What is the Pythagorean Theorem and what is the equation for it?
Answers
The Pythagorean Theorem is quite simply a mathematical equation used to determine the third side of a triangle. It can be used to find out ANY side of a given triangle.
For example, if you are given the hypotenuse of a triangle, as well as another leg, then you can quite simply plug everything in!
Here is the equation :
a² + b² = c²
Where :
a = random leg of the triangle
b = another random leg of the triangle
c = hypotenuse of the triangle
I've given you an example for future references, placed down below :)
~I hope this helped!~
Related Questions
Brody calculated the area of a square to be16/36 square foot. Which shows the side length of the square?
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s = √(16/36 ft^2) = 4/6 ft
The side length of the square is 2/3 ft, or 8 inches.
Gas prices in Cook county are at $3.30 per gallon. If a market scientist predicts a 20% increase in the price of gas in the coming month, what will the price of gas be?
Answers
$3.96 will be the new price of gas
The price of the gas is $3.96.
What is a percentage?A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.
Given:
Gas prices in Cook-County are at $3.30 per gallon.
If a market scientist predicts a 20% increase in the price of gas in the coming month,
that means,
100 + 20% = 120% increase = 1.2 in decimals.
The price of gas,
= 3.30 + 3.30 x 1.2
= 3.96
Therefore, the new price is $3.96.
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Kelly is having a party. She wants to make punch. The recipe for punch uses 3 pints of pineapple juice, 5 cups or orange juice, 1/4 gallon of lemonade, and 1 quart of apricot nectar. Kelly says her recipe will make 20 cups of punch. Is Kelly correct? Explain your answer. How does one arrive at the answer? Are all the ingredients added? Is anything multiplied?
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3 pints = 6 cups
5 cups = 5 cups
1/4 gallon = 4 cups
1 quart = 4 cups
Add all the ingredients.
6 + 5 + 4 + 4 = 19 cups
Therefore, Kelly does not make 20 cups of punch because her recipe is enough for only 19 cups of punch. All the ingredients are added and noting is multiplied.
Fawn plants 2/3 of the garden with vegetables. Her son plants the remainder of the garden. He decides to use 1/2 of his space to plant flowers and in the rest he plants herbs. What fraction of the entire garden is planted in flowers?
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Drawing it out helps too! Good luck!
what is the x intercept of the equation that passes through (1,-6) and is perpendicular to y=1/3x +1
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[tex]\bf slope = m\implies -3 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-6)=-3(x-1) \\\\\\ y+6=-3x+3\implies 0+6=-3x+3\implies 3=-3x\implies \cfrac{3}{-3}=x \\\\\\ -1=x\qquad \qquad \qquad \qquad \qquad \qquad \qquad (~-1~,~0~)[/tex]
Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.2, 0.4, and 0.4, respectively. what is the expected number of books a customer will purchase? the standard deviation of the customer's book purchases is
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x P(x)
0 0.2
1 0.4
2 0.4
Total .1.0
i] Expectation
Mean=Σxp
Variance=x²p-(∑xp)²
thus:
Mean=(0*0.2)+(1*0.4)+(2*0.4)
=0+0.4+0.8
=1.2
ii] Variance
Variance=[(0²*0.2)+(1²*0.4)+(2²*0.4)]-(1.2)²
=[0+0.4+1.6]-1.44
=0.56
hence:
standard deviation=sqrt(0.56)=0.74833
The expected number of books a customer will purchase is 1.2 books, and the standard deviation of their book purchases is approximately 0.78 books.
To find the expected number of books a customer will purchase,
use the formula for the expected value (also known as the mean) of a random variable:
Expected Value (μ) = Σ (x × P(x))
Where:
μ is the expected value.
x represents the possible values of the random variable (in this case, 0, 1, and 2).
P(x) is the probability associated with each value of x.
Probability of purchasing 0 books (P(0)) = 0.2
Probability of purchasing 1 book (P(1)) = 0.4
Probability of purchasing 2 books (P(2)) = 0.4
Now, calculate the expected value:
μ = (0 × 0.2) + (1 ×0.4) + (2 × 0.4)
μ = 0 + 0.4 + 0.8
μ = 1.2
To find the standard deviation (σ) of the customer's book purchases,
use the formula for the standard deviation of a discrete random variable:
Standard Deviation (σ) = √[Σ((x - μ)² × P(x))]
Where:
σ is the standard deviation.
x represents the possible values of the random variable.
μ is the expected value.
P(x) is the probability associated with each value of x.
In this case, you already calculated μ as 1.2, and you have the probabilities P(0), P(1), and P(2).
Now, calculate the standard deviation:
σ = √[((0 - 1.2)² × 0.2) + ((1 - 1.2)² × 0.4) + ((2 - 1.2)² × 0.4)]
σ = √[(1.44 ×0.2) + (0.16 × 0.4) + (0.64 × 0.4)]
σ = √[0.288 + 0.064 + 0.256]
σ = √0.608
σ ≈ 0.78
Therefore, the expected number and the standard deviation of books a customer will purchase is 1.2 books and approximately 0.78 books respectively.
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can someone help me with number 4
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Let n = number of nonmember tickets.
Let c = total cost
m number of member tickets cost 10m.
n number of nonmember tickets cost 24n.
The total cost is the sum of the two expressions.
c = 10m + 24n
Now we replace m w2 and n with 4, and we evaluate the expression.
c = 10m + 24n
c = 10(2) + 24(4)
c = 20 + 96
c = 116
Answer: The total cost is $116
The number of books borrowed from a library each week follows a normal distribution. When a sample is taken for several weeks, the mean is found to be 190 and the standard deviation is 30. There is a % chance that more than 250 books were borrowed in a week. ©
Answers
Answer:
2.28%
Step-by-step explanation:
Let X be the number of books borrowed from a library each week
Given that X is normal with mean = 190 and std dev = 30
Thus Z score would be
Z=[tex]\frac{x-190}{30}[/tex]
Required probability or chance = P(X>250)
=P([tex]z>\frac{250-190}{30}[/tex]
=P(Z>2)
=0.5-0.4772
=0.0228
=2.28%
Answer:
2.5 for plato
Step-by-step explanation:
#platolivesmatter
The sales tax in mike's state is 6%. mike bought a jetta having a sales tax of $820. what was the cost of the vehicle? round to the nearest dollar.
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because you would do 820 divided by 0.06 and you get 13,666.6667 which you round to 13,666.67
A farmer wants to build a rectangular garden 10ft long and 6ft wide. How many feet of fencing should he buy?
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Good luck, hope that helped.
The gift shop at Manatee mall was having a clearance sale everything was marked down 30% off the original price of a manatee that was $18 what is the clearance price
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Solve for C. See photo
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Select two rations that are equivalent to 3: 12.
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A sphere with a radius of 3 cm has the same volume as a cone with a radius of 6 cm. What is the height of the cone?
A) 2 cm
B) 3 cm
C) 4 cm
D) 5 cm
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Try this option:
[tex]if \ the \ volume \ of \ the \ sphere \ is \ the \ same \ one \ as \ a \ cone, \ then \ V_s=V_c; \ <=> \ \frac{4 \pi}{3}*3^3=\frac{1}{3} \pi*6^2*h_c; \ => \ h_c=3(cm)[/tex]
answer: B
B) 3 cm
Vsphere = [tex]\frac{4}{3}\pi r^{3} = \frac{4}{3}\pi(3)^{3} = 36\pi[/tex]
Vcone =
1
3
πr2h
36π =
1
3
π(6)2h
36π = 12πh
h = 3
Thus, the height is 3 cm.
Alternatively, the two equations could be set equal to each other and solved for the unknown height of the cone.
