Answer: 10 feet
Step-by-step explanation:
Let h be the height of lamppost.
Since both the person and the lamppost are standing vertical to the ground, making similar right triangles.
Because the two triangles are similar, the ratio of their sides is the same.
Therefore, we have
[tex]\frac{\text{height of lamppost}}{\text{distance of lampost from mirror}}=\frac{\text{height of person}}{\text{distance of person from mirror}}\\\\\Rightarrow\frac{h}{6}=\frac{5}{3}\\\\\Rightarrow\ h=\frac{6\times5}{3}\\\\\Rightarrow\ h=10[/tex]
Hence, the height of the lamppost = 10 feet.
Setting up a proportional relationship between mirror and lamppost, the height of the lamppost is 10 feets.
Height of person, Hp = 5 feets Distance of person form mirror, Dp = 3 feets Distance of Lampost from mirror, Dm = 6 feets Height of Lampost = Hl =?Setting up a proportional relationship :
[tex]\frac{Hp}{Dp} = \frac{Hl}{Dm} [/tex]
[tex]\frac{5}{3} = \frac{Hl}{6} [/tex]
Cross multiply :
Hl × 3 = 6 × 5
3Hl = 30
Hl = (30 ÷ 3)
Hl = 10
Therefore, the height of the lamppost is 10 feets.
Learn more :https://brainly.com/question/18109354
bailey can hit 42 golf balls in 3 1/2 hours. if she hits golf balls at a constant rate,
Bayley can hit a single golf ball every 5 minutes
Now Bayley can hit 42 golf balls in 3 1/2 hours
Thus converting the 3 1/2 hours in minutes:
3 hours + 1/2 hours = 180 minutes + 30 minutes = 210 minutes
Bayley can hit 42 golf balls in 210 minutes
Thus let's say she takes 'x' minutes to hit one ball
Calculating the value of 'x' using direct proportion theorem:
[tex]\frac{x}{210}=\frac{1}{42}[/tex]
[tex]x*42 = 210[/tex]
[tex]x= \frac{210}{42}[/tex]
[tex]x = 5[/tex]
Thus Bayley can hit 5 golf balls every 1 minute
tim estimates that 60÷5.7 is about 10. Will the actual quotient be greater then or less than 10? explain
The quotient of 10.52 is greater than 10 for 60 / 5.7.
Given that,
To justify whether tim estimates that 60÷5.7 is about 10. Will the actual quotient be greater than or less than 10
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Dividend = 60
Divisor = 10
Now,
= 60/ 5.7
= 10.52 = quotient which is greater than 10
Thus, the quotient of 10.52 is greater than 10 for 60 / 5.7.
Learn more about arithmetic here:
brainly.com/question/11424589
#SPJ2
How do you express 5/8 as a decimal?
To express 5/8 as a decimal, divide 5 by 8 to get 0.625.
Explanation:To express the fraction 5/8 as a decimal, you must divide the numerator (5) by the denominator (8). When you do the division, the result is 0.625.
Here's it in steps:
Take the numerator (5).
Divide it by the denominator (8).
The result is 0.625, which is the decimal form of 5/8.
To express 5/8 as a decimal, you need to divide the numerator (5) by the denominator (8).
5 divided by 8 is equal to 0.625.
So, 5/8 is equivalent to 0.625 as a decimal.
Learn more about Expressing Fractions as Decimals here:https://brainly.com/question/21289786
#SPJ2
A jet flies 510 miles in 2 hours.
a. What is the rate of speed of the jet (MPH)?
b. At this rate, how far can the jet fly in 15 hours?
Please fill out the function table.
Questions are in the photo.
Fumi's backyard has an area of 10,359 Sq ft. write this in scientific notation
The product of 10 and the difference of a number x and 14 is 90
Answer:
The product of 10 and the difference of 76 and 14 is 90
Step-by-step explanation:
90 - 14 = 76
76 + 14 = 90
90 - 10 = 80
I really tried to understand and came to this conclusion but I hope it helps I guess!
A-6 pack Of Undershirts cost $13.98.This is $3.96 less than the cost Of buying 6 individual shirts. if each undershirt costs the same amount,how much does each undershirt cost when purchased individually
sophina bought 3 yards of trim to put around a rectangular scarf . She wants the width of the scarf to be a whole number that is at least 6 inches and at most 12 inches. If she uses all the trim , what are the possible dimensions of her scarf? write your answer in inches
i need help with 64 x 57=
60 people rode a ferris wheel in 25 min how many can ride in 2 hrs
(mary found 2 seashells and jason found 5 seashells on the beach when they cleaned them they discovered thay that 8 were cracked how many seashells dis they find together)plz help
Sales Tax is percent
a)increase
b)decrease
Discount is percent
a)increase
b)decrease
Tip is percent
a)increase
b)decrease
One wall of Kevin's living room measures 8 ft by 15 ft. Windows make up 22% of the surface area. What is the window area?
a^b if a=6 and b=7...............
What is the quotation of the division problem -44/4
Mrs. Bennett has graded 20% of her 150 students' papers. How many papers does she still need to finish grading?
how to draw an area model for 1.1x2.4
which parachute has a slower descent: a red parachute that falls 10 feet in 4 seconds or a blue parachute that falls 12 feet in 6 seconds?
(1) The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy. Lola sold $2030 in ads, Ahmed sold $1540, and Tommy sold $1800. (a) What fraction of the total sales did each salesperson sell? (b) A $100 bonus was awarded to the three salespeople, which they had to share. It was awarded so that each salesperson received the same fraction of $100 as he or she sold of the total sales. How much did each person receive? Round to the nearest whole cent.
Answer: a) Fraction of the total sales did each salesperson sell:-
[tex]\text{Lola}=\frac{203}{537}[/tex]
[tex]\text{Ahmed}=\frac{154}{537}[/tex]
[tex]\text{Tommy}=\frac{180}{537}[/tex]
b) Each person receive=$33
Step-by-step explanation:
Given: The three salespeople for a local advertising firm are Lola, Ahmed, and Tommy.
Sales by Lola= $2030
Sales by Ahmed=$1540
Sales by Tommy=$1800
Thus, the total sales= $2030+$1540+$1800=$5370
Fraction of the total sales did each salesperson sell:-
[tex]\text{Lola}=\frac{\text{Sales by Lola}}{\text{total sales}}=\frac{2030}{5370}=\frac{203}{537}[/tex]
[tex]\text{Ahmed}=\frac{\text{Sales by Ahmed}}{\text{total sales}}=\frac{1540}{5370}=\frac{154}{537}[/tex]
[tex]\text{Tommy}=\frac{\text{Sales by Tommy}}{\text{total sales}}=\frac{1800}{5370}=\frac{180}{537}[/tex]
If $100 bonus was awarded to the three salespeople, then
Each person receive=[tex]\frac{\$100}{3}=33.33\approx\$33[/tex]
What is a conversion factor that you can use to convert gallons into pints?
of the students in Rosalie's dance class, 29 out of 59 have participated in dance class before. About how many of her students have participated in dance class before?
A)0
B) 1/2
C) 1
D) 2
A sofa is on sale for
$442, which is
35% less than the regular price.
What is the regular price?
the regular price of the sofa is $684.61.
What is percentage?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given, A sofa is on sale for $442, which is 35% less than the regular price.
Thus,
65% of the regular price = 442
The regular price = 445*100/65
Thus, Regular price = $684.61
Therefore, the regular price of the sofa is $684.61.
Learn more about percentages here:
https://brainly.com/question/29306119
#SPJ1
a square rug has an area 80ft which is the best approximation of the length of one side of the rug.....Explain...If you can show work
A ) 6.4ft
B ) 7.5ft
C ) 8.9ft
D ) 20ft
The length of one side of the square rug is found by taking the square root of the area of the rug, which is 80 square feet. The best approximation for this is 8.9 feet.
Explanation:This problem is about understanding the relationship between the area and the length of a side in a square. In a square, all sides are equal in length, and the area of a square is given by the equation Area = side*side. So, if the area is given, we can find the length of a side by taking the square root of the area.
Here, since the area of the square rug is 80 square ft., we find the length of one side by calculating the square root of 80. The square root of 80 is approximately 8.9ft
So, looking at the options given, the best approximation for the length of one side of the rug is option C) 8.9ft.
Learn more about Square area and side length here:https://brainly.com/question/33930998
#SPJ2
your bank account balance was $235.24 . After two checks were cashed (each for the same amount) your balance is now $-45.58. what was the amount of each check
After calculating the total reduction in the bank account balance, it was determined that each of the two equal checks cashed was for the amount of $140.41.
The problem at hand is a simple algebra question where we are solving for the amount of each check cashed when a bank account balance changes from a positive balance to a negative one.
Firstly, we must establish the initial and final bank balance amounts before and after the checks are cashed. We know that the beginning balance was $235.24 and after cashing two identical checks, the balance becomes -$45.58. The total reduction in the bank account reflects the total amount of the two checks combined.
To find the total reduction, we subtract the final balance from the initial balance:
Total reduction = Initial balance - Final balance
Total reduction = $235.24 - (-$45.58) = $235.24 + $45.58 = $280.82
Since there were two checks with equal amounts, we divide the total reduction by two to find the amount of each check:
Amount per check = Total reduction / 2
Amount per check = $280.82 / 2 = $140.41
Therefore, the amount of each check was $140.41.
identify the independent and dependent variables in the following y=4x+1
In the given equation y=4x+1, the independent variable is x, and the dependent variable is y. The independent variable is the cause, and the dependent variable is the effect. Therefore, any change in x will result in a change in y.
Explanation:In the given equation y=4x+1, the independent variable is x and the dependent variable is y. This is because the value of x is not dependent on any other variable, while the value of y depends on x. The variable y is dependent because it changes in response to the value of x.
Conceptually, the independent variable is what you have control over or manipulate, and the dependent variable is what you observe or measure. For example, in the equation y = a + bx, a is the y-intercept, b is the slope, x is the independent variable, while y is the dependent variable that changes according to the value of x.
Simply put, the independent variable is the cause, and the dependent variable is the effect. In the context of this equation, any change in x (independent variable) will cause a change in y (dependent variable).
Learn more about Variable Identification here:https://brainly.com/question/33409105
#SPJ12
Multiply whit regrouping
59
X 52=
Find the value of x when 2(x - 3) + 1 = 3x + 4
A) -1
B) -1/5
C) -9/5
D) -9
Answer: -9
Step-by-step explanation: Distribute: 2x - 6 + 1= 3x + 4. Combine like terms on the left side: 2x - 5 = 3x + 4. Subtract 2x from both sides: -5 = x + 4. Subtract 4 from both sides: x = -9.
what are all the common factors of 24,64 and 88
DDraw a model of 5.5 divided by 5