[tex]A=5m^4\times6m^2=\boxed{30m^6}[/tex]
What is the volume of a cylinder with base radius 3 and height 6?
Volume = 54π units³
Work is attached in the image provided.
Which number line shows the solutions to n > - 2
Answer:
C The shaded circle
Step-by-step explanation:
numbers greater than -2
-1,0,1,2,3....
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There are 13 bagels in a baker's dozen. Hillary,Mark, and Tam share the bagels equally. Will each friend get more than or fewer than 4 whole bagels? Explain.
Answer:
Each friend will get more than 4 whole bagels.
Step-by-step explanation:
First off, although the question asks for 13 bagels divided between 3 friends, let's use a number that results in a whole number when divided by 3, but is close to 13.
This number can be 12.
12 divided by 3 is 4, so each friend gets 4 bagels if there are a total of 12 bagels.
However, there are more than 12 bagels so we know that each of the the 3 friends will get more than 4 bagels each.
Each friend will get 4 whole bagels, with 1 bagel left over.
Explanation:In a baker's dozen, there are 13 bagels. Hillary, Mark, and Tam share the bagels equally. To determine if each friend will get more than or fewer than 4 whole bagels, we divide the total number of bagels by the number of friends.
13 bagels / 3 friends = 4 remainder 1
Each friend will get 4 whole bagels, with 1 bagel left over.
Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient.
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The symbol 5! means 5* 4*3*2*1. What is the greatest odd integer that is a factor of 5!?
Answer:
15
Step-by-step explanation:
5 ! = 120
Since 5 ! = 5 × 4 × 3 × 2 × 1, then
5 × 3 = 15 is the greatest odd factor of 5 !
The greatest odd integer that is a factor of 5 factorial (5!) is 5. This is because the definition of factorial involves multiplying a number by every number below it until reaching 1 and 5 is the largest odd number within this range.
Explanation:The greatest odd integer that is a factor of 5! (or 5 factorial) is 5. The factorial, represented by the symbol '!', is a function that multiplies a number by every number below it until it reaches 1. For example, 5! means 5 * 4 * 3 * 2 * 1. To find the greatest odd integer that is a factor of 5!, you simply need to identify the largest odd number that is a part of this multiplication, which is 5.
Let's clarify this with some simple math. Start from the number 5 itself, then move down: 5 (it's an odd number), 4 (it's even, exclude), 3 (it's odd, but less than 5), 2 (it's even, exclude), 1 (it's odd, but less than 5). Hence, the largest odd integer that is a divisor of 5! is 5.
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The area of a rectangle is [tex]14ft^2[/tex], and the length of the rectangle is [tex]3ft[/tex] less than twice the width. Find the dimensions of the rectangle.
Answer:
So, Width = 7/2 or 3.5
Length = 4
Step-by-step explanation:
Area of rectangle = 14 ft^2
Let width of rectangle 2 = x
and Length of rectangle = 2x-3
Formula used for area of rectangle
Area = Length * Width
14 = (2x - 3) x
14 = 2x^2 - 3x
=> 2x^2 -3x -14 = 0
Solving the quadratic equation using factorization
-28 x^2 = -7x * -4x
2x^2 -7x + 4x -14 = 0
x (2x -7) +2(2x-7) = 0
(x+2) (2x-7) =0
=> x + 2 =0 and 2x -7 = 0
x = -2 and x = 7/2
Since width cannot be negative so, x= 7/2
Width= x = 7/2
Length = 2x -3 => 2(7/2) - 3
=> 7 -3
=> 4
So, Width = 7/2 or 3.5
Length = 4.
Length= 2width-3
Width=x
Length=2x+3
X(2x-3)=14
x must equal 3.5
Length=4
Width=3.5
Use the data set below to answer the following question.
2,4,7,2,3,7,9,3, 1,7
What is the mean absolute deviation (MAD) of this data set?
3.5
2.4
4.5
1.2
Answer:
2.4
Step-by-step explanation:
We have to find the mean first
[tex]Mean = \frac{Sum}{No.\ of\ values}\\ = \frac{2+4+7+2+3+7+9+3+1+7}{10}\\ = \frac{45}{10}\\ = 4.5[/tex]
Now we have to find deviations.
