Mathematics High School

What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?

i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.

Answers

Answer 1
For rotation by an angle, θ, in the counter-clockwise direction about the origin, the transformation matrix is given by 
     [tex]\begin{pmatrix}cos\:\theta &-sin\:\theta \\ sin\:\theta &cos\:\theta \end{pmatrix}[/tex]

The given angle is θ=300°. 

The values we need are
     [tex]cos\left(300^{\circ} \right)=\frac{1}{2}[/tex]
     [tex]sin\left(300^{\circ} \right)=-\frac{\sqrt{3}}{2}[/tex]

Substituting these into the given transformation matrix, we have
     [tex]\begin{pmatrix}\frac{1}{2}&\frac{\sqrt{3}}{2}\\ -\frac{\sqrt{3}}{2}&\frac{1}{2}\end{pmatrix}[/tex]
Answer 2

the answer is B

hope this helps :)

Related Questions

"the placement test for a college has scores that are normally distributed with a mean of 600 and a standard deviation of 60.if the college accepts only the top 1​% of​ examinees, what is the cutoff score on the test for​ admission?"

Answers

The cutoff will be evaluated as follows:
let the cutoff be x

but
P(x>0.01)=1-P(x<0.01)=1-0.01=0.99
the z value corresponding to 0.99% is z=2.33
thus
2.33=(x-600)/60
solving for x we get:
139.8=x-600
x=739.8

How do you use properties of exponents and logarithms to rewrite functions in equivalent forms and solve equations?

Answers

Some of the logarithmic properties most used to solve equations are the following.
 1) log (a) ^ b = b * log (a)
 2) log (a * b) = log (a) + log (b)
 3) log (a / b) = log (a) - log (b)
 These logarithmic properties can be used to solve equations.
 For example:
 2 ^ x = 56
 If we apply to this equation the logarithm function on both sides that we have left
 log (2) ^ x = log (56)
 This function is equivalent to the first.
 If we now apply the property 1) of the previous logarithms, we can reveal x of the equation.
 x * log (2) = log (56)
 x = log (56) / log (2)
 x = 5,807
 Thus, thanks to the properties of the logarithms, this exponential function could be solved

Final answer:

To use properties of exponents and logarithms effectively, one must apply specific rules such as the logarithm of a product being the sum of the logarithms and the logarithm of a number raised to an exponent being the product of the exponent and the logarithm. Log transformations help linearize and solve equations involving exponents.

Explanation:

To rewrite functions in equivalent forms and solve equations using the properties of exponents and logarithms, one must understand several key rules and relationships. For example, the common logarithm (log) indicates the power to which 10 must be raised to equal a given number.

Two essential properties we use are:

The logarithm of a product of two numbers is the sum of the logarithms of the two numbers (log xy = log x + log y).The logarithm of a number raised to an exponent is the product of the exponent and the logarithm of the number (log x^n = n log x).

Exponential and logarithmic functions are inverses. This relationship allows us to simplify complex expressions and solve exponential equations by taking the logarithm of both sides. For instance, the natural logarithm (ln or loge) and the base e exponential are inverse functions, so ln (e^x) = x and e^(ln x) = x.

A log transformation can linearize functions that involve an exponent by taking the log of both sides of the equation. This technique is valuable in solving equations where the variable is an exponent.

peter put $8,000 into a savings account that pays 6% interest, compounded continuously. what will he have after 5 years?

Answers

So, continuous compound formula is:
[tex] Pe^{rt} [/tex]
P is Principal Amount
r is Rate
t is Time
P is 8000
r is 6%
t is 5
Therefore, you get $10,798.86.

suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. how high will the ball rebound after its third bounce? round to the nearest tenth

Answers

The answer would be 10.84

What is the simplified form of sqrt 400x100? 200x50 200x10 20x50 20x50

Answers

√400 x √100 = 40,000 
√40,000 = 200 

So your answer is 200 x 10.

Hope this Helps!!

Answer:  The required simplified form is 20 × 10.

Step-by-step explanation:  We are given to find the simplified form of the following radical expression :

[tex]E=\sqrt{400\times 100}.[/tex]

We will be using the following property of radicals :

[tex](i)~\sqrt{x}=x^\frac{1}{2}\\\\(ii)~\sqrt{a\times b}=\sqrt a\times\sqrt b.[/tex]

Therefore, we have

[tex]E\\\\=\sqrt{400\times 100}\\\\=\sqrt{400}\times\sqrt{100}\\\\=\sqrt{20^2}\times\sqrt{10^2}\\\\=((20)^2)^\frac{1}{2}\times(10^2)^\frac{1}{2}\\\\=20^{2\times\frac{1}{2}}\times(10)^{2\times\frac{1}{2}}\\\\=20\times10.[/tex]

Thus, the required simplified form is 20 × 10.

HELP!!!!!!NEED TO PASS!!!!WILL GIVE THE BRAIN!!!!!!!!!!!

Answers

Shifting left means adding a number to x.

So, x³ shifted 5 units to left will be (x + 5)³

Shifting 4 units upwards means adding 4 to the function value,

So, previous function shifted 4 units up will be (x + 5)³ + 4

Thus, g(x) = (x + 5)³ + 4

So, option b gives the correct answer



So, option b gives the correct answer

on Sunday Mary pay $6 each on two tickets to a movie theater movies for $9.58 each Mary paid with 3 $20 bills how much changed

Answers

$50.42







hjdjdjdjdbdhshssjdjdjdjdj

The angle of elevation to the top of a building in chicago is found to be 11◦ from the ground at a distance of 1000 feet from the base of the building. find the height of the building.

Answers

The height is 1943.8 feet. easiest way to do this is draw a little diagram. Draw the building and the unknown height can be "x". We know a 1000 feet away from the base of the building, the angle between the ground and top of the building is 11 degrees. If you draw this, you can see that you can use the tan function to find the missing "x". tan (angle) = opposite side/adjacent side. So tan(11) = x/1000. Isolate for x and you get 1943.8 feet

What is the linear function that best fits the data set?

Answers

Answer: Fourth option y=-3x+15
Please, see the attached file.
Thanks.

someone help me please

Answers

For this case we have the following functions:
 f (x) = 3x + 1
 g (x) = x ^ 2 - 6
 Subtracting both functions we have:
 (f-g) (x) = f (x) - g (x)
 (f-g) (x) = (3x + 1) - (x ^ 2 - 6)
 (f-g) (x) = 3x + 1 - x ^ 2 + 6
 (f-g) (x) = - x ^ 2 + 3x + 7
 Answer:
 (f-g) (x) = - x ^ 2 + 3x + 7
 option B

Help Geometry!!
AC is tangent to circle O at A. If , m<BY= 24 , what is m<YAC?

a) 48

b) 156

c) 78

d) 132

Answers

we know that
The inscribed angle measures half of the arc it comprises.
so
∡BAY=BY/2------> 24/2------> 12°

angles YAC and BAY are complementary angles
∡YAC+∡BAY=90°
∡YAC=90-∡BAY-------> ∡YAC=90-12-----> 78°

the answer is
78°

how do I solve (x-5)(x-1)=0

Answers

With this equation, you'd distribute one set of parenthesis into the other. Doing so you'd get "X^2 - 1x - 5x + 5 = 0". Simplified, you'd have "X^2 - 6x + 5 = 0"

Next, you'd find the factors of 5, that when multiplied equal 5, and when added, equal -6. Being that 5 is a prime number (a number that is only divisible by 1 and itself) those numbers are 1 and 5. Both numbers have to be negative, in order to get -6.

-1*-5 = 5
-1 + -5 = -6

Finally you split up the X^2 to a single x with each of the factors and make it equal to zero (X - 1 = 0) and (X - 5 = 0). Then you solve each.

(X - 1 = 0) Add 1 to each side. X = 1
(X - 5 = 0) Add 5 to each side. X = 5

I hope this helps!

Solve the quadratic equation. 8x2 + 16x + 8 = 0 A) 1 B) -1 C) 1 and 8 D) 1 and -1

Answers

[tex]8x^2+16x+8=0\\\\8(x^2+2x+1)=0\ \ \ |:8\\\\x^2+2x+1=0\\\\x^2+x+x+1=0\\\\x(x+1)+1(x+1)=0\\\\(x+1)(x+1)=0\\\\(x+1)^2=0\iff x+1=0\\\\\boxed{x=-1}[/tex]
Answer: B. -1

Simplify the square root of 864.
I cant remember this, please tell me how you got the answer.

Answers


[tex] \sqrt{864} [/tex]
[tex] \sqrt{4 \times 216} [/tex]
[tex] \sqrt{4 \times 4 \times 54} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 27} [/tex]
[tex] \sqrt{4 \times 4 \times 2 \times 9 \times 3} [/tex]
now take out the pairs.
[tex]4 \sqrt{2 \times 9 \times 3} [/tex]
take out any of the square roots like 9
[tex]4 \times 3 \sqrt{2 \times 3} [/tex]
Now put it all back together.
[tex]12 \sqrt{6} [/tex]
I believe that is the answer.

The difference of a number and 8 is the same as 34 less the number. find the number.

Answers

Let the number be x.

8 - x = x -34

2x = 8 + 34

2x = 42

x = 21

Answer: The number is 21.

Help me solve this please!

Answers

The problem statement suggests you use a calculator. A graphing calculator can give the answers you seek.

a) The calculator shows 5 solutions:
  {5π/23, 5π/17, 25π/23, 25π/17, 45π/23}
These have approximate decimal values of
  {0.6830, 0.9240, 3.4148, 4.6200, 6.1466}

b) The calculator shows 2 solutions with approximate decimal values of
  {1.2925, 4.4341}

c) The calculator shows 2 solutions with approximate decimal values of
  {1.3694, 4.9137}

_____
This (desmos) calculator displays intercepts to 3 decimal places. Since you want 4 decimal places, some additional refinement of the answer was necessary. That was accomplished using Newton's method iteration. The details are not shown. A suitable graphing calculator (for example, a TI-84) will supply the intercept coordinates to full calculator accuracy.

My brother owes me $10. I already have $10. My dads friend gave me and him $20 to split in half. He gave me the $20 and took my $10. Does he still owe me. Explain plz

Answers

Yes...     You have $10
               your brother is supposed to give you $10
               he gives you the money the friend told him to and you would have $20 PLUS the ten that he owes you. That would make you have $30. He took youre ten and gave you 20 but you were supposed to have 20 in the first place. He needs to give you the ten back he owes you. 

write an equation of an ellipse in standard form with the center at the origin and a height of 3 units and width of 1 unit

Answers

Final answer:

The equation of an ellipse with the specified attributes, using the center as the origin, is x2/0.25 + y2/2.25 = 1.

Explanation:

The question asks for the equation of an ellipse with the center at the origin and a height of 3 units and width of 1 unit. In an ellipse, the center is the midpoint of both the major and minor axes. The major axis can be the horizontal (width) or vertical (height) axis, and the minor axis is the other one.

Given that the height of the ellipse is 3 units, this determines the major axis and its length of 2a=3, which means a=1.5. The width of the ellipse is 1 unit, this determines the minor axis and its length of 2b=1, which means b=0.5.

Using these values, the equation of such an ellipse, centered at the origin, in standard form is x2/0.25 + y2/2.25 = 1

Learn more about Ellipse Equation here:

https://brainly.com/question/33868440

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Final answer:

The equation of an ellipse in standard form with the center at the origin, a height of 3 units and width of 1 unit is [tex]\(4x^2 + (y^2/2.25) = 1\).[/tex]

Explanation:

The equation of an ellipse in standard form with the center at the origin can be given by [tex]\(rac{{x^2}}{{a^2}} + rac{{y^2}}{{b^2}} = 1\)[/tex], where a is the semi-major axis and b is the semi-minor axis. Based on the information given in yourquestion, the height of the ellipse is 3 units which means the semi-major axis b is 1.5 units (since it's half the height). Similarly, the width of the ellipse is 1 unit which means the semi-minor axis a is 0.5 units (since its half the width). Substituting these values into the standard form of the ellipse we get: [tex]\(4x^2 + (y^2/2.25) = 1\)[/tex]

Learn more about Ellipse Equation here:

https://brainly.com/question/33868440

#SPJ12

What is the point-slope equation of the line with a slope 4/3 that goes through the point (-4,6)?

Answers

[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{6})~\hspace{10em}slope = m\implies \cfrac{4}{3}\\\\\\\begin{array}{|c|ll}\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-6=\cfrac{4}{3}[x-(-4)]\implies y-6=\cfrac{4}{3}(x+4)[/tex]

Answer:

The point-slope form of the equation is y - 6 = 4/3(x + 4), which is answer B.

Step-by-step explanation:

In order to find the point-slope form of any equation, start with the base form of the equation.

y - y1 = m(x - x1)

Now input the slope given as m, and the point in for x1 and y1.

y - y1 = m(x - x1)

y - 6 = 4/3(x - -4)

y - 6 = 4/3(x + 4)

A catapult is malfunctioning and not throwing objects in the intended manner. The builders have modeled the path of the objects thrown by using the following parametric equations. rewrite the parametric equations by eliminating the parameter.
x(t)=2t-1
y(t)= square root of t; t> or equal to 0

Answers

Answer:

The equation is [tex]y ^ 2 = \frac{x + 1}{2}[/tex]

Step-by-step explanation:

The parameter that we have is t. We want to eliminate this parameter in both equations, therefore in the first equation we solve for t and in the second equation we solve for the variable t.

We have:

[tex]x = 2t-1\\\\x + 1 = 2t\\\\t = \frac{x + 1}{2}[/tex]

Now we solve the other equation for t.

[tex]y= \sqrt{t}[/tex]

[tex]y ^ 2 = t[/tex]     because   [tex]t> 0[/tex]

As [tex]t = y ^ 2[/tex] and also [tex]t = \frac{x + 1}{2}[/tex]

Then:

[tex]y ^ 2 = \frac{x + 1}{2}[/tex]

The correct answer is:

D. [tex]x=2y^{2} -1, y\geq 0[/tex]

Alan is giving a basic math test in his class. One of the questions in the test is about finding two factors of the number 221. Which are the two factors of the given number? The two factors of the number 221 are ___ and ____.

Answers

1,13,17 are three of them 

The two factors of the number 221 are 13 and 17. 
A factor refers to a whole number, which fits evenly into another whole number. Thus, factors are the numbers, which we multiply together to get another number. The two numbers that can be multiply together to get 221 are 13 and 17.

giving brainliest please help, and give steps if possible. Im trying to learn this.

Answers

To find (fg)(x), you must mult. together the two binomial functions f and g:

(fg)(x) = (6-5x)(6x^2+x = 36x^2 + 6x - 30x^3 - 5x^2

and then you must combine like terms:   (fg)(x) = -30x^3 + 31x^2 + 6x

Answer:

[tex]f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]

Step-by-step explanation:

[tex](fg)(x) \\ (fx) = 6 - 5x \\ g(x) = {6x}^{2} + x \\ substitute \: and \: calculate: \\ f(x)g(x) = - 30x^{3} + 31 {x}^{2} + 6x[/tex]

Express answer in exact form.

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.

Answers

Hello,
Please, see the attached file.
Thanks.

A local movie theater charges $12 for an adult ticket and $10 for a child's ticket. a group of eight people spent a total of $86 on tickets to a movie. how many adults and how many children were in the group? write a system of linear equations based on the description. use x to represent the number of adults and y to represent the number of children.

Answers

3 adults and 5 kids. 

You can get this by setting up the following system of equations.

x + y = 8 (number of people)
10x + 12y = 86 (cost)

When he was 40 Keefer began investing $150 per month in various securities for his retirement savings. His investments averaged a 4.5% annual rate of return until he retired at age 70. What was the value of Keefer's retirement savings when he retired? Assume monthly compounding of interest.

Answers

At retirement, Keefer will have saved for 30 (that is, 70-40) years.
Monthly saving, P = $150, Annual rate of return, R = 4.5% = 0.045.

Therefore, future value (FV) at the time of retirement will be;

FV = P*[1+(R/12)^12*30]/(R/12)
Substituting all the parameters;
FV = 150*[1+(1+0.045/12)^360]/(0.045/12) = $113.907.92

PLEASE HELP 50 point will give brainlyest
Evaluate 81000−−−−√3 .


1/125

6/500

8/500

2/10

Answers

when I did it I got 140296.11541307
THE ANSWER IS B: 6/500 :) JUST LIKE IT AND VOTE ON IT PLZ THANK U AND HAVE A OOF DAY XD have a good day lel

A shell fits into a golden rectangle with a length of 8 in. What is the shell's width? write your answer is simplified radical form and rounded to the nearest tenth of an inch.
Select one:
a. About 4.9 inches
b. About 4.1 inches
c. About 5.3 inches

Answers

For this case we have the following relationship:
 l / w = (1 + root (5)) / 2
 Where,
 l: length of the rectangle
 w: width of the rectangle
 Clearing the width we have:
 w = (2 / (1 + root (5))) * (l)
 Substituting values:
 w = (2 / (1 + root (5))) * (8)
 Rewriting:
 w = 4.94427191 inches
 Rounding off we have:
 w = 4.9 inches
 Answer:
 the shell's width is:
 w = 4.9 inches
 a. About 4.9 inches

The correct answer is option(a) about 4.9 inches.

