Find the missing side lengths. leave your answers as radicals in simplest form 45 20v2
Answers
1) The missing side lengths are: Hypotenuse a = 4 Side b = 2√2
2) The missing side lengths are: Leg x = 2√2 Leg y = 2√2
1) In a right triangle with a 90° angle and an opposite angle of 45°, we can use the trigonometric ratios to find the missing side lengths.
Let's denote the hypotenuse as a, the side opposite the 45° angle as c, and the remaining side as b.
Using the sine function, we have:
sin(45°) = c / a
Since sin(45°) = √2 / 2, we can substitute the values:
√2 / 2 = 2√2 / a
To solve for a, we can cross-multiply and simplify:
√2 * a = 2√2 * 2
a√2 = 4√2
a= 4
Therefore, the hypotenuse (a) has a length of 4.
To find side b, we can use the Pythagorean theorem:
a² + b² = c²
Plugging in the known values:
(2√2)²+ b² = 4²
8 + b² = 16
b²= 16 - 8
b² = 8
b = √8 = 2√2
So, the missing side lengths are:
Hypotenuse (c) = 4
Side b = 2√2
2) In a right triangle with a 45° angle and a hypotenuse of 4, we can find the lengths of the other two sides. Let's denote the length of one leg as x and the length of the other leg as y.
Using the Pythagorean theorem, we have:
\(x^2 + x^2 = 4^2\\2x^2 = 16\\x^2 = 16 / 2\\x^2 = 8\)
x = √8 = 2√2
Therefore, one leg (x) has a length of 2√2.
To find the other leg, we can use the fact that the triangle is isosceles (since both acute angles are 45°). Therefore, the other leg (y) has the same length as x:
y = x = 2√2
So, the missing side lengths are:
Leg x = 2√2
Leg y = 2√2
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The complete question is:
Find the missing side lengths. leave your answers as radicals in simplest form
Related Questions
If p is the hypothesis of a conditional statement and q is the conclusion, which is represented by q→p?
O the original conditional statement
O the inverse of the original conditional statement
O the converse of the original conditional statement
O the contrapositive of the original conditional statement
Answers
Answer:
(c) the converse of the original conditional statement
Step-by-step explanation:
If a conditional statement is described by p→q, you want to know what is represented by q→p.
Conditional variationsFor the conditional p→q, the variations are ...
converse: q→pinverse: p'→q'contrapositive: q'→p'As you can see from this list, ...
the converse of the original conditional statement is represented by q→p, matching choice C.
__
Additional comment
If the conditional statement is true, the contrapositive is always true. The inverse and converse may or may not be true.
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Sixty tickets at $80 each cost
Answers
Answer:
$4800 is the total cost
Step-by-step explanation:
so each ticket costs $80 and there is 60 tickets
$80*60 = $4800
Have a nice day! :-)
A bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilopascals. What will it be in 4 minutes?
If necessary, round your answer to the nearest tenth.
Answers
Answer:
4x10=40
It will lose 40% pressure after four minutes
It will lose 40% pressure after four minutes
What is exponential growth or decay function?Consider the function:
\(y = a(1\pm r)^m\)
where m is the number of times this growth/decay occurs, a = initial amount, and r = fraction by which this growth/decay occurs.
We have been given that a bike tire just ran over a nail, and it is losing pressure at a rate of 10% every minute. The tire pressure is currently 1,060 kilo-pascals. We are asked to find the tire pressure in 4 minutes.
We will use exponential decay formula to solve our given problem.
\(y = a(1\pm r)^m\)
Let us convert 10% into decimal.
0.01
Initial value is 1,060 . Upon substituting our given values in above formula, we will get:
y = 1,060 (1 - 0.01)^4
Therefore, the tire pressure will be approximately 40% kilo-pascals in 4 minutes.
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Round $10,031.464 to the nearest dollar
Answers
Answer:
the answer is $10,031.00 because although the six is there it has no effect on the four. Four or below leave it alone 5 or above give it a shove..love yall hope i helped and can i get brainliest
Find the sum of the measures of the interior angles of a heptagon.
Answers
Answer:
the answer is 900 degrees
Step-by-step explanation:
The exterior angles of a polygon add up to 360º in measure. For a regular heptagon, each exterior angle has an equal measure xº, so that 7xº = 360º, or xº ≈ 51.43º. Interior angles supplement exterior angles, so they each have measure 180º - xº ≈ 128.57º. Multiply this by 7 to get a total of 900º.
ху
11
124
31 ?
410
513
The function table shown matches y = 3x - 2. Find the missing value in the table.
A) 5
B)
7
9
D)
10
Answers
What is the measure of angle A′OB′?
Answers
Answer:79°
Step-by-step explanation:
What is the difference between the absolute value of -8 and the absolue value of 6? O 2 O8 O 14 O 16
Answers
Answer:
A. 2Step-by-step explanation:
Absolute value is always positive:
|-8| = 8|6| = 6Their difference is:
8 - 6 = 2Correct choice is A
Let's spot out
|-8|-|6|8-62Answer is 2
Two numbers add to 200. The first is 20 less than the second. What are the numbers?
Answers
Answer:
Step-by-step explanation:
Let's call the first number x.
We can write an equation representing the problem using x:
x+x+20=200 (because the second number is 20 more than the first, or x)
Combine like terms: 2x+20=200
Subtract 20 from each side of the equation: 2x=180
Divide by 2: x=90
The first number is 90, the second number is 110.
Hope this helps!
Find the given and the solution set of the equation
Answers
Answer for 2: x = 11
Let me know if you need an explanation since it's pretty simple, but I could elaborate.
a museum room, circular in shape, has 5 equally spaced sensors on its walls. there are no dead or overlapping spots along the perimeter of the room. each sensor has the same angle of detection. what is the detection angle of each sensor?
Answers
According to the given information the detection angle is 72.
How would you define an angle?An angle is formed anytime two straight lines and rays meet at a single terminal. The intersection of two points at such an angle is known as the vertex. The word "angle" comes from the Latin word "angulus," which meaning "corner."
What is the math behind angles?Degrees are a measure representing circularity or rotation and are used to express angles. You would turn 360° in order to face back in the exact direction after completing a full revolution. As a result, a quarter-circle, or straight angle, is 90°, and a half-circle is 180°. The sum of any two or maybe more angles on the a straight line is 180°.
\(\begin{aligned}5\theta & =360^{\circ} \\\theta & =\frac{360^{\circ}}{6} \\& =72^{\circ}\end{aligned}\)
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Which of the type directions lie in the (110) plane? [101] [110] [o īl] (110
Answers
The type directions that lie in the (110) plane are Crystal planes are equivalent planes that represent a group of crystal planes with a common set of atomic indexes.
Crystallographers use Miller indices to identify crystallographic planes. A crystal is a three-dimensional structure with a repeating pattern of atoms or ions.In a crystal, planes of atoms, ions, or molecules are stacked in a consistent, repeating pattern. Miller indices are a mathematical way of representing these crystal planes.
Miller indices are the inverses of the fractional intercepts of a crystal plane on the three axes of a Cartesian coordinate system.Let us now determine which of the type directions lie in the (110) plane.[101] is not in the (110) plane because it has an x-intercept of 1, a y-intercept of 0, and a z-intercept of 1. So, this direction does not lie in the (110) plane.[110] is in the (110) plane since it has an x-intercept of 1, a y-intercept of 1, and a z-intercept of 0.
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You are about to run up a set of 100 stairs. The diagonal distance up the 100 stairs is 62.5
feet and the angle of elevation from the base of the stairs to the top is
31
62.5 ft.
h
31°
What is the height difference from where you start to where you finish?
Round your answer to the nearest hundredth.
h=
feet
Answers
Answer:
h = 32.2 ft
Step-by-step explanation:
Since we have a right triangle, to get the value of h, we will have to use the appropriate trigonometric ratio
From the diagram given, h faces the angle and that makes it the opposite side
62.5 ft faces the right angle and that makes it the hypotenuse
The trigonometric ratio that connects the two is the sine
thus, we have it that;
sine 31 = h/62.5
h = 62.5 * sin 31
h = 32.2 ft
Maria made some purchses at the Sunflower Market. She bought strawberries for $3.50, carrots for $2.25 and a bouquet of flowers for $9.95. If Maria uses a 20% coupon and has to pay 5.5% tax, how much will she pay in total? (Round your answer to the nearest hundredth)
Answers
Answer:
$13.25
Step-by-step explanation:
First you add everything up to get you to $15.70, then the 20% is changed to .2 which you then multiply 15.70 by .2 giving you 3.14. You then take 15.70 minus 3.14 which then gets you to 12.56. Then you take the tax of 5.5% and times $12.56 by it, giving you 69 cents, as your tax. Add those together to get 13.25, and then your finished.
Answer:
$13.25
Step-by-step explanation:
First let's add together the cost of all the items Maria bought:
3.50 + 2.25 + 9.95 = 15.70
The total cost of all the items without a coupon or tax is $15.70.
If Maria uses a 20% coupon, the value of the total cost will be 80% of its original value. So, multiply 15.7 by 0.8 to find the cost after the coupon:
15.7 * 0.8 = 12.56
The new total cost is 12.56. Now we need to find the sales tax. Multiply 12.56 by 0.055 to find the value of the sales tax:
12.56 * 0.055 = 0.6908
0.6908 rounds to 0.69. Add the cost of the sales tax to the total cost to get the final answer:
12.56 + 0.69 = 13.25
The total cost Maria will pay is $13.25
Hope this helps :)
Which of the following. Best describes the solution to the system of equations below?
Answers
Answer:
x=5/2 − 5y/4 => the first sentence
Step-by-step explanation:
Solve for x in the first equation.
x=5/2−5y/4
12x+15y=30
Replace all occurrences of x
with 5/2−5y/4 in each equation.
30=30
x=5/2−5y/4
Remove any equations from the system that are always true.
x=5/2−5y/4
if y=0 => x=5/2
Farmer Jones and Farmer Smith graze their cattle on the same field. If there are 20 cows grazing in the field each cow produces $4000 of milk. If there are more cows in the field, then each cow produces can eat less grass and the milk production falls. With 30 cows on the field each produces $3000 of milk, with 40 cows each produces $2000 of milk . Cows cost $1000 a piece. Assume that Farmer Jones and farmer Smith can buy either 10 cows or 20 cows, find out the Dominant Strategy of Farmer Jones and express the same in formal language. I want to see all the steps.
Answers
The dominant strategy of Farmer Jones is to buy 10 cows.
To determine the dominant strategy of Farmer Jones, we need to compare the outcomes of his two options:
buying either 10 cows or 20 cows.
Let's analyze the potential outcomes for each case:
Buying 10 cows:
If Farmer Smith buys 10 cows:
The total number of cows in the field would be 30, resulting in each cow producing $3000 of milk.
If Farmer Smith buys 20 cows:
The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.
Buying 20 cows:
If Farmer Smith buys 10 cows:
The total number of cows in the field would be 40, causing each cow to produce $2000 of milk.
If Farmer Smith buys 20 cows:
The total number of cows in the field would be 50, resulting in each cow producing less than $2000 of milk (exact value unknown).
From the given information, we can observe that regardless of the strategy chosen by Farmer Smith, Farmer Jones is better off buying 10 cows.
In all scenarios, the milk production per cow is higher when Farmer Jones buys 10 cows compared to buying 20 cows.
Therefore, the dominant strategy for Farmer Jones is to buy 10 cows.
Formally, we can express this as follows:
For Farmer Jones, no matter the strategy chosen by Farmer Smith, buying 10 cows yields a higher milk production per cow compared to buying 20 cows.
Hence, Farmer Jones' dominant strategy is to buy 10 cows.
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solve for n -8 = 6+n
Answers
Answer:
no solution
Step-by-step explanation:
n -8 = 6+n
Subtract n from each side
n-n -8 = 6+n-n
-8 = 6
This is never true so there is no solution
Answer:
n = -14
Explanation:
-8 = 6 + n
move n over to the left side of the equation
-8 - n = 6
-8 - (-14) = 6
Hailey planted
30 tomato seeds. Three out of every 5 seeds grew
into tomato plants. How many tomato plants
does Hailey have?
Answers
Answer:
18 seeds
Step-by-step explanation:
3 x 6 = 18 seeds
3/5 x 30 = 18 seeds
Hope that helps!
Is the relation a function? And why
A)No
B)Yes
Answers
Good luck
3. In one pond in the forest, scientists found that a sample of pond water contained 45 minnows for every 27 tadpoles. How many tadpoles would they expect to find in a sample that contained 315 minnows? Show all work and explain how you got your answer
Answers
Answer: 189
Step-by-step explanation:
for every 45 minnow there will be 27
315 minnow is 7 times 45 minnow 27*7 is 189
A company wishes to design a rectangular box that will have a volume of 9 cubic inches. The bottom (and top) of the box is a rectangle with the length 2 times the width.. What should the dimensions be to minimize the surface area of the box?
Answers
Given, a rectangular box that will have a volume of 9 cubic inches and the bottom (and top) of the box is a rectangle with the length 2 times the width.
We have to determine what should the dimensions be to minimize the surface area of the box.
Surface area of the rectangular box can be given by;S = 2lw + 2lh + 2wh
Where,l = Lengthw = Widthh = Height
Given,
Volume of the box = 9 cubic inchesLet's find the relation between l, w, and h using the formula for the volume of the rectangular box.Volume of the rectangular box can be given by;V = lwh
Substituting the values;9 = lwh -------- (1)Given,The bottom (and top) of the box is a rectangle with the length 2 times the width.i.e. l = 2w
Substituting the value of l in equation (1);9 = 2w * w * h ⇒ 9 = 2w²h ⇒ h = 9/2w² ----- (2)Now, substitute the values of l and h in the formula of surface area.S = 2lw + 2lh + 2wh = 2(2w)w + 2(9/2w²)w + 2wh
Simplifying the above equation;S = 4w² + 9/wSince we want to minimize the surface area of the box, we need to find the derivative of S with respect to w.dS/dw = 8w - 9/w²
Now, equating the derivative to zero;dS/dw = 0⇒ 8w - 9/w² = 0⇒ 8w³ - 9 = 0Solving for w,⇒ w³ = 9/8⇒ w = ∛(9/8)In order to minimize the surface area, we need to find the critical point by calculating the second derivative of the surface area function.d²S/dw² = 8 + 18/w³At w = ∛(9/8),d²S/dw² > 0
Therefore, the dimensions of the box with the smallest surface area is;l = 2w = 2∛(9/8)w = ∛(9/8)h = 9/2w² = 9/2(∛(9/8))².
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what is the values of 166 times 14
Answers
Answer:
2324
Step-by-step explanation:
166×14
=2324
.
.
.
..
..
Answer:
the value of 166 times 14 is 2324
Step-by-step explanation:
166 × 14 = 2324What do you think is the importance of having a hyperboloid structure in most of the power plants?
Answers
Answer:
Cooling Tower
A power plant consists of many components, but cooling towers are some of the most important. The function of a cooling tower is to release the excess heat (or waste heat) to the atmosphere by cooling down hot fluid (water, in most cases) to a lower temperature.
Step-by-step explanation:
suppose w is a subspace of rnspanned by n nonzeroorthogonal vectors. explain why w d r
Answers
As W is spanned by n linearly independent vectors in ℝ^n, it means that the dimension of W is also n. This implies that W has the same dimension as ℝ^n, and therefore, W is equal to ℝ^n.
If w is a subspace of rnspanned by n non zero orthogonal vectors, then w is at most n-dimensional because there are only n vectors that can be used to span w. Any vector outside of the span of these n vectors will not be in w. Therefore, the dimension of w is less than or equal to n. Since w is a subspace of rn, which is n-dimensional, w must be a subset of Rn with a dimension less than or equal to n. Therefore, w d Rn. Suppose W is a subspace of ℝ^n spanned by n nonzero orthogonal vectors. This means that W is a vector space that is a subset of ℝ^n, and it can be generated by taking linear combinations of the n nonzero orthogonal vectors. Since the vectors are orthogonal, they are linearly independent, and their linear combinations form a basis for the subspace W.
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jake travels 6 hours for a total of 444 miles on 20 gallons of gas, rate for gallons and hours.
Answers
Answer: 5 gallons per hour.
Step-by-step explanation: To find the unit rate, divide "gallons" by "hours." As we said, we need to find the unit rate. We want a unit rate where 1 is in denominator, so we divide the top and bottom by 6. (Remember, unit means 1.)
\(\frac{30/6}{6/6}=\frac{5}{1}\)
Therefore, our answer is 5.
Calculate y when x = 5
Y=2x+3
Answers
y=13
Step-by-step explanation:
given that,
x=5
to find,
y=2x+3, when x=5
substitute 5 in the place of "x" we get,
y=2×5+3
according to BODMAS rule( bracket of division multiplication addition and subtraction) first we have to multiply 5 with 2 and then add the product with 3 we get,
y=10+3
y=13
Answer: y=13
Step-by-step explanation:
\(y=2(5)+3\\multiply\\y=10+3\\add\\10+3=13\\y=13\)
URGENT!! ABCD is a quadrilateral. The point G is on the side which forms that AG=AB and CB=CG
The tangent to the circle at point A Is the along the side CD at point L
The extension of the leg CB is located at point K.
Prove AD=AG
Answers
ADG is an equilateral triangle, then, line AD is equivalent to line AG.
How to prove the statementFrom the information given, we have to prove that;
AD=AG
It is important to note that the triangle ADG is an equilateral triangle.
The properties of an equilateral triangle are;
All the sides are equalAll the angles are congruent and equal to 60°It is a polygon with three sidesSince ADG is an equilateral triangle, then, line AD is equivalent to line AG
Thus, since ADG is an equilateral triangle, then, line AD is equivalent to line AG.
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What is 3.5 in fraction form?
Answers
In fractional form, 3.5 equals 7/2 or 35/10. The number of zeros after the digit 1 in the fractional form's denominator equals the number of digits after the decimal point.
Fractional notation is the term used to describe writing a number in fractional form. It is written as a/b when neither a nor b are equal to 0. The two halves of a fraction are the numerator and denominator. How many components of the total are being addressed is indicated by the numerator, which is the number above the line. Fractions are used to represent the parts of an entity or collection of entities. A fraction consists of two components. The figure at the top of the line is the numerator. It tells us how many equal portions of the whole or collection were taken. The number that appears below the line is the denominator.
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if x 0 and y 0 where is the point (x y) located quadrant i quadrant ii quadrant iii quadrant iv
Answers
Answer:
true
Step-by-step explanation:
8 to the power of 2 x (2+6) / 4
Answers
Answer:
Below,...!
Step-by-step explanation:
\(8^2 = 64\\64*(2+6) = 64*8\\64*8 = 512\\512/4 = 128\\\\Answer=128\)
Chow,...!