each measured one of the circular objects from earlier. Priya says that the bike wheel is 24 inches. Han says that the yo-yo trick is 24 inches. Mai says that the glow necklace is 24 inches. 1. Do you think that all these circles are the same size? 2. What part of the circle did each person measure? Explain your reasoning.
Answer:
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
Each person measures the circumference of the circle.
Step-by-step explanation:
Given that :
Priya, Han, and Mai each measured one of the circular objects from earlier.
Priya says that the bike wheel is 24 inches.
Han says that the yo-yo trick is 24 inches.
Mai says that the glow necklace is 24 inches.
Do you think that all these circles are the same size?
Yes they are of the same size since they have the same number and standard unit of measurement (i.e 24 inches).
What part of the circle did each person measure?
Each person measures the circumference of the circle.
The circumference also known as the perimeter of the circle is denoted by :
C = 2π r
The circumference of a circle is the distance round the edges of the circle.
Given that C = 24
24 = 2π r
r = 24/(2π)
r = 3.8 inches
This confirms the claim that all the circle are of the same size since they possess the same radius.
Answer:
The person who answered first is WRONG
Step-by-step explanation:
I did this and these are the answers the teacher gave me:
the circles are NOT the same size
and they are measuring by diameter, radius, and circumfrence
22/100 simplist form
Answer:
11/50 is the simplified form of the given expression.
Step-by-step explanation:
22/100
We will cancel the values by the table of 2
11/50 is the simplified form of the given expression.
Hope it will help you :)
Solve the equation. 0.15 = y-0.45
Answer:
0.6
Step-by-step explanation:
0.6-0.45=0.15
The value of y from the given equation is 0.60.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The given equation is 0.15=y-0.45.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
Here, 0.15=y-0.45
y=0.15+0.45
y=0.60
Therefore, the value of y is 0.60.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
Nine new employees, two of whom are married to each other, are to be assigned nine desks that are lined up in a row. If the assignment of employees to desks is made randomly, what is the probability that the married couple will have nonadjacent desks
Answer:
P = 0,88 or P = 88 %
Step-by-step explanation:
The probability of having a married couple in nonadjacent desks is the total number of probabilities minus the probabilities of having them in adjacent places divide by total number of outcomes
The total possibilities (outcomes) of 9 elements in a row is:
P(₉) = 9!
P(₉) = 9*8*7*6*5*4*3*2*1
P(₉) = 362880
And the outcomes in which they are adjacent to each other is:
We consider them as one unit them we in this situation have 8 elements
P(₈) = 8!
P(₈) = 8*7*6*5*4*3*2*1
P(₈) = 40320
Then the probability that the married couple will have nonadjacent desks is:
P = P(₉) - P(₈) / P(₉)
P = 362880 - 40320 / 362880
P = 322560/ 362880
P = 0,88 or P = 88 %
Solve equation show all steps what 2x-3x+5=18
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Let's solve your equation step-by-step.
[tex]2x-3x+5=18[/tex]
Step 1: Simplify both sides of the equation.
[tex]2x-3x+5=18\\2x + -3x + 5 = 18[/tex]
[tex]( 2x + -3x ) + ( 5) = 18[/tex] (Combine Like Terms)
[tex]-x + 5 = 18\\-x + 5 = 18[/tex]
Step 2: Subtract 5 from both sides.
[tex]-x + 5 - 5 = 18 - 5 \\-x = 13[/tex]
Step 3: Divide both sides by -1.
[tex]\frac{-x}{-1} = \frac{13}{-1} \\x = -13[/tex]
Answer : [tex]\boxed {x = -13}[/tex]
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
[tex] \boxed{ \bold{ \mathsf{ \purple{x = - 13}}}}[/tex]Step-by-step explanation:
[tex] \mathsf{2x - 3x + 5 = 18}[/tex]
Collect like terms
[tex] \mathsf{ - x + 5 = 18}[/tex]
Move constant to R.H.S and change it's sign
[tex] \mathsf{ - x = 18 - 5} [/tex]
Calculate the difference
[tex] - x = 13[/tex]
Change the signs on both sides of the equation
[tex] \mathsf{x = - 13}[/tex]
---------------------------------------------------------------
[tex] \blue{ \mathsf{verification}}[/tex]
[tex] \mathsf{LHS \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: RHS}[/tex]
[tex] \mathsf{2x - 3x + 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 18}[/tex]
[tex] \mathsf{ = 2 \times ( - 13) - 3 \times ( - 13) + 5}[/tex]
[tex] \mathsf{ - 26 + 39 + 5}[/tex]
[tex] \mathsf{ = 13 + 5}[/tex]
[tex] = 18[/tex]
Thus, LHS = RHS
hope I helped!
Best regards!
given that -6,-6 is on the graph of f x find the corresponding point for the function f(3/4x)
Answer:
The corresponding point is (-8, -6).
Step-by-step explanation:
Given that
(-6,-6) lies on the graph of [tex]f(x)[/tex]
A function is represented in the form:
[tex]y = f(x)[/tex]
i.e. (-6,-6) means value of x = -6 is put and value y came out as -6.
[tex]f(-6) = -6[/tex]
Now, we have to find the corresponding point on [tex]f(\frac{3}{4}x)[/tex].
We know the value of [tex]f(-6)[/tex]
Let us find the value of x where [tex]\frac{3}{4}x[/tex] becomes equal to -6
[tex]\dfrac{3}{4}x=-6\\\Rightarrow 3x=-24\\ \Rightarrow x =-8[/tex]
So, let us put value of [tex]x = -8[/tex] in [tex]f(\frac{3}{4}x)[/tex]:
[tex]f(\frac{3}{4}\times (-8))\\\Rightarrow f(3\times (-2))\\\Rightarrow f(-6) = -6[/tex](as per given statement)
So, the corresponding point is (-8, -6).
The chemical element, silver, boils at a temperature of degrees Fahrenheit. What is the boiling point for silver in degrees Celsius? Round you answer to one decimal place.
Answer:
[tex]C=(x-32)\times\frac{5}{9}[/tex]
Step-by-step explanation:
The formula to convert the temperature in Fahrenheit to degrees Celsius is:
[tex]C=(F-32)\times\frac{5}{9}[/tex]
Here,
C = temperature in degrees Celsius
F = temperature in Fahrenheit
Suppose the boiling point for silver is x Fahrenheit, then then the temperature in degrees Celsius will be:
[tex]C=(x-32)\times\frac{5}{9}[/tex]
A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 90 9090 kilograms and gained weight at a constant rate. After 8 88 months, he weighed 138 138138 kilograms.
THIS IS THE COMPLETE QUESTION BELOW;
young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly. He started at 909090 kilograms and gained weight at a constant rate. After 888 months, he weighed 138138138 kilograms. Let W(t)W(t)W, left parenthesis, t, right parenthesis denote the sumo wrestler's weight WWW (measured in kilograms) as a function of time ttt (measured in months). Write the function's formula.
Answer:
W=6t+90
Step-by-step explanation:
We know that a linear equation in slope takes the form
y= mx+ c
where
m is the slope
c is the y-coordinate of the y-intercept
Let us denote W as the sumo weight in kg then
t as the time in months
Then forming a linear equation from this knowing t is a dependent variable then
W(t)= mt+90
But here we know that is our slope, W was given as 138kg and t is 8 months.
We we substitute this values in the equation we have
138= 8m+90
8m= 138-90
8m=48
m=6kg/month
Therefore, the function formula is W(t)= 6t+90
sometimes true, always true, or never true?
===========================================
Explanation:
I'll use x in place of n
Let y = x^2 - 4x + 5
If we complete the square, then,
y = x^2 - 4x + 5
y = (x^2 - 4x) + 5
y = (x^2 - 4x + 4 - 4) + 5
y = (x^2 - 4x + 4) - 4 + 5
y = (x-2)^2 + 1
The quantity (x-2)^2 is never negative as squaring any real number value is never a negative result. Adding on 1 makes the result positive. So y > 0 regardless of whatever x is. Replace x with n, and this shows how n^2 - 4n + 5 is always positive for any integer n.
------------
You could also use the quadratic formula to find that x^2 - 4x + 5 = 0 has no real solutions, so there are no x intercepts. Either the graph is entirely above the x axis or it is entirely below the x axis.
Plug in any x value you want, say x = 0, and the result is positive. Meaning that whatever x value you plug in will be positive (as the graph can't cross the x axis to go into negative territory)
I NEED HELP ON THIS QUESTION!!!!! I WILL GIVE BRAINLIEST TO THE BEST ANSWER!!!!
Answer:
D
Step-by-step explanation:
Both are exponential decay.
Answer:
D.Step-by-step explanation:
f(0) = 24, f(1) = 6 and f(2) = 0 means f(x) > 0 in (0,2)
and f(0) > f(1) > f(2) means f is decreasing in (0,2)
g(0) = 15 and g(2) = 0 means g(x) > 0 in (0,2)
and g(0) > g(2) means g is decreasing in (0,2)
Can someone please help me with this problem?? **It's high-school geometry.
Hello!
Answer:
[tex]\huge\boxed{59.04 units}[/tex]
To solve, we will need to use Right-Triangle Trigonometry:
Begin by solving for angles ∠S and ∠R using tangent (tan = opp/adj)
tan ∠S = a / (1/2b)
tan ∠S = 3√5 / 14
tan ∠S ≈ 0.479
arctan 0.479 = m∠S (inverse)
m∠S and m∠R ≈ 25.6°
Use cosine to solve for the hypotenuse, or the missing side-length:
cos ∠S = 14 / x
x · cos (25.6) = 14
x = 14 / cos(25.6)
x ≈ 15.52
Both triangles are congruent, so we can go ahead and find the perimeter of the figure:
RS + RQ + QS = 28 + 15.52 + 15.52 = 59.04 units.
Hope this helped you! :)
Answer:
[tex]\large \boxed{\mathrm{59.05 \ units}}[/tex]
Step-by-step explanation:
Take one small triangle, solve for hypotenuse.
[tex]\frac{b}{2} =\frac{28}{2} =14[/tex]
Use Pythagorean theorem.
[tex]c=\sqrt{(3\sqrt{5})^2 +14^2 }[/tex]
[tex]c= 15.524175...[/tex]
Add the hypotenuse twice because there are two triangles, then add to the length of b to find the perimeter.
[tex]15.524175...+15.524175...+28[/tex]
[tex]59.048349...[/tex]
Solve for 'x' in both of the following problems. Show all your work/explanations on your own paper and then submit a picture of your work and answers in the dropbox below.
Answer/Step-by-step explanation:
1. <B is an inscribed angle intercepting arc CA.
Therefore, m<B = ½*128 (inscribed angle theorem)
m<B = 64°
x = 180 - (m<B + m<A) (sum of angles in a triangle)
x = 180 - (64 + 43)
x = 180 - 107 = 73°
2. [tex] KH*HI = JH*HG [/tex] (intersecting chords theorem)
[tex] 10*x = 14*5 [/tex]
Solve for x
[tex] 10x = 70 [/tex]
[tex] \frac{10x}{10} = \frac{70}{10} [/tex]
[tex] x = 7 [/tex]
What is the area?
6 mm
5 mm
3 mm
13 mm
8 mm
9 mm
Answer:
none of above .
Step-by-step explanation:
because the unit of area is always in square forms.
