Answer:
y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) ⇒ 3rd answer
Step-by-step explanation:
Let us revise the rules of the trigonometric compound angles
cos(x + y) = cos x cos y - sin x sin y
sin(x + y) = sin x cos y + cos x sin y
Let us solve the problem using the rules above
y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )
∵ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[cos x cos [tex]\frac{\pi }{4}[/tex] - sin x sin [tex]\frac{\pi }{4}[/tex] ]
∵ cos [tex]\frac{\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex] and sin [tex]\frac{\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex]
- Substitute them in the right hand side
∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = 2[ [tex]\frac{\sqrt{2}}{2}[/tex] cos x - [tex]\frac{\sqrt{2}}{2}[/tex] sin x]
- Multiply the bracket in the right hand side by 2
∴ 2 cos (x + [tex]\frac{\pi }{4}[/tex] ) = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
∴ y = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
Now let us find the function which give the same right hand side of the function above
y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] )
∵ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[sin x cos [tex]\frac{3\pi }{4}[/tex] + cos x sin [tex]\frac{3\pi }{4}[/tex] ]
∵ sin [tex]\frac{3\pi }{4}[/tex] = [tex]\frac{\sqrt{2}}{2}[/tex] and cos [tex]\frac{3\pi }{4}[/tex] = [tex]-\frac{\sqrt{2}}{2}[/tex]
- Substitute them in the right hand side
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = 2[ [tex]-\frac{\sqrt{2}}{2}[/tex] sin x + [tex]\frac{\sqrt{2}}{2}[/tex] cos x]
- Multiply the bracket in the right hand side by 2
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = [tex]-\sqrt{2}[/tex] sin x + [tex]\sqrt{2}[/tex] cos x
- Switch the two terms of the right hand side
∴ 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
∴ y = [tex]\sqrt{2}[/tex] cos x - [tex]\sqrt{2}[/tex] sin x
- The same with right hand side of the function above
∴ y = 2 sin (x + [tex]\frac{3\pi }{4}[/tex] ) has the same graph of y = 2 cos (x + [tex]\frac{\pi }{4}[/tex] )
Answer:
y=2sin(x+3pi/4)
Step-by-step explanation:
Answer C
I NEED HELP THIS IS DUE IN 15 mins PLSSS SOMEBODY HELP ME!!!!!
Answer:
[tex] Standard \: form :\:y= {x}^{2} - 4x - 5\\
Factored\: from:\:y = (x + 1) (x - 5)[/tex]
Step-by-step explanation:
[tex]y = (x - 2)^{2} - 9 \\ y= {x}^{2} - 4x + 4 - 9 \\ \red{ \boxed{ \bold{y= {x}^{2} - 4x - 5}}} \\ is \: in \: standard \: form \\ \\ y = (x - 2)^{2} - 9 \\ y = (x - 2)^{2} - {3}^{2} \\ y = \{(x - 2) + 3\} \{(x - 2) - 3 \} \\ y = \{x - 2 + 3\} \{x - 2- 3 \} \\ \purple{ \boxed{ \bold{y = (x + 1) (x - 5)}}} \\ is \: in \: factored \: form[/tex]
Find the value of this expression.
2(4+1)-3x6
A) -9
B) -8
C) 8
D) 36
E) 42
Answer:
B) -8
Step-by-step explanation:
2*5-18=10-18=-8
Answer:
B
Step-by-step explanation:
4+1 = 5
2*5 = 10
3*6 = 18
10-18=-8
what is the standard form of y=6(x-3)²-2
Answer:
B
Step-by-step explanation:
y = 6(x^2-6x+9)-2
y = 6x^2-36x+54-2
y = 6x^2-36x+52
The standard form of the given quadratic equation y=6(x-3)²-2 is y = 6x² - 36x + 52 after expanding the squared binomial and simplifying.
