In right triangle ABC, m∠B ≠ m∠C. Let sin B = r and cos B = s. What is sin C – cos C?
Answers
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Explanation:
We'll need these trig ratios
sine = opposite/hypotenusecosine = adjacent/hypotenuseRefer to the diagram below.
sin(B) = r = r/1 which tells us that the side opposite angle B is r units long. The hypotenuse is 1.
cos(B) = s = s/1 means the adjacent side to angle B is of length s
sides r and s are the two legs of the right triangle.
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From that diagram, we can then say:
sin(angle) = opposite/hypotenuse
sin(C) = s/1
sin(C) = s
This is identical to cos(B). We can say cos(B) = sin(C)
Also, we can say:
cos(angle) = adjacent/hypotenuse
cos(C) = r/1
cos(C) = r
So cos(C) = sin(B)
This works because B+C = 90
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So,
sin(C) - cos(C) = cos(B) - sin(B) = s - r
Related Questions
Nolan was given a box of assorted chocolates for his birthday. Each night, Nolan treated himself to 3 chocolates. After 8 nights, there were 6 chocolates remaining in the box.
Answers
Step-by-step explanation:
i am trying to solve it but how
many chocolate were there in a box
You can retry this question below
The sum of two numbers is 71. The difference of the two numbers is 41. What are the two numbers.
Let x be the larger number and y be the smaller number.
Write an equation that expresses the information in the sentence "The sum of two numbers is 71."
Write an equation that expresses the information in the sentence "The difference of the two
numbers is 41."
Solve the system you have written above.
The larger number, x is
The smaller number, y is
Calculator
Answers
Answer:
x = 56
y = 15
Step-by-step explanation:
"The sum of two numbers is 71."
x + y = 71
"The difference of the two numbers is 41."
x - y = 41
Solve the system:
From the first eq.
x = 71 - y
Replacing this value in the second eq.
(71-y) - y = 41
71 - 2y = 41
71 - 41 = 2y
30 = 2y
y = 30/2
y = 15
From the second eq.
x - y = 41
x - 15 = 41
x = 41 + 15
x = 56
Check:
from the first eq.
x + y = 71
56 + 15 = 71
What is the radius of a circle whose equation is x2 y2â’10x 6y 18=0? 2 units 4 units 8 units 16 units.
Answers
The radius of the circle is 4 units.
Given to us:
[tex]x^2 + y^2 - 10x + 6y + 18 = 0[/tex]
The generalized format for radius of a circle is given by:
[tex]\\(x - h)^2 + (x - k)^2 = a^2\\where,\\h, k= coordinate\ of\ the\ center\ of\ the\ circle\\a= radius\ of\ the\ circle[/tex]
therefore after rearrangement of the equation we get,
[tex]x^2 + y^2 - 10x + 6y + 18 = 0,\\x^2 - 10x + y^2 + 6y =- 18,\\[/tex]
adding 25 and 9 on both the sides to bring it in the generalized format for radius of a circle,we get
[tex]x^2 - 10x+25 + y^2+ 6y+9 =-18+25+9,\\[/tex]
[tex](x - 5)^2 + (y + 3)^2 = 16\\(x - 5)^2 + (y + 3)^2 = 4^2\\[/tex]
Hence, the coordinate for this circle are x=5 and y=-3. And the radius of the circle is 4 units.
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Roger is paid $50 to sell videos of a play to an audience after the play is performed.
He also receives $2 for each video he sells. The equation E=50+2v
E=50+2v
models the amount of money Roger earns selling v videos. The play's audience consists of 230 people.
What is the practical range of the equation?
Question options:
The set of all even integers greater than or equal to 50 and less than or equal to 510
The set of all integers greater than or equal to 50 and less than or equal to 510
The set of all real numbers greater than 0 and less than 230
The set of all real numbers greater than 50
Answers
The set of all even integers greater than or equal to 50 and less than or equal to 510
In other words, [tex]0 \le E \le 510[/tex] where E is an even integer.
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Explanation:
The domain is the set of allowed inputs, while the range is the set of allowed outputs. For now, let's focus on the domain.
In this case, the domain is the set of integers between 0 and 230. We're dealing with the set {0,1,2,..., 229, 230} to represent the possible number of people who bought the video.
Let's plug in the smallest item from the domain (v = 0).
E = 50+2v
E = 50+2*0
E = 50+0
E = 50
This matches with the fact Roger gets paid $50 even if he didn't sell anything. This is the flat up front fee he got.
Now let's plug in the largest value for v (230).
E = 50+2v
E = 50+2*230
E = 50+460
E = 510
This tells us that $510 is the most Roger can get from the audience of 230 people. This is assuming that each person buys only one copy.
So we can see that the range of E values spans from $0 to $510.
Furthermore, notice that 2 can be factored from 50+2v to get 2(25+v). This shows that the expression 50+2v is always even. Therefore, we must clarify that we're dealing with the set of even numbers between 0 and 510
In symbolic form, we'd say [tex]0\le E \le 510[/tex] where E is an even integer.
In roster form, the range of possible E values is {0, 2, 4, ..., 506, 508, 510}.
Answer: the answer is A
Mean and median of 1024 divided by 16 and of these numbers 34,48,52,61,76,76,61,84,61,39,83,61,79,81,56,88
Answers
Answer:
8
Step-by-step explanation:
88888888888888888888888888888888888
Solve the inequality: 4(2x-11) is less than equal to -12 + 2(x-4) No "files" please and also need an explanation
Answers
[tex]4(2x-11) \leq -12 +2(x-4)\\\\\implies 8x - 44 \leq -12 + 2x -8\\\\\implies 8x -44 \leq 2x -20\\\\\implies 4x - 22 \leq x - 10~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 2}]\\\\\implies 4x -22 +22 \leq x -10 +22~~~~~~;[\text{Adding 22 to both sides}]\\\\\implies 4x \leq x+12\\\\\implies 4x -x \leq x+12-x~~~~~~~~~~~~~~~~;[\text{Subtracting x from both sides}]\\\\\implies 3x \leq 12\\\\\implies x \leq 4 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;[\text{Dividing both sides by 3}][/tex]
[tex]\text{Interval solution,} ~(-\infty, 4][/tex]
There are 16 pieces of candy. Jack
has 5 empty bogs and puts 3 pieces
of candy nto each bag How many
pleces of candy are left?
Answers
5 x 3 = 15
16 - 15 = 1
you take 5•3=15 and 16-15=1 so there is one left over
Margie says the set of numbers, 0. 1, -1, -21 4 , 3, are in order from least to greatest. What is her error? She did not use the correct common denominator. The 3 is in the wrong place. She treated all the numbers as positive. The â€"1 should be the first number on the list.
Answers
Answer:
3 is in the wrong place
Step-by-step explanation:
:)
One of the errors made by Margie by saying the set of numbers 0, 1, -1, -21, 4, 3 is that the -21 should be the first number on the list.
The given set of numbers is:
0, 1, -1, -21, 4, 3.
Margie says that the set of numbers above is in order from least to greatest
Kindly note that:
The negative number with the highest magnitude is the lowest
The positive number with the highest magnitude is the highest
Arranging this number by carefully following the note above, the set of numbers above from the least to greatest is:
-21, -1, 0, 1, 3, 4
It is obvious that Margie made a mistake in arranging the numbers, and one of the mistake is that the -21 should be the first number on the list since it is the most negative
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Victoria kicked a soccer ball laying on the ground. It was in the air for 5 seconds before it hit the ground. While the soccer ball was in the air, it reached a height of approximately 15 feet. Assuming that the soccer ball height (in feet) is a function of time (in seconds), what is the domain in the context of this problem?
Answers
Answer:
the Domain would be represented by Time in this problem, since time can only be positive, the domain would start at zero seconds and end at 5 seconds when the soccer ball hits the ground.
Step-by-step explanation:
Barbara has some dimes and quarters. If she has 16 coins worth a total of $2.50, how many of each type of coin does she have?
Answers
Answer:
10 dimes and 6 quarters.
Step-by-step explanation:
2.50-25-25=2.00-10 dimes = 1.00-4 0.25=0
so
10 dimes and 6 quarters.
Answer:
10 Dimes and 6 Quarters.
Step-by-step explanation:
Important info:
16 Coins
Total = $2.50
Note:
Dimes = 0.10 Cents
Quarters = 0.25 Cents
Question to answer:
How many of each type of coin does she have?
Solution:
10 Dimes = $1.00
6 Quarters = $1.50
$1.00+$1.50 = $2.50
Therefore 10 Dimes and 6 Quarters = $2.50 and = 16 Coin.
2
Which is the equation of a line that has a slope of 3 and passes through point
(-3,-1)?
2
1o -+1
O y=-3x+1
O y=-x+3
O y=-x-1
=
O y=-x-3
Answers
Answer:
Step-by-step explanation:
We'll start with the slope intercept form of a straight line equation:
y = mx + b, where x is the slope and b the y-intercept. The slope we are given is 3, so:
y = 3x + b
We need a value of b that will force the line to go through (-3,-1). Do this by entering that point in the equation and solving for b:
y = -3x + b
-1 = 3(-3) + b
b = 8
y = 3x + 8
Abigail must move a bucket of tomatoes from her garden to her kitchen, as represented on the grid below.
y
Kitchen
L(5, 1)
-1 0
2
Garden
-(-3, 4)
Answers
step by step explanation:
Answer:
Step-by-step explanation:
9.43
Gabriella earns $17 an hour and gets a 15%
raise. With her raise, how much will she earn after working 40 hours?
A. $680
B. $702
C. $782
D. $796
Answers
c: 782 dollars
.15 times 17 is 2.55
17+2.55= 19.55
19.55 times 40=782
please please i beg help for brainlist !!!!!!!!
Answers
Answer:
[tex]a_n=\frac{1}{2}a_{n-1}[/tex]
Step-by-step explanation:
Here, you can see every consecutive term is divided by 2. I think that's pretty obvious looking at it, but you can work it out like this if you'd like to. Divide each consecutive term by the one before it:
[tex]6\div12=\frac{1}{2}\\\\3\div6=\frac{1}{2}\\\\\frac{3}{2}\div3=\frac{1}{2}[/tex]
Each term is multiplied by 1/2 over the last, or divided by 2. In this case actually, we do want it in the form of "multiplied by 1/2", as the recursive equation is:
[tex]a_n=xa_{n-1}[/tex]
where x is the factor. Here, we're multiplying by x, so we want "multiplied by 1/2" as described above. x is 1/2, so you can write the equation:
[tex]a_n=\frac{1}{2}a_{n-1}[/tex]
You can simply interpret this as "each term is 1/2 of the term before it"
Can someone plz help me? I really don’t get this
Answers
Answer:
D.
Step-by-step explanation:
The question is asking which expressions are the same. To find the answer, or rather confirm it, you should simplify each expression.
A. 8+(3*y) and (8+3)*y
8+3y and 11y
This cannot be the answer, when simplified they are not equal
B. (7-3)*y and 7-(3*y)
4y and 7-3y
This cannot be the answer, when simplified they are not equal
C. (6/y)+13 and 13+(y/6)
13+6/y and y/6+13
This cannot be the answer, when simplified they are not equal
D. 7+(y*5) and 7+(5*y)
7+5y and 7+5y
This is the answer, when simplified they are equal
I hoped this helped and made it easier to understand! :)
Describe the end behavior of the function.
f(x)=3(1/5)^x-2
Answers
Answer:
The leading coefficient test requires a polynomial.
Not a polynomial
Step-by-step explanation:
Answer:
x → -∞, f(x) → ∞
x → ∞, f(x) → -2
Step-by-step explanation:
f(x) is an exponential function with a base less than 1. It represents decay, so will approach infinity as x approaches negative infinity. It will approach a horizontal asymptote for large positive x.
The -2 added to the exponential term moves the asymptote from y=0 to y=-2.
x → -∞, f(x) → ∞
x → ∞, f(x) → -2
what term is used to refer to the reverse order of a conditional statement
Answers
[tex] \: \: \: \: \: \: [/tex]
converseThe converse of a conditional statement is created when the hypothesis and conclusion are reversed.hope it helpsIdentify the domain and range of the following relation. {(3,-2), (5,2), (7,6), (9,10), (11,14)}
Answers
R: -2, 2, 6, 10, 14
"The square root of two times a number subtract five is equal to ten."
Answers
I think this is √2n-5 = 10.
Chef Ira has 613 pies he wants to sell at his restaurant. Each slice is 16 pie and costs $1.50. Chef Ira sells all the remaining slices of pie.
How much money will he earn?
A. $9.00
B. $9.50
C. $38.00
D. $57.00
Answers
What is the equation of the line that passes through the point (2,-2) and has a slope of -1/2?
Answers
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{1}{2}[/tex] , then
y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
To find c substitute (2, - 2 ) into the partial equation
- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1
y = - [tex]\frac{1}{2}[/tex] x - 1 ← equation of line
Answer:
y=-1/2x-1
Step-by-step explanation:
y-y1=m(x-x1)
y-(-2)=-1/2(x-2)
y+2=-1/2(x-2)
y=-1/2x+2/2-2
y=-1/2x+1-2
y=-1/2x-1
Each of three friends Lynn Jada and Andre has the goal of raising $40 how much money did each person raise according to the following Jada raise 50% of her goal
Answers
Answer:
is it 60$
Step-by-step explanation:
because if its 100% than it would be 40+40+40
due to 50% = 120 ÷50%
= 60
41)533
What is 533 divided by 41 using Partial Quotients?
Answers
Answer:
13
Step-by-step explanation:
533÷41=13 just use a calculator
______________ Angles have each of the pairs of opposite angles made by two intersecting lines *
1 point
Supplemnatary
vertical
adjacent
linear pair
Answers
[tex]\huge \bf༆ Answer ༄[/tex]
The Correct choice is B. Vertical
Vertical Angles have each of the pairs of opposite angles made by two intersecting lines .
Answer:
vertical
✌️❤️✌️
......
3 MS Wingate's coffee table is 7 feet wide the length of the coffe table is 8 times the width what is the perimeter of the coffe table?
Answers
15.
Write a direct variation equation if x = 7 and y = 42.
16.
Use the equation in example 15 to find x if y = 66.
Answers
Answer:
15. y = 6x
16. x = 11
Step-by-step explanation:
15. A direct variation equation is of the form ...
y = kx
Solving for k, we find ...
k = y/x = 42/7 = 6
The equation is y = 6x.
__
16. Filling in the given values, we have ...
66 = 6x
11 = x . . . . . . . divide by 6
Your family goes to a restaurant for dinner. There are
12 people in your family. Some order the chicken dinner for
$14.99 and some order the steak dinner for $25. if the total
bill was $219.92, how many people ordered each type of
dinner?
Answers
Answer:
8 chicken and 4 steak .
Step-by-step explanation:
8 x 14.99 = 119.29
4 x 25 = 100
I need help and I can’t find any sadly. Help!!
Answers
Answer: 1 is given, 2 is combine like terms, 3 is addition property of equality
Step-by-step explanation:
PLS HELP!!! WILL MARK BRAINLIEST!!
Answers
Answer:
D
Step-by-step explanation:
what is the rate of the graph shown below answer and i will make you branilest
Answers
Answer:
2
Step-by-step explanation:
Basically I use rise over run, or rise ÷ run.
The rise is 4 and the run is 2 in the section I chose. 4÷2 is equal to 2, so the rate of change is 2 feet per second.