The transformation of the function is illustrated below
How to match the transformation?Parent function is: f(x) = 2x - 6
Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10
stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24
shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14
compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6
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please help me with these calculus bc questions
4. Compute the derivative.
[tex]y = 2x^2 - x - 1 \implies \dfrac{dy}{dx} = 4x - 1[/tex]
Find when the gradient is 7.
[tex]4x - 1 = 7 \implies 4x = 8 \implies x = 2[/tex]
Evaluate [tex]y[/tex] at this point.
[tex]y = 2\cdot2^2-2-1 = 5[/tex]
The point we want is then (2, 5).
5. The curve crosses the [tex]x[/tex]-axis when [tex]y=0[/tex]. We have
[tex]y = \dfrac{x - 4}x = 1 - \dfrac4x = 0 \implies \dfrac4x = 1 \implies x = 4[/tex]
Compute the derivative.
[tex]y = 1 - \dfrac4x \implies \dfrac{dy}{dx} = -\dfrac4{x^2}[/tex]
At the point we want, the gradient is
[tex]\dfrac{dy}{dx}\bigg|_{x=4} = -\dfrac4{4^2} = \boxed{-\dfrac14}[/tex]
6. The curve crosses the [tex]y[/tex]-axis when [tex]x=0[/tex]. Compute the derivative.
[tex]\dfrac{dy}{dx} = 3x^2 - 4x + 5[/tex]
When [tex]x=0[/tex], the gradient is
[tex]\dfrac{dy}{dx}\bigg|_{x=0} = 3\cdot0^2 - 4\cdot0 + 5 = \boxed{5}[/tex]
7. Set [tex]y=5[/tex] and solve for [tex]x[/tex]. The curve and line meet when
[tex]5 = 2x^2 + 7x - 4 \implies 2x^2 + 7x - 9 = (x - 1)(2x+9) = 0 \implies x=1 \text{ or } x = -\dfrac92[/tex]
Compute the derivative (for the curve) and evaluate it at these [tex]x[/tex] values.
[tex]\dfrac{dy}{dx} = 4x + 7[/tex]
[tex]\dfrac{dy}{dx}\bigg|_{x=1} = 4\cdot1+7 = \boxed{11}[/tex]
[tex]\dfrac{dy}{dx}\bigg|_{x=-9/2} = 4\cdot\left(-\dfrac92\right)+7=\boxed{-11}[/tex]
8. Compute the derivative.
[tex]y = ax^2 + bx \implies \dfrac{dy}{dx} = 2ax + b[/tex]
The gradient is 8 when [tex]x=2[/tex], so
[tex]2a\cdot2 + b = 8 \implies 4a + b = 8[/tex]
and the gradient is -10 when [tex]x=-1[/tex], so
[tex]2a\cdot(-1) + b = -10 \implies -2a + b = -10[/tex]
Solve for [tex]a[/tex] and [tex]b[/tex]. Eliminating [tex]b[/tex], we have
[tex](4a + b) - (-2a + b) = 8 - (-10) \implies 6a = 18 \implies \boxed{a=3}[/tex]
so that
[tex]4\cdot3+b = 8 \implies 12 + b = 8 \implies \boxed{b = -4}[/tex].
PLEASE HELP ASAP WITH EXPLANATION: If f(x) = 2f(x − 1) for all integers x, and f(n) = 3 for some integer n, find the value of
[f(n − 5)][f(n + 5)].
Answer:F to the power of 2,N to the power of 2,—25,f to the power of 2
Step-by-step explanation: i really hope under stand
Suppose that $17,699 is invested at an interest rate of 6.6% per year, compounded continuously
a) Find the exponential function that describes the amount in the account after time t, in years.
b) What is the balance after 1 year? 2 years? 5 years? 10 years?
c) What is the doubling time?
[tex]s(t) = 17699(1 .066) {}^{t} [/tex]
b)[tex]s(1) = 17699(1.066) = 18867.13 \\ s(2) = 17699(1.066) {}^{2} = 20112.36 \\ s(5) = 17699(1.066) {}^{5} = 24363.22 \\ s(10) = 17699(1.066) {}^{10} = 33536.73[/tex]
c)[tex]s(t) = 2 \times initial \: capital \: \\ s(t) = 2 \times 17699[/tex]
[tex]17699(1.066) {}^{t} = 2 (17699) \\ 1.066 {}^{t} = 2 \\ t = log¹°⁰⁶⁶(2) = 10.84511 \: years[/tex]
if this graph of f(x)=a^(x+g) +k then;
A. the domain is (h,∞) and the range is (-∞,∞)
B. the domain is (-∞,∞) and the range is (h,∞)
C. the domain is (h,∞) and the range is (k,∞)
D. the domain is (-∞,∞) and the range is (k,∞)
The correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).
Given a function f(x)=[tex]a^{x+g} +k[/tex].
We are told to find the domain and range of the function.
The domain is basically the values which we enters in a function.
The range is basically the values which we are getting by entering some values in the function.
An exponential function is given in the function which has no restrictions hence the domain is (-∞,∞).The range depends on the vertical shift given by k. Hence the range of function is (k,∞).
Hence the correct option regarding the domain and the range of the function f(x)=[tex]a^{x+g} +k[/tex] is given by that the domain is (-∞,∞) and the range of the function is (k,∞).
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Como derivar cos(2x)/tan(2x)
Use the quotient and chain rules. If
[tex]y = \dfrac{\cos(2x)}{\tan(2x)}[/tex]
then the derivative is
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) \frac d{dx}\cos(2x) - \cos(2x) \frac d{dx}\tan(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{\tan(2x) (-\sin(2x)) \frac d{dx}(2x) - \cos(2x)\sec^2(2x) \frac d{dx}(2x)}{\tan^2(2x)}[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin(2x)\tan(2x) - 2 \sec(2x) }{\tan^2(2x)}[/tex]
and we can rewrite this by
• multiplying by [tex]\frac{\cos^2(2x)}{\cos^2(2x)}[/tex],
[tex]\dfrac{dy}{dx} = \dfrac{-2\sin^2(2x)\cos(2x) - 2 \cos(2x) }{\sin^2(2x)}[/tex]
• factorizing,
[tex]\dfrac{dy}{dx} = -\dfrac{2\cos(2x) \left(\sin^2(2x) + 1\right)}{\sin^2(2x)}[/tex]
etc
If a 90ml drink has 2 parts milk and 1 part chocolate topping, how many mls of milk and chocolate topping is that?
Answer:
The milk would be 60 ml and the topping would be 30 ml
Step-by-step explanation:
If there are 2 parts milk and 1 part toppings that would be a total of 3 (2+1 =3) So we are looking for 2/3 of 90 and 1/3 of 90.
Which statement correctly compares functions f and g? function f function g An exponential function passes through (minus 1, 5), and (2, minus 1.5) intercepts axis at (1, 0), and (0, 2) Function g is a decreasing exponential function with a y-intercept of 5 and no x-intercept. A. They have different end behavior as x approaches -∞ and different end behavior as x approaches ∞. B. They have different end behavior as x approaches -∞ but the same end behavior as x approaches ∞. C. They have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞. D. They have the same end behavior as x approaches -∞ and the same end behavior as x approaches ∞.
A statement correctly compares functions f and g is that: C. they have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
What is a function?A function can be defined as a mathematical expression that defines and represents the relationship between two or more variable, which is typically modelled as input (x-values) and output (y-values).
The types of function.In Mathematics, there are different types of functions and these include the following;
Periodic functionInverse functionModulus functionSignum functionPiece-wise defined function.Function g is represented by the following table and a line representing these data is plotted in the graph that is shown in the image attached below.
x -1 0 1 2 3 4
g(x) 24 6 0 -2
Based on the line, we can logically deduce the following points:
y-intercept approaches -2.43 to 24.86.x-intercept approaches negative infinity (-∞) to infinity (∞).This ultimately implies that, a statement correctly compares functions f and g is that both functions have the same end behavior as x approaches -∞ but different end behavior as x approaches ∞.
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Please help me with this question <3
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
For two lines to be parallel, there should be angles that follow some specific properties that is usually observed with parallel lines.
We can clearly see that :
[tex] \qquad❖ \: \sf \: \angle7 \cong \angle16[/tex]
( by Alternate interior angle pair )
[tex] \qquad \large \sf {Conclusion} : [/tex]
Lines l and m are parallel to each other.
Tamela plants 6 rows of t tomato plants each. How many tomato plants did she plant?
Answer:
6t tomato plants
Step-by-step explanation:
There are 6 rows, Tamala places t in each row. We multiply 6 by t.
If t were 5, the tomato plants would be 30 since we multiply the rows by the number of tomato plants
Answer:
6t
Step-by-step explanation:
number of rows × number of plants per row = total number of plants
6 × t = 6t
Answer: 6t
Find the missing segment in the image below
Answer:
42
Step-by-step explanation:
similar triangles
24/x = (24+8)/x+14
that looks complicated so we do
8/24 = 14/x
or
24/8 = x/14
3 = x/14
x = 3*14
x = 42
we test it with the first equation
24/42 = 32/56
simplify
4/7 = 4/7
true so 42 is correct
The function f(x)=58(1.6)x represents the possible bird population in a park x years from now. Each year, the expected number of birds is ____the number the year before.
Answer:
1.6 times or 60% more than
Step-by-step explanation:
The question seems to be asking about the growth factor in the given exponential function.
Exponential functionA generic exponential function will have the form ...
quantity = (initial value) × (growth factor)^(number of intervals)
Comparing this form to the given formula ...
f(x) = 58 × 1.6^x
we see the "growth factor" is 1.6. This is the multiplier from one interval (year) to the next.
Each year the expected number of birds is 1.6 times the number the year before.
__
Additional comment
A growth factor is sometimes expressed in terms of a growth rate, usually a percentage.
growth factor = 1 + growth rate
1.6 = 1 + 0.60 = 1 + 60%
The growth rate of this bird population is 60% per year. Each year, the population is 60% more than the year before.
Answer: 1.6
Step-by-step explanation:
help please.
Malaysia police traffic department claims that 54% of fatal car accidents are caused by driver error. A researcher studies 30 randomly selected accidents and founds that 14 were caused by driver error. Using a = 0.05, is that Malaysia police traffic department's statement is true?
Answer:
The Malaysia police departments statement was true, because 14/30 is extremely close to 54% (roughly 15.5/30).
Type: Probability
Please rate this answer based on how helpful it was!Which of the following is the equation of the line that passes through the point (-5,-7) and has a slope of 2/5?
No multiple choice
The equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
How did we get the values?To find the equation of a line, we can use the point-slope form of a linear equation:
y - y₁ = m(x - x₁),
where (x₁, y₁) is the given point on the line and m is the slope.
In this case, the given point is (-5, -7) and the slope is 2/5. Substituting these values into the equation, we have:
y - (-7) = (2/5)(x - (-5)).
Simplifying further:
y + 7 = (2/5)(x + 5).
Distributing the 2/5:
y + 7 = (2/5)x + 2.
Subtracting 7 from both sides:
y = (2/5)x - 5.
Therefore, the equation of the line passing through the point (-5, -7) with a slope of 2/5 is y = (2/5)x - 5.
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A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s . The ball's height h (in meters) after t seconds is given by the following.
The value of values of t for which the ball's height is 7 meters then is 4.79secs.
What is velocity?Velocity can be regarded as a vector measurement of the rate as well as direction of motion.
It is the the speed at which something moves in one direction and with the given velocity, the time as well as the distance can be calculated as :
Given:
h=2+25t-5t^2
But h=7
Then 2+25t-5t^2=7
-5t^2++25t +2-7=0
-5t^2+25t -5=0
we can then factorize as :
-5(t^2+5t -1)=0
Solving the equation using quadratic formula, the the roots of equations are: 4.79 and -5.0
The value of values of t for which the ball's height is 7 meters then is 4.79secs.
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COMPLETE QUESTION :
A ball is thrown from an initial height of 2 meters with an initial upward velocity of 25 m/s . The ball's height h (in meters) after t seconds is given by the following. h=2+25t-5t^2
Find all values of t for which the ball's height is 7 meters.
Round your answer(s) to the nearest hundredth.
What is the solution to x2 – 9x < –8? x < 1 or x > 8 x < –8 or x > 1 1 < x < 8 –8 < x < 1
In mathematics a linear inequality is an inequality involving a linear function. A linear inequality contains one of the inequality symbols.< is less than > is greater than ≤ is less than or equal to ≥ is greater than or equal to ≠ is not equal to.
x²− 9x < − 8Let's find the critical points of the inequality.
x² − 9x = − 8x² − 9x −(−8) = − 8 −(−8) (Subtract -8 from both sides)
x² − 9x + 8 = 0(x − 1)(x − 8) = 0 (Factor left side of equation)
x − 1 = 0 or x − 8 = 0 (Set factors equal to 0)
x=1 or x=8Check intervals in between critical points. (Test values in the intervals to see if they work.)x < 1 (Doesn't work in original inequality)
1 < x < 8 (Works in original inequality)
x > 8 (Doesn't work in original inequality)
Answer:1 < x < 8
The third option is the correct one.
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Write the equation y=-3x+3 in function notation using f(x) to denote the function.
The function notation form of the given equation; y = -3x +3 as in the task content is; f(x) = -3(x) +3.
What is the function notation form of the equation?According to the task content, the equation given; y = -3x +3 is to be written in function notation.
Consequently, since the function expression given is linear in variable X, it follows that the required function notation is;
f(x) = -3x +3.
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he polynomial of degree 5, P ( x ) has leading coefficient 1, has roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 Find a possible formula for P ( x ) .
f]
The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².
What is the polynomial in discuss whose roots and leading coefficient are as discussed?The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;
P(x) = (x-3) (x-3) (x) (x) (x+1)
The expanded form is therefore;
P(x) = x^5 - 5x⁴- 6x³+ 18x².
Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².
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ASAP Please help me with this questions ASAP
Answer:
an angle bisector
Step-by-step explanation:
This is showing the construction of the bisector of ∠LNM
– A BOX CONTAINS 9 RED AND 2 BLUE MARBLES. IF YOU SELECT
ONE MARBLE AT RANDOM FROM THE BOX, DETERMINE THE ODDS AGAINST
SELECTING A RED MARBLE.
The odds against selecting a red marble is =2/11
Calculation of probabilityThe number of marbles which were red = 9
The number of marbles which were blue = 2
The total amount of marbles in the Box = 11
When one marble is picked at random from the box, the odds against selecting a red marble can be gotten through the blue marble.
That is, the number of blue marble/ total marble
= 2/11
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please help urgently
Answer:
2
Step-by-step explanation:
Substitute:
2(1)(3)+2 / 2(1)(3)-2 =
6 + 2 / 6 - 2 =
8 / 4 =
2.
Hey there!
2ab + 2 / 2ab - 2
= 2(1)(3) + 2 / 2(1)(3) - 2
= 2(3) + 2 / 2(3) - 2
= 6 + 2 / 6 - 2
= 8 / 4
= 2
Therefore, your answer should be: 2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Which shapes have less than 3 lines of symmetry?
A) B and C
B) A and D
C) B and D
D) A and C
The shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
How to determine the shapes that have less than 3 lines of symmetry?The shapes are given as:
Isosceles trapezoidSquareIsosceles triangleRegular PentagonThe lines of symmetry are the lines that, when the shape is rotated through this line, the shape remains the same
As a general rule:
An Isosceles trapezoid and an Isosceles triangle have two lines of symmetry
Hence, the shapes that have less than 3 lines of symmetry are Isosceles trapezoid and Isosceles triangle
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divide the sum of 36 and the product of 18 and 6 by 12
Answer:
12
Step-by-step explanation:
Here is what you have defined:
(36+ (18 x 6) ÷ 12
(36 + 108) / 12
144/12
12
Your family borrowed $400,000 from the bank to purchase a new home. If the bank charges 3.8%
interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each
weekly payment be?
Answer:
472.19
Step-by-step explanation:
$472.19 weekly
Thus the required weekly installment is $402.30 for 25 years.
Given,
The family borrowed $400,000 from the bank to purchase a new home.
the bank charges 3.8% interest per year, compounded weekly, it will take 25 years to pay off the loan. How much will each weekly payment to be determined?
Statistics is the study of mathematics that deals with relations between comprehensive data.
The principle amount to refund = 400,000
Let the principle amount for weekly = P
Rate per year = 3.8%
Tenure = 25 year
For weekly installments,
52 Weeks in a year
Tenure = 25/52
Now,
[tex]Amount = P(1-(1+r)^{-tn})/i\\400000 = P (1-(1+0.038/52)^{-25*52}) / (0.038/52)\\400000 * 0.038/52 = P(1-(52.038)^{-25*52})\\292.30 = P(1-(1.001)^{-1300})\\292.30 = P(1-0.273)\\292.30=P * 0.727\\P = 402.30[/tex]
Thus the required weekly installment is $402.30 for 25 years.
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Describe the translation.
y=(x−5)2+5 → y=(x−0)2+0
A. T<−5,5>
B. T<5,−5>
C. T<−5,−5>
D. T<5,5>
Answer:
C
Step-by-step explanation:
This is a translation 5 units left and 5 units dowh.
Here, the translation is [tex]T < 5,-5 >[/tex].
What is translation?The translation is a coordinate transformation operation in which a point or a figure moves left/right/up or down in a coordinate system or a set of axes. After applying translation, the size of the figure remains unchanged, just the position changes. For example, consider a function [tex]y=f(x)[/tex]. If we translate it to the new function [tex]y'=f(x+a)+b[/tex], then the graph of [tex]y[/tex] moves [tex]a[/tex] units to the right and [tex]b[/tex] units to the up and in this case the translation is denoted by [tex]T < a,b >[/tex]Here, the translation is given as: [tex]y=2(x-5)+5\longrightarrow y=2(x-0)+0[/tex].
i.e. [tex]y=2(x-5)+5\longrightarrow y=2(x-5+5)+(5-5)[/tex].
So, the graph of [tex]y[/tex] moves 5 units to the right and (-5) units to the up i.e., 5 units to the down.
Therefore, here, the translation is [tex]T < 5,-5 >[/tex].
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2) Find the perimeter and area of the figures:
a)
P =
A =
8
8 ft.
b)
P =
A =
12
5m
Answer:
8+8+12+5= 33
Step-by-step explanation:
8+8+12+5=33
You inherit one million dollars. You invest it all in three accounts for one year. The first account pays 3% compounded annually, the second account pays 4% compounded annually, and the third account pays 2% compounded annually. After one year, you earn $34,000 in interest. If you invest four times the money into the account that pays 3% compared to 2%, how much did you invest in each account?
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
How to solve for the amount investedWe have x + y + z = 1000000
((1+0.03)x - x)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
4z + x + z = 1000000
((1+0.03)4z - 4z)+ ((1+0.04)y - y) + ((1 + 0.02)z-z) = 34000
((1+0.03)4z - 1)+ ((1+0.04)y - 1) + ((1 + 0.02)z-1) = 34000
12/100z + 4/100y +2/100z = 34000
2y + 7z = 1700000
-2y - 10z = -2000000
2y + 7z = 1700000
Solve through the use of the simultaneous linear equation
z = 100000
y = 500000
x = 400000
The amount that was invested are at 3% = 400000, at 4% = 500000 and at 2% = 100000
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If m = 4 and n = -7, what is the value of m + n?
The answer is -3.
If m = 4 and n = -7, we can evaluate the expression by substitution.
m + n
4 + (-7)
-3
❄ H there,
evaluate this expression by substituting the provided parameters –
[tex]\sf{m+n} \ | \ m=4 \ \& \ n=-7 \ | 4+(-7)=4-7=-3}[/tex]
That's it!
❄
HELP ASAP WITH EXPLANATION: If f(x) + f(2 − x) = 4 for all x, find f(y − 2) + f(4 − y)
Answer:
f(y-2)+f(4-y)=4
Step-by-step explanation:
Assume (let) x=y-2
So: y=x+2
f(y-2)+f(4-y)=f(x)+f(-x+2)=f(x)+f(2-x)
The value of that expression is 4 from the given.
A machinist needs 98 pieces of steel rod. The rods come in bundles of 8 pieces. How many bundles of steel rod does the machinist require?
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
How many bundles of steel rod does the machinist require?Given the data in the question;
Machinist needs 98 pieces of steel rodThe rods come in bundles of 8 piecesNumber of bundles of steel rods required by the mechanist = ?To determine the bundle of steel required, let y represent the bundle.
Since;
1 bundle = 8 piece
y bundle = 98 piece
We cross multiply
y bundle × 8 piece = 1 bundle × 98 piece
y = ( 1 bundle × 98 piece ) / ( bundle × 8 piece )
y = 98 pieces / 8 piece
y = 12.25 ≈ 13
Given that the pieces of steel rods comes in bundles, the mechanist will require 13 bundles of steel rods to get the 98 pieces of steel rod he needs.
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what is the best estiment of the mass of a bowling ball
Step-by-step explanation:
The heaviest legal bowling ball weighs 16 pounds. The lightest weight you can usually find at most bowling alleys is six pounds.
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