A ladder 13m long reaches a window which is 5m above the ground , on one side of the
street. Keeping its foot at the same point,
the ladder is turned to the other side of the street
to reach a window at a height of 12m. Find the
width of the street.
Answers
The ladder is 13 m long and leans against a window 5 m high, then the ladder leaned to the other side without moving its feet to reach the 12 m high window.
if we imagine a leaning ladder it will look like a right triangle and it will remind us of the Pythagorean theorem. do you remember the pythagorean theorem?
The Pythagorean theorem explains the relationship or relationship between the lengths of the sides of a right triangle.
The Pythagorean theorem reads: "The square of the length of the hypotenuse (hypotenuse) in a right triangle is equal to the sum of the squares of the lengths of the other sides".
in the picture, let's say if the width of the street is a, the height of the window is b and the length of the stairs is c.
in this case we will find the width of the street, namely a, then we use formula a² = c² - b² .
then it will be
b = 12
c = 13
a² = c² - b²
a² = 13² - 12²
a² = 169 - 144
a² = 25
a = 5
So the width of the street is 5 m
Related Questions
Suppose Mack's wage was $7.00 an hour in 2001 and was $12.00 per hour in 2012. The CPI was 94 in 2001 and 201 in 2012. The 2001 wage in terms of 2012 dollars is
A) $14.97.
B) $14.07.
C) $3.48.
D) $13.16.
E) $7.00.
Answers
The wage of 2001 in terms of wage in 2012 is option A $14.97
Given,
Mack's wages in 2001 = $7 per hour
Mack's wages in 2012 = $12 per hour
The CPI in 2001 = 94
The CPI in 2012 = 201
We have to fins the wage of 2001 in terms of wage in 2012;
CPI;- Consumer Price Index
The CPI is calculated by the Bureau of Labor Statistics each month using a sample of 94,000 prices. To determine the overall change in prices, the index for each good or service is weighted according to its share of recent consumer spending.
Here,
The wage of 2001 in terms of wage in 2012 = (CPI in present year / CPI in past year) x Wage of earlier year
= (201 / 94) x 7
= 14.97
That is,
The wage of 2001 in terms of wage in 2012 is option A $14.97
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Balance each of the following equations
Answers
Answer:
[tex]2Sb+3I_2=2SbI_3[/tex]
[tex]P_4+3O_2=2P_2O_3[/tex]
[tex]2SO_3=2S+3O_2[/tex]
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
Step-by-step explanation:
Each side of the equations need to have the same number of each element.
Equation 1
Since there are 2 I on one side of equation 1, and 3 on the other side, I will do the following:
[tex]Sb+3I_2=2SbI_3[/tex]
Now the number of Sb is unbalanced, so I balance it like so:
[tex]2Sb+3I_2=2SbI_3[/tex]
Equation 2
Using the same strategy, I focus on one element at a time. I can balance the P like this:
[tex]P_4+O_2=2P_2O_3[/tex]
Now, I can balance the O. There are 6 on the right, so if I put 3 on the left, there will be 6 there as well!
[tex]P_4+3O_2=2P_2O_3[/tex]
Equation 3
Starting with O this time, I put 2 on the left and 3 on the right to bring them both to 6.
[tex]2SO_3=S+3O_2[/tex]
Now there are 2S on the left and only 1 on the right, so I balance it:
[tex]2SO_3=2S+3O_2[/tex]
Equation 4
Starting with O again, there are 3 on the left and 2 on the right.
[tex]2Fe_2O_3+C=Fe+3CO_2[/tex]
Now, the Fe are unbalanced as well. There are 4 on the left and 1 on the right:
[tex]2Fe_2O_3+C=4Fe+3CO_2[/tex]
Finally, balance the C, there is 1 on the left and 3 on the right.
[tex]2Fe_2O_3+3C=4Fe+3CO_2[/tex]
Equation 5
This one is pretty hard to read, so I will assume that the equation looks like this (please comment if this is incorrect)
[tex]CH_4+O_2=CO_2+H_2O[/tex]
Let's balance the H first:
[tex]CH_4+O_2=CO_2+2H_2O[/tex]
Now the O. There are 2 on the left and 4 on the right.
