ERROR ANALYSIS Describe and correct the error in finding the area of the triangle.XAYB(5,1)A(4,3)2462C1,1)b=15-11=4h= V(5-4)2 + (1 - 3)2= 15- 2.2A = bh (4)(2.2) = 4.4The area is about 4.4 square units.
Answers
Answer
The error occurs in the calculationof the Height of the triangle.
The Height calculated is incorrect, the distance should be from y-coordinate 1 to y-coordinate 3.
Step-by-step Explanation
We want to find the error made in calculating the area of the triangle whose vertices are given by the coordinates A(4, 3), B(5, 1) and C(1, 1).
Note that
Area of a triangle = ½ × B × H
where
B = Base of the triangle
H = Perpendicular height of the triangle (that is the very straight vertical height of the triangle)
For the given triangle,
Base of the triangle lies between vertices C and B with coordinates (1, 1) and (5, 1) respectively.
We can easily see that B and C are on the same horizontal line (same y-coordinates), hence, the base of the triangle is simply the difference between the x-coordinates of B and C.
So,
Base = B = 5 -1 = 4
This is correct, no error there.
But, the perpendicular height of the triangle was calculated as the distance between vertices A and B.
This isn't a straight vertical line that makes a right angle with the horizontal. What was calculated as the perpendicular height is simply the length of a side of the triangle.
The triangle exists between y-coordinates 1 and 3, hence, the height of the triangle is where the error is.
The true height of the triangle = 3 - 1 = 2 units
The correct area of the triangle is
Area = ½ × B × H
= ½ × 4 × 2
= 4 square units.
Hope this Helps!!!
Related Questions
What is the answer to this combination lock
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Answer: 375
Step-by-step explanation:
Ruling out each number:
6: In the first two rows, the 6's placement did not change but the clue did, meaning that it is talking about a different number. Otherwise, it would say it's in the right place twice or in the wrong place twice.
3 & 5: Since we know 6 is already ruled out, both 5 & 3 would have to be correct.
2 & 4 & 8: Is proven wrong in the 4th clue.
7: 7 would have to be in the middle since the second clue says it's in the wrong place. If it was 1, it would say it's in the right space.
1: Is proven wrong after 7 is proven true.
Figuring out placement:
5: For the first clue, it says that it's in the correct place meaning that 5 is the last digit.
3: For both of the times 3 appears, it is in the wrong spot, revealing that it's the first digit.
7: In the second clue, it could either be 1 or 7. However, since 3 took the first spot and 5 took the last spot, 7 would have to be in the middle since the clue says it's in the wrong place. If it was 1, it would say it's in the right space.
Hi
What’s up y’all idek why I’m here
Answers
Answer
Which are equivalent expressions?
Check all that are true.
A)8xy = 4x + 4y
B)x + 6x = 7x
C)x + 6y = 6xy
D)9x + 6y = 3(3x + 2y)
E)9a + 6b + 3c = 3(3a + 2b + c)
Answers
Answer:
DE
Step-by-step explanation:
D)9x + 6y = 3(3x + 2y)
E)9a + 6b + 3c = 3(3a + 2b + c)
there have the same concept
3*3x equals 9x and 3*3a is 9a
if James can swim 10 laps in 23 minutes, what would be his expected time for 15 laps?
Answers
Answer:
34.5 minutes
Step-by-step explanation:
Suppose c(p) gives the number of calories burned doing p push-ups, and
p(t) gives the number of push-ups a person can do in t seconds.what is the meaning of the composite function c(p(45)).
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The meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds
How to interpret the meaning of the composite function c(p(45))?The functions are given as:
c(p) gives the number of calories burned doing p push-upsp(t) gives the number of push-ups a person can do in t secondsSo, the interpretation of the function c(p(t)) is
The number of calories burned doing push-ups in t seconds
In c(p(45)), the value of t is 45
Hence, the meaning of the composite function c(p(45)) is the number of calories burned doing push-ups in 45 seconds
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A store is selling a hat at a 55 percent markup. The store originally paid 16$ for the hat. What is the retail price for the hat?
Answers
Answer:
$24.8
Step-by-step explanation:
16 times 55% is 8.8
Which graph represents 12 = 3x + 4y line a, line b, line c
Answers
Answer:
green line or "b"
Step-by-step explanation:
we can set this up into the slope intercept form
y=mx+b
where m is the slope and b is y intercept
12=3x+4y
-3x -3x
-3x+12=4y
/4. /4. /4
-3/4x+3=y
we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"
hopes this helps please mark rainliest
What is an example of "A one-to-one function of P onto Q is an isomorphism of P and Q "?
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An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
How to Identify a One-to-One Function?An example of a one-to-one function that is an isomorphism between sets P and Q is the function f: P -> Q defined as f(x) = 2x, where P and Q are the sets of integers.
This function is one-to-one because for every element x in P, there is a unique element 2x in Q. It is onto because every element y in Q has a preimage x in P such that f(x) = y (e.g., y/2 = x).
Furthermore, this function preserves the group structure between P and Q, as it satisfies the properties of an isomorphism. In this case, the group structure is addition, and the function f preserves addition: f(x + y) = 2(x + y) = 2x + 2y = f(x) + f(y) for all x, y in P.
Therefore, the function f: P -> Q defined as f(x) = 2x is an example of a one-to-one function that is an isomorphism between sets P and Q.
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what is the range of f(x)= sin -1(x)
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This means that the output of the function can be any value between -π/2 and π/2, including the endpoints.
In other words, the range of f(x) = sin⁻¹(x) is [-π/2, π/2].
Which of the following shows the correct solution steps and solution to 2×+ 7 = -11?
Answers
Answer:
x = - 9
Step-by-step explanation:
2x + 7 = - 11 ( subtract 7 from both sides )
2x = - 18 ( divide both sides by 2 )
x = - 9
The answer is:
x = -9
Work/explanation:
The point of equations is to find the variable's value by isolating it step-by-step.
For this equation, the variable is x.
To isolate it, I will perform a few operations.
First, I will subtract 7 from each side:
\(\sf{2x+7=-11}\)
\(\sf{2x=-11-7}\)
\(\sf{2x=-18}\)
Divide each side by 2
\(\sf{x=-9}\)
Hence, x = -9.
\(\rule{350}{4}\)
Solve :
1) 5x – 15x²
2) 3x-9
Answers
Answer:
1) 5x(1 - 3x)
2) 3(x - 3)
Step-by-step explanation:
Question # 1:
= 5x - 15x²
Take 5x common
= 5x(1 - 3x)
Question # 2:
= 3x - 9
Take 3 common
= 3(x - 3)
\(\rule[225]{225}{2}\)
Hope this helped!
~AH1807Answer:
1)
\(\tt 5x - 15x^2\) (x^2=xx)
\(\tt 5x-15xx\)
let's rewrite 5x → 5×1, n' 15→ 5×3
\(\tt 5\times \:1\times \:x-5\times \:3xx\)
Factor out common term(5x)
\(\boxed{\tt 5x\left(1-3x\right)}\)
2)
\(\tt 3x-9\)
Rewrite 9 → 3×3
\(\tt 3x-3\times \:3\)
Factor out common term (3)
\(\boxed{\tt 3\left(x-3\right)}\)
Hope it helps! :)
The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Answers
The equations can be used to solve for y, the length of the room follows:
B. y² – 5y = 750, C. 750 – y(y – 5) = 0 and E. (y + 25)(y – 30) = 0
What is the area of the rectangle?The area of a rectangle is defined as the product of the length and width.
The area of a rectangle = L × W
Where W is the width of the rectangle and L is the length of the rectangle
As per the question, we have
length L = y
width W = y - 5
Since the area of a rectangular room is 750 square feet.
So L × W = 750
y(y - 5) = 750
y² – 5y = 750 ....(i)
This can be also written as:
750 – y(y – 5) = 0 ....(ii)
Factorizing the equation (i), we get
(y + 25)(y – 30) = 0
Thus, the correct answer would be options (B), (C), and (E).
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Brett and Margo have each thought about murdering their rich Uncle Basil in hopes of claiming their inheritance a bit early. Hoping to take advantage of Basil’s predilection for immoderate desserts, Brett has put rat poison into the cherries flamb´ e; Margo, unaware of Brett’s activities, has laced the chocolate mousse with cyanide. Given the amounts likely to be eaten, the probability of the rat poison being fatal is 0.60; the cyanide, 0.90. Based on other dinners where Basil was presented with the same dessert options, we can assume that he has a 50% chance of asking for the cherries flambe, a 40% chance of ordering the chocolate mousse, and a 10% chance of skipping dessert altogether. No sooner arc the dishes cleared away than Basil drops dead. In the absence of any other evidence, who should be considered the prime suspect?
Answers
Answer:
Step-by-step explanation:
The probability of asking for the cherries flambe and dying, P(A) = 0.5 × 0.6 = 0.3
The probability of asking for the chocolate mousse and dying, P(A) = 0.4 × 0.9 = 0.36
The probability of skipping dessert altogether = 0.1 × 0 = 0
The probability that the rich uncle dies, P(D) is
P(D) = 0.3 + 0.36 + 0 = 0.66
To determine the prime suspect, we would apply the concept of conditional probability. It is the probability of an event, A occurring given that event B has occurred. We would compare probabilities of the events A and B occurring given that event D also occurred
Therefore,
P(A|D) = 0.3/0.66 = 0.45
P(B|D) = 0.36/0.66 = 0.55
Therefore, the prime suspect is Margo because his probability is higher
The graph of a proportional relationship and an equation are shown.
What is the greater unit rate?
Answers
Answer:
Graph has the greater unit rate.
Step-by-step explanation:
From the graph attached,
Since, graph shows the proportional relationship,
y ∝ x
y = kx
Here, k = unit rate
If the line given in the graph passes through (0.2, 1.5)
Slope of this line will be,
k = \(\frac{1.5}{0.2}\)
k = 7.5
Therefore, unit rate = 7.5
Equation of the line given in the question is,
\(y=\frac{11}{2}x+3\)
Comparing this equation with the y-intercept form of the equation,
\(y=mx+b\)
Slope of this line 'm' = \(\frac{11}{2}\)
= 5.5
Unit rate of the given equation = 5.5
Therefore, graph has the greater unit rate.
The formula for the area of a rectangle is: A = lw
How could we solve this equation
for the width, w?
Answers
The way to solve the equation for the width, w, is to divide both sides by l. The correct option is A. We want to get w by itself, so we would divide both sides by l
Area of a rectangleFrom the question, we are to determine how we can solve the given formula for area of rectangle for the width, w
The given formula is
A = lw
To solve the given equation for w, we will divide both sides of the equation by l
That is,
A/l = lw/l
So that
A/l = w
and
w = A/l
Hence, the way to solve the equation for the width, w, is to divide both sides by l. The correct option is A. We want to get w by itself, so we would divide both sides by l
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Hi can u please help me with this ASAP
Answers
Answer: an altitude
Step-by-step explanation:
Alan used a total of 7 1/4 gallons of gas while driving his car. Each hour he was driving, he used 5/6 gallons of gas. What was the total number of hours he was driving?
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The required time for which alan drives his car is 8.7 hours.
Given that,
Alan used a total of 7 1/4 gallons of gas while driving his car. Each hour he was driving, he used 5/6 gallons of gas. The total number of hours he was driving is to be determined.
here,
Total fuel consumed = 7 + 1 / 4 = 29 / 4 gallons of fuel
Rate of fuel used per hour = 5 / 6
Total number of hours of driving = Total fuel/fuel used per hour
= 29/4 / 5/6
= 8.7 hours.
Thus, the required time for which alan drives his car is 8.7 hours.
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Howdy! Thanks for stopping by my question! I would really appreciate the help! I've attached the question below. Thanks!
I'd appreciate if you made sure to double check your answers and provide everything the question is asking! INCLUDE ALL STEPS!
Answers
Answer:
a) x = 1 ± (3/7)√7
b) (-∞, -5) ∪ [-2, 5) ∪ [6, ∞)
Step-by-step explanation:
You want solutions to the relations ...
7 +1/x = 1/(x-2)(x² -4x -12)/(x² -25) ≥ 0a) 7 + ...We like to solve these in the form f(x) = 0. It helps avoid extraneous solutions.
\(7+\dfrac{1}{x} -\dfrac{1}{x-2}=0\\\\\\\dfrac{7x+1}{x}-\dfrac{1}{x-2}=0\\\\\\\dfrac{(7x+1)(x-2)-x}{x(x-2)}=0\\\\\\ \dfrac{7x^2-14x-2}{x(x-2)}=0\)
The roots of the numerator quadratic are found by ...
x² -2x -2/7 = 0 . . . . . divide by 7
x² -2x +1 -9/7 = 0 . . . . add and subtract 1
(x -1)² = 9/7 . . . . . . . . . . write as a square, add 9/7
x -1 = ±√(9·7/49) = ±(3/7)√7 . . . . take the square root
x = 1 ± (3/7)√7
b) (x² - ...Rational inequalities are best solved by identifying the roots of numerator and denominator. These tell you where the function changes sign. The end behavior of the rational function tells you what the signs are changing from.
\(\dfrac{x^2-4x-12}{x^2-25}\ge 0\\\\\\\dfrac{(x+2)(x-6)}{(x+5)(x-5)}\ge0\)
This has a horizontal asymptote at y=1 for |x|→∞. It has vertical asymptotes at x=±5.
