Answer:
9
Step-by-step explanation:
ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (2, 2), B = (4, 3), and C = (6, 3), what is the length of ?
Answer:
Fourth option is correct. The length of B'C' is 1 unit.
Step-by-step explanation:
The vertices of triangle ABC are A = (2, 2), B = (4, 3), and C = (6, 3).
Distance formula:
The length of BC is 2 units.
It is given that ΔABC is dilated by a scale factor of 0.5 with the origin as the center of dilation, resulting in the image ΔA′B′C′.
It means the ΔABC and ΔA′B′C′ are similar and corresponding sides of ΔA′B′C′ and ΔABC are proportional.
The scale factor is 0.5.
Therefore the length of B'C' is 1 unit and fourth option is correct
Answer:
D= 1 unit
Step-by-step explanation:
The weight of a suitcase checked onto a plane by a male, is a random variable with mean 42 pounds and standard deviation 16 pounds. The mean and standard deviation of the weight of a suitcase checked on to a plane by a female, is a random variable with mean 40 pounds and a standard deviation of 10 pounds. (For the purposes of this problem, a married couple consists of one male and one female. All suitcases are considered independent of each other even if from the same person.) What is the mean and standard deviation for the weight of the suitcases for a married couple, with one suitcase per person? What is the mean and standard deviation for the 6 suitcases checked onto the plan by 2 married couples, if each couple checked on 2 female suitcases and 1 male suitcase? In a cost cutting move the airlines is now charging $1.50 per pound for checked luggage. What is the mean and standard deviation for the cost of: A suitcase checked by a female 2 suitcases checked by a male. In an unexplained move, a worker at the airport adds a 5 pound graphing calculator to each male’s suitcase. What is the new mean and standard deviation for the weight of a male’s suitcase? What are the mean and standard deviation for the weight of the suitcases of a married couple, if the man’s suitcase is given the 5 pound calculator added to it?
Answer:
1) The mean = 41
The standard deviation = 13.379
2) The mean = 40.67
The standard deviation = 12.365
3) The mean and standard deviation will remain the same
4) The new mean = 44.5
The new standard deviation = 13.58
5) The mean = 42.25
The standard deviation = 13.83
Step-by-step explanation:
The combines mean is given by the formula;
[tex]\overline {x_{12}} = \dfrac{n_1 \bar x + n_2 \bar x}{n_1 + n_2}[/tex]
The combined standard deviation is given as follows;
[tex]\sigma_{12} = \sqrt{\dfrac{n_1 \times \left (\sigma^2_{1} + d^2_1 \right) + n_2 \times \left (\sigma^2_{2} + d^2_2 \right)}{n_1 + n_2} }[/tex]
d₁ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_1}[/tex]
d₂ = [tex]\overline{x_{12}}[/tex] - [tex]\overline {x_2}[/tex]
Substituting the known values, we have;
[tex]\overline {x_{12}} = \dfrac{ 42 + 40}{2}=41[/tex]
d₁ = 41 - 42 = -1
d₂ = 41 - 40 = 1
[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 1 \right) + \left (10^2 +1 \right)}{2} } = 13.379[/tex]
2) When n₁ = 1, n₂ = 2, we have;
[tex]\overline {x_{12}} = \dfrac{ 2 \times 42 + 4 \times 40}{6} \approx 40.67[/tex]
d₁ = 40.67 - 42 = -1.33
d₂ = 40.67 - 40 = 0.67
[tex]\sigma_{12} = \sqrt{\dfrac{ 2 \times \left (16^2 + 1.33^2 \right) + 4 \times \left (10^2 +0.67^2 \right)}{6} } \approx 12.365[/tex]
3) The mean and standard deviation will remain the same
4) The new mean = (42 + 47)/2 = 44.5
The new standard deviation [tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +2.5^2\right)}{2} } \approx 13.58[/tex]
5) [tex]\overline {x_{12}} = \dfrac{ 44.5 + 40}{2}=42.25[/tex]
[tex]\sigma_{12} = \sqrt{\dfrac{ \left (16^2 + 2.5^2\right) + \left (10^2 +4.5^2\right)}{2} } \approx 13.83[/tex]
please walk me through how to do this so I can di the other questions
Answer:
Axis is a vertical line at x = 2
Vertex is (2, -1)
y-intercept is (0, 3)
Solutions are x = 1 and x = 3
Step-by-step explanation:
To draw the graph of the quadratic equation you must find at least 5 points lie on the graph by choose values of x and find their values of y
Let us do that
Use x = -1, 0, 1, 2, 3, 4, 5
∵ y = x² - 4x + 3
∵ x = -1
∴ y = (-1)² - 4(-1) + 3 = 1 + 4 + 3 = 8
→ Plot point (-1, 8)
∵ x = 0
∴ y = (0)² - 4(0) + 3 = 0 + 0 + 3 = 3
→ Plot point (0, 3)
∵ x = 1