Note that the deviations are calculated by subtracting the mean from the value. The distance is always positive so the deviations will be positive
Value Deviation
2 2-4.5 = |-2.5| = 2.5
4 4-4.5 = |-0.5| = 0.5
7 7-4.5 = 2.5
2 2-4.5 = |-2.5| = 2.5
3 3-4.5 = |-1.5| = 1.5
7 7-4.5 = 2.5
9 9-4.5 = 4.5
3 3-4.5 = |-1.5| = 1.5
1 1-4.5 = |-3.5| = 3.5
7 7-4.5 = 2.5
The last step is to find the mean of deviations.
[tex]Mean\ of\ deviations = \frac{(2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5}{10}\\ = \frac{24}{10} \\=2.4[/tex]
The mean absolute deviation of given data set is 2.4 ..
Suppose that ym has length 12 in. and its distance from point L is 5 in. Find the radius of ⊙L to the nearest tenth.
Answer:
The radius of circle L is [tex]7.8\ in[/tex]
Step-by-step explanation:
Remember that a line that passes through the center divide the circle into two equal parts
YV=VM=6 in
VL is perpendicular to YM
so
The triangle VLM is a right triangle
The radius is equal to LM ----> hypotenuse of the triangle VLM
Applying the Pythagoras Theorem
[tex]LM^{2}=VM^{2}+VL^{2}[/tex]
substitute the given values
[tex]LM^{2}=6^{2}+5^{2}[/tex]
[tex]LM^{2}=61[/tex]
[tex]LM=7.8\ in[/tex]
Can someone help me please
Answer:
2
Step-by-step explanation:
Step 1: Take the cube root of 8.
[tex] \sqrt[3]{8} = 2[/tex]
Answer:
The answer is 2.
Step-by-step explanation:
We need to find the value of
[tex]\sqrt[3]{8}[/tex]
We know ∛ = 1/3
and 8 = 2*2*2
2*2*2 can be written as 2^3 solving:
[tex]=\sqrt[3]{8} \\\\=\sqrt[3]{2*2*2}\\ =\sqrt[3]{2^3}\\= (2^3)^{1/3}\\= 2[/tex]
So, The answer is 2.
Josh made his school basketball team this year. He played 10 minutes in his first game, but he played twice that amount in each of the other games. Let y represent the total number of minutes Josh played in x games.
Which type of sequence does the situation represent?
A.
The situation represents an arithmetic sequence because the successive values have a common difference of 10.
B.
The situation represents an arithmetic sequence because the successive values have a common difference of 20.
C.
The situation represents a geometric sequence because the successive values have a common ratio of 2.
D.
The situation represents a geometric sequence because the successive values have a common ratio of 5.
Answer:
B. The situation represents an arithmetic sequence because the successive values have a common difference of 20.
Step-by-step explanation:
(x, y) values appear to be ...
(1, 10) . . . . 10 minutes played in the first game
(2, 30) . . . 20 minutes played in the second game, adding 20 to the total
(3, 50) . . . 20 minutes played in the third game, adding 20 to the total
From here, we can see that each additional game adds 20 minutes to the total (y), so the sequence is ...
an arithmetic sequence because the successive values have a common difference of 20
PLease Help i need it
What side length would be possible for a triangle if you already know the other two lengths are 19cm and 32cm
Please explain step by step
Answer:
13 < n < 51
Explanation:
Basically to find the lowest possible length, all you need to do is subtract the lower number from the higher number (32 - 19), and to find the greatest possible length, add the lower number and the higher number (32 + 19). Then you'd plug it in to this inequality: a < n < b, a being the difference, and b being the sum. But, if the triangle were a right triangle that would be a whole different story.
Scientists can estimate the depth of craters on the moon by studying the lengths of their shadows in the craters. Find the depth of a crater, if the shadow is estimated to be 400 m long and the angle of elevation of the sun is 48°.
It's a much more interesting problem when we have to estimate the shadow length from a photo.
The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.
The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.
[tex] d = 400 \sin 48 \approx 297 \textrm{ m}[/tex]
Answer: 297 m
The depth is 297.26 m.
Height and distanceIt is the application of trigonometry.
Right angle triangleIt is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.