Explanation:The student has asked for the standard form of the quadratic equation y=6(x-3)²-2. The standard form of a quadratic equation is ax² + bx + c = 0. To rewrite the given equation in standard form, expand the squared binomial and simplify:
Expand the binomial: y = 6(x² - 6x + 9) - 2.Distribute the 6: y = 6x² - 36x + 54 - 2.Simplify the constants: y = 6x² - 36x + 52.So, the standard form of the given equation is y = 6x² - 36x + 52.
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Pleaseeeeeeee help me
Answer:
x = 24
Step-by-step explanation:
10:8
10(3) = x(3)
x = 8
30 : 24
A trapezoid has an area of 95 square meters. If the bases are 7 meters and 12 meters, what is the height of the trapezoid? Formula: h = 2A / b1 +b2?
a.15meters
b.13meters
c.10m
pls answwerrr asap plssss answer asap
Answer:
answer is c
Step-by-step explanation:
Formula: h=2A/b1+b2
95(2)/(7+12)=h
190/19=h
10m=h
answer is c
What is the total amount of money earned if $5,000 was in a savings account for three years at 2.5% interest
Answer:
Daily: $5,389.41
Monthly: $5,389.00
Semi-annually: $5,386.92
Annually:$5,384.45
Step-by-step explanation:
Pat needs 14 sticks of pepperoni to make 28 pizzas. How many sticks of pepperoni are needed to make 36 pizzas?
Answer:
18
Step-by-step explanation:
It is 18 because 14 x 2 equal 28 so that would mean you need one stick to make 2 pizzas. Then you divide 36 by 2 and get 18
Pat needs 18 sticks of pepperoni to make 36 pizzas
What is unitary method?The unitary method is a method in which you find the value of a unit and then the value of a required number of units
How to find how many sticks of pepperoni are needed to make 36 pizzas?According to the problem,
Pat needs 14 sticks of pepperoni to make 28 pizzas.Using unitary method,
To make 28 pizzas Pat needs 14 sticks of pepperoni.
∴ To make 1 pizza, Pat need [tex]\frac{14}{28}[/tex] sticks of pepperoni
∴ To make 36 pizzas, Pat needs [tex]\frac{(14)(36)}{28}[/tex] sticks = 18 sticks of pepperoni
So, Pat needs 18 sticks of pepperoni to make 36 pizzas
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I need help ASAP please (radical expressions)
Answer:
D
Step-by-step explanation:
Using the rule of radicals
[tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] = [tex]\sqrt{\frac{a}{b} }[/tex]
Given
[tex]\frac{14\sqrt{14} }{7\sqrt{2} }[/tex] ← cancel 14 and 7
= 2 × [tex]\sqrt{\frac{14}{2} }[/tex]
= 2[tex]\sqrt{7}[/tex] → D
miss johnson is buying new chair and a table for the senior center. she has 150 to spend. she bought one table for $68 and each chair costs $18 which inequality shows the number of chairs, x, she can buy
A. 18x + 68 ≤ 150
B. 18x + 68 ≥ 150
C. 68x + 18 ≤ 150
D. 68x + 18 ≥ 150
A square root of paper 150 millimeters on a side is folded in half along a diagonal. The result is a 45° -45° -90° triangle. What is the length of the hypotenuse of this triangle in millimeters? Write your answer in simplified radical form, if necessary.
Answer:
The length of the hypotenuse of this triangle is 150√2 mm.
Step-by-step explanation:
Consider the square ABCD shown in the image below.
The sides are 150 mm each.
All the angles of a square are 90°.
Now The square is folded in half along the diagonal BD.
The angles A, B and D are: 45°, 45° and 90°.
The hypotenuse of the right angled triangle is BD.
Compute the length of BD using the pythagoras theorem as follows:
[tex]BD^{2}=AB^{2}+AD^{2}\\=150^{2}+150^{2}\\=2\times 150^{2}\\BD=\sqrt{2\times 150^{2}}\\=150\sqrt{2}[/tex]
Thus, the length of the hypotenuse of this triangle is 150√2 mm.