The sign changes occur at x ∈ {-5, -2, 5, 6}. The rational expression is positive (approaching +1) for x < -5 and for x > 6. It is negative in the adjacent intervals, so positive again for -2 < x < 5.
The inequality is satisfied for ...
x < -5-2 ≤ x < 56 ≤ xSolve for x
28=4(x+2)
x=
Answers
Answer:
Hi! The correct answer is x = 5!
Step-by-step explanation:
~Isolate the variable by dividing each side by factors that don't contain the variable~
Answer:
the correct answer is x =5
when calculating the size of the labor force, the bureau of labor statistics counts not only people who are employed, but also
Answers
people who are unemployed but actively searching employment.
The Bureau of Labor Statistics (BLS) is a US government agency that provides data on labor market activity, working conditions and price movements in the economy.
Part of the U.S. Department of Labor, it is responsible for the collection, analysis, and public dissemination of economic data. BLS produces a wide range of statistical information, including data on employment, unemployment, wages, productivity, consumer price inflation, and occupational injuries and illnesses.
They also conduct research and publish reports on various labor market and business issues. The BLS is an invaluable resource for policy makers, businesses, workers and others who need reliable and up-to-date information on the state of the economy and labor market.
The workforce is defined as the total number of people who are employed or unemployed but are actively looking for work. Pensioners, students and housewives are not included. To be considered an active job seeker, you must have taken certain steps to find a job within the last four weeks. The size of the labor force is an important indicator of the health of the economy as a whole, as it reflects the number of people contributing to economic activity or looking for work.
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i need help! ill give brainliest! please!
Answers
Solve the equation −11=−3m+7
Answers
Answer:
m = 6
Step-by-step explanation:
Step 1: Write out equation
-11 = -3m + 7
Step 2: Subtract 7 on both sides
-18 = -3m
Step 3: Divide both sides by -3
6 = m
Step 4: Rewrite
m = 6
Answer:
m = 6
Step-by-step explanation:
-11 = -3m + 7
Multiply -1 on both sides
11 = 3m - 7
11 + 7 = 3m
18 = 3m
18/3 = m
m = 6
Which ordered pair is on the inverse of f(x)?
(–4, –2)
(–2, –2)
(–1, –2)
The range of the inverse of f(x) is
.
Answers
Answer:
(-1,-2)
because the inverse of (-4,-2) is (-2,-4) so when we simplify both number or when we divide by both numbers by 2 we get (-1,-2)
so the inverse of f(x) _ (-4,-2) is (-1,-2)
An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3 ft long with a diameter of 1.8 ft. Suppose oil is drained at a rate of 1.7 ft³ per minute. If the tank starts completely full, how many minutes will it take to empty the tank? Use the value 3.14 for pi, and round your answer to the nearest minute. Do not round any intermediate computations.
Answers
Answer:
4 minutes
Step-by-step explanation:
You want to know how long it takes to drain a cylindrical tank 1.8 ft in diameter and 3 ft long at the rate of 1.7 ft³/minute. (π = 3.14)
VolumeThe volume of a cylinder can be found using the formula ...
V = (π/4)d²h . . . . . . . diameter d, height h
Then the volume of the oil tank is ...
V = 3.14/4(1.8 ft)²(3 fft) = 7.6302 ft³
TimeThe time it takes to empty the tank is found by dividing the volume by the rate:
(7.6302 ft³)/(1.7 ft³/min) ≈ 4.49 min ≈ 4 min
It will take about 4 minutes to empty the tank.
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Which graph has a domain of -∞ < x < ∞ and a range of -∞ < y
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The graph of the option in the question has a domain of -∞ < x < 3.5.
Please find attached the drawing of a graph that has a domain of -∞ < x < ∞ Which method can be used to find the graph that has a domain of -∞ < x < ∞?The domain of a graph are the possible x-values that can be obtained from the graph.
A graph that has a domain given by the inequality, -∞ < x < ∞ does not have a vertical asymptote.
An asymptote is a straight line to which a graph approaches, as either the x or y-value approaches infinity.
The given graph has a vertical asymptote at y ≈ 3.5
The domain of the given graph is therefore, -∞ < x < 3.5
Similarly, the graph has a horizontal asymptote at x ≈ 3
The range of the given graph is therefore, -∞ < y < 3.
A graph that has a domain of -∞ < x < ∞, extends to infinity to the left and the right of the graph.
A function that has a graph with a domain of -∞ < x < ∞ is one of direct proportionality.
An example is, y = x
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Solve the inequality and graph the solution on the line provided. 6x-6<-30
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The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.
To solve the inequality 6x - 6 < -30, we can follow these steps:
Step 1: Add 6 to both sides of the inequality to isolate the variable:
6x - 6 + 6 < -30 + 6
6x < -24
Step 2: Divide both sides of the inequality by 6 to solve for x:
(6x)/6 < (-24)/6
x < -4
The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.
To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.
On the number line, mark a point at -4 with a closed circle:
<--------●-----------------
Then, shade the region to the left of -4:
<--------●================
The shaded region represents the solution to the inequality x < -4.
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Suppose that $6000 is placed in a savings account at an annual rate of 4%, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the account to grow to $8670?
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The time taken for the money to grow to $8670 at compound interest is approximately 9.24 years.
Given the amount of money that is the principal = $6000
Rate = 4% compounded quarterly.
Time = t
Amount = $8670
Now we know that the amount is calculated by the formula:
A = P(1+r/4)ⁿ
8670 = 6000(1+0.01)ⁿ
Hence
log 1.445 = n log 1.01
or, n = 36.99
Number of years = 36.99 / 4 = 9.24 years.
The interest that is added to a loan or deposit is referred to as compound interest. Compound interest is computed for a sum utilizing both the principal and interest already paid. The main distinction between compound interest and simple interest is this.
If we look at our bank statements, interest is usually credited to our account once a year. While the principle remains constant, the interest changes annually.
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5.
5. Kara is zip-lining in the rainforest. She is standing at the top of Platform A
ready to zip-line to Platform B. If the horizontal distance between the
platforms is 500 feet and the length of the zip-line is 685 feet, find the
angle of depression from Platform Ato Platform B to the nearest tenth.
Answers
Answer:
The angle of depression from Platform A to Platform B is \(43.1^{\circ}\)
Step-by-step explanation:
Refer the attached figure
The horizontal distance between the platforms is 500 feet i.e. BC = 500
The length of the zip-line is 685 feet i.e. AB = 685
We are supposed to find the angle of depression from Platform A to Platform B
Hypotenuse = 685
Base = 500
\(Cos \theta = \frac{Base}{Hypotenuse}\\Cos \theta = \frac{500}{685}\\\theta = cos^{-1}(\frac{500}{685})\\\theta = 43.11^{\circ}\)
Hence the angle of depression from Platform A to Platform B is \(43.1^{\circ}\)
Wyatt is saving up to buy a new bicycle. He already has $60 and can save an
additional $6 per week using money from his after school job. How much total money
would Wyatt have after 6 weeks of saving? Also, write an expression that represents
the amount of money Wyatt would have saved in w weeks.
Answers
Answer:
Expression: 6w+$60 Money: $99
Step-by-step explanation:
So, let's find the ammount for 6 weeks
We know he can make $6 per week, so we ned to multiply 6*$6 to get your answer
So, 6 ( weeks ) * 6 ( dollars) = $36 for 6 weeks
Then, we ned to add the $60 he already has saved up, so $60+$39=$99
For the equation, We know that we need to multioply the number of weeks by 6, as shown by how we solved the last problem
So, 6*w=6w
Then we need to add $60
So, we get 6w+$60 for the expression
Answer:
96
Step-by-step explanation:
In a class of 60 students, 40 are Democrats, 10 are business majors, and 4 of the business majors are Democrats. If one student is randomly
selected from the class, find the probability of choosing a Democrat or a business major.
P(Democrat or business major) =
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In conclusion, the probability of selecting a Democrat or a business major is 11/15.
How to solve?
To find the probability of selecting a Democrat or a business major, we need to add the probabilities of selecting a Democrat and selecting a business major, and then subtract the probability of selecting a student who is both a Democrat and a business major (since we would be double counting this student).
So, let's calculate each of these probabilities:
Probability of selecting a Democrat: There are 40 Democrats out of 60 students, so the probability of selecting a Democrat is 40/60 = 2/3.
Probability of selecting a business major: There are 10 business majors out of 60 students, so the probability of selecting a business major is 10/60 = 1/6.
Probability of selecting a student who is both a Democrat and a business major: We know that there are 4 business majors who are also Democrats, so the probability of selecting one of these students is 4/60 = 1/15.
Now we can calculate the probability of selecting a Democrat or a business major:
P(Democrat or business major) = P(Democrat) + P(business major) - P(Democrat and business major)
= 2/3 + 1/6 - 1/15
= 11/15
Therefore, the probability of selecting a Democrat or a business major is 11/15.
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