Answer:
Step-by-step explanation:
To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:
a) g(0)
To find g(0), substitute x = 0 into the function:
g(0) = 2(0)^2 - 2(0) + 9
g(0) = 0 - 0 + 9
g(0) = 9
b) g(-1)
To find g(-1), substitute x = -1 into the function:
g(-1) = 2(-1)^2 - 2(-1) + 9
g(-1) = 2(1) + 2 + 9
g(-1) = 2 + 2 + 9
g(-1) = 13
c) g(2)
To find g(2), substitute x = 2 into the function:
g(2) = 2(2)^2 - 2(2) + 9
g(2) = 2(4) - 4 + 9
g(2) = 8 - 4 + 9
g(2) = 13
d) g(-x)
To find g(-x), substitute x = -x into the function:
g(-x) = 2(-x)^2 - 2(-x) + 9
g(-x) = 2x^2 + 2x + 9
e) g(1 - t)
To find g(1 - t), substitute x = 1 - t into the function:
g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9
g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9
g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9
g(1 - t) = 2t^2 - 2t + 9
Therefore:
a) g(0) = 9
b) g(-1) = 13
c) g(2) = 13
d) g(-x) = 2x^2 + 2x + 9
e) g(1 - t) = 2t^2 - 2t + 9
find the surface area of the composite figure 12cm x 2cm x 10cm x 3cm x 6cm x 8cm SA=
Answer:
If you are in Acellus trust me the answer is 394
Step-by-step explanation:
SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )
SA = 48 + 40 + 48 + 48 + 18 + 192
SA = 394 square cm.
please answer i am stuck
(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).
In 2011 the assets are about $669.6 billion
(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).
In 2016 the assets are about $931.5 billion.
(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).
In 2019 the assets are about $1135.4 billion.
How to estimate the cost of the assets in 2011?Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:
[tex]A(x)=324e^{0.066x}[/tex]
where:
A(x) is in billions of dollars.x = 7 corresponds to the year 2007.For the year 2011, the cost (in billions of dollars) is given by;
x = (2011 - 2007) + 7
x = 4 + 7
x = 11 years.
Next, we would substitute 11 for x in the exponential function:
[tex]A(11)=324e^{0.066 \times 11}[/tex]
A(11) = $669.6 billions.
Part b.
For the year 2016, the cost (in billions of dollars) is given by;
x = (2016 - 2007) + 7
x = 9 + 7
x = 16 years.
Next, we would substitute 16 for x in the exponential function:
[tex]A(16)=324e^{0.066 \times 16}[/tex]
A(16) = $931.5 billions.
Part c.
For the year 2019, the cost (in billions of dollars) is given by;
x = (2019 - 2007) + 7
x = 12 + 7
x = 19 years.
Next, we would substitute 19 for x in the exponential function:
[tex]A(19)=324e^{0.066 \times 19}[/tex]
A(19) = $1135.4 billions.
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Which equation, when graphed with the given equation, will form a system that has an infinite number of solutions?
77110
03-x--2
- 3-4-x
Oy+4x-1
Mark this and retum
C
Save and Exit
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Submit
The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
How to determine the equation, when graphed with the given equation, will form a system that has an infinite number of solutionsTo form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.
The given equation is: y + 4x - 1 = 0
To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.
Let's multiply the given equation by 2:
2(y + 4x - 1) = 2(0)
2y + 8x - 2 = 0
The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.
Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.
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Help excel college student
EOP511
The total petty cash expenditures would be =$130.84
How to calculate the petty cash expenditures?To calculate the petty cash expenditures, the following is added up as follows;
The cost for stamp = $12.50
The cost for coffee supplies = $25.19
The cost for pizza delivery = $15.50
The cost for white board markers = $20.00
The cost for sympathy greeting card= $5.78
The cost of flowers for Jean's retirement farewell = $39.87
The cost of courier = $12.00
Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84
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The ratio of the length to the width of a rectangle is 3:2. If the perimeter of the rectangle is 40, what is the length of the rectangle?
Answer:
Step-by-step explanation:
Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.
The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:
P = 2(3x + 2x)
40 = 2(5x)
Now, let's solve for x:
40 = 10x
x = 40/10
x = 4
Now that we have the value of x, we can find the length of the rectangle:
Length = 3x = 3(4) = 12
Therefore, the length of the rectangle is 12.
Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
En un punto de un cuerpo rigido se aplica una fuerza F = (4.501 - 3.25) N. Determine el torque que
experimenta dicho cuerpo si el radio vector trazado desde el punto de aplicación de la fuerza al punto de
giro es r = (1.801 + 2.50j) m
The torque experienced by the rigid body is -17.10375 k N·m.
To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.
Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:
Torque = r x F
The cross product between two vectors is calculated as follows:
Torque = (r_x * F_y - r_y * F_x)k
Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.
Substituting the given values, we have:
Torque = ((1.801 * -3.25) - (2.50 * 4.501))k
Calculating the cross product:
Torque = (-5.85125 - 11.2525)k
Simplifying:
Torque = -17.10375k
Therefore, the torque experienced by the rigid body is -17.10375 k N·m.
The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.
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What are the dimensions of the rectangle shown on the coordinate plane?
The base is 5 units and the height is 3 units.
The base is 4 units and the height is 7 units.
The base is 7 units and the height is 5 units.
The base is 7 units and the height is 3 units.
Answer:
D The base is 7 units and the height is 3 units.
Step-by-step explanation:
The answer is d I counted the width/base then the height/length and found answer.
help me please.. please
Step-by-step explanation:
Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:
y = -2
Answer:
y=-2
and m=0 must be your answer
Step-by-step explanation:
as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate
so
equation of line is y-y'=m(x-x')
so m=0 m is slope
y'=-2 and x'=4
so by substituting the values
y+2=0
so y=-2
and m=0 is your answer
A city currently has 2.08 thousand residents. Each year the city's population grows by around 420 persons.
After 14 years what will the approximate population of the city be? Round to three significant digits.
Approximately
thousand residents.
Answer:
the approximate population of the city after 14 years will be 7.96 thousand residents.
Step-by-step explanation:
to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.
Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:
14 years × 420 persons/year = 5,880 persons
To find the approximate population after 14 years, we add the total growth to the current population:
2.08 thousand + 5.88 thousand = 7.96 thousand
3. Determine whether the triangles are similar. If they are, write a similarity statement.
Look at picture for reference
Please show work
The triangles DEF and SRQ are not similar triangles
Identifying the similar triangles in the figure.From the question, we have the following parameters that can be used in our computation:
The triangles in this figure are
DEF and SRQ
These triangles are not similar
This is because:
The corresponding angles in the triangles are not equal
For DEF, the angles are
50, 90 and 40
For SRQ, the angles are
51, 90 and 39
This means that they are not similar by any similarity statement
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Which type of conic section is defined by the equation:... 100pts
Answer:
This is an equation of a parabola.
[tex](y+6)^2=4(x+1)[/tex]
Step-by-step explanation:
A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).
The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.
Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.
As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.
The conic form of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
(h, k) is the vertex.(h+p, k) is the focus.x = h-p is the directrix.To write the given equation in conic form, we need to complete the square for the y-variable.
Rearrange the equation so that the y-terms are on the left side:
[tex]y^2 + 12y = 4x - 32[/tex]
Add the square of half the coefficient of the y-term to both sides of the equation:
[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]
[tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]
[tex]y^2 + 12y+36 = 4x - 32+36[/tex]
[tex]y^2 + 12y+36 = 4x +4[/tex]
Factor the perfect square trinomial on the left side of the equation:
[tex](y+6)^2=4x+4[/tex]
Factor out the coefficient of the x-term from the right side of the equation:
[tex](y+6)^2=4(x+1)[/tex]
Therefore, the equation of the given conic section in conic form is:
[tex]\boxed{(y+6)^2=4(x+1)}[/tex]
where:
(-1, -6) is the vertex.(0, -6) is the focus.x = -2 is the directrix.The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola
Selecting the conic section of the equationThe given equation is
y² - 9x + 12y + 32 = 0
The above equation is an illustration of a parabola equation
The standard form of a parabola is
(x - h)² = 4a(y - k)²
Where
(h, k) is the center
While the general form of the equation is
Ax² + Dx + Ey + F = 0
In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form
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9.
Find the volume of the cylinder. All measurements are in
centimeters. Keep your answer exact.
5
Answer:
The volume of the cylinder is 628.318530718
Step-by-step explanation:
The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.
The radius is 5, and the height is 8. Plug these values into the equation and solve:
[tex]v =\pi *5^2*8[/tex]
[tex]v = 628.318530718[/tex]
So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32
Answer:
200π or 628
Step-by-step explanation:
Note: your picture is not clear so I am assuming the height to be 8.
r = 5
h = 8
Volume = πr²h
= π * 5² * 8
= (25*8) π
= 200π
= 200*3.14
= 628
The crew from Disneyland Entertainment launches fireworks at an angle. The height of the firework can be modeled by h(t) = -2t^2+ 8t + 300 where height, h, is measured in feet and the
time, t, in seconds. What is the greatest height the fireworks reach?
Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.
One more question thank you
Answer:
Step-by-step explanation:
n=30
r=12
Plug into formula
you get:
1.7 in²
Because f(x) ___ its inverse is a function.
○ is one to one
X is a function
○ Passes the vertical line test
The inverse of the function f(x) = 2·x - 4, is the option;
g(x) = (1/2)·x + 2
The completed statement is; Because f(x) is one to one, its inverse is a function
What is the inverse of a function?The inverse of a function is one that takes the output of a specified function to produce the input of the function.
The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;
f(x) = 2·x - 4
f(x) + 4 = 2·x
2·x = f(x) + 4
x = (f(x) + 4)/2 = f(x)/2 + 2
x = f(x)/2 + 2
Substituting f(x) = x and x = g(x) in the above equation, we get;
g(x) = x/2 + 2
The inverse of the function is therefore, g(x) = (1/2)·x + 2The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function
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Answer:
A
Step-by-step explanation:
is one to one
Chef Phillippe has 65 eggs and 46 lbs of flour in his bakery. He has a
recipe for Chocolate cake that requires 3 eggs and 2 lbs of flour. He has
another recipe for Red Velvet Cake that requires 4 eggs and 3 lbs of
flour. If all the supplies are used up making some ratio of both cakes,
how many Chocolate cake can he make?
