Answers
Answer:
g(-1 )=-1 and g(2)+g(1)=7
Step-by-step explanation:
If g(x) = x^3+x^2-x-2 find g(-1)
if we find g(-1)
we substitute all the x's in the function with -1
-1^3+-1^2-(-1)-2
-1^3 = -1
-1^2 = 1
-1+1+1-2
(two minuses make a plus)
-1+1 = 0
0+1 = 1
1-2 = -1
if x=-1, g(-1) is -1
g(2)+g(1)
substitute the x's in the function with 2 and 1 and add your results
2^3+2^2-2-2
2^3 = 8, 2^2 = 4
8+4-2-2
8+4= 12, 12-2 = 10, 10-2 = 8
g(2)=8
g(1) now
1^3 + 1^2-1-2
1^3=1, 1^2 = 1
1+1-1-2
1+1 = 2, 2-1 = 1, 1-2 = -1
g(3) = -1
g(2) (which equals 8) + g(3) (which equals -1) =
8+(-1) = 7
g(2)+g(3)=7
Related Questions
consider a triangle ABC. Suppose that a=16, b=30, and c=35. Solve the triangle. Carry your intermediate computations to at least four decimal places and round your answers to the nearest tenth
Answers
9514 1404 393
Answer:
A = 27.1°B = 58.8°C = 94.1°Step-by-step explanation:
An angle can be found using the Law of Cosines.
c² = a² +b² -2ab·cos(C)
C = arccos((a² +b² -c²)/(2ab)) = arccos((16² +30² -35²)/(2·16·30))
C = arccos(-69/960) ≈ 94.1217°
Then another angle can be found using the Law of Sines:
sin(B)/b = sin(C)/c
B = arcsin(b/c·sin(C)) ≈ 57.7516°
The third angle can be found from the sum of angles of a triangle.
A = 180° -94.1217° -58.7516° = 27.1267°
The angles of the triangle are about (A, B, C) = (27.1°, 57.8°, 94.1°).
A landscaper buys 1 gallon of plant fertilizer. He uses 1/5 of the fertilizer, and then divides the rest into 3 smaller bottles. How much does he put in each bottle?
Answers
Answer:
[tex]\frac{4}{15}[/tex] of a gallon per bottle
Step-by-step explanation:
1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{5}[/tex]
[tex]\frac{4}{5}[/tex] / 3 = [tex]\frac{4}{5}[/tex] x [tex]\frac{1}{3}[/tex] = [tex]\frac{4}{15}[/tex]
hello how are you today. Question 2(×+-5)+×=×+(-6)
Answers
Answer:
x = 2
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
2(x + -5) + x = x + (-6)
Step 2: Solve for x
[Distributive Property] Distribute 2: 2x - 10 + x = x - 6[Addition] Combine like terms (x): 3x - 10 = x - 6[Subtraction Property of Equality] Subtract x on both sides: 2x - 10 = -6[Addition Property of Equality] Add 10 on both sides: 2x = 4[Division Property of Equality] Divide 2 on both sides: x = 2Answer:
x=2 ( see Image below)
Step-by-step explanation:
cancel equal terms on both sides of the equation
2(x-5)=-6
move the constant to the right -hand side and change its sign
2x= -6 +10
Calculate the sum
2x=4
divide both sides of the equation by 2
x=2
Plsssss ans I am suffering
Answers
how to solve letters and numbers in a box
Answers
by selling 33m of cloth ,prabha gained the selling price 11 m.what is the gain percent
Answers
Answer:
The gain percent is 33.3 %
Step-by-step explanation:
Let the selling price of 1 m cloth is p.
Cost of 33 m = 33 p
gain = cost of 11 m = 11 p
The gain percentage is given by
[tex]\frac{11 p}{33 p}\times 100\\\\= 33.3 %[/tex]
The gain percent is 33.3 %.
what is 1.0185 rounded to the nearest thousandth???
Answers
Answer:
1.019 is the answer
Help me with this answer I don’t it
Answers
Answer:
f(-2) = g(-2) this is the answer
Please help me with solving these. Thank you very much. Have a great day!
Answers
Answer:
Problem 20)
[tex]\displaystyle \frac{dy}{dx}=(\cos x)^x\left(\ln \cos x-x\tan x\right)[/tex]
Problem 21)
A)
The velocity function is:
[tex]\displaystyle v(t) =2\pi(\cos(2\pi t)-\sin(\pi t))[/tex]
The acceleration function is:
[tex]\displaystyle a(t)=-2\pi^2(2\sin(2\pi t)+\cos(\pi t))[/tex]
B)
[tex]s(0)=2\text{, }v(0) = 2\pi \text{ m/s}\text{, and } a(0) = -2\pi^2\text{ m/s$^2$}[/tex]
Step-by-step explanation:
Problem 20)
We want to differentiate the equation:
[tex]\displaystyle y=\left(\cos x\right)^x[/tex]
We can take the natural log of both sides. This yields:
[tex]\displaystyle \ln y = \ln((\cos x)^x)[/tex]
Since ln(aᵇ) = bln(a):
[tex]\displaystyle \ln y =x\ln \cos x[/tex]
Take the derivative of both sides with respect to x:
[tex]\displaystyle \frac{d}{dx}\left[\ln y \right]=\frac{d}{dx}\left[x \ln \cos x\right][/tex]
Implicitly differentiate the left and use the product rule on the right. Therefore:
[tex]\displaystyle \frac{1}{y}\frac{dy}{dx}=\ln \cos x+x\left(\frac{1}{\cos x}\cdot -\sin(x)\right)[/tex]
Simplify:
[tex]\displaystyle \frac{1}{y}\frac{dy}{dx}=\ln \cos x-\frac{x\sin x}{\cos x}[/tex]
Simplify and multiply both sides by y:
[tex]\displaystyle \frac{dy}{dx}=y\left(\ln \cos x-x \tan x\right)[/tex]
Since y = (cos x)ˣ:
[tex]\displaystyle \frac{dy}{dx}=(\cos x)^x\left(\ln \cos x-x\tan x\right)[/tex]
Problem 21)
We are given the position function of a particle:
[tex]\displaystyle s(t)= \sin (2\pi t)+2\cos(\pi t)[/tex]
A)
Recall that the velocity function is the derivative of the position function. Hence:
[tex]\displaystyle v(t)=s'(t)=\frac{d}{dt}[\sin(2\pi t)+2\cos(\pi t)][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} v(t) &= 2\pi \cos(2\pi t)-2\pi \sin(\pi t)\\&=2\pi(\cos(2\pi t)-\sin(\pi t))\end{aligned}[/tex]
The acceleration function is the derivative of the velocity function. Hence:
[tex]\displaystyle a(t)=v'(t)=\frac{d}{dt}[2\pi(\cos(2\pi t)-\sin(\pi t))][/tex]
Differentiate:
[tex]\displaystyle \begin{aligned} a(t)&=2\pi[-2\pi\sin(2\pi t)-\pi\cos(\pi t)]\\&=-2\pi^2(2\sin(2\pi t)+\cos(\pi t))\end{aligned}[/tex]
B)
The position at t = 0 will be:
[tex]\displaystyle \begin{aligned} s(0)&=\sin(2\pi(0))+2\cos(\pi(0))\\&=\sin(0)+2\cos(0)\\&=(1)+2(1)\\&=2\end{aligned}[/tex]
The velocity at t = 0 will be:
[tex]\displaystyle \begin{aligned} v(0)&=2\pi(\cos(2\pi (0)-\sin(\pi(0))\\&=2\pi(\cos(0)-\sin(0))\\&=2\pi((1)-(0))\\&=2\pi \text{ m/s}\end{aligned}[/tex]
And the acceleration at t = 0 will be:
[tex]\displaystyle \begin{aligned} a(0) &= -2\pi ^2(2\sin(2\pi(0))+\cos(\pi(0)) \\ & = -2\pi ^2(2\sin(0)+\cos(0)) \\ &= -2\pi ^2(2(0)+(1)) \\ &= -2\pi^2(1) \\ &= -2\pi^2\text{ m/s$^2$} \end{aligned}[/tex]
Solve the equation by completing the square. Round to the nearest hundredth x^2 + 2x = 15
Answers
Answer:
x = 3, x = -5
Step-by-step explanation:
A perfect square trinomial is represented in the form a^2 + 2ab + b^2. We are already given the a^2 term, x^2, and the 2ab term, 2x. From this we can say:
a^2 = x^2
a = x
Now, we can substitute x for a in the other expression to create the equation:
2ab = 2x
2(x)b=2x
b = 1
From this, b^2 is one, so, to get our trinomial all on one side, we add 1 to both sides:
x^2 + 2x = 15
x^2 + 2x + 1 = 16
Now, we can factor. The perfect square trinomial factors into (a + b)^2. In this case, a is x, and b is one. We can factor and get:
(x + 1)^2 = 16
Now, we take the square root of both sides:
x + 1 = ± 4
We can separate this into two equations and solve:
x + 1 = 4
x = 3
x + 1 = -4
x = -5
Answer:
Step-by-step explanation:
x^2 + 2x = 15
x^2 + 2x + [1/2(2)]^2 = 15 + [1/2(2)]^2
(x + 1/2(2) )^2 = 15 + [(1/2)(2)]^2
(x + 1)^2 = 15 + 1^2
(x + 1)^2 = 15 + 1
(x+1)^2 = 16 Take the square root of both sides.
