Choose a justification for each step in the derivation of the sine difference identity.
Answer:
Step-by-step explanation:
The missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even and sine function is odd respectively.
Given:
The given expression is [tex]\sin (x-y)[/tex].
To find:
The justification for each step.
Explanation:
Cofunction identities:
[tex]\sin\left(\dfrac{\pi}{2}-x\right)=\cos x[/tex]
[tex]\cos\left(\dfrac{\pi}{2}-x\right)=\sin x[/tex]
Cosine difference identity:
[tex]\cos(x-y)=\cos x\cos y+\sin x\sin y[/tex]
Cosine function is even, so [tex]\cos(-x)=\cos x[/tex].
Sine function is odd, so [tex]\sin(-x)=-\sin x[/tex].
We have,
[tex]\sin (x-y)[/tex]
[tex]=\cos\left|\dfrac{\pi}{2}-(x-y)\right|[/tex] Step 1: Cofunction identity
[tex]=\cos\left|\dfrac{\pi}{2}-x+y\right|[/tex] Step 2: Distributive property
[tex]=\cos\left|\left(\dfrac{\pi}{2}-x\right)+y\right|[/tex] Step 3: Associative property
[tex]=\cos\left|\left(\dfrac{\pi}{2}-x\right)-(-y)\right|[/tex] Step 4: Factoring out
[tex]=\cos\left(\dfrac{\pi}{2}-x\right)\cos(-y)+\sin\left(\dfrac{\pi}{2}-x\right)\sin(-y)[/tex] Step 5: Cosine difference identity
[tex]=\sin(x)\cos(-y)+\cos(x)\sin(-y)[/tex] Step 6: Cofunction identity
[tex]=\sin(x)\cos(y)-\cos(x)\sin(y)[/tex] Step 7: Cosine function is even, sine function is odd
Therefore, the missing reasons are Cofunction identity, Cosine difference identity, Cofunction identity, Cosine function is even, sine function is odd respectively.
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if 1 cm represents 35 miles what is 1.25 cm in miles?
Answer:
43.75 miles
Step-by-step explanation:
You divide the 35 by 4 and then just add it to the original distance of 35 miles. 35/4=8.75
8.75+35=43.75
PLEASE SOMEONE HELP ME ASAP!!! I’ll make you BRAINLIEST!!!!
Write y=2x^2+24x+47 in vertex form. Also please explain/write the steps thanks.
Answer:
y=(2x^2+24x)+25
y=2x(x^2+12x)+25
y=2x(x^2+12x+36)+25-2x(36)
Y=2x(x+6)^2+25-72
Y=2x(X+6)^2-47
Step-by-step explanation:
sorry it was late
Answer: y=2(x+6)²-5
Step-by-step explanation: First you find the coefficient of x^2, which is 2, then take out 2 as a factor, 24/2 which will equal to 12. After that do 47 divided by 2 if you calculate that it will equal to 23.5. y=2(x²-12+23.5) y =2(x²-12x+23.5)
Next Step: Figure out the coefficient of x. To make it easier,look what is in front of x as you can see it is 12. Then you divide 12/2 which is 6. Then square 6, which is 36. Then you add and subtract 36. To write the first three terms as a square, you do ( x+6)^2. Then do -36 + 23.5 if you calculate that it will get you wil get -12.5 . Now that you have calculated that distribute 2, then do 2 times -12.5 which is -12.5. This is how it shoud look like y=2(x+6)² -12.5.
A basketball player attempted 15 field goals. He scored on 40 percent of his attempts. How many field goals did the player score? NEED HELP BADLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 10/21/2020
Answer:
He scored 6 field goals out of 15
Step-by-step explanation:
40% converted into a decimal is 0.4. "Of" means multiply. So you do 15 times 0.4 and get 6.
I need help finding the solution
✩ Answer:
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[tex]\bold{Hello!}\\\bold{Your~answer~is~below!}[/tex]
✩ Step-by-step explanation:
✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*
✺ Subtract [tex]5[/tex] from both sides:
[tex]3z<17-5[/tex]✺ Subtract [tex]5[/tex] from [tex]17[/tex] to get [tex]12[/tex]:
[tex]3z<12[/tex]✺ Divide both sides by [tex]3[/tex]. Since [tex]3[/tex] is positive, the inequality direction remains the same:
[tex]z<\frac{12}{3}[/tex]✺ Divide [tex]12[/tex] by [tex]3[/tex] to get [tex]4[/tex]:
[tex]\boxed{z<4}[/tex][tex]Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex[/tex]
"ටᆼට"
Help needed ASAP will give you BRAINLIEST and 5 stars rate :)
Answer:
The bicyclist is travelling at a rate of 20 km/h.
Step-by-step explanation:
When you plug the numbers into the formula (y2-y1/x2-x1=m) you get 20 km/h.
Analyze the number line below and answer the question that follows.
If jpg, where could point I be?
A.
–7
B.
–6
C.
–5
D.
