Answers
Answer:
The numbers are 16, 28
Step-by-step explanation:
Let the smallest number be x
Largest number = x + 12
x(x +12) = 448
Use distributive rule.
x*x + x *12 = 448
x² + 12x = 448
x² + 12x - 448 = 0
x² + 28x - 16x - 28*16 = 0
x(x + 28) - 16(x + 28) = 0
(x + 28)(x - 16) = 0
Given that the numbers are positive and so ignore (x+28)
x - 16 = 16
x = 16
Smallest number = 16
Largest number = x + 12 = 16 +12 = 28
Related Questions
HELPPPPPPPPPPPPPPPPPPP))))))))************
Answers
Answer:
The first option.
Step-by-step explanation:
5*6=30 and 9*6=54. We're just multiplying what we had originally by 6, meaning we'll have the same shade, but in a bigger quantity.
If y varies directly as x and y=15 when x=3 find y when x=12
Answers
y=kx
15=k3
divide by 3
15/3=k
5=k
y=5x
let x = 12
y=5*12
y=60
A vibrating string, with a damping force-opposing its motion that is proportional to the velocity, fol- lows the equation Tga'y ax² ar² where B is the magnitude of the damping force. Solve the problem if the length of the string is 5 ft with 7 = 24 lb, w = 0.1 lb/ft, and B= 2.0. Initial conditions are y(x) = 0≤x<3, 5 x X(X)|-==—=— 3≤x≤S, ay at -0 = x(x - 5). Compute a few points of the solution by difference equations.
Answers
The differential equation as a difference equation:
y(i,j+1) = [(∆x)²w²y(i,j) + (∆tB/2)(y(i,j-1) - y(i,j+1)) + 2Ty(i,j)] / [(∆x)²w² + 2T + ∆tB/2]
To solve the vibrating string problem with damping force, we can use the given equation:
T∂²y/∂t² - B∂y/∂t + w²y = 0
where T is the tension, B is the magnitude of the damping force, w is the angular frequency, and y(x,t) represents the displacement of the string at position x and time t.
Given:
Length of the string (L) = 5 ft
Tension (T) = 24 lb
Weight per unit length (w) = 0.1 lb/ft
Magnitude of damping force (B) = 2.0
We are also provided with initial conditions:
y(x) = 0 for 0 ≤ x < 3
y(x) = x(x - 5) for 3 ≤ x ≤ 5
∂y/∂t = 0 for all values of x
To solve this problem using difference equations, we can discretize the spatial domain (x-axis) into small intervals and the time domain (t-axis) into discrete time steps. Let's denote the spatial step size as ∆x and the time step size as ∆t.
For simplicity, let's assume ∆x = 1 and ∆t = 1.
To compute the points of the solution, we can use a finite difference method such as the central difference method.
Discretize the spatial domain:
Divide the interval [0, 5] into small intervals with a step size of ∆x = 1.
Let's denote the discrete spatial points as x0, x1, x2, ..., xn, where xi = i∆x.
Discretize the time domain:
Choose a time step size ∆t = 1.
Approximate the second derivative:
Using the central difference method, approximate the second derivative of y with respect to x as follows:
∂²y/∂x² ≈ (y(i+1) - 2y(i) + y(i-1)) / (∆x)²
Approximate the first derivative:
Using the central difference method, approximate the first derivative of y with respect to t as follows:
∂y/∂t ≈ (y(i,j+1) - y(i,j-1)) / (2∆t)
Apply the discretized equation:
Using the discretized versions of the derivatives, we can rewrite the differential equation as a difference equation:
T(y(i,j+1) - 2y(i,j) + y(i,j-1)) / (∆x)² - B(y(i,j+1) - y(i,j-1)) / (2∆t) + w²y(i,j) = 0
Simplify and rearrange the equation to solve for y(i,j+1):
y(i,j+1) = [(∆x)²w²y(i,j) + (∆tB/2)(y(i,j-1) - y(i,j+1)) + 2Ty(i,j)] / [(∆x)²w² + 2T + ∆tB/2]
Apply the initial conditions:
Set the initial conditions y(x,0) = 0 for 0 ≤ x < 3 and y(x,0) = x(x - 5) for 3 ≤ x ≤ 5.
Iterate the difference equation:
Using the obtained formula for y(i,j+1), iterate the difference equation for each spatial point and time step. Start with j = 0 (initial condition) and increment j by 1 for each time step.
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the sum of 8 and -13.
Answers
Answer:
-104 is the answer .....
Gasoline is an ident fuel for transportation because of has a _ L energy density and is is _ if making it highly partable. The statement above is completed correctly ty the information in row Select one: 4. highy a hquid b. high; fammabie c. low; a liguid d. low; flammable Considering haw most petroleum is used, the biggest concern we hove with its ute is Select one: In. add deposition emisalons b. ground level erane C. carbon diavide emissions d. particulates in the air
Answers
The statement "Gasoline is an ideal fuel for transportation because it has a high energy density and is highly portable" is completed correctly by the information in option (a): "high; flammable."
Gasoline is known for its high energy density, meaning it contains a significant amount of energy per unit volume. This characteristic allows vehicles to carry a sufficient amount of fuel for long-distance travel without requiring excessive storage space. Additionally, gasoline is highly portable due to its liquid form, which makes it easy to transport and dispense into vehicles.
Regarding the biggest concern associated with the use of petroleum, the correct option is (c): "carbon dioxide emissions." When petroleum products like gasoline are burned, they release carbon dioxide (CO2) into the atmosphere. CO2 is a greenhouse gas that contributes to global warming and climate change. The combustion of petroleum fuels, especially in the transportation sector, is a major source of CO2 emissions.
While other concerns such as air pollutants (particulates in the air) and environmental impacts (ground level emissions, oil spills) are also associated with petroleum use, the significant contribution of CO2 emissions to climate change makes it the most pressing concern. Addressing carbon dioxide emissions from the burning of petroleum fuels is essential to mitigate the impact of transportation on climate change and promote the use of more sustainable and cleaner energy sources.
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the expected value of an unbiased estimator is equal to the parameter whose value is being estimated. true/false
Answers
The statement "the expected value of an unbiased estimator is equal to the parameter whose value is being estimated" is true.
An estimator is a function of the sample data used to estimate the value of a population parameter. An estimator is said to be unbiased if its expected value is equal to the true value of the population parameter. In other words, if we were to repeatedly take samples from the population and calculate the estimator for each sample, the average value of the estimator over all the samples would be equal to the true value of the population parameter. The expected value of an unbiased estimator is a key property because it ensures that the estimator is not systematically overestimating or underestimating the population parameter. Instead, the estimator provides an unbiased estimate of the population parameter on average across all possible samples. It is important to note that not all estimators are unbiased. Biased estimators may systematically overestimate or underestimate the population parameter, leading to incorrect conclusions. Therefore, unbiasedness is a desirable property for an estimator to have.
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I will mark Brainliest!!! Hurry
Answers
Answer:
Yes
Step-by-step explanation:
Congruent means equal in size and they both are 84 cm therefore they are congruent
Question 5 of 5
Select ALL the correct answers.
Sophia has a book fund to save money for her college textbooks, and she also works at a part-time job. Sophia's grandmother has
given her $1,000 to help stårt the fund. Since Sophia is working, she also adds $50 to the fund each month from the money she earns.
Select all the functions that can be used to find the total amount of money, fin), in the college book fund after n months.
f(n)= 50n + 950
f(n)
950n + 50
f(1) = 950; f(n) =
f (1)
1,000; f(n)
f (1)
f(n)
=
=
=
=
50; f(n) =
50m + 1,000
f(n-1) + 50, for n ≥ 2
f(n-1)+ 50, for n ≥ 2
f(n-1) + 1,000, for n ≥ 2
Answers
Answer:
The correct answers are:
- f(n)= 50n + 950
- f(1) = 950; f(n) = 50n + 950
- f(n) = 50n + 1,000
- f(n-1) + 50, for n ≥ 2
Find the real solution(s) of the equation. Round your answer to the nearest hundredth. 12x^4 = 78
Answers
Answer:
x = 4√104/2
Step-by-step explanation:
Solve the factorial.
The factorial \(4!\) is equal to
Answers
Answer:
4! = 24
Step-by-step explanation:
\(4! = 4 * 3 * 2 * 1 \\\\4! = 12 * 2 * 1\\\\4!= 24 * 1\\\\\boxed{4!=24}\)
Hope this helps.
Answer:
24
Step-by-step explanation:
I just did the same lesson and got it right
Each day that Barney goes to college, he either goes by bus or he walks.
The probability that Barney will go to college by bus on any day is 0.3
When Barney goes to college by bus, the probability that he will be late is 0.2
When Barney walks to college, the probability that he will be late is 0.1
Barney will go to college on 200 days next year.
Work out an estimate for the number of days Barney will be late for college next year.
Answers
Let's break down the problem step by step:
1. Probability of going by bus: The probability that Barney will go to college by bus on any given day is 0.3. Since he will go to college on 200 days next year, we can estimate that he will go by bus on 0.3 * 200 = 60 days.
2. Probability of being late when going by bus: The probability that Barney will be late when he goes to college by bus is 0.2. Therefore, on the 60 days he goes by bus, we can estimate that he will be late on 0.2 * 60 = 12 days.
3. Probability of walking: Since Barney either goes by bus or walks, the remaining days (200 - 60 = 140) are the days he walks to college.
4. Probability of being late when walking: The probability that Barney will be late when he walks to college is 0.1. Therefore, on the 140 days he walks, we can estimate that he will be late on 0.1 * 140 = 14 days.
Finally, to estimate the total number of days Barney will be late for college next year, we sum the estimated days for each mode of transportation: 12 days (going by bus) + 14 days (walking) = 26 days.
Therefore, an estimate for the number of days Barney will be late for college next year is 26 days.
The probability of an event happening is 5/9 . What are the odds in favor of the event happening?
Answers
The odds in favor of the event happening are 5 to 4.
We have,
To find the odds in favor of an event happening, we use the formula:
Odds in favor = Probability of the event happening / Probability of the event not happening
In this case,
The probability of the event happening is 5/9.
The probability of the event not happening is 1 - 5/9, which simplifies to 4/9. So the odds in favor of the event happening are:
Odds in favor
= 5/9 / 4/9
= 5/4
Therefore,
The odds in favor of the event happening are 5 to 4.
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what is x in the expression 5x +7
Answers
Answer:
-1.4
Step-by-step explanation:
5x+7=0
5x=-7
x= -1.4
Answer:
1.4
Step-by-step explanation:
5x + 7
x +\(\frac{7}{5}\)
x = 1.4
How do you write coordinates in XY?
Answers
We use the format (x, y) to write the coordinates in format XY. Coordinates XY is a coordinate that use in Cartesian coordinate.
What is Cartesian coordinate?
Cartesian coordinate is system to draw a specific location of an unique point in the numerical condition that oriented in the two constant line where the vertical line called ordinate or Y and the horizontal line called abscess or X. The Cartesian coordinate commonly use in architecture or a design of a certain object that has a certain dilate with its original plan. This design later is use to control the construction process of the original object.
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if x is a positive integer, the expression (1/n)^−2/3
is equivalent to:
Answers
If n is a positive integer, then the expression is equivalent to option A) \(\sqrt[3]{n^2}\).
What are Rational Exponents?Rational exponents are numbers which are written in the form of \(x^\frac{p}{q}\), where x is the base with positive integer and p/q is the rational exponent and q ≠ 0.
The given expression is (\(\frac{1}{n}\))^\(^\frac{-2}{3}\).
A number in the form, 1/a can be written as a⁻¹.
So 1/n can be written as n⁻¹.
So,
(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)
We have a rule for exponent that (xᵃ)ᵇ = xᵃᵇ
Using the rule,
(\(\frac{1}{n}\))^\(^\frac{-2}{3}\) = (n⁻¹)^\(^\frac{-2}{3}\)
= \(n^{-1*\frac{-2}{3}\)
= \(n^\frac{2}{3}\)
= \(n^{2*\frac{1}{3}\)
= \((n^{2})^\frac{1}{3}\)
By the definition of radicals, \(\sqrt[n]{x}\) = \((x)^\frac{1}{n}\), where x is positive integer.
So, \((n^{2})^\frac{1}{3}\) = \(\sqrt[3]{n^2}\)
Hence the equivalent expression is \(\sqrt[3]{n^2}\).
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In a large population of mesquite trees, 13% are infested with mistletoe. A biologist selects a random sample of 25 mesquite trees from this population. About how far do you expect the sample proportion of infested trees to vary from the true proportion, on average?
(a) 0.005
(b) 0.026
(c) 0.067
(d) 0.072
(e) 0.130
Answers
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Reformulate this problem (except for the equality restriction) to fit our standard form of linear programming model.
Max (Z) = -2X1 + X2 - 4X3 + 3X4
Subject to
X1 + X2 + X3 +2X4 <= 4
X1 - X3 + X4 >= -1
2X1 + X2 <= 2
X1 + 2X2 +X3 +2X4 = 2
X1, X2, X3, X4 >= 0
Answers
Maximize Z = -2x1 + x2 - 4x3 + 3x4 subject to the following constraints:
x1 + x2 + x3 + 2x4 + s1 = 4,
-x1 + x3 + x4 - s2 = -1,
2x1 + x2 + s3 = 2,
and x1 + 2x2 + x3 + 2x4 = 2, where x1, x2, x3, x4, s1, s2, s3 ≥ 0.
To reformulate the given problem in the standard form of a linear programming model, we need to convert all the inequalities into equations and express all variables as non-negative.
The standard form of a linear programming problem is as follows:
Maximize (Z) = c1x1 + c2x2 + c3x3 + c4x4
Subject to:
a11x1 + a12x2 + a13x3 + a14x4 = b1
a21x1 + a22x2 + a23x3 + a24x4 = b2
a31x1 + a32x2 + a33x3 + a34x4 = b3
an1x1 + an2x2 + an3x3 + an4x4 = bn
x1, x2, x3, x4 >= 0
Now let's reformulate the given problem:
Maximize (Z) = -2x1 + x2 - 4x3 + 3x4
Subject to:
x1 + x2 + x3 + 2x4 <= 4
-x1 + 0x2 + x3 + x4 >= -1
2x1 + x2 + 0x3 + 0x4 <= 2
x1 + 2x2 + x3 + 2x4 = 2
x1, x2, x3, x4 >= 0
The reformulated linear programming problem in standard form is as follows:
Maximize (Z) = -2x1 + x2 - 4x3 + 3x4
Subject to:
x1 + x2 + x3 + 2x4 + s1 = 4
-x1 + x3 + x4 - s2 = -1
2x1 + x2 + s3 = 2
x1 + 2x2 + x3 + 2x4 = 2
x1, x2, x3, x4, s1, s2, s3 >= 0
Note: The reformulated problem includes slack variables s1, s2, and s3 to convert the inequalities into equations, and all variables are non-negative.
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A beacon is flashing on top of a 50 foot tower. A 6 foot tall man walks constantly away from the tower at 5 feet/sec. At the instant the man is 30 feet away from the tower, what rate is the tip of his shadow moving away from the tower
Answers
Answer:\(\frac{253}{44}\)
Step-by-step explanation:
ignore the "at the instant the man is 30 feet away" part, set it as X and the man's shadow as Y.
Similar triangles so we can do \(\frac{50}{x+y} = \frac{6}{y}\).
Solve for it we get 44y = 6x
Differentiate relative to time t, we get 44y' = 6x'.
change in x (x') is equal to 5. And we get the answer y' = \(\frac{33}{44}\).
the \(\frac{33}{44}\) ft/sec is the rate of which the length of the shadow is changing. add 5 to it for the rate of the tip of his shadow moving away from the tower.
HELP ME PLEASE !!!!!!
Answers
Answer:
13.08
Step-by-step explanation:
Step 1: find the sum of all numbers
= 104.65
Step 2: divide by how many values there are
=8
Step 3: solve
104.65 ÷ 8 = 13.08125....
Step 4: round to the hundredths place
= about 13.08
əz 22. Suppose z= z(x, y) is implicitly determined by ln(x+y+z) = x+2y+3z. Then dy (z.y.a)=(-1,5,-3)
Answers
the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
n the given problem, we have an implicit equation ln(x+y+z) = x+2y+3z that defines z as a function of x and y. We are given the values dy = (-1, 5, -3).
To find the derivative dy/dx, we can use the total derivative formula and apply it to the implicit equation. The total derivative is given by dy/dx = - (∂F/∂x)/(∂F/∂y), where F = ln(x+y+z) - x - 2y - 3z.
Differentiating F partially with respect to x and y, we have (∂F/∂x) = 1/(x+y+z) - 1 and (∂F/∂y) = 1/(x+y+z) - 2.
Plugging in the given values of dy = (-1, 5, -3), we can calculate dy/dx = - (∂F/∂x)/(∂F/∂y) = -(-1)/(5-2) = 1/3.
Therefore, the derivative dy/dx is equal to 1/3 based on the given information. It's important to note that this calculation assumes that the partial derivatives (∂F/∂x) and (∂F/∂y) are not zero at the given point (z.y.a).
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The points (0, 1), (7, 1), and (2, -3) represent the vertices of a triangle. What is the area, in square units, of the triangle?
Answers
Answer:
14 \(u^2\)
Step-by-step explanation:
The attached image shows the diagram of the triangle drawn on the Cartesian plane.
We can see that it has the following measures:
base: \(b=7u\)
height: \(h=4u\)
the area of a triangle is given by the formula:
\(A=\frac{b*h}{2}\)
substituting the values:
\(A=\frac{(7u)(4u)}{2}\\ \\A=\frac{28u^2}{2} \\\\A=14u^2\)
the area, in square units, of the triangle is 14
Your school is ordering computer equipment. If c represents the cost of one personal computer and p is the cost of one printer. Write an expression for the total cost of 16 computers and 5 printers.
Answers
Answer:
16c+5p
Step-by-step explanation:
an important quality characteristic to the manufacturing of telephones is the no. of surface defects. currently, the process is operating with an average defect rate of 3 per telephone unit. what's the probability of finding one or less surface defects at a randomly selected unit.
Answers
Theprobability of discovering one or fewer surface flaws in a randomly chosen unit is 0.35.
Let X shows the number of surface defects at a randomly selected unit. Here X has Poisson distribution with parameters \(\lambda\) =3. So the probablity of finding one or less surface defects at a randomly selected unit is
\(P(X\leq 1)=\frac{e^{-3}(3)^{0}}{0!}+\frac{e^{-3}(3)^{1}}{1!}=0.199\)
Hence, the required probability is 0.199.
The probability of finding more than 3 defects at a randomly selected unit is
\(P(X > 3)=1-P(X\leq 3)=0.35\)
Therefore, the probability of discovering one or fewer surface flaws at a randomly chosen unit is 0.35.
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On a snow day, Moussa created two snowmen in his backyard. Snowman A was built to a height of 59 inches and Snowman B was built to a height of 39 inches. The next day, the temperature increased and both snowmen began to melt. At sunrise, Snowman A's height decrease by 9 inches per hour and Snowman B's height decreased by 4 inches per hour. Let � A represent the height of Snowman A � t hours after sunrise and let � B represent the height of Snowman B � t hours after sunrise. Write an equation for each situation, in terms of � , t, and determine the number of hours after sunrise when both snowmen have an equal height.
Answers
Answer:
Step-by-step explanation:
Both snowmen will have an equal height after 4 hours after sunrise.
To understand the reasoning behind the equations and solutions, we can break down the problem into several steps.
First, we are given the initial heights of Snowman A and Snowman B, 59 and 39 inches, respectively.
Next, we are told that the height of Snowman A decreases by 9 inches per hour and the height of Snowman B decreases by 4 inches per hour. This means that after t hours, the height of Snowman A will be 59 - 9t and the height of Snowman B will be 39 - 4t.
To find the number of hours after sunrise when both snowmen have an equal height, we need to set A = B and solve for t. This gives us the equation:
59 - 9t = 39 - 4t
Solving for t, we get:
20 = 5t
t = 4
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what does it mean to say that the confidence interval methods for the mean are robust against departures from normality?
Answers
The confidence interval methods for the mean are robust against departures from normality, meaning they work well with distributions that aren't normal, provided that departures from normality are not too extreme.
What is confidence interval for a mean ?A confidence interval for a mean is a range of values that is likely to contain a population mean with a certain level of confidence.
We use the following formula to calculate a confidence interval for a mean:
Confidence Interval = x +/- z*(s/√n)
where:
x: sample mean
z: the chosen z-value
s: sample standard deviation
n: sample size
They work well with distributions that aren't normal, provided that departures from normality are not too extreme.
This means that the methods of this section are not robust against poor sampling method.
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An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated. (True or False)
Answers
The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.
Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.
In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.
This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.
However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.
As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.
As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.
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5) what is the relationship between the sample size and the sampling distribution of the sample mean? what does this relationship tell us about the accuracy of our sample mean
Answers
The central limit theorem says that the sampling distribution of the mean will always follow a normal distribution when the sample size is sufficiently large. This sampling distribution of the mean isn't normally distributed because its sample size isn't sufficiently large.
Sample Size: It refers to the number of participate or observation included in a study. This number is usually represented by n.
Sampling Distribution of Mean: The mean of a sampling distribution is equal to the mean of the population.
The parameters of the sampling distribution of mean are determined by the parameters of the population:
The mean of the sampling distribution is the mean of the population.μₓ = μ
The standard deviation of the sampling distribution is the standard deviation of the population divided by the square root of the sample size.σₓ = σ / √n
We can describe the sampling distribution of the mean using this notation:
X ~ N ( μ,σ /√n)
Where,
X is the sampling distribution of the sample mean.~ means follows the distribution.N is the normal distribution.μ is the mean of the population.σ is the standard deviation of the population.n is the Sample size.The larger the sample size, the more closely the sampling distribution will follow a normal distribution.
When the sample size is small, the sampling distribution of the mean is something non- normal. That's because the central limit theorem only holds true when the sample size is sufficient large.
For Example: -
We consider a sample size of 30 to be sufficiently large.
When n < 30,
The central limit theorem doesn’t apply. The sampling distribution will follow a similar distribution to the population. Therefore, the sampling distribution will only be normal if the population is normal.
When n ≥ 30,
The central limit theorem applies. The sampling distribution will approximately follow a normal distribution.
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Can someone help me please? :(
Answers
Answer:
X = 3
3 x 3 x 3 = 27
27 - 3 =24
Hope this helps!
Find the value of x.
please i need the answer today.
Thank you.
Answers
Answer:
x = 61.92751306
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opposite / adjacent
tan x = 15/8
Take the inverse tan on each side
tan ^ -1 (tan x) = tan ^ -1 (15/8)
x = 61.92751306
Answer:
Step-by-step explanation:
tan x = 15/8
tanx = 15/8 ... 1
cot x = 8/15..... 2
multiply 1 and 2
tanx * cotx = 15/8 * 8/15
x [ tan * 1/tan] = 1
x = 1
hope it is correct. i just tried
A heated piece of metal cools according to the function c(x) = (.5)x − 11, where x is measured in hours. A device is added that aids in cooling according to the function h(x) = −x − 3. What will be the temperature of the metal after five hours? (1 point)
−8° Celsius
26° Celsius
32° Celsius
56° CelsiusWhat is the answer?