Answer:
a. There is a phase shift to the left
Step-by-step explanation:
The correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
How does transformation of a function happens?The transformation of a function may involve any change.
Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming horizontal axis is input axis and vertical is for outputs, then:
Horizontal shift (also called phase shift):
Left shift by c units: [tex]y=f(x+c)[/tex]output, but c units earlier)Right shift by c units: [tex]y=f(x-c)[/tex] (same output, but c units late)Vertical shift:
Up by d units: f(x) + dDown by d units: y = f(x) - dStretching:
Vertical stretch by a factor k: [tex]y = k \times f(x)[/tex]Horizontal stretch by a factor k: [tex]y = f(\dfrac{x}{k})[/tex]For this case, the parent function y = cos(x) is transformed to make the function y = cos (x + pi/6)
Thus, there is left shift of the graph of the function y =cos(x).
The graphs of both functions (parent function in red color and transformed function in blue color) is given below.
Thus, the correct statement for the graph of y = cos (x + pi/6) compared to the graph of y = cos(x) is given by: Option A: There is a phase shift to the left.
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cual es el máximo común divisor de 72, 90 y 36?
Answer:
6
Step-by-step explanation:
6 x 6 = 36
6 x 12 = 72
6 x 15 = 90
what do you call the statements that are assumed to be true and do not need proof?
Answer:
A postulate :)
Step-by-step explanation:
This is because a postulate is a statement that is assumed true without proof, while a theorem is a true statement that can be proven.
Hope this helps!
Felix’s Feed Mill sells chicken feed for $8. 00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans. Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0. Plan B: Raise the price by 10 percent each week until the price reaches $12. 0. Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12. 0. Plan D: Raise the price by $0. 25 each week until the price reaches $12. 0. Which plan will result in the price of the feed reaching $12. 00 fastest? plan A plan B plan C plan D.
The plan will result in the price of the feed reaching $12.00 fastest is Plan B because it reaches within 5 weeks.
What is decision-making?The process of making choice is by identifying the correct decision, gathering information, and assessing alternative solutions.
Felix’s Feed Mill sells chicken feed for $8. 00 per bag.
This price is no longer high enough to create a profit.
Felix decides to raise the price. He is considering four different plans.
The plan will result in the price of the feed reaching $12.00 fastest will be
Plan A: Raise the price by $0. 10 each week until the price reaches $12. 0.
⇒ $0.10 × 20 = $2
This plan will take 20 weeks to reach at a price of $12.
Plan B: Raise the price by 10 percent each week until the price reaches $12.0. The price of this plan will be in t weeks is
[tex]12 = 8 *1.1^t\\\\t = 4.25 \approx 5[/tex]
This plan will take less than 5 weeks.
Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.0. The amount will be
Amount = 2/8 = $0.25
Plan D: Raise the price by $0.25 each week until the price reaches $12. 0.
⇒ 0.25 × 8 = $2
This will take 8 weeks.
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Answer quick and show work!
Aj and his two friends went out to dinner and the meal's total was $100. They decided to give the server a 20% tip. How much money will the total bill be?
Answer:
$120
Step-by-step explanation:
When you multiply the grouping by the exponent, what is the answer?
5+4 - (8 x 3 – 22)* x 4
Answer:
1
Step-by-step explanation:
5 + 4 - (8 x 3 – 22)* x 4
5 + 4 - (24 - 22) x 4
5 + 4 - 2 x 4
5 + 4 - 8
1
Answer:
16
Step-by-step explanation:
5+4- (8x3-22) ↑4 x4
16
5+4 - (24-22) ↑4 x4
5+4- (2) ↑4 x4
2x2x2x2=16
hope that helps:)
Write an equation in slope-intercept form for the line that passes through (6,6) and is
perpendicular to the line described
Answer:
Step-by-step explanation:
Solution :
Hello:
an equation for the line is : y =mx +b (m: is a slope )
perpendicular to the line described by : y = 2/3 x -2
So : product for two slopes = -1 means : m×2/3=-1
m = -3/2
now : y = -3/2 x+b
but this line :
through the point (6,6) : 6 =(-3/2)(6)+b....... b=15
conclusion :
the equation is : y = -3/2x +15
What is the value of y in the solution to the system of equations?
1 x + 2 y = 1
2x – 3y = -30
0-8
0-3
03
O 8
Answer: y = 32/7
Step-by-step explanation:
Solve the first equation for x by subtracting the 2y from the left side and getting: x = 1 - 2y.
Plug this in to the second equation: 2(1 - 2y) - 3y = -30 → 2 - 4y - 3y = -30 →
-7y = -32 → y = 32/7. Hope this helps!
If you were writing a two-column proof proving that ANQP APON, which of the following statements would have
"reflexive property of congruence" as its reason?
A. ON ON
B. OP=OP
C. OP=OP
D. NP NP
Answer:
NP NP
Step-by-step explanation:
this is the only solution that works for the question
When plotting an ordered pair, X comes before Y
Answer:
True
Step-by-step explanation:
I always remember it, over then up
Find the rule to complete the pyramid.
i think this should work good luck
The large rectangle below represents one whole.
What percent is represented by the shaded area?
%
Answer:
40%
Step-by-step explanation:
2/5 is shaded
100 divided by 5 is 20
2x20=40
What is the least common multiple? 46 and 12?
Answer:
2
Step-by-step explanation:
multiples of 12: 1, 2, 3, 4, 6, 12 (we don't use 1 in LCM)
Start with 2: 46/2 = 23, so the least common multiple is 2
What are the solution(s) for the quadratic equation?
Y=5x^2-9x+4
Show work
Let's see
[tex]\\ \rm\rightarrowtail 5x^2-9x+4=0[/tex]
[tex]\\ \rm\rightarrowtail 5x^2-5x-4x+4=0[/tex]
[tex]\\ \rm\rightarrowtail 5x(x-1)-4(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail (5x-4)(x-1)=0[/tex]
[tex]\\ \rm\rightarrowtail x=4/5,1[/tex]
During a phone call about the system of equations {5x + 2y = 8 , 8x + 4y = 8}, Dylan told Max, “It’s easy, just set them equal to each other.” But Max replied, “That doesn’t help — I get −2y = 3x. What good is that?” Help these two students solve the problem.
Answer:
x = 4
y = -6
Step-by-step explanation:
5x + 2y = 8
8x + 4y = 8
-2(5x + 2y) = -2(8)
8x + 4y = 8
-10x -4y = -16
8x + 4y = 8
-10x -4y + 8x + 4y = -16 + 8
-2x = -8
x = 4
plug 4 into x so y = -6
Subway creates a paid promotion featuring a different 6-inch sub of the day each day of the week. The sub of the day is only $3. 50. Subway utilizes the radio to spread the word. Which promotion method is subway using?.
Based on the information provided, the promotion method subway is using is sales promotion.
What is promotion?It is a marketing tool that involves letting know potential customers about a product that a company wants to sell.
What are the promotion methods?Most common methods include:
Direct selling.Public relations.Sales promotion.What is sales promotion?This involves promoting or advertising products through sales, which means customers are offered special discounts or lower prices. This is the method used by the subway because the sub of the day is a sales.
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1. Find the length of the arc shown in red:
2. Find the area of the circle:
Answer:
Step-by-step explanation:
Reflect the point (3,0) across the x axis.
Reflect the point (3,0) across the y axis.
Answer:
(3,0) reflection on x axis (3,0)
(3,0) reflection on y axis (-3,0)
simplify the following expression 4√72
Answer:
Hope this helps it is in the file below.
: Customers arrive at a shopping mart randomly at a rate of 7 per hour.
a) Find the probability that during any 90 minutes’ period, the number of customers arriving at the shopping mart is exactly 8
b) If a customer arrives at 11. 30 am, find the probability that the next patient arrives before
11. 45 am
Using the Poisson distribution, it is found that the probabilities are given by:
a) 0.1009 = 10.09%.
b) 0.8262 = 82.62%.
What is the Poisson distribution?In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
The parameters are:
x is the number of successese = 2.71828 is the Euler number[tex]\mu[/tex] is the mean in the given interval.Item a:
The mean is of 7 customers for 60 minutes, hence, for 90 minutes = 1.5 x 60 minutes, the mean is given by:
[tex]\mu = 1.5 \times 7 = 10.5[/tex]
The probability of exactly 8 customers is of P(X = 8), hence:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 8) = \frac{e^{-10.5}10.5^{8}}{(8)!} = 0.1009[/tex]
Item b:
Probability of at least one patient in 15 minutes, hence:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
For 15 minutes, the mean is given by:
[tex]\mu = 0.25 \times 7 = 1.75[/tex]
Then:
[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]
[tex]P(X = 8) = \frac{e^{-1.75}1.75^{0}}{(0)!} = 0.1738[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.1738 = 0.8262[/tex]
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Name any two timber plans found in the Terai region of Nepal? Where is Red panda found? Why is it called an endangered bird?
Step-by-step explanation:
red Panda is found in langtang national park and makalu-barun national park in Nepal .
timber planks for in the religion of Nepal sal, sissoo& Khair.
I'm injured birds are any bird fishing that is at risk of extinction because of a sudden rapid increase in population or a loss of its critical habitat .
BRAINLIEST FOR CORRECT ANSWER: What is the area of this figure?
Answer:
A = 253 sq ft
Step-by-step explanation:
see image. Section off the shape into rectangles. Sometimes you have to add to find the lengths of the sides. Sometimes you have to subtract. Area is length×width. see image.
¿Cuántos enteros divisibles por 9 hay entre 95 y 450?
Answer:
s so you're going to divide when you going to divide 95 why you take it to the other side it will become 95 * 450 equals to 42750 / 9 when we divide 42750 / 9 to give you 4750 that is your answe
Can someone help me please
Answer:
[tex]6x^2+8x[/tex]
Step-by-step explanation:
Hey there!
In order to find the answer to this question, what you need to do is first find the area of the whole grey box as a whole (including the white box to)
The dimensions for this is 3x+2 and 4x
Now we know that to find area, we need to multiply length by height
So (3x+2)(4x) is what we have to solve to get the area
Now we simplify:
1. Distribute
2. [tex]12x^2+8x[/tex]
So now we know that the total area is [tex]12x^2+8x[/tex]
Now what we do is take out the area of the white box from the area of the grey box
Lets find the area of the white box:
l=3x (l - length)
h=2x (h - height)
[tex]3x*2x=6x^2[/tex]
Now we have the area of both shapes
Since we have all the information we need to find the final answer, the following steps below will be using the information we found to find the final answer:
In order to find the final answer which is the area of the shaded region, we take out the area of the white region from the total area of the grey region (including the white region)
So now we can formulate this new equation:
[tex]12x^2+8x-6x^2= ta[/tex]
(ta= total area)
Now we simplify:
[tex]6x^2+8x\\[/tex] is going to be our final answer
So our final answer is [tex]6x^2+8x[/tex]
Solve the initial value problem d y d x = 2 x 1 , y ( 0 ) = 2
Using separation of variables, it is found that the solution to the initial value problem is of y(x) = x² + 2.
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is given by:
[tex]\frac{dy}{dx} = 2x[/tex]
Then, applying separation of variables:
[tex]dy = 2x dx[/tex]
[tex]\int dy = \int 2x dx[/tex]
[tex]y = x^2 + K[/tex]
Since y(0) = 2, we have that the constant of integration is K = 2, and the solution is:
y(x) = x² + 2.
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The differential equation is y(x) = x² + 2.
What is the differential equation?Differential Equations In Mathematics, a differential equation is an equation that contains one or more functions with their derivatives.
The given equation is;
[tex]\rm \dfrac{dy}{dx}=2x[/tex]
Applying the variable separation method;
[tex]\rm \dfrac{dy}{dx}=2x\\\\\int\limits \, dy=\int\limits\, 2x. dx\\\\y = 2 \times \dfrac{x^{1+1}}{1+1} +c\\\\y = 2 \times \dfrac{x^{2}}{2} +c\\\\y = x^2+c[/tex]
The value of c when y( 0 ) = 2 is c =2.
Hence, the required differential equation is y(x) = x² + 2.
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Write the expression as a product.
25-(a + 7)^2
pls help
Answer:
-(12+a)(a+2)
Step-by-step explanation:
this is to ez
The expression as a product is (a+12)(-a-2)
What is an expression?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Given that, is an expression, 25-(a+7)², we need to write it in product form, 25-(a+7)²
= 25 - (a²+49+14a)
= 25-a²-49-14a
= -a²-14a-24
Factorizing,
= -a²-12a-2a-24
= -a(a+12)-2(a+12)
= (a+12)(-a-2)
Hence, the expression as a product is (a+12)(-a-2)
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A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her
campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500
likely voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in
proportions of likely voters who would vote for this candidate was (-0.014, 0.064). What was the difference (pre-
debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
0.064 +-0.014)
= 0.025
0.064-(-0.014)
= 0.039
0 0.064 + (-0.014) = 0.050
0.064 - (-0.014) = 0.078
N
Considering the confidence interval given, the likely difference is given by:
[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]
What is the point estimate of a confidence interval?Given an interval (a,b), the point estimate is the mean of the bounds, that is:
p = (a + b)/2.
In this problem, the interval is (-0.014, 0.064), hence the expression for the likely difference is given by:
[tex]\frac{0.064 + (-0.014)}{2} = 0.025[/tex]
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Jimmy just left the movies. The
movie ended at 4:47 p.m. The
movie was two hours long.
What time did the movie start?
?
A long solenoid with radius r = 7 cm and n = 3,170 turns/m carries a current i = 6. 7 a. What is the magnitude of the magnetic field in the central area inside the solenoid, in t?
The magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T
Magnetic field inside solenoidThe magnetic field inside the central area of the solenoid is given by B = μ₀ni where
μ₀ = permeability of free space = 4π × 10⁻⁷ Tm/A, n = number of turns per unit length = 3,170 turns/m and i = current in solenoid = 6.7 ASince B = μ₀ni
Substituting the values of the variables into the equation, we have
B = μ₀ni
B = 4π × 10⁻⁷ Tm/A × 3,170 turns/m × 6.7 A
B = 4π × 10⁻⁷ Tm/A × 21239 A-turns/m
B = 84956π × 10⁻⁷ T
B = 266897.15 × 10⁻⁷ T
B = 0.026689715 T
B ≅ 0.0267 T
So, the magnitude of the magnetic field in the central area inside the solenoid, in T is 0.0267 T
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The magnitude of the magnetic field in the central area inside the considered solenoid (assuming in vaccum), is approx 2.67 × 10^{-2} T
What is the measurement of the magnetic field inside a long solenoid?Magnetic field = permeability constant x relative permeability x turn density x current
B = [tex]k\mu_0nI = \mu nI[/tex]
where turn density is calculated as:
n = N/L
Where N represents the number of turns of the wire and
L represents the length of the solenoid.
Assuming that the solenoid is placed in vaccum, we have:
[tex]\mu = k\mu_0 = \mu_0 = 4\pi \times 10^{-7} \: \rm T m/A[/tex]
And it is given that:
n = 3174 turns/mI = 6.7 amperesThus, we get:
[tex]B = \mu n I = 4\pi \times 10^{-7} \times 3170 \times 6.7 \approx 2.67 \times 10^5 \times 10^{-7} \\\\B = 2.67 \times 10^{5 + (-7)}B = 2.67 \times 10^{-2} \: \tm T[/tex]
Thus, the magnitude of the magnetic field in the central area inside the considered solenoid (assuming in vaccum), is approx 2.67 × 10^{-2} T
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The graphs of the functions (f) and (g) are shown where..
[tex]f(x) = 4.5 \sqrt{x} [/tex]
[tex]g(x) = \frac{1}{9} {x}^{2} [/tex]
Select the TWO closest approximations for solutions to the equations f(x) - g(x) = 0
A.x=0
B.x=5.0
C.x=11.7
D.x=13.5
E.x=20.0
Answer:
[tex]\red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}} \\ \red{ \rule{10pt}{999999pt}} \pink{ \rule{10pt}{999999pt}} \blue{ \rule{10pt}{999999pt}} \purple{ \rule{10pt}{999999pt}}[/tex]
\orange{ \rule{100pt}{999999pt}} < /p > < p > [tex]at < /p > < p > at</p><p>[tex]at</p><p>
Step-by-step explanation:
f(x) - g(x) = 0
f(x) = g(x)
4.5√x = ⅑ x²
4.5 × 9 = x√x
40.5 = x√x
square it on both side
1640.25= x².x
1640.25 =x³
x=11.7
what is the solution of the system of equations 4x+2y=-1 and 3x+4y=3
Answer:
7x+6y=2
Step-by-step explanation:
All you have to do is add both of the equations together.