–4
Please select the best answer from the choices provided
A
B
C
D
Answer:
c
Step-by-step explanation:
Assume you have 3,000 songs downloaded to your mobile phone. Of these songs, 50 songs are by your favorite artist. If you play the songs on random shuffle, how many songs would you have to listen in a row before you heard a song by your favorite artist?
Answer:
2950
Step-by-step explanation:
i just subtracted 3,000 with 50
There are 2950 songs would you have to listen in a row before you heard a song by your favorite artist.
What is random shuffle of songs?
Shuffle play is a type of music playback in which all tracks are selected at once and songs are played in a random order. Media player software, digital audio players, and CD players all frequently have it.
Given: You have 3,000 songs downloaded to your mobile phone.
Of these songs, 50 songs are by your favorite artist.
So, the number of songs would you have to listen in a row before you heard a song by your favorite artist are,
3000 - 50 = 2950.
Therefore, there are 2950 songs would you have to listen in a row before you heard a song by your favorite artist.
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6x +3 = 6x -20 - x equations with variables
Find the midpoint of AB if A(-3. 8) and B(-7. -6)
The midpoint of AB is (-5, 1).
To find the midpoint of a line segment AB, we average the x-coordinates of the two endpoints and the y-coordinates of the two endpoints.
Given that A has coordinates (-3, 8) and B has coordinates (-7, -6), we calculate the midpoint as follows:
x-coordinate of midpoint = (x-coordinate of A + x-coordinate of B) / 2
= (-3 + -7) / 2
= -10 / 2
= -5
y-coordinate of midpoint = (y-coordinate of A + y-coordinate of B) / 2
= (8 + -6) / 2
= 2 / 2
= 1
Therefore, the midpoint of AB is (-5, 1), where -5 is the x-coordinate and 1 is the y-coordinate. This means that the midpoint is equidistant from points A and B, dividing the line segment AB into two equal parts.
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Alex rents a car for one day. The charge is $18
plus $0.12 per mile. Alex wants to spend exactly
$30. How many miles can he drive?
Answer:
100
Step-by-step explanation:
30 - 18 = 12
12 / .12 = 100
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Miles that alex can drive is 100
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
The calculation is as follows;
Number of days alex rents a car = 1 day
The charge for the car = $18 plus $0.12 per mile
Alex wants to spend; $30
The number of miles he will drive can be calculated as follows
= $30 - $18
= $12
= 12÷0.12
= 100
Therefore, if Alex spends $30 he will drive for 100 miles
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What is the slope of the line through (-9,6) and (-6, -9)?
Choose 1 answer:
1/5
5
-5
-1/5
I hate algebra
10. A student solves the following problem:
Problem:
2 (x-3) + 3x = 19
2x - 6 + 3x = 19
(2x + 3x) - 6 = 19
5x - 6 - 19
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
5x - 6+ 6 = 19+ 6
5x = 25
X = 5
What property justifies step 4?
a. Commutative Property of Addition
c. Multiplication Property of Equality
b. Addition Property of Equality
d. Substitution
Answer:
Step-by-step explanation:
A.
Option A is correct. The property that justifies step 4 based on the calculation is the Commutative property of addition.
Equations are expressions separated by an equal sign.
Given the equation:
2(x-3) + 3x = 19
Expand the parenthesis using the distributive law
2x - 2(3) + 3x = 19
2x - 6 + 3x = 19
Collect the like terms
2x + 3x -6 = 19
Step 4
Since 2x+3x = 3x+2x = 5x (according to the commutative law), the expression becomes:
5x-6 = 19
Step 5
Add 6 to both sides
5x-6+6 = 19+6
5x = 25
x = 25/5
x = 5
Hence the property that justifies step 4 based on the calculation is the Commutative property of addition.
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(3.9 x 10^-3) + .0026 in scientific notation
The value of (3.9 × 10⁻³) + 0.0026 in scientific notation is 6.5 × 10⁻³.
What is Decimals numbers?Decimal numbers are numbers which has basically a whole number part and a fractional or decimal part after a point called decimal point.
Decimal number system describes the base 10 number system.
Given are numbers 3.9 × 10⁻³ and 0.0026 added together.
We have to do it in scientific notation.
0.0026 can be written as 2.6 × 10⁻³.
Adding these two numbers together, and taking the common term,
(3.9 × 10⁻³) + (2.6 × 10⁻³) = (10⁻³) (3.9 + 2.6)
= (10⁻³) (6.5)
= 6.5 × 10⁻³
Hence the answer of the sum of (3.9 × 10⁻³) + 0.0026 is 6.5 × 10⁻³ in scientific notation.
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Find value if x in the figure below
Easy buddy...
[tex]5x - 15 = 3x + 7[/tex]
Subtract the sides of the equation plus 15
[tex]5x = 3x + 7 + 15[/tex]
[tex]5x = 3x + 22[/tex]
Subtract the sides of the equation minus 3x
[tex]5x - 3x = 22[/tex]
[tex]2x = 22[/tex]
Divided the sides of the equation by 2
[tex]x = \frac{22}{2} \\ [/tex]
[tex]x = 11[/tex]
________________________________
And we're done.
