graph: y = |x+2| + 1
Consider a particle moving along the x-axis where
x(t)
is the position of the particle at time t,
x ′(t)
is its velocity, and
x ″(t)
is its acceleration
Regarding the velocity and acceleration functions, it is found that:
b) The particle is moving to right on these following intervals: (0,1) U (3,10).
c) The velocity when the acceleration is of zero is: -1 m/s.
When a particle is moving to right?A particle is moving to right when it's velocity is positive.
In this problem, the velocity function is presented as follows:
v(t) = 3t² - 12t + 9.
The velocity function is a concave up quadratic function, which is positive to left of the smaller root and to the right of the larger root.
The roots of the function are given as follows:
v(t) = 3(t² - 4t + 3)
Then:
3(t² - 4t + 3) = 0
t² - 4t + 3 = 0
(t - 1)(t - 3) = 0.
t - 1 = 0 -> t = 1.t - 3 = 0 -> t = 3.Considering the domain of the function, the intervals in which the car is moving right are:
(0,1) U (3,10).
What is the velocity when the acceleration is of zero?The acceleration is given by the following equation:
a(t) = 6t - 12.
It is of zero when:
6t - 12 = 0
6t = 12
t = 12/6
t = 2.
The velocity at this instant is of:
v(2) = 2² - 4(2) + 3 = -1 m/s.
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6. Solve for y. 12y - 10 = 14y
02
0 5
O-5
O-2
Answer:
can you pls clear your questions?
A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.
One sweatshirt before tax costs $19.20.
One sweatshirt before tax costs $12.80.
The sales tax for two sweatshirts is $1.92.
The sales tax for two sweatshirts is $2.88.
Total cost for two sweatshirts is $41.28.
Total cost for two sweatshirts is $27.52.
Answer: The correct statements are:
1 SS before tax costs $19.20
Sales tax for 2 SS is $2.88
Total cost for 2 SS is $41.28
Step-by-step explanation:
$16 x 1.20 = $19.20 cost before tax
$19.20 x 0.075 = $1.44 sales tax, one shirt
Sales tax for 2 shirts = $1.44 x 2 = $2.88
Total cost of a shirt = $19.20 + $1.44 = $20.64
Total cost for 2 shirts = $20.64 x 2 = $41.28
Which input value produces the same output value for the two functions on the graph?
f(x) equals negative StartFraction 2 Over 3 EndFraction x plus 1. g(x) equals StartFraction 1 Over 3 EndFraction x minus 2. A coordinate grid with two lines. One line labeled f(x) passes through (negative 3, 3), (0, 1), and point (3, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 3), (0, negative 2), and point (3, negative 1).
x = –3
x = –1
x = 1
x = 3
An input value that would produce the same output value for the first functions on the graph is 0. Also, an input value that would produce the same output value for the second functions on the graph is 3.
How to determine the correct input value?In this exercise, you are required to determine the input value that would produce the same output value for the two functions on the graph. This ultimately implies that, the two functions would be equated as shown below.
From the information provided above, the two functions include the following:
f(x) = -2/3(x + 1)
g(x) = 1/3(x - 2)
Equating the two equations, we have:
f(x) = g(x)
-2/3(x + 1) = 1/3(x - 2)
-2x/3 -2/3 = x/3 - 2/3
-2x/3 - x/3 = - 2/3 + 2/3
x = 0.
For the second function on the graph, the coordinates are as follows:
f(x) = (-3, 3), (0, 1), (3, -1)
g(x) = (-3, -3), (0, -2), (3, -1)
Therefore, the above function produces the same input value (x) at point 3.
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Answer:
D
Step-by-step explanation:
edge 23
Which of these types of angles have the same measure after being rotated, reflected, or translated in a coordinate plane?
I. Acute Angles
II. Right Angles
III. Obtuse Angles
a
I. II. and III.
b
I. and II. only
c
II. and III. only
d
I. only
The type of angles have the same measure after being rotated, reflected, or translated in a coordinate plane is a I. II. and III.
What is transformation?Transformation is a term used in mathematics to refer to the movements made by objects.
Transformation is basically of two major divisions
Rigid transformationnon rigid transformationNon rigid transformation are the transformation where the dimension or size of the object will be different from the image, example is dilation
In rigid transformation, the dimensions of the object is maintained through out the transformation examples of rigid transformation are
rotationreflectiontranslationSince the transformation types mentioned are all rigid transformation hence all the angles will remain same
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2.) lee has seven 5-dollar bills and le quarters
in his pocket. How much money would he have
left in his pocket if he buyes a leather jacket
worth $35.20.
Amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
As given in the question,
Conversion of quarter into dollars is :
1 quarter = 0.25 dollars
Amount of money with Lee in his pocket is equal to :
= ( 7 × 5) dollars + ( 6 × 0.25) dollars
= (35 +1.5) dollars
=$ 36.5
Cost of leather jacket buy by Lee = $35.20
Amount of money left in lee's pockets after purchasing jacket
= $( 36.5 - 35.20)
= $ 1.3
Therefore, amount of money left in Lee pocket after he buys a $35.20 leather jacket from the given amount is equal to $1.3.
The complete question is :
Lee has seven 5-dollar bills and 6 quarters in his pocket. How much money would he have left in his pocket if he buys a leather jacket
worth $35.20?
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Write log₂ A as a natural logarithm.
Answer:
ln A / ln 2
Step-by-step explanation:
Using the change of base rule: ln A / ln 2
Please help
A T-shirt company can produce and sell x T-shirts per day. The total cost C (in dollars) for producing x T-shirts is
C = 1,780 + 7x,
and the total revenue R (in dollars) is
R = 14x.
Find the profit (in dollars) obtained by selling 275 T-shirts per day.
Answer:
$145
Step-by-step explanation:
The revenue - the cost is the profit.
14x - (1708 + 7x) Distribute what is in the parentheses by -1
14x -1(1780) -1(7x) Simplify
14x - 1780 -7x Combine like tersm
7x - 1780 Plug in 275 for x
7(275) - 1780
1925 - 1780
145
a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph. how long does the Air Force plane need to fly before the planes are 3510 miles apart?
The time the airforce plane needs to before the planes are 3510 miles apart is 8.32 hours.
What is time?Time is the duration of an event
How to find how long before the planes are 3510 m apart?Since a jet left paris and flew toward moscow at an average speed of 410 mph. an air force plane left three hours later and flew in the opposite direction with an average speed of 160 mph.
The distance flown by the jet is d = vt where
v = speed of jet = 410 mph and t = time of flight of jet planeSo, d = 410t
Also, the distance flown by the airplane is D = vt' where
v = speed of airplane = 160 mph and t' = time of flight of airforce plane = t + 3 (since it flies 3 hours later)So, D = 160t'
= 160(t + 3)
Since the total distance apart of the both jet and airplane is D' = d + D, we have
D' = 410t + 160(t + 3)
Given that D = 3510 miles, we have that
410t + 160(t + 3) = 3510
Soving for t, we have
410t + 160t + 480 = 3510
570t = 3510 - 480
570t = 3030
t = 3030/570
t = 5.32 hours
Since t' = t + 3, we have
t' = 5.32 + 3
= 8.32 hours
So, the airforce plane needs to fly for 8.32 hours.
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Inga is solving 2x2 + 12x – 3 = 0. Which steps could she use to solve the quadratic equation? Select three options. 2(x2 + 6x + 9) = 3 + 18 2(x2 + 6x) = –3 2(x2 + 6x) = 3 x + 3 = Plus or minus StartRoot StartFraction 21 Over 2 EndFraction EndRoot 2(x2 + 6x + 9) = –3 + 9
Answer:
The answers are:
1. 2(x2 + 6x + 9) = 3 + 18
2. 2(x2 + 6x) = 3
Let's take a look at the first choice:
2(x² + 6x + 9) = 3 + 18
Now, we will multiply 2 with every member of the other multiplier on the left side:
2·x² + 2·6x + 2·9 = 3 + 18
2x² + 12x + 18 = 3 + 18
2x² + 12x - 3 = 18 - 18
2x² + 12x - 3 = 0
Let's take a look at the second choice:
2(x² + 6x) = 3
Now, we will multiply 2 with every member of the other multiplier on the left side:
2·x² + 2·6x = 3
2x² + 12x = 3
2x² + 12x - 3 = 0 Man that was so hard MARK ME Brainilest Thanks Peace
Step-by-step explanation:
Great by is reducing by 250% the regular price of a tally set selling it for $225 the regular price of the tally set is
The regular price of the tally set is $300.
How to calculate the price?From the information Illustrated, Great by is reducing by 250% the regular price of a tally set selling it for $225.
Let the regular price be represented by x.
Therefore, x - (25% × x) = 225
x - 0.25x = 225
0.75x = 225
Divide
x = 225 / 0.75
x = 300
The price is $300.
Note that the above percentage in the question is 25% and not 250%.
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The table represents a quadratic function. Write an equation of the function in standard form.
The equation of the quadratic function in standard form as required in the task content is; f(x) = -x² + 12x - 43.
Standard form equation of a quadratic function.It follows from the task content that the standard form equation of the quadratic function is to.be determined.
Since the standard form equation can be derived from the vertex form equation as follows;
f(x) = a (x - h)² + k
f(x) = a (x - 6)² - 7
Hence, to find the value of a, Substitute x = 8 and f(x) = -11 so that we have;
-11 = a (8 - 6)² - 7
-11 = 4a - 7
4a = -4
a = -1.
Hence, the equation in vertex form is; f(x) = -1 (x -6)² - 7 and when expressed in standard form we have;
f(x) = -1(x² - 12x + 36) - 7
f(x) = -x² + 12x - 43
Therefore, the required equation in standard form is; f(x) = -x² + 12x - 43.
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A hotel has a budget of $63,750 to repaint the lobby and some hotel rooms. The hotel spent $26,700 on painting the lobby. Each room costs $4,250 to paint. The inequality 26,700 + 4,250n ≤ $63,750 can be used to determine the number of rooms (n) the hotel can repaint.
Which statement about the number of rooms that can be painted is true?
A.
The hotel can repaint 9 rooms.
B.
The minimum number of rooms that can be repainted is 2.
C.
The maximum number of rooms that can be repainted is 2.
D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
The statement that is true about the number of rooms that can be painted using inequality is; D.
The hotel can repaint 2 rooms, but this number is neither the maximum nor the minimum.
How to solve Inequality Word problems?We are given;
Budget of hotel to repaint the lobby and some hotel rooms; $63750
Amount spent on painting the lobby = $26700
Cost to paint each room = $4250
Thus, the inequality to represent the given situation is;
26,700 + 4,250n ≤ $63,750
where;
n is number of rooms the hotel can repaint
Subtract 26700 from both sides of the inequality to get;
4250n ≤ 37050
n ≤ 37050/4250
n ≤ 8.717
Since we can't paint only a portion, we leave it as a maximum of 8 rooms
Looking at the given options, the only correct one is option D.
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The quotient is a multiple of 4 the dividend is a multiple of 9 the divisior is a factor of 12 possible solution
How did you compute sums of dollar amounts that were not whole numbers? For example, how did you compute the sum of $5.89 and $1.45? Use this example to explain your strategy.
The Sum of dollars in decimal is not a whole number.
Whole numbers are made up of natural numbers plus the number zero. In mathematics, the set of whole numbers is symbolized by the symbol W and is given as W = {0, 1, 2, 3, 4, …}.
To calculate a number of dollars that is not a whole number.
As an example, consider the sum of $5.89 and $1.45:
$5.89 + $1.45
Taking the whole numbers first:
$5 + $1 = $6
Take the sum of the decimals :
$0.89 + $0.45 = $1.34
sum of original whole + sum of decimal whole
$6 + $1 = $7
Remaining decimal: $1.34 - $1 = $0.34
$7 + $0.34 = $7.34
Therefore $7.34 is not a whole number
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a - domain and range
b - intercepts
c - horizontal asymptotes
d - vertical asymptotes
e - oblique asymptotes
From given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
In this question, we have been given a graph of a function.
From given graph we need to answer the following questions.
1) domain of function: (-∞, 3) ∪ (3, ∞)
the range of function : (-∞, 3) ∪ (3, ∞)
2) the intercepts:
x = 0, y = 0
3) horizontal asymptotes
A red dotted line y = 3 is a horizontal asymptotes
4) vertical asymptotes
A red dotted line x = 3 is a vertical asymptotes
5) Oblique asymptotes
The graph of function does not have any Oblique asymptotes
Therefore, from given graph,
a - domain and range: (-∞, 3) ∪ (3, ∞)
b - intercepts: x = 0 and y = 0
c - horizontal asymptotes: y = 3
d - vertical asymptotes: x = 3
e - oblique asymptotes: No
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12) m/GOP = 80°, m/ROP
and m/ROG= 32x + 4. Find x.
R
Q
= 3 +59x,
G
By using linear pair, we have found that the value of x is 3.
What is linear pair?Linear pairs of angles are produced when two lines intersect each other at a point. The sum of angles of the linear pair is always 180 degrees.
Given that Angle QGP = 80°, Angle ROP = 3 + 59x and Angle ROG= 32x + 4. Find x.
Therefore, we can see that Angle ROG and Angle QGP lie in a straight line.
Thus, by linear pair
Angle ROG + Angle QGP = 180
80° + 32x + 4 = 180
32x = 100 - 4
x = 96/32
x = 3
Hence, the value of x is 3.
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Do I need to apply the chain rule when I derive [ln(g(x))]^2?
To solve the given derivative we need to apply the chain rule.
Given that, [ln(g(x))]².
What is the differentiation?The process of finding derivatives of a function is called differentiation in calculus. A derivative is the rate of change of a function with respect to another quantity.
The chain rule is a formula that expresses the derivative of the composition of two differentiable functions [tex]f[/tex] and [tex]g[/tex] in terms of the derivatives of [tex]f[/tex] and [tex]g[/tex].
Find the derivative using the chain and power rules.
ln(g²x²)/x
Therefore, to solve the given derivative we need to apply the chain rule.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3, 5) and (1,−1)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]
Which question can be answered by finding the quotient of 5/6 divided by 1/20?
The question that can be answered by finding the quotient of 5/6 divided by 1/20 is C. Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag. How many bags can he make?
How to illustrate the information?It should be noted that the quotient is the value that is gotten when we divide the numbers given.
In this case, Jared has 5/6 of an hour left to finish making bags. It takes him 1/20 of an hour's to make each bag.
The number of bags will be:
= 5/6 ÷ 1/20
= 5/6 × 20
= 100 / 6
= 17 bags
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Answer:
17 bags
Step-by-step explanation:
A Norman window is a window with a semicircle on top of a regular rectangular window as shown in the diagram. What should the dimensions of the rectangular part of a Norman window be to allow in as much light as possible if there is only 12 ft of the framing material available?
The dimensions of the rectangular window that gives a maximum area are as follows;
Width = [tex]\dfrac{12}{2+\pi }[/tex] feet and length = 3 feet
What is the maximum value of a function?The maximum value of a function is given by the point at which the graph of the function has the highest value.
The parameters of the window are;
Length of the framing material available = 12 ft.
The shape of the window = A semicircle on top of a regular rectangular window
Required; The dimension of the rectangular part of the Norman window that allows the most light
Solution;
Diameter of the semicircular part of the window = The width of the rectangular part
Let x represent the width of the window, we have;
Perimeter of the semicircle = π·x/2
Side length of the rectangular window = (12 - π·x/2 - x)/2
Area of the rectangular part of the window, A = x × (12 - π·x/2 - x)/2
Area of the semicircle = π·x²÷4
Area of the window, is therefore;
[tex]A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} +\dfrac{ \pi \cdot x^2}{4}[/tex]
At the maximum area, of the rectangular part, we have;
[tex]A_r' =\dfrac{d}{dx}\left( A =\dfrac{ x \times (12 - \dfrac{\pi \cdot x}{2} - x)}{2} \right) = -\dfrac{x\cdot \pi +2\cdot x-12}{2} = 0[/tex]
x·π + 2·x - 12 = 0
The width, x = [tex]\dfrac{12}{2+\pi }[/tex] feet
The length of the rectangle is therefore;
[tex](12 - \pi \cdot \dfrac{6}{2+\pi } - \dfrac{12}{2+\pi })/2 = 6 - \pi \cdot \dfrac{3}{2+\pi } - \dfrac{6}{2+\pi } = 3[/tex]
The length of the rectangular window = 3 feet
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Jon can do 64 push-ups in 4 minutes. Paul can do 45 push-ups in 3 minutes. Whose rate is faster?
Answer:
John's rate is faster than Paul's Step-by-step explanation: John, 64 push-ups/4min = 16 push-ups per minute Paul,
:
??? brianlest?? help please
math
Answer:
try to show it step by step
The formula is у= 6х - 5 Determine the value of x, if y=7
Answer:
x=2
Step-by-step explanation:
You can put the equation as 7=6x-5
Move equation
12=6x
Divide
x=2
y = 3x + 6
What is the gradient?
What is the y-intercept?
Answer: Gradient: 3. y-intercept: 6
Step-by-step explanation:
7/2a+4/2a^2 as a fraction
Answer:
1/2a (4a+7)
Step-by-step explanation:
First You Divide:7/2a+ 2a^2
Rearrange Terms: 2a^2+ 7/2a
Find the Common Factor: 1/2(4a^2+7a)
Rewrite in the Fraction Form: 1/2a (4a+7)
I know this is the right answer because I learned this in 5th grade.
Please mark me Brainliest!!!
pls help ill give brainliest
Answer:
b= -2
Step-by-step explanation:
This is written in the y=mx+B form. This means that x is our slope, and -2 is our y-intercept (b). This meakes b= -2
-Hope this helped
Answer: x=6.
Step-by-step explanation: First go to the Algebra Calculator.
Encuentra el área de la región coloreada.
List all possible rational roots for the given equation. x^4 - 2 x^2 + 16 x - 15 = 0
The possible roots for the given equation are, -1,3, -1-2i, -1+2i.
What do you mean by the roots of an equation?
The values of the variable that fulfill the equation are known as the roots of a quadratic equation. In addition, they are referred to as the "solutions" or "zeroes" of the quadratic equation. For instance, x = 2 and x = 5 satisfy the quadratic equation x2 - 7x + 10 = 0 and are hence the roots of the equation.
F(x) = x4-2x2-16x-15 has a root (zero) that you should find.
Finding x values for which F(x)=0 is the goal of the Polynomial Roots Calculator method set.
A tool from the list above is the rational roots test. Only numbers x that can be represented as the quotient of two integers, or rational roots, would be found.
According to the Rational Root Theorem, P and Q are factors of the Leading Coefficient and the Trailing Constant, respectively, if a polynomial zeroes for a rational number P/Q.
The Leading Coefficient is 1 and the Trailing Constant is -15 in this instance.
The component(s) are:
1 is the Leading Coefficient, while 1 is the Trailing Constant.
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