The answer is choice D because we plug in something like x = pi/4 and it leads to
y = cos(2x)
y = cos(2*pi/4)
y = cos(pi/2)
y = 0
Use the unit circle to see why cos(pi/2) = 0.
Since we get y = 0 as a result, this shows x = pi/4 is one of the x intercepts.
You'll also get y = 0 if you plug in x = 3pi/4, x = 5pi/4, and x = 7pi/4. All of these values are on the interval [tex]0 \le x < 2\pi[/tex]
The solution of the equation y = cos(2x) will be π/4, 3π/2, 5π/4, and 7π/4. Then the correct option is D.
What is the solution to the equation?A solution to an equation is a number that can be plugged in for the variable to make a true number statement.
The equation is given below.
y = cos(2x)
The x-intercept of the equation in the interval 0 ≤ x < 2π will be given as,
y = 0
cos(2x) = 0
cos 2x = cos (n + 1) π/2
2x = (n + 1)π / 2
x = (n + 1)π / 4
x = π/4, 3π/2, 5π/4, 7π/4
The solution of the equation y = cos(2x) will be π/4, 3π/2, 5π/4, and 7π/4. Then the correct option is D.
Learn more about the solution of the equation;
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Ashton is depositing money into a checking account. After 3 months there is $120 in the account. After 6 months, there is $240 in the account. Determine the constant rate of change of the account.
The constant rate of change of the account is $40 or Increasing by $40 per month.
Step-by-step explanation:
Consider the provided information.
Joanne is depositing money into a bank account. After 3 months there is $120 in the account. After 6 months there is $240 in the account.
Rate of change is known as how one quantity change in relation to other.
The rate of change can be calculated as:
y2-y1/x2-x1
Now use the above formula to calculated the rate of change.
240 - 120/6-3
120/3
40
Hence, the constant rate of change of the account is $40 or Increasing by $40 per month.
A number increased by 35
Answer:
x+35
Step-by-step explanation:
___ divided by -6 = -4
what is ___ ?
brainliest and 40 points to correct answer only
Answer:
24
Step-by-step explanation:
i did was times -6 by -4
negative times negative equals positive
-6*-4 = 24
then divide to see if its true
24 ÷ -6 = -4
Consider the equation 3p - 7 + p = 13. What is the resulting equation after the first step in the solution?
Op-7 = 13-3p
O 2p-7 = 13
O 3p-7 = 13-
4p - 7 = 13
Answer:
4p - 7
General Formulas and Concepts:
Pre-Alg
Order of Operations: BPEMDASEquality PropertiesStep-by-step explanation:
Step 1: Define
3p - 7 + p = 13
Step 2: Solve for p
Combine like terms: 4p - 7 = 13Add 7 to both sides: 4p = 20Divide 4 on both sides: p = 5what ordered pair is -3x + 4y =14
Answer:
(0, 3.5)
Step-by-step explanation:
I just graphed it using desmos
I need to know what the probability of them purchasing a defective unit
Answer:
.5
Step-by-step explanation:
brainlies please
can someone help me plzzz
Factor the trinomial: 2x
Answer:
(2x+1)(x+3)
Step-by-step explanation:
[tex]2x^2+7x+3\\(2x+1)(x+3)[/tex]
Jason is 22 years older than his sister Ann. In 4 years, he will be twice as old as Ann. How old is each of them now?
Answer:
im not sure if this is rite
Step-by-step explanation:
jason=a+22
ann=a
a+22+4=2a+4
a+26=2a+4
a=22
help??
anyone??
7th grade math
Answer:
40 miles
Step-by-step explanation:
4x10 is 40 miles
Answer: 40 miles
1:10
4:40
4×10=40
I hope this is good enough:
HELPPP! WHAT ARE THE X AND Y INTERCEPTS OF THIS LINE?
Answer:
x-intercept=-1.2 y-intercept=-0.7
Step-by-step explanation:
Solving systems of linear equations algbraically.
Answer:
(3,-6)
Step-by-step explanation:
[1] x - 2y = 15
[2] 2x + 4y = -18
Graphic Representation of the Equations :
-2y + x = 15 4y + 2x = -18
Solve by Substitution :
// Solve equation [1] for the variable x
[1] x = 2y + 15
// Plug this in for variable x in equation [2]
[2] 2•(2y+15) + 4y = -18
[2] 8y = -48
// Solve equation [2] for the variable y
[2] 8y = - 48
[2] y = - 6
// By now we know this much :
x = 2y+15
y = -6
// Use the y value to solve for x
x = 2(-6)+15 = 3
Solution :
{x,y} = {3,-6}
Could you please help me
Answer:
4 3/4
Step-by-step explanation:
cueluisghvreiuasghfe;ahfuiealw
Answer:
Step-by-step explanation:
[tex]4\frac{3}{4}[/tex] - [tex]\frac{1}{3}[/tex] = [tex]4\frac{9-4}{12}[/tex] = [tex]4\frac{5}{12}[/tex] feet
Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in minutes). These are listed here. Determine the 95% confidence interval estimate of the population mean.
Complete Question
Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn and each reported the amount of the time spent at part-time jobs (in minutes). These are listed here 180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125. Determine the 95% confidence interval estimate of the population mean.
Answer:
The 95% confidence interval is [tex] 127.09 < \mu < 167.57 [/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 40[/tex]
The sample size is n = 15
The data given is 180, 130, 150, 165, 90, 130, 120, 60, 200, 180, 80, 240, 210, 150, 125
Generally the sample mean is mathematically represented as
[tex]\= x = \frac{ \sum x_i}{n }[/tex]
=> [tex]\= x = \frac{ 130 + 150 + \cdots + 125 }{ 15 }[/tex]
=> [tex]\= x = 147.33[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{40}{\sqrt{15} }[/tex]
=> [tex]E =20.24 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex] 147.33 -20.24< \mu < 147.33 + 20.24 [/tex]
[tex] 127.09 < \mu < 167.57 [/tex]
Two lines are represented by the equations:
y = 4x + 1
y - 4x = -9
Which statement below is true?
a
They are the same line.
b
They have zero slopes.
c
They have reciprocal slopes.
d
They have the same slope.
Answer:
d. have same slope
Step-by-step explanation:
3. Which equation fits the transformed quadratic
graph below.
A. y = (x + 1)2 + 2
B. y = (x - 1)2 + 2
C. y = (x + 1)2 – 2
D. y = (x - 1)2 – 1
Solve for x.
10x−3x+5=26
Answer:
x = 3
Step-by-step explanation:
10x−3x+5=26 (Given)
7x + 5 = 26 (Combine like terms)
7x = 21 (subtraction Property of equaity)
x = 3 (division Property of equaity)
Which expression is equivalent to 27 + 45? (1 point) 8(3+6) 8(19 + 37) 09(3 + 5) O 9(18 + 36)
Answer:
9(3+5)
Step-by-step explanation:
My favorite pancake recipe
2 cups all purpose | plain flour, (290 g | 10 oz)
1/4 cup granulated sugar or sweetener, (60g | 2 oz)
4 teaspoons baking powder
1/4 teaspoon baking soda
1/2 teaspoon salt
1 3/4 cups milk, (440ml)
1/4 cup butter, (60g | 2 oz)
2 teaspoons pure vanilla extract
1 large egg
Combine everything in a bowl (separate wet and dry) and cook at medium low heat until it is brown and there are bubbles on top. Then serve with syrup. Good luck!!!
Answer: 8(3+6)
Step-by-step explanation:
What is the area of a semicircle with a diameter of 10 cm?
Answer:
39.27 cm²Step-by-step explanation:
area of semi circle = π r² / 2
where r = 10/2 = 5 cm
area = π (5)² / 2
= 39.27 cm²
Answer:
39.3 cm2
Step-by-step explanation:
diameter=radius/2= 10/2 = 5
area of semicircle=pi(r^2) / 2
=pi(5^2) / 2
=39.26...
=39.3
round 0.918 to the nearest whole number
The principal at Riverside High School would like to estimate the mean length of time each day that it takes all the buses to arrive and unload the students. How large a sample is needed if the principal would like to assert with 90% confidence that the sample mean is off by, at most, 7 minutes. Assume that s=14 minutes based on previous studies.
Answer:
A
Step-by-step explanation:
I took test
12 less than the product of negative 8 and n
12 < -8n
(I'm not hundred percent sure I'm sorry but that's what I came up with)
David is traveling at a rate of 62 feet per second. Select all of the following rates that are equivalent or approximately equivalent to David’s rate of 62 feet per second.
Answer:
.68.0314 m/s
.42.272752125mph
68.0314km/h
Step-by-step explanation:
What is the function rule for the line?
Answer: f(x) = -3/2x -2
Step-by-step explanation:
Slope form of a line is y=mx+b, where b is the y-intercept and m is the slope. We find the y-intercept when we look at when x is 0 which would be -2. The slope is graphing to plots and determining if the slope is positive- going up- or negative- going down. The slope is going down and after using y2 - y1 / x2 - x1, I found the slope was -3/2.
What is the nth term rule of the linear sequence below?
-9, -5, -1,3,7,...
Answer:
Step-by-step explanation:
Given sequence
-9, -5, -1,3,7,...
Is A.P(,airthmetic progression)
So
nth term of an A.P =a+(n-1)d
Where a=first term (-9)
D=difference=(-5)-(-9)=4
So nth term=-9+(n-1)4
=4n-13
Answer is 4n-13
How do you do the last two questions?
Answer:
P = 6200 / (1 + 5.2e^(0.0013t))
increases the fastest
Step-by-step explanation:
dP/dt = 0.0013 P (1 − P/6200)
Separate the variables.
dP / [P (1 − P/6200)] = 0.0013 dt
Multiply the left side by 6200 / 6200.
6200 dP / [P (6200 − P)] = 0.0013 dt
Factor P from the denominator.
6200 dP / [P² (6200/P − 1)] = 0.0013 dt
(6200/P²) dP / (6200/P − 1) = 0.0013 dt
Integrate.
ln│6200/P − 1│= 0.0013t + C
Solve for P.
6200/P − 1 = Ce^(0.0013t)
6200/P = 1 + Ce^(0.0013t)
P = 6200 / (1 + Ce^(0.0013t))
At t = 0, P = 1000.
1000 = 6200 / (1 + C)
1 + C = 6.2
C = 5.2
P = 6200 / (1 + 5.2e^(0.0013t))
You need to change the exponent from negative to positive.
The inflection points are where the population increases the fastest.
If one of y’all know the answer could you please tell me I would really appreciate it<3
Rainfall was 6 inches in September and 4.9 inches in October. What was the difference in rainfall?
Answer:
1.1
Step-by-step explanation:
6-4.9=1.1
Hope I helped!
Please mark Brainliest!!!
Answer:
1.1
Step-by-step explanation:
it's easy you just subtract.
Help no troll answer plz
Answer:
Step-by-step explanation:
Q 4. (25m + 25m) ÷ 25 sec. = 2 m/sec.
Q 5. This question belongs to Physics and not Mathematics!!!
Wavelength (lambda) = Velocity (v) ÷ Frequency ( [tex]sec^{-1}[/tex] or Hz )
f = v / (lambda)
f = 3 / 2 = 1.5 (Hz)
Q 6. 0.060 ÷ 2 = 0.030 m
log_6(x+1)+log_6x=1
Answer:
x = -3, 2
Step-by-step explanation:
[tex]log_6(x+1)+log_6x=1 \\ \\ log_6 \{x(x+1) \} = 1 \\ \\ x(x + 1) = {6}^{1} \\ \\ {x}^{2} + x = 6 \\ \\ {x}^{2} + x - 6 = 0 \\ \\ {x}^{2} + 3x - 2x - 6 = 0 \\ \\ x(x + 3) - 2(x + 3) = 0 \\ \\ (x + 3)(x - 2) = 0 \\ \\ x + 3 = 0 \: \: or \: \: x - 2 = 0 \\ \\ x = - 3 \: \: or \: \: x = 2 \\ \\ x = - 3, \: \: 2[/tex]