The trigonometric identities equivalent to cos(2·x)/cos(x) are;
cos(x) - (sin(x))/(tan (x))
2·cos(x) - sec(x)
What are trigonometric identities?Trigonometric identities are equations of trigonometric functions that are correct for the values of the input and output variables in the equations.
The trigonometric identity for cos(2·x) is specified as follows;
cos(2·x) = cos²x - sin²x
Therefore;
cos(2·x)/(cos(x)) = (cos²x - sin²x)/(cos(x))
(cos²x)/(cos(x)) = cos(x)
sin²(x)/(cos(x) = sin(x) × sin(x)/(cos(x)) = sin(x)·tan(x)
(cos²x - sin²x)/(cos(x)) = (cos²x)/(cos(x)) - sin²(x)/(cos(x)
(cos²x)/(cos(x)) - sin²(x)/(cos(x) = cos(x) - sin(x)·tan(x)
cos(2·x)/(cos(x)) = cos(x) - sin(x)·tan(x)cos(2·x) = 2·cos²x - 1
Therefore; cos(2·x)/cos(x) = (2·cos²x - 1)/cos(x)
(2·cos²x - 1)/cos(x) = 2·cos(x) - 1/cos(x)
2·cos(x) - 1/cos(x) = 2·cos(x) - sec(x)
cos(2·x)/cos(x) = 2·cos(x) - sec(x)cos(2·x) = 1 - 2·sin²x
cos(2·x)/cos(x) = (1 - 2·sin²x)/cos(x)
(1 - 2·sin²x)/cos(x) = sec(x) - 2·sin(x)
The expressions equivalent to cos(2·x)/cos(x) are therefore;
cos x - (sin x)·(tan x) and 2·cos x - sec x, which are I and III
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Are these triangles similar?
O Yes
O No
By which way are the triangles
similar?
O AA Similarity
O The triangles are not similar.
O SSS Similarity
O SAS Similarity
Answer:no
Step-by-step explanation:
Lucas decides to use 5/8 cups of berries instead,but uses the same amounts of mango and yogurt. If he wants to make three 8 fluid ounce servings of smoothie,how much almond milk should he add
Using the mathematical operations of addition and subtraction, the quantity of almond milk that Lucas should add to his recipe to make three 8-fluid-ounce servings of the smoothie is 1¹/₈ cups.
What are mathematical operations?Mathematical operations include addition, division, subtraction, and multiplication.
In this situation, we can determine the needed quantity of almond milk using multiplication, subtraction, and addition.
The total quantity of smoothie is obtained by multiplying three cups by 8 fluid ounces. The quantity of almond milk is determined by subtracting the sum of other ingredients from the total quantity.
Lucas' usual recipe for two 8 fluid ounces:
Berries 3/8 cups
Mango 1/2 cups
Yogurt = 3/4 cups
Almond Milk = 3/8 cups
Total cups made = 2 cups (16 fluid ounces = 2 x 8)
New recipe for three 8 fluid ounces:
Berries 5/8 cups
Mango 1/2 cups
Yogurt = 3/4 cups
Almond milk = x
1 cup = 8 fluid ounces
Total cups to be made = 3 cups (24 fluid ounces = 3 x 8)
5/8 + 1/2 + 3/4 + x = 24/8
= 15/8 + x = 24/8
x = 9/8 (24/8 - 15/8)
= 1¹/₈ cups
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Question Completion:Lucas makes a smoothie using the recipe (berries 3/8, mango 1/2, yogurt 3/4 cups) and adds almond milk for two 8 fluid-ounce servings. (There are 8 fluid ounces in 1 cup.)
In an absolute value graph, the slope of one side of the graph is the ______________ of the other side.
Then give an example...If the slope of one side of an absolute value function is _________, then the other side of the equation has a slope of ________
Answer:
In an absolute value graph, the slope of one side of the graph is the negative of the other side.
For example, if the slope of one side of an absolute value function is 2, then the other side of the equation has a slope of -2.
. A bicycle store uses a young person's height as one factor to determine the wheel diameter of an appropriate bicycle. For heights of 44-48 inches , the store suggests 18 inch wheels. For heights of 47-53 inches, the store suggests 20 inch wheels. For heights of 52-57 inches , the store suggests 24 inch wheels. Is the relationship between a young person's height and the recommended wheel diameter a function? Explain your reasoning.
The relationship between a young person's height and the recommended wheel diameter is a function, as each input is associated to a single output.
When does a relationship represents a function?To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.
The input and output variables for this problem are given as follows:
Input variable: young person's height.Output variable: recommended wheel diameter.As for each height, there is only one recommended wheel diameter, we have that each input is mapped to a single output, and thus the relationship between a young person's height and the recommended wheel diameter is a function.
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graph the following system of equations and find the x coordinate of the soloution x3=3y=3 y=1/2x+2
Answer:
infinitely many solutions and x=y
Problem in the attached image! Pls help only 10 and 11
The alternate interior angles are the angles that are formed inside the two parallel lines, when it is intersected by a transversal, and are equal to its alternate pairs.
What is alternate interior angles?Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.
Alternate angles are shaped by the two parallel lines crossed by a transversal. Consider the given figure, EF and GH are the two parallel lines. If two parallel lines are cut by a transversal, then the alternate angles are equal.
In order to understand alternate interior angles, one must first picture a set of parallel lines, and then a line intersecting them. The intersecting line is called a transversal, and all the angles formed between the parallel lines are the interior angles.
At the point of intersection of transversal and two lines we have:
∠3 + ∠4 = 180 .........(1)
∠6 + ∠8 = 180 ...........(2)
We know that angle 4 and angle 8 are equal:
Thus, using 1 and 2 we have:
∠3 = ∠6
Hence, ∠3 and ∠6 are congruent.
Now, using the alternate interior angle we know that:
∠3 = ∠6
Also, we have:
∠5 + ∠6 = 180 (Straight line)
Substituting the value of ∠6 = ∠3 we have:
∠5 + ∠3 = 180
Thus, the two angles are supplementary.
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On Friday, Wall Street traders were anxiously awaiting the federal government's release
of numbers on the January increase in nonfarm payrolls. The early consensus estimate
among economists was for a growth of 250,000 new jobs (CNBC, February 3, 2006).
However, a sample of 20 economists taken Thursday afternoon provided a sample mean
of 266,000 with a sample standard deviation of 24,000. Financial analysts often call such
a sample mean, based on late-breaking news, the whisper number. Treat the "consensus
estimate" as the population mean. Conduct a hypothesis test to determine whether the
whisper number justifies a conclusion of a statistically significant increase in the consen-
sus estimate of economists. Use a = .01 as the level of significance.
Anazlysing the conditions given in the question we can conclude that there is a statistically significant increase in the consensus estimate of economists.
How do financial analysts use the whisper number in their decision making process?Financial analysts often use the whisper number, which is a late-breaking estimate of a key economic indicator, to make predictions about the stock market and inform their investment decisions. They may use it to identify potential opportunities for buying or selling stocks based on whether the whisper number is higher or lower than expected.
Can the whisper number be used to predict the stock market?While the whisper number can provide insight into the current economic conditions, it is not a foolproof way to predict the stock market. It is just an estimate based on a sample of economists' predictions and can be affected by various unpredictable factors. Therefore, it's important to take other economic indicators and market conditions into account when making investment decisions.
To conduct a hypothesis test, we need to first define the null hypothesis and alternative hypothesis.
Null Hypothesis: The whisper number (sample mean) is equal to the consensus estimate (population mean)
H0: μ = 250,000
Alternative Hypothesis: The whisper number (sample mean) is greater than the consensus estimate (population mean)
H1: μ > 250,000
The next step is to calculate the test statistic and p-value. We can use a one-tailed t-test since the sample size is less than 30 and we don't know the population standard deviation.
Test statistic:
t = (266,000 - 250,000) / (24,000 / sqrt(20))
P-value:
Using the t-distribution table with 19 degrees of freedom, the p-value is less than 0.01, which is the significance level we set.
Since the p-value is less than the significance level (0.01), we can reject the null hypothesis and conclude that there is a statistically significant increase in the consensus estimate of economists.
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7. Find the area of the triangle using trigonometry.
The area of the triangle shown is 51.96 unit²
What is an equation?An equation is a expression that shows the relationship between numbers and variables.
The area of a triangle can be found given two adjacent sides and an angle between the two sides. It is given as:
Area = (1/2) * product of adjacent sides * sin(angle)
Hence:
Area of triangle shown = (1/2) * 10 * 12 * sin(60) = 51.96
The area is 51.96
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A manufacturing firm want to determine the proportion of defects in a manufacturing process. How many of its products does it need to sample if it wants to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%?
The firm needs to sample 138.297 products to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%.
What is a manufacturing firm?Generally, To determine the sample size needed to achieve a ±5% accuracy at a 95% confidence level, with a maximum expected proportion of defects of 10%, you can use the formula for sample size for a proportion. The formula is:
n = (z^2 * p * (1-p)) / E^2
Where:
n is the sample sizez is the standard normal deviate corresponding to the desired level of confidence (1.96 for a 95% confidence level)p is the maximum expected proportion of defects (0.10 in this case)E is the margin of error (0.05 in this case)Plugging in the given values, we get:
n = (1.96^2 * 0.10 * (1-0.10)) / 0.05^2
n =138.297
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Solve for the interior of angle, x.
