Using the 45°-45°-90° triangle theorem in a right triangle, where 'a' represents the triangle's leg that is also the trapezoid's height, 'h' equals 'a' and the hypotenuse is 'a' times √2. Additional information would be needed to solve for a numerical value of 'h'.
Explanation:In this problem, the wall's shape is a trapezoid, and we are using the 45°-45°-90° triangle theorem to find 'h', the height of the wall. We know in a 45°-45°-90° triangle, the two legs are congruent (same length), and the length of the hypotenuse is √2 times the length of a leg (based on Pythagorean theorem). In this case, if 'a' is the length of the triangle's leg connected to the rectangle, then 'h' would be equal to 'a' (since they are the legs in a 45-45-90 triangle), and the hypotenuse would be a√2.
Given an additional variable or measurement in this problem such as the length of the wall or the hypotenuse of the triangle, we could plug it in to solve for 'h'. Without additional information, the exact numerical height cannot be determined.
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50779 divided by 590 equals
What is 51,908 rounded to the nearest hundred dollar?
Suppose that x is the age of a husband, and y is the age of his wife. if men always marry women who are 3 years younger than themselves, what is the equation for y (wife's age) as a function of x (husband's age)?
For each function f(n) and time t in the table, determine the largest size n of a problem that can be solved in time t, assuming that the algorithm to solve the problem takes f(n) microseconds
The question involves estimating the largest problem size a one-teraflop computer can solve in a given time, by equating the time complexity function of the problem to the number of operations the computer can perform per second, and solving for n.
The task is to estimate the largest problem size n that can be solved by a one-teraflop machine within a given time t. A teraflop machine is capable of performing 1012 operations per second. To determine n, we must consider the time complexity function f(n) that describes how the number of operations grows with the size of the problem. Given that the machine can perform 1012 instructions per second, and t is measured in microseconds, we first convert t to seconds.
For example, if the function f(n) follows a linear time complexity, such as f(n) = n, and the computation time t is 1 second, the largest problem size that can be solved is 1012, since the machine can perform 1012 operations in one second.
If the computational complexity is higher, say quadratic as f(n) = n2, we would solve for n in the equation n2 = 1012 to find the largest n that can be solved within 1 second.
Similarly, for more complex functions, we would find the value of n that satisfies the equation f(n) = 1012 * t in seconds, ensuring the result is within the operational constraints of the machine.
14-9x=-8(10+x) slove and show check
Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes. Find the distance Fritz travels to work if the train travels an average of 32 miles per hour faster than his driving. Assume that the train travels the same distance as the car.
The distance Fritz travels to work is 24 miles if Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
Let the distance Fritz travels to work is x.
As we know,
1 hour = 60 minutes
36/60 = 0.6 hrs
20/60 = 0.33 hrs
Speed = distance/time
Train speed - drive speed = 32
x/0.33 - x/0.6 = 32
After simplification:
9d - 5x = 96
4x = 96
x = 96/4
d = 24 miles
Thus, the distance Fritz travels to work is 24 miles if Fritz drives to work his trip takes 36 minutes, but when he takes the train it takes 20 minutes.
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Write y = 2x + 3 using function notation
Find the standard equation of the circle having the given center (6,-2) and radius 1/5.
Toby is making a picture graph each picture of a book is equal to 2 books he read the row for month 1 has 3 pictures of books how many books did T
oby read during month 1
Toby read 6 books during the first month by using the picture graph where each picture represents 2 books.
To determine how many books Toby read during month 1, follow these steps:
Understand each picture of a book represents 2 books read.Observe that Toby has 3 pictures of books for month 1.Multiply the number of pictures by the number of books each picture represents: 3 pictures * 2 books per picture = 6 books.Toby read 6 books during the first month.
What is 160,656 rounded to the nearest ten thousandth?
at 7 p.m. last night, the temputure was 10 degrees. At 7 a.m. the next morning, the temputure was -2 degrees. By how much did the temputure change From 7 p.m. to 7 a.m.
10 to 0 =10
0 to -2 = 2
10+2 =12
it changed by 12 degrees
Avery's class sold candy bars for a fundraiser. There were 20 bars in each box. Avery sold 4 boxes and an additional 8 bars. Express the total number of boxes that Avery sold as a mixed number. How many candy bars did Avery sell?
Answer:
she sold 4 2/5 boxes of candy bars.
In total, she sold 88 bars.
:))
Step-by-step explanation:
Go has 3 orange pick for every 2 green if ther are 25 picks in all how many picks are orange
Answer:
15
Step-by-step explanation:
It has been given that Go has 3 orange pick for every 2 green.
Hence, the ratio of Go to Green is 3:2
Total number of picks = 25.
Number of picks of orange in 25 picks is given by
[tex]\frac{3}{3+2}\times25[/tex]
Simplifying, we get
[tex]=\frac{3}{5}\times25[/tex]
Multiply the numerator, we get
[tex]=\frac{75}{5}[/tex]
Dividing, we get
[tex]=15[/tex]
Hence, the number of picks of orange are 15.
if bx-2=k then x equal
Tom jogged 3/5 mile on Monday and 2/6 mile on Tuesday how much farther did Tom joy on Monday then on Tuesday
An acidophilus culture containing 150 bacteria doubles in population every hour. Predict the number of bacteria after 12 hours.
The pie below is cut into 6 equal slices. Show shade 2/3 of this pie.
Can someone please help I need a clear explanation on how to solve this equation.
At Avery Middle School, 273 students responded to a survey asking whether a Bulldog, a Lion, or a Tiger should be the new school mascot. Four times as many students chose Bulldog as chose Tiger. Twice as many students chose Lion as chose Tiger. How many students chose Lion?
Answer:
78 students chose lion.
Step-by-step explanation:
Let x students chose tiger.
Let y students chose bull dog.
Let z students chose lion.
Total students = 273
[tex]x+y+z=273[/tex] ....(1)
Four times as many students chose Bulldog as chose Tiger.
[tex]y=4x[/tex]
Twice as many students chose Lion as chose Tiger.
[tex]z=2x[/tex]
Substituting the values of y and z in (1)
[tex]x+4x+2x=273[/tex]
=> [tex]7x=273[/tex]
x = 39 (students who chose tiger)
We have to find students who chose Lion or z (defined above)
[tex]z=2x[/tex]
[tex]z=2(39)[/tex]
So, z = 78
Therefore, 78 students chose lion.
Find a ·
b. |a| = 60, |b| = 30, the angle between a and b is 3π/4.
To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
Explanation:To find the dot product of vectors a and b, we can use the formula: a · b = |a| |b| cos θ, where |a| and |b| are the magnitudes of vectors a and b, and θ is the angle between them.
In this case, |a| = 60 and |b| = 30. The angle between a and b is given as 3π/4.
Therefore, a · b = 60 * 30 * cos (3π/4) = 60 * 30 * (-√2/2) = -1800√2.
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount xx (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Write your equation so that the units on each side of the equation are dollars per day.
Celia bought a bag of 12 goldfish for $3. What is the cost of 1 goldfish?
we know that
Celia bought a bag of [tex]12[/tex] goldfish for [tex]\$3[/tex]
so
by proportion
Find the cost of [tex]1[/tex] goldfish
[tex]\frac{3}{12} \frac{\$}{goldfish} =\frac{x}{1} \frac{\$}{goldfish} \\ \\x=3/12 \\ \\x=\$0.25[/tex]
therefore
the answer is
The cost of one goldfish is [tex]\$0.25[/tex]
Celia will pay 0.25 dollars for 1 goldfish. The cost of 1 goldfish is $ 0.25
The Total number of goldfish purchased is 12.
Cost price for 12 goldfish is $ 3.
Let the price of 1 goldfish be x dollars.
Therefore,
[tex]\begin{aligned}x \times\$12&=\$3\\x&=\dfrac{3}{12}\\x&=0.25\end{aligned}[/tex]
Hence, the cost of 1 goldfish is 0.25 dollars.
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15/16 is 1 sixteenth groups of what size
Differentiate
y=(6x)/(1-cot(x))
99 POINTS POSSIBLE!!!! I have a lot of math problems.....Please show your work also:) I will give Brainiest too!
1.Chase picked three buckets of blackberries that weigh: 2.79 pounds, 2.45 pounds, and 2.62 pounds. What is the average weight for the three buckets?
2. Ashley is baking cookies for math class. The recipe calls for 4 4/5 cups of flour. Ashley has to make 1 1/3 times the recipe to feed the whole class. How much flour does Ashley need?
3. Jordan finished her homework in 1 1/2 hours. It took Kasey 3/4 an hour longer than Jordan to finish her homework. How long did it take Kasey?
4. 32.5 divided by -0.08
5. 4.3x= 81.7 (Decimal Equation)
Thank you for helping me if you did!!!!!!!! I really appreciate it very much!!!!!!!
Hello!
1) 2.62
2) 4.8
3) 6.4
3) 2.25 hours
4) −406.25
5) X=19
I hope it helps!
how do you equally divide 12 cookies with 8 people. what fraction of cookies would each person receive?
Final answer:
To equally divide 12 cookies among 8 people, each person would receive 1 1/2 or 1.5 cookies, which is a fraction of 3/2 per person when simplified.
Explanation:
To divide 12 cookies equally among 8 people, we need to perform a simple division operation where 12 (total number of cookies) is divided by 8 (number of people). Mathematically, this can be represented as 12/8 which simplifies to 1 1/2 or 1.5 cookies per person. This means that each person would receive one and a half cookies.
If the problem requires the answer as a fraction, we can simplify 12/8 by dividing both numerator and denominator by their greatest common divisor, which is 4 in this case. Thus, we get 12/8 = (12÷4) / (8÷4) = 3/2. Therefore, each person gets 3/2 or one and a half cookies.
What is 8.478 in expanded form
The expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
Given:
The given number is [tex]8.478[/tex].
To find:
The expanded form of the given number.
Explanation:
Write the given number as the sum of the place values of its all digits to find the expanded form of the given number.
[tex]8.478=8+0.4+0.07+0.008[/tex]
Therefore, the expanded form of the given number is [tex]8+0.4+0.07+0.008[/tex].
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a jet descended 0.44 mile in 0.8 minute. What was the plane's average change of altitude per minute?
The next train will arrive in 32 minutes and 30 seconds. In how many seconds will the next train arrive
For rhombus LMNO, m∠LON = 102° and NP = 5 units. Use the diagram of rhombus LMNO to find the missing measures. The measure of ∠LPM is °. The measure of ∠PMN is °. The length of LN is units.
Answer:
1. 90
2. 50
3. 10
Step-by-step explanation:
Complete the general form of the equation of a sinusoidal function having an amplitude of 1, a period of pi/2, and a vertical shift up 3 units.
y =
(I don't have the option to use the characters "/" or "[tex] \pi [/tex]" so they must not be in the answer.
Answer:
y = sin 4x + 3
Step-by-step explanation:
A sine function is represented as y = a sin(bx + c) + d
Given values in the question are a = amplitude = 1
period = π/2 = 2π/b
Vertical shift d = 3 units up.
Horizontal shift c = 0
Since 2π/b = π/2
[tex]b=\frac{2\pi }{\frac{\pi }{2}} =\frac{4\pi }{\pi }=4[/tex]
Now the sinusoidal function will be
y = 1. sin( 4x ) + 3
y = sin 4x + 3