The value of function f(x) at point x = -2 is f(-2) = -13/4.
What is value of function?
The objective function's value at a solution is given by the value function of an optimization problem, which only depends on the problem's parameters.
Function value can mean: The result of applying a function to an argument in mathematics.
Consider, the given function
[tex]f(x) = \frac{x^2-5x-1}{x-2}[/tex]
We have to find value of function f(x) at point x = -2.
Plug x = -2 in the above equation, we get
[tex]f(-2) = \frac{(-2)^2 - 5(-2)-1}{-2-2} \\f(-2) = \frac{4 + 10 - 1}{-4}\\f(-2) = \frac{13}{-4} \\f(-2) = -\frac{13}{4}[/tex]
Hence, the value of function f(x) at point x = -2 is f(-2) = -13/4.
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PLEASE HELP!!!!!!!!
Given 2 and one-eighth times negative 7 times five tenths, determine the product.
negative fourteen and five eightieths
negative 7 and seven sixteenths
fourteen and five fortieths
7 and one eighth
Answer:
Negative seven and seven sixteenths
Step-by-step explanation:
2⅛ x (-7) x 5/10
= 17/8 x (-7) x 1/2
= - 119/16
= - 7 7/16
Please help me. I don't want to get the answer wrong
Answer:
photo?
Step-by-step explanation:
f(x) = 8 sin [2(x+3)] +9?
Answer:
Step-by-step explanation:
f(x) = 8 sin [2(x+3)] + 9
x = 8 sin [2(y+3)] + 9
isolate y [tex](f^{-1}(x))[/tex]:
x/8 - 9 = sin[2(y+3)]
[tex]sin^{-1}(\frac{x}{8} - 9) = 2(y+3)[/tex]
= 2y + 6
[tex]sin^{-1}(\frac{x}{8} - 9) = 2y + 6\\sin^{-1}(\frac{x}{8} - 9) - 6 = 2y\\\frac{sin^{-1}(\frac{x}{8} - 9) - 6}{2} = y[/tex]
100pts. Need Answer ASAP
Use the Substitution method, jan is solving the system of equations.
A. 3(−3x + 2) − 2x= −24
B. 3(−3x - 2) − 2x= −24
C. 3x − 2(−3x + 2)= −24
D. 3x − 2(−3x − 2)= −24
62/87,21
y = x + 5
3x + y = 25
Substitute x + 5 for y in the second equation.
Substitute the solution for x into either equation to find y.
The solution is (5, 10).
identify the measure of angle X:
Since the line is linear, the sum of the angles should be 180 degrees
x + 28 + 73 = 180
x = 180 - 28 - 73
x = 79 degrees
Hope this helped :)
2(x + 3) = 6(2x - 4) Solve linear equations
A new streaming service sent out a survey to 350 households to see who would be interested in its service. The company found that it could charge $55 per month, with a margin of error of ±1.3. If 1,000 people signed up for the service, what is the least amount of monthly revenue the company should expect?
$52,815
$53,700
$54,915
$56,300
Answer:
B) $53700-------------------------------------
The charge of $55 with error margin of ± 1.3 results in the least value of $(55 - 1.3) = $53.7 and greatest value of $(55 + 1.3) = $56.3.
If 1000 people signed up for the service, then the least total amount is:
$53.7*1000 = $53700Correct choice is B.
A sightseeing tour bus can carry 72 people. If 420 people want to go sightseeing on the bus, what is the minimum number of trips the bus will have to make for everyone to go sightseeing?
4
7
6
5
The solution is Option D.
The minimum number of trips of buses to carry 420 people is 5 trips
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is given as
The number of people the tour bus can carry = 72 people
The total number of people who want to go sightseeing = 420 people
So , the equation will be
The number of trips of bus to carry 420 people = total number of people who want to go sightseeing / number of people the tour bus can carry
Substituting the values in the equation , we get
The number of trips of bus to carry 420 people = 420/72
The number of trips of bus to carry 420 people = 5.8
The number of trips of bus to carry 420 people = 5 buses
Therefore , the minimum number of buses is 5 buses
Hence , The minimum number of trips of buses to carry 420 people is 5 trips
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3y= -6x+1. Find the value of y.
[tex]3y= -6x+1[/tex] for y
Divide both sides by 3:
[tex]\dfrac{3y}{3} =\dfrac{-6x+1}{3}[/tex]
[tex]\fbox{y = $-2x+\dfrac{1}{3} $}[/tex]
Which pair of equations corresponds to the two sets of
data in the table?
X
-2
-1
0
1
2
У1
-2
0
2
4
6
Y₂
4
4
4
4
4
Answer:
Step-by-step explanation:
Given △
△
M
T
S
and △
△
S
Q
P
, find SP.
Answer:
22
Step-by-step explanation:
Corresponding sides of similar triangles are proportional.
[tex]\frac{3x+2}{5x-4}=\frac{15}{20}=\frac{3}{4} \\ \\ 12x+8=15x-12 \\ \\ 3x=20 \\ \\ \therefore SP=20+2=22[/tex]
A coach is buying snacks for 22 players at a soccer match. She pays a total of $77 to
buy each player a bottle of water and an energy bar. The price of one energy bar is $2.
Let w equal the price of a bottle of water. Write an equation that
represents the situation.
Answer: 22( w + 2 ) =77 and the amount of the water bottle would be 1.50
Step-by-step explanation: i dont know what to write??
Seven less than the product of a number N and 1/4, is no more than 98.
The algebraic expression for the statement is 1/4N - 7 ≤ 98
How to determine the algebraic expression for the statement?From the question, we have the following parameters that can be used in our computation:
Mathematical statement: "Seven less than the product of a number N and 1/4, is no more than 98."
The above mathematical statement is an inequality statement
The term "no more than" means less than or equal to 98
So, we have the following representation
Seven less than the product of a number N and 1/4, ≤ 98.
Represent "number" with N
So, we have the following representation
Seven less than the product of N and 1/4, ≤ 98.
Express as products
Seven less than 1/4N ≤ 98
"less than" here means minus
So, we have
1/4N - 7 ≤ 98
Hence, the algebraic expression is 1/4N - 7 ≤ 98
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5 divided by 4.75 i need help
Answer:
1.05
Step-by-step explanation:
5/4.75
1 1/20
Marta walked at 2.9 miles per hour for 0.52 hours. How far did she walk?
Answer:
She walked 1.508 miles
Step-by-step explanation:
In 1 hour, Marta can walk 2.9 miles
In 0.52 hours, she can walk 2.9 x 0.52 = 1.508 miles
Identify the augmented matrix for the system of equations and the solution using row operations. 3x+4y=23.5x-y=23
The augmented matrix for the system of equations 3x + 4y = 23, 5x - y = 23 is [tex]\left[\begin{array}{ccc}3&4&|23\\5&-1&|23\end{array}\right][/tex].
What is an augmented matrix?A new matrix, referred to as an augmented matrix, is produced by combining the columns of two existing matrices. The augmented matrix is a crucial component when employing matrices to resolve straightforward linear equations. The number of rows in the augmented matrix is equal to the number of variables in the linear equation. The augmented matrix can be defined as the union of two straightforward matrices along the columns. If the first matrix has m columns and the second matrix has n columns, the augmented matrix will have m + n columns.
The given system of equations is
3x + 4y = 23
5x - y = 23
We can write the system as an augmented matrix:
[tex]\left[\begin{array}{ccc}3&4&|23\\5&-1&|23\end{array}\right][/tex]
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Find the values of x and y
Answer:
x = 20
y = 70
Step-by-step explanation:
It's rather difficult to explain since nothing is labeled but those are the answers
What is the average rate of change for the function over the interval [-6,-4]
Answer:20
Step-by-step explanation:
Oscar drove 3 hours in 105 miles. How many miles did he drive per minute?
Answer:
35
Step-by-step explanation:
1.divide the miles that Oscar drove to get 105÷3=35
please solve for x
5x+10y=25
[tex]5x+10y=25[/tex]
Add -10y to both sides:
[tex]5x+10y+-10y=25+-10y[/tex]
[tex]5x=-10y+25[/tex]
Divide both sides by 5:
[tex]\dfrac{5x}{5} =\dfrac{-10y+25}{5}[/tex]
[tex]\fbox{y = -2y + 5}[/tex]
Write the equation in standard form for the circle passing through (–
8,2) centered at the origin.
The standard form for a circle is (x - h)2 + (y - k)2 = r2, where (h, k) is the center and r is the radius. Since the radius is not given, we need to plug in the information given. Since the center is at the origin, this is the point (0, 0). Since another point on the circle is (6, 8), that is the (x, y) value. So let's plug it into the equation:
(8 - 0)2 + (8 - 0)2 = r2 --> 82 + 82 = r2 --> 100 = r2 --> 10 = r.
Since r = 10 and the center is (0, 0), the standard form equation of this circle is (x - 0)2 + (y - 0)2 = 102 or just x2 + y2 = 100.
What is radius?In classical geometry, a radius of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin radius, meaning ray but also the spoke of a chariot wheel.A radius is a straight line from the center of a circle to the circumference of a circle. The distance from the center point to any endpoint on the circle.To learn more about radius refer to:
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how to simplify this equation
Answer:
25x^2√(2x)
Step-by-step explanation:
2√(50x^5) + 5x√(18x^3) =
2√((2*25) * x^(4+1)) + 5x√((2*9) * x^(2+1)) =
2√(2 * 5^2 * x^4 * x^1) + 5x√(2 * 3^2 * x^2 * x^1) =
5*2√(2 * 1 * x^(2^2) * x) + 3*5x√(2 * 1 * x^2 * x) =
10√(2 * x^(2^2) * x) + 15*x*x√(2 * 1 * x) =
10√(2x * (x^2)^2) + 15*x^2√(2x) =
10x^2√(2x) + 15x^2√(2x) = 25x^2√(2x)
Is △XYZ equilateral, isosceles, or neither? Explain your reasoning. (Make sure to include how/why you know which of these categories the triangle falls into!)
Answer:
equilateral
Step-by-step explanation:
You want to know if the given triangle with angles marked (2x)°, (2x)°, and (3x-30)° is equilateral, isosceles, or neither.
AnglesOn the face of it, the triangle is at least isosceles, as two angles are marked identically as (2x)°.
When we apply the angle sum theorem, we find ...
(2x)° +(2x)° +(3x -30)° = 180°
7x -30 = 180
7x = 210
x = 30
2x = 2(30) = 60
3x -30 = 3(30) -30 = 60
All of the angles have the same measure, 60°, so the triangle is equilateral.
Answer:
3 equal angles = equilateral triangle
Step-by-step explanation:
the sum of the interior angles in a triangle is 180°
2x + 2x + 3x - 30 = 180
7x = 210
x = 210 : 7
x = 30
find angle Y & Z2 x 30 = 60°
find angle x3 x 30 - 30 = 60
3 equal angles = equilateral triangle
It takes a car 4 hours to reach a destination traveling at the speed of 63km/hr. How long will the way back take if the car travels at a speed of 56km/hr? Constant of variation?
Answer:
252
Step-by-step explanation:
A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.
Speed = distance / time
Distance = speed × time
Distance it took the car, travelling for 4 hours to a destination at a speed of 63 kilometers per hour would be
4 × 63 = 252 kilometers.
If the car travels at a different speed of 56 kilometers per hour and the distance remains 252 kilometers, the time it takes will be
Time = distance / speed
= 252/56 = 4.5 hours
The time varies inversely with the speed. The more the speed, the lesser the time and the lesser the speed, the more the time.
Let speed = s and let time = t
s varies inversely with t
Introducing constant of inverse variation k, it becomes
s = k/t
When s = 56, t = 4.5
56 = k/4.5
k = 4.5 × 56 =252
This is the distance
Hope this helps!!! :)
flight of a rocket the altitude in feet attained by a model rocket t seconds into flight is given by the function h(t). find the maximum altitude (in ft) attained by the rocket. (round your answer to the nearest foot.) h(t)
the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot) with time.
To find the maximum altitude attained by the rocket, we need to find the vertex of the function h(t). We can do this by taking the derivative of the function and setting it equal to 0.
h'(t) = -32t + 300
Setting h'(t) = 0, we get
-32t + 300 = 0
32t = 300
t = 300/32
hence the time t ≈ 9.375
Now, we can substitute the value of t in the original equation h(t) to get the maximum altitude attained by the rocket.
h(9.375) = -16(9.375)2 + 300(9.375)
h(9.375) = 300 ft
Therefore, the maximum altitude attained by the rocket is 300 ft (rounded to the nearest foot).
The complete question is :
flight of a rocket the altitude in feet attained by a model rocket t time seconds into flight is given by the function h(t). find the maximum altitude (in ft) attained by the rocket. (round your answer to the nearest foot.) h(t)= -16t2 + 300t
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Approximate square root 46
to the tenths place.
If y³ + x² - 1 = 0 then find dy/dx
at the point (-3, 2).
The value of the derivative of the function y³ + x² - 1 = 0 at x = -3 and y = 2 will be 1/3.
What is differentiation?The rate of change of a function with respect to the variable is called differentiation. It can be increasing or decrease.
the function is given below.
y³ + x² - 1 = 0
Differentiate the function with respect to 'x', then we have
(d/dx)(y³ + x² - 1) = 0
3y² y' + 2x = 0
3y² y' = - 2x
y' = - 2x / (3y²)
The value of dy/dx or y' at (-3, 2) will be given as,
y' = - 2(-2) / [3(2)²]
y' = 4 / 12
y' = 1/3
The worth of the subsidiary of the capability y³ + x² - 1 = 0 at x = - 3 and y = 2 will be 1/3.
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Look at picture, which answer out of the four.
Answer:im guessing 1
Step-by-step explanation:
cuz the other ones dont make sense to be the answer
a scientist makes a measurement and gets a value of . the true value is . calculate the absolute and relative error of the scientist's measurement. round your answers to a reasonable number of decimal places. also be sure your answers include any necessary symbols. absolute error: relative error:
The values of errors are found to be
(a) The absolute error = 3.1 m
(b) The relative error = 0.31 m
Given,
V = 10 m
V(approx) = 13.1 m
(A) To find absolute error
Absolute error = | Actual value - App. Value |
E = | V - V(approx) |
E = | V - V(approx) |
E = | 10 - 13.1 |
E = 3.1 m
Absolute error = 3.1 m
(B) To find the relative error
Relative error = | Absolute error / actual error |
n = | E / V |
E = 3.1 m
V = 10 m
n = | 3.1 / 10 |
n = 0.31 m
Relative error = 0.31 m
Therefore, the absolute error is 3.1 m and relative error is 0.31 m.
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[NOTE: THIS IS AN INCOMPLETE QUESTION. THE COMPLETE QUESTION IS: A scientist makes a measurement and gets a value of 13.1 m. The true value is 10.0 m. Calculate the absolute and relative error of the scientist's measurement. Round your answers to a reasonable number of decimal places. Also be sure your answers include any necessary symbols. Absolute error: relative error:]
A culture of bacteria has an initial population of 37000 bacteria and doubles
every 2 hours. Using the formula Pt = Po 2, where Pt is the population
after t hours, Po is the initial population, t is the time in hours and d is the
doubling time, what is the population of bacteria in the culture after 7 hours,
to the nearest whole number?
After 7 hours, the population of bacteria is obtained as 418544.
What are the rules of exponents?Some of the rules of exponents are as follows,
The product of two exponents having the same power is equal to the power of their base multiplied.
The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.
The initial population of bacteria is given as 37000.
And, the doubling time is 2 hours.
Then, the formula for the population of bacteria at t hour can be given as,
P(t) = P₀ × [tex]2^{t/2}[/tex] where P₀ is the initial population.
Substitute t = 7 and P₀ = 37000 to get,
P(7) = 37000 × [tex]2^{7/2}[/tex]
⇒ P(7) = 418544
Hence, the population of bacteria after 7 hours is 418544.
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