sqrt( (x + 1)^2 ) = sqrt(16)
x + 1 = +/- 4
x + 1 = 4
x = 4 - 1 = 3
x + 1 = -4
x = -4 - 1
x = - 5
So the roots are 3 and - 5
Ahmed can 8 1/3 km in one hour. how much distance will he cover in 2 2/5
Answers
Answer:
In 2 2/5 hours, he will cover 20 km.
Step-by-step explanation:
Given that,
Ahmed can 8 1/3 km in one hour.
We need to find the distance he cover in 2 2/5 h.
In 1 hour = 8 1/3 km = 25/3 km
2 2/5 hour means 12/5 hour
In 12/5 hour = 12/5 × 25/3 km
= 20 km
So, in 2 2/5 hours, he will cover 20 km.
Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows:
Category Product 1 Product 2 Product 3
Profit/unit $30 $50 $20
Machine 1 time/unit 0.5 2.0 0.75
Machine 2 time/unit 1.0 1.0 0.5
Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 100 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 20% of the units produced.
How many units of each product should be produced to maximize the total profit contribution?
Product # of units
1
2
3
What is the projected weekly profit associated with your solution?
Profit = $
How many hours of production time will be scheduled on each machine? If required, round your answers to two decimal places.
Machine Hours Schedule:
Machine 1 Hours
Machine 2 Hours
What is the value of an additional hour of labor? If required, round your answers to two decimal places.
$
Assume that labor capacity can be increased to 120 hours. Develop the optimal product mix, assuming that the extra hours are made available.
Product # of units
1
2
3
Profit = $
Would you be interested in using the additional 20 hours available for this resource?
Answers
Answer:
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
Step-by-step explanation:
Profit $ mach. 1 mach. 2
Product 1 ( x₁ ) 30 0.5 1
Product 2 ( x₂ ) 50 2 1
Product 3 ( x₃ ) 20 0.75 0.5
Machinne 1 require 2 operators
Machine 2 require 1 operator
Amaximum of 100 hours of labor available
Then Objective Function:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Constraints:
1.-Machine 1 hours available 40
In machine 1 L-H we will need
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
2.-Machine 2 hours available 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
3.-Labor-hours available 100
Machine 1 2*( 0.5*x₁ + 2*x₂ + 0.75*x₃ )
Machine 2 x₁ + x₂ + 0.5*x₃
Total labor-hours :
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
4.- Production requirement:
x₁ ≤ 0.5 *( x₁ + x₂ + x₃ ) or 0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
5.-Production requirement:
x₃ ≥ 0,2 * ( x₁ + x₂ + x₃ ) or -0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
The model is:
z = 30*x₁ + 50*x₂ + 20*x₃ to maximize
Subject to:
0.5*x₁ + 2*x₂ + 0.75*x₃ ≤ 40
1*x₁ + 1*x₂ + 0.5*x₃ ≤ 40
2*x₁ + 5*x₂ + 2*x₃ ≤ 100
0.5*x₁ - 0.5*x₂ - 0.5*x₃ ≤ 0
-0.2*x₁ - 0.2*x₂ + 0.8*x₃ ≥ 0
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
After 6 iterations with the help of the on-line solver AtomZmaths we find
z (max) = 1250 $
x₁ = 25 x₂ = 0 x₃ = 25
Find the Length of ST
Answers
Step-by-step explanation:
Consider Similarity and enlargement
To get the enlargement factor,
Take the ratio result of any two similar sides. i.e
PQ/AB = 3.6/2 = 1.8
The enlargement factor is 1.8
To get ST, consider ED then multiply it by the enlargement factor. i.e
= 5 x 1.8
= 9
What's the surface area of this shape???
Answers
Answer:
197 in^2
Step-by-step explanation:
Add the areas of each face:
2 trapezoid faces:
(5+9) ÷ 2 x 5 = 35
2(35) = 70 in^2
2 squares:
5 x 5 = 25
2(25) = 50 in^2
Rectangular base:
5 x 9 = 45 in^2
Area of slanted rectangle:
6.4 x 5 = 32 in^2
Add:
32 + 45 + 50 + 70 = 197
the line below are parallel. If green line has a slope of 2/5 what is the slope of the red line? enter your answer as an integer or fraction in lowest terms
Answers
Answer:
if they are parallel it would almost be opposite but they would be negative instead of positive
The ratio of copper to zinc in a certain alloy is 3 to 2. If 30 grams of copper are used, how many grams of zinc are needed to make this alloy?
Answers
Answer:
zinc is 20grams
Step-by-step explanation:
Given data
Ratio copper :zinc = 3:2
Copper =30 grams
Applying the ratio
3/2=30/x
Cross multiply
3x=30*2
3x=60
Divide both sides by 3
x=60/3
x=20
Hence zinc is 20grams
this question is much too hard would anyone please help me
Answers
Answer:
B and C are the same angles so if B is 60 so is C
Answer:
b= 60
c= 60
Step-by-step explanation:
<b and 120 form a straight line so the add to 180
b+120 =180
b = 180-120
b = 60
angles b and c are alternate interior angles so they are equal
b = c= 60
7)
8)
13x + 1/9x + 3
A) 6
C) -7
B) 8
D) 7
Α)
C)
I
Answers
Answer:
b) 8
Step-by-step explanation:
the angles are a linear pair meaning that they have a sum of 180. So 22x+4+180. Solve that and x=8
Answer:
B) 8
Step-by-step explanation:
(13x + 1) + (9x + 3) = 180
Combine like terms
22x + 4 = 180
Subtract 4 from both sides
22x = 176
Divide both sides by 22
x = 8
B
These triangles
are congruent by
the triangle
congruence
postulate [?].
D
E
A. SSS
B. SAS
C. Neither, they are not congruent
Answers
Answer:
SAS
Step-by-step explanation:
AC ≅ EC (Given), ∠ACB ≅∠ECD ( Vertical Angles), and BC ≅ DC
Use elimination to solve the system of equations.
10x + 5y = 55
y - 2x = -9
A. (1,1)
B. (1,5)
C. (5, 1)
D. (4,5)
Answers
Answer:
C. (5,1)
Step-by-step explanation:
10x+5y=55 equation 1
y-2x=-9 equation 2
y=-9+2x isolate y in equation 2
10x+5(-9+2x)=55 substitute value of y from equation 2 into equation 1
10x-45+10x=55
20x=100
x=5
solve for y by using x value (5) in either equation
y-2x=-9
y-2(5)=-9
y-10=-9
y=1
Solve the system by substitution. If the system is inconsistent or has dependent equations, say so.
y = 5x
20x - 4y = 0
Answers
Answer:
Dependent Equations
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 5x
20x - 4y = 0
Step 2: Solve for x
Substitution
Substitute in y [2nd Equation]: 20x - 4(5x) = 0Multiply: 20x - 20x = 0Combine like terms: 0 = 0Here we see 0 does indeed equal 0.
∴ our systems has an infinite amount of solutions.
Answer:
0
Step-by-step explanation:
y = 5x
20 x - 4 y = 0substitute the value of y in equation
= 20x - 4 ( 5x ) = 0multiply to get 20x
= 20x - 20x = 0collect like terms
= 0we can see here that 0 indeed equal 0.
so, system has an infinite solutions.
Workers employed in a large service industry have an average wage of $9.00 per hour with a standard deviation of $0.50. The industry has 64 workers of a certain ethnic group. These workers have an average wage of $8.85 per hour. Calculate the probability of obtaining a sample mean less than or equal to $8.85 per hour. (Round your answer to four decimal places.)
Answers
Answer:
The probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
Step-by-step explanation:
We are given that
Average wage, [tex]\mu=[/tex]$9.00/hour
Standard deviation,[tex]\sigma=[/tex]$0.50
n=64
We have to find the probability of obtaining a sample mean less than or equal to $8.85 per hour.
[tex]P(\bar{x} \leq 8.85)=P(Z\leq \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}})[/tex]
Using the values
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{8.85-9}{\frac{0.50}{\sqrt{64}}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq \frac{-0.15}{\frac{0.50}{8}})[/tex]
[tex]P(\bar{x}\leq 8.85)=P(Z\leq -2.4)[/tex]
[tex]P(\bar{x}\leq 8.85)=0.0082[/tex]
Hence, the probability of obtaining a sample mean less than or equal to $8.85 per hour=0.0082
Which statement correctly compares the centers of the distributions?
A. The median penguin height is greater at Park Zoo than at Cityview Zoo.
B. The median penguin heights are the same.
C. The median penguin height is greater at Cityview Zoo than at Park
Zoo.
D. The range of penguin heights is greater at Cityview Zoo than at
Park Zoo.
Answers
The median penguin height is greater at Cityview Zoo than at Park
Zoo, Option C is correct.
Mode is the most occuring number.
The range is the difference of the highest value and the lowest value.
The median is the middle value in a set of data
After finding the range and medians of the given data.
The median penguin at Cityview Zoo is 42 cm tall,
The median penguin at Park Zoo is barely 41 cm tall.
Cityview Zoo's median penguin height is higher than that of Park Zoo.
Hence, the median penguin height is greater at Cityview Zoo than at Park Zoo.
To learn more on Statistics click:
https://brainly.com/question/30218856
#SPJ7
Find the slope of each line (each block is one unit):
Answers
Answer:
-2
Step-by-step explanation:
Slope formula for any given two points
(y2 - y1 / x2 - x1)
The points chosen may vary but the points I chose were (0,1) and (2,-3)
Our next step is to identify the variables
y2 = -3
y1 = 1
x2 = 2
x1 = 0
We then plug in the values into the slope formula
slope = ( -3 - 1 ) / ( 2 - 0 )
Simply
Slope = -4 / 2
Simply even further
Slope = -2
the slope of each line is -2.
Answer:
Solution Given:
let's find out the given points.
1st point[tex] (x_1,y_1)=(0,1)[/tex]
another point is:
[tex](x_2,y_2)=(2,-3)[/tex]
now
By using slope formula
[tex] \green{\boxed{m=\frac{y_2-y_1}{x_2-x_1}}}[/tex]
now
substituting value
we get
m=[tex]\frac{-3-1}{2-0}=\frac{-4}{2}=-2[/tex]
A muffin recipe calls for 3 times as much flour as sugar.
Use this information for
Write an expression that can be used to
find the amount of flour needed for a given
amount of sugar. Tell what the variable in
your expression represents
use the variable ( s ) to represent the amount of sugar
Answers
f=3s
f = the amount of flour
Hope this helps! :)
the pizza Question i cant do and need desperate help
Answers
Answer:
the answer is c
Step-by-step explanation:
a solid wooden cube has 4.35cm long.calculate the volume of the cube
Answers
Answer:
82.31
Step-by-step explanation:
I believe this is correct, if it isn't feel free to let me know and I will fix it. I'm sorry in advance if this is incorrect.
anna opened a bank account she adds the same amount of money to it
Answers
Answer:
What’s the numbers? Or the question?
Step-by-step explanation:
công thức đạo hàm của ln(u) = ?
Answers
Answer:
U'/U
Step-by-step explanation:
A checker board is a square board that is divided into smaller squares, with eight squares along each side. Describe how to find the number of small squares on a checker board without counting.