After 7 hours, the population of bacteria is obtained as 418544.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The initial population of bacteria is given as 37000.
And, the doubling time is 2 hours.
Then, the formula for the population of bacteria at t hour can be given as,
P(t) = P₀ × [tex]2^{t/2}[/tex] where P₀ is the initial population.
Substitute t = 7 and P₀ = 37000 to get,
P(7) = 37000 × [tex]2^{7/2}[/tex]
⇒ P(7) = 418544
Hence, the population of bacteria after 7 hours is 418544.
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CHALLENGE:
Combine like terms:
3y + 4xy + x + 2y + 2xy + x + 10 + 1
Answer: 2x+6xy+5y+11
Step-by-step explanation:
miguel is mixing up a salad dressing. regardless of the number of servings, the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
44 is the proportion of the botched dressing will be olive oil.
Given, Miguel is mixing up a salad dressing. regardless of the number of servings,
the recipe requires that 58 of the finished dressing mix be olive oil, 14 vinegar, and the remainder an even mixture of salt, pepper and sugar. if he accidentally doubles the vinegar and forgets the sugar altogether,
we have to find the proportion of the botched dressing that will be olive oil.
first we will find the amount of the even mixture of salt, pepper and sugar.
as, olive oil + vinegar + even mixture of salt, pepper and sugar = 100
58 + 14 + mixture of salt, pepper and sugar = 100
mixture of salt, pepper and sugar = 100 - 72
mixture of salt, pepper and sugar = 28
if he mixed doubles of the vinegar i.e. 28 then olive oil be,
x + 28 + 28 = 100
x = 100 - 56
x = 44
Hence, 44 is the proportion of the botched dressing will be olive oil.
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Ramón makes nectar for a hummingbird feeder by mixing 8 cups of water with 2 cups of sugar. Tiffany makes nectar by mixing 9 cups of water with 3 cups of sugar. Whose nectar is more sugary? Explain.
Answer: Tiffany
Step-by-step explanation: Ramon Ratio 8:2 can be reduced to 1 cup of sugar every 4 cups of water. Tiffany Ration is 9:3 which is reduced to 1 cup of sugar every 3 cups of water.
Elijah bought stock in a company two years ago that was worth a dollars. During the
first year that he owned the stock, it increased by 35%. During the second year the
value of the stock increased by 11%. Write an expression in terms of a that represents
the value of the stock after the two years have passed.
Answer:
x + .35X - .11(x - .35x)
Step-by-step explanation:
Let x = the original price of the stock.
x + .35x This is first year
-.11( x + .35x) is the second year
x + .35X - .11(x - .35x)
A website offers a coupon to 50\%50%50, percent of its visitors, selected at random, each day. Yasemin visits the website for 444 days. What is the probability that yasemin will not be offered a coupon on at least one of the days she visits the website? round your answer to the nearest hundredth. P(\text{at least one day without coupon})=p(at least one day without coupon)=p, left parenthesis, start text, a, t, space, l, e, a, s, t, space, o, n, e, space, d, a, y, space, w, i, t, h, o, u, t, space, c, o, u, p, o, n, end text, right parenthesis, equals.
The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website will be;
⇒ 0.9375
What is mean by Probability?The term probability refers to the likelihood of an event occurring
Given that;
The probability that a visitor is offered a coupon (p) = 50%
Now,
Since, The probability that a visitor is offered a coupon (p) = 50%
Hence, The probability that he gets coupon all 4 days is,
⇒ p (4) = p⁴
⇒ p (4) = (50%)⁴
⇒ p (4) = 0.0625
Hence, By using the complement rule, the probability that he is not offered a coupon at least one day is,
⇒ p' = 1 - 0.0625
⇒ p' = 0.9375
Thus, The probability that Yasmin will not be offered a coupon on at least one of the days she visits the website = 0.9375
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Is 13,82,90 a right triangle
Answer:
it's not a right triangle (it's an obtuse triangle)
Step-by-step explanation:
If three numbers a, b and c verify the relation a^2+b^2=c^2 they are said to form a Pythagorean triple, therefore the triangle is right-angled.
verify
13^2 + 82^2 = 90^2
169 + 6724 = 8100
6893 = 8100
it's not a right triangle (it's an obtuse triangle)
Help meee please !!!???
Answer:
Step-by-step explanation:
it is c
meghan and sara are on their way to disneyland. they travel 65 mph (miles/hour) for 2.2 hours and then stop for a 45-minute lunch break. after lunch they travel 55 mph for another 3.8 hours until they reach disneyland. what is their average speed, in miles/hour, for the entire duration of the trip? (round your answer to the nearest whole number. d
The average speed for the entire duration of trip is 52 mph.
The total distance traveled by an object in a given time frame is defined as its average speed. It is computed by dividing the entire distance traveled by the total amount of time spent.
Given,
S1 = 65 mph , T1 = 2.2 hours
S2= 0 mph (during lunch break) , T2 = 45 min = 45 / 60 hour
=0.75 hour
S3= 55mph , T3 = 3.8 hours
Therefore, S avg =(S1T1 + S2T2 + S3T3)/(T1 + T2 + T3)
=(65×2.2 + 0 ×0.75 + 55×3.8)/(2.2 + 0.75 + 3.8)
= 52.148 mph
The average speed for the entire duration of trip is 52 mph.
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A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left
A triangle with coordinates (1,1) (4,2) (3,5) is translated three units down and five units to the left. New coordinates will be (-4,-2), (-1,-1),(-2, 2).
Define translation.A translation is a geometric change in Euclidean geometry that involves moving each point in a figure, shape, or space by the same amount in one direction. A translation can also be thought of as moving the origin of the coordinate system or as adding a constant vector to each point.
Given
A triangle with coordinates (1,1) (4,2) (3,5)
The value of a coordinate is impacted by translations left or right but not by translations up or down or left or right.
We multiply all of the numbers by 3 since we are translating the entire triangle down three units.
Additionally, we are converting the entire triangle to left-to-right units of five, thus we will multiply all values by 5.
A = (1 - 5, 1 - 3)
B = (4 - 5, 2 -3)
C = (3 - 5, 5 - 3)
New coordinates will be:
A = (-4,-2)
B = (-1,-1)
C = (-2, 2)
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Tickets for the school play cost $7 each. Each member of the cast gets 1 free ticket for a family member. For the run of the play, 210 tickets are collected, including all the free tickets, and the box office makes $1,358 from ticket sales. The equation that models this situation is
7(210 – c) = 1,358
where c is the number of cast members.
How many cast members are in the play?
I'm kinda stuck
The number of cast members are in the play given the equation is 16 cast members
How many cast members are in the play?7(210 – c) = 1,358
where,
The number of cast members = c7(210 – c) = 1,358
open parenthesis
1,470 - 7c = 1,358
Subtract 1,470 from both sides
- 7c = 1,358 - 1,470
- 7c = -112
divide both sides of by -7
c = -112 / -7
c = 16
Therefore, there are 16 cast members in the play.
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Brendan deposited $3,967 in an account earning 5% interest compounded annually.
To the nearest cent, how much interest will he earn in 5 years?
The interest earned in 5 years is $1096.
What is interest?Interest is the fee a business pays a lender (creditor) to borrow money.
Given that, Brendan deposited $3,967 in an account earning 5% interest compounded annually.
A = P(1+r/100)ⁿ
n = 5, r = 5% = 0.05, P = 3967 and a = amount earned
A = 3967(1+0.05)⁵
A = 3967(1.05)⁵
A = 5063
Interest earned = amount - principal
Interest = 5063-3967
Interest = $1096
Hence, Brendan earned $1096 as interest.
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Answer:
$1096.01
Step-by-step explanation:
miley believes that listening to white noise can enhance verbal exam performance. she takes a random sample of college students and randomly assigns each student to one of two groups-the quiet group and the white noise group. the quiet group is asked to take a verbal exam in a completely silent classroom. the white noise group is asked to take the same exam in a classroom in which white noise is playing in the background. all students have one hour to complete the exam. miley will then compare the mean exam score for the two groups. suppose miley makes a type i error. in terms of the scenario, what would this mean?
A Type I error in this scenario would mean that Miley would conclude that the noise impacts the students when in fact it doesn't.
What are Type I errors and Type II errors?The definitions of Type I errors and Type II errors are presented as follows:
Type I: Rejection of a true null hypothesis, meaning that the null hypothesis is true, but a sample gives you enough evidence to reject it.Type II: Non-rejection of a false null hypothesis, meaning that the null hypothesis is false, but the sample does not give you enough evidence to reject it.The hypotheses tested in this problem are given as follows:
Null hypothesis: not enough evidence to conclude that there are differences in the exam scores.Alternative hypothesis: enough evidence to conclude that there are differences in the exam scores.A Type I error would mean that she rejected a true null hypothesis, meaning that Miley would conclude that the noise impacts the students when in fact it doesn't.
(rejected null hypothesis means that there is enough evidence to conclude that there are differences).
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the mass of a radioactive substance follows a continuous exponential decay model. a sample of this radioactive substance has an initial mass of and decreases continuously at a relative rate of per day. find the mass of the sample after two days.
The initial mass of the sample after two days = 8483.45 kg
Given that,
It is known as exponential decay when a population or group of something is deteriorating and the quantity of decline is proportional to the size of the population. In an exponential decay, the overall value falls but the percentage that departs stays the same throughout time.
The exponential decay formula aids in determining the exponential drop, which is a rapid reduction over time. To calculate population decay, half-life, radioactivity decay, and other phenomena, one uses the exponential decay formula.
The standard formula for this type of behavior which is written below:
A = [tex]Pe^{-rt}[/tex]
Where
A refers the amount left after time t
P refers the initial amount at t = 0
r refers the rate
Here we have given that the mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day.
A sample of this radioactive substance was taken after two days.
And we need to find if the sample has a mass of today, then the initial mass of the sample.
Now, we have to substituting the values,
Let us assume,
P = 9575 kg
r = 0.12
t = 1
Then we get the equation as,
A = (9575 kg) [tex]e^{-0.12*1}[/tex]
When we simplify this one, then we get,
A = (9575 kg) [tex]e^{-0.12}[/tex]
A = (9575 kg) 0.886
A = 8483.45 kg
Therefore,
The initial mass of the sample after two days = 8483.45 kg
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One morning, Adrian stood tall and had a friend measure his shadow on the sidewalk. Adrian's friend also measured from the top of Adrian's head to the tip of his shadow. The diagram below shows these measurements. How tall is Adrian? A 4.5 ft B 5 ft C 5.5 ft D 6 ft
The length of Adrian's shadow measured by his friend and the distance directly from Adrian's head to the tip of his shadow can be used to find Adrian's height using Pythagorean Theorem. Using an example of the measurement values, Adrian's height is about 5.5 feet
What is Pythagorean Theorem?Pythagorean Theorem states that the sum of the square of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse side.
The diagram in the question appears left out. Please find attached a drawing made using the measurement lengths in the following example, created with MS Word.
The measurements Adrian had his friend to do are;
The length of Adrian's shadow on the sidewalk and the length from Adrian's head to the tip of the shadow.
Let x represent the length of Adrian's shadow, let r represent the distance from Adrian's head to the tip of the shadow, and let y represent Adrian's height
According to Pythagorean Theorem, we get;
r² = x² + y²
Therefore, the Adrian's height, h = √(r² - x²)
When r ≈ 8.14, and x = 6, we get;
h = √(8.14² - 6²) ≈ 5.5
Adrian's height is about 5.5 feet in the example situation
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Use technology to find an equation of the line of best fit for the data. Round the slope to
the nearest tenth and the y-intercept to the nearest integer.
X=0,1,2,3,5,6,7
Y=-8,-5,-1,-1,2,5,8
The equation of the line of best fit for the data is given as follows:
y = 2.1x - 7.
How to obtain the equation for the line of fit?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
(as there are multiple types of regression).
From the text in this problem, the points of the data-set are given as follows:
(0, -8), (1, -5), (2, -1), (3,-1), (5, 2), (6,5), (7,8).
Inserting these points into the linear regression calculator, the equation is defined as follows:
y = 2.1x - 7.
(rounding the slope to the nearest tenth and the y-intercept to the nearest integer.).
The slope for the line is of 2.1 and the intercept is of -7, following the slope-intercept definition of a linear function.
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 10(1.01)
The given exponential function represents the growth in the function. The percentage of growth (increase) is 1%.
What is the exponential growth function?An exponential growth function is a function where the quantity increases slowly and after some time, it increases rapidly.
It is represented by the formula,
y = a(1 + r)ˣ
Here the term 'a' is the initial amount of the quantity, the term 'r' is the rate of increase and the term 'x' is the period.
Calculation:The given exponential function is y = 10(1.01)ˣ
Here we can write the function as
y = 10(1.01)ˣ
⇒ y = 10(1 + 0.01)ˣ
Since 1.01 > 1, it is an exponential growth function.
So, when comparing with the formula, we get the rate of increase,
r = 0.01
Converting it into fractions, we get 1/100
Then, the percentage rate of increase is 1%.
Therefore, the given exponential function grows with a rate of 1% increase.
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Which of the following equations represent linear functions?Select all that apply
y = 7²,y + (1/2)x = 9 and 2.3 = y - 5.8x are the linear function thus option (A),(D) and (F) are correct.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
A linear function is a line in a coordinate plane with a constant slope and can be written in form of y = mx + c.
Thus the degree of x and y will be 1.
For example, y = 7² can be written as, y = 0(x) + 7² so it will be a linear line.
Another y + (1/2)x = 9 and 2.3 = y - 5.8x are can be written as y = mx + c so they will be linear functions.
Hence "the functions y = 7²,y + (1/2)x = 9 and 2.3 = y - 5.8x are the linear function".
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Jon has $412 in his bank account. He withdraws $20 each week for lunch. How many weeks it would take for him to have at most $12 left in his bank account
Answer: 20 weeks
Step-by-step explanation:
If he has $412 in his bank account, and he withdraws 20 each week, at 10 weeks he would have $212 left, at 20 weeks he will be left with $12.
Hence, the right answer is 20 weeks.
Answer question #8
Give a short answer responding the question that’s being asked
The response written in the box isn’t correct so I need help
The conclusion is that the angle which measures 120° is not Acute angle.
What are angles ?The construction of an angle is a type of geometric shape made by connecting two rays at their termini. Three letters that make up the form of the angle can alternatively be used to symbolise the angle, with the middle letter indicating the location of the angle (i.e.its vertex). Greek characters such θ, α, β, etc. are frequently used to denote angles.
In geometry, there are mainly six different kinds of angles. All angles have the following names and characteristics:
The acute angle ranges from 0° to 90°.The obtuse angle ranges from 90° to 180°.Right Angle: The angle that is 90 degrees precisely.Direct Angle: the angle that is exactly 180 degreesReflex Angle: The angle between 180 degrees and 360 degrees that is bigger than 180 degrees.360-degree full rotation: The whole rotation of an angle.Angle B measures 120°.
Here the angle is more than 90° so the angle is not acute.
The conclusion is that the angle which measures 120° is not Acute angle.
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What is the cubic polynomial with zeros (3,0), (-6,0), and (1,0)?
Question 15
The cubic polynomial with zeros (3,0), (-6,0) and (1,0) is given as follows:
D. x³ + 2x² - 21x + 18.
How to obtain the cubic polynomial?We are given the zeros of the polynomial, which then can be obtained using the Factor Theorem.
The zeros of the polynomial are given as follows:
x = 3, x = -6, x = 1.
Then, applying the Factor Theorem, considering a leading coefficient of 1, the polynomial is given as the product of it's linear factors as follows:
(x - 3)(x + 6)(x - 1)
(x² + 3x - 18)(x - 1)
x³ + 2x² - 21x + 18.
Meaning that option D is correct.
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This graph shows fuel consumption for a car during a test run. Three of the statements are true. Which is NOT?
Line graph. X axis labeled miles; y axis labeled gallons. Line with upward arrow extends from point where X and Y axes connect (0, 0) with one marked coordinate (73.5, 3.5).
The car used 312 gallons of gas to go nearly 75 miles.
The car used 70 gallons of gas to go 3 miles.
The car used gas at a unit rate of 21 miles per gallon.
At this rate, it would take 4 gallons of gas to travel 84 miles.
In the graph showing fuel consumption for a car during a test run the correct statement is
At this rate, it would take 4 gallons of gas to travel 84 miles.How to find the correct statementThe information given in the problem will help to find the equation of the graph in the form
y = mx + c
definition of variable to suit the problem
y = output variable = number of gallons
m = slope
x = input variable = number of miles
c = y intercept
The slope
= (3.5 - 0) / (73.5 - 0)
= 0.05
the y intercept is 0
the equation of the line is y = 0.05x
Only option the last option fits the equation as shown
number of gallons = 0.05 * number of miles
= 0.05 * 84 miles
= 4.2 gallons
= 4 gallons
hence the last option is the correct choice
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Joe bought a box of laundry that contains 195 scoops. Each load of laundry uses 1 1/2 scoops. If the box of detergent costs $19.99, how much is he paying per load of laundry?
0.563 $ is he paying per load of laundry
What is business mathematics?
Business mathematics is the branch of mathematics utilized by businesses to track and coordinate their operations. Accounting, inventory management, marketing, sales forecasting, and financial analysis are all areas where commercial businesses apply mathematics.
Simple arithmetic, elementary algebra, statistics, and probability are all frequently utilized in business. More complex arithmetic, such as calculus, matrix algebra, and linear programming, may be used to solve some management challenges.
According to question:
Total scoop contained in detergent box = 195 scoops.
Scoops used by each load of laundry = 11/2 scoops = 5.5 scoops
Number of laundry he can do with this box = 195/5.5
= 35.45 laundries.
Price of detergent box = 19.99 $
Price he paying for each load = Total price/ Number of loads
= 19.99/35.45
= 0.5638928067700
= 0.563 $ (Approx)
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Complete the equation of the line whose yyy-intercept is (0,-1)(0,−1)left parenthesis, 0, comma, minus, 1, right parenthesis and slope is 444.
The complete equation in the slope-intercept form is y = 4x-1.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
So, the equation is,
y - y₁ = m (x - x₁)
And the standard form of the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
From the question, we have
m = 4 and coordinates of b is (0, -1).
So, the equation is,
y + 1 = 4 (x - 0)
y +1 = 4x
y = 4x-1
Therefore, the equation is y = 4x-1.
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a student needs 11 more classes to graduate. if she has met the prerequisites for all the classes, how many possible schedules for next semester could she make if she plans to take 4 classes?
We can conclude that the number of possible schedules for next semester could she make is 7920.
In more mathematical terms, the factorial of a number (n!) is equal to
n(n-1). For example, if you want to calculate the factorial for four, you would write: 4! = 4 x 3 x 2 x 1 = 24.
Given that,
The student needs 11 more classes to graduate.
And, possible schedules for next semester could she make if she plans to take 4 classes
Based on the given expression, the calculation is as follows:
The combination formula is given to be:
[tex]n_{C} _{r} =\frac{n!}{r!(n-r)!}[/tex]
= [tex]11_{C} _{4}[/tex] ! * 4 !
= [tex]\frac{11 !}{4!(11-4)!}[/tex] * 4 !
= [tex]\frac{11!}{4!7!}[/tex] * 4 !
= [tex]\frac{11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1*7*6*5*4*3*2*1}[/tex] * 4 !
We can cancel the coefficients,
= [tex]\frac{11*10*9*8}{4*3*2*1}[/tex] * 4 !
= [tex]\frac{7920}{24}[/tex] * 4 !
= 330* 4 !
= 330 * 4*3*2*1
= 7920
Therefore,
We can conclude that the number of possible schedules for next semester could she make is 7920.
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Find the surface area 5 4 7 6 8 triangular
The surface area of the triangular prism is 136 square units
How to determine the surface areaFrom the question, we have the following parameters that can be used in our computation (see attachment):
Rectangles (2) = 7 units by 5 unitsRectangles (1) = 7 units by 6 unitsTriangles (2) = 4 units by 6 unitsThe surface area of the triangular prism is the sum of the areas of the above shapes
So, we have
Surface area = 2 * area of rectangle 1 + 1 * area of rectangle 2 + 2 * area of triangle 1
Substitute the known values in the above equation, so, we have the following representation
Surface area = 2 * 7 * 5 + 1 * 7 * 6 + 2 * 0.5 * 4 * 6
Evaluate
Surface area = 136
Hence, the surface area is 136 square units
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O
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 0≤x≤ 4.
x
0
1
2
32
4
5
3
6
12
24
48
96
The average rate of change of the function at the interval 0 ≤ x ≤ 4 is 11.25
How to determine the average rate of changeFrom the question, we have the following parameters that can be used in our computation:
x 0 1 2 3 4 5
y 3 6 12 24 48 96
The interval is given as
0 ≤ x ≤ 4
On the table, we have
x = 0 and y = 3
x = 4 and y = 48
This means that
f(0) = 3 and f(4) = 48
The average rate of change is then calculated as
Average rate of change = [f(4) - f(0)]/[4 - 0]
Substitute the known values in the above equation, so, we have the following representation
Average rate of change = [48 - 3]/[4 - 0]
Evaluate
Average rate of change = 11.25
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Please help
The linear combination method gives a solution of (-4,2) for which a of these systems of linear equations?
A) 3x+13y=14
6x+11y=-2
B)4x+5y=12
8x+3y=-4
C) 5x+4y=12
7x+8y=12
D) 10x+3y=8
17x+6y=10
Please show your work
Using the provided points, Applying the substitution of the points in these system of linear equations. The equations which satisfies the points are the required answer. The answer is A) 3x+13y =14 and 6x+11y=-2
What is a equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
What do you mean by system of linear equation?The set of two or more linear equations containing the same variables is known as a system of linear equations in mathematics. In this case, linear equations are first-order equations, where the maximum power of the variable is 1. One, two, or three variables may be present in a linear equation.
point = (-4,2)
for option A) 3*-4 +13*2 =14
14=14
and 6*-4 + 11*2 = -2
-2 = -2
For other options these equality doesn't holds.
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Which tatement i not true?
B. All counting number are rational number. D. Zero i not a rational number. C. A mixed number i a rational number. A. The et of rational number include the et of integer
Answer: D. Zero is not a rational number
Step-by-step explanation:
[tex]0=\frac{0}{1}[/tex]. Thus, by definition, zero is rational.
Which ordered pair is a solution of the
equation?
-3x + 5y = 2x + 3y
Answer:
Solve the equation for [tex]{y}[/tex].
[tex]y=\frac{5x}{2}[/tex]
Choose any value for [tex]{x}[/tex] that is in the domain to plug into the equation.
Choose [tex]{0}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(0,0)}[/tex]
Choose [tex]{1}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex](1,\frac{5}{2})[/tex]
Choose [tex]{2}[/tex] to substitute in for [tex]{x}[/tex] to find the ordered pair.
[tex]{(2,5)}[/tex]
These are three possible solutions to the equation.
[tex]{(0,0),}[/tex] [tex](1,\frac{5}{2} )[/tex], [tex]{(2,5)}[/tex]
The bottom of a ladder must be placed 5 feet from a wall. The ladder is x ft long. The ladder touches the wall 10 ft from the ground. How tall is the ladder? Round to the nearest whole number. 18 ft
Using Pythagoras theorem, the length of the ladder is 11 feet
Pythagoras TheoremThe Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle xyz, in which we have x² = y² +z². Here, y is the base, z is the altitude (height), and x is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Data;
x = hypothenuse = length of laddery = 5 feetz = 10 feetUsing Pythagoras theorem;
x = 5² + 10²
x = 25 + 100
x = 125
x = √25
x = 11ft
Learn more on Pythagoras theorem here;
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