∴ y = (1)² - 4(1) + 3 = 1 - 4 + 3 = 0
→ Plot point (1, 0)
∵ x = 2
∴ y = (2)² - 4(2) + 3 = 4 - 8 + 3 = -1
→ Plot point (2, -1)
∵ x = 3
∴ y = (3)² - 4(3) + 3 = 9 - 12 + 3 = 0
→ Plot point (3, 0)
∵ x = 4
∴ y = (4)² - 4(4) + 3 = 16 - 16 + 3 = 3
→ Plot point (4, 3)
∵ x = 5
∴ y = (5)² - 4(5) + 3 = 25 - 20 + 3 = 8
→ Plot point (5, 8)
→ Join all the points to form the parabola
From the graph
∵ The axis of symmetry is the vertical line passes through the vertex point
∵ x-coordinate of the vertex point is 2
∴ Axis is a vertical line at x = 2
∵ The coordinates of the vertex point of the parabola are (2, -1)
∴ Vertex is (2, -1)
∵ The parabola intersects the y-axis at point (0, 3)
∴ y-intercept is (0, 3)
∵ x² - 4x + 3 = 0
∵ The solutions of the equation are the values of x at y = 0
→ That means the intersection points of the parabola and the x-axis
∵ The parabola intersects the x-axis at points (1, 0) and (3, 0)
∴ Solutions are x = 1 and x = 3
236462700.806 to the nearest cent
Answer:
236462700.81
Step-by-step explanation:
The nearest cent refers to the hundreds place, because 100 pennies (or cents) make 1 dollar. We look at the number to the right of the hundredths place and if it is less than 5 we round down, but if it is 5 or more we round up. Since 6 is more than five we round up, and are left with 236462700.81.
Can someone please help me in this.
THIS IS 7TH GRADE MATH, PLEASE HELP!!
Answer:
Company B is offering the lowest price/lb at $12.72/lb.
Step-by-step explanation:
Six less than two times a number
Answer:
6<2x
Step-by-step explanation:
six less than 2 is 6<2
times a number would be 2 and any letter so 2x
Please help, thank you
Answer:
The answer is B
Step-by-step explanation:
8^1/3=2
Please help with this, all I need is for this paper to be done and then I’ll have a good grade in algebra
Answer:
use desmos.
Step-by-step explanation:
demos. All you have to do is out the equation into Desmos and it will graph it for you. You can look and learn.
What is 100000000000000x234500000020000030040040
Answer:
234500000020000000000000000
Step-by-step explanation:
hello everyone.
please answer……
The first water pipe fills the tank in 8 minutes and the second in 16 minutes. If both pipes are open in one minute, what part of the tank will not be filled with water?
have a nice day.good bye
Answer:
13/16 is the answer. Bad handwriting but try to understand .
What is the absolute value of 8.7
Answer:
absolute value of 8.7 is 8.7
2x/25 = 0.4/0.15. Please Help.
Answer:
x = 1.335
Step-by-step explanation:
2x = 10/3.75
2x = 2.67
x = 1.335
GUYS HELP! IS THIS CORRECT???
ILL MARK YOU BRAINIEST!
Answer:12
Step-by-step explanation:
it’s 12 because 4 x 3 = 12
Answer:
48π units³
Step-by-step explanation:
The volume (V) of a cylinder is calculated as
V = πr²h ( r is the radius of the base and h the height )
Here r = 4 and h = 3 , thus
V = π × 4² × 3
= π × 16 × 3
= 48π units³ ← exact answer
need help on this too
HELLLLLLLLLLLLLPPPPPPPPPPPPP please
1. When one-half of a number is subtracted
from its thrice, it gives 2500. Find the
number.
Answer:
let the number be x
thrice of the number=3x
one-half of the number=(1/2)x
so from the expression we:
3x-x/2=2500
(6x-x)/2=2500
6x-x=2*2500
5x=5000
x=5000/5
x=1000
What is the solution to the equation 5 (x minus 6) = 2 (x + 3)?
x =
Answer:
x = 12
Step-by-step explanation:
Solve for x:
[tex] \longrightarrow [/tex] 5 (x - 6) = 2(x + 3)
Expand out terms of the left hand side:
[tex] \longrightarrow [/tex] 5x - 30 = 2(x + 3)
Expand out terms of the right hand side:
[tex] \longrightarrow [/tex] 5x - 30 = 2x + 6
Subtract 2x from both sides:
[tex] \longrightarrow [/tex] (5x - 2x) - 30 = (2x - 2x) + 6
5x - 2x = 3x:
[tex] \longrightarrow [/tex] 3x - 30 = (2x - 2x) + 6
2x - 2x = 0:
[tex] \longrightarrow [/tex] 3x - 30 = 6
Add 30 to both sides:
[tex] \longrightarrow [/tex] 3x + (30 - 30) = 30 + 6
30 - 30 = 0:
[tex] \longrightarrow [/tex] 3x = 6 + 30
6 + 30 = 36:
[tex] \longrightarrow [/tex] 3x = 36
Divide both sides of 3x = 36 by 3:
[tex] \longrightarrow [/tex] [tex] \sf \dfrac{3}{3}x = \dfrac{36}{3} [/tex]
[tex] \sf \dfrac{3}{3} = 1: [/tex]
[tex] \longrightarrow [/tex] [tex] \sf x = \dfrac{36}{3} [/tex]
[tex] \sf \dfrac{36}{3} = 12: [/tex]
[tex] \longrightarrow [/tex] x = 12
Answer: 12
Step-by-step explanation: On Edge!!!!!!!!!!!!!!!!!!!
