Bradley and Kelly are out flying kites at a park one afternoon. A model of Bradley and Kelly's kites are shown below on the coordinate plane as kites BRAD and KELY, respectively:
Which statement is correct about the two kites?
They are similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK 1:2.
They are not similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:2.
They are not similar because Segment BR to segment DB is 1:2 and Segment KE to segment YK is 1:5.
They are similar because Segment BR to segment DB is 1:5 and Segment KE to segment YK is 1:5.
Answers
1. The vertices B, D and R have coordinates (9,9), (1,5) and (11,5), respectively. Then
[tex] BR=\sqrt{(11-9)^2+(5-9)^2}=\sqrt{4+16} = 2\sqrt{5} ,\\BD=\sqrt{(1-9)^2+(5-9)^2}=\sqrt{64+16} = 4\sqrt{5}. [/tex]
The ratio
[tex] \dfrac{BR}{BD}= \dfrac{2\sqrt{5}}{4\sqrt{5}} =\dfrac{1}{2}. [/tex]
2. The vertices K, E and Y have coordinates (13,9), (14,10) and (14,2), respectively. Then
[tex] KE=\sqrt{(13-14)^2+(9-10)^2}=\sqrt{1+1} = \sqrt{2} ,\\KY=\sqrt{(13-14)^2+(9-2)^2}=\sqrt{1+49} = 5\sqrt{2}. [/tex]
The ratio
[tex] \dfrac{KE}{KY}= \dfrac{\sqrt{2}}{5\sqrt{2}} =\dfrac{1}{5}. [/tex]
Answer: correct answer is C (they are not similar because segment BR to segment DB is 1:2 and segment KE to segment YK is 1:5.)
Related Questions
Use linear approximation to estimate 15^.25 ...?
Answers
f(x) ~ f(a) + f'(a) (x-a)
f(x) = x^1/4
2^4 = 16 i.e. a = 16
f(15) ~ f(16) + f'(16) (15-16)
f'(x) = 1/4 x^(-3/4)
f(15) ~ 2 + 1/4 (16)^-3/4 (-1)
~ 2 - 1/(32) = 1.96875
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a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing
Answers
We have 2+.8(2) + .8(.8(2)) + .8(.8(.8(2))) + ... =
2( .8^0 + .8^1 + .8^2 + .8^3 + ... ) =
2(.8^n -1) / (.8-1) . As n-->infinity, .8^n-->0 giving us
2(-1)/(-.2) = 2(5) = 10 meters.
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The distance traveled by the ball until it stops bouncing is:
18 meters
Step-by-step explanation:It is given that:
a ball bounces from a height of 2 meters and returns to 80% of its previous height on each bounce.
This means that the distance traveled by the ball is the distance it travels by going down as well as coming up on bouncing.
and is given as follows:
[tex]\text{Total Distance}=2+0.8\times 2\ up+0.8\times 2\ down+(0.8)^2\times 2\ up+(0.8)^2\times 2\ down+.....\\\\\text{Total distance}=2+4\times (0.8)+4\times (0.8)^2+4\times (0.8)^3+....\\\\\text{Total distance}=2+4\times [0.8+(0.8)^2+(0.8)^3+......]\\\\\text{Total distance}=2+4\times (\dfrac{0.8}{1-0.8})[/tex]
Since, the formula of infinite geometric progression is:
[tex]\sum_{n=1}^{\infty} ar^{n-1}=\dfrac{a}{1-r}[/tex]
i.e.
[tex]\text{Total distance}=2+4\times (\dfrac{0.8}{0.2})\\\\\text{Total distance}=2+4\times 4\\\\\text{Total distance}=2+16\\\\\text{Total distance}=18\ \text{meters}[/tex]
The number of students at marita's school decreased to 98% of last year's number currently there are 1170 students how many students were there last year round to the nearest whole number
Answers
There were about 1194 students at Marita's school last year.
To find the number of students last year when the current number is 1170 and represents 98% of last year's number, you can set up a simple equation.
Let "x" represent the number of students last year.
According to the given information, the current number of students is 98% of last year's number, which can be expressed as:
1170 = 0.98x.
To find the value of "x," you need to divide 1170 by 0.98:
[tex]\(x = \frac{1170}{0.98} = 1193.877\).[/tex]
Rounding to the nearest whole number, last year's number of students was approximately 1194.
So, there were about 1194 students at Marita's school last year.
please help with this #15
Answers
Guys i need help. My niece has come over my house and she need help with this question any help?
Loves from KIM.
A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot.
4.1 feet
17.0 feet
20.6 feet
21.4 feet
Answers
21²=4²+height²
441=16+height²
425=height²
height=√425=20.6
The ladder reaches a height of 20.6 ft on the building.
Answer:
C
Step-by-step explanation:
I took test on Edg
Which ordered pairs in the form (x,z) are solution to the equation 3x-4y?
Answers
D=20-1.95c how would I work this out correctly
Answers
if it was, you would take D=20-1.95c subtract 20 from both sides, so you can isolate your variable, c
then divide both sides by -1.95 and you get
( D - 20 ) ÷ -1.95 = c
The LCM of 50, 120, and 225 is 5. true or false?
Answers
50=2x5x5
120=2x3x4x5
225=3x3x5x5
LCM=2x3x3x4x5x5=1800.
Answer:
Its false
Step-by-step explanation:
well first i pt the answer in and it came out correct.
What percent of 150 is 135?
Answers
evaluate 3X^2-14X-49/X-7
the quotient of the equation is __X+__
Answers
Answer:
[tex]3x+7[/tex]
Step-by-step explanation:
[tex]\frac{3x^2-14x-49}{x-7}[/tex]
before dividing this fraction , lets factor the numerator
[tex]3x^2-14x-49[/tex]
Product is -49 and sum is -14, lets break the middle term using factors
[tex](3x^2+7x)+ (-21x-49)[/tex]
Take out GCF from each group
[tex]x(3x+7)-7(3x+7)[/tex]
[tex](3x+7)(x-7)[/tex]
Now we replace the factors in the numerator
[tex]\frac{(3x+7)(x-7)}{x-7}[/tex]
We have (x-7) at the top and bottom , so we cancel it out
[tex]3x+7[/tex]
Solve the inequality. Graph the solutions. h – 2 < –1
Answers
A triangle has sides of square root of 2 and 3. Which could not be the length of the third side if it is a right triangle?
Answers
Answer:
the root of 13
Step-by-step explanation:
9x^2-y^2=1
(a) find y' by implicit differentiation
(b) Solve the equation explicitly for y and differentiate to get y' in terms of x
(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a)
Answers
a.) 18x - 2y dy/dx = 0
2y dy/dx = 18x
dy/dx = 9x/y
b.) y^2 = 9x^2 - 1
y = √(9x^2 - 1)
y' = 9x / √(9x^2 - 1)
c.) substituting y = √(9x^2 - 1) into solution for part a gives
dy/dx = 9x / √(9x^2 - 1)
Thus the two solutions are consistent.
Finding the rate of change in something with respect to something is known as differentiation. For Example, Change in y with respect to x is known as the derivative of y with respect to x.
How to solve it?(a) [tex]9{x}^2-{y}^2 = 1[/tex]
Differentiating equation with respect to x :
[tex]9*2x - 2y\frac{dy}{dx} = 0\\ 18x = 2y\frac{dy}{dx}\\9\frac{x}{y} =\frac{dy}{dx}[/tex]
(b)
[tex]9{x}^2-{y}^2 = 1\\9{x}^2-1 = {y}^2 \\\sqrt[2]{9{x}^2-1} = y\\[/tex]
differentiating with respect to x gives:
[tex]\frac{1}{2\sqrt{9{x}^2-1} } *(18x) = \frac{dy}{dx}\\\frac{1}{\sqrt{9{x}^2-1} } *(9x) = \frac{dy}{dx}[/tex]
(c) [tex]9\frac{x}{y} =\frac{dy}{dx}[/tex]
substituting value of y
[tex]\sqrt[2]{9{x}^2-1} = y\\\\\frac{9x}{\sqrt[2]{9{x}^2-1}} = \frac{dy}{dx}[/tex]
Hence the solution is consistent.
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What is 57 divided by 4241
Answers
The result of dividing 4241 by 57 is approximately 74.40.
To divide 4241 by 57, we perform the division as follows:
74
____________
57 | 4241
- 3996
_______
245
- 228
______
170
- 171
______
-1
The quotient is 74 with a remainder of 1.
Therefore, [tex]\( \frac{4241}{57} = 74 \)[/tex].40 with a remainder of 1.
Complete question:
What is 4241 divided by 57?
Part 1 : When solving systems of equations, how do you determine what method to use?
Part 2 : Choose 1 system of equations from the choices below. Then, solve the system and post your solution, showing your steps so that other students can see which method you chose.
–y + 3x = 6
y = –6x + 12
6x – 4y = 54
–9x + 2y = –69
2y = x + 1
–2x – y = 7
...?
Answers
Part 2. I'll try solving the second system.6x-4y = 54-9x+2y = -69
Multiplying the first equation by 9 and the second equation by 6.
54x - 36y = 486-54x + 12y = -414
Adding the two equations,
-24y = 72y = -3
Subtitute back to one of the equations,-9x + 2y = -69-9x + 2(-3) = -6969 - 6 = 9x9x = 63x = 7
The solution is then (7, -3).
To solve systems of equations, select a method based on the system's setup; using substitution, we solve the given system and find the solution to be (2, 0).
Explanation:When solving systems of equations, one must choose the method that best fits the problem's constraints. Methods include substitution, elimination, and graphing. The method selected often depends on how the equations are presented and which method allows for the most straightforward calculation.
Choosing the system –y + 3x = 6 and y = –6x + 12, we can solve it using substitution since the second equation is already solved for y:
Substitute the expression for y from the second equation into the first.So –(–6x + 12) + 3x = 6.Simplify to get 6x – 12 + 3x = 6.Combine like terms to get 9x – 12 = 6.Add 12 to both sides to get 9x = 18.Divide by 9 to find x = 2.Plug x back into the second equation to get y = –6(2) + 12, hence y = 0.Our solution is (x, y) = (2, 0).
I HAVE 5 MATH QUESTIONS AND NEED HELP ASAP! ONLY COMMENT IF YOU ARE GOING TO HELP.
Answers
1) false,true
3) x=3 y=4
4) y= 2. (-1)+3=1
What multiplies to make 12 and adds up to 16
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A local civic theater has 22 seats in the first row and 21 rows in all. Each successive row contains 3 additional seats . How many seats are in thecivic theater
Answers
There are 840 seats in total in Cinema Hall.
What is arithmetic Progression?The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
Given:
First term, [tex]a_1[/tex] = 22
second row = 22 + 3 = 25
Third row = 25 + 3 = 28
So, the Recursive Formula is
[tex]a_n[/tex] = a + (n-1)d
[tex]a_n[/tex] = 10 + (n-1)3
[tex]a_n[/tex] = 10 + 3n - 3
[tex]a_n[/tex] = 7 + 3n
In 21th rows the seats are
= 7 +3 (21)
= 7 + 63 = 70
Now, to find the number of seats in hall we have to find the sum of seats from row 1 to row 21 using Formula
= n×([tex]a_1[/tex]+ [tex]a_n[/tex])/2
= 21 x (10 + 70) /2
= 21 x 80 /2
= 21 x 40
= 840
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Triangle LMN is congruent to triangle HIJ. Angle L measures 35 degrees angle M measures 65 degrees and angle H measures 2x + 10 degrees. Find the value of x.
Answers
so
2x + 10 = 65
2x = 55
x = 27.5
Answer: The value of x is 12.5°.
Step-by-step explanation:
Since we have given that
ΔLMN ≅ ΔHIJ
So, According to "Congruency rules":
∠L = ∠H -------------------------------------(1)
∠M = ∠I
∠N = ∠J
∠M = 65° , ∠L = 35° and ∠H = (2x+10)°
From eq(1), we get that
[tex]2x+10=35^\circ\\\\2x=35-10\\\\2x=25\\\\x=\dfrac{25}{2}\\\\x=12.5^\circ[/tex]
Hence, The value of x is 12.5°.
Under a dilation, a figure is enlarged and its orientation is preserved. Choose the statement that best describes the dilation.
A.
The image is along the same ray as the preimage but is farther from the center of dilation.
B.
The image is along the opposite ray from the preimage but is farther from the center of dilation.
C.
The image is along the same ray as the preimage but is closer to the center of dilation.
D.
The image is along the opposite ray from the preimage but is closer to the center of dilation.
Answers
Answer: C) The image is along the same ray as the preimage but is closer to the center of dilation.
find the median for the given set of data.
0.6, 1.1, 0.87, 2, 0.87, 1.23
a) 0.87
b)0.985
c)1.1
Answers
Hope I helped!! :))
In 0.57 which is the part and which is the whole
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The following curve passes through (3,1). Use the local linearization of the curve to find the approximate value of y at x=2.8. ...?
Answers
d/dx (2 x^2 y + y = 2x + 13)
4xy + 2x^2 y' + y' = 2
4xy + y'(2x^2 + 1) = 2
y' = (2- 4xy)/(2x^2 +1)
ow we can use this in a linear equation for a slope
Ty = -5x/8 +5(3)/8 +8/8
= -5x/8 +(15+8)/8
= -5x/8 +23/8
this will gives us an approximation at x=2.8 now
ANSWER:
y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105
STEP-BY-STEP EXPLANATION:
y = (2x+13)/(2x^2+1)
y' = ((2x^2+1)*(2) - (2x+13)(4x)) / (2x^2+1)^2
at x=3, this is
y'(3) = (19*2 - 19*12)/19^2 = -10/19
So, your linearization is
y ≈ (-10/19)*(x-3) + 1
At x=2.8, this is
y ≈ (-10/19)*(2.8 - 3) + 1 = 1 2/19 ≈ 1.105
Lisa ate 1/3 of pizza. Kate ate 4/12 of same pizza. What fraction did they eat altogether
Answers
640, 160, 40, 10, ...
Which correctly describe the graph of the geometric sequence? Check all that apply.
The graph will show exponential growth.
The graph will appear linear.
The domain will be the set of natural numbers.
The range will be the set of natural numbers.
The graph will show exponential decay.
Answers
The graph will show exponential decay and The domain will be the set of natural numbers.
Option C and D will apply.
What is a Geometric Sequence ?A geometric sequence is a sequence of numbers obtained by either multiplying or dividing by the same value.
The geometric sequence given is
640, 160, 40, 10, ...
Each number is divided by 4
So the nth term will be
[tex]\rm T_n = a_1 r^{n-1}[/tex]
where [tex]\rm a_1 \; is \; the \; first \; term[/tex]
and r is the common ratio
r =(1/4) for this sequence
The function is
[tex]\rm T_n = 640(\dfrac {1}{4})^{n-1}[/tex]
As from the function it can be understood , That The graph will show exponential decay and The domain will be the set of natural numbers.
Option C and D will apply.
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The sequence is a geometric sequence showing exponential decay with a factor of 0.25 (divisible by 4). The graph will show exponential decay and not appear linear. The domain is the set of natural numbers, while the range consists of specific values from the sequence, not all natural numbers.
Explanation:The sequence given is 640, 160, 40, 10, ..., which is a geometric sequence. We can determine this because each term is obtained by multiplying the previous term by a constant factor.
In this case, each term is divided by 4 to get the next term (160 is 640 divided by 4, 40 is 160 divided by 4, and so on). Therefore, the common ratio r is ¼ or 0.25, which is less than 1.
Now, let’s evaluate the statements provided:
The graph will show exponential decay because the ratio is between 0 and 1, which means the sequence is getting smaller.The graph will not show exponential growth since the terms are decreasing. Exponential growth would require the terms to get larger as the sequence progresses.The graph will not appear linear because the rate of decrease is not constant in terms of subtraction, but rather in division by a factor.The domain of a sequence typically consists of the set of natural numbers since it represents the position of each term in the sequence.The range will not be the set of natural numbers because the terms do not include all natural numbers but rather specific values determined by the geometric sequence.So, the correct statements are that the graph will show exponential decay and the domain will be the set of natural numbers.
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You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. How much money will be in the account after 4 years?
Answers
Answer:
A=2000(1+0.05)^4=2,431.01
Step-by-step explanation:
A bacteria culture begins with 15 bacteria which double in amount at the end of every hour. How many bacteria are grown during the 12th hour?
Answers
A = P * rⁿ
A - the final population
r - the growth rate
P - the initial number of bacteria
n - the number of hours
We know:
A = ?
r = 2 (it doubles)
P = 15
n = 12
After 11 hours
A(11) = 15 * 2¹²
A(11) = 15 * 2048
A(11) = 30720
After 12 hours
A(12) = 15 * 2¹²
A(12) = 15 * 4096
A(12) = 61440
How many bacteria are grown during the 12th hour?
A(12) - A(11) = 61440 - 30720 = 30720
Use the relationships in the diagram below to write an equation and solve for X
Answers
x^2 + 18^2 = 30^2
x^2 + 324 = 900
x^2 = 900 - 324
x^2 = 576
x = sqrt 576
x = 24 <===
b. (2x + 20) + (2x) + (x) + (3x + 20) = 360
8x + 40 = 360
8x = 360 - 40
8x = 320
x = 320/8
x = 40
2x + 20 = 2(40) + 20 = 80 + 20 = 100
2x = 2(40) = 80
3x + 20 = 3(40) + 20 = 120 + 20 = 140
Can someone answer the questions on the sheet for me please?
Answers
Kathleen and Arnob both run from the park entrance along a loop. Kathleen starts walking from the park entrance and gets a 5-mile head start on Arnob. The graph shows how far they have both traveled.
How many minutes does it take Arnob to catch up to Kathleen?
a. 9.8
b. 10
c. 73.5
d. 75
Answers
For this case, the first thing we must do is define variables.
We have then:
x: time in minutes
y: distance traveled.
We then have the following equations:
For Kathleen:
[tex] y = (\frac{1}{15}) x + 5
[/tex]
For Arnob:
[tex] y = (\frac{2}{15}) x
[/tex]
By the time Arnob reaches Kathleen we have:
[tex] (\frac{1}{15}) x + 5 = (\frac{2}{15}) x
[/tex]
From here, we clear the value of x.
We have then:
[tex] (\frac{2}{15}) x - (\frac{1}{15}) x = 5
[/tex]
[tex] (\frac{1}{15}) x = 5
x = (15) * (5)
x = 75 min
[/tex]
Answer:
it takes Arnob to catch up to Kathleen 75 minutes:
d. 75