Given:
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.
To find:
The coordinates of the vertices of triangle A’B’C’.
Solution:
If triangle ABC reflected across y-axis, then
[tex](x,y)\to (-x,y)[/tex]
[tex]A(-1,4)\to A_1(1,4)[/tex]
[tex]B(-4,1)\to B_1(4,1)[/tex]
[tex]C(-1,1)\to C_1(1,1)[/tex]
Coordinates of image after reflection across y-axis are [tex]A_1(1,4),B_1(4,1),C_1(1,1).[/tex]
Then triangle translated 4 units to the left to form triangle A’B’C’.
[tex](x,y)\to (x-4,y)[/tex]
[tex]A_1(1,4)\to A'(-3,4)[/tex]
[tex]B_1(4,1)\to B'(0,1)[/tex]
[tex]C_1(1,1)\to C'(-3,1)[/tex]
Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).
Hence, the correct option is B.
I don’t under this .
Answer:
The answer is QR,RS, and ST
Step-by-step explanation:
i hope this helps .
Find the area of the surface. The part of the paraboloid z = 1 - x2 - y2 that lies above the plane z = -6
Answer:
π/6 [(29)^³/₂ − 1]
81.247
Step-by-step explanation:
Surface area is:
S = ∫∫ √(fₓ² + fᵧ² + 1) dA
The partial derivatives are:
fₓ = -2x
fᵧ = -2y
Substituting:
S = ∫∫ √(4x² + 4y² + 1) dA
To make this easier, we can convert to polar coordinates.
S = ∫∫ √(4r² + 1) dA
S = ∫∫ √(4r² + 1) r dr dθ
S = ⅛ ∫∫ 8r √(4r² + 1) dr dθ
The limits for θ are 0 to 2π. The minimum of r is 0. The maximum of r is:
-6 = 1 − x² − y²
-6 = 1 − r²
r² = 7
r = √7
Integrating the first integral:
S = ⅛ ∫ ⅔ (4r² + 1)^³/₂ |₀ᴿ dθ
S = ⅛ ∫ [⅔ (4(7) + 1)^³/₂ − ⅔ (4(0) + 1)^³/₂] dθ
S = ⅛ ∫ [⅔ (29)^³/₂ − ⅔] dθ
S = ¹/₁₂ [(29)^³/₂ − 1] ∫ dθ
Integrating the second integral:
S = ¹/₁₂ [(29)^³/₂ − 1] θ |₀²ᵖⁱ
S = ¹/₁₂ [(29)^³/₂ − 1] (2π − 0)
S = π/6 [(29)^³/₂ − 1]
S ≈ 81.247
The area of a shape is the amount of space it covers.
The surface area is approximately 81.3 unit squares
The given parameters are:
[tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{z = -6}[/tex]
Calculate the partial derivatives of [tex]\mathbf{z = 1 - x^2 - y^2}[/tex]
[tex]\mathbf{f_x = -2x}[/tex]
[tex]\mathbf{f_y = -2y}[/tex]
So, the surface area is:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(f_x^2 + f_y^2 +1 )}} \, dA }[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{((-2x)^2 + (-2y)^2 +1 )}} \, dA }[/tex]
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4x^2 + 4y^2 +1 )}} \, dA }[/tex]
Factor out 4
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4(x^2 + y^2) +1 )}} \, dA }[/tex]
Substitute
[tex]\mathbf{r^2 = x^2 + y^2}\\\mathbf{dA = rdr d\theta}[/tex]
So, we have:
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r\ dr\ d\theta }[/tex]
Multiply by 1
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times 1\ dr\ d\theta }[/tex]
Express 1 as 8/8
[tex]\mathbf{A = \int\limits^a_b\int\limits^a_b {\sqrt{(4r^2 +1 )}} \, r \times \frac{8}{8}\ dr\ d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
From the question,
[tex]\mathbf{z = -6}[/tex]
So, we have:
[tex]\mathbf{1 - r^2 = -6}[/tex]
Add 6 to both sides
[tex]\mathbf{7 - r^2 = 0}[/tex]
So, we have:
[tex]\mathbf{r^2 = 7}[/tex]
Integrate [tex]\mathbf{A =\frac{1}{8} \int\limits^a_b\int\limits^a_b {8r \sqrt{(4r^2 +1 )}}, \ dr\ d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \int\limits^a_b {\frac{8}{12} (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{8} \times \frac{8}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32}}, |\limits^R_0 d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4r^2 +1 )^{\frac 32} -(4 \times 0^2 +1 )^{\frac 32} }, d\theta }[/tex]
Substitute [tex]\mathbf{r^2 = 7}[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b { (4\times 7 +1 )^{\frac 32} - 1^{\frac 32}}, d\theta }[/tex]
[tex]\mathbf{A =\frac{1}{12} \int\limits^a_b {29^{\frac 32} - 1}, d\theta }[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \int\limits^a_b d\theta }[/tex]
Integrate
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times \theta |\limits^{2\pi}_0}[/tex]
So, we have:
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times (2\pi - 0) }[/tex]
[tex]\mathbf{A =\frac{1}{12} (29^{\frac 32} - 1), \times 2\pi}[/tex]
Rewrite as:
[tex]\mathbf{A =\frac{2\pi}{12} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =\frac{\pi}{6} (29^{\frac 32} - 1)}[/tex]
[tex]\mathbf{A =81.3}[/tex]
Hence, the surface area is approximately 81.3 unit squares
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The mean life of a television set is 138 months with a variance of 324. If a sample of 83 televisions is randomly selected, what is the probability that the sample mean would be less than 143.4 months
Answer: 0.9968
Step-by-step explanation:
Let [tex]\overline{X}[/tex] be the sample mean life of television.
Given: [tex]\mu=138,\ \ \ \sigma^2=324\Rightarrow\ \sigma=\sqrt{324}=18,\ \ \ , n=83[/tex]
The probability that the sample mean would be less than 143.4 months will be :
[tex]P(\overline{X}<143.4)=P(\dfrac{\overline{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}<\dfrac{143.4-138}{\dfrac{18}{\sqrt{83}}})\\\\=P(Z<2.733)=0.9969\ \ \ [\text{By p-value table}][/tex]
hence, the required probability = 0.9968
Paige mows
1
4
acre in
1
2
hour. How many acres does Paige mow per hour?
Answer:
1.16
Step-by-step explanation:
you have to divide 14 by 12 since the amount of acres mowed in 12 hours is how much acres she's mowed.
Ali"s dog weighs 8 times more than her cat. Together the animals weigh 54 lbs. How much does Ali's dog weigh?
Answer:
48 lbs
Step-by-step explanation:
say that the cat weighs x pounds. then the dog weighs 8x pounds. together they weigh 54 pounds. So our equation is x+8x=54. solve for x to get the cat's weight, and you get x=6. The cat weighs 6 lbs. all I need to do now is multiply 6 by 8 so this the dog weighs 8 times as much as the cat. 8•6=48. the dog weighs 48 pounds.
You spend 5/6 of your money on new clothes for school. The amount you spend on jeans for school is 2/5 of the total amount you spend on all your school clothes.
What fraction of money do you spend on jeans?
A. 7/30 on jeans
B. 10/30 on jeans
C. 1/3 on jeans
D. 5/30 on jeans
Answer:
C
Step-by-step explanation:
well when we multiply to get a common denominator we get 25/30 and 12/30 so the only possible answer is 1/3
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Henry, Ladaris
DISTRICT SWI CA GRADE 6 MATH 20-21
D3101 2. P N →
Eat Test
4
BO
In a TV contest show, Thomas has 280 points. To determine his final score in the game, Thomas will spin the spinner shown below, and multiply his current number of points by the
fraction the spinner lands on
Which statement correctly describes the effect of multiplying his current score by the fractions shown on the spinner?
A Multiplying by will decrease his score
B Multiplying by will decrease his score.
Copyright 2020 laminate Education, Inc. All Rights Reserved
US 2:41
Answer:
Step-by-step explanation:
3x+2=11 what is the answer
x = 3
Step-by-step explanation:Hi there !
3x + 2 = 11
3x = 11 - 2
3x = 9
x = 9/3
x = 3
Good luck !
what is the increase of y=26(0.904)x
Evaluate −b2−2bx2−x when x=−2.
An expression is defined as a set of numbers, variables, and mathematical operations. The value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The value of the expression −b²−2bx²−x will be,
−b² − 2bx² − x
= − b² − 2b(-2)² − (-2)
= − b² − 8b + 4
Hence, the value of −b²−2bx²−x when the value of x=-2 is −b²−8b + 4.
Learn more about Expression:
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A recipe for salad dressing calls for 3 teaspoons of oil for every 2 tablespoons of vinegar
Answer:
6
Step-by-step explanation:
Answer:
1,1.5 is the answer
Step-by-step explanation:
4. What's the least common multiple of each group of numbers?
a. 5 and 6
b. 2 and 9
c. 6 and 8
d. 2,5, and 6
Answer:
D. 2,5, and 6
Step-by-step explanation:
Because if u mutiply 2*5 = 10 and 2*6 is 12 as 5*6 is 30 and 2*9 is 18 .
Choose the graph of y < -x^2 + 4x + 5
edge2020
First one the one that has the blue inside
A=4 b= -5 and c=-8
HELLPPPPPP
which of the following should one consider when choosing a career?
Answer:
all of the above
have a good day keep working
IM GONNA FAIL OMG HELP ME ILL GOVE YOU POINTS!!
Answer:
Step-by-step explanation:
1. yes
2. no
3. -10 and 5
4. -6
5. 3x+3
6. 3x+4
7. 14xy^2-3y+7
8. -3y-7x
9. 10x -5
Answer:
1) yes they are if y is alone its just 1y so yes their like terms.
2)no 5xy^2 is different bc the exponent
3)5x-5
4)-6
5)3x+3
6)4+4x
7)14xy^2-3y+7
8)3y-7x
9)10x-5
Step-by-step explanation:
Kermit's favorite iced tea is made with 15 tea bags in every 2 liters of water. Peggy made a 12-liter batch of iced tea with 90 tea bags.
What will Kermit think of Peggy's iced tea?
Answer:
He will love the Tea
Step-by-step explanation:
12 divided by 2 is 6
We take 6 ( the liter that he likes ) and multiply it by 15. This gives us 90, exactly what Peggy made.
Answer:
It is just right!
Step-by-step explanation:
12 divided by 2 is 6 . We take 6 and multiply it by 15. This gives us 90, which is exactly what Peggy made.
Please help I’m in a hurry
Answer:
I believe it is A 20,
however id wait for another answer to confirm lol
Write in slope intercept form:
(-4,6) slope= -3/4
Answer:
y=-3/4x+0
Step-by-step explanation:
A line segment has endpoints at (-1, 4) and (4,1). Which reflection will produce an image with endpoints at (-4,1)
and (-1,-4)?
a reflection of the line segment across the x-axis
O a reflection of the line segment across the y-axis
O a reflection of the line segment across the line y = x
O a reflection of the line segment across the line y = -X
Answer:B
Step-by-step explanation:
A reflection of the line segment across the line y = - x, will produce an image with endpoints at (- 4, 1) and (- 1, - 4).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
We know, A reflection across the 180° about the origin transforms
(x, y) to (-x, - y)
Therefore A line segment has endpoints at (-1, 4) and (4,1) will have an image at (- 4, 1), and (- 1,- 4) is a reflection of the line segment across the line y = - x.
learn more about reflection here :
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In the diagram, quadrilateral LMNO is a parallelogram. What is the length of ?
A.
6
B.
5.66
C.
5.39
D.
2.24
Answer:
NP = 5.39
Step-by-step explanation:
This is the answer because opposite diagonals have equal lengths.
In quadrilateral LMNO which is a parallelogram, diagonals bisect each other, hence NP = LP = 5.39
What is a polygon?A polygon can be defined as a two-dimensional closed shape with straight sides and no curved side. Types of polygons are triangle, quadrilateral, pentagon, hexagon, etc.
A parallelogram is a quadrilateral (four sides and four angles) in which opposite sides are equal and parallel. Opposite diagonals bisect each other.
In quadrilateral LMNO:
NP = LP = 5.39 (diagonals bisect each other)
In quadrilateral LMNO which is a parallelogram, diagonals bisect each other, hence NP = LP = 5.39
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Twice the difference of a number and 7 is at least 18
Answer: n=16
Step-by-step explanation:2(n-7) = 18
n - 7 = 9
+7 +7
Answer:
2(x-7) ≥ 18
2x - 7 ≥ 18
+7 +7
2x ≥ 25
2 2
x ≥ 12.5
Check
2((12.5) -7) ≥ 18
2(5.5) ≥ 18
11 ≥ 18
I think this works
Suppose Phil reads a book that contains 16 conspiracy theories. When he researches the theories, he finds that 75% of them are false. How many of the theories are true?
Answer:
4
Step-by-step explanation:
Does the following relation represent a function?
{(14, 15), (5, 7), (3, 10), (11, 1), (5,8)]
Yes
O No
Pls help soon
Answer: This is not a function.
Step-by-step explanation: A function CANNOT have a repeating x-value.
6 is added to three-fifths of p
Answer:
Is that the question? I don't think it is
car rental agency charges a base rate plus a certain amount per day (d) and can be modeled using the expression 15+ 18d. What is the meaning of 18d in the expression? *
4 points
It is the base rate to rent a car.
It is the cost of renting a car for a day.
It is the total number of days a car can be rented.
It is the portion of the cost based on renting a car for d days.
Answer:
It is the portion of the cost based on renting a car for d days
Step-by-step explanation:
Given:
Total cost = 15 + 18d
Total cost = fixed cost + variable cost
Fixed cost are cost that do not change.
Fixed cost = base rate = 15
Variable cost changes during production process. The variable cost in the above varies with the number of days (d)
Therefore, 18d is the portion of the cost based on renting a car for d days.
If you rent the car for 1 day
Total cost = 15 + 18d
= 15 + 18(1)
= 15 + 18
= 33
5x-25=-10
Please HELP
= 5x - 25 = -10
= 5x = -10 + 25 ( transposing-25 from LHS to RHS changes -25 to +25 )
= 5x = 15
= x = 15 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 l
= x = 3
Let us check whether or not we have found out the correct value by keeping 3 in the place of x :
= 5 × 3 - 25 = -10
= 15 - 25 = -10
= -10 = -10
LHS = RHS
We have found out the correct value of x .
Therefore x = 3 .
How do we shift the graph of y=f(x) to get the graph of y = f(x) +5?
A Move the graph down by 5 units.
B Move the graph up by 5 units.
Answer:
B, Up 5 units
Step-by-step explanation:
because of the +
At a grocery store, the price of 3 cans of soul is 6.90.
At this rate, how much would 10 cans of soup cost ?
Answer: answer is $23
Step-by-step explanation:
first divide 6.90 by 3
and you should get 2.3
Then you multiply 2.3 by 10
and you should get $23
d+fg=h (solve for the variable “g”)
Answer:
g = h/f - d/f
Step-by-step explanation: