Answer:
165
Step-by-step explanation:
we solve this by sum over the possible symmetry groups of the colorings.
1.If the board has 90 degree rotational symmetry, then all four squares are the same color. There are 5 such boards.
2. If the board has 180 degree rotational symmetry (but not 90 degree), then it has to be a 2-color checkerboard pattern. There are ⁵c₂=10 such boards.
All the remaining boards have no rotational symmetry. We can count these boards by taking all possible colorings, subtracting the ones counted above, and dividing by four (since each of these boards corresponds to four colorings). The result is (54−2×10−5)÷4=600÷4=150.
so, total number of boards= 5+10+150= 165.
What is the simplified form of k-5+7
Answer:
k+2 or k=2
Step-by-step explanation:
combine -5 and 7 to get your answer
Answer:
K+2
Step-by-step explanation:
K - 5 + 7 ....add -5 and 7
K+2
The table below shows the distribution of students who speak some Ghanaian languages.
Language Number of students .
Nzema 5
Ga 20
Twi 30
Ewe 25
Fante 10
i. Draw a pie chart to illustrate the data.
ii. What percentage of the students speaks Ewe?
iii. What is the modal language?
iv. What fractions of the students speak either Ga or Fante
Answer:27.78% ; Twi; 1/3
Step-by-step explanation:
Given the data :
Language - - - - - - - Number of students
Nzema - - - - - - - - - - - 5
Ga - - - - - - - - - - - - - - - 20
Twi - - - - - - - - - - - - - - - 30
Ewe - - - - - - - - - - - - - - - 25
Fante - - - - - - - - - - - - - - 10
1.) To prepare pie chart:
Total number of students :
(5 + 20 + 30 + 25 + 10) = 90 students
Nzema: (5/90) × 360 = 20
Ga : (20/90) × 360 = 79.99 = 80
Twi : (30/90) × 360 = 119.99 = 120
Ewe : (25/90) × 360 = 79.99 = 100
Fante : (10/90) × 360 = 39.99 = 40
Total = 360
Pie chart is attached in the picture below
2)Percentage students that speak Ewe = (25/90) * 100 = 27.78%
Or (100/360) * 100 = 27.78%
3.) Modal language : This is the language spoken by majority of the students = Twi
4.) Fraction of student that speak either GA or Fante :
(GA or Fante) = (20 + 10) / 90 = 30/90 = 1/3
Which statements are true regarding the system of equations? Check all that apply. 8 x + 10 y = 30. 12 x + 15 y = 60. The lines coincide. The lines are parallel. The slopes are equal. The y-intercepts are different. The system has one solution. The system has an infinite number of solutions. The system has no solution. Mark this and return
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations: [tex]a_1x+b_1y=c_1\\\\a_2x+b_2y=c_2[/tex]
They coincide if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}[/tex]
They are parallel if [tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
They intersect if [tex]\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}[/tex]
Given equations: [tex]8 x + 10 y = 30\\ 12 x + 15 y = 60[/tex]
Here,
[tex]\dfrac{a_1}{a_2}=\dfrac{8}{12}=\dfrac{2}{3}\\\\ \dfrac{b_1}{b_2}=\dfrac{10}{15}=\dfrac{2}{3}\\\\ \dfrac{c_1}{c_2}=\dfrac{30}{60}=\dfrac{1}{2}[/tex]
⇒[tex]\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}\neq\dfrac{c_1}{c_2}[/tex]
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
[tex]y=-\dfrac{8}{10}x+\dfrac{30}{10}\Rightarrow\ y=-0.8x+3[/tex]
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
[tex]y=-\dfrac{12}{15}x+\dfrac{60}{15}\Rightarrow\ y=-0.8x+4[/tex]
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
Answer: The lines are parallel.
The slopes are equal.
The y-intercepts are different.
The system has no solution.
Step-by-step explanation:
For a pair of equations:
They coincide if
They are parallel if
They intersect if
Given equations:
Here,
⇒
Hence, The lines are parallel.
It has no solution. [parallel lines have no solution]
Write 8 x + 10 y = 30 in the form of y= mx+c, where m is slope and c is the y-intercept.
i.e. slope of 8 x + 10 y = 30 is -0.8 and y-intercept =3
Write 12 x + 15 y = 60 in the form of y= mx+c, where m is slope
i.e. slope of 12 x + 15 y = 60 is -0.8 and y-intercept =4
i.e. The slopes are equal but y-intercepts are different.
Pls answer the 9th question...plsss fast
Answer:
i) x = 65° ii) x = 60° iii) x = 34°
y = 50° y = 80° y = 124°
Step-by-step explanation:
i) x = 180-115= 65°
y = 65+65= 130
= 180-130= 50°
ii) x = 90+30= 120
180-120= 60°
y = 60+20= 80
180-80 = 100
180-100= 80°
iii) y = 34+90= 124
x = 180-124= 56
56+90= 146
180-146= 34°
I hope this helped, mark me brainliest please :)
Robert buys $3 shirts at $16.90 each, and a pair of jeans for $20.50. The shop has a sale on, and so he receives a $7.12 discount.
Write and solve a numerical expression for how much he spends in total.
Answer:
64.08
Step-by-step explanation:
3^16.90+1*20.50-7.12
. A car bought for $20,000. Its value depreciates by 10% each year for 3 years. What is the car's worth after3 years?
Answer:
$14,580
Step-by-step explanation:
To start off, 10% of 20,000-one easy way to do this is to multiply 20,000 by 0.1, which is 10% in decimal form
-In doing that, you get 2,000
-Now the question says that the value is depreciated which means it goes down in value, so subtract 2,000 from 20,000 to 18,000
-the value of the car after one year is now $18,000
Now, let's move to the second year. This time find 10% of 18,000
-multiply 18,000 by 0.1 to get 1,800
-since the value is depreciating, or becoming less, we will subtract 1,800 from 18,000 to get 16,200
-the value of the car after two years is now $16,200
Finally, let's look at the value of the car after three years. Only this time, we will now find 10% of 16,200
-multiply 16,200 by 0.1 to get 1,620
-since value is being depreciated, or lessened, we will once again be subtracting. Subtract 1,620 from 16,200 to get 14,580
Therefore, the value of the car after three years is now $14,580.
Which expression can be used to determine the slope of the linear function represented in the table?
х
0
у
5
9
4
9-5
4-0
O
4-0
9-5
o
5-0
9-4
O
9-4
5-0
Answer:
to find the slope of a linear function, there is only one formula
this formula requires two points, which are stated in tables and graphs alike
these points do not need to be one after the other as it is slope and slope predicts what the next point graphed will be.
Formula for Slope:
y2 - y1______x2 - x1this should help. take any two points and substitute for each; y values in the correct spots and x values in their correct spots
make sure to put the values of second point where it is labelled y2 and x2 And make sure to substitute first point values in those labelled y1 and x1
It is important to remember that if this becomes a fraction, SIMPLIFY
We can write the slope of the function as -
{m} = (9 - 5)/(4 - 0).
What is function?A function is a relation between a dependent and independent variable. We can write the examples of function as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is a table for the function as -
{x} 0 4
{y} 5 9
We can write the slope of the function as -
{m} = (9 - 5)/(4 - 0)
Therefore, we can write the slope of the function as -
{m} = (9 - 5)/(4 - 0).
To solve more questions on functions, visit the link below-
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For every 2 males birds in a birdcage, there are 5 females. What is the ratio of
males to females? *
Answer:
2:5
Step-by-step explanation:
The structure of a ratio is x:y.
So all you have to do is place the former as the first digit and the latter as the second and separate them by a colon.
Match the correct property of operations to each pair of equivalent expressions so that the property can be applied to
the first expression to generate the second expression Drag the items on the left to the correct location on the right
(x+20) + 12 and 7x +(24+12)
Distributive Property
Commutate Property
x+4y-Sy and x-5y
Associative Property
21x+28y and 7(3x + 4y)
combining like terms
Ty + 6x and 6x + 7y
Answer:
Check below
Step-by-step explanation:
Hi, let's check
1.[tex](7x+20) + 12 \:and\: 7x +(24+12)\\[/tex]
In this case we have the Associate Property, since we can associate two, or even three terms without modify the final result.
2.[tex]21x+28y \:=\: 7(3x + 4y)[/tex]
Distributive Property, note that that the right side is the left side rewritten as a product, with the GCF outside the brackets.
3. Commutative Property
[tex]7y + 6x \:and\: 6x + 7y[/tex]
The order of these sum does not compromise the result.
4. [tex]x+4y-Sy \:and\: x-5y[/tex]
Combining like terms, similar terms are operated together.
simplify:
[tex](2x) ^{ \frac{1}{2} } \times (2x ^{3} ) ^{ \frac{3}{2} } [/tex]
Answer:
[tex]\huge\boxed{(2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}=4x^5}[/tex]
Step-by-step explanation:
[tex](2x)^\frac{1}{2}\times(2x^3)^\frac{3}{2}\qquad\text{use}\ (ab)^n=a^nb^m\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{3}{2}(x^3)^\frac{3}{2}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^{(3)(\frac{3}{2})}=2^\frac{1}{2}x^\frac{1}{2}\times2^\frac{2}{3}x^\frac{9}{2}\\\\\text{use the commutative and associative property}\\\\=\left(2^\frac{1}{2}\times2^\frac{3}{2}\right)\left(x^\frac{1}{2}\times x^\frac{9}{2}\right)\qquad\text{use}\ a^n\times a^m=a^{n+m}[/tex]
[tex]=2^{\frac{1}{2}+\frac{3}{2}}x^{\frac{1}{2}+\frac{9}{2}}=2^\frac{1+3}{2}x^{\frac{1+9}{2}}=2^\frac{4}{2}x^\frac{10}{2}=2^2x^5=4x^5[/tex]
Answer:
[tex] 4x^5 [/tex]
Step-by-step explanation:
[tex] (2x)^\frac{1}{2} \times (2x^3)^\frac{3}{2} = [/tex]
[tex]= (2x)^\frac{1}{2} \times (2x \times x^2)^\frac{3}{2}[/tex]
[tex]= [(2x)^\frac{1}{2} \times (2x)^\frac{3}{2}] \times (x^2)^\frac{3}{2}[/tex]
[tex]= (2x)^{\frac{1}{2} + \frac{3}{2}} \times x^{{2} \times \frac{3}{2}}[/tex]
[tex]= (2x)^{\frac{4}{2}} \times x^{\frac{6}{2}}[/tex]
[tex] = 2^2x^2 \times x^3 [/tex]
[tex] = 4x^5 [/tex]
Pls help ASAP will make brailist
Answer:
B. 1296 in.^2
Step-by-step explanation:
The rectangles are similar, and sides ST and YZ are corresponding sides.
The linear scale factor is k = YZ/ST = 24/8 = 3
The area scale factor is k^2 = 3^2 = 9
A = 144 sq in. * k^2 = 144 sq in. * 9 = 1296 sq in.
Answer: B. 1296 in.^2
Answer:
4)1,296in^2
5)510.4ft
Step-by-step explanation:
4)
24/8=3 This is the dilation
144/8=18 This is the side length for QRST
18*3=54 The side length for WXYZ
24*54=1296 The area of WXYZ
5)
319*8/5 Your fence with a scale factor of 8/5
319*1.6 Changing 8/5 into fraction form
319*1.6=510.4 The length of the friend's fence.
Hope this helps. I could not see the end of the last question so I am sorry if it is not written properly.
Have a good day!
Find the product.
(3x2+6x-5)(-3x)
PLEASE HELP!!! ASAP!!!
Answer:
[tex]\boxed{-9x^3-18x^2 + 15x}[/tex]
Step-by-step explanation:
(3x²+6x-5)(-3x)
Apply distributive law.
-3x(3x²)-3x(6x)-3x(-5)
Simplify.
-9x³ - 18x² + 15x
Answer:
[tex] \boxed{\red{ - 9 {x}^{3} - 18 {x}^{2} + 15x}}[/tex]
Step-by-step explanation:
[tex] ( - 3x)(3 {x}^{2} + 6x - 5) \\ - 3x(3 {x}^{2} ) - 3x(6x) - 3x( - 5) \\ = - 9 {x}^{3} - 18 {x}^{2} + 15x[/tex]
Two circles are drawn below. The diameter of the smaller circle is a radius of the larger circle. What is the ratio of the smaller circle's circumference to the larger circle's circumference? Give your answer in fully simplified form. It should look like "x:y", where x and y are replaced by integers. [asy] size(4cm); pair o=(0,0); pair x=(0.9,-0.4); draw(Circle(o,sqrt(0.97))); draw(Circle((o+x)/2,sqrt(0.97)/2)); dot(o); dot(x); dot(-x); draw(-x--x); [/asy] Hint(s): Read the question carefully. Does it ask about a ratio of areas? Of radii? Of diameters? Of circumferences? Which question did you answer? Which was asked?
Answer:
1 : 2
Step-by-step explanation:
The ratio is ...
small dia : large dia = 1 : 2 = small circumference : large circumference
__
Further explanation
The diameter of the small circle is the radius of the large circle. Since the large circle's diameter is twice the length of its radius, the ratio of circle diameters is ...
small : large = 1 : 2
We multiply the diameter by π to get the circumference. Multiplying both these numbers by π will give the ratio of the circumferences. In order to reduce the ratio to lowest terms we must divide by π again:
dia ratio = circumference ratio = lowest terms ratio
1 : 2 = π : 2π = 1 : 2
Answer: 1:2
Step-by-step explanation:
Triangles ABC and EDC are outlined on a bridge. The triangles share vertex C and angles D and B are right angles. A new bridge structure requires triangles that are in a ratio of 1:1. If AC = 5x − 5 and EC = 3x + 9, find the distance between the top and bottom of the bridge, in feet.
CHECK THE ATTACHED FIQURE FOR THE BRIDGE
Answer:
60 ft
Step-by-step explanation:
From the question we know that triangles ABC and EDC are in a 1:1 with this given ratio it implies that
triangles ABC and EDC are congruent then we can say
side EC = side AC
3x + 9 = 5x - 5
Then we can simplify to know value of x
3x + 14= 5x
2x = 14
x = 7
But we know that AC= 5x - 5 , then substitute value of x into it
AC = 5x + 5 = 5(7) - 5
= 35 - 5
AC= 30 ft
Also EC= 3x + 9 then substitute value of x into it
EC = 3x + 9 = 3(7) + 9
= 21 + 9
EC= 30 ft
Then the the distance between the top and bottom of the bridge, in feet, = EC+AC
= 30 + 30 = 60 ft
Answer:
60 ft
Step-by-step explanation:
i did the test
Sherman entered the following values into the TVM Solver on his graphing
calculator
N=
I%=3.7
PV=-49
PMT=0
FV=98
P/Y=1
C/Y=1E11
PMT:ENU BEGIN
What does the rule of 69 predict will be the approximate value of N?
A. 13.2
B. 18.6
C. 19.5
D. 26.5
Answer:
B. 18.6
Step-by-step explanation:
The 'rule of 69' says the value will be doubled in 69/i years, where i is the annual interest rate in percent (compounded continuously). The interest rate is given as 3.7%, so the prediction is
n = 69/3.7 = 10.649
n ≈ 10.6
juice is $1.79 for 8-4.23 ounce boxes. What is the unit price
Answer:
I believe the unit price would be 2.39 per unit
Step-by-step explanation:
Round the following numbers to 1 significant figure:
a) 25 637
b) £2.51
c)9877 m
Answer:
b
Step-by-step explanation:
you need to round 2.51 to 3 because it was the correct answer
Lines e and f are parallel. The mAngle9 = 80° and mAngle5 = 55°.
Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Where lines e and c intersect, the angles are: 1, 2, 4, 3. Where lines f and c intersect, the angles are 5, 6, 8, 7. Where lines e and d intersect, the angles are 9, 10, 12, 11. Where lines f and d intersect, the angles are 13, 14, 16, 15.
Which angle measures are correct? Select three options.
Answer:
Fist if all u will draw ur Parallel lines e and f are cut by transversal c and d. All angles are described clockwise, from uppercase left. Secondly u will draw ur Parallel lines or angle.
Answer:
a c e
Step-by-step explanation:
There are 6 different colored pens in a box. Each pen has a unique color. In how many orders can 4 pens be chosen? In other words, what is the number of permutations of picking 4 pens from the box?
Answer:
360 different permutations.
Step-by-step explanation:
It goes 6*5*4*3 because as you pick the pens the amount of pens in the jar would obviously decrease. Picking one leaves you with 5 new options. If you repeat that 4 times then you are left with 360 options.
The number of permutations of picking 4 pens from the box is 6P4, or 6!/(6-4)! = 654×3 = 360.
We have 6 pens and we are picking 4 of them. The order in which we pick the pens matters, so we are dealing with permutations.
The number of permutations of n objects is given by n!, or n factorial. So, the number of permutations of 6 objects is 6!.
However, we need to divide by the number of permutations of the 2 pens that we are not picking. There are 2 pens that we are not picking, so the number of permutations of those pens is 2!.
Therefore, the number of permutations of picking 4 pens from the box is 6!/(6-4)! = 654×3 = 360.
Learn more about permutations here: brainly.com/question/3867157
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write a compound inequality that the graph could represent
Answer:
second option
Step-by-step explanation:
Marked price of a camera is Rs.5000. If it
sold at 15% discount, what will be discount amount?
The discount is 15%, multiply the price y 15%:
5000 x 0.15 = 750
The discount is 750
74 divided by 3 times 7 equals what?
Answer:
518 / 3.
Step-by-step explanation:
(74 / 3) * 7 = (74 * 7) / 3 = 518 / 3 = 172 and 2/3 = 172.6666666667.
Hope this helps!
Find the value of x for the triangle.
37
37
45°
45°
Answer:
[tex]x=37\,\sqrt{2}[/tex]
Step-by-step explanation:
Notice you are dealing with a right angle triangle, since one of the angles measure [tex]90^o[/tex]. Now, what you are asked to find is the hypotenuse of that triangle, given an angle of [tex]45^o[/tex] and the opposite side: 37 units. Then, we can use for example the sine function which relates opposite, and hypotenuse:
[tex]sin(45^o)=\frac{opposite}{hyp} \\hyp=\frac{opposite}{sin(45^o)} \\hyp=\frac{37}{\sqrt{2}/2}\\hyp=37\,\sqrt{2}[/tex]
Simplify each expression.
1) 3(8Z² - 52 - 7)
2) 8d(2d-4)
6) 6(5x - 4)
7) 6q- 4
Answer:
1) 24Z^2 - 177.
2) 16d^2 - 32d.
6) 30x - 24.
7) 6q - 4.
Step-by-step explanation:
1) 3(8Z^2 - 52 - 7)
= 3(8Z^2 - 59)
= 24Z^2 - 177
2) 8d(2d - 4)
= (8d * 2d) - (8d * 4)
= 16d^2 - 32d
6) 6(5x - 4)
= (6 * 5x) - (6 * 4)
= 30x - 24
7) Already simplified. 6q - 4.
Hope this helps!
Which statement about the function is true? The function is positive for all real values of x where x > –4. The function is negative for all real values of x where –6 –3. The function is negative for all real values of x where x < –2.
Answer:
Which statement about the function is true?
The function is positive for all real values of x where
x > –4. <<<CORRECT
The function is negative for all real values of x where
–6 < x < –2.
The function is positive for all real values of x where
x < –6 or x > –3.
The function is negative for all real values of x where
x < –2.
Step-by-step explanation:
November Edge 2021
Function f(x) is positive for the values x ≤ -6 and x ≥ -2 and negative in the interval -6 ≤ x ≤ -2.
What is parabola?A parabola is a plane curve that is mirror-symmetrical and roughly U-shaped in mathematics. It fits several seemingly disparate mathematical descriptions, all of which can be shown to define the same curves.
The graph of the function f(x) = (x + 2)(x + 6) is a downward facing parabola that intersects the x-axis at x = -6 and x = -2.
Therefore, we can conclude that the function is negative for all real values of x where x < -6 or x > -2 (outside the x-intercepts).
The function is positive for all real values of x where x lies between the x-intercepts, which means -6 < x < -2.
Therefore, the statement that is true is: "The function is negative for all real values of x where x < -6 or x > -2. The function is positive for all real values of x where -6 < x < -2."
For more details regarding parabola, visit:
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Your question seems incomplete, the probable complete question is:
Which statement about the function is true?
O The function is positive for all real values of x where
The function is negative for all real values of x where
-6exs-2.
O The function is positive for all real values of x where
X-6 orr-3
O The function is negative for all real values of x where
x<-2
The area of a rectangle is given by the expression 2x^3+5x^2-2x+3 . If the length of the rectangle is given by the expression x + 3, find the expression that represents the width
Answer:
2x^2 - x + 1
Step-by-step explanation:
This is polynomial long division:
Divide x + 3 into 2x^3 + 5X^2 - 2x + 3:
Divide 2x^3 by x = 2x^2
Multiple 2x^2 by (x + 3) = 2x^3 + 6x^2
Subtract that from 2x^3 + 5X^2 - 2x + 3 = -x^2 -2x + 3
Divide -x^2 by x = -x
Multiple -x by (x + 3) = -x^2 - 3x
Subtract that from -x^2 - 2x + 3 = x + 3
Divide x by x = 1
Multiple 1 by (x + 3) = x + 3
Subtract from x + 3 = 0
Assume that adults have it scores that are normally distributed with a mean of 100 standard deviation of 15 find probability that randomly selected adult has an Iq between 89 and 111
Answer:
0.5346
Step-by-step explanation:
Find the z-scores.
z = (x − μ) / σ
z₁ = (89 − 100) / 15
z₁ = -0.73
z₂ = (111 − 100) / 15
z₂ = 0.73
Find the probability.
P(-0.73 < Z < 0.73)
= P(Z < 0.73) − P(Z < -0.73)
= 0.7673 − 0.2327
= 0.5346
What is the value of a for the exponential function in the
graph represented in the form of f(x) = a(b)?
O -4
O -3
O 3
O 4
Answer:
Option (4)
Step-by-step explanation:
If the given exponential function is in the form of f(x) = [tex]a(b)^x[/tex]
From the graph we find that two points (0, 3) and (0.5, 6) lie on the graph.
For (0, 3),
f(0) = [tex]a(b)^0[/tex]
3 = a
For (0.5, 6),
f(0.5) = [tex]3(b)^{0.5}[/tex]
6 = [tex]3\sqrt{b}[/tex]
[tex]\sqrt{b}=2[/tex]
b = 4
Therefore, value of b in the given function 'f' is 4.
Option (4) will be the answer.
Answer:
(D) 4
Step-by-step explanation:
♥☺
The school play has two leading roles. The play's director decides to choose the leading actors by drawing two names from a hat that contains the names of four students who want the lead parts. You and your best friend both want to be leads. What is the probability that you will be selected first, and then your best friend will also be selected for a leading role? A. 1/4 B. 1/8 C. 1/12 D. 1/16
Answer:
1/12
Step-by-step explanation:
Answer:
The answer is: C. 1/12
Step-by-step explanation:
I know this is correct because I have the same question on my assignment and it was right.
Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2
Answer:
The length of segment A'E' is 5 units
Explanation:
From the included graph the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;
A- (0, 0)
E- (0, 2)
The length of the segment AE = √((2-0)² + (0 - 0)²) = √2² = 2
When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;
Length of segment A'E' = 5/2 × Length of segment AE
Therefore;
Length of segment A'E' = 5/2 ×2 = 5 units.
The length of segment A'E' is 5 units.
This question is based on distance formula.The length of segment A'E' is 5 units.
Given:
Pentagon A’B′C′D′E’, is the image of pentagon ABCDE under a dilation with a scale factor of 5/2.
From the given graph, the coordinates of the points A and E, in the pentagon ABCDE with reference to point A are;
A- (0, 0)
E- (0, 2)
The length of the segment AE = [tex]\sqrt{(2-0)^{2} +(0-0)^{2} }=\sqrt{2^{2} } =2[/tex]
When a pentagon ABCDE is dilated to pentagon A'B'C'D'E' with a scale factor of 5/2, we have;
Length of segment A'E' = 5/2 × Length of segment AE
Therefore;
Length of segment A'E' = 5/2 ×2 = 5 units.
Therefore, the length of segment A'E' is 5 units.
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