Please answer this question now
Answer:
m∠C = 102°
Step-by-step explanation:
This is a quadrilateral inscribed in a circle
The sum of opposite angles in a cyclic quadrilateral is equal to 180°
m∠D + m∠B = 180°
m∠B = 180° - m∠D
m∠B = 180° - 80°
m∠B = 100°
We know what m∠B
We have external angles outside the circle.
m∠CDA is opposite m∠B
m∠CDA = 2 × m∠B
m∠CDA = 2 × 100°
m∠CDA = 200°
m∠CDA is the sum of m∠CD and m∠DA
m∠CDA = m∠CD + m∠DA
m∠DA = m∠CDA - m∠CD
m∠DA = 200° - 116°
m∠DA = 84°
m∠DAB is an exterior angle also, hence,
m∠DAB is the sum of m∠DA and m∠AB
m∠DAB = m∠DA + m∠AB
m∠DAB = 84° + 120°
m∠DAB = 204°
Finally we can solve for m∠C
m∠DAB is Opposite m∠C
So, m∠C = 1/2 × m∠DAB
m∠C = 1/2 × 204
m∠C = 102°
A ship travels due north for 100 miles from point C to point A. From point A the ship travels to point B at 60° east of north. From point B, the ship returns to point C heading 45° west of south. What approximate distance did the ship travel from point A to point B? How far does it travel in total?
Answer:
AandB=80miles
Total=240miles
Step-by-step explanation:
Draw the figure first indicating the figures then find the distance each degrees then find the total
The distance ship travels from A to B is 273.2 miles and total distance covered by ship is 707.82 miles.
What is laws of sines?The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.
The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.
Given distance from C to A = 100 miles north
From B to A ship travels 60° east of north,
and From B to C 45° west of south,
the figure for problem is attached,
from figure we can calculate the angles of A, B and C
so ∠A makes supplementary with 60°
∠A + 60° = 180°
∠A = 120°
for ∠B we need to draw an imaginary perpendicular on the line extending from A, we get
∠B + 45° + 30° = 90° (30° is angle of imaginary right triangle)
∠B = 90 - 75 = 15°
and ∠C can be found by,
∠A + ∠B + ∠C = 180°
∠C = 180 - 15 - 120
∠C = 45°
now use sine formula for triangles,
sinA/a = sinB/b = sinC/c
where A, B and C are angles of triangle and a, b and c are length of opposite side of angle A, B and C respectively.
a = BC, b = AC, and c = AB
so
sinA/BC = sinB/AC = sinC/AB
we have AC = 100 miles
substitute the values
sinC/AB = sinB/AC
sin(45)/AB = sin(15)/100
AB = 100/(√2sin(15))
AB = 100/0.3659
AB = 273.298 miles
and sinA/BC = sinB/AC
BC = AC sinA/sinB
BC = 100(sin 120/sin15)
BC = 100(0.866/0.2588)
BC = 100 x 3.3462
BC = 334.62 miles
total distance = AB + BC + AC
total distance = 334.62 + 273.2 + 100
total distance = 707.82 miles
Hence the distance from A to B is 273.2 miles and total distance is 707.82 miles.
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The test to detect the presence of respiratory syncytial virus is 97% accurate for a person who has the virus and 99% accurate for a person who does not have the virus. In a given population, 0.55% of the people are infected.
The probability that a randomly chosen person gets an incorrect result is
.
Answer:
The probability that a randomly selected person gets incorrect result is 2.2 × 10⁻⁴
Step-by-step explanation:
The parameters given are;
The accuracy of the test for a person who has the respiratory synctial virus = 97%
The accuracy of the test for a person who does not have the respiratory synctial virus = 99%
We have;
a = TP =
b = FP
c = FN
d = TN
a/(a + c) = 0.97
d/(d + b) = 0.99
a/(a + b) = 0.97*0.0055/(0.97*0.0055 + (1 - 0.99)*(1-0.0055))
PPV = 0.349 = 34.9%
Therefore, we have;
a/(a + c) = 0.97 and
a/(a + b) = 0.349
0.97(a + c) =0.349(a + b)
(0.97 - 0.349)a = 0.349·b - 0.97·c
a = (0.349·b - 0.97·c)0.621
b × (1 - 0.0055) = (1 - 0.97)×(1 - 0.0055)
b = 1 - 0.97 = 0.03
Similarly,
c = 1 - 0.99 = 0.01
The proportion of the population that have false positive and false negative = 0.03 + 0.01 = 0.04 = 4%
The probability that a randomly selected person gets incorrect result = 0.04×0.0055 = 0.00022.
Answer:
0.01011
Step-by-step explanation:
