Triangle LMN has vertices at L(-1,5),M(-1,0),N(-2,5), then the vertices are L'(-5, -1), M'(0, -1), N'(-5, -2).
To rotate a point counterclockwise:
For a point (x, y):
x' = x*cos(theta) - y*sin(theta)
y' = x*sin(theta) + y*cos(theta)
In this situation, rotate the triangle 90° counterclockwise about the origin.
The transformation equations to each vertex of the triangle states that:
For vertex L(-1, 5):
x' = -1*cos(90°) - 5*sin(90°) = -1*0 - 5*1 = -5
y' = -1*sin(90°) + 5*cos(90°) = -1*1 + 5*0 = -1
Therefore, vertex L' is (-5, -1).
For vertex M(-1, 0):
x' = -1*cos(90°) - 0*sin(90°) = -1*0 - 0*1 = 0
y' = -1*sin(90°) + 0*cos(90°) = -1*1 + 0*0 = -1
Therefore, vertex M' is (0, -1).
For vertex N(-2, 5):
x' = -2*cos(90°) - 5*sin(90°) = -2*0 - 5*1 = -5
y' = -2*sin(90°) + 5*cos(90°) = -2*1 + 5*0 = -2
Therefore, vertex N' is (-5, -2).
Thus, the vertices of the image triangle L'M'N' after rotating the original triangle 90° counterclockwise about the origin are: L'(-5, -1), M'(0, -1), N'(-5, -2).
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Use the distributive property to simplify 3 + 5c(2 + 6c) completely.
Answer:
Distributive property says that:
(A + B)*C = A*C + B*C
Now let's try to use it in our expression:
3 + 5*c*(2 + 6*c)
Here we can take the two terms inside the parentheses as A and B, and the term that multiplies them as C, then distributing we get:
3 + (5*c)*2 + (5*c)*(6*c)
Now remember that the multiplications are associative and commutative, then we can write this as:
3 + (2*5)*c + (5*6)*(c*c)
3 + 10*c + 30*c^2
And we can't simplify it anymore.
What number should be added to both sides of the equation to complete the square? x^2-40x=0
Answer:
+40
Step-by-step explanation:
Answer:
400
Step-by-step explanation:
When completing the square, all you need to do is take half the coefficient of x, and square it.
In this case the coefficient of x is -40, and half of that is -20. -20 squared is 400, and that is what you need to add to both sides.
Note that when completing the square, you'll always be adding a positive number unless coefficient you're working with is an imaginary or complex number.
GEOMETRY find the angle of PRQ NO LINKS!!
Answer:
55
Step-by-step explanation:
Remark
This is a really good question to know the answer to. <PRQ = 1/2 POQ (the central angle. )
The central angle for this question is 110o. So any angle that has its vertex on the circumference is 1/2 110 = 55. The central angle and the angle on the circumference must be related as they are as this question is. (Both are on the same side of PQ which is not drawn but you can draw it).
Which set of shapes could you use to form a net for a
triangular prism?
O 5 triangles
О 4 triangles, 1 rectangle
O 3 triangles, 2 rectangles
O 2 triangles, 3 rectangles
Find The distance between the pair of points
G(0, - 5) and H(0, - 10
Answer:
5
Step-by-step explanation:
7. The area of a triangle is 2.1 square feet. Its base is 2 feet. What is its height
Step-by-step explanation:
area of a triangle is (bh)/2
b=base
h=height
2.1=(2h)/2
2.1=height
Hope that helps :)
Answer:
4.2
Step-by-step explanation:
Multiply 2.1 and 2 to get 4.2
Find the measurement indicated. Round to the nearest tenth.
9514 1404 393
Answer:
22.015.030.0°137.0°Step-by-step explanation:
These are all Law of Cosine problems. A generic expression for the length of side 'c' opposite angle C, which is defined by sides 'a' and 'b' is ...
c² = a² +b² -2ab·cos(C)
The square root of this gives the side length:
c = √(a² +b² -2ab·cos(C))
Rearranging the equation, we can obtain an expression for the angle C.
C = arccos((a² +b² -c²)/(2ab))
These two formulas are used to solve the offered problems.
__
1) AC = √(13² +14² -2·13·14·cos(109°)) ≈ √483.506
AC ≈ 22.0
__
2) BC = √(7² +10² -2·7·10·cos(123°)) ≈ √225.249
BC ≈ 15.0
__
3) ∠B = arccos((24² +28² -14²)/(2·24·28)) = arccos(1164/1344)
∠B ≈ 30.0°
__
4) ∠B = arccos((6² +9² -14²)/(2·6·9)) = arccos(-79/108)
∠B ≈ 137.0°
What value of x makes this equation true?
12x - 15 = 6 - 36
what is one-tenth of 0.90?
Answer:
0.09
Step-by-step explanation:
Two closets can store 16
chairs. How many chairs
can 8 closets store?
Answer:
64
Step-by-step explanation:
Given a center of (3,-5) and a radius of 4, write an equation for the circle.
Answer:
(x-3)²+(y+5)²=16
Step-by-step explanation:
[tex] \large \boxed{ {(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} }[/tex]
The equation above is an equation of circle with a centre at (h,k) and has radius = r
Substitute h = 3, k = -5 and r = 4 in the equation.