Only the ones that are circle. I NEED THEM QUICK PLEASE
Answer:
10
Step-by-step explanation:
183.35
What is the interquartile range of this set of data?
15, 19, 20, 25, 31, 38, 41
Explanation:
If the data wasn't sorted, then the first step would be to arrange the elements from smallest to largest. However, that is already done for us.
The middle most value in the set {15, 19, 20, 25, 31, 38, 41} is 25 because there are three values below it {15,19,20} and three values above it {31,38,41}
Focus on the lower half {15,19,20} and note the middle of this subset is element 19. This is the value of Q1 or the first quartile.
The third quartile Q3 is 38 because the middle of the upper half data set {31,38,41} is 38.
We now subtract the values of Q3 = 38 and Q1 = 19 to get the interquartile range (IQR)
IQR = Q3 - Q1 = 38 - 19 = 19
Answer:
19
Step-by-step explanation:
Hope this helps and I got it right on the quiz on edge
The difference of a number and 8
Answer:8
Step-by-step explanation:
from least to greatest -2.1,-2,-3,0 help plz
Answer:
-3, -2.1, -2, 0
Step-by-step explanation:
Least to greatest
Hope this helped you!
Answer:
-2,2-2.1,-3,0 that's your
what is -1/3 (9x + 42) - 5x = -70
Answer:
The answer is x= 7 good luck though. also what you want to do it get the x's together and also get rid of the 42
Write the first four terms of a geometric sequence. Using the values you have written, calculate the common ratio and write the rule for the nth term. Show all calculations.
Answer:
FIRST FOUR (4) TERM = 6, 18, 54,162.
COMMON RATIO = 3
Step-by-step explanation:
In geometric expression.
Tn = the nth term
a = first term
r = common ratio.
Let's take the First term of the G.P as 6 and the third term as 54. Let's find the common ratio.
3rd term will be written as:
T3 = ar² = 54
Given the first term as 6.
T3 = 6r² = 54
6r² = 54
r² = 54 / 6
r² = 9
r= √9
r = 3
Therefore common ratio = 3.
Let's use this information to get the fourth term.
T4 = ar³
when a = 6
and r = 3.
T4 = 6 * 3³
T4 = 6 * 27
T4 = 162
The first four terms of the geometric sequence are [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\).[/tex] The common ratio is r= 3 and the rule for the nth term is [tex]\(a_n = 5 \cdot 3^{(n-1)}\).[/tex]
To find the common ratio r of a geometric sequence, one divides a term in the sequence by the previous term.
Given the first four terms as [tex]\(a_1 = 5\), \(a_2 = 15\), \(a_3 = 45\), and \(a_4 = 135\),[/tex] we can calculate the common ratio using the first two terms:
[tex]\[ r = \frac{a_2}{a_1} = \frac{15}{5} = 3 \][/tex]
We can verify this by calculating the ratio of the third term to the second term:
[tex]\[ r = \frac{a_3}{a_2} = \frac{45}{15} = 3 \][/tex]
And again with the fourth term and the third term:
[tex]\[ r = \frac{a_4}{a_3} = \frac{135}{45} = 3 \][/tex]
Since the ratio is consistent across these terms, we can confirm that the common ratio r is indeed 3.
The rule for the nth term of a geometric sequence is given by:
[tex]\[ a_n = a_1 \cdot r^{(n-1)} \][/tex]
[tex]\[ a_n = 5 \cdot 3^{(n-1)} \][/tex]
This is the rule for the nth term of the given geometric sequence.
Maria has a metal candle holder without a top that has a height of 3 cm and a radius of 3 cm how much metal was used to make holder?
Answer:
27pi cm^2
Step-by-step explanation:
Answer:
27 Pi cm2
Step-by-step explanation:
which of the following options have the same value as 60% of 94
60% of 94 is calculated by multiplying 94 by 0.60, which results in 56.4.
To find 60% of 94, you will multiply 94 by 0.60. Performing this calculation:
60% of 94 = 0.60 * 94
0.60 * 94 = 56.4
So, 60% of 94 equals 56.4.
