5. The two figures are scaled copies of each other.
a. What is the
scale factor that
takes Figure 1
to Figure 2?
e
P
ס
R
С
A
A
b. What is the
scale factor that
takes Figure 2.
to Figure 1?
D
Figure 1
Figure 2
S
Answers
The quadrilaterals are similar and are related by a scale factor, taken from
a specific location, that maps the points on one figure to the other.
a. The scale factor that takes Figure 1 to Figure 2, is 3
b. The scale factor that takes Figure 2 to Figure 1 is [tex]\dfrac{1}{3}[/tex]
Reasons:
From the question, we have that Figure 1 is a scaled copy of Figure 2, therefore;
Let ABCD represent Figure 1, we have;
ABCD ~ PQRS
Length of [tex]\overline{AD}[/tex] = √(2² + 3²) = √(13)
Length of [tex]\overline{PS}[/tex] = √(6² + 9²) = √(117) = √(9 × 13) = 3·√(13)
Therefore;
a. The scale factor that takes Figure 1 to Figure 2, SF₁₂, is therefore;
[tex]SF_{12} = \mathbf{\dfrac{\overline{PS}}{\overline{AD}}}[/tex]
Which gives;
[tex]SF_{12} = \dfrac{3 \cdot \sqrt{13} }{\sqrt{13} } = 3[/tex]
The scale factor that takes Figure 1 to Figure 2, SF₁₂ = 3
(3 times the lengths of Figure 1 gives the lengths on Figure 2)
b. The scale factor that takes Figure 2 to Figure 1, SF₂₁, is given as follows;
[tex]SF_{21} = \mathbf{\dfrac{\overline{AD}}{\overline{PS}}}[/tex]
Which give;
[tex]SF_{21} = \dfrac{\sqrt{13} }{3 \cdot \sqrt{13} } = \mathbf{\dfrac{1}{3}}[/tex]
The scale factor that takes Figure 2 to Figure 1, SF₂₁ is [tex]\underline{\dfrac{1}{3}}[/tex]
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Related Questions
Here is a list of numbers:
1.9, 0.1, 7.7, 6.8, 6, 7, 7.8, 2.8, 6.9, 3.5
State the median.
Give your answer as a decimal.
Answers
Answer:
So I added, 1.9, 0.1, 7.7, 6.8, 6, 7, 7.8, 2.8, 6.9, 3.5, which equals 50.5.
Then, I divided 50.5 by 9 since that is how many number sections there are.
Therefore, I get 5.61.
Three consecutive integers add up to 51. The integers are *
16,17,18
15,16,17
17,18,19
18,19,20
Answers
Answer:
1st option
Step-by-step explanation:
let the three consecutive integers be n , n + 1 , n + 2 , then adding gives
n + n + 1 + n + 2 = 51, simplifying
3n + 3 = 51 ( subtract 3 from both sides )
3n = 48 ( divide both sides by 3 )
n = 16
n + 1 = 16 + 1 = 17
n + 2 = 16 + 2 = 18
The 3 consecutive integers are 16, 17, 18
need a little help on this?
Answers
d = 122
e = 58
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40 POINTS! Thank you so much if you answer!
Answers
Answer:
o
Step-by-step explanation:
o
thx for the points :D
can someone please help me with this
Answers
Answer:
if the question is what is the are of the circle without the rectangle inside it, then we could solve it easily using the Mathematical formula for A Circle's area which is
[tex]\pi {r}^{2} [/tex]
since a radius is half a diameter, and the diameter is 8cm, the radius becomes 4 cm
Step-by-step explanation:
π×4^2
3.14×16
50.24
Mr. Benson’s gross pay is $789.18. The amount of social security deducted is 6.2% of gross pay. How much of his gross pay will be deducted for the social security tax?
Answers
Answer: $48.93
Step-by-step explanation: 789.18 x 0.062
Answer:
$48.93
Step-by-step explanation:
789.18 x (0.062) = 48.92916 $48.93
took the test
Help me with this please
Answers
Answer:
f(-5) = 4(-5) + 1 = -20 + 1 = -19
f(-1) = 4(-1) + 1 = -4 + 1 = -3
f(2) = 4(2) + 1 = 8 + 1 = 9
f(3) = 4(3) + 1 = 12 + 1 = 13
f(5) = 4(5) + 1 = 20 + 1 = 21
Find the EQUATION of the line through (-10,-12) and (-15,3). Use the form y=mx+b.
Answers
Refer to the attachment
I need help please!!!
Answers
Answer:
yes (the given angles are co-interior {130+50=180} )yes( corresponding angles are equal) .....yes (exterior alternate angles are equal)yes ( vertically opposite angles are equal)7) 3x=45( corresponding angles formed on parallel lines)
x=45/3
x=15
8)120=2x+10(corresponding angles formed on parallel lines)
or,120-10=2x
or,110/2=x
or,x=55
2,631 dividido entre 24
Answers
Answer:
2631 divided by 24 = 109.625
Step-by-step explanation:
The result of 2631/24 is a terminating decimal with 3 digits to the right of the decimal point.
2631 divided by 24 in decimal = 109.625
2631 divided by 24 in fraction = 2631/24
2631 divided by 24 in percentage = 10962.5%
Note that you may use our state-of-the-art calculator above to obtain the quotient of any two integers or decimals, including 2631 and 24, of course.
Repetends, if any, are denoted in ().
The conversion is done automatically once the nominator, e.g. 2631, and the denominator, e.g. 24, have been inserted.
SPANISH:
El resultado de 2631/24 es un decimal final con 3 dígitos a la derecha del punto decimal.
2631 dividido por 24 en decimal = 109,625
2631 dividido por 24 en fracción = 2631/24
2631 dividido por 24 en porcentaje = 10962,5%
Tenga en cuenta que puede utilizar nuestra calculadora de última generación anterior para obtener el cociente de dos enteros o decimales cualesquiera, incluidos 2631 y 24, por supuesto.
Los repetends, si los hay, se indican en ().
La conversión se realiza automáticamente una vez que el nominador, por ejemplo, 2631, y el denominador,
136 is 0.8% of what number? Use pencil and paper. Would you expect the answer to be a lot less than 136, slightly less than 136, slightly greater than 136, or a lot greater than 136? Explain.
Answers
Find the value of x, and please explain how you got x
Answers
The work is shown in the picture. I hope this helps.
Write a statement and reason proof.
Answers
Answer:
l want to do all your math
Answer:
<XPE = <ENY
Step-by-step explanation:
<1=<2 (GIVEN)
SO <3+<4= <5+<6
<3=<4 (PE Bisects <APN)
<5=<6 (EN bisects <ANP)
so <3=<5
than <XPE=< ENY
Someone help me and answer these ASAP PLS
1. What are the three major responsibilities of the county commissioners?
2. What are the three major responsibilities of the county sheriff?
3. What is the fundamental purpose for county government?
Answers
Answer:
1. The powers include: budgeting and appropriation of funds for all county activities; building and maintaining county roads; making and enforcing civil and criminal resolutions and ordinances not in conflict with state law, including those for land use and building construction; supporting and implementing.
2. Serves as a licensed peace officer and is responsible for enforcing the criminal laws of the state. Manages and operates the county jail. Provides security for the courts.
3. County governments perform essential administrative functions such as registering voters, supervising elections, keeping records, providing police protection, and administrating health and welfare services.
Step-by-step explanation:
Jonathon is paid biweekly. His annual salary is $39,000. What is his biweekly salary? Include a $ in your answer.
plzzzzzzzzzzzzzzzz help me
Answers
Answer: Jonathon gets paid $1,500 biweekly
for cases of n objects taken n at a time the number of possible combinations is _____________ the number of possible permutations.
Answers
Answer:
I believe your answer is less than or equal to. I hope this helps.
Solve the system of equations by the substitution method.
x−2y=−4 x+8y=16
Answers
Answer:
x=0, y=2
Step-by-step explanation:
x-2y=-4
-x+8y=16
-10y=-20
y=2
x-2y=-4
x-2(2)=-4
x-4=-4
x=-4+4
x=0
= Homework: Section 9.6
Question 16, 9.6.61
O Point
The perimeter of a rectangle is to be no greater than 160 centimeters and the width must be 35 centimeters. Find the maximum length of the rectangle.
Answers
Answer:
here is an an example
Step-by-step explanation:
Let x = the width of the rectangle
P = 2l + 2w
2(40) + 2x ≤ 150
80 + 2x ≤ 150
2x ≤ 70
x ≤ 35 cm
PLS HELP I GOTTA TURN THIS INNN
Answers
Answer:
Lauren
Step-by-step explanation:
1/2 is Erin
3/4 is Lauren
Answer:
1/2 for Eric and 6/8 for lauren
Eric: 1/2 = 4/8
Lauren: 6/8
Lauren was more succesful
Step-by-step explanation:
can i get help for number 3???!?! please!!
Answers
Answer:
1.) 40 degrees
2.) 75 degrees
3.) 105 degrees
4.) 140 degrees
Step-by-step explanation:
Straight lines are = 180 degrees. Each of the angles you must solve have a given exterior angle. All you have to do is subtract the exterior angle from 180 to find the interior angle
1.) angle = 180-140
2.) angle = 180-105
3.) angle = 180-75
4.) angle = 180-40
Answer:
Measure of angle 1 is: 40 degrees
Measure of angle 2 is: 75 degrees
Measure of angle 3 is: 105 degrees
Measure of angle 4 is: 140 degrees
Step-by-step explanation:
Each of these angles is supplementary, meaning it adds up to 180 degrees,Thus, we can just subtract the measurement given from 180 to get our angle's measurement :)
What is m if 14 + 9m = -13
Answers
Answer:
-3m
Step-by-step explanation:
everyone knows we should take the unknown letter to a one side and numbers to another side.
so first ;
9m + 14 = -13
9m = -13 - 14
9m =-27
9m/9 = -27 / 9
m = -3
-3 is the finale answer
There are 4 times as many dogs as cats if the total number of dogs and cats is 20
how many dogs are there
Answers
Answer:5
Step-by-step explanation: 4*5=20
[tex]\sqrt{x^{2}-16 }-3\sqrt{x-4}=0[/tex]
Answers
Answer:
[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 \\ [/tex]
Step-by-step explanation:
[tex]\tt{} \sqrt{ {x}^{2} - 16 } - 3 \sqrt{x - 4} = 0[/tex]
[tex]\tt{} \sqrt{ {x}^{2} - 16 } = 3 \sqrt{x - 4} [/tex]
[tex]\tt{}{x}^{2} - 16 = 9(x - 4)[/tex]
[tex]\tt{}(x - 4).(x + 4) = 9(x - 4)[/tex]
[tex]\tt{}(x - 4) \times (x + 4 - 9) = 0[/tex]
[tex]\tt{}( x - 4) \times (x - 5) = 0[/tex]
[tex]\tt{}x - 4 = 0 \\ \tt{}x - 5 = 0[/tex]
[tex]\tt{}x = 4 \\ \tt{}x = 5 \\ \\ [/tex]
[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 [/tex]
Answer:
x = 4, 5.
Step-by-step explanation:
√(x^2 - 16) - 3√(x - 4) = 0
√(x^2 - 16) = 3√(x - 4)
Square both sides of the equation:
x^2 - 16 = 9(x - 4)
x^2 - 9x - 16 + 36 = 0
x^2 - 9x + 20 = 0
(x - 4)(x - 5) = 0
x = 4, 5.
As the original equation contained square roots:
We test for extraneous solutions:
x = 4:
√(4^2 - 16) - 3√(4 - 4) = 0 - 3*0 = 0 so x = 4 is OK.
x = 5:
√(5^2 - 16) - 3√(5 - 4) = √9 - 3√1 = 0 so x = 5 is also OK.
120−96×[5 ÷ {23 − 3 × (12 − 22 − 16)}]
Answers
Answer:
115.248
Step-by-step explanation:
120−96×[5 ÷ {23 − 3 × (12 − 22 − 16)}]
120−96×[5 ÷ {23 − 3 × (-26)}]
120−96×[5 ÷ {101}]
120−96×[0.0495]
115.248
Just remember PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
Free 10 pointss oh:>
Answers
Answer:
oh it's 5 not 10 xD
The hazard management process consists of a number of activities designed to reduce loss of life and destruction of property. Natural hazard management has often been conducted independently of development planning. A distinctive feature of OAS technical assistance is the integration of the two processes.
Step-by-step explanation:
plz mark me as brainliest
have a great day
Thank you
Find the slope of the y intercept of the graph linear equation 2x+y=7
Answers
2x+y=7
-2x -2x
y=-2x+7
slope of -2
Hope this is right, feel free to correct me in the comments
Answer:
-2
nsskwiwkwnwhsisnenwnwjw w w
Benjamin has a bag of 50 marbles. 25 are red, 10 are blue, and 15 are yellow.
Give the ratio of red marbles to total marbles. __ : __
Answers
Answer:
25:50
or
25/50
or
25 to 50
Step-by-step explanation:
Simply take the number of red marbles and place it before the number of total marbles
Paying $38.50 for 12 pounds of apples
Answers
Answer:
If you pay $38.50 for 12 pounds of apples it costs $3.20833333333 per pound.
Step-by-step explanation:
Use a model to explain why any number – (–7) is the same as that number + 7.
(PLEASEEEE HELPPP)
Answers
Answer:
say you buy something for 10 dollars, you are going to get charged for it, but if you take item off of your shopping cart you are taking away the -10 dollars that wouldve been charged.
Step-by-step explanation:
the reason this works is because you take away something that makes it less.
- (-7) is basically just saying delete that -7. that's why - (-7) is the same as +7
Alex wrote the expanded form for the number 165.038 as “100 + 60 + 5 + 30 + 8.” Was he correct? If not, give the correct expanded form. P.S I really need the answer asap!
Answers
Answer:
no he is not correct.
the correct expanded form: 100+60+5+0.0+0.30+0.008
Step-by-step explanation:
Hope this helps also i learned about this r u in 5th grade
Alex's expanded form for the number 165.038 is not correct. The correct expanded form for the number 165.038 is 100 + 60 + 5 + 0.03 + 0.008.
The number 165.038 can be broken down into its individual place values:
Hundreds: 100
Tens: 60 (6 tens)
Ones: 5
Tenths: 0.03 (3 hundredths)
Hundredths: 0.008 (8 thousandths)
So, the correct expanded form for the number 165.038 is:
100 + 60 + 5 + 0.03 + 0.008
Hence, Alex's expanded form for the number 165.038 is incorrect. The correct expanded form is: 100 + 60 + 5 + 0.03 + 0.008.
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