The equation which is a function of x is x²=y.
Given an equation that is a function of x.
A function may be a relation between a collection of inputs and a collection of permissible outputs with the property that every input is said to precisely one output.
If we input a value of x then we get the output f(x) = y, which is the function of x.
We are given four options out of which we are to pick the one which may be a function of 'x'.
The first option is x=5 in which no term of y is included and its a constant. So, option 1 is not correct.
The second option is x=y²+9 in which y contains a power 2. So, option 2 is not correct.
The third option is x²=y in which y contains power 1. So, option 3 is correct.
The fourth option is x²=y²+16 in which y contains a power 2. So, option 3 is not correct.
Hence, the equation which is a function of x is x²=y.
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A ferris wheel is 15 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).
The equation for h = f(t) will be, [tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].
What is a function?A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.
The given data in the problem is;
Ferris wheel diameter,d= 15 meters
The platform is 5 m above the ground.
The Ferris wheel function is;
h(t) = A sin(Bt + C) + D
Here,
A is Amplitude
D is the midline
B is period
C is a phase shift
t is the time
The amplitude of the function is half of the diameter;
A = d/2
A=15 m /2
A = 7.5 m
The value of the mid-line is found as;
Mid-line = amplitude + distance from the mid-line;
D= 7.5 + 5
D = 12.5
From the given data, the wheel completes 1 full revolution in 2 minutes
The period of the wheel is T.
B = 2
The phase shift is found as;
[tex]\rm \frac{C}{\pi}=\frac{-1}{2}\\\\ {C}=\frac{-\pi}{2}[/tex]
The Ferris wheel function is;
h(t) = A sin(Bt + C) + D
Substitute the obtained values we get;
[tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex]
Hence, the equation for h = f(t) will be, [tex]\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5[/tex].
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PLEASE HELP
Graph the following exponential function. Show work in how you find the y intercept, talk about the end behavior, and state if it is a growth or decay function. See image.
The y-intercept of the function is -9,25
How to graph the function?The function is given as:
[tex]y = -5(.8)^{x - 1} - 3[/tex]
See attachment for the graph of the function
From the graph, we have the following highlights:
y-intercept = -9,25As x increases, y approaches -3As x decreases, y approaches negative infinityRead more about exponential functions at:
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Suppose that a forest on a flat terrain has perimeter 200 kilometers, but there is no information on the shape of the forest. What shape will give the largest possible area for the forest? what is this area?
The largest possible area of the forest is 2500 km^2
How to determine the largest area?The perimeter is given as:
P = 200 km
The shape that will give the largest possible area for the forest is a square, and the area is calculated as:
A = (P/4)^2
This gives
A = (200/4)^2
Evaluate
A = 2500 km^2
Hence, the largest possible area of the forest is 2500 km^2
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Anderson's Solar Systems manufactures solar panels, and their business is growing. Last year,
they hired 90 new employees. This year, they hired 20% more new employees than they hired las
year. How many new employees were hired this year?
your family is driving from cincinnati to st louis. the graph relates your distance from st.louis d in miles and travel time h (in hours). The equation of the line is d=360-60h
The solution is about a distance-time graph. The interpretation of the graph is that it took the family 6 hours to travel a distance of 360 miles. Note that the distance is plotted on y-axis and time on the x-axis.
What is a distance-time graph?A distance time graph is a simple graph that shows the relationship between the time travelled the distance covered while doing do.
The slope-intercept form is
y= mx+b−⋯(1)
The y-intercept is 360
⇒b = 360; and m = −60
Substituting the value of m = −60
and b = 360
in (1) above,
⇒y = −60x +360
The x-intercept is
y = 0,
⇒0= −60x+360
hence, x=6
The y-intercept is
x=0
⇒y=−60(0)+360
⇒y=360
In conclusion, the x - intercept is the time in hours between Cincinnati and St. Loui: and
The y - intercept is the distance between Cincinnati and St. Louis.
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Okay, I am getting familiar with quadratic equations by I'm not sure of X=m+/- n... Help!
The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
x² + 6x - 5 = 0
x² + 6x = 5
x² + 6x + 9 = 5 + 9
(x + 3)² = 14
x + 3 = ±√14
x = -3 ± √14
The value of m and n to show the solution of the equation x² + 6x - 5 = 0 is m = -3 and n = ± √14
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Which graph represents this inequality? 3x + y ≤ 1
Answer:
Step-by-step explanation:
PLEASE HELP SOON THX SO MUCH
an airplane flies 3300 miles with the wind in 3 hrs 18 minutes. it takes 4 hrs 24 mins to make the return flight against the same wind. find speed of airplane and wind.
