Answers
Answer:
Option B is correct
the degree of rotation is, [tex]-90^{\circ}[/tex]
Step-by-step explanation:
A rotation matrix is a matrix that is used to perform a rotation in Euclidean space.
To find the degree of rotation using a standard rotation matrix i.e,
[tex]R = \begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex]
Given the matrix: [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
Now, equate the given matrix with standard matrix we have;
[tex]\begin{bmatrix}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix}[/tex] = [tex]\begin{bmatrix}0 & 1 \\ -1 & 0\end{bmatrix}[/tex]
On comparing we get;
[tex]\cos \theta = 0[/tex] and [tex]-\sin \theta =1[/tex]
As,we know:
[tex]\cos \theta = \cos(-\theta)[/tex][tex]\sin(-\theta) = -\sin \theta[/tex][tex]\cos \theta = \cos(90^{\circ}) = \cos( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
and
[tex]\sin \theta =- \sin (90^{\circ}) = \sin ( -90^{\circ})[/tex]
we get;
[tex]\theta = -90^{\circ}[/tex]
Therefore, the degree of rotation is, [tex]-90^{\circ}[/tex]
The degree of rotation represented on a matrix is measured in angles, such as degrees or radians.
Explanation:The degree of rotation represented on a matrix is typically measured in terms of angles, such as degrees or radians. In order to determine the degree of rotation on a matrix, you need to identify the angle of rotation.
If the matrix is rotated clockwise, the angle is considered negative (-). If the matrix is rotated counterclockwise, the angle is considered positive (+).
For example, if a matrix is rotated 90 degrees counterclockwise, the degree of rotation would be +90°.
Related Questions
The perimeter of a rectangle is 34 units. Its width is 6.5 units. Write an equation to determine the length of the rectangle.
Answers
Answer:
The length for a rectangle with a perimeter of 34 units and a width of 6.5 units would be 10.5 units.
Step-by-step explanation:
To find the length, you can use the equation [34 - (6.5 x 2) ÷ 2 = the length]. So, 6.5 x 2 = 13, then 34 - 13 = 21, finally, 21 ÷ 2 = 10.5 . So the length of the rectangle is 10.5 . To double check, (6.5 x 2) + (10.5 x 2) (=) 34. So this answer is correct.
Can I please get someone who is good at Geometry to help me? PLEASE AND THANK YOU!!!! (You just have to do problem A. Thanks again)
Answers
Answer:
x=6
Step-by-step explanation:
We can find < PMN by using the law of triangles.
The sum of the angles of a triangle adds to 180
<M + <N + < PMN = 180
32 + 64+ < PMN = 180
96 + < PMN = 180
Subtract 96 from each side
96 -96 < PMN = 180-96
< PMN =84
<PMN + <NPQ forms a straight line so it equals 180
<PMN + <NPQ=180
84 + <NPQ=180
Subtract 84 from each side
84-84 + <NPQ=180-84
<NPQ=96
<NPQ = 6x
96 = 6x
Divide each side by 6
96/6 = 6x/6
16 =x
Which of the functions below could have created this graph?
Answers
Answer:
A
Step-by-step explanation:
Two facts need to guide your answer.
One
The highest power is odd: you know this because an even power would start on the left come down do it's squiggles if had any and wind up on the right going up.
This graph comes down on the left does it's squiggles and then goes further down on the right. That's the behavior of something whose highest power is odd.
Two
The leading coefficient, the number in front of the highest power must be minus. If it was positive as in y = x^3 the graph would be the mirror image of what it is.
Argument
B and D cannot be true. The highest power is even.
C is false because the leading coefficient is + 1.
So that leave A which is the answer.
The graph is included with this answer
The position graph shown in the question represents an object that is undergoing uniform motion. To create this graph, you would need a linear function that describes linear motion.
Explanation:The position graph shown in the question represents an object that is undergoing uniform motion. Uniform motion occurs when an object travels at a constant speed in a straight line. The graph shows a linear relationship between position and time, with the object consistently moving in the same direction.
To create this graph, you would need a function that describes linear motion. A linear function in the form of y = mx + b, where y represents position, x represents time, m represents the slope (rate of change of position with respect to time), and b represents the initial position. The slope of the line in the graph represents the speed of the object.
For example, the function y = 2x would create a position vs. time graph with a slope of 2, indicating that the object is moving at a constant speed of 2 units per time interval. Similarly, any other linear function with a constant slope could create this graph.
Jack's pancakes recipe calls for 2 teaspoons baking powder and 3 cups of flour. How how much baking powder is needed if Jack uses 9 cups of flour
Answers
Answer:
6
Step-by-step explanation:
Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
To determine how much baking powder is needed if Jack uses 9 cups of flour instead of 3, you can set up a proportional relationship because the quantity of baking powder required is directly proportional to the amount of flour used.
If the original recipe calls for 2 teaspoons of baking powder for every 3 cups of flour, for 9 cups of flour (which is 3 times as much), you would need 3 times as much baking powder. Hence, the calculation would be as follows:
2 teaspoons baking powder / 3 cups flour = x teaspoons baking powder / 9 cups flour
By cross-multiplication, we can find the value of x:
2/3 * 9 = x
x = 2 * 3 = 6 teaspoons of baking powder
Therefore, Jack would need 6 teaspoons of baking powder for 9 cups of flour to maintain the ratio given in the original recipe.
What Is the Slope And Y Intercept Of This Line?
Y = X -5
Answers
Answer:
slope = 1 , y- intercept = - 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = x - 5 is in this form
with slope m = 1 and y- intercept c = - 5
"If a - 7 = b(x + 2), then x = ?"
Please help!!!!
I need a step by step explanation too.
Answers
Answer: choice (3), x = (2b+7)/(a-b)
==============================
Explanation:
The idea is to get all the x terms to one side (after distributing), then factoring out the common term x, finally divide both sides by (a-b) as shown below
ax-7 = b(x+2)
ax-7 = bx+2b .... distribute
ax-7+7 = bx+2b+7 ... add 7 to both sides
ax = bx+2b+7
ax-bx = bx+2b+7-bx ... subtract bx from both sides
ax-bx = 2b+7
(a-b)x = 2b+7 .... factor out the GCF x
x = (2b+7)/(a-b) ... divide both sides by (a-b)
We have all of "2b+7" over "a-b" as one big fraction. This is what choice (3) is showing.
Question 3(Multiple Choice Worth 5 points) (06.08A) Simplify negative 15.5 divided by 5 .. −3.1 3.1 −3.3 3.3
Answers
A negative divided by a positive gives a negative result
So the answer is -3.1
Hope this helps!
this was correct on my test, hope it helps! ;)
(Brainliest would help a lot btw)
Which of the following could be the equation of the function below?
Answers
Answer:
Option C is the correct option.
Step-by-step explanation:
In the given cosine graph we can draw some parameters of the equation as below
y = a cos(bx + c) + d
1) amplitude a = (1+3)/2=2
2) Period = π
3) phase shift = -π ( to the left)
4) Vertical shift = -1 ( downwards on y-axis)
Therefore the equation of the graph will be
y = -2cos[2(x + π)] - 1
Option C is the correct answer.
Use the diagram to answer the question
Line m is parallel to line p. M angle HEF IS 39 degrees. And m IGF is 13 degrees. Find the m EFG. Explain in detail how you know you are correct. I WILL MARK THE BRAINLIEST
Answers
Answer:
[tex]m\angle EFG=52^{o}[/tex]
Step-by-step explanation:
We have been given that line m is parallel to line p, [tex]m\angle HEF=39^{o}[/tex] and [tex]m\angle IGF=13^{o}[/tex].
Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.
We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.
We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.
[tex]m\angle EFG=m\angle IGF+m\angle EJG[/tex]
Upon substituting our given values we will get,
[tex]m\angle EFG=13^{o}+39^{o}[/tex]
[tex]m\angle EFG=52^{o}[/tex]
Therefore, measure of angle EFG is 52 degrees.
I do not get this. Evaluate.
Simplify your answer as much as possible.
3!6!/5!2!
Answers
Answer:
18
Step-by-step explanation:
[tex]\frac{3!6!}{5!2!}[/tex]
n! = n * (n-1)!
For example 7! can be written as 7 * 6!
3! is 3* 2!
6! is 6 * 5!
[tex]\frac{3!6!}{5!2!}[/tex]
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
Cancel out 5! from the top and bottom . Also cancel out 2! from top and bottom.
[tex]\frac{3*2!6*5!}{5!2!}[/tex]
3*6= 18
what is the midpoint between -9 and 15 on the number line? A. 3
B. 12
C. 6
D. 2
Answers
Answer:
A. 3
Step-by-step explanation:
To find the midpoint between two numbers, we add the two numbers and divide by 2
midpoint = (x1+x2)/2
midpoint = (-9+15)/2
midpoint = (6)/2
midpoint =3
Plz I need by tonight
Answers
Answer: Yes
Step-by-step explanation: 4x5 is 20 + 2 is 22 then when you multiply that by 9 you get 198
36x5 is 180 + 18 is 198
Both answers equal each other
which is greater .513 or .5129
Answers
Answer:
.513 is larger
Step-by-step explanation:
1st method is the thousandths place larger or smaller
.1 tenths
.01 hundredths
.001 thousandths
In this case the thousandths is larger for .513
2nd method
subtract the two number
.513 - .5129 = .0001
Since the number recieved is positive this means .513 is larger
Which factors can be multiplied together to make the trinomial 5x2 + 8x – 4? Check all that apply. (x + 1) (2x + 1) (x + 2) (5x + 1) (5x – 2) Mark this and return Save and Exit
Answers
Answer:
(5x-2) and (x+2)
Step-by-step explanation:
Answer:
the factors are (5x-2) and (x+2)
Step-by-step explanation:
5x^2 + 8x – 4
first we multiply 5 and -4= -20
product is -20 and sum is +8
find out two factors whose product is -20 and add upto +8
10 * (-2) = 20
10 +(-2)= 8
5x^2 +10x-2x – 4
group the terms and factor out GCF
(5x^2 +10x)+(-2x – 4)
5(x+2) -2(x+2)
(5x-2)(x+2)
the factors are (5x-2) and (x+2)
Ashley is the utilities manager at a paper mill. She's watching over one of her holding tanks. It takes of an hour to fill the tank. At this rate, how many holding tanks will she fill in 1 hour?
Answers
Answer: 5/8
Step-by-step explanation:
Consider the steps to simplify the expression. Which property is used to reach Step 3?
Expression: -4
3
7
+ 7 + (-3
4
7
)
Step 1: = -4
3
7
+ (-3
4
7
) + 7
Step 2: = -4 + (-
3
7
) + (-3) + (-
4
7
) + 7
Step 3: = -4 + (-
3
7
) + (-
4
7
) + (-3) + 7
Step 4: = -4 + (-1) + (-3) + 7
Step 5: = -8 + 7
Step 6: = -1
A) The associate property of addition.
B) The commutative property of addition.
C) The opposite of a sum is the sum of its opposites.
D) Subtracting a number is the same as adding its inverse.
Answers
NOTE: I ACCIDENTALLY clicked one star. That DOES NOT count as a real rating, and this DOES NOT mean my answer is bad!
Answer:
Commutative Property of Addition
Step-by-step explanation:
Step 2: -4 + (-37) + (-3) + (-47) + 7
Step 3: -4 + (-37) + (-47) + (-3) + 7
Because the order was changed, it is the Commutative Property.
Find all the zeros of the quadratic function:
y=x^2+15x+36
Answers
Answer:
x=-12 and -3
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. We will substitute a=1, b=15 and c=36.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-15+/-\sqrt{(15)^2-4(1)(36)} }{2(1)}\\x=\frac{-15+/-\sqrt{225-144} }{2}[/tex]
We will now simplify and solve.
[tex]x=\frac{-15+/-\sqrt{81}}{2}\\x=\frac{-15+/-9}{2}[/tex]
x=-12 and x=-3
Find the slip of the line that passes through each pair of point (-6,1), (4,8).
Answers
X1 = -6
Y1= 1
X2= 4
Y2 = 8
8 - 1
____
4 + 6
7
_ is your answer
10
Marshall Earns a salary of 36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise. How many years will it take before Marshall and Jim earn the same salary
Answers
Answer:
It will take 6 years
Step-by-step explanation:
Marshall starts at 36,000 dollars and Jim starts at 51,000, multiply the pay raises by 6 and for Jim you get $9,000 and Marshall gets $24,000 pay raise in 6 years.
Sorry If It Is a bit confusing, I'm not really good with words. :/
Both of them will get the same salary after 6 year.
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, Marshall Earns a salary of $36,000, and each year he receives a $4,000 raise. Jim earns a salary of $51,000, and each year he receives a $1,500 raise.
Let x be the year in which they will get the same salary
Establishing the equation, we get
36000+4000x = 51000+1500x
Simplifying the equation,
36+4x = 51+1.5x
2.5x = 15
x = 6
Hence, Both of them will get the same salary after 6 year.
For more references on equations, click;
https://brainly.com/question/29657983
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20 Points!! Will give Brainliest!!! Need Help ASAP!!! PLzz!!
Ray knows that the m<3 = m<6.
Which of the following conclusions can Ray make based on the given information?
A. Lines l and m are parallel because alternate interior angles are equal.
B. Lines l and m are parallel because alternate exterior angles are equal.
C. Lines l and m are parallel because corresponding angles are equal.
D. No conclusion can be made about the lines.
Answers
Answer:
The answer is B
Step-by-step explanation:
3 and 6 are alternate exterior angles which make lines l and m parallel.
Answer: c
Step-by-step explanation:
In trapezoid ABCD AC is a diagonal and ∠ABC ≅ ∠ACD. Find AC if the lengths of the bases BC and AD are 14m and 28m respectively.
Answers
Answer:
[tex]AC=14\sqrt{2}m[/tex]
Step-by-step explanation:
we are given trapezoid ABCD
AC is a diagonal
∠ABC ≅ ∠ACD
we know that
BC and AD are parallel
so, <DAC = <ACB
so, ΔABC ≅ΔACD
Since, both triangles are similar
so, their ratios must be equal
we get
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now, we can plug values
[tex]\frac{14}{AC} =\frac{AC}{28}[/tex]
[tex]AC^2=14\times 28[/tex]
[tex]AC^2=14^2\times 2[/tex]
[tex]AC=14\sqrt{2}m[/tex]
To find the length of AC, the diagonal in trapezoid ABCD, we can use the fact that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD. By setting up a proportion using the corresponding sides of the similar triangles ABC and ACD, we can find that AB/AC = 1/2. Multiplying the length of AB by 2 gives us AC = 28m.
Explanation:Given that ∠ABC ≅ ∠ACD and the lengths of the bases BC and AD are 14m and 28m respectively, we can find the length of AC, which is a diagonal in trapezoid ABCD.
Because the two angles are congruent, triangle ABC is similar to triangle ACD. This means their corresponding sides are proportional.We can set up a proportion using the corresponding sides of the triangles:BC/AD = AB/ACSubstituting the values, we get 14/28 = AB/AC. Simplifying this equation gives us AB/AC = 1/2.Since the lengths of AB and AC have a ratio of 1/2, we can determine AC by multiplying the length of AB by 2.Therefore, AC = 2 * AB = 2 * 14 = 28m.
A kite, flying 50 feet high in the air is attached by a string to a stake in the sand. How long is the string to the nearest tenth of a foot? A) 50.0 feet B) 70.7 feet C) 77.9 feet D) 88.6 feet
Answers
we need at least 2 values to find the length. (3 if it's not a right triangle)
do we know the angle? the horizontal distance? what other information is given?
Answer:
Hello, the answer tho this question is C.) 70.7 feet.
If you roll 2 dice, what is the probability that the sum is 9?
thanks :) will give brainliest!
Answers
Answer:
0.1111%
Step-by-step explanation:
2 dice, each with 6 sides. 36 possible outcomes.
Possible sums for 9 are 1,8 2,7 3,6 4,5
That means there is only 4 possible ways to get 9 out of 36 possible outcomes. 4/36 is your probability
the ratio of 6th graders to 7th graders at a basketball game is 4:1. if there are eight 6th 7th graders how many 6th graders are there
Answers
Answer:
if there are 8 7th graders there are 32 6th graders. 4*8=32
Step-by-step explanation:
How to write 21/6 as a mixed number
Answers
3 and 3 over 6
The calculated fraction 21/6 to a mixed number is 3 1/2
How to change the fraction 21/6 to a mixed numberFrom the question, we have the following parameters that can be used in our computation:
Number = 21/6
Divide 21 by 6
So, we have
Quotient = 3
Next, we have
Remainder = 21 - 6 * 3
Evaluate the products
Remainder = 3
So, we have
Fraction = 3 3/6
Simplify
Fraction = 3 1/2
Hence, the fraction to a mixed number is 3 1/2
Read more about fraction at
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6a. Suppose you need to find a box that you can fit your cube-shaped gift into. You know that you will need to find a box that is 4 inches longer than the cube’s length, 3 inches wider than the cube’s width, and 7 inches taller than the cube’s height. Create a polynomial that represents the gift box’s volume in terms of the cube’s length/width/height, in factored and standard form
Answers
Answer:
( l + 4) * ( w + 3 ) * ( h + 7)
let l represent the length, w represent the width, and h represent the height of your cub-shaped gift.
Though, if your gift is in the shape of a cube, that would mean all the sides are the same length.
( 2 + 4 ) * ( 2 + 3 ) * ( 2 + 7 )
6 * 5 * 9 = 270
(I haven't done geometry in awhile though, so this may be incorrect unless it actually makes sense.)
Answer:
V = (x+ 4)(x + 3)(x + 7); V = x³ + 14x² + 61x + 84
Step-by-step explanation:
Let x = the side of the cube
Then the dimensions of the gift box are
l = x + 4
w = x + 3
h = x+ 7
V = lwh
V = (x+ 4)(x + 3)(x + 7) Multiply the first two terms
V = (x² + 7x + 12)(x+ 7) Remove parentheses
V = x³ + 14x² + 61x + 84
If there’s a negative before brackets you do the opposite terms right?
Answers
Answer:Yes
Step-by-step explanation:
When the negative is on the outside of the bracket you distribute the negative to each term inside the parentheses.
Answer:
yes you would change the signs that are inside the parenthesis
Step-by-step explanation:
you do so because the negative outside the parenthesis mean you are distributing the negative to the terms.
Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces. what is true about the length of each piece of fabric. I need the answer as a fraction.
Answers
.6=6/10
6/10=3/5
Answer:
The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
Step-by-step explanation:
Given : Dai has 3 meters of fabric that he wants to cut into 5 equal sized pieces.
To find : What is true about the length of each piece of fabric ?
Solution :
Dai has 3 meters of fabric.
He cuts the fabric into 5 equal sized pieces.
So, The length of each piece is defined as
[tex]L=\frac{3}{5}[/tex]
Therefore, The length of each piece of fabric is [tex]L=\frac{3}{5}[/tex]
Wells college Aurora New York Was previously an all girls college.In 2005 the college began to allow boys to enroll.By 2012 The ratio of boys to girls was 3 to 7. If there were 200 more girls than boys in 2012 how many boys in enrolled that year
Answers
Answer:
150
Step-by-step explanation:
The ratio of boys to girls is 3 to 7.
We don't know the number of boys or girls. The number of boys and the number of girls are multiples of 3 and 7, respectively. Since they are in the ratio of 3 to 7, then by multiplying both 3 and 7 by the same number, you will get the number of boys and the number of girls. We need to find that number. Call that number x.
The ratio of boys to girls is:
3x to 7x
There are 3x boys and 7x girls.
The number of girls is 200 more than the number of boys.
7x = 3x + 200
Subtract 3x from both sides.
4x = 200
Divide both sides by 4.
x = 50
The number of boys is 3x, so
3x = 3(50) = 150
150 boys and 350 girls were enrolled that year.
Since a college was previously an all girls college, and then it began to allow boys to enroll, and by 2012 the ratio of boys to girls was 3 to 7, to determine, if there were 200 more girls than boys in 2012, how many boys were enrolled that year, the following cross multiplication calculation must be performed:
7 - 3 = 200 3 = X 4 = 200 3 = X 3 x 200/4 = X 600/4 = X 150 = X 150/3 = 50 (150 + 200) / 3 = 50
Therefore, 150 boys and 350 girls were enrolled that year.
Learn more in https://brainly.com/question/13904768
In a triangle the sides has 82 degrees ,2x+10 degrees and x degrees what is x
Answers
Answer:
x = 29 1/3 degrees
Step-by-step explanation:
A triangle has 3 angle that total 180 degrees.
The three angles given are 82 degrees ,2x+10 degrees and x degrees.
So,
82+ (2x+10) + x = 180
Combine like terms.
92 + 3x = 180
Subtract 92 from each side
3x = 180 -92
3x = 88
divide each side by 3
3x/3 = 88/3
Change 88/ 3 to a mixed number
3 goes in to 88 29 times with 1 left over.
x = 29 1/3 degrees