find the area of the triangle which has sides ~u = 〈3, 3, 3〉, ~v = 〈6, 0, 6〉, and ~u −~v.
Answers
The area of the triangle formed by the given sides is 9√2 square units.
To find the area of the triangle, we first need to find the length of the third side, ~u - ~v.
~u - ~v = 〈3, 3, 3〉 - 〈6, 0, 6〉 = 〈-3, 3, -3〉
Next, we can use the formula for the area of a triangle given the lengths of its sides:
Area = 1/4 * √(4a²b² - (a² + b² - c²)²)
where a, b, and c are the lengths of the sides.
Using this formula with the lengths of the sides ~u, ~v, and ~u - ~v, we get:
a = ||~u|| = √(3² + 3² + 3²) = 3√3
b = ||~v|| = √(6² + 0² + 6²) = 6√2
c = ||~u - ~v|| = √((-3)² + 3² + (-3)²) = 3√2
Plugging these values into the formula, we get:
Area = 1/4 * √(4(3√3)²(6√2)² - (3√3)² - (6√2)² - (3√2)²)
= 9√2
To know more about area of the triangle, refer here:
https://brainly.com/question/29183952#
#SPJ11
Related Questions
the percentage of children ages 1 to 14 living in poverty in 1985 compared to 1991 for 12 states was gathered. part a: determine and interpret the lsrl. (3 points) part b: predict the percentage of children living in poverty in 1991 for state 13 if the percentage in 1985 was 19.5. show your work. (3 points) part c: calculate and interpret the residual for state 13 if the observed percent of poverty in 1991 was 22.7. show your work. (4 points)
Answers
Answer:
Part A: The LSRL is y^ = 7.76 + 0.6x.
Part B: y^ = 7.76 + 0.6(19.5) = 19.46
y^ = 19.46%
Part C: 22.7 - 19.46 = 3.24. The residual is 3.24. This means that the value was underpredicted.
Step-by-step explanation:
A line passing through the point (12, –5) has a slope of One-third.
Complete the work shown:
1. Substitute known values for m, x1, and y1:
2. Distribute the slope through the parentheses:
3. Distribute the slope through the parentheses:
4. Solve for the y-variable:
y minus (negative 5) = one-third (x minus 12). Y + 5 = one-third (x minus 12). Y + 5 = one-third x minus 4.
Answers
Answer:
-9
Step-by-step explanation:
Answer:
its -9
Step-by-step explanation:
got it right on edge
an inequity that can be written in the form ax by < c (where a and b are not both zero) is called a ____?____ inequality in two variables.
Answers
An inequality that can be written in the form ax + by < c (where a and b are not both zero) is called a linear inequality in two variables.
An inequality that represents a line in a two-dimensional coordinate system is referred to as a linear inequality. The set of points that satisfies the inequality is a half-plane bounded by a line that may be dashed or solid.
In contrast to a linear equation, which represents a line, a linear inequality represents a half-plane. The points on one side of the line, rather than the points on the line, are solutions to the inequality.
The method of shading is used to graph a linear inequality in two variables. First, graph the boundary line, which is usually represented by a solid or dashed line, and then select a test point on one side of the line. Shaded regions of the half-plane containing the test point satisfy the inequality.
Learn more about linear inequality here: https://brainly.com/question/30440630
#SPJ11
Simplify (4s+7 -2S) +4 (3s-5^2) 
Answers
Answer:
14S -93
Step-by-step explanation:
(4s+7 -2S) +4 (3s-5^2)
= 2S +7 +12S -4*25
=14S -93
Which of the following is equivalent to 5sqrt 13^3
Answers
Answer: D) 13^(3/5)
Step-by-step explanation: This is assuming that the question is asking the √13^3. With the five as the y root.
Write an Equation and solve.10. If tickets to a concert cost $18. How many tickets can you buy with $150?Let x =EquationX=
Answers
Let x = Number of tickets
So, the equation is
\(18x=150\)Solve for x:
\(\begin{gathered} \frac{18x}{18}=\frac{150}{18} \\ x=8.33 \end{gathered}\)Answer: x = 8.33
Dig deeper! a police dog spends of his workday in a police car, of his workday in public, and the rest of his workday
at the police station. what fraction of the dog's day is spent at the police station?
fraction of workday
Answers
The police dog spends 1/6 of its workday at the police station.
To find the fraction of the police dog's workday spent at the police station, we need to add up the fractions of time spent in each location and subtract them from 1, since the dog spends the rest of the day at the police station.
Fraction of time spent in police car = \(1/3\)
Fraction of time spent in public = \(1/2\)
To add these fractions, we need to find a common denominator:
\(1/3 = 2/6\\1/2 = 3/6\)
So, the fraction of the dog's day spent at the police station is:
\(1 - (2/6 + 3/6) = 1 - 5/6\)
= \(1/6\)
Therefore, the police dog spends 1/6 of its workday at the police station.
Learn more about Police Station at
brainly.com/question/12816186
#SPJ4
Please help! I will mark as brainliest IF answer is right. <3
Answers
Answer:
7x-26
Step-by-step explanation:
Answer:
f(x - 4) = 7x - 26
Step-by-step explanation:
Since the original equation was f(x) = 7x + 2, then to solve the following equation, you need to use the substitution method in relation to the added number (-4). So, if f(x - 4), you would now substitute the (x - 4), in place of the previous (x). Therefore the new problem would be f(x - 4) = 7(x - 4) + 2; after distributing, you would get 7x - 28 + 2. Then further simplifying, this would be 7x - 26, after doing -28 + 2. Finally, the answer would be f(x - 4) = 7x -26.
A local food truck specializes in gourmet grilled cheese sandwiches. Each month, the owners of the truck have a constant total of $7,900 in expenses (salaries, truck loan, etc.) and it costs $1.70 per sandwich to make each sandwich. The food truck sells its sandwiches for $7.75 each.
a) Write an inequality to represent how many sandwiches, s, the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs.
b) Solve the inequality. Show your steps or explain your answer.
c) To gain more sales, the food truck offers a discount one month of $1.50 off its sandwiches.
How many more sandwiches will it need to sell to earn more money from selling sandwiches than it pays in expenses and food costs? Explain your answer, mathematically or in words.
Answers
Answer:
a) s × ($7.70 - $1.70) > $7,900
b) s > 1,306 sandwiches
c) 431 more sandwiches
Step-by-step explanation:
The question is
The given parameters are;
The constant total expenses (fixed cost), C = $7,900
The cost it takes to make each sandwich, \(p_s\) = $1.70
The price at which the food truck sells its sandwiches, \(c_s\) = $7.75
Where "s" represent the number of sandwiches sold, we have;
a) Therefore, the inequality that represent the number of sandwiches the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs is given as follows;
s × (\(c_s\) - \(p_s\)) > C
Substituting the known values, gives;
s × ($7.75 - $1.70) > $7,900.00
b) From the inequality, which we have;
s > $7,900/($7.75 - $1.70)
However, $7,900/($7.75 - $1.70) = 158,000/121 ≈ 1,305.79
We round up to the nearest whole number since we are counting sandwiches which are counted per each piece
Therefore;
s > 1,306 sandwiches
An explanation is that the food truck will have to sell more than 1,305 sandwiches to be earn more money than it pays in expenses and sandwich costs.
c) The amount in discount the food truck offers in a specific month = $1.50
Therefore, the amount the food truck sells the sandwich in the given month \(c_s\) = $7.75 - $1.50 = $6.25
Therefore the number of sandwich the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;
s × (\(c_s\) - \(p_s\)) > C
s × ($6.25 - $1.70) > $7,900, which gives;
s > $7,900/($6.25 - $1.70)
$7,900/($6.25 - $1.70) ≈ 1,73.26
We round up to get, s > 1,737
We round up
Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;
At $7.75 the number of sandwiches the food truck has to sell s > 1,306
At $1.70 the number of sandwiches the food truck has to sell is s > 1,737
The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches
The more number of sandwiches it has to sell = 431 more sandwiches
(From which we check to have; 1306 + 431 = 1737 which is correct)
The inequality represents how many sandwiches, the food truck is \(s \times ($7.75 - $1.70) > $7,900.00\)
The solution of the inequality is,1,305.79
The more number of sandwiches it has to sell is 1373 more sandwiches
Given that,
A local food truck specializes in gourmet grilled cheese sandwiches.
Each month, the owners of the truck have a constant total of $7,900 in expenses (salaries, truck loan, etc.) and it costs $1.70 per sandwich to make each sandwich.
The food truck sells its sandwiches for $7.75 each.
We have to determine,
Write an inequality to represent how many sandwiches, the food truck.
Solve the inequality.
To gain more sales, the food truck offers a discount one month of $1.50 off its sandwiches.
How many more sandwiches will it need to sell to earn more money from selling sandwiches than it pays in expenses and food costs
According to the question,
The constant total expenses (fixed cost), C = $7,900
The cost takes to make each sandwich, = $1.70
The price at which the food truck sells its sandwiches, = $7.75
Where "s" represents the number of sandwiches sold.
The inequality that represents the number of sandwiches the food truck will have to sell each month to earn more money from selling sandwiches than it pays in expenses and sandwich costs is given as follows;\(s \times (c_s-p_s)>c\)
Substituting the known value in the equation,
\(s \times ($7.75 - $1.70) > $7,900.00\)
The inequality, which we have; s > $7,900/($7.75 - $1.70)$7,900/($7.75 - $1.70)
= 158,000/121
≈ 1,305.79
The nearest whole number since we are counting sandwiches which are counted per piece.
Therefore;
s > 1,306 sandwiches
An explanation is that the food truck will have to sell more than 1,305 sandwiches to earn more money than it pays in expenses and sandwich costs.
The amount in discount the food truck offers in a specific month = $1.50 Therefore, the amount the food truck sells the sandwich in the given month = $7.75 - $1.50 = $6.25The number of sandwiches the food truck company will have to sell on that month to earn more money from selling sandwiches than it pays the in expenses and sandwich cost, "s" is given as follows;
\(s \times (c_s-p_s)>c\)
s × ($6.25 - $1.70) > $7,900, which gives;
s > $7,900/($6.25 - $1.70)
$7,900/($6.25 - $1.70) ≈ 1,73.26
s > 1,737
Therefore, the number of more (extra) sandwiches the food truck have to sell to earn money from selling sandwiches than it pays in expenses and food costs is the difference in the number of sandwiches it has to sell at $7.75 and $6.25 to earn more money than it pays in fixed expenses (costs) and the sandwich cost which is given as follows;
At $7.75 the number of sandwiches the food truck has to sell s > 1,306
At $1.70 the number of sandwiches the food truck has to sell is s > 1,737
The more number of sandwiches it has to sell = 1,737 - 1,306 = 431 more sandwiches
The more number of sandwiches it has to sell = 431 more sandwiches
= 1306 + 431 = 1737
To know more about Inequality click the link given below.
https://brainly.com/question/21620502
A participant is randomly selected. let c be the event that the participant prefers country music and let t be the event that the participant is a teen. what is the value of p(cc and tc)
Answers
The value of the probability \(P(C^c ~and ~T^c)\) is 0.45 and option C is the correct answer.
We have,
Number of people = 520
\(C^c\) = event that people do not like country music
\(T^c\) = event that people are not teens
Now,
From the table,
Add all the people who are not teen and does not like country music.
= 84 + 54 + 36 + 62
= 236
Now,
\(P(C^c ~and ~T^c)\)
= 236/520
= 0.45
Thus,
The value of the probability \(P(C^c ~and ~T^c)\) is 0.45 and option C is the correct answer.
Learn more about probability here:
https://brainly.com/question/14099682
#SPJ12
Tameka pilots a hot air balloon. She lowers the balloon
five times, going down an equal distance each time. In
all, Tameka lowers the balloon 75 m.
What integer represents the change in the hot air
balloon’s elevation each time Tameka lowers it?
What does this integer tell you?
Answers
Answer:
15 m
Step-by-step explanation:
Given that :
Change in distance is the same each time Ballon is lowered ;
Number of times Ballon is lowered = 5 times ;
Total change in distance = 75 m
Change in distance per time lowered equals ;
(Total change in elevation / Numbe rof times Ballon is lowered)
75m / 5
= 15 m
Hence, Ballon height changes by 15 m each time it is lowered.
The integer gives the lowering rate.
What is the behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero?.
Answers
The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is the polynomial's final behavior will be "down" on the left and "up" on the right.
Define polynomial function.In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable. For instance, the polynomial 2x+5 has an exponent of 1. Expressions that contain variables of various intensities, non-zero coefficients, positive exponents (of variables), and constants are known as polynomial functions. For instance, the polynomial in "b" of degree 2 is f(b) = 4b² - 6.
Given,
The behavior of the graph of a polynomial function when the leading coefficient of an odd degree polynomial is greater than zero is:
This odd-degree polynomial's end behavior will resemble that of a positive cubic because its leading coefficient is positive. As a result, the polynomial's final behavior will be "down" on the left and "up" on the right.
To learn more about polynomial function, visit:
https://brainly.com/question/12976257
#SPJ4
-5/12 - (-9/3) what is the answer for this equation
Answers
Answer:
2 7/12
Step-by-step explanation:
Simple fraction problem
What multiplication equattion can be used to explain the solution to 15 / 1/3
Answers
Step-by-step explanation:
15 / (1/3) is equal to 15 x 3/1 = 15 x 3 = 45
Reciprocal of 1/3 = 3/1
So, the multiplication equation that explains the solution is:
15 * (3/1) = 45
Therefore, 15 divided by 1/3 is equal to 45.
2(x+3) = 5x + 6 - 3x is it true or false
Answers
Answer:
True
Step-by-step explanation:
2(x+3) = 5x+6-3x
2x+6=5x-3x+6
2x+6=2x+6
Answer
True
Step-by-step explanation:
Cause 2×X=2x and 2×3=6
so total = 2× + 6 =5× + 6 - 3x
or, 2x + 6 = 5x - 3x + 6
or, 2x + 6 = 2x + 6
A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.
First Randomization
Group A Group B
13.6 9.2
12.1 8.2
15.9 11.5
11.2 13.8
9.7 14.6
Second Randomization
Group A Group B
8.2 12.1
13.8 14.6
15.9 13.6
9.2 11.2
9.7 11.5
Third Randomization
Group A Group B
8.2 12.1
9.7 13.8
11.5 13.6
14.6 11.2
15.9 9.2
For each table, calculate the mean weight for each group,
x
A
¯
and
x
B
¯
, and find the difference of the mean of group A and the mean of group B (
x
A
¯
−
x
B
¯
).
After the first randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the second randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
After the third randomization,
x
A
¯
is ,
x
B
¯
is , and (
x
A
¯
−
x
B
¯
) is .
Answers
Therefore, the mean weight for each group in the three randomizations are:
First Randomization:
Group A: 12.5
Group B: 11.46
Second Randomization:
Group A: 11.56
Group B: 12.4
Third Randomization:
Group A: 12.18
Group B: 12.18
What is mean?The mean, also known as the average, is a measure of central tendency in statistics. It is found by adding up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to extreme values, or outliers, in the data set, and can be influenced by them. It is one of the most commonly used measures of central tendency, along with the median and mode.
Here,
First Randomization:
Group A: (13.6 + 12.1 + 15.9 + 11.2 + 9.7) / 5 = 12.5
Group B: (9.2 + 8.2 + 11.5 + 13.8 + 14.6) / 5 = 11.46
Second Randomization:
Group A: (8.2 + 13.8 + 15.9 + 9.2 + 9.7) / 5 = 11.56
Group B: (12.1 + 14.6 + 13.6 + 11.2 + 11.5) / 5 = 12.4
Third Randomization:
Group A: (8.2 + 9.7 + 11.5 + 14.6 + 15.9) / 5 = 12.18
Group B: (12.1 + 13.8 + 13.6 + 11.2 + 9.2) / 5 = 12.18
To know more about mean,
https://brainly.com/question/14724376
#SPJ1
Answer:
LOOK BELOW FOR ANSWER !!
Step-by-step explanation:
After the first randomization,
A is 12.5
B is 11.46
and A-B is 1.04
After the second randomization,
A is 11.36
B is 12.6
A and B is -1.24
After the third randomization,
A is 11.98
B is 11.98
A and B is 1
.
промінь ділить розгорнутий кут на два кути. знайди ці кути, якщо один з них на 20градусів більший за другий
Answers
Answer:
write it in English so I can understand
What is the answer to this equation cause I can’t figure it out 16-(-12)=
Answers
If someone pays off a loan you have they take away your debt which is the same as giving you money.
16 - (-12) = 16 + 12 = 28
♡ The Question/Task ♡
What's the answer to this equation?
16-(-12)
16 - (-12)
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
28
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
-No Step-By-Step/Explanation provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-I recommend copy and pasting your equation/question, for example, 16 - (-12), into a browser! It'll automatically solve with a calculator, and the answer will appear in an answer bar!
What are the coordinates of B” under the composition:
Reflect over the x-axis, then rotate 90° CW
Answers
The coordinates of B” under the transformations is (-4, -2)
Calculating the coordinates of B” under the transformationsfrom the question, we have the following parameters that can be used in our computation:
B = (-2, -4)
The transformation is given as
Reflect over the x-axis, Rotate 90° CWSo, we have
Reflect over the x-axis
B' = (-2, 4)
Rotate 90° CW
B'' = (-4, -2)
Hence. the coordinates of B” are (-4, -2)
Read more about transformation at
https://brainly.com/question/31898583
#SPJ1
Anyone? i need help asap plzzz i’ll mark you as brainlist and like it
Answers
Answer:
x = 50°
Step-by-step explanation:
Recall that for a triangle, the exterior angle is equal to the sum of its two remove interior angles (also see attached for reference).
in our case, the exterior angle is given as 105° and its two remote interior angles are x and 55°
therefore
105° = 55° + x
x = 105° - 55°
x = 50°
Answer:
B. 50°
Step-by-step explanation:
In a test run, a certain car accelerates uniformly from zero to 22.4 m/s in 2.10 s. (a) what is the magnitude of the car's acceleration?
Answers
A specific car accelerates consistently from zero to 22.4 m/s in 2.10 seconds during a test session. The car's uniform acceleration is 8.1356 meter/\(sec^{2}\).
What is acceleration?The rate at which an object's velocity with respect to time changes is known as acceleration in mechanics. Accelerations are vector quantities (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration.
For instance, a car accelerates in the direction of motion when it begins at rest (zero velocity in an inertial frame of reference) and moves at increasing speeds in a straight path. When a vehicle turns, its motion vector is altered and accelerates in the new direction. A linear acceleration is the acceleration of the car in the direction it is moving, and it is this acceleration that the occupants of the car feel.
Calculations:
Acceleration=(\(\frac{change in speed}{change in time}\))= (24 m/s) / (2.95 s) = 8.1356 meter/\(sec^{2}\)
To learn more about acceleration , visit:
https://brainly.com/question/12134554
#SPJ4
What is an equation of the line that passes through the points (-5, -6) and (5, 6)?
Answers
Answer:
It would be -5 + -6 = 65
Step-by-step explanation:
Add it up to together by removing the -
2-2 webassign: problems and exercisesFind the absolute maximum and absolute minimum values of f on the given interval.f(x) = 6x^3 − 9x^2 − 216x + 9, [−4, 5]absolute minimum absolute maximum
Answers
The absolute maximum value is 412 and the absolute minimum value is -617.
A function's absolute maximum point is the location at which it can reach its highest value. A similar absolute lowest point is where the function's maximum value is obtained.
The absolute maximum and minimum values of f(x) = 6x^3 − 9x^2 − 216x + 9 on the interval [-4, 5] can be found using the First and Second Derivative Tests.
First, find the critical points of f(x) by setting its first derivative equal to zero and solving for x:
f'(x) = 18x^2 - 18x - 216 = 0
Using the quadratic formula, we get x = 4,-3.
Next, use the second derivative test to determine if the critical points are maxima or minima:
f''(x) = 36x - 18
At x = 4, f''(x) > 0, so x = 6 is a local minimum.
At x = -3, f''(x) < 0, so x = -9 is a local maximum.
Finally, check the endpoints of the interval to see if they contain the absolute maximum or minimum:
At x = -4, f(-4) = 6(-4)^3 - 9(-4)^2 - 216(-4) + 9 = 345
At x = 5, f(5) = 6(5)^3 - 9(5)^2 - 216(5) + 9 = -546
At x= 4, f(4) = -617
At x= -3, f(-3) = 412
Therefore, the absolute maximum value is 412 and the absolute minimum value is -617.
To know more about absolute maximum refer to:
brainly.com/question/29030328
#SPJ4
Please help ASAP!!!!
Answers
Answer:
It'll have an open circle on both 7 and 21, with a line connecting.
Which is none of the options, unless one isn't shown?
Step-by-step explanation:
-23 > -4x + 5 > -79
So:
-23 > -4x + 5
-23 - 5 > -4x
-4x < -28
x > -28 / -4
x > 7
-4x + 5 > -79
-4x > - 79 - 5
-4x > -84
x < -84 / -4
x < 21
find the critical numbers of the function on the interval 0 ≤ θ < 2π. g(θ) = 4 θ - tan(θ)
Answers
The critical numbers of g(θ) on the interval 0 ≤ θ < 2π are: θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.
To find the critical numbers of g(θ) = 4θ - tan(θ) on the interval 0 ≤ θ < 2π, we need to find the values of θ where the derivative of g(θ) is equal to 0 or undefined.
First, we find the derivative of g(θ) using the chain rule and quotient rule:
g'(θ) = 4 - sec²(θ)
To find where g'(θ) is equal to 0, we set the derivative equal to 0 and solve for θ:
4 - sec²(θ) = 0
sec²(θ) = 4
Taking the square root of both sides, we get:
sec(θ) = ±2
Since sec(θ) = 1/cos(θ), we can rewrite this as:
cos(θ) = ±1/2
We know that on the interval 0 ≤ θ < 2π, the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.
Therefore, we need to find the values of θ in the first and fourth quadrants where cos(θ) = 1/2, and the values of θ in the second and third quadrants where cos(θ) = -1/2.
For cos(θ) = 1/2, we have:
θ = π/3 or 5π/3 in the first quadrant
θ = 7π/3 or 11π/3 in the fourth quadrant
For cos(θ) = -1/2, we have:
θ = 2π/3 or 4π/3 in the second quadrant
θ = 8π/3 or 10π/3 in the third quadrant
Therefore, the critical numbers of g(θ) on the interval 0 ≤ θ < 2π are:
θ = π/3, 2π/3, 4π/3, 5π/3, 7π/3, 8π/3, 10π/3, and 11π/3.
Learn more about critical numbers
brainly.com/question/29743892
#SPJ11
Needing help...again giving out many points if right (90 to be exact)
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x=12
Step-by-step explanation:
4x-10=3x+2
Subtract 3x on both sides:
x-10=2
Add 10 on both sides:
x=12
Hope this helps!
A square sheet of paper has area $15. The front side is white and the back side is black. A corner of the sheet is lifted and placed so that the crease is at a $45 angle. If the fold is such that the visible black area is equal to the visible white area, how many centimeters long is the crease?
Answers
The length of the crease is √10cm
How to determine the lengthTo determine the length of the crease, we have;
Let the equal sides of the black triangle = x = length of the fold
From the information given, we have the area of the square is 15cm²
Then, we have;
The area of this triangle = (1/2)x² = x²/2
Substitute the value and we get that the length of one side of the square is:
= √15 cm
For the whit area = x ( √15 -x) + √15 ( √15 - x)
= (x + √15) (√15 - x)
= -x² + 15
Since the two areas are equal, we have;
x²/2 = -x² + 15
add x² to both sides
3x² / 2 = 15
multiply both sides by 2/3
x² = 10
take the positive root of both sides
x = √10cm
Learn more about square at: https://brainly.com/question/25092270
#SPJ4
A car wash detailed 288 cars in 8 hours. At what rate did the car wash detail cars in cars per hour?
A.
34 cars per hour
B.
37 cars per hour
C.
36 cars per hour
D.
35 cars per hour
Answers
Answer:
a
Step-by-step explanation:
Which of these sets of side lengths are Pythagorean triples? Check all that apply.
A. 10, 24, 26
B. 14, 48, 49
C. 9, 12, 16
D. 9, 40, 41
E. 15, 20, 25
Answers
The sets of lengths that are Pythagorean triples are:
A. 10, 24, 26
D. 9, 40, 41
E. 15, 20, 25
What is a Pythagorean Triple?A Pythagorean triple can be described as a set of three numbers of the side lengths of a right triangle whereby the square of the longest side is equal to the sum of the squares of the two other sides.
For 10, 24, 26, we have:
10² + 24² = 26²
676 = 676 [true]
The set, 10, 24, 26 is a Pythagorean triple.
For 14, 48, 49, we have:
14² + 48² = 49²
2,500 = 2,401 [not true]
The set, 14, 48, 49, is NOT a Pythagorean triple.
For 9, 12, 16, we have:
9² + 12² = 16²
225 = 256 [not true]
The set, 9, 12, 16, is NOT a Pythagorean triple.
For 9, 40, 41, we have:
9² + 40² = 41²
1,681 = 1,681 [true]
The set, 9, 40, 41, is a Pythagorean triple.
For 15, 20, 25, we have:
15² + 20² = 25²
625 = 625 [true]
The set, 15, 20, 25, is a Pythagorean triple.
The correct set of options are, A, D, and E.
Learn more about the Pythagorean triple on:
https://brainly.com/question/11994763
#SPJ1
Kimberly has 2 1/3 bottles of milk in her refrigerator.
She used 3/4 bottle in the morning and 1 1/8 bottle in the afternoon.
How many bottles of milk does Kimberly have left over?
Answers
Answer:
1 3/20
Step-by-step explanation: