Answer:
ffhjjrhjzxuzdjzdjzsjezjdifi
12, 3.1.52
If f(x) = x and g(x) = 2x³, find f[g(x)], and g[f(x)]
Given that [tex]f(x) = x[/tex] and [tex]g(x) = 2x^3[/tex], we have
[tex]f(g(x)) = f(2x^3) = 2x^3[/tex]
and
[tex]g(f(x)) = g(x) = 2x^3[/tex]
The shadow of a tree is 10m longer when the angle of elevation of the sun is 45° than when it is 60°, find the height of the tree.
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The length of the tree is 23.66 meters.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Let the height of the tree be represented by x.
The length of the shadow when the angle of elevation is 45°.
Length of shadow = x/ Tan(45°)
The length of the shadow when the angle of elevation is 60°.
Length of shadow = x/ Tan(60°)
Now, since the difference between shadows is 10 meters. Therefore, we can write,
x/ Tan(45°) - x/ Tan(60°) = 10m
x[1/ Tan(45°) - 1/ Tan(60°) ] = 10 m
x (0.42265) = 10 m
x = 23.66 m
Hence, the length of the tree is 23.66 meters.
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Multiply or divide the following expression: Reduce all answers to lowest terms. Factor the following completely.
Let f(x) = -x^2-4x+5
f(-3) = _______
f(3) + f(-3) = _______
A function assigns the values. The value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
Given the function f(x)=-x²-4x+5, therefore, the value of f(x) when the value of x is -3 is,
f(-3) = -(-3)² - 4(-3) + 5
f(-3) = -9 + 12 + 5
f(-3) = 8
Now, the value of f(x) when the value of x is 3 is,
f(3) = -(3)²-4(3)+5
f(3) = - 9 - 12 + 5
f(3) = -16
further, the value of f(3) + f(-3) is,
f(3) + f(-3) = -16 + 8
f(3) + f(-3) = -8
Hence, the value of f(-3) and f(3) + f(-3) is 8 and -8, respectively.
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Kubin Company's relevant range of production is 29,000 to 33,000 units. When it produces and sells 31,000 units, its average costs per unit are as follows:
Direct materials $8.90
Direct labor $5.90
Variable manufacturing overhead $3.40
Fixed manufacturing overhead $6.90
Fixed selling expense $5.40
Fixed administrative expense $4.40
Sales commissions $2.90
Variable administrative expense $2.40
1. If 29,000 units are produced and sold , what is the variable cost per unit produced and sold ?
2. If 33,000 units are produced and sold , what is the variable cost per unit produced and sold ?
3. If 29,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
4. If 33,000 units are produced and sold , what is the total amount of variable cost related to the units produced and sold ?
5. If 29,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
6. If 33,000 units are produced , what is the average fixed manufacturing cost per unit produced ?
7. If 29,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
8. If 33,000 units are produced , what is the total amount of fixed manufacturing overhead incurred to support this level of production ?
Give the slope and the y-intercept of the line y=10x+9
Answer:
Slope: 10
Y-intercept: +9
Step-by-step explanation:
An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.
Name the marked angle in 2 different ways.
W
T
V
U
The marked angle can be named in two different ways as: ∠HFG and ∠GFH.
How to Name an Angle?To name an angle, the letter representing the vertex would always be at the middle.
Given the angle marked in the image below, where F is the vertex, we can name the marked angle in two different ways with F at the center as:
∠HFG and ∠GFH
Thus, the two different ways to name the marked angle are:
∠HFG and ∠GFH.
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St^2 e^-10t dt
Evaluate the intergral
It looks like you're talking about the indefinite integral
[tex]\displaystyle \int t^2 e^{-10t} \, dt[/tex]
Integrate by parts:
[tex]\displaystyle u\,dv = uv - \int v\,du[/tex]
Let
[tex]u = t^2 \implies du = 2t \, dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
Integrate by parts again, this time with
[tex]u = t \implies du = dt[/tex]
[tex]dv = e^{-10t} \, dt \implies v = -\dfrac1{10} e^{-10t}[/tex]
Then
[tex]\displaystyle \int t e^{-10t} \, dt = -\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt[/tex]
Putting everything together, we get
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \int t e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} + \frac15 \left(-\frac1{10} t e^{-10t} + \frac1{10} \int e^{-10t} \, dt\right)[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \int e^{-10t} \, dt[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} + \frac1{50} \left(-\frac1{10} e^{-10t}\right) + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = -\frac1{10} t^2 e^{-10t} - \frac1{50} t e^{-10t} - \frac1{500} e^{-10t} + C[/tex]
[tex]\displaystyle \int t^2 e^{-10t} \, dt = \boxed{-\frac{e^{-10t}}{500} \left(50t^2 + 10t + 1\right) + C}[/tex]
helpp me please
Find the missing term.
The roots of x2 − ( ) + 34 are 5 ± 3i.
Answer: 10
Step-by-step explanation:
The sum of the roots is [tex](5+3i)+(5-3i)=10[/tex], so the answer is 10
Daniel plays a shooting game in a funfair. He needs 48 points to get a skateboard. Each shot that hits the target will be given 6 points while 4 points will be deducted for every failed attempt. Daniel has already failed in three attempts. how many shots that are needed to hit the target for him to win the skateboard
If a-4b=18,what is 3a/81b
Answer:
You cannot solve this problem with only one given equation
Step-by-step explanation:
You need at least 2 equations to solve for two variables.
algebra 2 help needed image below urgent !!!
Answer:
Domain = x ≥ 0
Range = y ≥ 20
Step-by-step explanation:
The equation in slope-intercept form would look like this:
y = 4x + 20
The slope is $4 because that is the money that can be made depending on the week. Because he received a random $20 at the beginning, this is just an additional income.
---------------------------------------------------------------------------
In this scenario, the domain (x-values) represent the number of weeks. The range (y-values) represent the total money made.
So the domain is asking, what is the lowest/highest amount of weeks he can save for? We know the number of weeks cannot be negative because he can't save for negative weeks. However, he could save for zero weeks. He can be saving for theoretically infinite weeks. Therefore, the domain is x ≥ 0.
The range is asking, how much money can he save? Since he starts out with a baseline of $20, this is the lowest amount of money he can have. If he were to save for an infinite amount of weeks, he could make an infinite amount of money. Therefore the range is y ≥ 20.
what is the number you must add to complete the square x^2 - x
lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol lol
Which pair of equations below represents two lines that are not parallel?
Select one:
a.
y = 2x + 8 and y = 2x + 8
b.
y = ( 1 / 6 ) x + 1 /2 and y = (1 / 6 ) x + 2
c.
y = ( 1 / 6 ) x + 8 and y = 6x + 4
d.
y = ( 1 / 2 ) x + 9 and y = ( 1 / 2) x + 4
The pair of equations (c) y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
How to determine the pair of equations?A linear equation is represented as:
y = mx + b
Where m is the slope of the line
Two lines are said to be parallel if their slopes are the same
i.e. y = mx + b and y = mx + c
Using the above as a guide, the option (c) represents lines that are not parallel, because they do not have the same slope
Hence, y = (1 / 6) x + 8 and y = 6x + 4 are not parallel
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A triangular pyramid has a triangular base with height of 1.5 inches and base length of 4 inches, and height of 9 inches. What is the volume?
18 cubic inches
27 cubic inches
3 cubic inches
9 cubic inches
Answer:
V = 9 in^3
Step-by-step explanation
Comment
The formula for a Pyramid of any B is V = B * h / 3. You have to be able to calculate the Base or just be given in it.
In this case the Base is a triangle. So the first thing needed is the area of the base.
Base
Area_triangle = base length * height / 2
Neither the Base length nor the height need to be the same as the B and h used for the volume of the Pyramid
Givens
b = 4 inches
h = 1.5 inches
Area_triangle = 4 * 1.5 / 2
Area_triangle = 2 * 1.5
Area_triangle = 3 inches^2
Solution
Base (triangle) Area = 3
h = 9
V = B * h / 3
V = 3 * 9 / 3
V = 9 cubic inches
Answer V = 9 in^3
The graph of y = is reflected over the y-axis and then translated down 2 units to form f(x). Which is the graph of f(x)?
If the function is reflected over the y-axis and then translated down 2 units. the resulting function will be -∛x - 2
Transformation of coordinatesTransformation is a technique used to change the position of an object on an xy-plane.
Given the function y = ∛x
If the function is reflected over the y-axis and then translated down 2 units to form f(x), the resulting function f(x) will be:
f(x) = -∛x - 2
The graph of the resulting function is attached
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Answer:
B
Edge 2023
The other answer is incorrect!!!
Multiply by this number to make the coefficient of the variable 1
Multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have a given linear equation.
After solving the linear equation we get:
[tex]\rm \dfrac{25}{9}x = 25[/tex]
To make the coefficient of the variable 1
Multiply by 9/25 on both sides.
[tex]\rm \dfrac{9}{25}\times\dfrac{25}{9}x = 25\times \dfrac{9}{25}[/tex]
x = 9
Thus, multiply by 9/25 to make the coefficient of the variable 1 the answer is 9/25.
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Answer: the answer is 9/25
Step-by-step explanation: Multiplying both sides of the equation by 9/25 isolates x
What is the units digit of the sum 1! + 2! + 3! + 4! + 5! + ... + 1000!?
please help if you can
Which absolute value function defines this graph?
The vertex of the graph is at (-2, 3).
This means the equation is of the form [tex]f(x)=a|x+2|+3[/tex].
Substituting in the coordinates of one of the other points on the graph that is not the vertex, such as (-1, -1),
[tex]-1=a|-1+2|+3\\\\-1=a+3\\\\a=-4[/tex]
So, the equation is [tex]\boxed{f(x)=-4|x+2|+3}[/tex]
What is the distance between the two end points in the graph below
Step-by-step explanation:
10 that's what my teacher told me
5 ice creams cost 6.50 pounds. How much do 11 ice creams cost
Answer:
14.30
Step-by-step explanation:
6.50/5=1.3
so one ice cream is 1.30 pounds
1.30X11=14.3
so 11 ice creams is 14.30 pounds
A student needed to find the measure of angle b. She incorrectly said mZb=118°. Find the correct measure of angle b. What mistake did she likely make?
Answer:
D
Step-by-step explanation:
To find angle B, you should subtract 62 from 90 since because a right angle is 90 degrees.
5. Dan is making the perfect shade of purple paint for his Nana. The perfect shade of purple mixes red and blue paint at a
ratio of 4 to 5. Accidently Dan mixed five cups of red and four cups of blue, using up all his red paint. How much blue must
he add to fix his mistake?
Answer:
2 and 1/4 cups
Step-by-step explanation:
4 cups-5 cups
5 cups-?
(5×5)÷4=6 cups and 1/4
6 and 1/4-4=2 cups and 1/4
Which of the following is a geometric sequence?
• A. 6, 18, 54, 162
O B. 1, 4, 5, 9, 14
O C. 3, 6, 9, 12, 15
O D. 3, 5, 8, 13, 21
Answer: A. 6, 18, 54, 162
Step-by-step explanation:
Each term is 3 times the last, meaning the common ratio is 3.
The quantity of a good demanded rises from 1000 to 1500 units when the price falls from $1.50 to $1.00 per unit. The price elasticity of demand for this product is approximately
The price elasticity of demand for this product is approximately will be 1.
What is the price elasticity?The price elasticity is given as
[tex]\rm PE = \dfrac{\dfrac{Q_f-Q_i}{Q_f+Q_i}}{\dfrac{P_f-P_i}{P_f+P_i}}\\\\\\[/tex]
The quantity of a good demanded rises from 1000 to 1500 units when the price falls from $1.50 to $1.00 per unit.
The price elasticity of demand for this product is approximately will be
[tex]\rm PE = \dfrac{\dfrac{1500-1000}{1500+100}}{\dfrac{1.5-1}{1.5+1}}\\[/tex]
On further solving, we have
PE = (500 / 2500) x (2.5 / 0.5)
PE = 1
The price elasticity of demand for this product is approximately will be 1.
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A 3-gallon bucket of paint costs $108.60. What is the price per quart?
Answer:
9.05
Step-by-step explanation:
make gallons into quarts
quar prefix in many languages means 4
1 gallon is 4 quarts
3 gallons is 4 times 3 -> 12 quarts
just by seeing 108 and 12 the answer will be around 9
108.90 ÷ 12 = 9.05
The sum of 9 consecutive integers is 369. The middle integer is:
A. 38
B.35
C.41
D.10
PLEASE ANSWER QUICKKKk
We have an odd number of consecutive integers, therefore the middle one is equal to the average of all of them. And since the average is equal to the sum of the numbers divided by their number, the middle integer in this problem is equal to 369 divided by 9, which is equal to 41.
Each conditional statement below is true. Write its converse. If the converse is also true, combine the statements as a biconditional.If x = —10, then x2 = 100.
The converse of the statement will be : if x^2 = 100 then x = -10, which is not true.
How to find the true statement?In order to write a converse of a conditional statement "p then q", will be "q then p" the hypothesis and conclusion interchanges.
Then the converse of the statement will be :
if x^2 = 100 then x = -10,
which is not true.
Since , x = +10, then x^2 = 100
Therefore, if x^2 = 100 then x = -10, which is not true.
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Given the exponential growth function f ( x ) = 75 ( 1.02 ) x f ( x ) = 75 ( 1.02 ) x What is the initial value of the function? What is the growth factor, or growth rate of the function (as a percent)? %
Answer:
Step-by-step explanation:
The initial vale is when x = 0
- That is 75,
The growth factor is 2%.
Please help! Which choice belongs in space number 3?
Answer:
The Answer is [B]
Step-by-step explanation:
i actually dont have one
Answer:
∠MOP ≅ ∠NOQ
Step-by-step explanation:
Vertical Angle Theorem
When two straight lines intersect, they form two pairs of angles. The vertically opposite (non-adjacent) angles are congruent.
Therefore:
∠MON ≅ POQ and ∠MOP ≅ ∠NOQ
The graph of the quadratic function f(x) = - 1/2 x ^ 2 + 3 is shown. Describe the end behavior of the function.