90°
130°
130⁰
130
120%
Xo
Please help I need help!!!!!!!!!!!!!!!!!!!!!
Jackie wants to buy a new van for work.
She wants to borrow £7,500 to buy the van and looks at two bank loans for this amount.
an image
Formula for simple interest is: I=PRT100
I
=
P
R
T
100
Formula for compound interest is: A=P(1+r100
A
=
P
(
1
+
r
100
)n
n
What is the difference in the interest charged between the two banks?
Answer: The interest rates charged in both formulas are different.
Step-by-step explanation:
To begin with, the simple interest = PRT/100
In this, the interest is the same as the number of years.
For example, P=10,000 R=10% T=2yrs
SI = PRT/100
= 10,000*10*2/100
= 2000
This rupee 2000 is the same interest for two years.
compound interest = A= P(1+r/100)^n
In this, the interest changes every year up to the period of time.
For example, P= 10,000 R=10% N=2yrs
A= 10,000(1+10/100)^2
= 10,000*11/10*11/10
= 12100
I= A-P
=12100-10000
= 2100
This interest varies for 2 years.
Which choice shows 13 • (7 • 4) correctly rewritten using the associative property and then correctly simplified?
The choice that shows 13 · (7 · 4) correctly rewritten using the associative property and then correctly simplified is presented as follows;
(13 · 7) · 4 = 91 · 4 = 364What is the associative property of multiplication?The associative property of multiplication stated that the multiplication of three numbers produces the same result in any way the numbers are grouped.
Mathematically, the associative property of multiplication can be presented as follows;
(a × b) × c = a × (b × c)
The specified operation involving the multiplication of three numbers are presented as follows;
13 · (7 · 4)
The associative property of multiplication indicates that we get;
13 · (7 · 4) = (13 · 7) · 4
13 × 7 = 91
Therefore, (13 · 7) · 4 = (13 × 7) × 4
(13 × 7) × 4 = 91 × 4 = 364
The option that shows the associative property correctly written and then correctly simplified is therefore;
(13 · 7) · 4 = 91 · 4 = 364The possible options in the question, obtained from a similar online question are;
(13 · 74) = 96213 · 4 · 7 = 52 · 7 = 364(13 · 7) · 4 = 91 · 4 = 36413 · (4 · 7) = 13 · 28 = 364
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Please please look at the picture and answer the question thank you
Answer:
[tex]\boxed{-2 < x\le1}[/tex]
Representation on number line is in attached image.
Notice that -2 has an unfilled circle and 1 has a filled circle. Important
Step-by-step explanation:
The given inequality is
[tex]2 < 4x+10\le14[/tex]
Subtract 10 throughout:
[tex]2-10 < 4x+10-10\le14-10\\\[/tex]
[tex]-8 < 4x\le4[/tex]
Divide throughout by 4:
[tex]-2 < x\le1[/tex]
Answer: [tex]\boxed{-2 < x\le1}[/tex]
This is represented on the number line as follows: Notice the use of the
Graph the piecewise function
The graph of the given piecewise function is as attached below.
Piecewise function is a function consisted of pieces of different functions over different intervals.
From the case we have:
f(x) = 3x - 5 if x ≤ -1
f(x) = -2x + 3 if -1 < x < 4
f(x) = 2 if x ≥4
To construct the piecewise function, we can try to find the base points of each functions.
f(x) = 3x - 5; if x ≤ -1
We will take x = -1 to approximate the line position
f(-1) = 3(-1) - 5
f(-1) = -3 - 5 = -8
f(x) = -2x + 3; if -1 < x < 4
(x = -1)
f(-1) = -2 (-1) + 3
f(-1) = 2 + 3 = 5
(x = 4)
f(4) = -2 (4) + 3
f(4) = -8 + 3 = -5
f(x) = 2; if x ≥ 4
(x = 4)
f(4) = 2
We can put each points on the graph and try to construct the piecewise function.
Please refer to the attached graph below for the piecewise function graph
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Nevaeh has $2,131.50 in a savings account that earns 6% interest per year. If she initiall
deposited $2,100 how many months has she been investing her money?
We know that Nevaeh initially deposited $2,100, and now she has $2,131.50 in her account. The interest earned is $2,131.50 - $2,100 = $31.50. To find out how many months has she been investing her money, we can use the following formula:
Time (in months) = (Interest / Principal) x (12 / Interest Rate)
Where Principal is the initial deposit amount, Interest Rate is the annual interest rate, and Interest is the amount of interest earned.
Plugging in the given values, we get:
Time (in months) = ($31.50 / $2,100) x (12 / 0.06)
Time (in months) = 0.0149 x 200
Time (in months) = 2.98
Since time cannot be in fraction of months, it has to be rounded off. So, Nevaeh has been investing her money for approximately 3 months.
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years. Predict the account balance after 0, 1, and 2 years. Round your answers to the nearest dollar.
Tiles:
$845
$758
$952
$765
$750
Boxes:
initial deposit
balance after 1 year
balance after 2 years
According to the given expression, the account's initial deposit is 750, the balance after one year is 845, and the balance after two years is 952.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given, The amount of money in a savings account is modeled by A(x) = 750(1.01)^12x, where x represents number of years.
Expression for money is given
Thus, balance at x = 0
Balance A(0) = 750
Balance at x = 1
Balance A(1) = 750(1.01)^12*1
A(1) = 845.11
Balance at x = 2
Balance A(2) = 750(1.01)^12*2
A(2) = 952.43
Therefore, In the account initial deposit is 750, balance after 1 year is 845, and balance after 2 years will be 952 as per the given expression.
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what is solution set for 2x2+15=-11x?
A{2.5,3} C{-3,-2.5}
B[1.5,5} D{-5,-1.5}
Answer:
C{-3,-2.5}
Step-by-step explanation:
Brainliest pls
which of the following fractions has been Simplified to lowest terms 25/95,21/49,3/17,10/15,44/52
3/17
Both 3 and 17 are prime numbers, therefore they cannot be simplified by any number expect 1 and itself.
The number of phone calls between two nearby cities during a given time period, N , varies directly as the populations P₁ and P₂ of the two cities. If 109,000 calls are made between two cities with populations 74,000 and 189,000, how many calls are made between two cities with population 125,000 and 175,000?
Answer:
170,483
Step-by-step explanation:
You have N varying jointly with P1 and P2, such that N=109,000 for P1=74000 and P2=189000. You want to know N for P1=125000 and P2=175000.
Varies jointlyThe relation "N varies jointly with P1 and P2" can be described by the equation ...
N = k·P1·P2
The value of k can be found as ...
k = N/(P1·P2)
k = 109000/(74000·189000) ≈ 7.793508×10^-6
New citiesThen the number of calls given the populations P1=125000 and P2=175000 is predicted to be ...
N = (7.793508×10^-6)(125000)(175000) ≈ 170482.982...
N ≈ 170483
About 170,483 calls are expected between cities with populations of 125 and 175 thousand.
If the number of phone calls between two nearby cities during a given time period. The number of calls that are made between two cities with population 125,000 and 175,000 is: 170,482,987,500.
How to find the number of calls?Calls made between two cities with populations 74,000 and 189,000,
Call = 109,000/(74000 × 189000)
Call = 109,000 / 13,986,000,000
Call = 7.793508
Calls made between two cities with populations 125,000 and 175,000?
Calls = 7.793508 × 125000 ×175000
Calls =170,482,987,500
Therefore the calls made is 170,482,987,500.
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Consider the quadratic equation x squared minus 7 x minus 18 equals 0
Find the solutions by factoring.
x = -9, x = 2
x = -2, x = 9
x = -6, x = 3
x = -3, x = 6
Answer:
x = -2, x = 9
Step-by-step explanation:
Given quadratic equation:
[tex]x^2-7x-18=0[/tex]
To factor a quadratic in the form ax²+bx+c, first find two numbers that multiply to ac and sum to b.
[tex]\implies ac=1 \cdot -18=-18[/tex]
[tex]\implies b=-7[/tex]
Therefore, the two numbers are: -9 and 2.
Rewrite b as the sum of these two numbers:
[tex]\implies x^2-9x+2x-18=0[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies x(x-9)+2(x-9)=0[/tex]
Factor out the common term (x - 9):
[tex]\implies (x+2)(x-9)=0[/tex]
Apply the zero-product property:
[tex]\implies x+2=0 \implies x=-2[/tex]
[tex]\implies x-9=0 \implies x=9[/tex]
Therefore, the solutions to the given quadratic equation are:
x = -2, x = 9there are 28 questions on a test i got 16 wrong what percent did i get correct? round to the nearest percent
Answer:
43%
Step-by-step explanation:
28 questions - 16 wrongs = 12 correct
(12/28) × 100= 42.857.....%
To the nearest percent=43%
Please help me with this question.
The constants A and B for the differential equation are given as follows:
A = 0.B = -64.How to obtain the constants A and B?The solutions to the differential equation are given as follows:
y(t) = e^(8t).y(t) = e^(-8t).This means that the roots of the characteristic equation are given as follows:
r = -8 and r = 8.
Considering that the leading coefficient is of 1, as 1 multiplies y'', the characteristic equation is given as follows:
(r + 8)(r - 8) = r² - 64.
Hence the differential equation is given as follows:
y'' - 64y = 0.
Hence the constants are given as follows:
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112 divide by 0.16 with solutions
The solution for the expression 112 ÷ 0.16 is 700.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
112 ÷ 0.16
This can be written as,
= 112/0.16
= 700
Thus,
The solution is 700
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PLS PLS HELp, i dont get what it means by for
Answer:
don't
Step-by-step explanation:
get that one wrong don't spend to much time on it
A pyramid has a(n) for a base and a number of that all meet at the
same
о
-
A. two-dimensional object; faces; vertex
B. point; vertices; point
C. polygon; edges; face
D. edge; faces, point
Answer:
B. point; vertices; point
Step-by-step explanation:
A pyramid is a 3-dimensional geometric shape that has a base, which is typically a polygon, and a number of triangular faces that all meet at a single point called the vertex. The pyramid has vertices at the corners of the base and all other points where the triangular faces meet.
Given these observed times (in minutes) for five elements of a job, determine the observed time (OT) for each element. Note: Some of the elements occur only periodically.
The observed time cycles of five given elements are 2.1, 1.01, 3.4, 4.1, 1.5 respectively
How to determine the observed time?To determine the observed time (OT),
The observed time (OT) of each cycles will be added together for each element. and divided by total number of cycles for each element.
This is done in the following ways
1) (1.2+2.0+2.2+2.1+2.1)/5 = 10.5/5 = 2.1
2) (1.1+1.0+1.2) = 3.3/3 = 1.1
3) (3.4+3.5+3.3+3.5+3.4+3.3)/6 = 20.1/6 = 3.4
4) 4.0+4.2)/2 = 8.2/2 = 4.1
5) (1.4+1.4+1.5+1.5+1.5+1.4)/6 = 8.7/6 = 1.5
therefore each elements total cycle OT is added and then it is divided with each elements relevant number of cycles and this as a result provides the answer to the question
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factorise 14x squared-x-13
Answer:
(14x+13)(x-1)
Step-by-step explanation:
14x²-x-13
14 × 13 = 182
Search for factors of 182 that contain a difference of 1 when subtracted because -x is the same as -1x.
Since 14 × 13 = 182
and
13 - 14 = -1
They are our 2 chosen numbers which will be displayed as :
14x² - 14× + 13x - 13
where -x is replaced by -14x + 13x
Proceed to factorise normally
14x(x-1) + 13(x-1)
Grouping
(14x+13)(x-1)
The prism shown has a volume of 35 cm³.
Work out h, the height of the triangular cross section.
Optional working
h
base = 4 cm
Length = 7 cm
[tex]35 cm ^{3}[/tex] is the volume of the prism displayed. The triangular cross section is 1.25 cm tall.
What is the height of the prism ?length , l = 7 cm , width w = 4 cm , height , h= 1.25 ,diagonal , d=8.15858444 cm , total surface area, [tex]$S_{\text {tot }}=83.5 \mathrm{~m}^2$[/tex] , lateral surface area , [tex]$S_{\text {lat }}=27.5 \mathrm{~m}^2$[/tex] , top surface area , [tex]$S_{\text {top }}=28 \mathrm{~m}^2$[/tex] , bottom surface area , [tex]$S_{\text {bot }}=28 m^2$[/tex] , volume [tex]$V=35 \mathrm{~m}^3$[/tex] .
To calculate the height of a prism, divide its volume by its area at the base. Let's say that the prism has a volume of 600 cubic inches to wrap up this scenario. The height is determined by multiplying 600 cubic inches by 100 square inches.
A prism's volume is calculated using the formula V=Bh, where B denotes the base area and h the height. A rectangular area makes up the prism's base. The rectangle's dimensions are 9 cm long by 7 cm wide. The formula V=Bh, where V stands for volume, B for the prism's area at its base, and h for its height, can be used to determine a prism's volume. B should be replaced with the area of a rectangle formula because this is a rectangular prism.
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Huilan is 14 years older than Thomas. The sum of their ages is 113. What is Thomas age
Answer: 49.5
Step-by-step explanation:
Let Thomas' age be [tex]T[/tex]. Then, Hulian's age is [tex]T+14[/tex].
[tex]T+T+14=113\\\\2T+14=113\\\\2T=99\\\\T=49.5[/tex]
