a person standing 20 feet from a street light casts a shadow as shown. how many times taller is the streetlight than the person? assume the triangles are similar.
Answers
We have two similar triangles; triangle ABC and triangle DBE
We can work out the scale factor of the two triangles by checking the corresponding lines
We have line EB correspond to line CB
The scale factor is EB ÷ CB = 30 ÷ 10 = 3
Line EB is 3 times longer than line CB
So, line DE is 3 times longer than line AC
The street light is the line DE and the person standing is the line AC
So, the street light is 3 times taller than the person standing.
Using the concept of similar triangles to calculate the scale factor, the height of the streetlight is 3 times the height of the person.
Length of shadow cast = 10 feets
Height of person = 6 feets
Distance of person from streetlight light = 20 feets
Since the triangles are similar :
Comparing the length of both triangles :
Bigger triangle = 30 feets Smaller triangle = 10 feetsThe scale factor is :
(Bigger triangle / Smaller triangle) = (30/10) = 3 Therefore, the scale factor is 3Using the scale factor ; the height of the streetlight will be :
Height of person × 3 = 6 feets × 3 = 18 feetsHeight of streetlight = 18 feets
Height of person = 6 feets
Therefore, the streetlight is (18/6 = 3) 3 times the height of the person.
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Related Questions
Find the number is 900% of it is 450.
Answers
50
Hope this helped!
The number whose 900% is 450 is 50.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
The number is 900% of it is 450.
let the number be x.
900% of x= 450
900/ 100 x= 450
9x = 450
x= 50
Hence, 900% of 50 is 450.
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Expressions cannot _____.
Answers
Matthias walked around the track for 9.28 minutes. What is the value of the digit 2 in 9.28
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Which reason justifies the statement that KLC is complementary to KJC?
Answers
hope it helps
Answer:
Angles that are congruent are complementary to the same angle
Step-by-step explanation:
see that attached figure to better understand the problem
we know that
Two angles are complementary if their sum is equal to [tex]90\°[/tex]
[tex]m<KJM=m<KLM=90\°[/tex]
[tex]m<KJC=m<MLC[/tex] -----> equation A
[tex]m<KJM=m<KJC+m<CJM[/tex]
so
[tex]m<KJC+m<CJM=90\°[/tex] -----> equation B
[tex]m<KLM=m<KLC+m<MLC[/tex]
so
[tex]m<KLC+m<MLC=90\°[/tex] -----> equation C
Substitute equation A in equation C
So
[tex]m<KLC+[m<KJC]=90\°[/tex]
That means------> angles ∠KLC and ∠KJC------> are complementary angles
therefore
Angles that are congruent are complementary to the same angle
Is 16.45 greater, less than or equal to 16.454
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again I think I am right but I just want to check myself
Answers
Explain how using basic fact can help find 10x20x30x40 mentally
Answers
Add the 4 zeros to the end
240,000
Fill in the missing operation (+,-,* or /) below to make the number sentence correct from to left to right
4_9_6_6_25=25
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4*9/6-6+25=25
Some students reported how many textbooks they have. The dot plot shows the data collected: A dot plot is titled Students Textbooks and labeled Number of Textbooks. The values on the horizontal line are 2, 3, 4, 5, and 6. There is 1 dot above 2, 2 dots above 3, 4 dots above 4, 5 dots above 5, and 4 dots above 6. What do the dots above the number 6 indicate? There are exactly 6 students with 4 textbooks. There are exactly 4 students with 6 textbooks. There are exactly 6 students with less than 4 textbooks. There are exactly 4 students with less than 6 textbooks.
Answers
Answer:
B
Step-by-step explanation:
Subtract using the number line.
−1/3 − (−1/2)
Answers
The answer is 1/6 after using the number line if the number expression is −1/3 − (−1/2).
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
The fraction numbers are 1/3 and -1/2
As we know,
Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
The number expression is:
−1/3 − (−1/2)
From the number line:
Drawing line segment length of 1/3 left side
Drawing line segment length of 1/2 left side
Taking difference using number line:
= 1/6
Also, the arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= −1/3 − (−1/2)
= -1/3 + 1/2
= (-2+3)/6
= 1/6
Thus, the answer is 1/6 after using the number line if the number expression is −1/3 − (−1/2).
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What is the best estimate for the product of 289 and 7
Answers
Estimate means you have to round to the nearest 10, 100, ect...
300*10= 3000
The exact value though is 2023
289 -> 290
7 -> 10
290 x 10
= 2900
Please give an equation to this word problem...
1. Kim's age is twice that of her sister. When you add Kim's age to her sister's age, you get 36. How old is each sister?
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I'm not entirely sure
Fill in the blank to make the solution correct
5.6 x _ = -19.04
Answers
So 5.6*(-3.4)= -19.04
The value of x is -3.4.
Product of IntegersThe product of different integers is different as given below.
[tex](+)interger \times (+)interger = (+)interger\\(+)interger \times (-)interger = (-)interger\\(-)interger \times (+)interger = (-)interger\\(-)interger \times (-)interger = (+)interger\\[/tex]
Given to us,[tex]5.6 \times \_\_} = -19.04[/tex]
AssumptionLet the number be x.
SolutionAs we can see the first number is positive while the result is negative, therefore, the other number must be negative as well.
[tex]5.6 \times x = -19.04\\\\x = \dfrac{-19.04}{5.6}\\\\x = -3.4[/tex]
Hence, the value of x is -3.4.
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how much money must you deposit in a simple interest account to earn $500 in interest in 5 years at 4% annual interest?
Answers
Let me know if I wrong
The $2500 money must you deposit in a simple interest account to earn $500 in interest in 5 years at 4% annual interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given that:
simple interest account to earn $500 in interest in 5 years at 4% annual interest
As we know the simple interest formula is:
I = Prt
Here
I = $500
t = 5 years
r = 4% = 0.04
500 = P(0.04)(5)
P = 500/0.2
The money that must be deposited in a simple interest account to earn $500 is:
P = $2500
Thus, the $2500 money must you deposit in a simple interest account to earn $500 in interest in 5 years at 4% annual interest.
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Assume each tick mark represents 1 cm. Calculate the total displacement from 0 if an object moves 3 cm to the left, then 7 cm to the right, and then 6 cm to the left
Answers
Answer:
Calculate the final displacement from 0 if an object first moves 3 cm to the left and then 5 cm to the right.
The final displacement is 2 cm to the RIGHT .
Step-by-step explanation:
use the model to solve for x
Answers
3x+1 = 2x-5
3x = 2x-6
x = -6
Use the Distributive Property to solve 3e - 8 = 2( e - 4). How do I do this please help I’m in the 8th grade and this is pre algebra
Answers
3e - 8 = 2e - 8
+8 +8
3e = 2e
-2e -2e
e = 0
Pauline spent $7.50 every day for 3 days. Which expression is the best choice to help her determine the total amount of money she spent?
(7.50)(−3) = −22.50; she spent $22.50
(−7.50)(3) = −22.50; she spent $22.50
(−7.50)(−3) = 22.50; she spent $22.50
(7.50)(3) = 22.50; she spent $22.50
Answers
Answer:
The correct option is 2.
Step-by-step explanation:
It is given that Pauline spent $7.50 every day for 3 days.
Amount spent on each day = $7.50
Number of days = 3
Spent amount and expenditure are always negative.
Total amount of money she spent is
[tex]Total =(-7.50)(3)[/tex]
On simplification we get
[tex]Total =-22.50[/tex]
She spent $22.50 and required expression is (−7.50)(3) = −22.50. Therefore the correct option is 2.
Which of the following would be equivalent to 11 to the 8th power over 11 to the 3rd power?
A)11 to the 7th power over 11 to the 7th power
B)11 ⋅ 114
11 to the 0 power over 11 to the 5th power
110
Answers
although you should have an option that either is 11^5 or equals 11^5 like 11^15/11^10 for example
the third answer is almost correct, but it would have to be 11^5/11^0
Answer:
[tex]11 .11^4[/tex]
Step-by-step explanation:
Given phrase,
11 to the 8th power over 11 to the 3rd power
[tex]\implies \frac{11^8}{11^3}[/tex]
[tex]=11^{8-3}[/tex] [tex](\because \frac{a^m}{a^n}=a^{m-n})[/tex]
[tex]=11^5[/tex]
Since,
[tex]11.11^4[/tex]
[tex]=11^{1+4}[/tex]
[tex]=11^5[/tex]
Hence, the equivalent expression to 11 to the 8th power over 11 to the 3rd power is,
[tex]11.11^4[/tex]
Venus is about 10^8 kilometers from the Sun. Saturn is about 10^9 kilometers from the Sun. About how many times farther from the Sun is Saturn than Venus?
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what is the product? (3a^2b^7)(5a^3b^8)
Answers
the second of three numbers is 1 less than the first. The third number is 5 less than twice the second. If the number exceeds the first number by 12, find the three numbers
Answers
The three numbers are found by forming and solving a system of equations: the first number is 19, the second is 18 (which is one less than the first), and the third is 31 (which is 5 less than twice the second and exceeds the first by 12).
To solve the problem of finding the three numbers, we can set up a system of equations based on the information given:
The first number is x.The second number is one less than the first, so it is x - 1.The third number is 5 less than twice the second, which translates to 2(x - 1) - 5.The third number also exceeds the first by 12, so 2(x - 1) - 5 = x + 12.Now we can solve for x:
2(x - 1) - 5 = x + 122x - 2 - 5 = x + 122x - x = 12 + 2 + 5x = 19The first number is 19. The second number is 18 (19 - 1), and the third number is 31 (2(18) - 5).
Thus, the three numbers are 19, 18, and 31.
6(5-8v)+12=-54 please answer
Answers
Multiply 6 by 5 to get 30.30+6(−8v)+12=−54
Multiply −8 by 6 to get −48.30−48v+12=−54
Add 30 and 12 to get 42.−48v+42=−54
Subtract 42 from both sides.−48v=−42−54
Subtract 54 from −42 to get −96.−48v=−96
Divide each term -48
-48/-48v=-96/-48
Divide 96 by −48 to get −2v=2
How many 1/4 ft pieces can you cut from a string that is 15 feet long
Answers
so the answer is 60 pieces
You can cut 60 pieces of 1/4 foot each from a string that is 15 feet long by carrying out the operation 15 ÷ 1/4, which turns into multiplication by the reciprocal of the fraction, 15 x 4 equals 60.
Explanation:The question is asking how many 1/4 ft pieces you can cut from a 15 feet long string. In other words, you want to divide the total length of the string by the length of each piece you're cutting out. So you will carry out a division operation: 15 ÷ 1/4. When dividing by a fraction, you actually multiply by its reciprocal. The reciprocal of 1/4 is 4, so 15 ÷ 1/4 becomes 15 × 4, which equals 60. Therefore, you can cut 60 pieces of 1/4 foot each from a string that's 15 feet long.
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The unit rate for $18 for 24 pounds
Answers
Final answer:
To find the unit rate of $18 for 24 pounds, you divide the total cost by the number of pounds, resulting in a unit rate of $0.75 per pound.
Explanation:
The student is asking how to calculate the unit rate of a product that costs $18 for 24 pounds. To find the unit rate, you divide the total cost by the total number of units (in this case, pounds). So, the calculation for the unit rate in this question would be:
$18 ÷ 24 pounds = $0.75 per pound
Thus, the unit rate is $0.75 per pound. This means for every pound of the product, you pay $0.75.
0.9c+0.5c=7 answer for c
Answers
1.4c=7
c=7/1.4
c=5
you’re going to add 0.9+0.5c
1.4c is going to be your answer so then you’re going to equal 1.4c=7.
then you divide 1.4 on both sides.
1.4c divided by 7 is 5.
Why does 30+(-8)+(-6) equal 16? I'm so confused on this one
Answers
30-8-6
22-6
16
30 + (-8) + (-6) = 16
first combine your negative numbers
30 + (-14) = 16
30 - 14 = 16
16 = 16
You want to make a large bowl of salad to share with your friends. Your brother eats 1/3 of it before they come over.
a.) you want to divide the leftover salad evenly among six friends. What expression describes the situation? Exlplain.
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How would you write -4.5 as a rational number in the form of a/b?
Answers
Simplify each expression
√3 (√27 - √3)
plz explain how to do it, thx
Answers
Simplify Root 27
√3( 3√3-√3)
Combine like terms
√3(2√3)
Multiply
√3* √3= 3
3*2=6
Final answer: 6