Answers
By translation, the image of the triangle X is equivalent to the triangle E.
How to determine the image of a figure by rigid transformations
Herein we find the representation of a triangle, whose vertices are described below:
A(x, y) = (5, 5), B(x, y) = (5, 6), C(x, y) = (7, 5)
Whose image must be determined by a rigid transformation known as translation:
P'(x, y) = P(x, y) + T(x, y)
Where:
P(x, y) - Original point.P'(x, y) - Image of the point.T(x, y) - Translation vector.Now we proceed to determine the images of the vertices of the triangle:
A'(x, y) = (5, 5) + (4, - 3)
A'(x, y) = (9, 2)
B'(x, y) = (5, 6) + (4, - 3)
B'(x, y) = (9, 3)
C'(x, y) = (7, 5) + (4, - 3)
C'(x, y) = (11, 2)
Therefore, the triangle E is the image of the triangle X.
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Related Questions
Convert the polar equation r
4 = 2 sin θ cos θ into an equation in Cartesian (rectangular) coordinates.
Answers
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos²θ sinθ
y = 4 sin²θ cosθ
We have,
We can use the following conversions from polar to Cartesian coordinates:
x = r cosθ
y = r sinθ
To convert the polar equation r = 4 sin(θ)cos(θ) into Cartesian coordinates, we substitute r with its equivalent value 4 sin(θ)cos(θ) and use the above conversions:
x = (4 sinθ cosθ) cosθ
y = (4 sinθ cosθ) sinθ
Simplifying these expressions, we get:
x = 4 cos^2θ sinθ
y = 4 sin^2θ cosθ
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos^2θ sinθ
y = 4 sin^2θ cosθ
or, in standard form:
x = 4xy
This is the Cartesian equation in terms of x and y, obtained by replacing sinθ and cosθ with x and y, respectively.
Thus,
The Cartesian equation of the polar equation r = 4 sin(θ)cos(θ) is:
x = 4 cos²θ sinθ
y = 4 sin²θ cosθ
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help please i need to know what the answer is
Answers
A=(sin x.secx)² - (tan x.cosec.x)² B=2-2 cos² x + cos⁴ x - sin⁴ x için 2A+3B toplamını ayrıntılı bir şekilde bulunuz
Answers
Öncelikle verilen A ve B ifadelerinin değerlerini hesaplayalım:
A = (sin x . sec x)² - (tan x . cosec x)²
A = (sin x / cos x)² - (sin x / cos x)²
A = sin² x / cos² x - sin² x / cos² x
A = 0
B = 2 - 2cos² x + cos⁴ x - sin⁴ x
B = 2 - 2cos² x + (cos² x)² - (sin² x)²
B = (cos² x)² - 2cos² x + 2
Şimdi 2A + 3B'yi hesaplayalım:
2A + 3B = 2(0) + 3[(cos² x)² - 2cos² x + 2]
2A + 3B = 3cos⁴ x - 6cos² x + 6
Bu şekilde 2A + 3B ifadesinin ayrıntılı hesaplanması tamamlanmış oldu.
I am truely not sure how to do
Answers
Answer:
[tex]x=4.865[/tex]
Step-by-step explanation:
We know the area of a rectangle to be [tex]base*height[/tex]. In this instance, [tex]base=(2x+10)in[/tex], [tex]height=(3x) in[/tex], and [tex]area=288in^2[/tex]
The next step is to plug these known values into the [tex]area=base*height[/tex] equation. It'll look like this:
[tex]288=(2x+10)*(3x)=6x^2+30x[/tex]
This simplifies to:
[tex]48=x^2+5x[/tex]
Next, we want to rewrite the equation so we can apply the quadratic formula to it. We are going to do this by subtracting 48 from each side. The new equation looks like this:
[tex]x^2+5x-48=0[/tex]
Next, we plug this into the quadratic formula:
[tex]x=\frac{-(5)+\sqrt{5^2-4(1)(-48)} }{2(1)}=4.865[/tex]
[tex]x=\frac{-(5)-\sqrt{5^2-4(1)(-48)} }{2(1)}=-9.865[/tex]
The second value of x is negative, and since a side length cannot be negative this leaves us with just the first answer of [tex]x=4.865[/tex].
Answer:
[tex]\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
Step-by-step explanation:
The area of a rectangle is equal to the base × height:
[tex]\large \textsf{$\rm A $ $= (2x+10)\times(3x)$}\\ \\\large \textsf{$\rm \phantom{A}=$ $6x^2+30x$, and since A = 288,}\\ \\\large \textsf{$\therefore 288 = 6x^2+30x$}[/tex]
Rearranging this equation, we get:
[tex]\large \textsf{$6x^2+30x-288=0$}\\\\\large \textsf{$6(x^2+5x-48)=0$}\\\\\large \textsf{$\therefore x^2+5x-48=0$}[/tex]
Here we are left with a quadratic equation, which we can solve using the quadratic formula:
[tex]\Large \boxed{\textsf{$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$}} \textsf{ where $ax+bx+c=0$}[/tex]
Plugging values into the formula, we get:
[tex]\Large \textsf{$x = \frac{-(5)\pm \sqrt{(5)^2-4(1)(-48)}}{2(1)}$} \\\\\Large \textsf{$x=4.87, -9.87$,} \large \textsf{ but length cannot be negative.}\\\\\Large \boxed{\boxed{\textsf{$\therefore x=4.87 $ in}}}[/tex]
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Someone pls help me with this.
Answers
The value of angle k is 129⁰.
The value of angle b is 64.5⁰.
What is the value of angle b and angle k?
The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.
k + 113 + 118 = 360 (sum of angles in a circle)
k + 231 = 360
k = 360 - 231
k = 129⁰
The value of angle b is calculated by applying the principle of intersecting chord theorem.
b = ¹/₂ arc k
b = ¹/₂ x 129
b = 64.5⁰
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CONSTRUIRE UN TRIANGLE EQUILATERAL ABC DE 3 cm.
Answers
The construction of an equilateral triangle is shown in the solution.
Steps -
When the length of three sides of the triangle is given, then follow the below steps to construct the required triangle.
Draw a line segment AB, of length equal to the longest side of the triangle.Now using a compass and ruler take the measure of the second side and draw an arc.Again, take the measure of the third side and cut the previous arc at a point C.Now join the endpoints of the line segment to point C and get the required triangle ABC.Learn more about equilateral triangle click;
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Someone pls help me with this.
Answers
The value of angle k is 129⁰.
The value of angle b is 64.5⁰.
What is the value of angle b and angle k?The value of angle b and angle k is calculated by applying the following principle of intersecting chord theorem.
k + 113 + 118 = 360 (sum of angles in a circle)
k + 231 = 360
k = 360 - 231
k = 129⁰
The value of angle b is calculated by applying the principle of intersecting chord theorem.
b = ¹/₂ arc k
b = ¹/₂ x 129
b = 64.5⁰
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Bear Mountain Ski Resort is building a new ski lift. They want to add weather-resistant paint to the cylindrical poles that will support the ski lift.
Each pole is 22 feet tall and have a diameter of 1.6 feet. There are 11 poles in all. How much paint will they need to paint all the surfaces of the 11 poles? Use 3.14 for m, and round your final answer to the nearest whole number.
Answers
The amount of paint needed to paint all the surfaces of the 11 poles is; 1260 ft².
What is the quantity of paint required for all the surfaces of the 11 poles?It follows from the task content that the amount of paint required to paint all the surfaces of the 11 poles is required to be determined.
First, since the surface area of a cylindrical pole is; A = 2πr (r + h).
where height,h = 22 and radius, r = diameter / 2 = 1.6 / 2 = 0.8 feet.
Therefore, A = 2 × 3.14 × 0.8 (22 + 0.8)
A = 114.5472 ft²
Therefore, for all 11 poles; the total area is; 11 × 114.5472 = 1260 ft² to the nearest whole number.
Ultimately, the quantity of paint needed is such that it is sufficient for an area of; 1260 ft².
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The area of a rectangle is 40 square feet. What
could be the perimeter of the rectangle? Circle
the letter for all that apply.
A 82 ft
B
C
44 ft
40 ft
D 28 ft
E 26 ft
Answers
The possible perimeter for the rectangle would be 28(Letter D)
Are these right? And if not can someone help me with this pleeease, this is geometry btw
Answers
The measure of arc CFE is 246⁰.
The measure of arc FED is 190⁰.
The value of the angle CFE is 57⁰.
The value of the angle DEF is 85⁰.
What are the values of the angles?The value of the angles is calculated by applying intersecting chord theorem.
This theorem states that the angle at tangent is half of the arc angle of the two intersecting chords.
angle CFE = 180 - 123 (opposite angles of a cyclic quadrilateral)
angle CFE = 57
arc CDF = 2 x 57
arc CDF = 114
arc CFE = 360 - 114 = 246⁰
angle DEF = 180 - 95
angle DEF = 85
arc DCF = 2 x 85 = 170
arc FED = 360 - 170 = 190
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Write the expression in complete factored form.
3b(p+2) - 7(p + 2) =
Enter the correct answer.
Answers
Answer:
(p + 2)(3b - 7)
Step-by-step explanation:
3b(p + 2) - 7(p + 2) ← factor out common factor (p + 2) from each term
= (p + 2)(3b - 7)
The radius of the earth is about 3960 miles.
The length of a 1°
arc on the equator to the nearest tenth of a mile is ____ miles.
Answers
The length of arc on equator is 69.08 miles.
We have
Radius of Earth = 3960 miles
Angle = 1 degree
So, the length of arc on equator is
= θ/360 x 2πr
= 1/360 x 2 (3.14) (3960)
= 69.08 miles
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an athlete eats 55kg of protein a day while training. How much protein will she eat during 23 days of training?
Answers
Answer:
1265 kg of protein
Step-by-step explanation:
If 55kg is eaten in one day then in 23 days there will be x kgs.
To find 'x':
55 x 23 = 1265
At a circus, 135 clowns are getting into cars. Blue cars hold 20 clowns and red cars only hold 15. There are a total of 8 cars. How many of each are there?
Answers
The number of blue cars and the number of red cars are 3 and 5 respectively
How to find how many of each car are there?Let b and r represent the number of blue cars and the number of red cars respectively.
There are a total of 8 cars, we have:
b + r = 8
There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:
20b + 15r = 135.
Thus, we have a system of equations with two variables:
b + r = 8 ---- (1)
20b + 15r = 135 ---- (2)
We can use elimination to solve for b and r.
Let's use elimination. Multiplying the first equation by 20 and second equation by 1:
20 * (b + r = 8) = 20b + 20r = 160 (subtract)
1 * (20b + 15r = 135) = 20b + 15r = 135
...............................................
5r = 25
...............................................
r = 25/5
r = 5
Using (1):
b + r = 8
b + 5 = 8
b = 8 - 5
b = 3
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Answer this for me please
Answers
The function values are f(10) = 198 and g(-6) = 24/7; the range of h(x) is 3/5 < h(x) < 31/25 and the inverse function is p-1(x) = -(1 + 3x)/(5 + x)
Calculating the function valuesGiven that
f(x) = 2x^2 - 2
g(x) = 4x/(x - 1)
So, we have
f(10) = 2(10)^2 - 2 = 198
g(-6) = 4(-6)/(-6 - 1) = 24/7
The range of h(x)Here, we have
h(x) = (7x - 4)/5x
Where
1 < x < 5
So, we have
h(1) = (7(1) - 4)/5(1) = 3/5
h(5) = (7(5) - 4)/5(5) = 31/25
So the range is 3/5 < h(x) < 31/25
The inverse of p(x)Here, we have
P(x) = (5x - 1)/(3 - x)
So, we have
x = (5y - 1)/(3 - y)
This gives
3x - xy = 5y - 1
So, we have
y(5 + x) = -1 - 3x
This gives
y = -(1 + 3x)/(5 + x)
So, the inverse function is p-1(x) = -(1 + 3x)/(5 + x)
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14. Evaluate the indefinite integral.
Answers
The indefinite integral of ∫ (4x⁴ - 5)⁵ . 32x³ dx is (4x⁴ - 5)⁶/3 + C.
What is the indefinite integral?The solution of the indefinite integral is calculated by using substitution method.
Let u = 4x⁴ - 5
du/dx = 16x³
dx = du/(16x³)
Substituting into the integral;
∫ (4x⁴ - 5)⁵ . 32x³ dx = ∫ u⁵ . 32x³ du/(16x³)
∫ u⁵ . 32x³ du/(16x³) = ∫ 2u⁵ du
∫ 2u⁵ du = 2∫u⁵ du
2∫u⁵ du = 2 (u⁶/6 + C)
2 (u⁶/6 + C) = u⁶/3 + C
Substituting back for u;
∫ (4x⁴ - 5)⁵ . 32x³ dx = (4x⁴ - 5)⁶/3 + C
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A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?
HELO
Answers
The amount of dry ingredients used in the cake recipe is approximately 7 cups.
We have,
3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa.
Now, first convert all quantity in same unit.
