Type the correct answer in the box.
A printer creates a right triangular card where the hypotenuse, h, is three times as long as the shorter leg. What is the length of the longer leg, l, in terms of h? Write the answer in simplest form by replacing a, b, and c with the correct values.
Answers
Answer:
\(l=\dfrac{2\sqrt{2}h}{3}\)
Step-by-step explanation:
Define the variables:
Let h be the hypotenuse of the right triangle.Let s be the shorter leg of the right triangle.Let l be the longer leg of the right triangle.If the hypotenuse is three times as long as the shorter leg, then:
\(\implies h=3s\)
\(\implies s=\dfrac{h}{3}\)
Pythagoras Theorem explains the relationship between the three sides of a right triangle:
The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.Using Pythagoras Theorem and the given values, create an equation and solve for l:
\(\implies h^2=s^2+l^2\)
\(\implies h^2=\left(\dfrac{h}{3}\right)^2+l^2\)
\(\implies l^2=h^2-\left(\dfrac{h}{3}\right)^2\)
\(\implies l^2=h^2-\dfrac{h^2}{3^2}\)
\(\implies l^2=h^2-\dfrac{h^2}{9}\)
\(\implies l^2=\dfrac{9h^2}{9}-\dfrac{h^2}{9}\)
\(\implies l^2=\dfrac{9h^2-h^2}{9}\)
\(\implies l^2=\dfrac{8h^2}{9}\)
\(\implies \sqrt{l^2}=\sqrt{\dfrac{8h^2}{9}}\)
\(\implies l=\dfrac{\sqrt{8}\sqrt{h^2}}{\sqrt{9}}\)
\(\implies l=\dfrac{2\sqrt{2}h}{3}\)
Therefore, the length of the longer leg in terms of h is:
\(\boxed{ l=\dfrac{2\sqrt{2}h}{3}}\)
Related Questions
Please just help with these questions!
Answers
5/7= -----------
0.714285
Convert the fraction to a decimal by dividing the numerator by the denominator.
6/10= 0.6
Convert the fraction to a decimal by dividing the numerator by the denominator.
16/20= 0.8
Convert the fraction to a decimal by dividing the numerator by the denominator.
9/10= 0.9
Convert the fraction to a decimal by dividing the numerator by the denominator.
Write a divison problem whose quotient has its first digit in the hundreds place
Answers
Answer: 500/2 = 250
Step-by-step explanation:
The quotient only has to have an answer with the first digit in the hundreds place.
This means you can really use any other equation like:
13,750/25 = 550
8,775/13 = 675
A pair of shoes usually sells for $63. If the shoes are 40% off, and a sales tax of 7% is applied to
the discounted cost, what is the total price of the shoes, including tax? Round your answer to
the nearest penny
A.$37.08
B.$40.45
C.$40.82
D.$42.2
Answers
Answer: 40.45 or B
Step-by-step explanation:
63 x 0.6(100%-40%) = 37.8
37.8 x 1.07 = 40.446
40.446 rounded is
40.45
simplify 4y - (7y + 3) + 12
Answers
Step-by-step explanation:
..... . .. . . . . . .. . . .. .
10. Which of the following numbers are perfect squares?
(1) 36
(ii) 82
(iii) 120
(vi) 100
(vii) 343
(viii) 1296
(iv) 256
(ix) 396
Answers
Hope this help
Answer:1, 4, 6, & 7 (or 26, 100, 1296, 256)
Step-by-step explanation:
1. 36 is a perfect square because 6*6=36
2. 82 is not a perfect square
3. 120 is not a perfect square
4. 100 is a perfect square because 10*10=100
5. 343 is not a perfect square
6. 1296 is a perfect square because 36*36=1296
7. 256 is a perfect square because 16*16=256
8. 396 is not a perfect square
Hope this helps! I would really appreciate if you marked this as brainliest :)
i need help it is due today
Answers
Answer:
8
Step-by-step explanation:
Using the Heron's formula we can find that the total area of the triangle is 84 inches.
Then, to find the height of the triangle, you have to multiply the area by 2 since the formula for the area of a triangle is (h*b)/2
Now, when we multiply 84 and 2 we get 168, so you have to divide 168 by 21 to find 8.
0.26÷1.56 ...........................................................................................
Answers
Answer:the answer is 0.16 in the calculator its 0.166666666667 but just take the first 3 numbers at thats your answer.
Step-by-step explanation:
You are running a lower tail test and obtained a p-value equal
to 0.8. If your sample contains 35 observations, what is the value
of the t-statistic?
Answers
The value of the t-statistic is 0.