Answer:
Step-by-step explanation:
12
Calc II Question
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x axis
x = 4y^2 - y^3
x = 0
Michelle had 5 paperback books and 3 hardcover books on the shelf by her bed. Write a ratio to represent the ratio of paperback books to hardcover books.
3:5
five over three
3 to 8
5:8
Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.
given f(x) = x^3 - 10x + k, and the remainder when f(x) is divided by x + 3 is 6, then what is the value of K?
Answer:
Step-by-step explanation:
(x^3 - 10x + K)/(X+3) = 6 GIVEN
for different values of x there are many possible values of k some i will show
when we substitute x=1
we get k=33
at x=2
weget k=42
so many values are possible for k
because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k
50 Points! Multiple choice geometry question. Photo attached. Thank you!
Answer: D
Step-by-step explanation:
Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.
D) 4x2=8
12x2=24
15x2=30 All sides were multiplied by 2 so D is similar
Answer:
D)
Step-by-step explanation:
Figure D is similar in all mesurements .
...
Determine the measure of the interior angle at vertex F.
A. 54
B. 108
C. 36
D. 72
The measure of the interior angle at vertex F is 72 degrees.
How to find the interior angle at vertex FA hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.
The angle of the hexagon is given in terms of x,
The sum of the angle is equal to 720 degrees
[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]
[tex]20\text{x} = 720[/tex]
[tex]\text{x} = 36[/tex]
[tex]\bold{2x = 72^\circ}[/tex]
Therefore, the measure of interior angle at vertex F is equal to 72 degrees.
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number 33!!!! this is a test !!!
33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)
How to calculate the volume of a triangular prism?To calculate the volume of a triangular prism, the formula that should be used is given as follows;
Volume= BH
where;
B= area of base = 1/2 × base×height
= 1/2×4×3
= 6
H= 6
Volume= 6×6= 36.
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Find the value of x.
The circle below is centered at the origin and has radius of 8. what is the equation ?
Step-by-step explanation:
h,k center is 0,0 and radius is 8
(x-0)^2 + ( y-0)^2 = 8^2
x^2 + y^2 = 64
IM NOT SURE, DO YOU WANT ME TO WORK IT OUT FOR YOU?
A boat is traveling in a river that is floating downstream at a speed of 10 km/h. the boat can travel 40 km upstream in the same time it would take to travel 80 km down the stream. what is the speed of the boat in Still water?
The speed of the boat in still water is 3 times the speed of the river current.
To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.
Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.
When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.
The boat's speed relative to the ground is given by (v - c) km/h.
Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.
The boat's speed relative to the ground is given by (v + c) km/h.
According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.
Since time is constant in both cases, we can set up the following equation:
40/(v - c) = 80/(v + c)
To solve this equation, we can cross-multiply and simplify:
40(v + c) = 80(v - c)
40v + 40c = 80v - 80c
40c + 80c = 80v - 40v
120c = 40v
Dividing both sides by 40, we get:
3c = v.
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In a class of 34, girls 21 play tennis and 18 play netball. If all the girl play at least one of the Games, how many of them play both games.
Solution:
Formula: Total = Group 1 + Group 2 - Both + Neither
where:
- Total = total number of girls in the class (34)
- Group 1 = number of girls playing tennis (21)
- Group 2 = number of girls playing netball (18)
- Both = number of girls playing both games (what we want to find)
- Neither = number of girls playing neither game (0, since all the girls play at least one game)
Plugging in the values, we get:
34 = 21 + 18 - Both + 0
Simplifying:
34 = 39 - Both
Both = 39 - 34
Both = 5
√7
7. Given that the sin(E)= 4 and TE = 4, determine the
remaining sides of A THE. Give exact answers.
E
Answer:
Step-by-step explanation:
To determine the remaining sides of triangle THE given that sin(E) = 4 and TE = 4, we can use the sine ratio.
The sine ratio is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle.
In this case, sin(E) = 4/TE, which means the side opposite angle E is 4 and the hypotenuse TE is 4.
Using the Pythagorean theorem, we can find the length of the remaining side TH:
TH^2 = TE^2 - HE^2
TH^2 = 4^2 - 4^2
TH^2 = 16 - 16
TH^2 = 0
TH = 0
Therefore, the length of side TH is 0.
PLSS HELP ASAPPP
PLS HELP HURRYYY
I NEED HELP RIGHT NOW!!!
What is the units digit of 2013 to the power
2013?
Step-by-step explanation:
a number consists of digits in the place of certain values of the powers of 10.
2013 consists of a digit 2 in the thousands units position.
of a digit 0 in the hundreds units position.
of a digit 1 in the tens units position.
and of a digit 3 in the (single) units position.
so, to which power do we need to have this 3 ?
I think you made a mistake there. you say we need it to the power of 2013 ?
3²⁰¹³ = 2.786671338...e960 =
= 2.786671338... × 10⁹⁶⁰