3 ½ cups of flour
= 3 cups + 0.5 cups
= 3 cups and 8 ounces.
and, 2 ⅔ cups of sugar
= 2 cups + 0.67 cups,
= 2 cups and 10.72 ounces.
and, 1 ¾ cups of cocoa
=1 cup + 0.75 cups
= 1 cup and 12 ounces.
So, the total amount
= 3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces
= 7 cups
Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.
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Which of the following statements is TRUE?
The volume of a_________
A. prism is thrice the volume of a pyramid.
B. pyramid is thrice the volume of a prism.
C. cylinder is twice the volume of a cone.
D. cone is twice the volume of a cylinder.
Answers
The volume of C.a .cylinder is twice the volume of a cone.
How is the volume of cylinder related to the volume of cone?The formula fro the cylinder is πr²h and that of the cone is ⅓ the volume It should be noted that the volume of a cone can be equated to theone-third of the volume of a cylinder , this can be established when they are having same base radius and height.
The cylinder's volume can be expressed as π r² h, along with the surface area which can be expressed as 2π r h + 2π r² and this can be used to get the values.
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To plan for retirement, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly. Payments will be made at the end of each quarter. Find the total value of the annuity in 26 years.
Do not round any intermediate computations, and round your final answer to the nearest cent. If necessary, refer to the list of financial formalas.
Answers
The total value of the annuity in 26 years is 179163.85 dollars.
Given that, Deandre deposits $97 each month in an annuity that pays 7.7 % interest, compounded quarterly.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Here, 26 years = 26×4
= 104
Now, A=97(1+7.5/100)¹⁰⁴
A=97(1+0.075)¹⁰⁴
A=97(1.075)¹⁰⁴
A=97×1847.05
A=$179163.85
Therefore, the total value of the annuity in 26 years is 179163.85 dollars.
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On an assignment, there are two true or false questions. You have no idea what the correct answer is to either one so you guess. What is the probability that you get both of them right by guessing? Explain your answer.
Answers
Step-by-step explanation:
a probability is airways the ratio
desired cases / totally possible cases
2 questions, each with a true or false answer option.
that gives us
2 × 2 = 4 answer options in total (the totally possible cases).
but only one of the four combinations is completely right.
so, the probability is
1/4
the 4 possibilities are
true true
false false
true false
false true
formally we can get to the result that way :
the first question has 2 options.
the probabilty to get it right is therefore
1/2
the same for the second question
1/2
but both have to be right for the desired result (question 1 AND question 2 have to be right), so, we need to combine both individual probabilities :
1/2 × 1/2 = 1/4
Note that the probability of both questions being right by guessing is 0.25 or 1/4.
How is this so ?P (both correct) = P(correct on Q1 ) x p(correct on Q2)
= 0.5 x 0.5
= 0.25 or 1/4
Note that probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are.
Statistics is the study of occurrences guided by probability.
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help please pcture !!really fast please!!!!
Answers
Answer:
13 years
Step-by-step explanation:
Which of the following is the graph of f(x) = 5 cos (2x)? Select one: a. graph with points 0, 5 and pi over 4, 0 and pi over 2, negative 5 and 3 pi over 4, 0 and pi, 5 b. graph with points at 0, 0 and pi over 4, negative 3 and pi over 2, 0 and 3 pi over 4, 3 and pi, 0 c. graph with points 0, negative 5 and pi over 4, 0 and pi over 2, 5 and 3 pi over 4, 0 and pi, negative 5 d. graph with points at 0, 5 and pi over 4, 2 and pi over 2, negative 1 and 3 pi over 4, 2 and pi, 5
Answers
The required graph has been attached below that represents the function f(x) = 5 cos (2x).
The graph of the function f(x) = 5 cos(2x) is a periodic function that oscillates between its maximum and minimum values as x changes.
Specifically, the function is a cosine function with amplitude 5 and period π, since the coefficient of x is 2 in the argument of the cosine function.
The graph of the function f(x) = 5 cos(2x) has a maximum value of 5 when cos(2x) = 1 (i.e., at 2x = 0 + 2πk, where k is an integer), and a minimum value of -5 when cos(2x) = -1 (i.e., at 2x = π + 2πk, where k is an integer).
Thus, the graph has been attached below that represents the given function.
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Simplify the following expression 12a3b6c5/3a2b4c5
Answers
4ab² is the simplified value of the given expression.
To simplify the expression, we can divide the coefficients and variables separately:
[tex]12a^3b^6c^5 / 3a^2b^4c^5\\\\= (12/3) * (a^3/a^2) * (b^6/b^4) * (c^5/c^5)\\\\= 4 * a^{3-2}* b^{6-4} * c^{5-5}\\\\= 4a * b^2 * 1\\\\= 4ab^2\\[/tex]
Therefore, the simplified expression is 4ab².
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The graph of part of an exponential function is given below. Write the domain and range as Inequalities.
Answers
The domain and range of the exponential function for the given graph is equal to Domain = [ -1 , 3 ) and range = [ -36 , -1/36 ).
For the plotted graph of exponential function f(x),
Plotted graph represents the endpoints.
In the fourth quadrant ( -1 , -36 ) represents the closed interval.
In the first quadrant ( 3 , -1/36 ) represents the open interval.
Domain of the function is represented by all input values.
Here x-values represents the domain.
Domain of the exponential function = [ -1 , 3)
Or -1 ≤ x < 3
Range of the function is all output values.
Here y-values represents the range.
Range of the exponential function = [ -36 , -1/36 ).
Therefore, the domain and range of the exponential function of the graph is equal to [ -1 , 3 ) and [ -36 , -1/36 ).
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The drawer contains 18 spoons and 12 forks. you randomly choose two utensils. What is the probability that both utensils are spoons?
Answers
Answer:8.52%
Step-by-step explanation:
There are 14 utensils in the drawer, and then there will be one less in the bowl after each successive utensil is removed. There are then 3 possibilities for the same kind being removed on all pulls:
P(3 spoons) = (6/14)*(5/13)*(4/12)
P(3 forks) = (5/14)*(4/13)*(3/12)
P(3 knives) = (3/14)*(2/13)*(1/12)
Add all of these outcomes together and you'd get about 8.52%
help !)There are 30 students in her class.
⅕ paid for the trip with a check.
½ paid for the trip with cash.
30% have paid half of their money.
The rest have not paid anything for the trip yet.
How many students have not paid for the trip?
Answers
The number of students have not paid for the trip is 0.
Given that, there are 30 students in her class.
⅕ paid for the trip with a check.
That is, 1/5 ×30=6 students
½ paid for the trip with cash.
Now, 1/2 ×30 =15 students
30% have paid half of their money.
Here, 30% of 30
30/100 ×30
= 900/100
= 9 students
Total students = 6+15+9
= 30
So, rest of students = 30-30=0
Therefore, the number of students have not paid for the trip is 0.
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Find the measure of arc LN. Fill in the blank with the
number only.
Assume that segments that appear to be tangent are
tangent.
Answers
The value of arc LN in the intersecting chords is 100⁰.
What is the value of arc LN?
The value of arc LN is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
arc LN = 2 x m∠LMN
From the diagram, we have, m∠LMN = 50⁰
The value of arc LN is calculated as follows;
arc LN = 2 x 50⁰
arc LN = 100⁰
Thus, the value of arc LN is based on intersecting chord theorem.
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The heaviest freshwater fish caught in region A weighs 286 lb, and the heaviest freshwater fish caught in region B
weighs 614 lb. How much does each weigh in kilograms?
A. The fish from region A weighs about _______ in kg.
(Round to the nearest whole number.)
B. The fish from region B weighs about _______ in kg.
(Round to the nearest whole number.)
Answers
Answer:
A. To convert pounds to kilograms, we need to multiply by 0.453592. Therefore, the fish from region A weighs about 130 kg (286 x 0.453592), rounded to the nearest whole number.
B. Similarly, the fish from region B weighs about 279 kg (614 x 0.453592), rounded to the nearest whole number.
A foot all coach needs to choose 11 players to start on offense. There are 6 freshmen 6sophmores,8 juiniors, and 7 seniors. How many ways can the starting 11 be chosen if the coach wants all seniors to play
Answers
The number of ways to choose the starting 11 players with all seniors playing is 4845.
We have,
Since the coach wants all seniors to play, we must choose the remaining
(11 - 7 = 4) players from the remaining (6 + 6 + 8 = 20) players who are not seniors.
The number of ways to choose 4 players from 20 players is given by the combination formula:
[tex]^{20}C_4[/tex]
= 20! / (4! * 16!)
= 4845
Therefore,
The number of ways to choose the starting 11 players with all seniors playing is 4845.
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Evaluate the function below it’s a given output value of 6
f(x)=72/2x-2
Answers
f(6) = 72/(2(6)-2)
f(6) = 72/(12-2)
f(6) = 72/10
f(6) = 7.2
Therefore, the output value of the function f(x) = 72/(2x-2) when x is 6 is 7.2.