Given,
Sample size n = 35 p-value = 0.8
Lower tail test
We know that t-value or t-statistic can be calculated by using the formula,
t-value or t-statistic = [x - μ] / [s / √n] where,
x = sample
meanμ = population mean,
here it is not given, so we consider as x.s = standard deviation of the sample.
n = sample size
Now we can use the formula for t-value or t-statistic as,t-value or t-statistic = [x - μ] / [s / √n]
Since the test is a lower tail test, then our null hypothesis is,
Null Hypothesis : H0: μ ≥ 150 (Claim)
Alternate Hypothesis : H1: μ < 150 (To be proved)
Now the claim is that mean is greater than or equal to 150.
Then the sample mean is also greater than or equal to 150 i.e., x ≥ 150.
Now the sample mean is,x = 150
From the given p-value, we know that, p-value = 0.8
And the level of significance, α = 0.05
Since p-value > α, we can say that we fail to reject the null hypothesis.
Hence we accept the null hypothesis.i.e., μ ≥ 150
Then the t-value can be calculated as,t-value or t-statistic =
[x - μ] / [s / √n] = [150 - 150] / [s / √35]
= 0 / [s / 5.92] (since √35 = 5.92)
= 0
Now the t-value is 0.
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Find the discounted price of the item.
Jacket: $125.00
Discount: 25%
Answers
$93.75 is the discounted price
what is \( {i}^{84} \)I need extra help with imaginary numbers
Answers
The given expression is
\(i^{84}\)Remember that i = -1, so.
\((-1)^{84}\)We know by definition that all powers with even exponents give a positive number. So,
\((-1)^{84}=1\)Therefore,\(i^{84}=1\)hey there, can help me to solve this
what is the value of x, if
\(x = \cos {}^{2} (60) + \sin {}^{2} (60) \)
Answers
Answer:
may be the answer is 120
Find the value of x in kite EFGH
Answers
Answer:
x = 105
Step-by-step explanation:
the sum of all interior angles of any four-sided figure has 360 degrees
∡F and ∡H are equal
add all four expressions and set them equal to 360
x + (x + 5) +( x + 5) + (140 - x) = 360
combine like terms
2x + 150 = 360
2x = 210
x = 105
The value of x = 105
The sum of all interior angles of any four-sided figure has 360 degrees
∡F and ∡H are equal
Add all four expressions and set them equal to 360
x + (x + 5) +( x + 5) + (140 - x) = 360
combine like terms
2x + 150 = 360
2x = 210
x = 105
What are interior angles for instance?Interior angles are those that lie in the interior of a polygon. For instance, a triangle has three interior angles. The other way to outline indoor angles is "angles enclosed in the interior place of two parallel traces while intersected by means of a transversal are known as interior angles".
The exterior is described by means of Merriam-Webster as "being on an outside surface: located at the outside" and "appropriate for use on door surfaces." Defines outdoors as "outer; being on the outer side," and "intended or suitable for outside use."
The system for calculating the scale of an interior perspective is the interior perspective of a polygon = sum of interior angles ÷ wide variety of aspects. The sum of outside angles of a polygon is 360°. The formulation for calculating the size of an outdoors perspective is the outside attitude of a polygon = 360 ÷ wide variety of aspects.
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She needs to unpack 38 boxes. if each box takes the same amount of time. and she can unpack 4 boxes in 3 hours, how long will it take to unpack 38 boxes
Answers
Answer:
It will take 28.5 hours
Step-by-step explanation:
Make the boxes amount compatible to divide with 38
4/2=2
3/2=1.5
When you divide one part of the boxes and hours, you divide the other half too. So you divide 3 by 2, which is 1.5
Then you divide 38 by 2 which is 19
Then 19 times 1.5 to find out how many hours, which gives you 28.5
How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent 3
x
+
y
=
−
3
and 6
x
−
6
y
=
−
30
?
Answers
The system of equations is consistent and has a unique solution at (-4, 1).
To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.
The given system of equations is:
1) 3x + y = -3
2) 6x - 6y = -30
Let's graph these equations:
For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.
For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.
Now, let's plot these lines on a graph:
The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).
The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).
Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).
Now, let's analyze the system:
Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).
In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.
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Pre-LAB ASSIGNMENT After teading through the introduction and skimming the procedure, complete the pre-lab assignment, which is to be handed in at the beginning of lab class session. INTRODUCTION Chemical reactions are often accompanied by formation of a precipitate, evolution of a gas, a change in color, and/or a pronounced temperature change. In this experiment, you will observe these characteristics of chemical reactions as copper is cycled through a series of reactions that produce a number of compounds. The cycle begins with cogysr metal and ends with cogner metal. Because no copper is added or removed between the beginning and end of the experiment, and because each reaction goes to completion, you should theoretically be able to quantitatively recover all the copper you stanted with as long as you are careful and skillful. This is an example of the law of conservation of matter, which states that matter is neither created nor destroyed during a chemical reaction. In the end, you will compare the mass of the copper you recovered to the mass of your starting material to determine how well you were able to carry out the experimental techniques with the equipment available. Three major types of reactions are encountered in this experiment, including precipitation reactions, redox reactions, and acid-base reactions. Precipitation reactions result in the formation of a solid when two solutions are mixed. The solid is called a precipitate (ppt). You observed several examples of this type of resction in the last experiment. Redox reactions involve the transfer of electrons from one chemical substance to another. As a result of the process, one substance loses electrons and another gains them. The substance that loses electrons becomes more positive in charge, and is said to be oxidized. The substance gaining electrons becomes more negative in charge and is said to be reduced. "Redox" is a combination of these terms. Redox reactions often involve the reduction (Cu
2+
to Cu) or the oxidation (Cu
to
Cu
2
) of a metal. Acid-base reactions in general are reactions involving a transfer of hydrogen ions, H
’.
. from an acid substance to another substance - the base. If a reaction yoa observe in this experiment does not involve a precipitate or redox, then it is likely an acid-base H
+
transfer. Look to see if an acid or base substance is one of the reactants involved. As you carry out each step of the cycle of copper reactions think about what is happening in each reaction, and try to fit it into one of the three categories just deseribed. Along the way. you will ste how a single element and its ions can exhibit different colors depending both on the charge on the ion and the nature of its environment. SAFETY Safety information for this lab is mentioned throughoat the procetare, Be sure to pay attention to the safety concerns, Wear gloves! PRE-LAB #5: CHEMICAL REACTIONS OF COPPER: NAME: 1. What is/are the Question(s) of the Day? 2. Balance all five reactions listed in the procedure. (Write it in the procedure, not here). 3. Write the chemical equation for the reaction of copper (II) hydroxide and hydrochloric acid to give copper (II) chloride and water (note: don't forget to balance). This is an example of an acid-base reaction. Label the acid and the base reactants. 4. Write the formula and name for the solid that copper (HI) hydroxide becomes when beated. 5. Watch the video posted on Brightspace to revicw about how to properly use an analytical balance. Outline the key steps below and state how many decimal places can be measured (are signiffeant) with this type of balance? How many decimal places can be measure with a standardrop-loading balance? 6. A student was given a sample of Cu wire that weighed 0.3015 grams, After completing the experiment, she recovered only 0.2331 grams of solid copper. What was her percent recovery? See Tutorial 1, p. 140 in this lab manual.
Answers
The main questions in the pre-lab assignment are:
1. What is/are the Question(s) of the Day?
2. Balance all five reactions listed in the procedure.
3. Write the chemical equation for the reaction of copper (II) hydroxide and hydrochloric acid to give copper (II) chloride and water.
4. Write the formula and name for the solid that copper (II) hydroxide becomes when heated.
5. Outline the key steps for properly using an analytical balance and indicate the number of decimal places that can be measured.
6. Calculate the percent recovery for a student who obtained 0.2331 grams of solid copper from a sample that initially weighed 0.3015 grams.
In the given pre-lab assignment, there are several questions and tasks related to the upcoming lab session on the chemical reactions of copper. The first question asks about the "Question(s) of the Day," which is not explicitly mentioned in the provided text. It might refer to the specific focus or objectives of the lab session.
The second task requires balancing all five reactions listed in the procedure, which is expected to be completed in the designated procedure section of the assignment, not in this particular section.
The third question asks to write the chemical equation for the reaction between copper (II) hydroxide and hydrochloric acid, producing copper (II) chloride and water. This reaction is an example of an acid-base reaction. In the equation, it is important to label the acid and base reactants.
The fourth task involves writing the formula and name for the solid that copper (II) hydroxide becomes when heated. The provided information does not mention the exact outcome, so it might be necessary to refer to additional resources or experimental data to determine the formula and name of the resulting solid.
The fifth task is to outline the key steps for properly using an analytical balance. The explanation should also include the number of decimal places that can be measured with this type of balance. It is important to follow the guidelines provided in the video posted on Brightspace, which will likely cover the necessary steps for accurate measurements using an analytical balance.
The final task involves calculating the percent recovery for a student who obtained 0.2331 grams of solid copper from a sample initially weighing 0.3015 grams. The formula for percent recovery is determined by dividing the actual yield (0.2331 g) by the theoretical yield (0.3015 g) and multiplying by 100%. The resulting percentage indicates how successful the student was in recovering the copper.
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Can someone plz help me with this one problem!!!
Answers
Answer:
Add all the given side lengths:
1 + 16 + 16 + 4 = 37!
In the diagram below of triangle KLM, N is a midpoint of KL and P is a midpoint
of LM. If mZPNL = 2x + 61, and MKN = 97 - 7x, what is the measure of
ZPNL?
Answers
Answer:
Solution:
(1/12)^(-2b) * 12^(-2b+2) = 12
(12^-1)^(-2b) (12)^(-2b+2) = 12
(12^2b)(12)^(-2b+2) = 12
12^(2b-2b+2) = 12
12^2 = 12
144 does not equal 12
No solution.
Step-by-step explanation:
The measure of angle PNL will be equivalent to 69 degrees.
What is triangle?A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -
∠x + ∠y + ∠z = 180°
The sum of two sides of a triangle is greater then the third side. Mathematically -
a + b > c
There are different types of triangles such as -
equilateral triangle , scalene triangle , isosceles triangle etc.
Given is a triangle KLM such that N is a midpoint of KL and P is a midpoint of LM.
Triangles LMP and LKM are similar to each other. Therefore, PN will be parallel to MK. So angle PNL will be equal to angle MKN. Therefore -
2x + 61 = 97 - 7x
9x = 97 - 61
9x = 36
x = 4
So, angle PNL will be equal to -
2 x 4 + 61
69 degrees
Therefore, the measure of angle PNL will be equivalent to 69 degrees.
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A sporting goods store specializes in mountain bikes. Each week, two dozen mountain bikes are randomly selected from the store's warehouse to undergo a performance test.
What is the population for the performance test?
A.
The population is all of the mountain bikes in the store's warehouse.
B.
The population is the salespersons at the store.
C.
The population is all of the merchandise sold by the store.
D.
The population is the mountain bikes that are not randomly selected
Answers
Answer:
A
Step-by-step explanation:
A population is a set of similar items or events which is of interest for some question or experiment.
Could someone please help me? Thank you and explain the work because I don’t get this
Answers
Answer:
5.59 times per second.
Step-by-step explanation:
Direct variation is in the form:
\(y=kx\)
Where k is the constant of variation.
Inverse variation is in the form:
\(\displaystyle y=\frac{k}{x}\)
In the given problem, the frequency of a vibrating guitar string varies inversely as its length. In other words, using f for frequency and l for length:
\(\displaystyle f=\frac{k}{\ell}\)
We can solve for the constant of variation. We know that the frequency f is 4.3 when the length is 0.65 meters long. Thus:
\(\displaystyle 4.3=\frac{k}{0.65}\)
Solve for k:
\(k=4.3(0.65)=2.795\)
So, our equation becomes:
\(\displaystyle f=\frac{2.795}{\ell}\)
Then when the length is 0.5 meters, the frequency will be:
\(\displaystyle f=\frac{2.795}{.5}=5.59\text{ times per second.}\)
A study by a business professor at Arizona State University showed that, on average, his students' grades went down one full grade for every __________ classe(s) they missed.
Answers
A study by a business professor at Arizona State University found that students who missed two classes had grades that were one full letter grade lower than those who attended all classes. This suggests that attending class is essential for academic success.
There are a few reasons why missing class can lead to lower grades. First, students who miss class may miss important information that is covered in lectures. Second, they may miss opportunities to ask questions and get help from the professor. Third, they may fall behind on assignments and readings.
To avoid falling behind, it is important to attend all classes. If you must miss class, be sure to get notes from a classmate and ask the professor for any missed assignments or readings. By attending class and staying on top of your work, you can improve your chances of academic success.
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Complete question:
A study by a business professor at Arizona State University showed that, on average, is students' grades wet down one full grade for every _ classes they missed.
a. one
b. two
c. three
d. four
which graph of ordered pais shows a proportional relationship? i need help lol
Answers
rate x time = distance how far will a boat travel moving 20 km per hour for 3.5 hours?
Answers
the boat will travel 70 kilometers in 3.5 hours when moving at a rate of 20 kilometers per hour.
To calculate the distance traveled by a boat, we can use the formula: Rate x Time = Distance.
In this case, the rate of the boat is 20 km per hour, and the time is 3.5 hours.
Using the formula, we have:
Distance = Rate x Time
Distance = 20 km/h x 3.5 hours
Calculating the result:
Distance = 70 km
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Isoke is solving the quadratic equation by completing the square. 10x2 40x-13=0 10x2 40x=13 a(x2 4x)=13
Answers
The value of a is 10 by solving the quadratic equation by completing the square method.
In this question,
Completing the square is a method in algebra that is used to write a quadratic expression in a way such that it contains the perfect square. It is a method that is used for converting a quadratic expression of the form ax^2 + bx + c to the vertex form a(x - h)^2 + k.
The quadratic equation is
10x^2 + 40x - 13 = 0
Solving the quadratic equation by completing the square as
Step 1:
10x^2 + 40x = 13
Step 2:
10(x^2 + 4x) = 13
Thus on comparing the step 2 with the equation a(x^2 + 4x) = 13, the value of a is 10.
Hence we can conclude that the value of a is 10 by solving the quadratic equation by completing the square method.
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HELP!! The aquarium has 6 fewer yellow fish than green fish. 40 percent of the fish are yellow. How many green fish are in the aquarium? Show your work.
Answers
Answer:
Answer is 36 I think
Step-by-step explanation:
im not sure
2. How many bits are needed to represent decimal values ranging from 0 to 12,500?
Answers
To represent decimal values ranging from 0 to 12,500, we need 14 bits.
To determine the number of bits needed to represent decimal values ranging from 0 to 12,500, we need to find the smallest number of bits that can represent the largest value in this range, which is 12,500.
The binary representation of a decimal number requires log base 2 of the decimal number of bits. In this case, we can calculate log base 2 of 12,500 to find the minimum number of bits needed.
log2(12,500) ≈ 13.60
Since we can't have a fraction of a bit, we round up to the nearest whole number. Therefore, we need at least 14 bits to represent values ranging from 0 to 12,500.
Using 14 bits, we can represent decimal values from 0 to (2^14 - 1), which is 0 to 16,383. This range covers the values 0 to 12,500, fulfilling the requirement.
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y=2x+6,2x-y=2 system of equation
Answers
Jack's father is three times older than Jack. Five years ago, the sum of their ages was 34. How old is Jack's father now?.
Answers
Answer:
jacks father is x
jack is 3x
34 =
Please help
5(-3+ k) = 20
Answers
Hey there!
5 (-3 + k) = 20
-15 + 5k = 20
5k = 20 + 15
5k = 35
k = 35 ÷ 5
k = 7
Hope it helps ya!
\(\boxed{\underline{\bf \: ANSWER}}\)
\( \tt \: 5( - 3 + k) = 20 \\ \tt = (5 \times - 3 )+( 5 \times k) \\ = \underline{ \bf{ - 15 + 5k}}\)
Hope it helps!
RainbowSalt2222
Show that the scaled symmetric random walk {W() (t): 0 ≤ t ≤ T} converges in distribution to the Brownian motion.
Answers
The scaled symmetric random walk {W(t) : 0 ≤ t ≤ T} converges in distribution to the Brownian motion. Therefore, as T tends to infinity, the scaled symmetric random walk converges in distribution to the Brownian motion.
The scaled symmetric random walk {W(t) : 0 ≤ t ≤ T} is a discrete-time stochastic process where the increments are independent and identically distributed random variables, typically with zero mean. By scaling the random walk appropriately, we can show that it converges in distribution to the Brownian motion.
The Brownian motion is a continuous-time stochastic process that has the properties of independent increments and normally distributed increments. It is characterized by its continuous paths and the fact that the increments are normally distributed with mean zero and variance proportional to the time interval.
To show the convergence in distribution, we need to demonstrate that as the time interval T approaches infinity, the distribution of the scaled symmetric random walk converges to the distribution of the Brownian motion. This can be done by establishing the convergence of the characteristic functions or moment-generating functions of the random walk to those of the Brownian motion.
The convergence in distribution implies that as T becomes larger and larger, the behavior of the scaled symmetric random walk resembles that of the Brownian motion. The random walk exhibits similar characteristics such as continuous paths and normally distributed increments, resulting in convergence to the Brownian motion.
Therefore, as T tends to infinity, the scaled symmetric random walk converges in distribution to the Brownian motion.
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Knowing your personal strengths and weaknesses will help to keep your goal a. within your skills and abilities c. both of these b. within its timeline d. none of these please select the best answer from the choices provided a b c d
Answers
The correct choice is within your skills and abilities.
Once you get to determine things you are capable of and things you are not capable of, you will be able to concentrate on your strengths more. This will in turn produce big results as compared to if you opted to concentrate on your weaknesses.
It will also result in no or less time wasted in doing what you are less capable of.
Its almost close to impossible to be able to do everything. Each person is gifted in a certain area or skill or capability. We are all different and that's okay.
Its so important to concentrate in the areas you are more comfortable with. This will help you much with improving your skills and abilities.
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Answer:
Step-by-step explanation:
a you just had to say a