Given
The shadow is estimated to be 400 m long.
And the angle of elevation of the sun is 48°.
To findThe depth of a crater.
How to get the depth of a crater?Hypotenuse = 400m
Angle = 48°
The by the sine rule
[tex]\begin{aligned} \rm sin \theta &= \rm \dfrac{Depth}{Hypotenuse}\\\\\rm sin 48^o &= \rm \dfrac{depth}{400}\\\\\rm depth &= \rm sin 48^o * 400\\\\\rm depth &= 297.2579 \approx 297.26 \end{aligned}[/tex]
Thus, the depth is 297.26 m.
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PLEASE HELP Match each function formula with the corresponding transformation of the parent function y = - (x + 2)2. 1. y = - (x + 4)2 Reflected across the x-axis and the y-axis 2. y = - (x + 2)2 - 2 Translated right by 2 units 3. y = (x - 2)2 Translated left by 2 units 4. y = 2 - (x + 2)2 Translated down by 2 units 5. y = -x2 Translated up by 2 units 6. y = (x + 2)2 Reflected across the x-axis
So we are given the following function: [tex]y=-(x + 2)^{2}[/tex].
Before we can solve this problem, we need to know the following:
Given g (x) = f (x) + k; The graph of g(x) equals f(x) shifted k units vertically. If k > 0, the base graph shifts k units upward, and if k < 0, the base graph shifts k units downward. Given g(x) = f (x - k); The graph of g(x) equals f(x) shifted k units horizontally. If k > 0, the base graph shifts k units to the right, and if k < 0, the base graph shifts k units to the left.The reflection of the point (x,y) across the x-axis is the point (x,-y).The reflection of the point (x,y) across the y-axis is the point (-x,y).Know we can solve the problem!
1. [tex]y=-(x + 4)^{2}[/tex]. Translated left by 2 units.
2. [tex]y=-(x + 2)^{2} - 2 [/tex] Translated down by 2 units
3. [tex]y=(x - 2)^{2}[/tex] Reflected across the x-axis and the y-axis
4. [tex]y= 2-(x + 2)^{2}[/tex] Translated up by 2 units
5. [tex]y=-(x)^{2}[/tex] Translated right by 2 units
6. [tex]y=(x + 2)^{2}[/tex] y = (x + 2)2 Reflected across the x-axis
the area of a rectangle is represented by x^2 - 5x - 14. what are the dimensions?
Answer:
Step-by-step explanation:
A = x² - 5x - 14
Factor using AC method. Here, a = 1, b = -5, and c = -14.
ac = 1×-14 = -14
Factors of -14 that add up to -5 are -7 and 2.
A = (x - 7)(x + 2)
So the dimensions are x-7 and x+2.
The dimensions of the rectangle represented by the quadratic equation x² - 5x - 14 could be 7 and -2, but in a physical context we only consider the positive value 7.
Explanation:The area of a rectangle is given by multiplying its length and width. In this case, the area is expressed as a quadratic equation, x² - 5x - 14 = 0. Quadratic equations typically represent parabolas when graphed on a two-dimensional plot, but in this case, we're looking for linear dimensions of a rectangle. To find the dimensions of the rectangle, we need to factor this equation.
The factors of this quadratic equation are (x - 7) and (x + 2). Therefore, the two dimensions of the rectangle could be 7 and -2. However, in real-world scenarios, dimensions are often positive values due to physical constraints (you can't have a rectangle with negative length or width). So, normally, we would only consider the dimension of 7 (from the factor x - 7) as the real solution to this problem.
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3x-8y=-16 -5x-10y=7 give y intercept
Answer:
3x-8y=-16
The y intercept is;
(0, 2)
-5x-10y=7
The y intercept is;
(0, -0.7)
Step-by-step explanation:
The y-intercept refers to the point where the graph of an equation intersects or crosses the y-axis. At this point, the corresponding value of x is 0.
From the first equation given;
3x-8y=-16
Substitute x with 0 in the equation and solve for y;
3(0) -8y = -16
-8y = -16
y = 2
The y intercept is thus;
(0, 2)
From the second equation;
-5x-10y=7
Substitute x with 0 in the equation and solve for y;
-5(0) - 10y = 7
-10y = 7
y = -0.7
The y intercept is thus;
(0, -0.7)
What is the solution to the system of equations? Use the linear combination method. {2x−3y=93x+5y=4 Enter your answer in the boxes. ( , )
Answer:
(36.692,-6.538) or simplified (36.7,-6.5)
Step-by-step explanation:
2x-3y=93
x+5y=4
You would multiply both sides of the bottom equation by -2
-2(x+5y)=4(-2) > -2x-10y=-8
2x-3y=93
+ -2x-10y=-8
---------------------
-13y=85
divide both sides by -13
y=-6.538
plug in y for any of the two original equations, I chose the first one
2x-3(-6.5)=93
2x+19.5=93
-19.5 -19.5
2x=73.5
divide both sides by 2
x=36.692
Answer:
3 and -1
Step-by-step explanation:
Took the test.
what is indirect measurement
Answer:
Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.
Answer/ Explanation:
Indirect Measurement is a method of measuring liquids, gas or solids within a system indirectly. This method is utilized when there are no means of direct methods of measurement available.
Have a nice day :]
Alison's car travels at 65 miles per hour. How far does she travel in 4.5 hours?
Answer:
292.5 miles
Step-by-step explanation:
Ok so what you want to do is multiply 4.5 and 65 together.
She travels at 65 miles per hour and she travels for 4.5 hours
You have averaged $62,500.00 for the last five years of work. Your company has agreed to pay you a yearly pension of 75 %. What is your yearly pension?
[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of 62500}}{\left( \cfrac{75}{100} \right)62500}\implies 46875[/tex]
2sqrt3 +2i to polar representation
Recall that
[tex]\cos\dfrac\pi6=\dfrac{\sqrt3}2[/tex]
[tex]\sin\dfrac\pi6=\dfrac12[/tex]
Then
[tex]2\sqrt3+2i=4\left(\dfrac{\sqrt3}2+\dfrac12i\right)=4\left(\cos\dfrac\pi6+i\sin\dfrac\pi6\right)=4e^{i\pi/6}[/tex]
Find the exact circumference of a circle with the given radius 5” c=?
Answer: 10pi
Step-by-step explanation:
C=2*pi*r
C=2*pi*5
C=10*pi (exact)
This is exact if u want numbers, you’ll have to round-off and you can just put 10xpi into a calculator If u want to see.
Answer:
C = 31.42
Step-by-step explanation:
radius = 5
C = 2 π r
C = 2 · π · 5
C = 31.41593
then you round so it equals 31.42 instead
−6⋅f(−3)−5⋅g(−7) = ?
Answer:
-12
Step-by-step explanation:
According to the graph, [tex]f(-3)=-3[/tex] and [tex]g(-7)=6[/tex]
When given the equation [tex]-6*f(-3)-5*g(-7)[/tex] we can substitute in the values on the graph that we have found.
[tex]-6*f(3)-5*g(-7)\\\\-6*(-3)-5*(6)\\\\18-30=-12[/tex]
An animal shelter spends $5.50 per day to care for each bird and $8.50 per day to care for each cat. Anna noticed that the shelter spent $291.50 caring for birds and cats on Thursday. Anna found a record showing that there were a total of 41 birds and cats on Thursday. How many birds were at the shelter on Thursday?
Answer:
19
Step-by-step explanation:
We can solve this problem using a system of equation in two unknowns.
Let b = number of birds.
Let c = number of cats.
The care of a bird costs $5.50, so for b number of birds, the cost of care is 5.5b.
The care of a cat costs $8.50, so for c number of cats, the cost of care is 8.5c.
The total cost of care for the birds and cats is 5.5b + 8.5c.
The total cost of care is $291.50. This must equal the expression we have above, so we get our first equation.
5.5b + 8.5c = 291.5
The total number of birds and cats is b + c, but we are told it is 41, so our second equation is:
b + c = 41
We now have the following system of two equations in two unknowns.
5.5b + 8.5c = 291.5
b + c = 41
Rewrite the first equation.
Multiply both sides of the second equation by -8.5, and write it under the first equation. Then add the equations.
5.5b + 8.5c = 291.5
+ -8.5b - 8.5c = -348.50
--------------------------------------
-3b = -57
Divide both sides of the equation by -3.
b = 19
Answer: there were 19 birds
By defining the number of birds and cats as variables and setting up a system of equations, we solved for the number of birds to be 19.
Let's define the number of birds as b and the number of cats as c. From the problem, we have the following equations:
b + c = 41 (total number of birds and cats)
5.50b + 8.50c = 291.50 (total cost of caring for birds and cats)
To solve for the number of birds, we follow these steps:
Step 1: Express the number of cats in terms of birds.
From the first equation, we get:
c = 41 - b
Step 2: Substitute this expression into the second equation.
5.50b + 8.50(41 - b) = 291.50
Expand and simplify the equation:
5.50b + 348.50 - 8.50b = 291.50
Combine like terms:
-3b + 348.50 = 291.50
Step 3: Solve for b.
Subtract 348.50 from both sides:
-3b = 291.50 - 348.50
-3b = -57
Divide both sides by -3:
b = 19
Therefore, there were 19 birds at the shelter on Thursday.
There are 52 people in a conference room.
The ratio of females to males in the room is 15 to 11.
How many females need to leave the room so that the ratio of females to males
in the room is 1 to 1?
8 Females have to leave the room which then it would be 22 males and 22 females which is a 1-1 ratio
A ratio shows us the number of times a number contains another number. The number of females who should leave the conference room is 8.
What is a Ratio?A ratio shows us the number of times a number contains another number.
The ratio of females to males in the room is 15 to 11, therefore, the numbers of female to male ratio can be represented by 15x to 11x.
The sum of the total number of people in the room is 52, and can be represented as,
15x + 11x = 52
26x = 52
x = 2
Thus, the number of females in the conference room is 30(15x=15×2), while the number of males in the conference room is 22(11x=11×2).
Now, for the ratio to be 1:1, the number of males should be the same and the number of females should be equal to the number of males. Therefore, the number of females who should leave the conference room is,
Number of females who should leave conference room = Number of females before - Number of females after
Number of females who should leave conference room = 30 - 22 = 8
Hence, the number of females who should leave the conference room is 8.
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25 points
Please explain your answer, thank you!
Which expression is not a polynomial?
A. -5x+6y
B. -3/x
C. 2p^3q^2-pq^3
D. 7-z
Answer: The correct answer is: [B]:
_________________________________________
" [tex]\frac{-3}{ x}[/tex] " .
_________________________________________
Step-by-step explanation:
_________________________________________
Note: A number; "divided by a variable" ; is Not a "polynomial" .
Answer choice: [B]: " [tex]\frac{-3}{ x}[/tex] " ;
is a "number; divided by a "variable" ; and as such, is Not a "polynomial".
_________________________________________
Help! Using complete sentences, explain how to find the maximum value for each function and determine which function has the largest maximum y-value. F(x)=-4(x-6)^2+3.
Answer:
Final answer is that function g(x) has the largest maximum value, which is 6.
Step-by-step explanation:
Given function is [tex]F(x)=-4(x-6)^2+3[/tex].
Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.
Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].
Comparing both we get: h=6, k=3
We know that maximum value occurs at the vertex where maximum value is given by "k"
Hence maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] is = 3
From graph we can clearly see that function g(x) has maximum height at 6.
So the final answer is that function g(x) has the largest maximum value, which is 6.
I need help please???
False.
For a point to lie on the X-axis, the second number needs to be 0, not the first one.
When the first number is 0, the point is on the Y-Axis.
Convert the expression to simplified radical form.
32^(1/2)x^(5/2)y^(3/2)
Answer:
[tex] {32}^{ \frac{1}{2} } {x}^{ \frac{5}{2} } {y}^{ \frac{3}{2} } = \sqrt{32 {x}^{5} {y}^{3} } = (4 \sqrt{2} )( {x}^{2} \sqrt{x} )(y \sqrt{y} ) = 4 {x}^{2} y \sqrt{2xy} [/tex]
Determine the best unit of measurement to represent each description
Answer:
see the attached figure
Step-by-step explanation:
The best unit of measurement that represent each description in the attached figure
Answer:
Step-by-step explanation:
Miles
1. Distance traveled on a bike ride
2. Length of the border between Texas and Oklahoma
3. Distance around a lake.
Feet
1. Distance traveled by a base ball.
2. Height of a mature tree
Inches
1. Diagonal of a computer screen
2. Diameter of a basket ball
3. Width of a sheet of a paper.
The coordinates G(7,3), H(9, 0), (5, -1) form what type of polygon?
an obtuse triangle
an acute triangle
an equilateral triangle
o a right triangle
Answer:
an acute triangle
Step-by-step explanation:
Given:
vertex 1 = (7,3)
vertex 2 = (9,0)
vertex 3 = (5,-1)
Now finding the length of each side of the triangle
Using distance formula, to find the length of side between vertex 1 and 2
d=[tex]\sqrt{(x2-x1)^{2}+ (y2-y1)^{2} }[/tex]
Putting values of x1=7 , x2=9, y1=3 and y2=0
d=[tex]\sqrt{(9-7)^{2}+ (0-3)^{2} }\\ =\sqrt{2^{2}+ 3^{2} }\\ =\sqrt{4+9} \\=\sqrt{13}[/tex]
Using distance formula, to find the length of side between vertex 1 and 3
Putting values of x1=7 , x2=5, y1=3 and y2=-1
d=[tex]\sqrt{(5-7)^{2}+ (-1-3)^{2} }\\ =\sqrt{2^{2}+ 4^{2} }\\ =\sqrt{4+16} \\=\sqrt{20[/tex]
Using distance formula, to find the length of side between vertex 2 and 3
Putting values of x1=9 , x2=5, y1=0 and y2=-1
d=[tex]\sqrt{(5-9)^{2}+ (-1-0)^{2} }\\ =\sqrt{4^{2}+ 1^{2} }\\ =\sqrt{16+1} \\=\sqrt{17[/tex]
Hence the three sides of triangle are:
√13, √20, √17
by Pythagoras theorem
if c^2= a^2 + b^2 then triangle is right triangle
if c^2> a^2 + b^2 then triangle is obtuse triangle
if c^2<a^2 + b^2 then triangle is acute triangle
Now let a=√13 b=√17 and c=√20 then:
a^2 + b^2 = 13+17
= 30
c^2=20
and 20 < 30 which means c^2<a^2 + b^2 then triangle is acute triangle !
To determine the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1), one needs to calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem to determine if it is a right, acute, or obtuse triangle.
Explanation:The coordinates G(7,3), H(9, 0), and (5, -1) can form a triangle on a Cartesian plane, and we need to determine the type of triangle they form. To solve this problem, we need to calculate the lengths of the sides of this triangle using the distance formula, which is √((x2-x1)² + (y2-y1)²) for two points (x1, y1) and (x2, y2). Once we have all three sides, we can determine the type of triangle by applying the Pythagorean theorem, where the square of the length of the longest side (the hypotenuse 'c') is equal to the sum of the squares of the other two sides (a and b).
By applying the Pythagorean theorem, if the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle. If the square of the longest side is greater than the sum of the squares of the other two sides, it is an obtuse triangle. And if it’s less, the triangle is an acute triangle.
Given the way the coordinates are arranged in the fragmented information, it appears the triangle they form is relevant to understanding relationships between sides and angles. The mnemonic SOHCAHTOA is often used to remember the ratios of sides in a right triangle. Since the information for determining the lengths of the sides directly is not fully provided, we can't explicitly state the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1) without further calculation.
What degree of rotation will cause the triangle below to map onto itself ?
Answer:
The triangle is rotated 360° ⇒ answer D
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 90° anti-clock wise
∴ Its image is (-y , x)
- If point (x , y) rotated about the origin by angle 90° clock wise
∴ Its image is (y , -x)
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
* There is no difference between rotating 180° clockwise or
anti-clockwise around the origin
- If point (x , y) rotated about the origin by angle 360°
∴ Its image is (x , y) the point itself
* There is no difference between rotating 360° clockwise or
anti-clockwise around the origin
* Now lets solve the problem
∵ The vertices of the triangle ABC are:
A is (-6 , 3) , B is (-5 , 7) , C is (-4 , 3)
∵ The triangle map onto itself
∴ A = A'
∴ B = B'
∴ C = C'
∴ The triangle is rotated 360° about the origin
D= 360
When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.