Answer:
The speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
Step-by-step explanation:
Let’s assume the speed of the plane =x miles/hr
And let the speed of wind =y miles/hr
So, the speed of the aeroplane in the direction of wind =(x+y) miles/hr
Speed of the aeroplane in the opposite direction of wind =(x–y) miles/hr
We know that, distance=speed×time
Then according to the given conditions, we have
3300=(x+y)×(3+(18/60))
here convert 18mins to hour by dividing by 60 and add to 3hrs.
⇒x+y= 3300/3.3
⇒x+y=1000 … (i)
And,
3300=(x-y)×(4+(24/60))
here convert 24mins to hour by dividing by 60 and add to 4hrs.
⇒x-y= 3300/4.4
⇒x-y=750 … (ii)
Adding equation (i) and (ii), we get
2x=1750
⇒x= 1750/2
=875
Substituting the value of x in equation (ii), we get
875−y=750
⇒y=875-750
⇒y=125
Therefore, the speed of aeroplane =875 miles/hr and the speed of wind =125 miles/hr.
what's the numerator for the following rational expression? 6/t+7/t=?/t
The numerator for the following rational expression is 13
How to determine the numeration?The rational expression is given as:
6/t + 7/t
Take the LCM of the denominator;
The LCM of t and t is t
So, we have:
6/t + 7/t = (6 + 7)/t
Evaluate the sum
6/t + 7/t = 13/t
13 is the numerator, while t is the denominator
Hence, the numerator for the following rational expression is 13
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a square pyramid has side length 9 in. and volume = 270 in^3. find the height.
If the square pyramid has side length 9 inches and volume of 270 inches cube then by putting the values within the formula of volume height are going to be 10 inches.
Given Length and volume of a square pyramid are 9 inches and 270 inches cube. Square pyramid is the pyramid having square base. It is a right square pyramid.
We know that the amount of square pyramid is 1/3 *[tex]l^{2} *h[/tex]
Put the values in formula to induce the values oh h.
Volume=1/3*[tex]9^{2}*h[/tex]
270=1/3* 81*h
h=(270*3)/81
h=810/81
h=10
Hence the peak of the square pyramid having length 9 inches and volume of 270 inches cube is 10 inches.
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In △ABC, we are told that c=11, ∡C=75∘, and ∡B=29∘. Solve for a and b.
The value of a and b are 5.5 and 11.0.
How to find side of a triangle?
The sides a and b of the triangle can be found as follows:
∠B = 29°
c = 11
∠C = 75°
∠A = 180 - 75 - 29 = 76°
Using sine ratio,
b / sin 29° = 11 / sin 75
b sin 75 = 11 sin 29
b = 11 sin 29 / sin 75
b = 5.33290582271 / 0.96592582628
b = 5.51816958277
b = 5.5
Let's find a,
a / sin 76 = 11 / sin 75
a sin 75 = 11 sin 76
a = 11 sin 76 / sin 75
a = 10.673252989 / 0.96592582628
a = 11.0466922042
a = 11.0
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2y + 3x = -6 in slop intercept form
Answer:
[tex]y=-\frac{3}{2}x-3[/tex]
Step-by-step explanation:
The slope-intercept form is written as y= mx +c, where m is the slope and c is the y-intercept.
For the equation to be in the slope-intercept form, first leave the y term on the left-hand side of the equation and bring the rest to the right-hand side.
2y= -3x -6
Ensure that the coefficient of y is 1. In this question, we can divide both sides of the equation by 2 to achieve the slope-intercept form.
[tex]y=\frac{-3x}{2}-\frac{6}{2}[/tex]
Simplify:
[tex]\bf{y=-\frac{3}{2}x-3 }[/tex]
Additional:
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If the Federal Reserve sets the reserve rate to 4%, what is the resulting money
multiplier?
Answer:
The money multiplier is the ratio of money supply to the money base. The money base is the sum of currency in circulation and reserves held by commercial banks.
The reserve rate is the percentage of deposits that commercial banks must hold in reserve.
If the reserve rate is 4%, the money multiplier is 10.
Step-by-step explanation:
Math interest, I, P, R,T
I will give more points to you once questions are completed.
The interest based on the information given is $2564.
How to calculate the interest?From the information given, the following can be deduced:
Principal = $36900
Time = 178 days
Rate = 14.25%
The simple interest will be:
= (PRT)/100
= (36900 × 14.25 × 178/365)/100
= $2564
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what is the product? (7x^2)(2x^3+6)(x^2-4x=9)
Answer:
14x^7-56x^6=9
Step-by-step explanation:
distribute
(7x^2)(2x^3 +6)(x^2 -4 * 9=x)
(2x^3+6)(x^2 -4 * 9=x)=2x^5-8x^4=9
(7x^2)(2x^5-8x^4=9)
14x^7-56x^6=9
Note: When solving for k, round to four decimal places.
A country's population in 1994 was 107 million. In 1997 it was 112 million. Estimate the population in 2008 using the exponential growth formula. Round your answer to the nearest million.
Answer: 132 million
Exponential growth formula: [tex]P=A e^{rt}[/tex]
[P is final amount, A is initial amount, r is growth rate, x is time intervals]
To find growth rate:
[tex]112 = 107 e^{r(3)}[/tex]
[tex]3r= ln(112/107)[/tex]
[tex]r= ln(112/107)/3 = 0.01522334561[/tex]
Population in 2008:
[tex]P_{2008}=107 e^{(0.01522334561(14))}[/tex]
[tex]P_{2008}=132.4169522[/tex]
[tex]P_{2008}=132\:million \quad (rounded \:to\:nearest\:million)[/tex]
QUESTION IS DOWN BELOW 15 POINTS EACH
Answer:
See below
Step-by-step explanation:
density = mass/volume
re-arrange to density * volume = mass
20 * 64 = 1280 gm
Density = mass/volume
re-arrange to volume = mass / density
560 / 14 = 40 cm^3
S and Tare mutually
exclusive events. Find P(sort)
P(S) = 12% P(T) =27%
The value of the probability P(S or T) is 39%
How to determine the probability?The probability values are given as:
P(S) = 12% P(T) =27%
For mutually exclusive events,
P(S or T) = P(S) + P(T)
This gives
P(S or T) = 12% + 27%
Evaluate the sum
P(S or T) = 39%
Hence, the value of the probability P(S or T) is 39%
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Which of the following results in the difference of two squares?
The difference of two squares expression is (c) (5x + 3y)(5x - 3y)
How to determine the difference of two squares?The difference of two squares expression is represented as:
a^2 - b^2 = (a + b)(a - b)
Using the above as a guide, we have the following expression in option (c)
(5x + 3y)(5x - 3y)
Hence, the difference of two squares expression is (c) (5x + 3y)(5x - 3y)
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You have been saving $25 a week to make the trip; you now have $200. This money will be budgeted to include gas, food, and entertainment. Write an equation to model your savings plan and then graph it. What would be the domain and range in this situation?
Could someone help me out?
The values of the functions are f(4) = 47, f(k) = 2(k)^2 + 4(k) - 1 and f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4
How to evaluate the expression?The function is given as:
f(x) = 2x^2 + 4x - 1
To calculate f(4), we have:
f(4) = 2(4)^2 + 4(4) - 1
Evaluate the expression
f(4) = 47
To calculate f(k), we have:
f(k) = 2(k)^2 + 4(k) - 1
To calculate f(x + h), we have:
f(x + h) = 2(x + h)^2 + 4(x + h) - 1
Expand
f(x + h) = 2(x^2 + 2hx + h^2) + 4x + 4h - 4
Expand
f(x + h) = 2x^2 + 4hx + 2h^2 + 4x + 4h - 4
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How can I solve this?? Please help
Answer:yes
15x times 2=30x
15x times 3= 45x
3y tines 2 =6y
3y times 3=9y
Step-by-step explanation:
This circle is centered at the origin, and the length of its radius is 10. What is
the circle's equation?
A. x+y=10
B. x¹° + y¹° = 100
C. X²+ y² =10
D. X² +y²=100
Answer:
D
Step-by-step explanation:
If you substitute the radius, 10, and the center of the circle, the origin (also known as (0,0) into the equation of a circle, you should get: [tex](x - 0)^{2} + (y - 0)^{2} = 10 ^{2} [/tex]
Multiplying this out should leave you with D as your answer.
helppppppp!!! pleaseeeeeeeee
Answer:
62,400 J
Step-by-step explanation:
As the problem statement tells you, the work done to lift the mass is the product of the force applied and the distance the mass is lifted. Here, the force decreases as the height of the mass increases.
SetupFor x meters of exposed cable, the force required to lift it is 3x newtons. The force required to lift the object is 1500 newtons, so the total force required to lift the masses an incremental distance (dx) is (3x +1500) newtons.
The work done lifting the mass that distance is the product of force and distance. The total work done is the integral of the incremental work over the total of distance lifted:
[tex]\displaystyle W = \int_0^{40}(3x+1500)\,dx[/tex]
SolutionThe value of the integral is ...
[tex]\displaystyle W=\left.\left(\dfrac{3}{2}x^2+1500x\right)\right|_{x=0}^{x=40}=40\left(\dfrac{1}{2}(3\cdot40)+1500\right)=62\,400\qquad\text{joules}[/tex]
The work done to lift the cable and weight is 62,400 joules.
__
Additional comment
One reason for writing the integral evaluation this way is to demonstrate that the total of work done is that required to lift the weight (1500 N, 40 m) and that required to lift the center of mass of the cable (120 N, 20 m).
This will generally be the case for "disappearing mass" or "increasing distance" problems. Pumping from a pool is a similar kind of problem with a similar kind of solution.
Effectively, you're doing work on the center of mass of the system, moving it from its initial position to the top of the building.
The shaded region under a Normal distribution with mean 100 and standard deviation 5 is shown. Which of the following is the best choice that corresponds to the shaded region? Select one. mean The shaded region under a Normal distribution with mean 100 and standard deviation 5 is shown . Which of the following is the best choice that corresponds to the shaded region ? Select one .
The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:
z = (raw score - mean)/standard deviation
The diagram represents z < 1.5 mean = 100, standard dev = 5 hence:
-1.5 = (x - 100)/5
x = 92.5
The shaded region shown in the graph of the normal distribution corresponds to P(x < 92.5).
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Find the area of the following figure ( i don't know how to get that answer plsss, help)
The area of the figure is 11. 27 cm²
How to determine the areaThe figure given is a parallelogram
The formula for the area of a parallelogram is given thus;
Area = base × height
From the figure, we have that
base = 2. 3 cm
height = 4. 9 cm
Substitute into the formula
Area = 2. 3 × 4. 9
Area = 11. 27 cm²
Thus, the area of the figure is 11. 27 cm²
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angle sum theory find Y
25
Step-by-step explanation:The angle sum theory says that the sum of all the interior angles in a triangle is 180 degrees.
Finding X
To solve for y, we must first find x. This way we know 2 of the interior angles. Luckily, angle x is a part of a linear pair.
Linear Pairs are 2 adjacent angles that create a straight line together. This means that the sum to 180 degrees.Angle x and the angle with a measurement of 115 form a linear pair. Thus, we can create an equation to find x.
115 + x = 180By subtracting 115 from both sides we know that x = 65.
Solving for Y
Now that we know x, we can find y. We know that one of the interior angles is 65 and that the other is 90 degrees. The square marking the bottom angles in the middle show that they are right angles.
Right angles are usuaslly denoted with a square drawn in the angle and have a measurement of 90 degrees.Lastly, we can create a formula to find y with the angle sum theory.
90 + 65 + y = 180Combine like terms
155 + y = 180Subtract 155 from both sides
y = 25This means that the angle y is 25 degrees.
Write 4.714 as a mixed number
Answer:
47/14 is a mixed number i think
A farmer needs to mix 8 ounces of fertilizer for every 10 pounds of soil. How many pounds of fertilizer will the farmer need to make a mix that contains 80 pounds of soil? ( Remember- 16 ounces = 1 pound)
4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
What is Ratio ?The relationship between two things is called Ratio. It is written in p:q form.
It is given that
For 10 pounds of soil , farmer mixes 8 ounces of fertilizer.
=8/16 = 0.5 pounds of fertiliser
The ratio is 10 : 0.5
Suppose he mixes x pounds of fertilizer for 80 pounds of soil
to determine x
The ratio is 80 : x
As they are in Proportion
10 / 0.5 = 80 /x
x = 80 * 0.5 /10
x = 4 pounds
Therefore 4 pounds of fertilizer is mixed to make a mix of 80 pounds of soil.
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A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 594 inch to the 3 in, what were the original dimensions of the piece of metal?
The original dimensions of the metal sheet are 22 inches by 52 inch
What is volume?The volume is defined as the space occupied by any object in three dimensions. For a rectangular box, the volume will be calculated by multiplying the length, width, and height of the object.
If the Width of the metal = x
The length is 30 inches longer than its width= x+30
If Squares with sides 6 in long are cut from the four corners and the flaps are folded.
The length of the pre-folded box =x+30-12=(x+18)inch
The width of the pre-folded box = (x-6-6)inch = (x-12) inch
The height of the flap= 6 inch
The volume of the box = 2400-inch cubed
Volume of a Cuboid = LWH
6(x-12)(x+18)=2400
6x²+36x-1296=2400
6x²+36x-1296-2400=0
6x²+36x-3696=0
6(x-22)(28+x)=0
x-22=0 or x+28=0
Therefore the original dimensions of the metal sheet are 22 inches by 52 inch
The complete question with correct data is given below:-
A rectangular piece of metal is 30 in longer than it is wide. Squares with sides 6 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 2400 incubatedwhat were the original dimensions of the piece of metal?
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