Answers
Answer:
\(2\sqrt{51}\)
Step-by-step explanation:
first, you have to look pythagoras theorem (in picture)
then; x² + 14² = 20²
x² + 196 = 400
x² = 204
x = \(\sqrt{204}\) = \(2\sqrt{51}\)
Hope this helps ^-^
The length of the unknown side ( x )
Solution:We'll have to use pythagoras Theorem.
\(\huge\boxed{\sf{Formula: {a}^{2} + {b}^{2} = {c}^{2} }}\)
In this question hypotenuse is given so we'll have to subtract.
Let the unknown be "x"
\( {c}^{2} = {a}^{2} - {b}^{2} \)
\( {x}^{2} = {20}^{2} - {14}^{2} \)
\(x = 204\)
\( {x}^{2} = \sqrt{204} \)
\(x = 14.28285686\)
\(\large\boxed{\sf{x = 14.3 \: (nearest \: tenth)}}\)
Hence, the unknown side of the given triangle is 14.3
Related Questions
Show that y(t)=0 and y(t)=(1/16)t^4 are both solutions of the initial value problem y'=t*y^(1/2), where y(0)=0. Explain why this fact does not contradict theorem.
Answers
Both y(t) = 0 and y(t) = (1/16)t^4 are solutions to the initial value problem y' = t * y^(1/2), where y(0) = 0.
To verify if a function is a solution to a differential equation, we need to substitute it into the equation and check if it satisfies both the equation and the initial condition.
For y(t) = 0:
y'(t) = t * (0)^(1/2) = 0
Since y'(t) = 0, this satisfies the differential equation. Additionally, y(0) = 0 satisfies the initial condition.
For y(t) = (1/16)t^4:
y'(t) = t * [(1/16)t^4]^(1/2) = t * [(1/16)^(1/2) * t^2] = (1/16)t^3
This also satisfies the differential equation. And y(0) = 0 is satisfied as well.
The fact that both y(t) = 0 and y(t) = (1/16)t^4 are solutions to the initial value problem does not contradict any theorem. It simply means that there are multiple solutions to the differential equation.
The existence of multiple solutions is possible and consistent with the nature of certain differential equations, and it is not contradictory as long as each solution satisfies the equation and the initial condition.
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one third of a student class is absent today. one half of those were also absent yesterday. about wayt percent of the class has been absent for two straight days?
Answers
About 50% of the students have missed class for the two days.
Fractions and PercentagesFractions are written in the form a/b. From the information given:
Fraction of students that missed class today = 1/3 Fraction of those that missed yesterday = 1/2(1/3 ) = 1/6percentage of the resulting fractionThe percent of the class has been absent for two straight days will be (1/3+1/6) *100%
The percent of the class has been absent for two straight days will be 3/6 * 100 = 50%
Hence about 50% of the students have missed class for the two days.
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In order to maintain a healthy weight, an average adult dog that weighs 21 kilograms must consume 11 grams of dog food per
kilogram of its body weight each day. A specialty pet store sells dog food by the cup, where 4 cups of dog food weighs 356 grams.
About how many cups of dog food should the dog consume each day in order to maintain a healthy weight?
A. 2.60
B. 0.39
C. 2.75
D. 0.65
Answers
The price of a man's shirt went from $15 to $20. What was the percent of increase of the price of the shirt? A. 25% A. , 25%, B. 3313% B. , 33 and 1 over 3 percent, C. 20% C. , 20%, D. None of these D. , none of these,
Answers
Answer: 33 1/3%
Step-by-step explanation:
Percentage increase of the shirt will be calculated as:
= Price Increase / Old price × 100%
Price Increase = $20 - $15 = $5
Old price = $15
Percent increase = Price Increase / Old price × 100%
= 5/15 × 100
= 1/3 × 100
= 33 1/3%
Answer:
it would be -25% because 15 is less than 20
URGENT HELP NEEDED!!!
Subtract the cube root of the product of x and 3y from the square of the sum of a and b.
Answers
Answer:
\((a+b)^{2}- \sqrt[3]{x . 3y}\)
Step-by-step explanation:
Subtract the cube root of the product of x and 3y from the square of the sum of a and b.
A = The square of the sum of a and b is \((a+b)^{2}\)
B = The cube root of the product of x and 3y is \(\sqrt[3]{x . 3y}\)
They want us to subtract B from A so B - A, therefore the following.
\((a+b)^{2}- \sqrt[3]{x . 3y}\)
CONVERT
5 1/2 to and
IMPROPER
FRACTION.
Answers
Explanation:
Step 1: Multiply the denominator by the whole number
2 × 5 = 10
Step 2
Add the answer from Step 1 to the numerator
10 + 1 = 11
Step 3
Write answer from Step 2 over the denominator
11/2
=112
Answer:
Hi There!! :-D
Step-by-step explanation:
5 1/2 as an improper fraction is 11/2.
We know that 5 x 2 is 10, and 10 + 1 is 11, therefore your answer is 11/2 !!!
Hope this helps you! ∩__∩
- abakugosimp
In her proof, Ensley wrote the formula Va + b = c? Which of the following explains why her formula
is incorrect?
A. The sum of the square of a and the square of b should be equal to the square root of c.
B. The square root of the sum of a and b should be equal to the square root of c.
C.The sum of the square of a and the square of b should be equal to the square of c.
D.The sum of the square root of a and the square root of b should be equal to the square of c
Answers
Answer:
C. a^2 + b^2 = c^2
Step-by-step explanation:
Wich is the same as moving the decimal point 3 places to the left in a decimal number
Answers
Answer:
dividing # by 100
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
1÷1000=
.001
Moved 3 points to the left
please answer quickly 2x^2-x-6= (2x+ ) (x- )
Answers
Answer: I hope this is the correct answer for you.
Step-by-step explanation:
2x^2 + x - 6 = 2x^2 + 4x - 3x - 6
= 2x(x + 2) - 3(x + 2) = (x +2)(2x - 3) (Ans)
Or by completing the square method,
2x^2 + x - 6 = 2[x^2 + (1/2)x] - 6
=2[x^2 + (1/2)x + (1/4)^2 - (1/4)^2] - 6
=2[(x+1/4)^2 - 1/16] - 6
=2(x + 1/4)^2 - 1/8 - 6
=2(x + 1/4)^2 - 49/8
=2[(x + 1/4)^2 - 49/16]
=2[(x + 1/4)^2 - (7/4)^2]
=2[x + 1/4 + 7/4][x + 1/4 -7/4]
=2(x + 2)(x - 3/2)
=(x + 2)(2x - 3) (Ans)
f(x) = a x2 + b x + c
then
f(x) = a (x - x1) (x - x2)
For your problem we have the roots given by
\displaystyle \frac{-1 \pm \sqrt{1^2 - 4 (2) (-6)}}{2 (2)}= \frac{-1 \pm \sqrt{49}}{4} = \frac{-1 \pm 7}{4}
2(2)
−1±
1
2
−4(2)(−6)
=
4
−1±
49
=
4
−1±7
which gives -2 and 3/2 as the roots
So
f(x) = 2x2 + x - 6 = 2 (x + 2) (x - 3/2) = (x + 2) (2 x - 3)
Which, thankfully, is the same thing given above.
Write the expression. Then, check all that apply. six times the sum of nine and a number
Answers
The sum of 9 and a number (x in this case) needs to be In Parentheses to be done first then that result is multiplied by 6
Camila goes out to lunch. The bill, before tax and tip, was $9.20. A sales tax of 3% was added on. Camila tipped 19% on the amount after the sales tax was added. How much was the sales tax? Round to the nearest cent.
Answers
Answer:
$0.276
Step-by-step explanation:
Given data
Bill= $9.20
Tax= 3%
Tip= 19%
Let us find the amount of the tax and the tip
Tax
=3/100*9.20
=0.03*9.2
=$0.276
Amount after sales tax
= 0.276+9.20
=$9.476
Tip
=19/100*9.476
=0.19*9.476
=$1.80044
Therefore the sales tax
=$0.276
X2+Y2−8X+6Y+21=0 Use the process of completing the square to rewrite the equation above as the equation of a circle in standard form , and identify the center and radius . The center is at the point ( , ) The radius is
Answers
Answer:
Step-by-step explanation:
hello : here is an solution
Find the hypotenuse.
(4 Points)
Answers
Answer:
x = 13
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
x² = 5² + 12² = 25 + 144 = 169 ( take the square root of both sides )
x = \(\sqrt{169}\) = 13
Answer:
a²+b²=c²
5²+12²= c²
25+144=c²
169=c²
\( \sqrt{169 =} \sqrt{c} \)
13=c
An angle measures 12° less than three times it’s supplement. Find the measure of the angle
Answers
Answer:
132 degrees.
Step-by-step explanation:
Let the supplement be x and the angle be y.
x + y = 180 degrees.
y = (3x - 12) degrees.
x + 3x - 12 = 180
4x = 192
x = 48 degrees
y = 132 degrees
Hope this helped!
the height of a bell tower is 22 meters. max, who is standing near to the bell tower, casts a 8 meter shadow and is 1.75 meters tall. how long is the shadow of the tower? round your answer to the nearest tenth, if necessary.
Answers
The length of shadow of tower y is 100.6 meters.
Given that,
Height of tower, H= 22 meters(given)
Height of Max, h= 1.75 meters (given)
Length of shadow of Max, x= 8 meters
Length of shadow of tower is represented by using y = unknown
To find : The length of shadow of tower
In triangle ABC,
tanθ = H/y = 22/y = opposite /adjacent
also tanθ = h/x
By equating tanθ,
H/y = h/x
22/y = h/x
22/y = 1.75/8
y = 100.57
Therefore, length of shadow of tower = y = 100.6 meters.
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Para pagar una sala de 12 meses las mensualidades son de 850 cuanto se pagara mensualmente si se paga en 15 meses
Answers
The monthly payment for a plan of 15 months is given as follows:
680.
How to obtain the monthly payment?The monthly payment for a plan of 15 months is obtained applying the proportions in the context of the problem.
For a 12 month plan, the monthly cost is of 850, hence the total cost is given as follows:
12 x 850 = 10200.
Hence the monthly payment for a plan of 15 months is given as follows:
10200/15 = 680.
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Help!!! A teacher divided the class into two groups of equal size.
3 5 of the first group are right-handed.
80% of the second group are right-handed.
What fraction of the class is right-handed?
A.4/5
B.7/10
C.5/7
D.8/9
Answers
7/10 answer ///////////
The following pedigree shows the inheritance of a mild, but very rare condition in Siberian Husky dogs. If individuals 1 and 2 are crossed, what is the probability that they will produce an affected pup?
Answers
The probability of producing an affected pup from the cross between individuals 1 and 2 is 25%.
The pedigree shows that the mild, but rare condition in Siberian Husky dogs is inherited in an autosomal recessive manner, meaning that an individual must inherit two copies of the mutated gene (one from each parent) to express the condition.
In this pedigree, individual 1 is unaffected, but a carrier of the mutated gene, as indicated by the half-filled circle. Individual 2 is also a carrier, but it is unclear whether or not they are affected, as indicated by the half-filled square.
If individuals 1 and 2 are crossed, we can use a Punnett square to determine the probability of producing an affected pup.
The Punnett square would have two columns and two rows, representing the two alleles each parent can contribute to their offspring. The probabilities for each possible outcome are:
25% chance of producing an affected pup (homozygous recessive)50% chance of producing a carrier pup (heterozygous)25% chance of producing an unaffected pup (homozygous dominant)Therefore, the probability of producing an affected pup from the cross between individuals 1 and 2 is 25%.
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If you have to divide by a variable, be sure to explain why it is not zero or why it cannot be zero
1. Let A(x,y,z) = 12 +3+ y2 - 2y MULTIPLIERS
(a) Find the global maximum and minimum of A(3,7.2) subject to the constraint ar* + y + z = 2
(b) Find the global maximum and minimum of Als, y.) on the closed bounded dornain ** + y + x2 <16.
Answers
(a) There is no extreme value of A subject to the given constraint,
(b) For x = 0, y + z² ≤ 16.
y is between -4 and 4. In this case, f(y,z) = y² and the maximum value is 16.
For x = ±y, z = 4 - y².
y is between -2 and 2. In this case, f(y,z) = 2y² - y⁴ and the maximum value is 2.
When dividing by a variable, one should always keep in mind that the variable cannot be equal to zero. In other words, if the value of the variable is zero, the function or expression will not be defined or will give an undefined result. The reason is that division by zero is not defined in the set of real numbers.
Therefore, one should exclude the value of zero from the domain of the function or expression.
In part (a) of the given question, we are asked to find the global maximum and minimum of A(x,y,z) = 12 + 3x + y² - 2y subject to the constraint x + y + z = 2.
Let's find the partial derivatives of A with respect to x, y, and z.
∂A/∂x = 3
∂A/∂y = 2y - 2 = 2(y - 1)
∂A/∂z = 0
Now, we have to solve the system of equations consisting of the partial derivatives and the constraint equation.
\(3 = \lambda_1 + \lambda_2,\\2y - 2 = \lambda_1 + \lambda_2,\\\lambda_1x + \lambda_2x = 0,\\\lambda_1y + \lambda_2y - 1 = 0,\\\lambda_1z + \lambda_2z = 1.\)
Substituting the values of the partial derivatives, we get:
\(\lambda_1 + \lambda_2 = 3,\\\lambda_1 + \lambda_2 = -2,\\\lambda_1(3) + \lambda_2(0) = 0,\\\lambda_1(y - 1) + \lambda_2(y - 1) = 0,\\\lambda_1(0) + \lambda_2(1) = 1.\)
The second and third equations are contradictory. So, under the given constraint, A has no extreme value.
In part (b), we are asked to find the global maximum and minimum of A(x,y,z) = x² + y² on the closed bounded domain x² + y + z² ≤ 16.
Let's use the method of Lagrange multipliers to solve the problem. We have to find the critical points of the function f(x,y,z) = x² + y² subject to the constraint x² + y + z² = 16.
We have to solve the system of equations consisting of the partial derivatives of f, the partial derivatives of the constraint function, and the equation of the constraint function.
2x = λ(2x),
2y = λ(1),
2z = λ(2z).
Substituting the value of λ from the second equation into the first equation, we get: x = 0 or x = ±y.
Substituting the values of x and λ from the first and second equations into the third equation, we get:
z = 4 - y² or z = 0.
Since the constraint is x² + y + z² ≤ 16, we have to consider the following cases:
Case 1: x = 0, y + z² ≤ 16.
So, y is between -4 and 4. The maximum value of f(y,z)=y² is 16 in this case.
Case 2: x = ±y, z = 4 - y².
So, y is between -2 and 2. The maximum value of f(y,z) = 2y² - y⁴ is 2 in this case.
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I’ll rate u 5 stars quick response really fast what is the domain image
Answers
*oo= infinity
What are the values of x 2x 2 4x 7?
Answers
The values of x for the given quadratic equation 2x² = 4x - 7
are given by:
\(x = \frac{2 +i\sqrt{10} }{2}\)
\(x = \frac{2 -i\sqrt{10} }{2}\)
What is the solution of a quadratic equation?
The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations.
According to the given question:
For this case we have the following quadratic equation:
2x² = 4x - 7
Rewriting the equation we have:
2x² - 4x + 7 = 0
From here, we have:
a = 2b = -4c = 7
Substituting values in the quadratic equation we have:
x = (-b ± √b² - 4ac)/2a
x = (-(-4) ± √(-4) - 4(2)(7)/2(2)
Rewriting the equation we have:
x = (4 ± √16 - 56)/4
x = (4 ± √-40)/4
x = (2 ± i√10)/2
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PLEASE ANSWER QUICKLY I WILL LOVEEE YOU FORREVERRRRRR
Mrs. Robinson surveyed her class about what flavor cake and ice cream they wanted for their class party. The results were split evenly between the cake with 15 choosing chocolate cake and 15 choosing yellow cake. Of the students who chose chocolate cake, 12 also chose vanilla ice cream. There were 7 students in all that chose strawberry ice cream. Construct a two -way table summarizing the data
Answers
Answer:
Answer would be 12
Step-by-step explanation:
i'm not always accurate but your welcome!
Jeffrey has a fish tank that holds 8 liters of water. He already has the tank filled with 1 liter of water. How many more milliliters of water does Jeffrey need to completely fill the fish tank
Answers
Jeffrey has a fish tank that holds 8 liters of water. He already has the tank filled with 1 liter of water. Thus, to fill the fish tank completely with water, Jeffrey needs 7000 milliliters of water.
This is because 1 liter is equal to 1000 milliliters. Thus, 8 liters are equal to 8 × 1000 = 8000 milliliters.
Therefore, the amount of water Jeffrey needs to completely fill the fish tank is 8000 - 1000 = 7000 milliliters of water.
Jeffrey has a fish tank of 8 liters of water that already has 1 liter of water in it.
The amount of water Jeffrey needs to completely fill the fish tank is calculated by subtracting the liters of water already present in the tank from the total liters of water the tank can hold.To completely fill the fish tank, Jeffrey needs to fill the remaining 7 liters with water. One liter of water is equivalent to 1000 milliliters. Thus, Jeffrey needs to multiply the remaining liters of water he needs to fill by 1000 milliliters.
7 × 1000 = 7000
Therefore, Jeffrey needs 7000 milliliters of water to completely fill the fish tank with water.
To completely fill the fish tank, Jeffrey needs 7000 milliliters of water because he has already filled it with 1 liter of water, and the fish tank can hold 8 liters of water.
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This table shows the running time, in hours, for each of the three widget producing machines over the course of three months. Find the number of widgets produced per hour by each machine. Let x1, x2, and x3 represent widgets produced per hour for each machine.
Answers
Answer:
100 x1 + 130 x2 + 16 x3 = 4758
120 x1 + 180 x2 + 28 x3 = 6504
160 x1 + 190 x2 + 10 x3 = 6720
pt 2
x1 = 15
x2 = 21
x3 = 33
Step-by-step explanation:
From the linear system , number of widgets produced per hour for each machine are x1 = 0.015 units, x2 = 0.021units, and x3 = 0.033units.
What is linear system?" Linear system is defined as the model of the given system which represents set of two or more linear equations."
According to the question,
Linear system formed as per the data given,
\(100x_{1} +130x_{2} +16x_{3} = 4.758\) ____(1)
\(120x_{1} +180x_{2} +28x_{3}= 6.504\) ____(2)
\(160x_{1} +190x_{2} +10x_{3} = 6.720\) ____(3)
Multiply linear equation (1) by 7 and ( 2) by 4 we get,
\(700x_{1} +910x_{2} +112x_{3} = 33.306\\480x_{1} +720x_{2} +112x_{3} = 26.016\)
Subtract above linear equation to eliminate \(x_{3}\) we get,
\(220x_{1} +190x_{2} = 7.29\) ____(4)
Multiply linear equation(2) by 5 and ( 3) by 14 we get,
\(600x_{1} +900x_{2} +140x_{3} = 32.52\\2240x_{1} +2660x_{2} +140x_{3} =94.08\)
Subtract above linear equation to eliminate \(x_{3}\) we get,
\(1640x_{1} +1760x_{2} = 61.56\\\\4( 410x_{1} +440x_{2}) = 61.56\)
\(410x_{1} +440x_{2}= 15.39\) ____(5)
Multiply linear equation (4) by 88 and ( 5) by 38 we get,
\(19360x_{1} +16720x_{2} = 641.52\\\\15580x_{1} +16720x_{2} = 584.82\)
Subtract above linear equation to eliminate \(x_{2}\) we get,
\(3780x_{1} =56.7\)
⇒\(x_{1} =0.015\)
Substitute the value of \(x_{1}\) in (5) we get,
\(410(0.015) +440x_{2}= 15.39\)
⇒\(x_{2} =0.021\)
Substitute the value of \(x_{1} and x_{2}\) in (1) we get,
\(100(0.015) +130(0.021) +16x_{3} = 4.758\)
⇒\(x_{3} = 0.033\)
Hence, number of widgets produced per hour for each machine are x1 = 0.015 units, x2 = 0.021units, and x3 = 0.033units.
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what is the probability that the censorship attack will succeed in terms of α? hint: express the probability of the fork succeeding from each active state in the state machine above
Answers
The probability of a censorship attack succeeding in terms of α (the attacker's mining power) can be calculated using the state machine representing the possible chain forks.
The attacker's success probability relies on their ability to maintain a longer private chain and ultimately replace the honest chain. The success probability depends on the attacker's mining power (α), the honest network's mining power (1-α), and the current state of the chain forks.
In general, the probability of a fork succeeding from each active state in the state machine can be calculated using a recursive approach, taking into account the likelihood of the attacker mining a block and the honest network mining a block. By evaluating these probabilities for different values of α, one can estimate the likelihood of a successful censorship attack. Remember that higher α values increase the attacker's chances of success, while lower values make it more difficult to carry out such an attack.
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name all of the radii of the circle shown in the figure.
PLS HELP ME ASAP
Answers
I need help with this
Answers
help which one is it
Answers
Answer:
I think it's 3 units to the left and 6 units down
Step-by-step explanation:
Hope I helped!
help, and please explain
Answers
The value of trigonometric ratio Cos(U) as a fraction in simplest term is 3/5.
Cosine of an angle is denoted by dividing the length of the adjacent side of the angle by the hypotnuse of the triangle .
Cos = length of the adjacent side/hypotnuse .
In the ΔSTU
ST = 8
TU = 6
SU is the hypotnuse .
To find SU , Pythagoras Theorem is used
SU² = ST² + TU²
SU² = 8² + 6²
SU² = 64 + 36
SU² = 100
SU = √100
SU = 10
For finding Cos , the adjacent side corresponding to angle U is TU
and the hypotnuse is SU .
So Cos(U) = TU/SU
Cos(U) = 6/10
Writing in Simplest Form we get ,
Cos(U) = 3/5
Therefore , the value of trigonometric ratio Cos(U) as a fraction in simplest term is 3/5.
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PLEASE ANSWER THANK YOU!
Match each equation to a value that makes it true.
Answers
1.) 1/2x = -5 goes with x=-10
2.) -2x = -9 goes with x = 4 1/2
3.) x+ (-2) = 1/2 goes with x= -4.5
4.) -2x = 7 goes with x= -3.5
5.) -2 + x = 1/2 goes with x = 2 1/2
6.) -1/2x = 1/4 goes with x= -1/2