Polygon ABCD is rotated 90º counterclockwise about the origin to create polygon A′B′C′D′. Match each set of coordinates to the vertices of polygon A′B′C′D′. Tiles A′ (-1, 3) B′ (-2, 2) C′ (-2, 1) D′ (-1, 1)
<---->
<---->
<---->
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Answers
Look at the picture.
Answer:
A'(-1, 1), B'(-2, 1), C'(-2, 2), D'(-1, 3)
Answer:
A' = (-1,3) - A = (3,11)
B' = (-2,2) - B = (2,2)
C' = (-2,1) - C = (1,2)
D' = (-1,1) - D = (1,1,)
Step-by-step explanation:
We have the polygon ABCD transformed to the polygon A'B'C'D' with the co-ordinates,
A' = (-1,3), B' = (-2,2), C' = (-2,1) and D' = (-1,1).
Since, the polygon is rotated 90 counterclockwise about the origin.
The co-ordinates (x,y) of ABCD will change to (-y,x) for A'B'C'D'.
So, we will change the co-ordinates (-y,x) of A'B'C'D' to (x,y) which gives the co-ordinates of ABCD.
That is,
Take the y-value to the 1st position and x-value to the second multiplied by negative sign.
Thus, we have,
A' = (-1,3) ------------------ A = (3,1)
B' = (-2,2) ------------------ B = (2,2)
C' = (-2,1) ------------------ C = (1,2)
D' = (-1,1) ------------------- D = (1,1,)
Related Questions
Does this set of ordered pairs represent a function? Why or why not?
{(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)}
A. Yes, because there are two x-values that are the same.
B. No, because two of the y-values are the same.
C. Yes, because every x-value corresponds to exactly one y-value.
D. No, because one x-value corresponds to two different y-values.
Answers
C. Yes, because every x-value corresponds to exactly one y-value.
Final answer:
The set of ordered pairs represents a function Yes, because every x-value corresponds to exactly one y-value(C).
Explanation:
The set of ordered pairs {(–5, –5), (–1, –2), (0, –2), (3, 7), (8, 9)} represents a function because every x-value corresponds to exactly one y-value. In a function, each input (x-value) has only one output (y-value). The set does not have two different y-values for the same x-value, so option D is incorrect. Therefore, option C is the correct answer.
(C). Yes, because every x-value corresponds to exactly one y-value.
You can see that each unique x-value corresponds to exactly one y-value, and there are no repeated x-values. Therefore, this set of ordered pairs represents a function.
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Both Dale and Chan went running for an hour. Dale ran 5 miles and Chan ran 2.5 miles. How did Dale’s distance compare to Chan’s? (Use division to compare.)
Answers
Chan = 2.5 miles
5 ÷ 2.5 = 2
Dale ran twice as fast as Chan
In the given hour, Dale ran 5 miles and Chan ran 2.5 miles.
Let Dale's running miles be represented by the variable D and let Chan's running miles be represented by the variable C.
In-order to compare Dale's running miles to Chan's by using division we get:
[tex] \frac{D}{C}=\frac{5}{2.5} = \frac{2}{1} [/tex]
[tex] D=2C [/tex]
Thus, Dale ran twice the distance Chan ran in the same amount of time of 1 hour.
Equivalently we can say that Chan ran half the distance Dale ran in the same amount of time of 1 hour.
What is the 4th term in the sequence of
c(n)=-7+6(n-1)
....Please help ME!!!
Answers
.. c(4) = -7 +6(4 -1)
.. = -7 +18
.. = 11
The 4th term is 11.
Natalie opened a bank account that earns 2.5% simple interest. If her account earned $180 over the next ten years, how much was Natalie’s initial deposit when she opened the account?
Answers
Answer: $720.
Step-by-step explanation:
The formula to find the simple interest is given by :-
[tex]I=Prt[/tex], where P is the principal amount , r is the rate of interest in decimal and t is the time in years.
Given : Rate of interest : r= 0.025
Simple interest : I= $180
Time : t=10
Let P be the Natalie’s initial deposit when she opened the account, then we have:-
[tex]180=P(0.025)(10)\\\\\Rightarrow\ P(0.25)=180\\\\\Rightarrow\ P=\dfrac{180}{0.25}=\dfrac{18000}{25}=720[/tex]
Hence, the Natalie’s initial deposit when she opened the account was $720.
A tree standing vertically on level ground casts a 140 foot long shadow. The angle of elevation from the end of the shadow to the top of the tree is 24.7°. Find the height of the tree to the nearest foot.,
Answers
A cafe offers senior citizens a 15% discount off its regular price of $8.95 for the dinner buffet. How much of a discount does a senior citizen receive off of the $8.95 price?
Answers
:)
Hope this helps
Answer:
$1.3425
Step-by-step explanation:
The regular price of the dinner buffet is 8.95. If this has a discount of 15%, we would have to multiply the total price by 0.15 and this would give us how much of the total amount is 15% and therefore it would give us how much of a discount the senior receives off of the 8.95 price
8.95 x 0.15 = 1.3425
Therefore, a senior citizen gets $1.3425 discount.
Two isosceles triangles have the same base length. the legs of one of the triangles are twice as long as the legs of the other. find the lengths of the sides of the triangles of their perimeters are 23 cm and 43 cm.
Answers
Final answer:
To find the lengths of the sides of two isosceles triangles with equal bases and perimeters of 23 cm and 43 cm, we calculate based on the known relations. The smaller triangle has sides of 10 cm and 3 cm, while the larger triangle has sides of 20 cm and 3 cm.
Explanation:
The problem involves two isosceles triangles with the same base length, but the legs of one triangle are twice as long as the other. One triangle has a perimeter of 23 cm, and the other has a perimeter of 43 cm. To solve this, let's denote the common base of both triangles as b, the legs of the smaller triangle as l, and the legs of the larger triangle as 2l.
For the smaller triangle, the perimeter P is given by P = b + l + l or P = b + 2l. For the larger triangle, the perimeter P is P = b + 2l + 2l or P = b + 4l. Since the perimeters are 23 cm and 43 cm respectively, we can set up two equations: b + 2l = 23 and b + 4l = 43.
Solving these simultaneous equations, subtract the first from the second to find 2l = 20, so l = 10. Substituting l = 10 into the first equation gives us b + 20 = 23, thus b = 3.
Therefore, the sides of the smaller triangle are 10 cm (legs) and 3 cm (base), and the sides of the larger triangle are 20 cm (legs) and 3 cm (base).
Solve the triangle.
A = 48, a = 32, b = 27
I am completely blanking on how to do this, so if you could please do a step by step process, that would be greatly appreciated :)
Answers
sin B = (27/32)*sin 48 = 0.6270 or
B = 39°; C=180-48-39 = 93°
c^2 = a^2 +b^2 -2abcos C = 32^2 +27^2 -{2*32*27*cos 93}=1843 or
c =43
Answer:
The triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
Step-by-step explanation:
We have sine rule,
[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
Here given A = 48°, a = 32, b = 27
Substituting
[tex]\frac{32}{sin48}=\frac{27}{sinB}=\frac{c}{sinC}\\\\sinB=0.627\\\\B=38.83^0[/tex]
We have
A + B + C = 180°
48 + 38.83 + C = 180
C = 93.17°
Using sine rule again
[tex]\frac{32}{sin48}=\frac{c}{sin93.17}\\\\c=42.99[/tex]
So the triangle is A = 48°, a = 32, B = 38.83°, b = 27, C = 93.17° and c = 42.99
A 32 ft ladder liens against a building so that the top of the ladder touches the building at a point 23 ft above the ground. To the nearest 10th of a foot how far from the bottom of the building is the bottom of the ladder
A. 27.5 ft
B. 39.4 ft
C. 22.2 ft
D. 30.1 ft
Okay so I’m thinking between C and B. I’m more so C because I did 32 as c and 23 as be so... or it could be the other way around
I just know it’s Pythagorean theorem help. Sending stars
Answers
529 + b^2 = 1024
b^2 = 1024 -529 = 495
b = sqrt(495) = 22.24
Answer = C. 22.2 ft
describe the graph of a quadratic function
Answers
The graph of a quadratic function, or a parabola, is U or n-shaped and its direction depends on the sign of the coefficient of the x-squared term. The vertex and line of symmetry can be found using formulas based on this coefficient.
Explanation:The graph of a quadratic function, also known as a parabola, generally takes on a 'U' or 'n' shape. The direction that the 'U' faces depends on the sign of the coefficient, which is the number associated with the x-squared term in the equation. If this coefficient is positive, the graph opens upwards; if it's negative, the graph opens downwards. The vertex (the highest or lowest point on a parabola) can be calculated using the formula -b/2a. The line of symmetry can be found using the equation x = -b/2a.
For example, consider the quadratic function f(x)=x^2. This equation represents a parabola that opens upwards. Its vertex is at the point (0,0) and its line of symmetry is x=0.
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Let f(x)=x^2−3x−4 .
What is the average rate of change from x = 7 to x = 10?
Enter your answer in the box.
Answers
https://brainly.com/question/9030327
The cylinders are similar. The volume of the larger cylinder is 9648 cubic inches. What is the volume of the smaller cylinder?
Answers
The volume formula of a cylinder is:
V = [tex] \pi [/tex]r²h
The volume of the larger volume is given to be 9648³ and the height is 18 in
We need to find the radius first
9648 = [tex] \pi [/tex]r²(18)
[tex] \frac{9648}{18} [/tex] = [tex] \pi [/tex]r²
536 = [tex] \pi [/tex]r²
[tex] \frac{536}{ \pi} [/tex] = r²
[tex] \sqrt{ \frac{536}{ \pi } } [/tex] = r
r ≈ 13.06
The ratio of the big cylinder to small cylinder is:
18 : 9 (given height)
So the big cylinder is 2 times bigger than the small cylinder
Therefore the radius of the big cylinder is as well 2 times bigger
[tex] \frac{13.06}{2} = r [/tex]
r ≈ 6.53 ( the radius of the small radius )
V (of small cylinder) = [tex] \pi [/tex](6.53)²(9)
= 1206 in³
HELP PLS
Let f(x)=2/5 x^2−2 .
The function g(x) is a vertical stretch of f(x) by a factor of 2.
What is the equation of g(x)?
Enter your answer in the box.
Answers
To graph y = a*f (x)
if a> 1, the graph of y = f (x) is expanded vertically by a factor a.
We have then:
f (x) = 2/5 x ^ 2-2
The function g (x) is a vertical stretch of f (x) by a factor of 2:
g (x) = 2f (x)
g (x) = 2 (2/5 x ^ 2-2)
g (x) = 4/5 x ^ 2-4
Answer:
The equation of g (x) is:
g (x) = 4/5 x ^ 2-4
Answer:
We have then:
f(x) = 2/5x^2-2 The function g (x) is a vertical stretch of f(x) by a factor of 2:
g(x) = 2f (x)
g(x) = 2 (2/5x^2-2)
g(x) = 4/5 x^2-4 is a required equation.
Two angles of a triangle measure 58° and 42°. What is the measure, in degrees, of the third angle?
A.60 degrees
B. 90 degrees
C.75 degrees
D.80 degrees
The correct answer will receive full points and the brainiest
Answers
ANSWER THIS BEFORE 3 MINUTES, AND I WILL GIVE YOU BRAINIEST AND 15 POINTS!!!
PROBLEM:
In a heptagon, the degree measures of the interior angles are
x, x, x-2, x-2, x + 2, x + 2 and x + 4 degrees. What is the degree measure of the largest interior angle?
Answers
The largest interior angle of the heptagon, given the angle measures as x, x, x-2, x-2, x+2, x+2, x+4, is 132 degrees after solving for x.
The problem is to determine the degree measure of the largest interior angle in a heptagon. The degree measures of the interior angles are given as x, x, x-2, x-2, x+2, x+2, and x+4 degrees. To solve this, we first use the fact that the sum of the interior angles of a heptagon (7-sided polygon) is given by the formula (n-2) 180 degrees, where n is the number of sides. So, for a heptagon, the sum is
(7-2) 180 = 900 degrees.We then set up the equation based on the given interior angles: 3x + (2x - 4) + (2x + 4) + (x + 4) = 900. Simplifying, we get 7x + 4 = 900. Solving for x, we find x = 896/7 = 128 degrees. The largest interior angle is x + 4, which equals
128 + 4 = 132 degrees.Ellen has a $19,750 balance on a credit card with an APR of 18%. If she makes minimum monthly payments of $300, how much will it cost Ellen to repay the total amount on the credit card? $
Answers
If t(n) 2n+3 what is the 3rd term
Answers
t(3)=2(3)+3
6+3 = 9
On Chris' birthday in 1992, he was half the age of his brother Joseph. On Chris' birthday in 1998, he was two-thirds the age of Joseph. How old will Chris be on his birthday in 2018?
Answers
Step 1: Form an equation.
We know that in 1992, Chris was HALF the age of Joseph. So Chris was x years old, while his brother was twice his age, or 2x. 6 years later, he was two-thirds the age of his brother. So, he was (x+6) while his brother was (2x+6).
So, we can form this:
(X+6)=(2/3)(2x+6)
Step 2: Simplify the equation. Distribute, Subtract, multiply
(X+6)=(2/3)(2x+6)
Distribute: X+6=(2/3)(2x)+(2/3)(6)
X+6=4/3x+4
Subtract:
X+6-4/3x=4/3x+4-4/3x
-1/3x+6=4
Subtract:
-1/3x+6-6=4-6
1/3x=-2
Multiply:
(3/-1) * (-1/3x)=(3/-1)*(-2)
X=6
This means in 1992, Chris was indeed 6 years old, while his brother was 12. 6 years later, Chris was 12 years old, while his brother was 18. (6/12=1/2; 12/18=2/3)
So, from 1992-2018=26 years.
In 1992 Chris was already 6.
26+6=32
In 2018, Chris is 32 years old, his brother is 6 years older, 38.
Chris is 32 years old.
~Hope this helps!
Which of the following is not an identity?
A. cos^2 x csc x - csc x = -sin x
B. sin x(cot x + tan x) = sec x
C. cos^2 x - sin^2 x = 1- 2sin^2 x
D. csc^2 x + sec^2 x = 1
***i don't really get this one :( @terenzreignz? what do u think?,
Answers
The process for each option is to rewrite the equation, attempting to obtain the identity sin^2 x + cos^2 x = 1. In general convert each function to its equivalent using just sin and cos.
A. cos^2 x csc x - csc x = -sin x
cos^2 x * 1/sin x - 1/sin x = -sin x
(cos^2 x * 1/sin x - 1/sin x) * sin x = -sin x * sin x
cos^2 x * 1 - 1 = -sin^2 x
cos^2 x = -sin^2 x + 1
cos^2 x + sin^2 x = 1
Option A is an identity.
B. sin x(cot x + tan x) = sec x
sin x(cos x/sin x + sin x/cos x) = 1/cos x
cos x + sin^2 x/cos x = 1/cos x
cos^2 x + sin^2 x = 1
Option B is an identity.
C. cos^2 x - sin^2 x = 1- 2sin^2 x
cos^2 x - sin^2 x + 2sin^2 x = 1- 2sin^2 x + 2sin^2 x
cos^2 x + sin^2 x = 1
Option C is an identity.
D. csc^2 x + sec^2 x = 1
1/sin^2 x + 1/cos^2 x = 1
cos^2 x/(cos ^2 x sin^2 x) + sin^2 x/(cos^2 x sin^2 x) = 1
(cos^2 x + sin^2 x)/(cos ^2 x sin^2 x) = 1
1/(cos ^2 x sin^2 x) = 1
1 = cos ^2 x sin^2 x
Option D is NOT an identity.
3 is less than or equal to x, and x is less than or equal to 9
Answers
Hope this helped!
in the formula for a sphere what is decimal that represents the fraction 4.3
Answers
the volume of a sphere is V = 4/3 πr³
the fraction (4/3) is equal to 1.33
the answer is 1.33
how do i solve problem a. and problem b? (using the pythagorean theorem). a. the median to the hypotenuse. b. the altitude to the hypotenuse.
Answers
from mathopenref: median: "A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side."
if we draw a median to the hypotenuse, then we have to draw from the right angle to the hypotenuse.
we use a theorem: "In a right triangle, the median drawn to the hypotenuse has the measure half the hypotenuse. "
the length of the median to the hypotenuse is half the hypotenuse: 5
for altitude:
we draw line on hypotenuse that is perpendicular to hypotenuse to a vertex of the angle opposite to it.
look at my diagram: h is the altitude length
x and y are segments of the original hypotenuse
we have ΔABD with legs of x and h and hypotenuse of 6
ΔABD: x² + h² = 6²
we have ΔBCD with legs of 10-x and h and hypotenuse of 8
ΔBCD: (10-x)² + h² = 8²
this is a system of equations
x² + h² = 6²
(10-x)² + h² = 8²
isolate h² in x² + h² = 6² so that we can substitute:
h² = 6² - x²
h² = 36 - x²
substituting into (10-x)² + h² = 8² we have
(10-x)² + h² = 8²
(10-x)² + (36 - x²) = 8² ...............substitution done
(10-x)² expands to 100 - 20x + x²
100 - 20x + x² + (36 - x²) = 64
+x² and -x² cancel
100 - 20x + 36 = 64
136 - 20x = 64
-20x = -72
x = 3.6
Since h² = 36 - x², then h = √(36 - x²) and
h = √(36 - 3.6²) =4.8
the altitude is 4.8
will give medal to best answer!
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used.
C = 38°, a = 19, c = 10,
Answers
Begin with applying the Law of Sines to find angle A:
[tex] \frac{sin A }{a} [/tex] = [tex] \frac{sin C }{c} [/tex]
Then, solve for sin A:
sin A = [tex] \frac{a sinC}{c} [/tex]
Now, plug in numbers:
sin A = 19 × sin(38) / 10 = 1.17
We know that it does not exist an angle whose sin is bigger than 1, therefore
no triangle is formed.
Answer:
No triangle is formed
Step-by-step explanation:
took test
Ppose you have two coins, one biased, one fair, but you don't know which coin is which. coin 1 is biased. it comes up heads with probability 2/3, while coin 2 comes up heads with probability 1/2. suppose you pick a coin at random and flip it. let ci denote the event that coin i is picked. let h and t denote the possible outcomes of the flip. given that the outcome of the flip is a head, what is p[c1|h], the probability that the biased coin is picked?
Answers
(Please Help~! 20 Points~!)
Which of the following is the solution to the equation 3/4y = 24?
y = 18
y = 32
y = 64
y = 72
Answers
Brainliest please?
I am trying to move up my rank to Ace!
[tex] \dfrac{3}{4}y = 24[/tex]
Rewrite into single fractions
[tex] \dfrac{3y}{4} = \dfrac{24}{1} [/tex]
Cross multiply
[tex]3y = 24 \times 4[/tex]
Evaluate the right side
[tex]3y = 96[/tex]
Divide by 3 on both sides
[tex]y = 32[/tex]
-------------------------------
Answer: y = 32
-------------------------------
Use the Law of Sines to find the missing side of the triangle. Find b.
Answers
Answer:
43.82 units.
Step-by-step explanation:
We have been given a triangle. We are asked to find the value of b using Law of Sines.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], where, a, b and c are opposite sides of angles A, B and C respectively.
Upon substituting our given values in above formula, we will get:
[tex]\frac{50}{\text{sin}(58^{\circ})}=\frac{b}{\text{sin}(48^{\circ})}[/tex]
Switch sides:
[tex]\frac{b}{\text{sin}(48^{\circ})}=\frac{50}{\text{sin}(58^{\circ})}[/tex]
[tex]\frac{b}{0.743144825477}=\frac{50}{0.848048096156}[/tex]
[tex]\frac{b}{0.743144825477}*0.743144825477=\frac{50}{0.848048096156}*0.743144825477[/tex]
[tex]b=43.81501643866[/tex]
[tex]b\approx 43.82[/tex]
Therefore, the value of b is approximately 43.82 units.
Find the value of a and b
Answers
Answer:
The value of a is 14 unit and the value of b is [tex]6\sqrt{2}[/tex] unit
EXPLANATION:
Draw a perpendicular line from vertex B to DC at E.
Labeling the diagram as shown in the attachment:
Now, as you can see from the Figure as shown in the attachment that [tex]ABDE[/tex] represents the rectangle because a rectangle is a quadrilateral with four right angles and their opposite sides would be parallel.
Therefore, we have the sides [tex]AB=DE=8[/tex] unit , and [tex]AD=BE=6[/tex] unit.
Consider the right triangle BEC
BY 45 45 90 triangle is a special type of isosceles right triangle where the two legs are congruent to one another and the non-right angles are both equal to 45 degrees.
therefore, the length of side, [tex]BE=EC=6[/tex] unit
Using trigonometric ratio; to find the value of b:
[tex]\sin \theta =\frac{perpendicular}{Hypotenuse}[/tex]
∴ using trigonometric sine ratio in triangle BEC, we have
[tex]\sin 45^{\circ} =\frac{6}{b}[/tex] or
[tex]\frac{1}{\sqrt{2} }= \frac{6}{b}[/tex]
On Simplify:
[tex]b=6\sqrt{2}[/tex] unit
and the value of a = DC = DE+EC=8+6=14 unit
Therefore, the value of a is 14 unit and b is [tex]6\sqrt{2}[/tex] unit
3x+11y=8 SOLVE FOR Y
Answers
-3x -3x
11y = 8 - 3x
/11 /11
y = 0.72 - 3x/11
To solve 3x + 11y = 8 for y, first subtract 3x on both sides to isolate 11y.
3x + 11y = 8
-3x -3x
----------------------
11y = -3x + 8
divide both sides by 11.
11y = -3x + 8
y = -3/11 +8/11
Hope this helped! :)
An acidophilus culture containing 150 bacteria doubles in population every hour. (a) Write a function representing the bacteria population for every hour that passes. (b) Graph the function. (c) Use the graph to predict the number of bacteria after 12 hours.,
Answers
We have then:
y = A * (b) ^ t
Where,
A: Initial population
b: Population growth as time passes
t: time
y: population after t hours.
Part A:
The equation for this case is:
y = 150 * (2) ^ t
Part B
See attached image.
Part C:
For this case we should evaluate the function for t = 12
We have then:
y = 150 * (2) ^ (12)
y = 614400
y = 150 * (2) ^ t
t= 12
y = 150 * (2) ^ (12)
y = 614400
The answer to your questions is y is equals to 614400.
The musical frequency of notes is decreasing between beat numbers ___ and ___
Answers
we have that
between beats 2 and 3----------> (392-261.6)=130.4-------> increases
between beats 3 and 4----------> (392-392)=0-----> it stays with the same value
between beats 4 and 5----------> (444-392)=52--------> increases
between beats 5 and 6----------> (444-444)=0-----> it stays with the same value
between beats 6 and 7----------> (392-444)=-52-------> decreases
the answer is
between beats 6 and 7----------> (392-444)=-52-------> decreases