Answer:
2 cos (2x)
Step-by-step explanation:
[tex]\frac{4 -2 sec^2x}{sec^2x} \\=\frac{4-\frac{2}{cos^2x} }{\frac{1}{cos^2 x} } \\=\frac{\frac{4 cos^2x-2}{cos^2 x} }{\frac{1}{cos^2x} } \\=\frac{2(2 cos^2x-1)}{cos^2x} \times \frac{cos^2x}{1} \\=2(2cos^2x-1)\\=2cos(2x)[/tex]
Abby used the law of cosines for TriangleKMN to solve for k.
k2 = 312 + 532 – 2(31)(53)cos(37°)
Triangle K N M is shown. The length of K N is 53, the length of N M is k, and the length of K M is n.
Law of cosines: a2 = b2 + c2 – 2bccos(A)
What additional information did Abby know that is not shown in the diagram?
mAngleK = 37° and n = 31
mAngleK = 37° and k = 31
mAngleN = 37° and n = 31
mAngleN = 37° and k = 31
Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
a² = b² +c² -2bc·cos(A)k² = 31² +53² -2·31·53·cos(37°)ComparisonComparing the two equations, we note these correspondences:
a = kb = 31c = 53A = 37°Comparing these values to the given information, we see that ...
KN = c = 53 . . . . . . . . . . matching values 53NM = a = k . . . . . . . . . . . matching values kKM = b = n = 31 . . . . . . . matching values 31∠K = ∠A = 37° . . . . . . . matching side/angle namesAbby apparently knew that ∠K = 37° and n = 31.
__
Additional comment
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
Identify one pair of vertical angles in the diagram below,
Answer:
b and d
Step-by-step explanation:
there are two
but only one is an answer choice
b and d
the other which is not an answer choice is
a and c
gathmath
Solve the formula d = rt for t
The Scooter Company manufactures and sells electric scooters. Each scooter cost $150 to produce, and the company has a fixed cost of $2,000. The Scooter Company earns a total revenue that can be determined by the function R(x) = 400x − 2x2, where x represents each electric scooter sold. Which of the following functions represents the Scooter Company's total profit?
−2x2 − 150x − 2,000
−2x2 + 250x − 2,000
−2x2 + 150x − 1,600
−300x3 − 4,000x2 + 60,000x + 800,000
The function that represents the Scooter Company's total profit is given by:
P(x) = -2x² + 250x - 2,000.
How to calculate the profit function?The profit function is calculated by the revenue function subtracted by the cost function, hence:
P(x) = R(x) - C(x).
In this problem, we have that:
The revenue function is: R(x) = 400x - 2x².The cost function is: X(x) = 150x + 2000.Hence the profit function is:
P(x) = R(x) - C(x).
P(x) = 400x - 2x² - (150x + 2000).
P(x) = -2x² + 250x - 2,000.
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What is the initial value of the sequence? Please help
The initial value of the sequence is 1
How to determine the initial value?From the graph, we have the following ordered pairs
(x, y) = (1, 1), (2, 4) and (3, 8)
Remove the x values
y = 1, 4, 8
The first value in the above sequence is 1
Hence, the initial value of the sequence is 1
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What is the product?
- 6(x²-1)-8(x+1)
O 6(x-1)²
O 6(x²-1)
O(x + 1)(6x-1)
O(x-1)(6x - 1)
Answer: C
Explanation:i got it right on my test
Assuming two hikers begin at a trail start, which scenarios must be true based on the table? Check all that apply.
Melissa and Corey started on different trails.
Melissa hiked up the trail for a longer period of time than Corey.
Melissa and Corey crossed paths between 60 and 90 minutes.
Corey began his descent before Melissa.
As Melissa’s time increased from 0 to 60 minutes, her elevation decreased.
The true statements are (A), (B) and (D)
What is data?Data is information that has been translated into a form that is efficient for movement or processing.
As, from the given table we can see that
Melissa and Corey started on different trails.Melissa hiked up the trail for a longer period of time than Corey.Corey began his descent before Melissa.Learn more about this concept here:
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A woman passed gas silently. I said "it stinks", and she said "I apologize. Excuse me". Why did she say both of those things?
That's because there's this thing called polite people
Answer:
Because she is nice unlike me
Step-by-step explanation:
give me brainiest pls
see? I am not nice :) But seriously can I get brainliest?
simplify 12 + 15 ÷ 3 × 6 – 4
The average production cost for major movies is 57 million dollars and the standard deviation is 22 million dollars. Assume the production cost distribution is normal. Suppose that 17 randomly selected major movies are researched. Answer the following questions. Give your answers in millions of dollars, not dollars. Round all answers to 4 decimal places where possible. What is the distribution of X ? X ~ N( , ) What is the distribution of ¯ x ? ¯ x ~ N( , ) For a single randomly selected movie, find the probability that this movie's production cost is between 55 and 58 million dollars. For the group of 17 movies, find the probability that the average production cost is between 55 and 58 million dollars. For part d), is the assumption of normal necessary? NoYes
Using the normal distribution, we have that:
The distribution of X is [tex]X \approx (57,22)[/tex].The distribution of [tex]\mathbf{\bar{X}}[/tex] is [tex]\bar{X} \approx (57, 5.3358)[/tex].0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 57, \sigma = 22, n = 17, s = \frac{22}{\sqrt{17}} = 5.3358[/tex]
Hence:
The distribution of X is [tex]X \approx (57,22)[/tex].The distribution of [tex]\mathbf{\bar{X}}[/tex] is [tex]\bar{X} \approx (57, 5.3358)[/tex].The probabilities are the p-value of Z when X = 58 subtracted by the p-value of Z when X = 55, hence, for a single movie:
X = 58:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{58 - 57}{22}[/tex]
Z = 0.05.
Z = 0.05 has a p-value of 0.5199.
X = 55:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 57}{22}[/tex]
Z = -0.1.
Z = -0.1 has a p-value of 0.4602.
0.5199 - 0.4602 = 0.0597 = 5.97% probability that a single movie production cost is between 55 and 58 million dollars.
For the sample of 17 movies, we have that:
X = 58:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{58 - 57}{5.3358}[/tex]
Z = 0.19.
Z = 0.19 has a p-value of 0.5753.
X = 55:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{55 - 57}{5.3358}[/tex]
Z = -0.38.
Z = -0.38 has a p-value of 0.3520.
0.5753 - 0.3520 = 0.2233 = 22.33% probability that the average production cost of 17 movies is between 55 and 58 million dollars. Since the sample size is less than 30, assumption of normality is necessary.
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Line l passes through point (−2,37) and line p is the graph of y+3=−5(x+4) .
If l is parallel to p what is the equation of l ?
The slope of line p is -5, so substitute into point-slope form, we get
[tex]\boxed{y-37=-5(x+2)}[/tex]
Basically look at the picture I don’t even know what to say
Answer:
C
Step-by-step explanation:
x = [tex]\frac{2}{3}[/tex] πr³ ( multiply both sides by 3 to clear the fraction )
3x = 2πr³ ( divide both sides by 2π )
[tex]\frac{3x}{2\pi }[/tex] = r³ ( take cube root of both sides )
[tex]\sqrt[3]{\frac{3x}{2\pi } }[/tex] = r
Answer:
[tex]r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
Step-by-step explanation:
This question make look scary, but don't judge its book by its cover.
[tex]x=\frac{2}{3} \pi r^{3} \\\frac{2}{3} \pi r^{3}=x\\r^{3} =x / \frac{2\pi }{3} \\r^{3} =x*\frac{3}{2\pi } \\r^{3} =\frac{3x}{2\pi } \\r=\sqrt[3]{\frac{3x}{2\pi }}[/tex]
y = ( x + z) ( x+ 2x)
Answer:
3x^2 + 3xz
Step-by-step explanation:
Under the assumption that I need to distribute,
(x + z)(x + 2x)
(x + 2x) is (3x)
3x(x + z) becomes 3x*x and 3x*z
3x*x = 3x^2
3x*z = 3xz
combine, 3x^2 + 3xz
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Circle G is shown. Line segment F G is a radius with length 3.
In circle G, r = 3 units. Maria draws a circle with double the area of circle G.
What is the area of Maria’s circle?
6Pi units squared
9Pi units squared
12Pi units squared
18Pi units squared
The area of Maria’s circle is 18π square units option fourth is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
The figure is missing.
Please refer to the attached picture for the figure.
We have given the radius of the circle as 3 units
r = 3 units
Area of circle = πr² = π(3)² = 9π square units
The area of Maria’s circle = 2(9π) = 18π square units
Thus, the area of Maria’s circle is 18π square units option fourth is correct.
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The temperature is 20 degrees and is expected to fall 2 degrees each hour.
Write a linear equation in slope-intercept form to model this situation.
Answer:
20-2h
Step-by-step explanation:
20 is the original amount. The variable stands for the number of hours. You are TAKING AWAY 2 degrees every hour so you would subtract.
Liliana decides to crop a square photo 2 inches on each side to fit it into a frame. The area of the original photo was 121 square inches. In the equation (x + 2)2 = 121, x represents the side measure of the cropped photo.
What are the dimensions of the cropped photo?
8 inches by 8 inches
9 inches by 9 inches
12 inches by 12 inches
13 inches by 13 inches
Answer:
x = 9 or B
Step-by-step explanation:
Formula
(x + 2)^2 = 121
Comment
The easiest way to do this is to take the square root immediately, which is usually possible.
Solution
√(x + 2)^2 = √121 Take the square root
x + 2 = 11 Subtract 2 from both sides
x + 2 - 2 = 11 - 2
x = 9
Answer: B) 9 inches by 9 inches
Step-by-step explanation:
Edg 2022
A
Find the value of x.
6
X
B
D
x = [?]
8
4
C
Answer:
x = 3
Step-by-step explanation:
8/2 = 4
6/2 = 3
x = 3
distance between (-5,1) and (0,-4)?
Answer:
7.07106781187
The percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995. (a) Predict when the percentage will be 47% (b) Predict the percentage in 2005
Using a linear function, we have that:
The percentage will be 47% during the year 2001.
The predicted percentage in 2005 is of 44.97%.
Given that, the percentage of automobile consumers who are under 50 years of age decreased approximately linearly from 58.8% in 1980 to 50.5% in 1995.
What is a linear function?Linear functions are those whose graph is a straight line. The standard form of the linear function is f(x)=y= mx + b. A linear function has one independent variable and one dependent variable.
Where, m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
b is the y-intercept, which is the value of y when x = 0 and can also be interpreted as the initial value of the function.
The percentage in 1980 is considered as the initial amount, so b = 58.8. In 15 years, the percentage decreased from 58.8% to 50.5%, hence the slope is given by: m = (50.5 - 58.8)/15 = 0.5533.
Thus, the percentage in t years after 1980 is P(t) = 58.8 - 0.5533t.
Now, t + 1980, for which P(t) = 47.
So, P(t) = 58.8 - 0.5533t
47 = 58.8 - 0.5533t.
0.5533t = 11.8.
t = 11.8/0.5533
t = 21.3.
1980 + 21 = 2001, so the percentage will be 47% during the year 2001.
Now, 2005 is 25 years after 1980, so the percentage is P(25), given as follows: P(25) = 58.8 - 0.5533x25 = 44.97%.
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F10) How many Solutions Does this
System Have?
y=2X
y = -x + 2
Answer:
See below.
Step-by-step explanation:
Problem:
Solve y=2x;y=−x+2
Steps:
I will solve your system by substitution.
y=2x;y=−x+2
Step: Solve y=2 x for y:
Step: Substitute 2x for y in y=−x+2:
y=−x+2
2x=−x+2
2x+x=−x+2+x(Add x to both sides)
3x=2
3x/3 = 2/3 (Divide both sides by 3)
x=2/3
Step: Substitute 2/3 for x in y = 2x
y=2x
y = 2(2/3)
y = 4/3 (Simplify both sides of the equation)
Answer:
x = 2/3 and y = 4/3
Answer:
only one at x = 2/3 y = 1 1/3
Step-by-step explanation:
At the same solution point Y = Y so
2x = -x + 2
3x = 2
x = 2/3
A table is in the shape of a regular
hexagon. The perimeter of the table is 12
feet. What is the length of each side of
the table?
A 1 ft
B 2 ft
C 3 ft
D 4 ft
Answer:
B
Step-by-step explanation:
A hexagon has 6 sides. If you divide the perimeter(12) by the number of sides(6), you get the length of one side(2).
If a heart beats 36 times in 30 seconds, how many times will it beat in 60 seconds
Pepperidge Farm Goldfish is a snack food for which 40% of it's calories come from fat. Rold Gold Pretzels receive 9% of their calories from fat. How many grams of each would be needed to make 620 g of a snack mix for which 15% of the calories are from fat?
Can y’all please help me with this ! Everybody have a good day!
Answer: A. She substituted incorrectly into the distance formula
She should be subtracting x from x and y from y but she is subtracting y from x.
Lily pads increase by 25% every 10 days.lf a pond starts with 22 lily pads,how many will there be after 50 days?
We conclude that after 50 days, there will be 67 lily pads.
how many will there be after 50 days?
We know that the number increases by 25% every 10 days.
In 50 days we have 5 groups of 10 days, so there will be five increases of 25%.
We know that the initial number is 22 lily pads, if we apply five consecutive increases of the 25% we get:
N = 22*(1 + 25%/100)*...*(1 + 25%/100%)
( the factor (1 + 25%/100%) appears five times)
So we can rewrite:
N = 22*(1 + 25%/100%)⁵
N = 22*(1 + 0.25)⁵ = 67.1
Which can be rounded to the nearest whole number, which is 67.
So we conclude that after 50 days, there will be 67 lily pads.
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Construct a polynomial function with the following properties fifth degree, 3 is a zero of multiplicity 3, - 4 is the only other zero, leading coefficient is 3
The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²
How to construct polynomial functions?Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
We need to form a polynomial expression with the following properties;
fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;
y = 2(x - 3)³(x + 4)²
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The graphs below have the same shapes. What is the equation for the red graph?
The equation for the red graph is f(x) = -x².
How to depict the equation?From the information given, g(x) = 4 - x².
The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:
(x, y) = (x, y -4).
The equation of the function will be:
f(x) = g(x) - 4
f(x) = (4 - x²) - 4
f(x) = -x²
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A satellite orbits the Earth with an elliptical orbit modeled by x squared over 43 million eight hundred twenty four thousand four hundred plus y squared over forty seven million one hundred ninety six thousand nine hundred equals 1 comma where the distances are measured in km. The Earth shares the same center as the orbit. If the radius of the Earth is 6,370 km, what is the maximum distance between the satellite and the Earth?
250 km
500 km
6,620 km
6,870 km
"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is
D= 510 km. Option B. This is further explained below.
What is Kepler Orbit?Generally, In the study of astrodynamics, an ellipse of the satellite is often referred to as a Kepler Orbit
The function of the elliptical orbit is
[tex]\frac{(x-h)^2}{a^2}+\frac{(x-k)^2}{b^2}=1[/tex]
compared to
[tex]\frac{(x^2)^2}{47334400}+\frac{(y^2)^2}{43956900}=1[/tex]
Hence
a = √(47,334,400 km²)
a= 6,880 km.
In conclusion, The distance of the satellite above the Earth's surface.
D = a - r
D= 6,880 km - 6,370 km
D= 510 km
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"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is D= 510 km. Option B.
What is Elliptical Orbit?An elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.
The function of the elliptical orbit is
[tex]\frac{{(x-h)}^2}{a^2}+ \frac{{(y-k)}^2}{b^2} = 1[/tex]
compared to
√([tex]\frac{({x^2)}^2}{47,334,400} + \frac{({y^2)}^2}{43956900} = 1[/tex]
a = √(47,334,400 km²)
a= 6,880 km.
Now,
D = a - r
D= 6,880 km - 6,370 km
D= 510 km
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If f(x) = 2x+6 and g(x)= x3 what is (g f)(0)?
Answer:
[tex]27[/tex]
Step-by-step explanation:
[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]
Find the 7th term in the
sequence
-, -1, -5, -25, . . .
Hint: Write a formula to help you.
1st term. Common Ratio (desired term - 1)
Enter
Answer: -15625
Step-by-step explanation:
The explicit formula for the sequence is
[tex]a_{n}=-1(5)^{n-1}\\\\\implies a_{7}=-1(5)^{7-1}=\boxed{-15625}[/tex]