The average speed of a car decreased by 3 miles per hour every successive 8-minute interval. If the car traveled 4.8 miles in the sixth 8-minute interval, what was the average speed of the car, in miles per hour, in the first 8-minute interval?
Answer:
13.5 mi/h
Step-by-step explanation:
The average speed of the car can be written as
[tex]v=\frac{d}{t}[/tex]
where
d = 4.8 miles is the total distance covered
[tex]t=6\cdot (8 min) = 48 min \cdot \frac{1}{60}=0.8 h[/tex] is the time elapsed
So the average speed is
[tex]d=\frac{4.8}{0.8}=6 mi/h[/tex]
We also know that the total time consists of 6 8-minutes interval, and the speed of the car decreased by 3 mi/h each interval.
Calling [tex]v_1[/tex] the average speed in the 1st interval, we have:
[tex]v_2=v_1-3\\v_3=v_1-6\\v_4=v_1-9\\v_5=v_1-12\\v_6=v_1-15[/tex]
The average speed in each interval can be written as [tex]v_i=\frac{d_i}{t}[/tex], where [tex]d_i[/tex] is the distance covered in each interval and [tex]d_i = 8 min =0.133 h[/tex] is the duration of each interval, so we can write
[tex]\frac{d_2}{t}=\frac{d_1}{t} -3 \rightarrow d_2 = d_1 -3t[/tex]
And similarly,
[tex]d_3=d_1-6t\\d_4=d_1-9t\\d_5=d_1-12t\\d_6=d_1-15t[/tex]
Since the total distance is [tex]d=d_1+d_2+d_3+d_4+d_5+d_6[/tex], we have:
[tex]d=6d_1 - 3t-6t-9t-12t-15t=6d_1-45t[/tex]
And since we know that
d = 4.8 miles
and t = 0.133h, we can find d1:
[tex]d_1=\frac{d+45t}{6}=\frac{4.8+(45)(0.133)}{6}=1.8 mi[/tex]
So the average speed in the first 8-minute interval is:
[tex]v_1=\frac{d_1}{t_1}=\frac{1.8}{0.133}=13.5 mi/h[/tex]
If the zeros of a quadratic function are 3 and 8, what are the factors of the function?
Answer:
(x-3)(x-8)
Step-by-step explanation:
the zero are what cancel out the factors.
Answer:
(x-8) and (x - 3)
Step-by-step explanation:
Enjoy your day:)
There are 6 crayons in a box. Only one of them is gold. A crayon is selected at random. Find the probability that it is not gold.
Answer:
1/6
Step-by-step explanation:
Answer:
5/6 or 83.33%
Step-by-step explanation:
There are 6 total crayons but only one is gold. The other five aren't. If you were to randomly pick one you'd have a 1/6 chance(16.67%)to pull out the gold crayon. That means there is a 5/6(83.33%)chance that you wouldn't pull out the gold one.
A group of students auditioned for a theater performance and 3/4 of the group less six students made up the cast of 42 students. Write an equation to represent the total number of students who auditioned, t.
Answer:
3/4x-6=42
x=64
Step-by-step explanation:
Let the number of students be x hence 3/4 of this number will be 3/4x
Since the number was 42 if they were 3/4x less six, it means minus six hence
3/4x-6=42
Therefore, the equation will be
3/4x-6=42
Solving the equation
3/4 x=42+6=48
3/4x=48
X=62
I need help with transversals!’
Answer:
∠ TWV = 106°
Step-by-step explanation:
∠ TWV and ∠ SVW are same- side interior angles and are supplementary, thus
∠ TWV + ∠ SVW = 180°, that is
3x - 5 + 2x = 180
5x - 5 = 180 ( add 5 to both sides )
5x = 185 ( divide both sides by 5 )
x = 37
Thus
∠ TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106°
Use the equation n2 + n = 56 to determine which figure has 56 blocks.
Answer:
7
Step-by-step explanation:
it is the 7th figure
What is the first step in solving the equation
x^2-16/25=0
What is the second step in solving the equation?
Answer:
First Step: separate x^2 from -16
Second Step: add -16/25 to the other side.
Step-by-step explanation:
x^2 - 16/25 = 0
^^ this might be easier if you separate x^2 and -16
First Step-
so rewrite the problem as x^2/25 -16/25 = 0
then...
Second Step-
add -16/25 to the other side. This makes it: x^2/25 = 16/25
Continuation-
Now, you can multiply 25 on both sides to cancel it out.
so you have x^2 = -16
Message me if you want to solve for x.
Solve for x ? Help me please
In one minute,kayla can read 142 words.if she keeps this same rate, how many words can she read in 1 hour ???show your work
Answer:
8,760
Step-by-step explanation:
If Kaylah is reading 142 words in one minute, there is 60 minutes in an hour.
therefore,
142 x 60 = 8,760
Answer:
8520 minutes
Step-by-step explanation:
To solve, make a proportion
142 words in 1 minute, and x words in 60 minutes (1 hour).
142/1=x/60
Cross multiply
142*60=1*x
8520=x
Another way to solve is to know that each hour has 60 minutes, and she can read 142 words in 1 minute. So, we can just multiply 60 and 142.
60*142=8520
Solve for ddd: d+\left(-5.004\right)=2.826d+(−5.004)=2.826d, plus, left parenthesis, minus, 5, point, 004, right parenthesis, equals, 2, point, 826 d =d=
Answer:
The value of [tex]'d'[/tex] is 7.83.
Step-by-step explanation:
Given:
[tex]d+(-5.004)=2.826[/tex]
We need to solve for [tex]'d'[/tex] .
Solution:
[tex]d+(-5.004)=2.826[/tex]
Now we know that;
By the rule of Addition and subtraction for positive and negative numbers
when a positive and negative signs are met then the result is negative.
So we can say that;
[tex]d-5.004=2.826[/tex]
Now Adding both side by 5.004 using addition property of equality we get;
[tex]d-5.004+5.004=2.826+5.004\\\\d= 7.83[/tex]
Hence The value of [tex]'d'[/tex] is 7.83.
Answer:
7.83
Step-by-step explanation:
Khan academy
plz rate 5 stars and press thanks. :)
The lines below are perpendicular. If the green line has a slope of -3, what is
the slope of the red line? Enter your answer as an integer or fraction in lowest
terms.
Answer:
⅓
Step-by-step explanation:
For two perpendicular lines,
m1 × m2 = -1
-3 × m2 = -1
m2 = -1/-3
m2 = 1/3
Lucy spends 4 hours a week babysitting. Her sister Lily spends seven eighths as much time babysitting. Does Lily babysit for more or less than 4 hours.
Answer:
Lily babysit for less than 4 hours.
Step-by-step explanation:
Given:
Lucy spends in a week babysitting for 4 hours.
Lily spends seven-eighths of 4 hours.
Now, to find whether Lily babysit for more than 4 hours or less than that.
Number of hours Lucy babysit = 4 hours.
So, to get the hours Lily babysit:
[tex]\frac{7}{8}\ of\ 4\ hours.[/tex]
[tex]=\frac{7}{8}\times 4\\\\=\frac{28}{8} \\\\[/tex]
On simplifying we get:
[tex]=\frac{7}{2} \\\\=3\frac{1}{2}\ hours.[/tex]
Thus, Lily spends [tex]3\frac{1}{2}\ hours[/tex] for babysitting which is less than 4 hours.
Therefore, Lily babysit for less than 4 hours.
Lily babysits for 3.5 hours weekly, which is less than Lucy's 4 hours of babysitting.
Explanation:Lucy spends 4 hours a week babysitting, and Lily spends seven eighths as much time babysitting. To calculate how much time Lily spends, we multiply Lucy's hours by seven eighths:
4 hours × (7/8) = 28/8 hours = 3.5 hours.
So, Lily babysits for 3.5 hours a week, which is less than 4 hours.