Please try this, I forget absolutely everything about rhombuses. Thanks for all the help, shouldn't be too hard
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the volume of a pyramid is, 1/3 ( base area)(height).
well, we know the base is a rhombus, and rhombuses diagonals meet at right-angles, therefore the center O has 4 right-angles where they meet.
since we know the angle at A, 50°, and since rhombuses are quadrilaterals with all equal sides, we know all the sides are 6 long, and the angle at C is 50° as well, and the remaining angles are 130°, as shown there.
now, if we tease out one of those triangles from the rhombus, as shown on the 1st section in the picture, we can say use the angle of 65° to get "x" and "y" lengths
[tex]\bf cos(65^o)=\cfrac{x}{6}\implies 6cos(65^o)=x \\\\\\ sin(65^o)=\cfrac{y}{6}\implies 6sin(65^o)=y[/tex]
now, we'll use those to get the area of the rhombic base.
and then onto the second section
is a right-triangle with a perpendicular line through it, which creates 3 similar triangles, by using the "geometric mean" of "w" there.
anyhow, we used the medium-sized and large-sized triangles there, to draw proportions and get what the "w" distance is, and you can see there what "w" is.
and onto the 3rd section
now that we know how long "w" is, we can use the triangle containing the 40° angle, in order to get the pyramid's height of "h", by using the tangent function, as you see there.
and we also use the same triangle, to get the "z" distance, which is namely the slant-height of the pyramid, however, is also the "altitude" of the triangular faces.
and onto the 4 and last section in the picture
that's a triangular face by herself, it has a base of 6, and an altitude of "z".
now, all that said, let's plug those values to get the volume, and then the surface area, keeping in mind the surface area is just the area of the rhombus plus the area of all four triangles.
[tex]\bf V=\cfrac{1}{3}\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right](h) \\\\\\ SA=\left[ \stackrel{\textit{area of the rhombic base}}{4\left( \frac{1}{2}xy \right)} \right]~~+~~\left[ \stackrel{\textit{area of the four triangles}}{4\left[ \frac{1}{2}(6)(z) \right]} \right][/tex]
x ≈ 2.54 y ≈ 5.44 w ≈ 2.298 h ≈ 1.93 z = 3
V ≈ 17.7265 SA ≈ 63.58
The goal of an optimization problem is to find the maximum or minimum value of the
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An optimization problem seeks to maximize or minimize an objective function, involving endogenous and exogenous variables and is widely used in various fields. Linear optimization uses linear equations and can often be solved with gradient-based techniques in software like MS Excel.
The goal of an optimization problem is to find the maximum or minimum value of a specific function, which is known as the objective function. This function typically represents a scenario such as profit maximization or cost minimization in different fields such as business, economics, and engineering. In an optimization model, there are typically three components: the goal (e.g., maximize profits), the endogenous variables (e.g., the amount of goods produced or the number of hours worked), and the exogenous variables (e.g., price of the goods, wage rates). Linear optimization problems, in particular, represent the objective function and constraints as linear equations and are solved using various mathematical techniques.
Most optimization techniques, such as those used in MS Excel, are gradient-based and offer a systematic approach for finding the optimal solution that either maximizes or minimizes the objective function while satisfying a set of constraints. Whether the objective is to maximize utility or minimize costs, similar approaches can be applied, and sometimes the objective function can be stated in the minimization form in any linear optimization problem by using a transformation.
ONLY ANSWER IF YOU KNOW THE ANSWER Which shows a correct order to solve this story problem? The Johnson Chair Factory used 165.6 pounds of nails in 6 weeks. The Martinez Table Factory used 154.2 pounds of nails in 6 weeks. How many pounds of nails did the two factories use altogether in one week? A. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. B. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Add the two amounts. Step 4: Multiply the sum by 2. C. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Divide the two amounts by 6. D. Step 1: Calculate how many pounds of nails the Johnson Chair Factory used in a week. Step 2: Calculate how many pounds of nails the Martinez Table Factory used in a week. Step 3: Multiply the two amounts by 6.
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Answer:
A if you look close at the story you will learn alot! hope this helps!
Mr. lee drove his car 297.6 miles while using 16 gallons of gas . How many miles does he get to the gallon ?
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How many triangles are with two sides each 6 inches long and one angle measure of 90°.
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So the triangle is a Right Isosceles triangle
The description relates to an isosceles right triangle.
An isosceles right triangle can be described as the triangle that has two sides that are both equal while it also has an angle that will be 90° which is the right angle.
In this case, the two equal sides are given as 6 inches while it also has an angle of 90°. Therefore, it's an isosceles right triangle.
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Milli plans to rent a room for her birthday party for $40. The catering charge is $12 per person but there is no charge for Milli's meal since she is the guest of honor. If Milli has $100 to spend on her birthday party, what is the maximum number of friends Milli can invite?
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Derive the equation of the parabola with the focus
is (-7,5) and the directrix of y=-11
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keep in mind that the vertex is half-way between those two fellows, and the distance from the vertex to either one of them is "p" units, check the picture below.
with that focus point and that directrix, the half-way over the axis of symmetry will be -7, -3, that's where the vertex is at, and notice the distance "p", is 8 units.
since the parabola is opening upwards, "p" is positive 8.
[tex]\bf \textit{parabola vertex form with focus point distance}\\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \boxed{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}\\\\ -------------------------------\\\\ \begin{cases} h=-7\\ k=-3\\ p=8 \end{cases}\implies 4(8)[y-(-3)]=[x-(-7)]^2 \\\\\\ 32(y+3)=(x+7)^2\implies y+3=\cfrac{1}{32}(x+7)^2 \\\\\\ y=\cfrac{1}{32}(x+7)^2-3[/tex]
What happens to the force of gravity between two maser if they are moved father apart A. It increases. B. It decreases. C. It stays the same D. It fluctuates. ( Question two ) Earths path around the sun is ____. A elliptical. B circular. C . random. D. Triangular. (Question three). The asteroid belt separates what ? A. Sun and stars B. Earth in moon C. Inner and outer planets D. Milky Way from other galaxies ( Questikn four ) the tilt of the earth its axis causes ____. A. Day in night. B. The seasons. C. A year D. A month umm it right will mark brilliant
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B. The seasons.
Form a seven-letter word by mixing up the letters in the word FIXTURE.
How many ways can you do this if no vowel is isolated between two consonants?
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6x24=144ways
You have the main rule: no vowel is isolated between two consonants.
The word FIXTURE consists of 4 consonants and 3 vowels.
There are such possible cases:
1. Formed word begins with three vowels and ends with 4 consonants.
The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]
2. Formed word begins with two vowels and ends with one vowel (between them stand all consonants).
The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]
3. Formed word begins with one vowel and ends with two vowels (between them stand all consonants).
The number of such words is [tex]3\cdot 2!\cdot 4!=6\cdot 24=144.[/tex]
4. Formed word begins with with 4 consonants and ends with 3 vowels.
The number of such words is [tex]3!\cdot 4!=6\cdot 24=144.[/tex]
5. In total 144+144+144+144=576 different words.
Find the equation of the tangent plane to the surface z=e−x/17ln(y) at the point (3,3,0.920883)
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A cable hangs between two poles of equal height and 30 feet apart. set up a coordinate system where the poles are placed at x=−15 and x=15, where x is measured in feet. the height (in feet) of the cable at position x i
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The length of the cable is the number of units on it.
The cable is 35.26 feet long
How to determine the cable lengthThe function is given as:
[tex]h(x) = 15\cos(x/15)[/tex]
For all the lengths, we have the following differential equation
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (\frac{dy}{dx})^2} \, dx[/tex]
So, we have:
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + (15 * \frac{1}{15} * \tanh^2(\frac{x}{15}))} \, dx[/tex]
Evaluate
[tex]Length = \int\limits^{15}_{-15} {\sqrt{1 + \tanh^2(\frac{x}{15})} \, dx[/tex]
This gives
[tex]Length = \int\limits^{15}_{-15} {\sqrt{cosh^2(\frac{x}{15})} \, dx[/tex]
Evaluate the exponents
[tex]Length = \int\limits^{15}_{-15} {cosh(\frac{x}{15}) \, dx[/tex]
The above function is an even function.
So, we have:
[tex]Length = 2\int\limits^{15}_{0} {cosh(\frac{x}{15}) \, dx[/tex]
Integrate
[tex]Length = 2 * [\frac{sinh(\frac{x}{15})}{1/15}]|\limits^{15}_{0}[/tex]
Simplify
[tex]Length = 30 * [\sinh(\frac{x}{15})]|\limits^{15}_{0}[/tex]
Expand
[tex]Length = 30 * [\sinh(\frac{15}{15}) - \sinh(\frac{0}{15})][/tex]
Solve
[tex]Length = 35.26[/tex]
Hence, the length of the cable is 35.26 feet
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given right triangle XYZ what is the value of tan 60°
Answers
Answer:
tan (60) = √3
Explanation:
The given triangle is right-angled triangle, therefore, we will use Pythagorean theorem to get the length of the third side.
third side = sqrt [(hypotenuse)^2 + (second side)^2]
third side = 21√3 units
Since the given triangle is a right-angled triangle, we can apply the special trigonometric identities.
Therefore:
tan θ = opposite / adjacent
In the given triangle:
θ = 60°
The opposite side = 21√3
The adjacent side = 21
Substitute in the above equation to get tan 60 as follows:
tan (60) = (21√3) / (21) = √3
Hope this helps :)
Answer:
√3
Step-by-step explanation:
got 100%
Pietro buys 20 candy bars for $6 he plans to sell all 20 candy bars in 1 day he need to make a profit of $10 per day to meet his fundraising goal how much must he charge for each candy bar?
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Solve the inequality and graph its solution: 2t + 1 > 9 or –18 > 5t – 3
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To solve the inequality and graph its solution, solve the two separate inequalities: 2t + 1 > 9 and -18 > 5t - 3. The solution is t > 4 or t < -3.6. Graph the solution by plotting the points 4 and -3.6 on a number line, and shading the area to the right of 4 and the left of -3.6.
Explanation:To solve the inequality and graph its solution, we need to solve the two separate inequalities:
1) 2t + 1 > 9
2) -18 > 5t - 3
For the first inequality, we can subtract 1 from both sides and divide by 2 to obtain t > 4.
For the second inequality, we can add 3 to both sides and divide by 5 to obtain t < -3.6.
Thus, the solution to the original inequality is t > 4 or t < -3.6.
To graph the solution, we would plot the points 4 and -3.6 on a number line, and shade the area to the right of 4 and the left of -3.6.
To solve the inequalities 2t + 1 > 9 and –18 > 5t – 3, we must solve each separately, and since it's an 'or' inequality, we combine the solution sets. The solutions are t > 4 and t < -3. Graphically, these solutions represent non-overlapping shaded regions on a number line.
Explanation:To solve the inequality 2t + 1 > 9 or –18 > 5t – 3, we need to consider them separately as each inequality represents a different solution set.
For the first inequality:
Subtract 1 from both sides to obtain 2t > 8.Divide by 2 to isolate t, yielding t > 4.For the second inequality:
Add 3 to both sides to get –15 > 5t.Divide by 5, which flips the inequality because we are dividing by a positive number, resulting in t < –3.We interpret these results as two separate conditions:
t > 4: This suggests that t is any value greater than 4.t < –3: This suggests that t is any value less than -3.Since the original statement uses 'or', the solution set includes all the values that satisfy either inequality. Therefore, graphically, we would show these on a number line with a shaded region to the right of 4 and another shaded region to the left of -3. The areas do not overlap because there are no t values that can simultaneously be greater than 4 and less than -3.
Choose the correct answers for (a) the total installment price, (b) the carrying charges, and (c) the number of months needed to save the money at the monthly rate to buy the item for its cash price.
a stereo with a cash price of $1,200 at $119.00 per month for 12 months
Answers
Answer:
(a) $1428
(b) $228
(c) 11 months
Step-by-step explanation:
(a) Total installment price = 119 × 12 = $ 1428
(b) The carrying charges = amount paid - cash price
= 1428 - 1200 = $ 228
(c) No. of needed to save the money = 1200 ÷ 119 = 10.08 ≈ 11 months
Answer: A=1428.00
B=228.00
C=11
"If you share 7 apples equally with 3 people, then there are 2 1/3
Answers
Answer:
Part A
"If you share 7 apples equally with 3 people, then there are
2 1/ 3 ..."
First, complete the sentence. Then, briefly explain what the whole number 2, the denominator 3, and the numerator 1 mean in this problem.
Step-by-step explanation:
here is the full question just say answer by commenting