The basis for Col A is linearly independent.
When are two matrices called being equal?Two matrices are equal if and only if their shapes are same, and they've got the same elements for each corresponding row and column positions.
We are given that;
A = [3 7 3 3 6 4 0 -4 4 3 10 0] ~ [1 0 0 2 1 0 4 4 0 -2 -3 0]
Now,
To find a basis for Col A, we need to find the columns of A that correspond to the pivot columns of the echelon form. The pivot columns are the columns that have a leading 1 in a row. In this case, the pivot columns are the first, second, and fourth columns. Therefore, a basis for Col A is given by the vectors in those columns of A. We can write them as:
3303,76−410,3440
These three vectors are linearly independent and span Col A, so they form a basis for Col A.
Therefore, by matrices the answer will be linearly independent.
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A manufacturer produces a commodity where the length of the commodity has approximately normal distribution with a mean of 13.2 inches and standard deviation of 2.3 inches. If a sample of 37 items are chosen at random, what is the probability the sample's mean length is greater than 12.1 inches? Round answer to four decimal places.
The probability that the sample's mean length is greater than 6.3 inches is0.8446.
Here, we have,
Given mean of 6.5 inches, standard deviation of 0.5 inches and sample size of 46.
We have to calculate the probability that the sample's mean length is greater than 6.3 inches is 0.8446.
Probability is the likeliness of happening an event.
It lies between 0 and 1.
Probability is the number of items divided by the total number of items.
We have to use z statistic in this question because the sample size is greater than 30.
μ=6.5
σ=0.5
n=46
z=X-μ/σ
where μ is mean and
σ is standard deviation.
First we have to find the p value from 6.3 to 6.5 and then we have to add 0.5 to it to find the required probability.
z=6.3-6.5/0.5
=-0.2/0.5
=-0.4
p value from z table is 0.3446
Probability that the mean length is greater than 6.3inches is 0.3446+0.5=0.8446.
Hence the probability that the mean length is greater than 6.3 inches is 0.8446.
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i need the answer for this asap Please!
The system of inequalities for the graph is
a) y < 3x - 4
b) y = x + 3
Given data ,
Let the inequality equations be represented as A and B
where
Let the first point be P ( 0 , 3 )
Let the second point be Q ( -3 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( 3 - 0 ) / ( 0 + 3 )
m = 1
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 0 = 1 ( x + 3 )
y = x + 3
And , the second equation is
Let the first point be R ( 0 , -4 )
Let the second point be S ( 2 , 2 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
m = ( -4 - 2 ) / ( 0 - 2 )
m = -6/-2
m = 3
Now , equation of line is y - y₁ = m ( x - x₁ )
y - 2 = 3 ( x - 2 )
Adding 2 on both sides , we get
y = 3x - 4
Since , it is a dotted line ,
y < 3x - 4
And , the solution to the inequality is point of intersection
where A ( 3.5 , 6.5 ) is the solution
Hence , the inequality equations are solved and A ( 3.5 , 6.5 ) is the solution
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If ARSU-AVST, then the triangles are
similar by:
Answer:
AA sim post
Step-by-step explanation:
They DO have equal (similar) angles.....but they do not have equal sides
HELP PLEASE PHOTO INCLUDED
Answer:
Eat that cookie and you will not regret about it
Can someone pls explain
163. The distance between A(-5, 6) and B(5, -5) is: AB ≈ 14.9 units
164. Applying the Pythagorean theorem, we have: Diagonal ≈ 21.2 ft.
165. Marissa's final answer is wrong. It should be, c = √676 = 26 units.
166. Missing side = 29 ft.
What is the Pythagorean Theorem?The Pythagorean theorem states that c² = a² + b², given that a and b are shorter legs and c is the hypotenuse or longest leg of the right triangle.
163. The distance between A(-5, 6) and B(5, -5):
AB = √[(5−(−5))² + (−5−6)²]
AB = √221
AB ≈ 14.9 units
164. Apply the Pythagorean theorem to find the diagonal:
Diagonal = √(15² + 15²) ≈ 21.2 ft.
165. The answer Marissa got is wrong. The final answer which is the square root of 676 is:
c = √676 = 26 units.
166. Missing side = √(20² + 21²) = 29 ft.
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The Nut Shack sells cashews for $6.80 per pound and Brazil nuts for $4.70 per pound. How much of
each type should be used to make a 37 pound mixture that sells for $5.78 per pound?
Round answers to the nearest pound.
pounds of cashews
pounds of Brazil nuts
> Next Question
Answer:
Step-by-step explanation:
$6.80 x 19 pounds = $129.2
$4.70 x 18 pounds = $84.6
+___________________
37 pounds = $213.8
$213.8 divided by 37 pounds = 5.77837......
= $5.78 per pound
Help My Daughter we not understanding?
Representation of a number in three different ways:
133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]
678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]
877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]
543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]
453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]
341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]
555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]
485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]
789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]
864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]
652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]
Here given an example to write a particular number in different representations.
13 tens and 12 ones = 13*10 + 12*1 = 130 + 12 = 142.
14 tens and 2 ones = 14*10 + 2*1 = 140 + 2 = 142.
1 hundred, 4 tens and 2 ones = 1*100 + 4*10 + 2*1 = 100 + 40 + 2 = 142.
So three representations are of number 142.
Rest blanks should be filled in same manner taking different numbers for each rows and three columns of each row should be filled with three different representation of that assumed numbers.
Representations for some numbers:
133: [12 tens and 13 ones], [13 tens and 3 ones], [1 hundred, 3 tens and 3 ones]
678: [67 tens and 8 ones], [60 tens and 78 ones], [6 hundreds, 7 tens and 8 ones]
877: [80 tens and 77 ones], [87 tens and 7 ones], [8 hundred, 7 tens and 7 ones]
543: [54 tens and 3 ones], [50 tens and 43 ones], [5 hundreds, 4 tens and 3 ones]
453: [45 tens and 3 ones], [40 tens and 53 ones], [4 hundreds, 5 tens and 3 ones]
341: [30 tens and 41 ones], [34 tens and one], [3 hundreds,4 tens and one]
555: [50 tens and 55 ones], [55 tens and 5 ones], [5 hundreds, 5 tens and 5 ones]
485: [48 tens and 5 ones], [40 tens and 85 ones], [4 hundreds, 8 tens and 5 ones]
789: [78 tens and 9 ones], [70 tens and 89 ones], [7hundreds, 8 tens and 9 ones]
864: [86 tens and 4 ones], [80 tens and 64 ones], [8 hundreds, 6 tens and 4 ones]
652: [65 tens and 2 ones], [60 tens and 52 ones], [6hundreds, 5 tens and 2 ones]
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Carlos is a door to door vacuum salesman. His weekly salary, S, is $400 plus $35 for each vacuum he sells.
This can be written as S = 400+35v , where v is the number of vacuums sold.
If Carlos earns $1590 for a week's work, how many vacuums did he sell?
Answer:
34
Step-by-step explanation:
1. Plug in the week's salary into the formula
S=400+35v
1590=400+35v
2. Solve for v.
1590=400+35v
Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.
1190=35v
Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.
34=v
what do you add to get the pattern 1, 8, 15, 22, 29 36, 43
Answer:
7
Step-by-step explanation:
Finding the common difference of an arithmetic sequence is easy peasy lemon squeezy. All you have to do is take any term and subtract it from the next one. For instance, if you take 1 and subtract it from 8, you get 7. If you take 8 and subtract it from 15, you get 7 again. You can do this for any pair of terms and you will always get 7. That's the common difference of the sequence 1, 8, 15, 22, 29, 36, 43. It means that you just add 7 to each term to get the next one. Isn't that neat?
what is the resultant displacement of 6m north 8m east and 10m north west?
The resultant displacement is approximately 13.071m north and 8m east.
To find the resultant displacement, we need to combine the given displacements in a vector-like manner.
Let's break down the displacements into their components and then add them up.
The first displacement is 6m north.
Since it is purely in the north direction, its components would be 6m in the north direction (along the y-axis) and 0m in the east direction (along the x-axis).
The second displacement is 8m east.
As it is purely in the east direction, its components would be 0m in the north direction and 8m in the east direction.
The third displacement is 10m northwest.
To find its components, we can split it into two perpendicular directions: north and west.
The northwest direction can be thought of as the combination of north and west, each with a magnitude of 10m.
Since they are perpendicular, we can use the Pythagorean theorem to find the components.
The north component would be 10m multiplied by the cosine of 45 degrees (45 degrees because northwest is halfway between north and west).
Similarly, the west component would be 10m multiplied by the sine of 45 degrees.
Calculating the components:
North component = 10m [tex]\times[/tex] cos(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m
West component = 10m [tex]\times[/tex] sin(45°) = 10m [tex]\times[/tex] 0.7071 ≈ 7.071m
Now, let's add up the components:
North component: 6m (from the first displacement) + 7.071m (from the third displacement) = 13.071m north
East component: 8m (from the second displacement).
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There are 5,144 blocks to be placed
evenly into 8 storage containers. How
many blocks are in each storage
container?
Divide the total number of blocks by the total number of storage containers.
5144/8 = 643 blocks in each storage container.
If r = 5 units and x = 11units then what is the volume if the cylinder shown above
The volume of cylinder which is having radius as 5 units and height as 11 units, is 863.5 cubic units.
A "Cylinder" is a 3-dimensional geometric shape that consists of a circular base and a curved surface which extends up from base to fixed height.
The volume(V) of a cylinder is the amount of space enclosed by the cylinder, and it is given by the formula : V = πr²h;, where π is = 3.14, "r" denotes radius of base; "h" denotes the height;
Given that the radius is 5 units and the height is 11 units,
Substituting the values,
We get,
V = π × (5)² × (11);
V = 275π cubic units;
V = 275×3.14 = 863.5 cubic units;
Therefore, the required volume is = 863.5 cubic units.
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The given question is incomplete, the complete question is
If radius is 5 units, and height is 11 units, Find the Volume of the Cylinder.
if gender would not have mattered, what would have been the number of males that would have survived, given the data for the number of females who survived (296/402) and the total number of passengers on the ship (1207).
If gender did not matter then the number of males who would have survived would be 593 males
How to find the number who would have survived ?If gender would not have mattered, the survival rate would be the same for both genders. So, we would use the survival rate of females (which is 296/402) to calculate the expected number of males that would have survived.
First, calculate the survival rate of the females:
Survival rate = Number of females who survived / Total number of females
= 296 / 402
= 0.737
Expected number of male survivors = Number of males * Female survival rate
= 805 x 0.737
= 593 males
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A natural food company produces and sells organic almond milk for $9.00 per gallon. This company
estimates its fixed costs to be 1121 dollars per month and the variable cost to produce each gallon of
almond milk is $7.50.
What is the margin of profit if 1494 gallons of almond milk are produced and sold each month?
A Select an answer of $
Okay, here are the steps to solve this problem:
Fixed costs per month: $1121
Variable cost per gallon: $7.50
Selling price per gallon: $9.00
Monthly sales (gallons): 1494
Cost of goods sold = Variable cost per gallon * Monthly sales
= $7.50 * 1494 gallons
= $11,105
Gross margin = Revenue - Cost of goods sold
= $9 * 1494 gallons
= $13,446
- $11,105 (Cost of goods sold)
= $2,341
Margin of profit = Gross margin - Fixed costs
= $2,341 - $1121
= $1,220
So the margin of profit if 1494 gallons are produced and sold each month is $1,220.
The answer is:
B $1,220
Peter set off from Town A at 10 am, driving at an average speed of 84 km/h. He reached
Town B at 2 pm. If William set off 1 hour 25 minutes earlier than Peter and took the
same route at an average speed of 70 km/h, at what time would William reach Town B?
Peter left Town A around 10 a.m., traveling at an average speed of 84 km/h. William would reach Town B at 1:23 PM.
Firstly, we need to find the distance between Town A and Town B which can be calculated by calculating the distance travelled by Peter
Time taken by Peter = 2PM - 10AM
= 4 hrs
Speed of Peter = 84 km/h
Distance travelled by Peter = speed × time
= 84 × 4
= 336 km
So, the distance between Town A and Town B = distance travelled by Peter = 336 km.
Now, we will calculate time taken by William.
Speed of William = 70 km / hr
Distance travelled by William = distance between Town A and town B = 336 km
Time taken by William = distance / speed
= 336 / 70 hr
= 4.8 hr
This can b converted into hrs and minutes
4.8 hr = 4 hr + 0.8 × 60
= 4 hr 48 mins
Time William took off = 10 AM - 1hr 25 mins
= 8:35 AM
Now, we will calculate the time William would reach town B.
Time = 8:35 + 4hr 48 mins
= 1:23 PM
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Real World Scenario: Sara and Kim are both three years old. Both have recently talked to their parents about doing chores around the house to earn some money. Both Sara and Kim's parents have agreed to start giving them a constant allowance every week. Sara currently has $1 in her piggy bank. Her parents have agreed to give her $.60 per week for doing her chores. Kim currently has $2.20 in her piggy bank. Her parents have greed to give her $.20 per week for doing her chores.
What equation and graph help support scenario?
The equation that represents the amount of money in Sara's piggy bank is y = 0.6x + 1 and the equation that represents the amount of money in Kim's piggy bank is y = 0.2x + 2.2.
The equation that represents the amount of money in Sara's piggy bank over time can be written as
Y = 0.6x + 1
Where Y represents the total amount of money in Sara's piggy bank and x represents the number of weeks.
Similarly, the equation that represents the amount of money in Kim's piggy bank over time can be written as
Y = 0.2x + 2.2
Where Y represents the total amount of money in Kim's piggy bank and x represents the number of weeks.
To visualize these equations, we can create a graph where the x-axis represents the number of weeks and the y-axis represents the amount of money in the piggy bank. We can plot the points for each week and draw a line connecting them. The resulting graph will show the trend of the amount of money in each piggy bank over time.
Here is a graph that represents the scenario
In the graph, the red line represents the amount of money in Sara's piggy bank and the blue line represents the amount of money in Kim's piggy bank. As we can see, Sara's piggy bank grows faster than Kim's piggy bank due to the higher allowance she receives for doing her chores.
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Need help on please
Answer:
12
Step-by-step explanation:
The figure is a right triangle with hypotenuse = QS
The base from the graph = 4 units
(or you can just subtract the x-coordinates 2 - (-2) = 4)
The height from the graph is 3 units
(Or you can subtract the y-coordinates: 1 - (-2) = 3)
Since this is a right triangle the square of the hypotenuse = sum of squares of the other two sides
QS² = 3² + 4² = 9 + 16 = 25
QS, the hypotenuse = √25 = 5
The perimeter = sum of the sides = 3 + 4 + 5 = 12 units
someone please answer this its confusing me
Tommy and Ruth are cycling to meet each other. Tommy cycles twice as fast as Ruth and they both set off at the same time. At which coordinate will they meet?
Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point.
In this problem, Tommy and Ruth are cycling towards each other. We are given that Tommy cycles twice as fast as Ruth and they both start cycling at the same time. Our goal is to determine at which coordinate they will meet.
To solve this problem, we need to use the concept of distance, speed, and time. Let's assume that Ruth cycles at a speed of "x" km/hr. Since Tommy cycles twice as fast as Ruth, his speed will be "2x" km/hr.
Let's say that Tommy and Ruth meet at a distance of "d" km from Ruth's starting point. Now, let's calculate the time taken by both Tommy and Ruth to reach this point.
Time taken by Ruth = Distance/Speed = d/x
Time taken by Tommy = Distance/Speed = d/2x
Since they both start cycling at the same time, we can set these two equations equal to each other:
d/x = d/2x
We can then simplify this equation by multiplying both sides by 2x:
2d/x = d
Now we can solve for "d" by multiplying both sides by "x":
2d = dx
d = 0.5x
This means that Tommy and Ruth will meet at a coordinate that is 0.5x km away from Ruth's starting point. To determine the exact coordinates, we need to know where Ruth started cycling from and in which direction they are cycling. If we assume that Ruth started cycling from the origin (0,0) and they are cycling towards each other on a straight path, then they will meet at the coordinate (0.5x, 0).
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Mario was given the following enlargement.
A figure with top measurement A and side measurement 6 centimeters. Side A corresponds to a side with length 24 centimeters. A side with length 6 centimeters corresponds with a side with length 12 centimeters.
Figures not drawn to scale.
What is the length of side A, in centimeters?
12
15
24
33
The length of side A, in centimeters is 12. Option A
How to determine the valueTo determine the value, we need to know that;
When two sides of a figure are equal in length, that is in (measure).
For example in a square all sides are equal in length so they're all corresponding measurements.
From the information given, we have that;
Side A corresponds to 24 cm
Length 6 cm corresponds to Length 12 cm
The given parameters can be represented mathematically as;
A/24 = 6/12
cross multiply the values, we have;
12A = 6(24)
Multiply the values
12A = 144
Divide by the coefficient, we have;
A = 12 centimeters
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The correct answer is, A (aka 12)
A student has scores of 63, 65, and 73 on his first three tests. He needs an average of at least 70 to earn a grade of C in the class.
What is the minimum score that the student needs on the fourth test to ensure a C?
Answer: 79
Step-by-step explanation:
63+65+73+×/4=79
multiply by 4 on both sides
201+x=280
subtract 201 from both sides
x= 79
Need help asap, please and thank you
If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.
In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;
where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;
Substituting the values,
We get;
⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;
Simplifying this expression,
We get;
⇒ P = (111.3 million) × (1.0078)³⁷;
⇒ P ≈ 148.37 million;
Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.
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XZ.P Point P(-7, 2) is mapped onto P¹ (3, -11) by the reflection y=mx+c. find the values of the constants m and c.
The values of the constants m and c include the following:
m = -1.3
c = 7.1
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;
2 = -7m + c ...equation 1.
-11 = 3m + c ...equation 2.
By solving the system of equations simultaneously, we have:
2 = -7m - 3m - 11
11 + 2 = -10m
13 = -10m
m = -1.3
c = 7m + 2
c = 7(-1.3) + 2
c = -7.1
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Question 1b Identify the amount in this statement. 6 is 30% of 20. The amount = The solution is
The amount in this statement, 6 is 30% of 20 is 6.
The amount in the statement "6 is 30% of 20" is 6.
This statement means that if we take 30% of 20, we get 6.
In other words, the amount 6 is 30% of 20.
We can also verify this by calculating 30% of 20:
30% of 20
= (30/100) × 20
= 0.3 × 20
= 6
Hence, the amount in this statement is 6.
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An object in the shape of a rectangular prism has a length of 9 inches, a width of 5 inches, and a height of 4 inches. The object's density is 11.1 grams per cubic centimeter. Find the mass of the object to the nearest gram.
Answer:
32.741 kg---------------------------
Mass is the product of the volume and density and the volume of the rectangular prism is the product of its three dimensions.
Find the volume first:
V = 9*5*4 = 180 in³Convert volume to cm³, taking 2.54 cm per in:
180*(2.54)³ = 2949.67152 cm³Find the mass:
Mass = 11.1*2949.67152 = 32741.353872 g ≈ 32.741 kg (rounded)879 divided by 8 with remainder as fraction
Find the 15th term of the geometric sequence 2,6,18,...
Answer:
In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).
In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:
r = 6 / 2 = 3
Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:
aₙ = a₁ * r^(n-1)
Substituting the values, we have:
a₁ = 2
r = 3
n = 15
a₁₅ = 2 * 3^(15-1)
Calculating the exponent first:
3^(15-1) = 3^14 = 4782969
Now, substituting this value back into the formula:
a₁₅ = 2 * 4782969
a₁₅ = 9565938
Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.
Step-by-step explanation:
Roughly how much more does auto insurance cost for a 16 year old compared to a middle aged (40-50 year old) driver
A 16-year-old on their own policy pays on average $4,000 more per year than a 50-year-old would have to pay
The cost of insuranceAuto insurance costs vary significantly depending on factors such as location, vehicle type, and driving history. However, on average, a 16-year-old driver can expect to pay significantly more for auto insurance compared to a middle-aged driver (40-50 years old).
The exact amount varies, but it's not uncommon for a 16-year-old driver to pay two to three times more for auto insurance than a middle-aged driver. This is mainly because younger drivers are considered riskier due to their inexperience and higher likelihood of being involved in accidents.
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1.
A 50 foot rope is stretched tight from the roof of a building to a spot 20 feet from the base of the
building. How tall is the building? Round your answer to TWO decimal places.
The required height of the building is approximately 45.82 feet.
Given that, a 50-foot rope is stretched from a building's top to a point 20 feet from the building's base.
We can use the Pythagorean theorem to solve the question.
Let h be the height of the building.
Pythagoras's theorem states that in a right-angled triangle, "the square of one side is equal to the sum of the squares of the other two sides".
Then, we have:
h² + 20² = 50²
Simplifying and solving for h, we get:
h² = 50² - 20²
h² = 2500 - 400
h² = 2100
h = √(2100)
h ≈ 45.82
Therefore, the height of the building is approximately 45.82 feet.
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please help fast i don’t feel like typing
Answer:
he should have subtracted 17 from both sides of the equation
Step-by-step explanation:
x+ 17 = 22
subtract 17 from both sides
X + 17 = 22
-17 -17
x = 5