[tex] \large{ {(x - 3)}^{2} + {(y - ( - 5))}^{2} = {4}^{2} } \\ \large{ {(x - 3)}^{2} + {(y + 5)}^{2} = 16}[/tex]
01:11:1
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The population, P, of six towns with time t in years are given by the following exponential equations:
(0) P - 1000(1.08)'
(ii) P-600(1.12)
(iii) P - 2500(0.9)'
(iv) P - 1200(1.185)
(V) P - 800(0.78)
(vi) 2000(0.99)
Which towns are decreasing in size?
i, ii, and iv
c. i, ii, and iii
b. iii, v, and vi
d. vi, i, and ii
a.
Please select the best answer from the choices provided
А
B
е с
D
9514 1404 393
Answer:
b. iii, v, and vi
Step-by-step explanation:
We assume your equations are intended to be P=(something) where the something has a final factor of ( )^t.
The final factor is called the "growth factor". Subtracting 1 from it gives the "growth rate". When that value is negative, the population is declining.
Equations (iii), (v), and (vi) have growth rates that are negative, so those represent towns decreasing in size.
NEED HELP ASAP FREE BRAINLIST
Answer:
the correct answer is 904.78 cubic. inches
Brainliest for correct answer
Answer:
similiar and congruent
Step-by-step explanation:
Can someone please help ?
Given f(x) = -x^2 - 2x + 4, find each of the following,
Symmetric point:
Minimum of f:
Maximum of f:
Is f a one-to-one
Does f have an inverse?
Increasing on
Decreasing on
Answer:
Symmetric point: x = -1; (-1, 5)
Minimum of f: None; approaches -∞.
Maximum of f: y = 5.
Is f(x) a one-to-one: No, it fails the horizontal line test and is not injective.
Increasing from: -∞ to -1; (-∞, -1)
Decreasing from: -1 to ∞. (-1, ∞)
Answer:
Given f(x) = -x^2 - 2x + 4, find each of the following,
Step-by-step explanation:
f(x) = -x²-2x+4
f(2) = (-2)²-2×2+4
f(2) = 4-4+4
f(2) = 4
Factor out the greatest common monomial factor from polynomial. Show your work or explain your reasoning
Answer:
7(1 +3x)
Step-by-step explanation:
The simplest monomial is a constant that is a prime number. That constant is a factor of the coefficient of the only other monomial in the expression, so it can factored from both terms.
= 7 + 7·3x
= 7(1 +3x)
baby yoda needs help
Answer:
= 162
1782 divided by 11 equals
162 with a remainder of 0
Solution:
162
11[tex]\sqrt[n]{x}[/tex]1782
-11
------
68
66
--------
22
-22
Step-by-step explanation:
Only 3 more questions to go
What is the shape of the cross-section formed when a cone intersects a plane as shown in the drawing
Answer:
triangle
Step-by-step explanation:
only look at the cut off part
Answer:
I believe that the shape is formed to be a circle
Find the volume of the cylinder below. Leave your answer in terms of pi.
Find the explicit form of the arithmetic function of p if the first term is 12 and the common difference is 2. Then find the seventh term.
Answer:
1st
Step-by-step explanation:
3. The third side of a triangle measures (3x-5) cm. If the length of the midline is 14 m,
what is ?
A 8
C. 10
B. 9
D. 11
Answer:
The correct answer is D, 11 cm.
Step-by-step explanation:
Given that the third side of a triangle measures (3x-5) cm, if the length of the midline is 14 m, to determine the length of the third side and the correct option, the following calculations must be performed:
X (third side) = midline x 2
X = 14 x 2
X = 28
3X - 5 = 28
3X = 28 + 5
3X = 33
X = 33/3
X = 11
Therefore, the correct option is D: 11 cm.
What is the solution to the inequality 7x + 2 < 3x + 1?
Ο Α. α
<
1
10
OB.
<
3
4
O C.
3
>
O D. I
>
- 1 금
10
Know
Answer:
x < -1/4
Step-by-step explanation:
7x + 2 < 3x + 1
4x + 2 < 1
4x < -1
x < -1/4
Select all of the given trigonometric equations that are true statements. sin(180°) = cos(0°) cos(74°) = sin(16°) sin(20°) = cos(70°) sin(A°) = cos(90° - A°) sin(A°) = cos(180° - A°) cos(140°) = sin(40°)
Answer:
Cos 74°= Sin 16°
Sin 20°= Cos 70°
Sin A°=Cos (90°- A°)
Step-by-step explanation:
This is because the three pairs are complementary i.e they add up to 90° and in trigonometric ratios, complementary ratios are equal.
Evaluate the expression x + 23, when x = 17
Answer:
40
Step-by-step explanation:
If we have to evaluate an expression, we spsolve for whatever variable there is, and simplify. Here, we know x is 17, so we can plug it into the original expression.
17 + 23 = 40
PLEASE HELP ME! I AM NOT SURE OF MY ANSWERS.
(Only correct or possible answers. I am on Edmentum.)
Answer:
Your answers are correct
multiplicative identity
multiplication property of zero
addition property of zero
multiplicative inverse
additive inverse
communicative
reflexive
distributive
symmetric
Two families are saving money for a vacation. The Juarez family has saved $1000 and will save $50 more each week. The Kim family has saved $500 and will save $75 more each week. Write a system of equations to represent how much money each family will save.
Answer:
There are many ways you could put this let me demonstrate.
Step-by-step explanation:
If they were to do this for a year (52 weeks) that would be 50x52=2600+1000=3600. Then 75x52=$3900+500=$4400. but if you were to cut that time in half to 6 months it would go something like this. 50x26=1300+1000=2300. Then 75x26=1950+500=2450. It all has to do with the time. I hope this helped.
guys thank you for everyone who has helped me im almost done
Answer:
y = 4
y = 7
x = 6
Hope that helps! :)
Step-by-step explanation: