Answer:
Step-by-step explanation:
To solve the system of equations using substitution, we first need to isolate one of the variables in one of the equations. We can start by solving the first equation for y:
x - 5y = -6
y = (x + 6) / 5
Now we can substitute this expression for y into the second equation:
7x - 3y = 42
7x - 3((x + 6) / 5) = 42
Simplifying and solving for x:
(35/5)x - (3/5)x - 18/5 = 42
32x = 210+18
x=57/8
Now we can substitute this value of x back into the first equation to find the value of y:
y = ((57/8) + 6) / 5
y = 21/8
So the solution of the system is (x, y) = (57/8, 21/8).
5.
For the exponential function f(x)= a(b)' we know that f(3) =17 and f(7)=3156. Which of the
following is closest to the value of b?
The closest to the value of b is 3.6912.
An exponential function is a Mathematical function in the form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.
f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b
Set up both equations with values
When x = 3, f(3) = 17, so we have a(b)^3 = 17
When x = 7, f(7) = 3156, so we have a(b)^7 = 3156
Isolate a in each equation
a = 17/(b)^3
a = 3156/(b)^7
Now set them equal to each other
17/(b)^3 = 3156/(b)^7
Cross Multiply
17b^7 = 3156b^3
Divide each side by b^3
17b^4 = 3156
Divide each side by 17
b^4 = 185.6471
b = 3.6912
Therefore, the closest to the value of b is 3.6912.
To learn more about exponential function visit : brainly.com/question/14355665
#SPJ4
please help im very confused how to do this.
Step-by-step explanation:
(a)
[tex] \frac{b + x}{3} = \frac{b - x}{4} \\ 4b + 4x = 3b - 3x \\ b = - 7x[/tex]
(b)
[tex]p = \frac{y}{1 + y \\ } \\ p + py = y \\ y - py = p \\ y = \frac{p}{1 - p} [/tex]
(c)
[tex] \frac{1}{a} = \frac{1}{b} - \frac{1}{c} \\ \frac{1}{c } = \frac{1}{b} - \frac{1}{a} \\ \frac{1}{c} = \frac{a - b}{ab} \\ c = \frac{ab}{a - b} [/tex]
The Ahmad family uses propane gas to heat their home in the winter. The cost to fill their
propane tank varies directly with the number of gallons of propane they buy. The Ahmads have a
budget of $750 to buy propane for their tank this winter, and the gas costs $3.83 per gallon. Give
the direct variation equation that describes how much propane the Ahmads can purchase with
their $750 budget and state the meaning of the variables x, y, and k for this situation.
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
what is equation ?Using the equal symbol (=) to indicate equivalence, a mathematical equation is a formula that joins two statements. An equation in algebra is a statement of mathematics proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign places the variables 3x + 5 and 14 apart. The relationship between two sentences on either side of a letter is described by a mathematical formula. A single variable, which also serves as the symbol, is frequently present. like in 2x - 4 = 2, for instance.
given
Let the direct variation equation
be x + $3.83y = 750,
Let the direct variation equation be x + $3.83y = 750,
The number of gallons they buy is directly connected to the size of the propane tank: x + $3.83y = $750.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
p(x)=x²+x2-10x+8 (b) Using long division express p(x) as product of linear factor (e) Hence solve x¹+x²-10x +8=0 Qu. 3. The polynomial p/x) is given (a) Show that x-2 is a factor of p(x)
Answer:
b. To express p(x) as a product of linear factors using long division, we divide p(x) by (x - 2) and get a quotient of (x + 5) and a remainder of 0. This means that p(x) = (x - 2)(x + 5)
e. To solve p(x) = 0, we set each factor equal to zero and find the solutions:
x - 2 = 0, x = 2
x + 5 = 0, x = -5
Thus, the solutions to the equation p(x) = 0 are x = 2 and x = -5.
a. To show that x-2 is a factor of p(x), we can use synthetic division or polynomial long division.
let's use polynomial long division to divide p(x) by (x-2)
p(x) = x²+x²-10x+8
| x-2 |
x²-2x+x
| -x²-x²+10x+8
--------------
0
As we can see, after dividing p(x) by (x-2) we get remainder as 0, which implies that (x-2) is a factor of p(x)
Hence, we can say that x-2 is a factor of p(x)
How do you solve an algebraic equation with 3 variables?.
Answer:
using the linear combination method
Step-by-step explanation:
hope this helps
determine whether the table repersents a discrete probability distribution
The discrete probability distribution is discussed above.
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.Given is discrete probability distribution.
A probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment.A discrete probability distribution is the probability distribution of a random variable that can take on only a countable number of values which means that the probability of any event {E} can be expressed as a (finite or countably infinite) sum.Mathematically, we can write it as : [tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}P(X=\omega )}[/tex].A discrete probability distribution is often represented with Dirac measures, the probability distributions of deterministic random variables. If {E} is any event, then : [tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)}[/tex].Mathematically, we can write the equivalent formula as -[tex]${\displaystyle P(X\in E)=\sum _{\omega \in A}p(\omega )\delta _{\omega }(E)} =[/tex]
[tex]${\displaystyle P(X\in E)=\int _{E}f(x)\,dx=\sum _{\omega \in A}p(\omega )\int _{E}\delta (x-\omega )=\sum _{\omega \in A\cap E}p(\omega )}[/tex]
Therefore, the discrete probability distribution is discussed above.
To solve more questions on probability distribution, visit the link below-
brainly.com/question/1041084
#SPJ1
find sin2x, cos2x, and tanx2x if sinx= 15/17 and x terminates in quadrant 2
The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
What is trigonometric?Trigonometry is a branch of mathematics that studies the relationships between the sides and angles of triangles and circles. Trigonometry is used to calculate the measurements of angles, lengths, and areas of different geometric figures. It is also used to solve problems involving forces, motion, and velocity.
Sin2x = (2*15/17)*(-12/17) = -30/289
Cos2x = (2*15/17)*(-5/17) = -30/289
Tan2x = (2*15/17)/(-12/17) = -5/12
Since sinx = 15/17 and x terminates in quadrant 2, then x = -3π/17. The trigonometric identities for double angles can be used to solve for sin2x, cos2x, and tan2x.
Sin2x = 2*sinx*cosx = 2*(15/17)*(-12/17) = -30/289
Cos2x = 2*cosx*cosx - 1 = 2*(-12/17)*(-12/17) - 1 = -5/289
Tan2x = (2*sinx*cosx)/(cosx*cosx - sinx*sinx) = (2*(15/17)*(-12/17))/((-12/17)*(-12/17) - (15/17)*(15/17)) = -5/12
To learn more about trigonometric
https://brainly.com/question/24349828
#SPJ1
2(3b+6) =78 : Answer is 11
-2(6c-3) = -72 : Answer is 6.5
Check Right and Left side of the equation
The right side of the first equation is 78 and the right side of the second equation is -72. Both sides of the equations are constants (numbers with no variable in them)
The left side of the first equation is 2(3b+6) and the left side of the second equation is -2(6c-3). Both sides of the equations are products of a constant and a variable or a sum/difference of variables.
To find the value of b and c in the equation, you need to solve the equation.
For the first equation:
2(3b + 6) = 78
3b + 6 = 39
3b = 33
b = 11
For the second equation:
-2(6c - 3) = -72
6c - 3 = 36
6c = 39
c = 6.5
So, the value of b is 11 and the value of c is 6.5
What are the 4 inverse operations in math?.
The four main inverse operations in math are addition, subtraction, multiplication, and division. These are the operations that reverse the effects of the operation.
When you use the word "inverse," you want to move backward in time or space. The Latin term "inversus," which means to turn inside out or upside down, is where the word's name originates. An inverse operation in mathematics is a procedure that reverses the effects of a preceding one.
Multiplication, division, subtraction, and addition are the four fundamental mathematical operations. Subtraction, and vice versa, are the opposites of addition. Division and vice versa are the opposites of multiplication.
To learn more about operations, visit the link below:
brainly.com/question/29196320
#SPJ4
What are the 3 rules to solving an equation?.
The Golden Rule to Solve an Equation are:-
Simplify both sides of the equation.Move all parts of the equation that contain the variable you're solving for to the same side.Isolate the variable using multiplication, division, exponentiation, or by taking roots.Check your solution!In arithmetic, an equation is a system that expresses the equality of two expressions, by connecting them with the equals signal =. The phrase equation and its cognates in different languages may additionally have subtly one-of-a-kind meanings; as an example, in French, an équation is defined as containing one or more variables, whilst in English, any well-formed method together with expressions associated with an equals signal is an equation.
solving an equation containing variables includes figuring out which values of the variables make the equality real. The variables for which the equation must be solved are also called unknowns, and the values of the unknowns that fulfill the equality are called answers to the equation. There are kinds of equations: identities and conditional equations. An identity is real for all values of the variables. A conditional equation is handiest authentic for particular values of the variables.
To learn more about Equation visit here:
brainly.com/question/19770987
#SPJ4
A polar vortex causes the temperature to decrease from 3°C at 3 PM to -2°C at 4 PM the temperature continues to change by the same amount each hour until 8 PM find the total change in temperature for 3 PM to 8 PM
The total change in temperature from 3 PM to 8 PM is 25°C.
The first step is to calculate the temperature difference.
Temperature at 3 PM = 3°C
The temperature at 4 The period2°C
The difference = 3 - (-2) = 3 + 2 =5°C
The second step is to calculate the difference time.
Period from 3 PM to 8 PM:
To find the difference between two numbers, subtract the number with the smallest value from the number with the largest value.
So,
8-3 = 5 hours
The third step is to calculate the total temperature change.
5°C × 5 hours = 25°C.
The total change in temperature from 3 PM to 8 PM is 25°C.
Read more on difference here
https://brainly.com/question/17864807
#SPJ1
A student says x^2+36=(x+6)^2
Answer:
x=0
Step-by-step explanation:
-Use (a+b)^2=a^2+2ab+b to expand the expression.
-Cancel equal terms on both sides of the equation
-Swap the sides of the equation
-Divide both sides of the equation by 12
-Solution
x=0
Surface Area and Volume
Z
X
X
Note: Figure not drawn to scale.
Height has been rounded for computational ease.
If X = 13 units, Y = 11 units, and Z = 15 units, then what is the surface area of the right triangular pyramid shown above?
OA.
390 square units
OB. 266.5 square units
OC. 435.5 square units
OD. 364 square units
The surface area of the right triangular pyramid is 435.5 square units.
What is a surface area of a triangle?
A triangle is a three-sided polygon with three vertices. The triangle's internal angle, which is 180 degrees, is constructed. It implies that the internal angles of a triangle add up to 180 degrees. It is the polygon with the fewest sides.
Here, we have
Given: X = 13 units, Y = 11 units, and Z = 15 units
We have to determine the surface area of the right triangular pyramid.
Surface area = base area + 1/2 (perimeter × slant height)
A = xy + 1/2 (3x × z)
A = 13 × 11 + 1/2 (3× 13 × 15)
A = 143 + 292.5
A = 435.5 square units.
Hence, the surface area of the right triangular pyramid is 435.5 square units.
To learn more about the surface area of triangle from the given link
https://brainly.com/question/1297098
#SPJ1
What are the four rules of multiplication?.
The four rules of multiplication is explained below.
The term multiplication in math is defined as the process of when you take one number and add it together a number of times
Here we need to define the four rules of multiplication.
Here the first rule of multiplication is written as that any number times zero is always zero.
And the next rule is that any number times one is always the same number.
And the another rule is written as add a zero onto the original number when multiplying by 10.
And if the order of factors does not affect the product then switching the roles of multiplier and multiplicand results in the same answer.
Where the other rule is that products are always positive when multiplying numbers with the same signs.
And the final rule is the products are always negative when multiplying numbers with different signs.
To know more about multiplication here.
https://brainly.com/question/11799672
#SPJ4
What is a solution Class 7?.
In class 7, a solution is typically defined as a type of mixture where one or more substances are evenly dispersed in another substance.
The substance that is being dispersed is called the solute, and the substance that it is being dispersed in is called the solvent. Solutions can be liquids, gases, or even solids, and they can be formed by dissolving a solute in a solvent.
In class 7, students learn about different types of solutions, such as:
Liquid solutions: These are solutions where the solvent is a liquid, such as sugar dissolved in water to make a sweet drink.
Gas solutions: These are solutions where the solvent is a gas, such as air, and the solute is a gas or a solid, such as the dissolved oxygen in the air we breathe.
Solid solutions: These are solutions where the solvent is a solid, such as a metal alloy, and the solute is a metal or a non-metal.
To know more on solution
https://brainly.com/question/19466295
#SPJ4
How do you write 2 more than 3 times?.
The correct equation to write 2 more than 3 times is 3x + 2.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Let us assume that, the number is 17 .
So,
→ Three time of x = 3 * x = 3x
then,
→ 2 more than three time of x = (3x + 2)
given that, 2 more than three time of x is equal to 17 .
therefore,
→ 3x + 2 = 17
→ 3x = 17 - 2
→ 3x = 15
→ x = 5 (Ans.)
Hence, the required number is 5 .
Verification :-
→ 2 more than three times of 5 = 17
→ 3 * 5 + 2 = 17
→ 15 + 2 = 17
→ 17 = 17 .
hence, the correct equation to write 2 more than 3 times is 3x + 2.
To learn more about equation visit : brainly.com/question/10413253
#SPJ4
o the solutions tell you
y = (x + 1)² + 3
y = 2x + 4
The equation y = (x + 1)² + 3 tells that it is quadratic equation and the equation y = 2x + 4 tells that it is a linear equation.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The first equation is - y = (x + 1)² + 3
The second equation is - y = 2x + 4
The first equation is a quadratic equation.
To solve the first equation use the formula (a + b)² = (a² + 2ab + b²) -
y = (x + 1)² + 3
y = (x² + 2x + 1) + 3
y = x² + 2x + 4
The second equation is a linear equation y = 2x + 4.
On graphing both the equations it is seen that the first equation forms a parabola while the second forms a straight line.
Therefore, first equation is quadratic and second is linear.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
Please help me again
Answer:83
Step-by-step explanation: sum of the angles should be 180
44+53+x=180
x=180-97
x=83
Answer:
Step-by-step explanation:
The addition of three angles in a triangle is 180°.
Therefore, if we add all the angles, it's
180° = x + 53° +44 °
180° - ( 53°+44° ) = x
180°-97° = x
83 ° = x
Then the answer is obvious, it's 83°.
What will be the solution of linear equation 3x 4y 10 and 2x 2y 2?.
The solutions of the system of linear equations 3x+ 4y= 10 2x+ 2y= 2 can be found by using the method of substitution or elimination.Solve one of the equations for one of the variables in terms of the other variable.
Let's solve the first equation for x: 3x + 4y = 10 3x = -4y + 10 x = -4/3y + 10/3
Substitute this expression into the other equation and solve for the remaining variable.
2(-4/3y + 10/3) + 2y = 2 -8/3y + 20/3 + 2y = 2 -8/3y + 2y = -20/3 + 2 -2/3y = -18/3 y = 9
Use the value of y to find the value of x.
x = -4/3y + 10/3 x = -4/3(9) + 10/3 x = -4 + 10/3 x = -4 + 10/3
The solution of the system of equations is (x,y) = (-4 + 10/3, 9)
To learn more about the variables question:
https://brainly.com/question/17344045
#SPJ4
16. If AABC-ADBE, find the values of x and y.
The values of x and y for the given similar triangles are 3 and 10 respectively.
Define the term similarity of the triangle?If two figures have the same shape, they are termed to be comparable. In more formal terms, two figures are said to be comparable if their respective angles are congruent and their corresponding side length ratios are identical. The scale factor is the name given to this usual ratio.For the stated question-
Using the similarity for the triangle ABC and DBE,
Taking the ratios of the sides.
x/9 = 4/12
x = 9/3 = 3
And,
5/y = 4/(12 - 4)
5/y = 4/8
y = 5*2 = 10
Thus, the values of x and y for the given similar triangles are 3 and 10 respectively.
To know more about the similarity of the triangle, here
https://brainly.com/question/14285697
#SPJ1
Jacob picks a 5-digit even number.
The first digit is a prime number.
The third digit is odd.
The four digit is 8
How many different 5-digit number could he pick
Answer:
Total no ways can be taken
Step-by-step explanation:
You are interested in exploring the relationship between hours studying and test grades. which of these statements would be her null hypothesis?
a. There is no relation between hours studying and grades on a test. b. There is a relation between hours studying and grades on a test.
c. There is no relation between hours studying and grades on a test.
d.The more hours one studies, the higher their grades will be.
e. None of the above.
There is no relation between hours studying and grades on a test. this statements would be her null hypothesis .
What is the definition of a null hypothesis?
The null hypothesis presupposes that any variation between the selected attributes you observe in a set of data is the result of chance.
For instance, if the predicted profits from the gambling game genuinely equal zero, then any discrepancy between the data's average profits and zero results from chance.
The null hypothesis doesn't exist.
A null hypothesis may declare, for instance, that the population mean return is equal to zero. The null hypothesis is typically an equality hypothesis for population parameters.
It might be said that the alternative hypothesis is the exact opposite of a null hypothesis (e.g., the population mean return is not equal to zero).
Learn more about null hypothesis
brainly.com/question/28920252
#SPJ4
What is the graph of the inequality y ≤-22 - 3?
Answer:
would look like the picture down below meaning it has a ZERO slope
Please help! I’m really bad at math
Answer:
14.6
Step-by-step explanation:
In the example
x =kh
k is the constant of proportionality
A weight attached to the end of a long spring is bouncing up and down. As it bounces, its distance from the floor varies sinusoidally with time. You start a stopwatch. When the stopwatch reads 1.7 seconds the spring is 58 cm above the floor and is on a downward path. It takes 4.4 seconds for the spring to bounce from a distance of 36 cm to 80 cm above the ground.
A. Write an equation expressing distance from the floor in terms of the number of seconds the stopwatch reads
B. Predict the distance from the floor when the stopwatch reads 6 seconds
C. What was the distance from the floor when you started the stopwatch?
The answers to all parts are shown below.
what is wave Equation?One of the most crucial equations in mechanics is the wave equation. It describes the movement of fluid surfaces, such as water waves, in addition to the movement of strings and wires.
Define constants:
t0 = 1.7seconds h0 = 58cm highest point
t1 = 4.4 seconds h1 = 44 cm lowest point
t2 = 6 seconds h2 = (h0 + h1)/2 = 51 cm center height
Half a cycle passes between t0 and t1, so the period T is
T = 2(t1 - t0) = 2(4.4-1.7) seconds = 5.4 seconds
The amplitude A is half the total height change between h0 and h1:
A = (h0 - h1)/2 = 7 cm
a) Equation of motion in terms of height H above the floor is
H(t) = h2 + A Co s[2π(t - t0)/T]
H(t) = 51 cm + (7cm) Cos[0.1775(t - 1.7second)/second]
b) Let t = 6 seconds in the equation:
H(t) = 51 cm + (7cm) Cos[0.1775(6 - 1.7second)/second]
= 51 + 7 x (-0.4008)
= 48.1944 cm
c) Let t = 0 seconds in the equation:
H(0 seconds) = 51 cm + (7cm) Cos[0.1775(0 - 1.7second)/second]
= (51+ 7[0.99999986]) cm
= 57.99cm
Learn more about Wave Equation here:
https://brainly.com/question/12931896
#SPJ1
my mother purchased 8 pepsi products at Bi-Lo for $14.00 what is the price per product
Answer:
$1.75
Step-by-step explanation:
We take
14 / 8 = $1.75
So, one product cost $1.75
Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
The three angles of the triangle can be found by using the formula for the sum of angles of a triangle, which is 180°. Then, the measure of angle A + angle B + angle C = 180°.
1. Using the sum of angles formula, angle A + angle B + angle C = 180°
2. Use the Law of Cosines to calculate the angle between two sides of the triangle.
3. Subtract the sum of those two angles from 180° to find the measure of the third angle.
The three angles of a triangle can be found using the sum of angles formula, which states that the sum of the angles of a triangle equals 180°. This means that angle A + angle B + angle C = 180°. To find the individual angles, we can use the Law of Cosines which states that c2 = a2 + b2 - 2ab cos C, where C is the angle between two sides of the triangle. This formula allows us to calculate the angle between two sides of the triangle. Once we have calculated the sum of the two angles, we can subtract this sum from 180° to find the measure of the third angle. For example, if the sum of the two angles is 120°, then the third angle would be 180° - 120° = 60°. This method allows us to find the three angles of the triangle with the given vertices.
Learn more about triangle here
https://brainly.com/question/2773823
#SPJ4
What is the slope of 4x 2y =- 12?.
After solving, the slope of equation 4x + 2y = -12 is -2.
In the given question, we have to find the slope of 4x + 2y = -12.
The given equation is 4x + 2y = -12.
The general equation of line is y = mx + c, where m is the slope of the line and c is the y-intercept of the line.
To find the slope of the line we have to convert the given equation in the form of general equation.
We have to isolate y.
4x + 2y = -12
Subtract 4x on both side, we get
2y = -4x - 12
Divide by 2 on both side, we get
y = -4/2 x - 12/2
y = -2x - 6
On comparing the equation by general equation, we get
m = -2
Hence, the slope of the equation 4x + 2y = -12 is -2.
To learn more about slope of equation link is here
brainly.com/question/29099807
#SPJ4
The complete question is:
What is the slope of 4x + 2y = -12?
2/3 x 22/7 x 5.25 x 5.25 x 5.25 =?
Please explain this step by step because i am weak at math.
Answer:
Step-by-step explanation:
step 1: NUMERATOR:
2 x 22 x (5.25)³
= 44 x 144.703125
Numerator = 6366.9375
step 2: DENOMINATOR:
= 3 x 7
Denominator = 21
step 3: CALCULATION:
= numenator / denominator
= 6366.9375 / 21
Answer = 303.1875
RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.
RAMP The height of a ramp can be
modeled by f(x) = -1/2 x − 241 +2,
where f(x) is the height of the ramp, in
feet, and x is the distance from one
side of the ramp. Graph the function
on a separate piece of paper. Find and
interpret the key features of the graph
in the context of the situation.
The vertex is located at ( , )This means that the maximum height of the ramp is _ feet when the distance from one side is _ feet. Because the distance cannot be negative, and the ramp is _ feet long, the relevant domain is {x | 0 ≤ x ≤ __}.
Because the height cannot be negative, and the ramp is _ feet tall, the relevant range is {y | 0 ≤ y ≤ __ }. The graph is symmetric in the line x = _ This means that the height from a distance of 0 to _ feet away from one side of the ramp is the same as the height from a distance of _ to _ feet away from one side of the ramp.
It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.
What is the parabola?
A parabola is a symmetric, U-shaped geometric curve that can be defined as the set of all points that are equidistant to a fixed point (the focus) and a fixed line (the directrix). It is a conic section, which means it is the intersection of a plane and a cone. In algebraic terms, a parabola can be defined as the graph of a quadratic equation of the form y = ax^2 + bx + c, where a, b, and c are constants.
The height of a ramp can be modeled by f(x) = -1/2 x − 241 +2, where f(x) is the height of the ramp, in feet, and x is the distance from one side of the ramp. To find the vertex of the parabola, we need to complete the square.
The vertex is located at (-b/2a, f(x) + (b^2-4ac)/4a) = (-1/2, -241 +2) = (0, -240)
This means that the maximum height of the ramp is -240 feet when the distance from one side is 0 feet.
Because the distance cannot be negative, and the ramp is unknown length, the relevant domain is {x | 0 ≤ x ≤ unknown}.
Because the height cannot be negative, and the ramp is unknown tall, the relevant range is {y | 0 ≤ y ≤ unknown }.
The graph is symmetric in the line x = 0. This means that the height from a distance of 0 to an unknown feet away from one side of the ramp is the same as the height from a distance of an unknown to an unknown feet away from one side of the ramp.
It is a downward parabola, which means the height of the ramp decreases as the distance from one side of the ramp increases.
To learn more about parabolas, Visit
https://brainly.com/question/25651698
#SPJ1