Thanks for watching buddy good luck.
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Please help if you can. And please explain
Answer: Choice B) 0.63
==============================================
Work Shown:
1.1 is 174% of what number
1.1 = 174% of what number
1.1 = 174% of x
1.1 = 1.74*x
1.74x = 1.1
x = 1.1/1.74
x = 0.632183908045977 which is approximate
x = 0.63
-4(–7m – 10m – 4) – 2m
Answer:
Im assuming you need to simplfy as far as you can so
Step-by-step explanation:
-4 ( -17m -4 ) - 2m
distribute
68 m + 16 -2m
combine like terms
66m + 16
Answer: 66m + 16
Step-by-step explanation:
At the market five lightbulbs cost nine dollars how much do seven lightbulbs cost
Answer:
$12.60
Step-by-step explanation:
Answer:
12.60
Step-by-step explanation:
9 dollars divided by 5 lightbulbs is 1.8
so 1.80 dollars × 7 lightbulbs = 12.60
9÷5=1.8
1.8×12.60
I am thinking of a slope equivalent to 1/4→ What are two points from the line? List your coordinate pairs below.
→ Prove that the slope equals 1/4.
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Mathematics
the points or conditions for the slope to be 1/4 are as
1.) (-2,2) ,(2.3)
2.) (-4,4),(4,6)
A statistics teacher was interested in the relationship between you and the number of days students waited to start a project
and the score that project received (out of 100 points). Information was collected on several students and was used to
obtain the regression equation = -3.64x + 96.5, where x represents the number of procrastination days and 9 is the
predicted grade. What is the predicted grade of a student who procrastinated for 2 days?
0 25.96
0 85.58
O 89.22
0 103.78
Answer:
C. 89.22
Step-by-step explanation:
hope it helps!
edge 2020
Which equation represents a proportional relationship
Answer: B y=100/x
Step-by-step explanation:
Given the points (2,4),(-2,6),(1,3), and (0,3), categorize the domain and range.
Domain
Range
No Answers Chosen
ING
1
Possible answers:
2
3
All real numbers
-2
0
4
6
2
3
4
Answer: range: 3, domain: 4
Step-by-step explanation:
the range of a problem is basically the difference between the smallest and the largest y value. the largest y value here is 6 and the smallest is 3, so 6-3 = 3 -> 3 is your range! now for domain: the domain of a problem is the difference between the smallest and largest x value. the largest x value is 2 and the smallest is -2, so 2 - -2 = 4 -> the domain is 4! hope this helped!
Which of the following expressions cannot be simplified?
A) √24
B) √32
C) √27
D) √38
Answer:
C
Step-by-step explanation:
Answer:
The answer is c
Step-by-step explanation:
5(x −1) < 3x + 10 − 8x
Answer:
x < [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
I hope this help
Answer:
Step-by-step explanation:
5x - 5 < -5x + 10
10x - 5 < 10
10x < 15
x < 15/10
x< 3/2
Please help I’ll give brainiest!!
Answer:
-1
Step-by-step explanation:
f(x)=√8+2
Find the range
Answer:
what does f or x mean
Step-by-step explanation:
7 + 9 – (–3) – 1 + 2
Answer: 20
Step-by-step explanation:
Hope helps
Answer:
7 + 9 - (-3) - 1 + 2
16 - (-3) - 3
19 - 3
16
The slope of a vertical line is....?
a) undefined
b) not enough information given
c) horizontal
d) 0
Solve x2 − 8x + 15 < 0. The solution set for the quadratic inequality is:
Answer:
3<x<5
Step-by-step explanation:
[tex]x^2 - 8x + 15 < 0\\\\\mathrm{Factor}\:x^2-8x+15:\quad \left(x-3\right)\left(x-5\right)\\\left(x-3\right)\left(x-5\right)<0\\\\\mathrm{Find\:the\:signs\:of\:the\:factors\:of\:}\left(x-3\right)\left(x-5\right)\\\\\mathrm{Identify\:the\:intervals\:that\:satisfy\:the\:required\:condition:}\:<\:0\\\\3<x<5[/tex]
Solve the equation x2 + + 7x= 30
O A. x= 15 and x= -2
0 B x=-6 and x = 5
0 C x= -10 and x= 3
O D. x= 10 and x= -3
Answer:
x^2+7x=30
x^2+7x-30=0
Here a=1,b=7 and c=-30
Now,
Discriminant(D)=b^2-4ac
=7^2-4×1×(-30)
=49+120=169
By applying Quadratic formula
x=-b+- root over b^2-4ac÷2a
=-7+- root over D ÷ 2×1
=-7 +- root over 169 ÷2
=-7 +- 13 ÷2
Now,
Either x=-7+13÷2=6÷2=3
Or x=-7 -13 ÷2=-20÷2=-10
Hence, ans is (C) x=-10 and x=3