Maggie made three withdrawals of $30 each from her bank account how would you create this into an equation using multiplication or division are there any positive or negative numbers and why
Answer:
-30x3 because you are subtracting 30 3 times
Step-by-step explanation:
please help me........please:)
Step-by-step explanation:
2/3 x 2/2 = 4/6
2/3 x 3/3 = 6/9
2/3 x 4/4 = 8/12
Need answers for parallelogram LMNO
Answer:
what does lmno means
Step-by-step explanation:
help plz plzzzzzzzzzzzzzzzzzzzzzzzzzzz
Answer:
slope: 4/6
Y intercept: -2
Equation: y=4/6x-2
1 + b/2 = 19, b = ____?
Answer:
b = 8.5
Step-by-step explanation:
hope this halps ya!
If k(x) = x^2 and p(x) = k(x) + n, what is the value of n?
Pleaseee help ASAP!
I will give brainliest :)
Answer:
The value of n is -6
Step-by-step explanation:
If the function f(x) is translated k units up, then its image is g(x) = f(x) + kIf the function f(x) is translated k units down, then its image is g(x) = f(x) - kThe vertex form of the quadratic function is f(x) = a(x - h)² + k, where a is the coefficient of x² and (h, k) is the vertex∵ k(x) = x²
→ Its graph is a parabola with vertex (0, 0)
∴ The vertex of the prabola which represents it is (0, 0)
∵ The given graph is the graph of p(x)
∵ Its vertex is (0, -6)
∴ h = 0 and k = -6
∵ a = 1
→ Substitute them in the form above
∴ p(x) = 1(x - 0)² + -6
∴ p(x) = x² - 6
→ Substitute x² by k(x)
∴ p(x) = k(x) - 6
∵ p(x) = k(x) + n
→ By comparing the two right sides
∴ n = -6
∴ The value of n is -6
Look at the attached figure for more understanding
The red parabola represents k(x)
The blue parabola represents p(x)
The value of the n is -6.
Equation of a parabolay = a(x-h)2 + k
where,
(h, k) are the coordinates of the vertex of the parabola in form (x, y);
a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.
Given to usk(x) = x^2
p(x) = k(x) + n
Substitutionsubstituting the value of k(x) in p(x).p(x) = k(x)+n
p(x) = x² + n
ComparingComparing with the Equation of a parabola,
y = a(x-h)2 + k
p(x) = x² + n
Therefore, the value of n is k which is the y coordinate of the vertex of the parabola.
Coordinates of the vertex of the parabolaLooking at the coordinates of the vertex of the parabola,
(h, n) = (0, -6)
Hence, the value of the n is -6.
Learn more about Parabola:
https://brainly.com/question/4443998
can anyone help i will give brainlist!! also you have to solve the equations using elimination
Step-by-step explanation:
5x+2y=29
5x-2y=41
add the equations
10x=70
divide both sides by ten
x=7
substitute 7 in the first equation
5(7)+2y=29
simplify
35+2y=29
subtract 35 from both sides
2y=-6
simplify
y=-3 x=7
3x+2y=9
5x+2y=12
subtract the equations
-2x=-3
simplify
x=1.5
substitute
3(1.5)+2y=9
simplify
4.5+2y=9
subtract 4.5 from both sides
2y=4.5
simplify
y=2.25 x=1.5
5x+2y=-9
2x-3y=4
multiply first equation by three and second by two
15x+6y=-27
4x-6y=8
add equations
19x=-19
simplify
x=-1
substitute
15(-1)+6y=-27
simplify
-15+6y=-27
add 15 to both sides
6y=-12
simplify
y=-2 x=-1
It costs $20 to get into Dollywood. Each ride costs an extra $4. f(x) = 20 + 4x is a function representing the total cost of a trip to Dollywood.
Answer:
f(x)=20+4x = -5
Step-by-step ;
answer is -5 .
By 10 a.m., Andrew has read 85% of his emails he received on Tuesday. If Andrew received 40 emails, how many emails has he read so far?
Answer: 35
Step-by-step explanation: 85% of 40 basically you multiply 0.85 by 40 :)
Solve for t.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
4t - 3 > 370 - 50
Answer:
t<47/33
Step-by-step explanation:
If 18 meters of high-resistance wire with a diameter of 1.2 mm has a resistance of 10 ohms, what is the resistance of 27 m of the same type of wire with a diameter of 1.5 mm?
20% of what number is 47?
Answer:
235
Step-by-step explanation:
Answer:
235
20 percent (calculated percentage %) of what number equals 47? Answer: 235.
Step-by-step explanation:
I hope this Helps c: