help please
Given the vertices of ∆ABC are A (2,5), B (4,6) and C (3,1), find the vertices following each of the transformations FROM THE ORIGINAL vertices:
a. Rx-axis
b. Ry = 3
c. T<-2,5>
d. T<3,-6>
e. r(90◦, o)
Answers
a.) A transformation, R_x-axis means that the vertices of the rectangle were reflected across the x-axis.
When a point on the coordinate axis is refrected across the x-axis, the sign of the y-coordinate of the point changes.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule R_x-axis are A'(2, -5), B'(4, -6), C'(3, -1)
b.) A transformation, R_y = 3 means that the vertices of the rectangle were reflected across the line y = 3.
When a point on the coordinate axis is refrected across the a horizontal line, the distance of the point from the line is equal to the distance of the image of the point from the line.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule are A'(2, 1), B'(4, 0), C'(3, 5)
c.) A transformation, T<-2, 5> means that the vertices of the rectangle were shifted 2 units to the left and 5 units up.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<-2, 5> are A'(0, 10), B'(2, 11), C'(1, 6).
d.) A transformation, T<3, -6> means that the vertices of the rectangle were shifted 3 units to the right and 6 units down.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule T<3, -6> are A'(5, -1), B'(7, 0), C'(6, -5).
e.) A transformation, r(90°, o) means that the vertices of the rectangle were rotated 90° to the right about the origin.
When a point on the coordinate axis is rotated about the origin b 90°, the quadrant of the point changes to the right with the x-value and the y-value of the point interchanging.
Therefore, the vertices of the triangle A'B'C' resulting from the transformation of triangle with vertices A(2, 5), B(4, 6) and C(3, 1) with the rule r(90°, o) are A'(5, -2), B'(6, -4), C'(1, -3)
Answer with explanation:
Vertices of ∆ABC are A (2,5), B (4,6) and C (3,1).
Plotting the points on coordinate plane
a.→ [tex]R_{x}[/tex]
We have to find vertices of image , that is ΔA'B'C' when ∆ABC is reflected across x axis.
The Distance from each of the vertices of ∆ABC from X axis will be same as Perpendicular distance from each of vertices of ∆A'B'C' from X axis.
Result is shown in the image 1.
b.→[tex]R_{y}=3[/tex]
We have to find the image of vertices of triangle through line, y=3.
The Distance from each of the vertices of ∆ABC from line,y=3 will be same as Perpendicular distance from each of vertices of ∆A'B'C' from line, y=3.
Result is shown in the image 2.
c. →T(-2,5)
Translation of vertices of triangle ABC by 2 units left and 5 units up.
[tex]A(2,5)_{-2,5} \rightarrow (2-2,5+5)\rightarrow (0,10)\\\\B(4,6)_{-2,5} \rightarrow (4-2,6+5)\rightarrow (2,11),\\\\C(3,1)_{-2,5} \rightarrow (3-2,1+5)\rightarrow (1,6)[/tex]
d.→T(3,-6)
Translation of vertices of triangle ABC by 3 units right and 6 units left.
[tex]A(2,5)_{3,-6} \rightarrow (2+3,5-6)\rightarrow (5,-1)\\\\B(4,6)_{3,-6} \rightarrow (4+3,6-6)\rightarrow (7,0),\\\\C(3,1)_{3,-6} \rightarrow (3+3,1-6)\rightarrow (6,-5)[/tex]
e.→Rotation by 90° with respect to Origin
When rotated in clockwise direction ,vertices of ΔABC changes by the rule ,that is (x,y)→(y,-x) and in anticlockwise direction ,(x,y)→(-y,x).
In clockwise direction
A(2,5)→A"(5,-2)
B(4,6)→B"(6,-4)
C(3,1)→C"(1,-3)
In Anti clockwise direction
A(2,5)→A'(-5,2)
B(4,6)→B'(-6,4)
C(3,1)→C'(-1,3)
Image is depicted below.
Related Questions
Given: AC is the hypotenuse and BD is the altitude of △ABC. AD=27, CD=40, AB=e, BD=j, and BC=h
Find the value of e
How the literal devil am i supposed to do this, legit i've tried for hours first answer gets Brainliest
Answers
In triangle ABC:
m(B)=90°, let m(A)=α, and let m(C)=β
so m(B)+m(A)+m(C)=180°, so α+β=90°
In triangle ABD, m(A)=α, m(ADB)=90° so m(ABD) must be β, so that the sum completes to 180.
By the same logic, m(DBC)=α
so we have the following similarities of triangles: (let's go by the order α-β-90°):
ACB ≡ ABD ≡ BCD,
consider ABD ≡ BCD:
[tex] \frac{AB}{BC} = \frac{BD}{CD} = \frac{AD}{BD} [/tex]
substitute with the givens:
[tex] \frac{e}{h} = \frac{j}{40} = \frac{27}{j} [/tex]
from
[tex]\frac{j}{40} = \frac{27}{j}[/tex]
we have
[tex] j^{2}=40*27 =1080[/tex]
In triangle ABD, from the pythagorean theorem:
[tex] e^{2} = j^{2}+27^{2}=1080+729=1089[/tex]
so [tex]e= \sqrt{1089}= 42.53 (units)[/tex]
Remark: a direct solution can be given by Euclid's theorem, AB^2=AD*AC
[tex]AB^2=AD*AC[/tex] so
[tex] e^{2}=27*47[/tex], then take square root of e
Answer: 42.53 units
Find the least common multiple of 8c4 and 6c2 .
Answers
Marcus loves baseball and wants to create a home plate for his house. Marcus needs to calculate the area of the home plate at the ball field so he can reconstruct it when he gets home. Calculate the area of the polygon.
50 in2
59 in2
85 in2
90 in2
Answers
---------------------------------------------------------------------
---------------------------------------------------------------------
Work Shown:
A1 = Area of rectangle = length*width = 7*4 = 28 square inches
A2 = Area of triangle on top = 0.5*base*height = 0.5*7*6 = 21 square inches
A3 = Area of triangle on right side = 0.5*base*height = 0.5*4*5 = 10 square inches
Total Area = A1 + A2 + A3
Total Area = 28 + 21 + 10
Total Area = 59 square inches
(4.4*10^6)*(3.9*10^4)
Scientific notation please help and explain
Answers
and
(3.9*10^4) = 39000
The exponents on top of the 10 tells you how many decimals you're supposed to move it to. If it's a negative number, you'll need to move the same amount of decimals, but to the left side instead.
for example: 4.3*10^-3 =0.0043
in this case, however, you should refer to the Laws of Exponents.
(4.4*10^6)*(3.9*10^4)
= 4.4 * 3.9 * 10^6 * 10^4
= 17.16 * 10^(6+4) <-- Law of Exponents say that when you multiply exponents with the same base, you add the exponents together.
= 17.16 * 10^10
May I pretty please have some math help?
Answers
The point on the graph of f⁻¹ (x) is (-5,4)
Explanation
Let f(x) = -(5/4)x.
This function passes through (4, -5) as specified, because
f(4) = -(4/5)*(4) = -5
Construct f⁻¹ (x) as follows:
Set y = f(x).
y = -(4/5)x
Switch x and y.
x = -(4/5)y
Solve for y
y = -(5/4)x
Set f⁻¹ (x) to y.
f⁻¹ (x) = - (4/5)x.
Test x=-5 to see if y=4.
f⁻¹ (-5) = -(4/5)*(-5) = 4 Correct!
Find the difference.
Correct and best explained answer gets brainliest.
Answers
9-5 =4
-4 +7=3
-1-6 =-7
so 4x^3+3x^2-7
A is the correct answer
Is -1/2 rational or irrational
Answers
-1 and 2 are both integers because they are either whole numbers or of the opposite value (negative).
What is the area of a regular pentagon with an apothem of 14 inches long and a side 20 inches long?
Answers
Answer:
[tex]\text{Area of regular pentagon is }700 inches^2[/tex]
Step-by-step explanation:
Given that a regular pentagon with an apothem of 14 inches and a side of 20 inches.
we have to find the area of pentagon.
Apothem=a=14 inches
Side of pentagon= 20 inches
[tex]Perimeter=s=20\times 5=100 inches[/tex]
[tex]\text{Area of regular pentagon=}\frac{1}[2}\times perimeter \times apothem[/tex]
[tex]=\frac{1}{2}\times 100\times 14=700inches^2[/tex]
[tex]\text{Area of regular pentagon is }700 inches^2[/tex]
Answer:700in
Step-by-step explanation:
In △ABC , m∠A=53°,m∠B=17°, and a=27. Find the perimeter of the triangle.
Answers
The third angle is C is 180-53-17=110°
27/sin53=b/sin17=c/sin110
b=27sin17/sin53, c=27sin110/sin53
And the perimeter is a+b+c so
p=27+27sin17/sin53+27sin110/sin53 units
p≈68.65 units (to nearest hundredth of a unit)
Answer:
69
Step-by-step explanation:
I got it correct on founders edtell
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Write a cosine model, d = acos(bt) + k, for the depth as a function of time. This amplitude is meters. a =
Answers
Answers:
1.5, -1.5, 12.5, 4pi/25, 4, D
Step-by-step explanation:
Answer:
1.5 meters
a = -1.5
12.5 hours
b = 4 pi/25
k = 4 meters
last option is D
Step-by-step explanation:
edg 23'
The following system of equations can be used to find the roots of the equation x3 + 72 = 5x2 + 18x. y = x3 + 72 y = 5x2 + 18x Graph this system of equations on the graphing calculator. How many intersection points can you see in the default viewing window?
Answers
Answer:
he following system of equations can be used to find the roots of the equation
x3 + 72 = 5x2 + 18x.
y = x3 + 72
y = 5x2 + 18x
Graph this system of equations on the graphing calculator.
How many intersection points can you see in the default viewing window?
✔ 1
Adjust the window so you can find all of the points of intersection for the system of equations.
What are the roots of the original polynomial equation? Check all that apply.
–6
0
✔ 6
✔ –4
✔ 3
8
Step-by-step explanation:
no
which of the following represents the zeros of the function f(x) = 4x3 -13x2 -37x +10
Answers
Help plz.. Evaluate this expression: -(-(-(-1)))?
Thanks.
Answers
every pair of negative cancel out
-(-a)=a
so we can just keep flipping the signs
go inside to out
-(-(-(-1)))=
-(-(1))=
-(-1)=
1
There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?
Answers
The answer is 66.
The measure of angle C in triangle ABC is 66 degrees, calculated by subtracting the sum of angles A and B from 180 degrees.
The measure of angle C can be determined by using the fact that the sum of angles in any triangle is always 180 degrees. Given that the measure of angle A is 68° and the measure of angle B is 46°, we can calculate the measure of angle C as follows:
C = 180° - A - B
C = 180° - 68° - 46°
C = 180° - 114°
C = 66°
Thus, the measure of angle C in ΔABC is 66 degrees.
Identify the domain of the exponential function shown in the following graph: y=10x
Answers
We can replace x with any real number we want without worrying about restrictions. There won't be any issues such as dividing by zero or applying the square root to a negative number.
Using technology, we found that Juan’s investment account can be modeled by the function, c(x)=3x2-2x+10, in thousands of dollars. What was Juan’s initial investment?
A)$5
B)$10
C)$5,000
D)$10,000
Answers
Initial investment is given when [tex]x=0[/tex], so substituting this into [tex]c(x)[/tex] we have
[tex]c(0)=3 (0)^{2}-2(0)+10 [/tex]
[tex]c(0)=10[/tex]
Hence, correct answer is B $10
Answer:
D) $10,000.
Step-by-step explanation:
We have been given a function [tex]c(x)=3x^2-2x+10[/tex], which represents Juan’s investment account in thousands of dollars. We are asked to find Juan's initial investment.
To find Juan's initial investment, we will substitute [tex]x=0[/tex] in our given function.
[tex]c(0)=3(0)^2-2(0)+10[/tex]
[tex]c(0)=3*0-0+10[/tex]
[tex]c(0)=10[/tex]
Since the function gives Juan's investment in thousands of dollars, so Juan's initial investment would be [tex]10\times \$1,000=\$10,000[/tex], therefore, option D is the correct choice.
The table shows the outputs, y, for different inputs, x: Input (x) 2 5 9 12 Output (y) 20 15 12 8 Part A: Do the data in this table represent a function? Justify your answer. (3 points) Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points) Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)
Answers
=====================
data in the table : when x = 9....this is already a point on the table (9,12)...so the value on the table, when x = 9, is 12
f(x) = 5x + 14....when x = 9
f(9) = 5(9) + 14
f(9) = 45 + 14
f(9) = 59
the relation with the greater value would be : f(x) = 5x + 14
=====================
f(x) = 5x + 14....when f(x) = 64
64 = 5x + 14
64 - 14 = 5x
50 = 5x
50/5 = x
10 = x <==
Answer:
D 17 2/9
Step-by-step explanation:
Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0
Answers
1. let's factorize the expression [tex]x^{5} -9x ^{3} [/tex]:
[tex]f(x)= x^{5} -9x ^{3}= x^{3} ( x^{2} -9)=x^{3}(x-3)(x+3)[/tex]
the zeros of f(x) are the values of x which make f(x) = 0.
from the factorized form of the function, we see that the roots are:
-3, multiplicity 1
3, multiplicity 1
0, multiplicity 3
(the multiplicity of the roots is the power of each factor of f(x) )
2.
The end behavior of f(x), whose term of largest degree is [tex] x^{5} [/tex], is the same as the end behavior of [tex] x^{3} [/tex], which has a well known graph. Check the picture attached.
(similarly the end behavior of an even degree polynomial, could be compared to the end behavior of [tex] x^{2} [/tex])
so, like the graph of [tex] x^{3} [/tex], the graph of [tex]f(x)= x^{5} -9x ^{3} [/tex] :
"As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity. "
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex] and all the zeroes of f(x) wiil be: -3 with multiplicity 1, 3 with multiplicity 1, 0 with multiplicity 3.
Given :
[tex]f(x) = x^5-9x^3[/tex] --- (1)
The value of x at which f(x) becomes zero can be determine by eqaution the equation (1) to zero.
[tex]x^5-9x^3=0[/tex]
[tex]x^3(x^2-9)=0[/tex]
[tex]x^3(x-3)(x+3)=0[/tex]
Therefore, all the zeroes of f(x) will be:
-3 with multiplicity 1,
3 with multiplicity 1,
0 with multiplicity 3.
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex]. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.The graph of f(x) is attached below.
For more information, refer the link given below:
https://brainly.com/question/24153248
Find the range of the data. Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88 A) 22
B)24
C)28
D)23
Answers
96-72= 24
B.)24
Answer:
Option B - 24
Step-by-step explanation:
Given : Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88
To find : The range of the data?
Solution :
Range is defined as the difference between the smallest and the largest element of the data.
First we arrange the data into ascending order:
72,73,79,79,80,81,86,88,88,96
The smallest number is 72
The largest number is 96
The range of the data = largest number - smallest number
The range of the data = 96 - 72
The range of the data = 24
Therefore, Option B is correct.
The adams family is remodeling their family room. the room measures 14 feet by 20 feet, and the contractor wants $35 per square foot to remodel it. how much will it cost to remodel?
Answers
$35 * 280 sq ft = $ 9,800
Answer:
It would cost $9800 to remodel the room.
Step-by-step explanation:
The Adams family is remodeling their family room.
Length of the room = 20 feet
Width of the room = 14 feet
To get area of the room we use the formula
Area = Length × Width
A = 20 × 14 = 280 feet²
The contractor wants $35 per square foot to remodel it.
So it would cost = 280 × 35 = $9800
It would cost $9800 to remodel the room.
What is the length of x-component of v?
Answers
answer is B. 2
Solve the following system of equations algebraically. 2x = 5y + 8. 3x + 2y = 31
Answers
x=−12.301587 and y= 31/ 2
3x + 2y = 31 so 3x = -2y + 31 (2nd)
multiply (1st equation) by 3 and (2nd equation) by 2
6x = 15y + 24
6x = -4y + 62
-----------------------subtract
0 = 19y - 38
19y = 38
y = 2
2x = 5y + 8
2x = 5(2) + 8
2x = 18
x = 9
answer
solution (9, 2)
What rank of the marine corps do you get the stripe on your pants?
Answers
This red stripe is :
2 inches (5.1 cm) for general officers,
1.5 inches (3.8 cm) for other officers, and
1.12 inches (2.8 cm) for enlisted Staff Noncommissioned Officers and Noncommissioned Officers.
Answer:
cpl and above. E-4 and above.
Step-by-step explanation:
A 12 foot rope is cut into two pieces so that one piece is 3 feet less than twice the length of the other piece. how long is each piece?
Answers
12 feet long
1st piece = x
2nd piece = 2x-3
3x-3 =12
3x=15
x = 5
1st piece = 5 feet
2nd piece = 2*5=10-3=7 feet
What value of x makes the denominator of the function equal zero? y= 4/3x-33
Answers
3x = 33
x = 11
answer is 11
Answer: 11 is your answer
Step-by-step explanation:
A cricket ball is dropped into a cylindrical tank of water.
The ball sinks to the bottom of the tank.
The diameter of the cricket ball is 7.2 cm
The diameter of the cylindrical tank is 15 cm
Calculate the increase in height of the water in the tank.
Answers
the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)
the ball is 7.2 cm in diameter. Hence its volume is 4*(3.6)^3 * π/3
So, the volume the water occupies increases by this amount.
because the tank is cylindrical, this increase must also be cylindrical.
and the volume of the ïncreased cylinder is π*15^2 * h, where h is the increase in height of the water.
so h = (4*(3.6)^3 * π/3)/(π*15^2) = 4*(3.6)^3/(3*15^2)
Which number produces a rational number when added to 0.42?
Answers
William can run 5 laps in 9 2/3 minutes. If one lap is 2/5 of mile how fast is William running in miles per minute?
Answers
Final Answer ( 0.21 miles per minute)
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
Answers
The sides should satisfy the equation (a^2)+(b^2)=(c^2).
Hope it helps
Answer:
Any set of numbers that fit in Pythagoras theorem will represent that set.
Step-by-step explanation:
Though options are not given, but there is a standard way to get such combinations of number.
As it is a right triangle, we have to work on Pythagoras theorem.
The sum of squares of two other sides is equal to square of the hypotenuse.
Like : [tex]3^{2} +4^{2} =5^{2}[/tex]
(20 points)In 2008, there were 6.7 × 10^9 people living on earth. What is that number in standard notation?
A. 6,700,000
B. 67,000,000
C. 6,700,000,000
D. 67,000,000,000
Answers
C. 6,700,000,000
6.7*1,000,000,000
6,700,000,000
So, the answer is
C)6,700,000,000