To find the width of a golden rectangle with a given length,  we will use the golden ratio formula  that is

l / w = (1 + √5) / 2

Where, l = length of rectangle &  w = width of rectangle

By applying the above formula we get  the golden ratio, which is ≈ 1.618.

The formula for a golden rectangle is length(l) = 1.618 × width.

Given that length is 8 inches, we set up the equation:

8 = 1.618 × width

Solving for width:

width = 8 / 1.618 = 4.948...

The simplified radical form of 4.948... is ≈ 4.9 inches.

Thus, the correct answer is about 4.9 inches or option (a).

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency

Answers

the answer is the third one

f''(x)<0 is the answer

A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute. To the nearest tenth of an inch, what is the diameter of each car wheel? (Note: 1 mile = 5,280 feet)

Answers

Answer: 21.8 inches

Given:

A car is traveling at a speed of 50 miles per hour. Each wheel of the car makes 770 revolutions per minute.

To get the diameter of each car wheel

Get first the length of revolution (circumference of the wheel) in inches.

Speed=50 miles/hr

=50miles/60 minutes

= 0.833333 miles/minute

=.833/5280=4400ft= 52,800 inches/minute

Since there are 770 revolutions per minute, per revolution  (circumference of the wheel) =

=52,800/770

=68.57 inches

Formula of diameter given the circumference is:

D=C/π 

D=68.57/3.14

D= 21.8 inches 

Answer:

21.8

Step-by-step explanation:

just took test

12x2 = 18x
i need someone to explain this

Answers

we have that
12x² = 18x------> 12x²-18x=0-----> divided by 12----> x²-(3/2)*x=0
this is the equation of a vertical parabola 
x²-(3/2)*x=0-----> x*(x-1.5)=0
the x-intercepts of the parabola are
x=0
x=1.5

using a graph tool
see the attached figure
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Which of the following can you infer about the Napoleonic Code from the map?It was influential in the development of legal systems throughout Europe.It was influential in Europe, but its influence did not spread overseas.It was short-lived in a few European countries, as most countries reverted back to their own legal systems.Most European countries rejected it. N a hearing test, subjects estimate the loudness (in decibels) of a sound, and the results are: 68, 67, 70, 71, 68, 75, 68, 62, 80, 73, 68. what is the mean? At the start of an experiment , there are 30 bacteria dish. The bacteria population is expected to grow at a rate of 180% each day. Which is the best prediction for the bacteria population after 7 years?A.51,750B.40,479C.2682D.1837 Which best explains why some radioisotopes decay in a decay series? Radioactive materials will always be radioactive. Multiple decays are always required to achieve stability. Some unstable materials decay radioactively into other unstable materials. Unstable materials have varying half-lives. Who chooses the prime minister? The press conference ending the russo-japanese war took place in which country? Ma asks patient why are you not following your diet how is the patient likely to act How many dimes in 1898.59 ___________ is the ability to understand that certain physical characteristics remain unchanged even when their outward appearance changes.a. conservationb. a formal operationc. stabilityd. a sensory operation The daily intakes of milk (in ounces) for ten randomly selected people were: 26.0 13.0 13.5 14.8 19.1 13.6 21.6 30.8 15.8 14.1 find a 99% confidence interval for the population standard deviation . dehydration synthesis definition A cylinder has a height of 16 cm and a radius of 5 cm. A cone has a height of 12 cm and a radius of 4 cm. If the cone is placed inside the cylinder as shown, what is the volume of the air space surrounding the cone inside the cylinder? (Use 3.14 as an approximation of .) 452.16 cm3 840.54 cm3 1,055.04 cm3 1,456.96 cm3 NextReset How does the latin language impact life in the united states? How many turning points are in the graph of the polynomial function?2 turning points3 turning points4 turning points5 turning points If the building absorbed so much heat that it turned into a liquid, then it would have undergone a phase change known as _____.freezingvaporizingcondensingmelting Jamal baked muffins for the school bake sale. He made 12 corn muffins and 15 blueberry muffins. What is the ratio of blueberry muffins to all muffins? How did the practice of imperialism push Europe toward World War I? Which would be a stronger electromagnet, the one with the larger coils (a) or the smaller coils (b)? Who does tireisias say is responsible for the plague? Which sentence uses an adverb of manner? A.The horses frequently galloped together. B.The horses once galloped together. C.The horses rapidly galloped together. D.The horses often galloped together.