A has the coordinates (-4, 3) and B has the
coordinates (4, 4). If Do,1/2(x, y) is a dilation of AABC,
what is true about the image AA'B'C'? Check all that
apply.
Answers
If [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex] exists a dilation of △ ABC, the facts regarding the image
△A'B'C' exist AB exists parallel to A'B'.
What is a coordinate plane?Any point in the coordinate plane exists directed by a point (x, y), where the x value exists the position of the point with respect to the x-axis, and the y value exists the position of the point with respect to the y-axis.
A dilation exists a transformation [tex]$D_{o,k} \frac{1}{2} (x, y)[/tex], with center O and a scale factor of k that exists not zero, that maps O to itself and any other point P to P'. The center O exists as a fixed point, P' exists as the image of P, and points O, P, and P' exist on the exact line.
In a dilation of [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex], the scale factor, 1/2 exists mapping the original figure to the image in such a manner that the distances from O to the vertices of the image exist half the distances from O to the original figure.
Also, the size of the image exists half the size of the original figure.
If [tex]$D_{o,\frac{1}{2}} \frac{1}{2} (x, y)[/tex] exists a dilation of △ ABC, the facts regarding the image △A'B'C' exist AB is parallel to A'B'.
[tex]$D_{o,k} \frac{1}{2} (x, y) = (\frac{1}{2} x, \frac{1}{2}y)[/tex]
The distance from A' to the origin exists half the distance from A to the origin.
Therefore, the correct answer is option A). △ A'B'C' exist AB is parallel to A'B'.
To learn more about the image AA'B'C' refer to:
https://brainly.com/question/4421026
#SPJ9
Related Questions
Consider the following pair of equations:
y = x + 4
y = −2x − 2
Explain how you will solve the pair of equations by substitution. Show all the steps and write the solution in (x, y) form.
Source
StylesFormatFontSize
Answers
Answer:
(-2, 2)
Step-by-step explanation:
Given system of equations:
[tex]\begin{cases}y=x+4\\y=-2x-2 \end{cases}[/tex]
To solve by substitution, substitute the first equation into the second equation:
[tex]\implies x+4=-2x-2[/tex]
Add 2x to both sides:
[tex]\implies x+4+2x=-2x-2+2x[/tex]
[tex]\implies 3x+4=-2[/tex]
Subtract 4 from both sides:
[tex]\implies 3x+4-4=-2-4[/tex]
[tex]\implies 3x=-6[/tex]
Divide both sides by 3:
[tex]\implies \dfrac{3x}{3}=\dfrac{-6}{3}[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the first equation and solve for y:
[tex]\implies y=-2+4[/tex]
[tex]\implies y=2[/tex]
Therefore, the solution to the given system of equations is (-2, 2).
Learn more about systems of equations here:
https://brainly.com/question/27868619
https://brainly.com/question/27868564
Substitute y value from first eqn in second equation
y=-2x-2x+4=-2x-23x=-6x=-2Put in first one
y=-2+4=2(-2,2) is the solution
10 points please help me!!!
Answers
Step-by-step explanation:
16-19 -> 3 (16, 17, 19)20-23 -> 1 (21)24-27 -> 3 (24, 26, 26)28-31 -> 4 (28, 29, 30, 31)32-35 -> 5 (32, 33, 34, 34, 35)3\sqrt(6)*6\sqrt(6)
Please quick reply!
Answers
Answer: 3
Step-by-step explanation:
Multiply the numerator to get 3 x 6 is 18
Multiply the denominator to get √6 x √6 = 6
Divide 18 by 6 to get the answer is 3
A population of a particular yeast cell develops with a constant relative growth rate of 0.4311 per hour. The initial population consists of 3.9 million cells. Find the population size (in millions of cells) after 5 hours. (Round your answer to one decimal place.)
Answers
A population of a particular yeast cell develops with a constant relative growth rate of [tex]0.4311[/tex] per hour. The initial population consists of [tex]3.9[/tex]million cells. Find the population size (in millions of cells) after 5 hours. Population size after [tex]5hrs[/tex] is [tex]33.6million[/tex].
How can we find the population size ?
The projection of population growth in yeast is given by
[tex]N=N_{0} e^{rt}[/tex]
Where [tex]N_{0}[/tex]=initial population which is [tex]3.9million[/tex]
[tex]r[/tex]=intrinsic rate of natural increases which is [tex]0.4311million per hour[/tex]
N is population size
Substitute the values
[tex]N=N_{0} e^{rt}\\N=3.9(e^{0.4311*5} )\\\\N=33.6 million[/tex]
Learn more about population size here :
https://brainly.com/question/28045705
#SPJ4
Write y=5x-9 in standard form
Will give brainliest!
Answers
Answer:
5x - y = 9
Step-by-step explanation:
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
given
y = 5x - 9 ( subtract 5x from both sides )
- 5x + y = - 9 ( multiply through by - 1 )
5x - y = 9 ← in standard form
mel cuts a slice of cake if her slice is 4/15 of the cake, what is the central angle of her slice, please give answer in degrees
Answers
Answer:
Below in bold.
Step-by-step explanation:
That would be 4/15 * 360 as there are 360 degrees in a circle
= 96 degrees.
solve for x -
[tex] x^{2} + 5x + 6 = 0 \\ \\ [/tex]
ty! :)
Answers
Hello,
x² + 5x + 6 = 0
a = 1 ; b = 5 ; c = 6
∆ = b² - 4ac = 5² - 4 × 1 × 6 = 25 - 24 = 1 > 0
2 solutions :
[tex] x_{1} = \frac{ - b - \sqrt{\Delta} }{2a} = \frac{ - 5 - 1}{2 \times 1} = \frac{ - 6}{2} = - 3[/tex]
[tex]x_{2} = \frac{ - b + \sqrt{\Delta} }{2a} = \frac{ - 5 + 1}{2 \times 1} = \frac{ - 4}{2} = - 2[/tex]
S = { -3 ; -2}
Which of the following is an equivalent form of the equation of the graph shown in the xyxyx, y-plane above, from which the coordinates of vertex AAA can be identified as constants in the equation
Answers
The equivalent form of the equation y=[tex]x^{2} -2x-15[/tex]given is y=(x+3)(x-5).
Given an equation y=[tex]x^{2}[/tex]-2x-15 and we are required to find the equivalent form of the equation.
Equation is like a relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c. It may be linear equation, quadratic equation, cubic equation or any other equation depending on the powers of the variable.
To find the equivalent equations we are required to form factors of the equation. Equivalent equation are those equations which when solved gives the same solution as the equation when solved gives.
y=[tex]x^{2}[/tex]-2x-15
y=[tex]x^{2}[/tex]-5x+3x-15
y=x(x-5)+3(x-5)
y=(x+3)(x-5)
Hence the equivalent form of the equation y= [tex]x^{2}[/tex]-2x-15 given is
y=(x+3)(x-5).
Learn more about equation at https://brainly.com/question/2972832
#SPJ4
Question is incomplete as question should includes the equation
y= [tex]x^{2}[/tex]-2x-15.
A movie ends at 7:45 P.M. The next movie begins 50 minutes later. What time does the next movie begin?
Answers
Answer:
8:35 PM
Step-by-step explanation:
First, subtract 15 from 50.
50-15=35
Add that 15 taken from 50 to 7:45.
7:45 + 0:15 = 8:00
Add 35 to 8:00
8:00 + 0:35 = 8:35
The next movie will start at 8:35 PM.
Hope this helps!
find the value of x from the figure
Answers
Answer:
x = 30
Step-by-step explanation:
110 and 3x - 20 are supplementary angles, sum to 180° , then
110 + 3x - 20 = 180
90 + 3x = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
Answer:
x = 30
Step-by-step explanation:
Please refer to the attached photo. (Apologies for the terrible drawing.)
For this question, you must be clear of the angle properties.
z + 110 = 180 (Sum of Angles on a straight line)
z = 180 - 110 = 70
z = 3x - 20 (Corresponding Angles)
3x - 20 = z
3x - 20 = 70
3x = 70 + 20
3x = 90
x = 90 / 3 = 30
2+8+32+128…..,n=9
Evaluate each geometric series described
Answers
The value of 2+8+32+128…..,n=9 is 174762
How to evaluate the series?The series is given as:
2+8+32+128…..,n=9
Start by calculating the common ratio (r)
r = 8/2
r = 4
The sum of the series is then calculated as:
[tex]S_n = \frac{a *(r^n - 1)}{r -1}[/tex]
This gives
[tex]S_9 = \frac{2 *(4^9 - 1)}{4 -1}[/tex]
Evaluate the difference
[tex]S_9 = \frac{2 *( 262143)}{3}[/tex]
Evaluate the quotient
[tex]S_9 = 174762[/tex]
Hence, the value of 2+8+32+128…..,n=9 is 174762
Read more about series at:
https://brainly.com/question/7882626
#SPJ1
A helicopter is 665 feet above the ground. A girl is looking up at the helicopter to form a line. Her line of sight is 5 feet off the ground. The distance between the girl and the helicopter is 280 feet.
A helicopter flies 665 feet above ground. What is the measure of the angle of depression from the helicopter to the girl’s line of sight? Round to the nearest degree.
23°
25°
65°
67°
Answers
The measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
What is a right angle triangle?A right angle triangle has one of its angle as 90 degrees. The sides and angles can be found using trigonometric ratios.
Therefore, angle of depression from the helicopter can be found as follows:
tan x = opposite / adjacent
where
x = angle of depression
Hence,
tan x = 660 / 280
tan x = 2.35714285714
x = tan⁻¹ 2.35714285714
x = 67.1231281953
x = 67°
Therefore, the measure of the angle of depression from the helicopter to the girl’s line of sight is 67 degrees.
learn more on right triangle here: https://brainly.com/question/26253402
#SPJ1
Answer:
D = 67
Step-by-step explanation:
Let k be a positive integer. In how many ways can one select three distinct numbers from the set {1,2,..., 3k} such that their sum is divisible by 3
Answers
Reduce the numbers in the list modulo 3 to get the set
{1, 2, 0, 1, 2, 0, …, 1, 2, 0}
containing [tex]k[/tex] copies each of 1, 2, and 0.
Take any 3 elements from the list. Their sum is divisible by 3 if those elements' residues also sum to 3 ≡ 0 (mod 3). To get a sum of 0, we must make one of the following choices:
3 elements each with the same residue, so0 + 0 + 0 ≡ 0 (mod 3)
1 + 1 + 1 ≡ 3 ≡ 0 (mod 3)
2 + 2 + 2 ≡ 6 ≡ 0 (mod 3)
1 element each with different residues, so0 + 1 + 2 ≡ 3 ≡ 0 (mod 3)
There are
[tex]\dbinom k3 \dbinom k0 \dbinom k0 = \dfrac{k(k-1)(k-2)}6[/tex]
ways of choosing 3 elements with a given residue and 0 elements with any other residue, hence
[tex]3\dbinom k3\dbinom k0\dbinom k0 = \dfrac{k(k-1)(k-2)}2[/tex]
ways of choosing any 3 elements with the same residue, and there are
[tex]\dbinom k1 \dbinom k1 \dbinom k1 = k^3[/tex]
ways of choosing any 3 elements with distinct residues.
So, the total number of ways of making the selection is
[tex]3\dbinom k3\dbinom k0^2 + \dbinom k1^3 = \boxed{\dfrac32 k^3 - \dfrac32 k^2 - k}[/tex]
Read the following description of a relationship:
Ron is making a banner by stringing letters on a cord. The cord weighs 8
ounces, and each letter weighs 10 ounces.
Let n represent the number of letters and w represent the weight of the banner.
This relationship can also be shown in a table. Complete the equation that represents the
relationship between n and w
Answers
The equation that represents the relationship between n and w is w = 10n + 8.
How to illustrate the expression?From the information, Ron is making a banner by stringing letters on a cord and the cord weighs 8
ounces and each letter weighs 10 ounces.
Let represent the number of letters
Let w represent the weight of the banner.
In this case, when n = 6, w = 68 and when n = 7, w = 78.
Therefore, the relationship will be:
w = 10n + 8
To confirm let's use n = 6
10n + 8
10(6) + 8
= 68
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
Answer:
Step-by-step explanation:
w=10n+8
A sphere and a cylinder have the same radius and height. The volume of the cylinder is . Amie found the volume of the sphere. Her work is shown below. What is Amies error
Answers
Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
In the question, we are given that a sphere and a cylinder have the same radius and height.
We assume the radius of the sphere to be r, and its height to be h.
Now, the height of a sphere is its diameter, which is twice the radius.
Thus, the height of the sphere, h = 2r
Given that the sphere and the cylinder have the same radius and height, the radius of the cylinder is r, and its height is 2r.
The volume of a sphere is given by the formula, V = (4/3)πr³, where V is its volume, and r is its radius.
Thus, the volume of the given sphere using the formula is (4/3)πr³.
The volume of a cylinder is given by the formula, V = πr²h, where V is its volume, r is its radius, and h is its height.
Thus, the volume of the given cylinder using the formula is πr²(2r) = 2πr³.
Now, to compare the two volumes we take their ratios, as
Volume of the sphere/Volume of the cylinder
= {(4/3)πr³}/{2πr³}
= 2/3.
Thus, the volume of the sphere/the volume of the cylinder = 2/3,
or, the volume of the sphere = (2/3)*the volume of the cylinder.
Given the volume of the cylinder to be 54 m³, Amie should have multiplied 54 by 2/3 instead of adding the two.
Thus, Amie's error while measuring the volume of a sphere is that Amie should have multiplied 54 by 2/3. Thus, the first option is the right choice.
Learn more about volumes at
https://brainly.com/question/12398192
#SPJ4
For the complete question, refer to the attachment.
A square pool is surrounded by a paved area that is 2 metres wide. If the area of the paving is 72m2, what is the length of the pool?
Answers
The length of the square pool is 8. 49cm
How to determine the areaNote that the formula for finding the area of a square is given as;
Area = length^2
We have
Area = 72 m²
Substitute into the formula
I^2 = 72
Find the square root of both sides
I= √72
I = 8. 49cm
The length of the square pool given as I is 8. 49cm
Thus, the length of the square pool is 8. 49cm
Learn more about area of a square here:
https://brainly.com/question/486778
#SPJ1
A chemist wants to make 45 ml of a 17% acid solution by mixing a 13% acid solution and a 19 % acid solution. How many milliliters of each solution should the chemist use?
Answers
Answer:
22 millilitres of 13% solution
23 millilitres of 19% solution
Step-by-step explanation:
A + B = 45
13A + 19B = 45 x 17 = 765
-13A - 13B + 13A + 19B = -650 + 765 = 115
5B = 115
B = 23
22 + 23 = 45
A = 22
Study the illustration. Write the ratio
of flowers to bees. Complete the sentence.
For every 5 flowers there are _______
bees.
Answers
Answer: 6 bees
Step-by-step explanation:
The picture has 12 bees and 10 flowers. Thus, the ratio of flowers to bees is 10 to 12, which simplifies to 5 to 6.
Therefore, for every 5 flowers, there are 6 bees.
Select the correct answer.
Which statement correctly compares functions f and g?
Answers
Answer:
C
Step-by-step explanation:
Exponential functions have 2 things in common
-They increase infinitely once they approach a certain point
-They don't decrease anymore once they approach a certain point
For the geometric series 1 - 2/3 + 4/9 - 8/27....
find s8
Answers
Answer:
Step-by-step explanation:
The sum of an alternating geometric series SUM((-1)^n*ar^n) = a/(1+r). The given series has r=2/3 and a=1. The sum will be 1/(1+2/3)= 3/5
Hello,
We have s0 = 1 and q = -2/3
[tex]S _{n} = S _{0} \times q {}^{n} = 1 \times ( - \frac{2}{3} ) {}^{n} [/tex]
[tex]S _{8} = ( - \frac{2}{3} ) {}^{8} = \frac{2 {}^{8} }{3 {}^{8} } = \frac{256}{6 561} [/tex]
Solve:
2a + 6 = 12
a =
Answers
Answer:
8
Step-by-step explanation:
because hhhhhh
gghhhh
jkkkkk
lllll
vvvvv
dddfff
oooooo
eeeerer
kkkkkk
lllll.ssss
16. c= vλ. If c = 2.998 x 10^8 m/s, v= 4.41 x 10¹4 s-¹; find a value for λ.
Answers
Answer:
6.80 x 10⁻⁷ m
Step-by-step explanation:
You can find the value of λ by inserting the given values into the equation and simplifying.
c = vλ <----- Given equation
2.998 x 10⁸ m/s = (4.41 x 10¹⁴ s⁻¹)λ <----- Insert values
6.80 x 10⁻⁷ m = λ <----- Divide both sides by 4.41 x 10¹⁴
check out the pic first
Answers
Answer: (0, 16)
Step-by-step explanation:
y = mx + c
c is the y intercept
from the equation, c = 16
(it's not exactly mx but you don't need to solve for x)
Please please help me. It’s due right now! it would mean a lot :))<3 Pls show work!!!
Answers
Answer: 9 triangles.
Step-by-step explanation:
Just make a dot in the middle and make lines and connect each line to an edge or bend.
Which triangles are similar to ABC? Explain.
Answers
Answer: △JKL & △ MNP
Step-by-step explanation:
△JKL is similar because:
5 x 1.6 = 8
2.5 x 1.6 = 4
3.75 x 1.6 = 6
△MNP is also similar because:
4 x 2 = 8
2 x 2 = 4
3 x 2 = 6
If 3 square feet of fabric costs $3.75. what would 7 square feet cost?
Answers
Answer:
8.75
Step-by-step explanation:
3.75/3=1.25
1.25=1 square feet
1.25(7)=8.75
At 3:20, what is the measure in degrees of the lesser angle formed by the hour hand and the minute hand
Answers
Answer: 30 degrees
Step-by-step explanation:
The quadratic parent function has been reflected down, stretched vertically by a factor of 1/3
Answers
1a) f(x) = -1/3(x + 12)² + 9
1b) f(x) = -1/3x² - 8x - 39
Lets simplify it,
Expand by FOIL (First Outside Inside Last)
Standard Form: ax² + bx + c = 0
Transformations Graph: f(x) = a(bx - c)² + d
Reflected down and vertically stretched by 1/3: a = -1/3
Shifted vertically by 9 units: d = 9
Shifted horizontally by -12 units: c = -12
Vertex Form:
f(x) = a(bx - c)² + d
f(x) = -1/3(x + 12)² + 9
Standard Form:
f(x) = -1/3(x + 12)² + 9
f(x) = -1/3(x² + 24x + 144) + 9
f(x) = -1/3x² - 8x - 48 + 9
f(x) = -1/3x² - 8x - 39
Learn more about Quadratic Function on:
https://brainly.com/question/11064204
#SPJ4
Given the right triangle, use the pythagorean theorem to find "a" (one of the legs) when c=85 and b= 53. (round answer to nearest tenth).
Answers
Answer:
a= 100.2
Step-by-step explanation:
You solve it like you ate looking for the hypotenuse
The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable x. Group of answer choices mean: 1.39; standard deviation: 0.80 mean: 1.18; standard deviation: 0.64 mean: 1.39; standard deviation: 0.64 mean: 1.18; standard deviation: 1.30
Answers
The value of the Mean & Standard deviation is 1.30 and 1.18.
According to the statement
we have a given that the random variable x represents the number of computers that families have along with the corresponding probabilities.
And we have to find the mean and standard deviation from the given data which is related to the probabilities values
So, according to the given data
The formula to compute the mean is:
Mean = summation [x*p(x)]
Compute the mean as follows:
Mean = summation [x*p(x)]
Mean = summation [0*0.49 + 1* 0.05 + 2*0.32 + 3*0.07 + 4*0.07]
Mean = 0 +0.05 + 0.64 + 0.21 + 0.28
Mean = 1.18
The mean of the random variable x is 1.18.
And after calculating the variance from the formula get
The value of standard deviation is 1.30
So, The value of the Mean & Standard deviation is 1.30 and 1.18.
Learn more about mean and standard deviation here https://brainly.com/question/14650840
#SPJ4