[tex]CH_4+2O_2=CO_2+2H_2O[/tex]
is 0 a solution to 2x +0 =4x+10 explain how
Answers
Answer:
No, x=-5 is the answer
Step-by-step explanation:
Did this before, trust me
what’s the correct answer,
the last one says “apply the distributive property” please help. marking brainliest
Answers
Answer:
Subtract 6 from both sides
Step-by-step explanation:
pls guys i need help whats 1 + 1
Answers
Answer:
2
Step-by-step explanation:
Answer: 1 + 1 is two!
Step-by-step explanation:
We know this because, we can count our fingers. Your pointer finger and your index finger put together is a total of two fingers!
There are other ways to do simple addition, but I find counting fingers the easiest!
Hope this helped you! Have a great day :)
can someone help please!
Answers
Answer:
Step-by-step explanation:
After changing the smaller exponent (-3) to the larger exponent (-1), what does its coefficient change to?
(6.2 x 10-1) + (2.3 x 10-3)
A) .23
B) 230
C) 23
D) .023
Answers
After changing the smaller exponent (-3) to the larger exponent (-1), its coefficient change to?l A. 0.23.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
From the information, it should be noted that the value was illustrated as:
= 2.3 × 10^-1
= 2.3 × 0.1
= 0.23
Therefore, the correct option is A.
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is y = x/2 + 6 a linear or nonlinear function
Answers
An electric guitar costs $830, with a $225 full-replacement warranty. If the manufacturer sells 532,475 warranties and has to honor 12% of them, how much profit did the manufacturer gain from the warranties? a. $105,430,050 b. $66,772,365 c. $53,034,510 d. $508,726,615 please select the best answer from the choices provided a b c d.
Answers
A guitar manufacturer sells 532,475 warranties and has to honor 12% of them. The profit the manufacturer gains from the warranties is $66,772,365 (option b)
Profit is calculated as:
Profit = revenues - total cost
While,
Revenues = number of goods sold x price per unit
In the given problem,
Revenues = number of warranty sold x price per warranty
= 532,475 x 225
= 119,806,875
Cost of honored warranty = number of honored warranty x guitar cost
= 12% x 532,475 x 830
= 53,034,510
Hence,
profit from warranty = 119,806,875 - 53,034,510
= 66,772,365
The profit from warranty is $66,772,365 (option b)
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Answer:
its b
Step-by-step explanation:
Which expressions are equivalent to 3^4 * 3^x select all that apply
A. 3^(4+x)
B. 3^(4x)
C. 81 * 3^x
D. 3^(4-x)
E. 9^4x
F. (3*x)^4
Answers
Expression which are equivalent to the given expression 3⁴ × 3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.
As given in the question,
Given expression is equal to :
3⁴ × 3ˣ
Using law of indices for multiplication we have ,
mᵃ × mᵇ = mᵃ⁺ᵇ
Here in the given expression m = 3 , a= 4 and b = x
Equivalent expression for the given expression is given by,
3⁴ × 3ˣ
= (3⁴⁺ˣ )
Also,
Now simplify the given expression we get,
3⁴ × 3ˣ
= ( 3 × 3 × 3 × 3) × 3ˣ
= 81 × 3ˣ
Therefore, expression which are equivalent to the given expression 3⁴ × 3ˣ are as follow: (3⁴⁺ˣ ) and 81 × 3ˣ.
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10 A car depreciates in value at 15% per year If the car is bought for £20,000, how much will it be worth in 5 years.
Answers
Answer:
£8884.10625
Step-by-step explanation:
15% of £20,000:
20000x15/100=£3000
20000-3000=£17000
15% of £17000:
17000x15/100=£2550
17000-2550=£14450
15% of £14450:
14450x15/100=£2167.5
14450-2167.5=£12282.5
15% of £12282.5:
12282.5x15/100=£1842.375
12282.5-1842.375=£10440.125
15% of £10440.125:
10440.125x15/100=£1556.01875
10440.125-1556.01875=£8884.10625
Since the car loses 15% of it's value each year, it retains 85% of the value.
Value after 1 year = 85% of original value.
Value after 2 years = 85% of value after year 1
Value after 3 years = 85% of value after year 2
and so on...
We could calculate this year by year or we could do a single calculation to obtain the value. We need to take 85% of the original value a total of 5 times, since we're wondering about the value in 5 years.
value after 5 years = 20000(0.85)(0.85)(0.85)(0.85)(0.85)
value after 5 years = 20000(0.85)^5
value after 5 years ≈ 8874.10625
So the value will be 8874.11 pounds in 5 years.
O LINEAR EQUATIONS
Word problem involving a conversion between U.S. Customary.....
2/5
Jenny is uering 3 bags of cat food from Canada. Each bag has a mass of 5 kg. To determine the shipping costs, Jenny needs to know the total weight in
pounds. What is the weight of the cat food in pounds?
Use 1 kg = 2.2 lb and do not round any computations.
Chloe
Español
Answers
Unit conversion is the conversion of one unit to another unit with its standard conversion.
1 kg = 2.2 lb
The weight of the cat food in pounds is 33 lb.
What is unit conversion?It is the conversion of one unit to another unit with its standard conversion.
Example:
1 minute = 60 seconds
1 km = 1000 m
We have,
Number of bags of cat food = 3
Weight of each bag = 5 kg
1 kg = 2.2 lb ______(1)
Weight of 3 bag = 3 x 5 = 15 kg _______(2)
From (1) and (2) we get,
1 kg = 2.2 lb
Multiplying 15 on both sides.
15 x 1 kg = 15 x 2.2 lb
15 kg = 33 lb
Thus,
The weight of the cat food in pounds is 33 lb.
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(The lines are parallel)
What is the value of x?
Answers
Answer:
x = 14 y = 37
Step-by-step explanation:
180 - (9x + 12) = 3x
180 - 9x - 12 = 3x
168 = 12x
x = 14
4y - 10 + 3(14) = 180
4y - 10 + 42 = 180
4y + 32 = 180
4y = 148
y = 37
Given f(x) = 4x+2 find f(x+3) find terms of x
Answers
The function f(x+3) in terms of x is 4x+14.
It is given that -
f(x) = 4x + 2
We have to find out f(x+3) in terms of x.
Now, f(x) = 4x + 2
=> f(x+3) = 4(x+3) + 2 [Substituting (x+3) in place of x]
=> f(x+3) = 4x + 12 + 2
=> f(x+3) = 4x + 14
Thus, the function f(x+3) in terms of x is 4x+14.
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a small dataset contains 5 numbers: 21, 32, x, 99, 40 (where x is unknown). if the average is known to be 50, what is the median?
Answers
The median of the given data set is, 40.
What is median?
The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory. It could be referred to as "the middle" value for a data set.
Let, a data set contains 5 numbers: 21, 32, x, 99, 40.
x is the unknown number.
The average is to be 50.
Since,
Average = Sum of numbers / total numbers
50 = (21 + 32 + x + 99 + 40) / 5
50 x 5 = 192 + x
250 = 192 + x
x = 250 - 192
x = 58
Hence, the unknown number is 58.
Now to find the median,
Since median is the middle number of a data set.
So, write the numbers in ascending order.
21, 32, 40, 58, 99.
In this data set the middle number is, 40.
Therefore, the median is 40.
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Your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37. Will you be able to outbid your competitor?.
Answers
No, It will not be able to outbid your competitor if your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.
Define cost.A cost is the worth of money that has been expended to produce something or provide a service and is therefore no longer available for use in production, research, retail, and accounting. In the case of an acquisition cost, the money spent on the acquisition is considered the cost. Any system for allocating expenses to a business component is known as costing. Costing is frequently used to establish expenses for customers, distribution channels, personnel, regions, goods, product lines, processes, subsidiaries, and whole businesses.
Given,
Your cost to produce is $30 and you need to make a markup of 30% on an upcoming bid. A competitor placed a bid for $37.
No, It will not be able to outbid your competitor.
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what is the product of 6 x 2/3
Answers
Answer: 4
Step-by-step explanation:
6 * 2/3 First simplify the expression.
Then you would get 2 * 2/1 = 2*2
The answer is 4
In a ale, the cot of a coat i reduced from $85 to $67. 50. Calculate the percentage reduction in the cot of the coat
Answers
The percentage reduction in the cost of the coat is 20.58 %
As given,
Cost of coat = $ 85
Price in sale= $ 67.50
Reduced price =$ 85 - $ 67.50= $ 17.5
Therefore to find the percentage reduction in the cost of the coat
% Reduction = (Reduced price / original price) x 100
= ( 17.5 / 85 ) x 100
= 20.58 %
Hence, the percentage reduction in the cost of the coat is 20.58 %
The percentage reduction formula is a mathematical tool that helps determine how much of a substance can be removed from a sample. This formula can be used to calculate the percentage of a substance that can be removed from a sample if the starting concentration and the ending concentration are known.
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OMG PLS HELP I SWEAR ITS NOT THAT HARD please yall?
Proving angles are congruent; write a two column proof
Answers
Using the Side Angle Side Theorem, ∆KWL ≅ ∆ALW.
In the given question we have to
Prove: ∆KWL ≅ ∆ALW
Given: ∠KWL ≅ ∠WLK, ∠AWL ≅ ∠WLK
As given that
∠KWL ≅ ∠WLK
∠AWL ≅ ∠WLK
WL = WL (Diagonal)
Equal Parallel Sides
WK = AL
WA = KL
From Corresponding Angle Theorem
∠KWL=∠WLK and ∠AWL = ∠WLK
So ∠W=∠L
So from the Side Angle Side(SAS) Theorem
∆KWL ≅ ∆ALW.
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I have no idea how to do this. Please help.
Answers
Answer:
None
Step-by-step explanation:
In order to solve an inequality you must isolate x on one side, so begin bringing the numbers from one side to another to make x the subject.
(numbers change their sign when brought to the other side)
5 > - 6 - 2x
5 + 6 > - 2x
11 ÷ - 2 > x
-5.5 < x (the sign switches when you divide or multiply by a negative number)
The solution is -5.5, which means none of the values provided are the solution.
The weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons, find the weight of each.
Answers
The weight of meteorite A is 207 tons and meteorite B is 23 tons.
How to calculate the value?Let the weight of B = w
Let the weight of A = 9 × w = 9w
Since the weight of meteorite A is 9 times the weight of meteorite B. If the sum of their weights is 230 tons. This will be illustrated as:
9w + w = 230
10w = 230
Divide
w = 230/10
w = 23
meteorite B = 23 tons
meteorite A will be:
= 9w
= 9 × 23
= 207 tons
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Without using a calculator, order the following numbers from least to greatest.
Answers
Answer:
√78,9,10
Step-by-step explanation:
we know [tex]9^{2}[/tex] is 81
so √78 is less than √81(9) and 10 is obviously more than 9
Please mark as brainliest
the following information will be used for parts 1 and 2 of this assignment. in 1978 congress established a gas guzzler tax to discourage the production and purchase of fuel-inefficient vehicles. every vehicle currently produced is labeled as a guzzler if its fuel efficiency in mpg is below a certain amount. trucks, suvs and minivans were uncommon in 1978 so are exempt from the tax. if interested, read more: https://www.epa.gov/fueleconomy/gas-guzzler-tax each vehicle in the data set epafe2021data.csv has a projected annual fuel cost that estimates how much the vehicle will cost over a year in fuel. for example, the volkswagen passat has an estimated annual fuel cost of $1450. use the epafe2021data.csv dataset and the comparingtwomeans da6.r script to compare the average annual fuel cost in dollars between guzzlers and non-guzzlers from 2021 vehicles. part 1. (6 points) exploring the data. a. (2 points) visualize the data with a side by side boxplot. i. (1 point) paste the side-by-side box plot of the data. ii. (1 point) add a title and axis labels. iii. optional to change the color of the plot. b. (2 points) describe the distribution in context. is there visual evidence the average annual fuel cost is different between the guzzler and non-guzzler vehicles? explain. c. (2 points) provide an organized table of the summary statistics. include the sample means, standard deviations and sample sizes for each group. round to nearest whole number. mean standard deviation sample size guzzler non-guzzler
Answers
This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
A) 1: proportion of gas-guzzlers manufactured by American firms.
p2: proportion of gas-guzzlers manufactured by international firms.
In this way, the boundary of interest is p1 - p2.
B) H_0: p_1-p_2=0
H_1: p_1-p_2\neq0
C) The following requirements must be satisfied: n (1 p) 10 and np 10.
American Guzzlers do not meet this requirement because np = 7.
D) If H0 is true, the test statistics are as follows: frac(hat p_1-hat p_2)-(p_1-p_2)surfactant p_1(1-hat p_1)n_1+frachat p_2(1-hat p_2)n_2sim N(0,1)
E) The p-value is calculated by multiplying p-value by P(z-3.75) = 0.
F) The 95% confidence interval is calculated as follows: p_1-p_2=hat p_1-hat p_2pm z_0.975sqrtfrachat p_1(1-hat p_1) n_1+frachat p_2(1-hat p_2) n_2 -0.0859 p_1-p_2 -0.0269
g. H0 should be rejected because the p-value is less than the 0.05 significance level.
There is enough evidence for us to reject H0. There is sufficient evidence to draw the conclusion that the proportion of Guzzlers in 2017 automobile models produced by American and international automakers differs.
Additionally, the 95% CI does not contain zero, does it?This also leads us to the conclusion that we are 95 percent certain that the proportion of Guzzlers in the 2017 automobile models produced by American and international automakers differs.
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A scientist uses a submarine to study ocean life. • She begins at sea level, which is an elevation of o feet. • She travels straight down for 36 seconds at a speed of 2.9 feet per second. • She then ascends for 24 seconds at a speed of 1.8 feet per second. At this point, what is her elevation, in feet?
Answers
Answer:
61.2
Step-by-step explanation:
(36x2.9)-(24x1.8)
Find the sum of 102 + (-97) + 3 =
Answers
Answer:
8
Step-by-step explanation:
You can solve this a few different ways.
Firstly I did 102 - 97 = 5
Then I took 5 and added 3 to it
5 + 3 ---> which gets us 8 as our final answer.
Hope I helped!
Have a great day!
A cruise ship can cover 21 nautical miles in 378 minutes. How many nautical miles will it travel in 108 minutes?
A. 4
B. 8
C. 10
D. 6
Answers
Answer: D/ 6.
Step-by-step explanation: First, you have to do division to find out how many minutes = 1 nautical mile.
378 divided by 21= 18.
Then, you would do 108 divided by 18, to find out the answer; 6.
To double check your work, get the answer you got and multiply it by the minutes per mile which is 18.
18 x 6 = 108.
Therefore, it will be 6 nautical miles in 108 minutes.
The large number of two numbers is nine less than four times the smaller number. If the sum of the two numbers is 76, find both numbers.
Answers
Answer: the larger number is 59 and the smaller number is 17.
Step-by-step explanation:
Margot is sewing a ribbon on a seam along the perimeter of a square pillow. The side length of the pillow is
2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What
expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?
Answers
The expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .
Given:
The side length of the pillow is 2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches.
The length of ribbon :
= 4([tex]2x^{2} +1[/tex]) + 4(4x - 7)
= 4(2[tex]x^{2} +1[/tex]+4x - 7)
= 4([tex]2x^{2} +4x-6[/tex])
The length at x = 3.5 is,
= 4(2([tex]3.5^{2}[/tex])+4(3.5) - 6)
= 4(24.5+14-6)
= 4(24.5+8)
= 130 inches.
Therefore the expression and the length of ribbon that she needs for both pillows is [tex]4(2x^{2} +4x-6)[/tex] , 130 inches .
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Answer:
Step-by-step explanation:2x2+1 inches. She plans to make a similar pillow, including the ribbon, whose side length is 4x-7 inches. What
expression can be used for the length of ribbon that she needs for both pillows, and what is the length if x = 3:5?
Select the point that is solution to the system of inequalities.
y x^2-6
A. (0,-2) B. (0,6) C.(1,6) D. (-4,-2)
Please help!
Answers
The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.
Given that,
The system of inequality
y < x² + 2
y > x² - 6
We have to find the common point of the system of inequality.
We know that,
The graph is shown in the image.
Using the graphing technology,
A will be the first equation's vertex (0,2)
The parabola's outer region will be shaded and its boundary will be a dotted line because y is less than the value required by the quadratic equation.
In a similar way, the second equation's vertex, (0,-6), will be a dotted parabola with shaded inner portions.
The common shaded zone, as illustrated in the graph attached, will represent the answer to the set of equations. There isn't a common location where the two equations intersect.
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what is 3/36 times 60
Answers
Answer:
5
Step-by-step explanation:
to multiply fractions we multiply numerator with numerator and denominator with denominator
[tex]\frac{3}{36}x\frac{60}{1}[/tex]
[tex]\frac{3x60}{36x1}[/tex]
[tex]\frac{180}{36}[/tex]
5
Hopes this helps please mark brainliest