To find the angle of rotation θ between the previous x and y axes and the new x′ and y′ axes, we use the formula: cotangent of 2 theta equals A minus C all over B , where 2θ lies on the interval (0°, 180°).TrueFalse
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The equation is the given one:
[tex]\cot 2\theta=\frac{A-C}{B}[/tex]Which is the same as:
[tex]\tan 2\theta=\frac{B}{A-C}[/tex]And the interval of the angle θ must be (0°,90°) so, 2θ must be (0°,180°).
So the statement is True.
Related Questions
A changes and8. The graph of y = cos z is transformed to y = a cos (2-c) + d by a vertical expansion by a factor of 2, then translated units right and 2 units up.The new equation is:y=2 cos (x + 5) - 2y= 2 cos (x - 1) +2y= {cos (x - 1) + 2y=2 cos ( - ) - 2
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Option 2 is correct.
What criteria can you use to show these two triangles are congruent?choice:SSAAASHLSAS
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ANSWER
SAS
EXPLANATION
SAS criterion is an acronym for Side-Angle-Side criterion. Two triangles are congruent if the two sides and included angle of one triangle are equal to the corresponding sides and included angle of the second triangle, according to this criterion.
make your own quadratic function in standard form then determine the vertex of your propolis the axis of symmetry the y-intercept then graph using Circle curve line tools
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The general form of a quadratic equation is expressed as
ax^2 + bx + c
An example of a quadratic equation is
2x^2 - 4x - 2
The graph of this equation is shown below
The vertex of the graph is value of x and y at the bottom of the curve. Looking at the curve, the vertex is (1, - 4)
The axis of symmetry is the vertical line that divides the curve into two equal halves. The axis of symmetry of this curve is the line, x = 1
The y intercept is the point where the curve cuts through the y axis. From the graph, y intercept = - 2
&Maps CClever | Portal e Learner Home e Learning Path - Eng... Mail- Makayla D. Submit Test R Pretest: The Real Number System rag the tiles to the boxes to form correct pairS. atch the pairs of equivalent expressions. (-1440)-1+ 46+ (54-26)+(28+) 8-15 -3-(8+6) -11 -10+8)+(76-5) -15 Dor Moxt
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hello
to solve this question, we need to write out the expressio
Jeff's restaurant sells hamburgers. The amount
charged for a hamburger (h) is based on the cost for a plain hamburger plus an additional charge for each topping (t) as shown in the equation below.
h = 0.60t+5
What does the number 0.60 represent in the equation?
A. the number of toppings
B. the cost of a plain hamburger
C. the additional cost for each topping
D. the cost of a hamburger with 1 topping
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Answer:
Step-by-step explanation:
b the cost of the plain burger
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition. He agreed to pay Julio in 6 months with simple annual interest at 6.2% a.) how much will the interest amount to ?b.) what amount must Miguel pay Julio at the end of 6 months ?
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Given:
Miguel Rodriguez borrowed $500 from his brother Julio to pay for books and tuition.
He agreed to pay Julio in 6 months with simple annual interest at 6.2%
So, the interest = r = 6.2% = 0.062
the time = t = 6 months = 6/12 years = 1/2 year
a.) how much will the interest amount to?
The interest is given by the formula:
[tex]I=P\cdot r\cdot t[/tex]Substitute with the given values:
[tex]I=500\cdot0.062\cdot\frac{1}{2}=15.5[/tex]So, the interest = I = $15.5
b.) what amount must Miguel pay Julio at the end of 6 months?
So, Miguel will pay the amount that he borrowed and the interest
so, he will pay:
[tex]P+I=500+15.5=515.5[/tex]So, the answer will be: $515.5
the function g(x) was obtained by transforming f(x)=1/x Use the description of the transformation to write the equation representing g(x).f(x) Is vertically stretched by a factor of 2, reflected about the X axis, then shifted 5 units.
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Since f(x) is vertically strectched by a factor 2, we get
[tex]f(x)\longrightarrow\frac{2}{x}[/tex]next, it is reflectec about the x-axis, then we have
[tex]\frac{2}{x}\longrightarrow-\frac{2}{x}[/tex]Finally, its shifted 5 units on x axis, then we have
[tex]-\frac{2}{x}\text{ --> }-\frac{2}{x+5}[/tex]which corresponds to option 2
Two farmers John and Harry cultivates twovarieties of rice namely Basmati and Naura.The sale price of these varieties of rice by boththe farmers are as follows:John sells Basmati at $5.00/kg and Naura at$3.50/kg. While Harry sells Basmati at$6.50/kg and Naura at $2.60/kg.Use the matrix to present the prices of rice bytwo farmers.
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Sales price for the rice varieties:
John:
Basmati cost = $5 per kg
Naura cost = $3.5 per kg
Harry:
Basmati cost = $6.5 per kg
Naura cost = $2.6 per kg
Writing in the form matrix:
[tex]\begin{gathered} let\text{ first column represent basmati rice} \\ let\text{ the 2nd column represent Naura rice} \\ In\text{ matrix, x and y can be represented as:} \\ \begin{bmatrix}{x\text{ column}} & {y\text{ column}} \\ {}{{x\text{ column}}} & {{y\text{ column}}}\end{bmatrix} \end{gathered}[/tex][tex]\begin{gathered} x\text{ = Basmati, y = Naura} \\ \\ \begin{bmatrix}{5.00} & {3.50} \\ {6.50} & {2.60}\end{bmatrix}\text{ \lparen option B\rparen} \end{gathered}[/tex]use distributive property to fill in the blanks (4×7) - (4×3) = ___ × (7-3)
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hi! i was wondering how to find the volume of a figure?
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Answer: Volume of solid = 700 ft^3
Explanation:
The solid figure can be sectioned into 2 parts; a rectangular prism and a triangular prism.
Considering the rectangular prism, the formula for calculating the volume is
Volume = length x width x height
From the diagram,
length 10
height = 10
width = 5
Volume of rectangular prism = 10 x 10 x 5 = 500
Considering the triangular prism, the formula for calculating the volume is
Volume = base area x length
The base is a triangle
Area of triangle = 1/2 base x height
From the diagram,
base = 10
height = 8
Base area = 1/2 x 10 x 8 = 40
Length = 5
Volume of triangular prism = 40 x 5 = 200
Thus,
Volume of solid = 500 + 200
Volume of solid = 700 ft^3
A teenager in a highrise building looks out his window at another building across the street and realizes a crime is being committed. If the buildings are 60 feet apart, and the teenager is looking down into the other building with an angle of depression of 20°, how many feet lower is the floor where the crime is being committed? If each floor is 10 feet, about how many floors down is it?
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Hello!
The first step to solving this exercise is to draw the situation, look:
Now we can solve this exercise. Notice that we want to know the height that I called "X".
To find it, we must use the tangent of 20º, look:
[tex]\tan (20\degree)=\frac{opposite}{adjacent}[/tex][tex]\begin{gathered} \frac{0.364}{1}=\frac{60}{x} \\ \\ 0.364x=60 \\ x=\frac{60}{0.364} \\ \\ x\cong164.83 \end{gathered}[/tex]If each floor is 10 feet:
[tex]\frac{164.83}{10}=16.483\text{ floors}[/tex]If you have to approximate, you can say that it is 16.5 floors down.
15/2 as a mixed number
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We must express the number 15/2 as a mixed number, which is a number consisting of an integer and a proper fraction. To do that, we compute the quotient in the following way:
[tex]\frac{15}{2}=\frac{14+1}{2}=\frac{14}{2}+\frac{1}{2}=7+\frac{1}{2}=7\frac{1}{2}\text{.}[/tex]Answer
The number 15/2 expressed as a mixed number is:
[tex]7\frac{1}{2}\text{.}[/tex]What is the volume of the figure below?9 feet14 feet5 feet30ft60ft90ft120ft
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The length of rectangular pyramid is l = 5 feet.
The width of rectangular pyramid is w = 4 feet.
The height of rectangular pyramid is h = 9 feet.
The formula for the volume of rectangular pyramid is,
[tex]V=\frac{l\cdot w\cdot h}{3}[/tex]Since there are two rectangular pyramid so net volume of figure is,
[tex]V^{\prime}=\frac{2}{3}\cdot l\cdot w\cdot h[/tex]Substitute the values in the formula to obtain the volume of figure.
[tex]\begin{gathered} V^{\prime}=\frac{2}{3}\cdot5\cdot4\cdot9 \\ =10\cdot4\cdot3 \\ =120 \end{gathered}[/tex]So volume of figure is 120 feet cube.
Mira was solving for y in the following problem l. However, she did something wrong. Describe and correct the error in the work shown.2x-y=5y=-2x+5
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The initial equation is:
[tex]2x-y=5[/tex]Then, in order to isolate y, we need to subtract 2x from each side of the equation:
[tex]\begin{gathered} 2x-y-2x=5-2x \\ -y=-2x+5 \end{gathered}[/tex]Then, we multiply both sides by -1:
[tex]y=2x-5[/tex]The equation Mira wrote is y=-2x+5. So we can see that her error was not changing the signs of the terms in the right side of the equation.
In order to correct her error, we just need to change the signs in the right side of the equation:
[tex]\begin{gathered} y=-(-2x+5) \\ y=2x-5 \end{gathered}[/tex]The vertices of ACDE are C(-1, 1), D(3,5), and E(5. - 4). Translate ACDE using vectorr(3. – 1).Enter the correct ordered pair for C', D', and E'. Do NOT use any spaces in your answer.C'D'E
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C (-1,1)
D (3,5)
E (5,-4)
now we are going to translate ACDE using vector r(3,-1)
C'(2,0)
D'(6,4)
E'(8,-5)
How many general tickets should the college sell to maximize revenue
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Notice that, since 5000 tickets are reserved for students, there are 13000 available tickets that can be acquired by students or the general public.
Since the cost of a general public ticket is greater than that of a student ticket, we can increase the revenue to its maximum by selling the remaining 13000 tickets to the general public only.
Therefore, the answer is 13,000
Tom's Bakery recently spent a total of $800 on new equipment, and their average hourlyoperating costs are $10. Their average hourly receipts are $90. The bakery will soon makeback the amount it invested in equipment. What would the total expenses and receipts bothequal?TimeelapsedWrite a system of equations, graph them, and type the solution1.000SmartScore
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Hello there. To solve this question, let's call the average hourly operating costs as C and the average hourly receipts as R.
We get that 90R - 10C = 800, since this is the amount the bakery has spent on equipments and it is said he will soon get back this invested money.
Dividing both sides by 10, we get 9R-C = 80
The graph will be a line. We want to find then C = R, so we can get:
-R + 9R = 80
8R = 80
R = 10
So, we have a cost of $100 and receipt of $900 in order to get back that money.
Hello! I need help with this questionTriangle DOG was rotated to create triangle D'O'G''. Describe the transformation using details and degrees.
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Answer:
180 degrees rotation about the origin
Explanation:
First, we need to identify the coordinates of DOG and D'O'G' as follows
D(-2, 1) ---> D'(2, -1)
O(-3, 3) ---> O'(3, -3)
G(1, 1) ---> G'(-1, -1)
Therefore, the rule for the transformation is
(x, y) ---> (-x, -y)
This rule is the rule for a 180 degrees rotation about the origin. So, the transformation is a 180 degrees rotation about the origin.
supposed your friend was born, your friends parents deposited $2000 in an account paying 3.5% interest compound monthly. what will the account balance be after 15 years?
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If we have a deposit of $2000, invested at an an annual interest rate of 3.5% compounded monthly, we can calculate the final value of that deposit in 15 years as:
[tex]FV=PV(1+\frac{r}{m})^{m\cdot n}[/tex]where:
FV: final value of the deposit.
PV: initial deposit (PV = 2000)
r: annual interest rate (r = 0.035)
m: subperiod (as the compound is monthly, and there are 12 months in a year, we have m = 12).
n: period (n=15)
Then, the expression gives us a value of:
[tex]\begin{gathered} FV=PV(1+\frac{r}{m})^{m\cdot n} \\ FV=2000(1+\frac{0.035}{12})^{12\cdot15} \\ FV\approx2000(1.002917)^{180} \\ FV\approx2000\cdot1.689 \\ FV\approx3378 \end{gathered}[/tex]Answer: the account balance after 15 years will be $3378.
4. Describe the pattern. Choose the correct answer below. O A. The difference in the powers is equal to the sum of the bases. OB. The difference in the powers is equal to the difference in the bases. O C. The sum of the powers is equal to the sum of the bases. OD. There is no pattern.
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Problem
Solution
Lets analyze one by one the possible options and we have:
O A. The difference in the powers is equal to the sum of the bases.
FALSE 2^2 and 1^2, we have 2-2=0 is different from 2+1=3
OB. The difference in the powers is equal to the difference in the bases.
FALSE , again if if we check 2^2 and 1^2 we have 2-1=1 and 2-2=0 and are not equal
O C. The sum of the powers is equal to the sum of the bases.
FALSE if we check 2^2 and 1^2 we have 2+1=3 and 2+2=4 and are not equal
OD. There is no pattern.
The best choice would be this one
What is the effect on the graph of f(x) = 1 when it is transformed to g(x) = 1 + 17? O A. The graph of f(x) is shifted 17 units up. O B. The graph of f(x) is shifted 17 units to the left. O C. The graph of f(x) is shifted 17 units to the right O D. The graph of f(x) is shifted 17 units down.
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What is the effect on the graph of f(x) = 1 when it is transformed to g(x) = 1 + 17? O A. The graph of f(x) is shifted 17 units up. O B. The graph of f(x) is shifted 17 units to the left. O C. The graph of f(x) is shifted 17 units to the right O D. The graph of f(x) is shifted 17 units down.
we have that
f(x)=1 ----> is a horizontal line (y intercept is (0,1)
f(x)=1+17=18 -----> is a horizontal line (y -intercept is (0,18)
therefore
there are a translation 17 units up
the answer is the option Anot really sure what to do here??
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Answer:
[tex]d=-6[/tex]
[tex]a_9=-49[/tex]
Step-by-step explanation:
If the first term of a sequence is [tex]-1[/tex] and the second term is [tex]-7[/tex], then each successive term in the sequence is [tex]6[/tex] less than the previous term. The common difference is [tex]-6[/tex] ( [tex]d=-6[/tex] ).
The formula representing the arithmetic sequence is:
[tex]a_n=-6n+5[/tex]
Therefore, the ninth term in the sequence is:
[tex]a_9=-6(9)+5[/tex]
[tex]a_9=-54+5[/tex]
[tex]a_9=-49[/tex]
FACTS:In 2010, the glacier was 1000 meters in length; it had retreated 255 meters in 15 years.Questions:1. Calculate the average annual rate of retreat of the glacier
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Let's represent the given (length, years) as (x, y)
at time 0 year, the glacier is 1000 meters
at time 15 years, the glacier retreated 255 meters and that's 1000 - 255 = 745
so we have the points (0, 1000) and (15, 745)
Using the slope formula :
[tex]m=\frac{y_2-y_1_{}}{x_2-x_1}[/tex]where m represents the average annual rate of retreat.
[tex]m=\frac{745-1000}{15-0}=\frac{-255}{15}=-17[/tex]The average annual rate of retreat of the glacier is 17 meters per year
write an inequality: n is at most 40
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If a value is at most 40, it means that such value cannot be greater than 40. The values will always take a value that is less tha 40 wih 40 inclusive.
To express this using inequality, we will use the less than or equal to sign in our expression as shown
[tex]n\leq40[/tex]A candle is 4 inches tall and burns at the rate of 0.6 inch per hour. If the height of the candle after x hours is 1.5 inches, write an equation to represent the situation. Then use this equation to find the expected number of hours in which the candle melted to 1.5 inches.I think the way to start this is x = 1.5 inches but I'm stuck.
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Given the following question:
Candle = 4 inches tall
Burns at a rate of 0.6 inches per hour
x = hours
[tex]4-0.6x=1.5[/tex]4 representing the height of the candle
0.6 representing the rate the candle burns
x = the amount of time in hours the candle burns
1.5 = the height of the candle after it burned for x hours
[tex]\begin{gathered} 4-0.6x=1.5 \\ 0.6x=4-1.5 \\ 0.6x=2.5 \\ x=2.5\div0.6 \\ x=4.166 \\ =4.166\text{ hours} \end{gathered}[/tex]Driving down a mountain, Bob Dean finds that he descends 3300 feet in elevation by the time he is 4.5 miles (horizontally) away from the high point on the mountain road. Find the sic
descent. (1 mile 5280 feet).
The slope is
(Type an integer or decimal rounded to two decimal places as needed.)
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Answer:
[tex]-0.14[/tex]
Step-by-step explanation:
Slope is defined as the change in [tex]y[/tex] divided by the change in [tex]x[/tex].
The change in [tex]y[/tex] is a decrease of 3,300 feet.
The change in [tex]x[/tex] is an increase of 4.5 miles. Converting to feet so that both measurements are in identical units:
[tex]\frac{4.5\text{ mi}}{1}\times\frac{5280\text{ ft}}{1\text{ mi}}=23760\text{ ft}[/tex]
Therefore, the slope is:
[tex]\frac{\Delta{y}}{\Delta{x}}=\frac{-3300}{23760}=-\frac{5}{36}[/tex]
As a decimal rounded to two places:
[tex]-\frac{5}{36}\approx{-0.14}[/tex]
E Which point is located at (4, -2)? 3 G 다
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The given coordinate tells us that when x = 4, y = - 2
Looking at the graph, the point where x = 4 and y = - 2 is point D
The functions f and g are defined as follows:f(x)=2x^2-3xg(x)=-5x-1Find f(-3) and g(7)Simplify your answers as much as possible
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f(x) = 2x^2 - 3x
f(-3) = 2(-3)^2 - 3(-3)
f(-3) = 2(9) + 9
f(-3) = 18 + 9
f(-3) = 27 This is the first solution
g(x) = -5x - 1
g(7) = -5(7) - 1
g(7) = -35 - 1
g(7) = -36 This is the second solution
The main printer in the Ivy Tech library can produce an average of 639copies every hour. For every 36 pages, it costs the college $0.06 forelectricity and supplies. If the library is open from 9AM to 9PM, howmuch money does the college use on printing each day?
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You know that:
- An average of 639 copies per hour can be produced by the main printer.
- The cost for electricity and supplies is $0.06 for every 36 pages produced.
- The library is opened for 12 hours.
Let be "x"the cost (in dollars) for electricity and supplies for 639 copies produced in 1 hour.
You can set up the following proportion:
[tex]\frac{0.06}{36}=\frac{x}{639}[/tex]Solve for "x":
[tex]\begin{gathered} (\frac{0.06}{36})(639)=x \\ \\ x=1.065 \end{gathered}[/tex]Knowing that the cost for electricity and supplies for 639 copies produced in 1 hour is $1.065, youo can multiply it by 12, in order to calculate how much money the college uses on printing each day:
[tex](1.065dollars\text{)}(12)=12.78dollars[/tex]The answer is: The college uses $12.78 on printing each day.
For this assignment, leave all answers as simplified fractions.A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the theoretical probabilityof drawing one tile at random for each of the following.1. P(M)2. P(S)3. P)4. P(not M)5. P(not S)6. P(not 1)
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ANSWER
[tex]\begin{gathered} 1)\frac{1}{11} \\ 2)\frac{4}{11} \\ 4)\frac{10}{11} \\ 5)\frac{7}{11} \end{gathered}[/tex]EXPLANATION
From the given question;
MISSISSIPPI has 11 words
The number of M is 1
The number of S is 4
Hence;
1.
[tex]P(M)=\frac{1}{11}[/tex]2. P(S);
[tex]P(S)=\frac{4}{11}[/tex]4. P(not M) ;
[tex]\begin{gathered} 1-P(M) \\ =1-\frac{1}{11} \\ =\frac{10}{11} \end{gathered}[/tex]5. P(not S);
[tex]\begin{gathered} P(not\text{ S})=1-P(S) \\ =1-\frac{4}{11} \\ =\frac{7}{11} \end{gathered}[/tex]