The rate of gaining altitude for the hiker is 530 feet per hour.
What is differentiation?The differentiation of a function is defined as rate of change of its value at a point. It can be written as g'(x) = (g(x + h) - g(x)) /(x + h - x).
Its geometric aspect is the slope of the function at a given point.
The given equation for hiker's altitude is as below,
a = 12850 + 530h
Here a is the altitude in feet and h is time in hours.
In order to find the rate of gaining altitude, the equation for altitude has to be differentiated with respect to hours as below,
a = 12850 + 530h
Differentiate the above equation w.r.t h as,
da/dh = 0 + 530
= 530
Hence, the rate of gaining altitude is 530 feet per hour.
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4y-5x=3(4x-2y+1) in standard form
Answer:
7x+10y=3
Step-by-step explanation:
Standard Form= Ax+By=c
Distribute first
4y-5x=12x-6y+3
Add 6y
10y-5x=12x+3
Add 12x
7x+10y=3
Can someone sketch the graph plsss? I rlly need help to sketch it
Answer:
1. Plot x = 0
(A. IF YOU CAN EASILY FIND IT, PLOT Y = 0)
(B. BONUS: PLOT A FEW EASY TO CALCULATE POINTS LIKE X = 1 & X = -1)
2. Figure out what happens when x is really big (in the positive and negative direction)
3. Optional: look for any “significant” x-values
4. Connect the dots and finish!
Step-by-step explanation:
1. Plot x = 0
The first thing we want to do is get some points up on our graph, so we want to pick the ones that will be easy to calculate. For almost any equation, plugging in x = 0 and solving for y is fast and easy to do by eye, and almost always doable without a calculator. For our example equation:
So, the first point we’ll put on our graph is (0, -4).
WILL GIVE BRAINLIEST !!
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
a) What is the distance of the helicopter’s flight?
b) What is the displacement of the helicopter’s flight? Show your work
Distance is the total length covered by an object.
Displacement is the distance between the final point and the initial point.
The distance of the helicopter's flight is 150 m
The displacement of the helicopter's flight is zero.
What is displacement?Displacement is the distance between the final point and the initial point.
We have,
A helicopter lifts 75m vertically into the air and then comes back down to the ground.
Distance is the total length covered by an object.
Distance of the helicopter's flight.
= 75m + 75m
= 150 m
Displacement of the helicopter's flight.
= Final point - Initial point
= 0 - 0
= 0
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The formula for distance is expressed as d = rt, where d is distance, r is the rate, and t is time.
How long would it take a car to travel 348 miles if it is traveling at a rate of 60 miles per hour?
hours
Answer:
5.8 hours
Step-by-step explanation:
First, you just plug it the given information.
Turn the equation to t=d/r by dividing the rate by both sides.
Plug it in 348miles/ 60 miles per hour
It'll take 5.8 hours for the car to travel 348 miles at the rate of 60 miles per hour.
Drag the tiles to the correct boxes to complete the pairs.
Determine whether each pair of lines is perpendicular, parallel, or neither.
2y = 4x + 4
y=-2x-2
4y= 2x - 4
y=-2x+9
Perpendicular
Parallel
y = 2x+4
2y = 4x - 7
Neither
Answer:
neitherperpendicularparallelStep-by-step explanation:
You want to know whether the pairs of equations describe lines that are parallel, perpendicular, or neither.
ParallelParallel lines have the same slope. When the equations are written in slope-intercept form, the coefficients of x are identical.
PerpendicularPerpendicular lines have opposite reciprocal slopes. When the equations are written in slope-intercept form, the product of the x-coefficients is -1.
Application1. 2y = 4x +4; y = -2x -2Solving the first equation for y gives ...
y = 2x +2
The x-coefficients are 2 and -2, so the lines are neither parallel nor perpendicular.
2. 4y = 2x -4; y = -2x +9Solving the first equation for y gives ...
y = 2/4x -1 = 1/2x -1
The x-coefficients are 1/2 and -2, which have a product of -1. These lines are perpendicular.
3. y = 2x +4; 2y = 4x -7Solving the second equation for y gives ...
y = 2x -7/2
The x-coefficients are 2 and 2, which are identical. These lines are parallel.
Convert the height of a person who is 5.2 feet tall to centimeters. Include the inches-centimeter conversion
factor. Use the table given to create conversion factors. Show all conversion factors needed.
Round final answer to 2 decimal places if needed. The setup below should look like the typical dimensional
analysis that you learned.
The height of the 5.2 feet person in centimeters is 158.496 cm.
Explain unit conversion.A conversion factor must be added, subtracted, multiplied, or divided throughout the multi-step process of unit conversion. Additionally, selecting the appropriate number of significant digits and rounding may be necessary.
Different conversion units are used to quantify various measurements. By definition, unit conversion is the process of converting two measures of the same quantity between distinct units by multiplying or dividing them.
In mathematics, conversion is the process of changing a value's form, such as from millimeters to inches or liters to gallons. Units are used for measurements of length, weight, capacity, temperature, and speed.
Given,
Height of a person = 5.2 feet.
The conversion between inches and centimeters must also be included.
First, convert feet to inches.
1 foot = 12 inches
Converting the given height to inches,
Height = 5.2 × 12
= 62.4 inches
Now, we will convert the height into centimeters,
To convert, we will multiply by 2.54
Height = 62.4 × 2.54
= 158.496 cm
Therefore, the height of the person in centimeters is 158.496 cm
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For all real values of x if f((x)=(x-3)^2 and g(x)=(x+3)^2 what is f(x)-g(x)?
The composition f(x) - g(x) has its value to be 12x
How to evaluate the composite function?The definitions of the functions are given as
f(x) = (x - 3)²
Also, we have the definition of another functions to be given as
g(x) = (x + 3)²
To find the composition f(x) - g(x), we make use of the following equation
f(x) - g(x) = f(x) - g(x)
So, we have the following equation
f(x) - g(x) = f(x) - g(x)
Substitute the known values in the above equation
So, we have the following equation
f(x) - g(x) = (x + 3)² - (x - 3)²
Apply the differece of two squares rules
So, we have
f(x) - g(x) = (x + 3 + x - 3)(x + 3 - x + 3)
So, we have
f(x) - g(x) = (2x)(6)
This gives
f(x) - g(x) = 12x
Hence, the value of the composition is f(x) - g(x) = 12x
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At 2 hours before sunset, the temperature is 0°F. At 2 hours after sunset, the temperature is −4°F. Identify the equation representing the temperature y, in degrees Fahrenheit, at x hours after sunset
The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
At 2 hours before sunset, the temperature is 0°F.
And, At 2 hours after sunset, the temperature is −4°F.
Now,
Let the temperature in degrees Fahrenheit = y
So, We can formulate;
⇒ y = - 4°x + 0°
Thus, The correct equation to representing the temperature y, in degrees Fahrenheit, at x hours after sunset will be;
⇒ y = - 4°x + 0°
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use the distributive property to solve the equation 2x - 4(x - 2) = - 8 + 4x + 4
so many points if dine quickly
If f(x) = 2x + 1, find f(1). Just write the answer no equals or variable!!!
Answer:
3
Step-by-step explanation:
f(1)=2(1)+1
f(1)=3
Consider the equation and the following ordered pairs: (1,y) and (x,−3).
6x+3y=15
Step 1 of 2 : Compute the missing x and y values so that each ordered pair will satisfy the given equation.
Answer
Keyboard Shortcuts
Complete the table below.
x y
row 11 Answer
row 2 Answer
−3
Answer:
(1,3)
(4,-3)
Step-by-step explanation:
To find y, replace x with 1 in the equation and solve for y
6x + 3y = 15
6(1) + 3y = 15
6 + 3y = 15 Subtract 6 from both sides
3y = 9 Divide both sides by 3
y = 3
(1,3)
To find x, replace y with -3 in the equation and solve for x
6x + 3y = 15
6x + 3(-3) = 15
6x - 9 = 15 Add 9 to both sides
6x = 24 Divide both sides by 6
x = 4
(4, -3)
If a truck weighs 20% more than a car, then the truck's weight is % of the car's weight.
This is a statistics/applications question
Using percentages, the answer to all the subparts are shown:
(A) % who scored between 46 and 106: 67% approx(B) % who scored less than 46: 17% approx(C) % who scored between 61 and 91: 33% approx(D) % who scored between 76 and 121: 50%What are percentages?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.So, calculate the percentages as follows:
(A) % who scored between 46 and 106:
Total marks: 121 - 30 = 90Students between 46 and 106: 106 - 46 = 60Then,
60/90 × 1002/3 × 10066.66Rounding off: 67% approx
(B) % who scored less than 46:
Total marks: 121 - 30 = 90Students who scored less than 46: 46 - 31 = 15Then,
15/90 × 10016.66Rounding off: 17% approx
(C) % who scored between 61 and 91:
Total marks: 121 - 30 = 90Students between 61 and 91: 91 - 61 = 30Then,
30/90 × 1001/3 × 10066.6633.33Rounding off: 33% approx
(D) % who scored between 76 and 121:
Total marks: 121 - 30 = 90Students between 76 and 121: 121 - 76 = 45Then,
45/90 × 10050%
Therefore, using percentages, the answer to all the subparts are shown:
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A group of 3 students plants 141 seeds. Each student plants the same number of seeds.
How many seeds does each student plant?
Write an expression you can use to solve
the problem.
Answer:
to find the answer you just need to divide 3 out of 141
141÷3=47seeds per each student
3x=141
x=141÷3
x=47
The equation is represented as A = S/3 , where S is the total number of seeds and A is the number of seeds planted by each student and the value of A = 47 seeds
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total number of seeds by each student be A
Now , the equation will be
The total number of seeds be S = 141 seeds
The number of students be n = 3 students
So , the total number of seeds planted by each student A = total number of seeds S / number of students n
A = S / n
Substituting the values in the equation , we get
Total number of seeds planted by each student A = 141 / 3
Total number of seeds planted by each student A = 47 seeds
Therefore , the value of A is 47 seeds
Hence , the number of seeds is 47 seeds
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stu took a test. There were 60 questions. He answered 35 correctly. What grade did Stu make
Answer:
58%
Step-by-step explanation:
35/60=0.58333=58/100=58%
8x - 6 = 2(4x-3)
Does the equation have one
none, or infinite solutions?
Explain why.
The given linear equation has only one solution i.e. x = 3/4
What is a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
A linear equation in one variable has
(a) Only one solution
(b) Two solutions
(c) More than two solutions
(d) No solution
Here,
On solving we have 8x - 6 = 0 or x = 3/4. The above linear equation is only true if x = 3/4 and
Hence, the given linear equation has only one solution i.e. x = 3/4.
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In a raffle, 100 tickets are sold. George buys 10 tickets Julia by 5 tickets. There is one winning ticket. Find a probability that
a. George will win
b. jullia will win
Probability of (a) George winning is 0.1
(b) Julia winning is 0.05
Given in question,
Total ticket sold = 100
George bought tickets = 10
Julia bought tickets = 5
Winning ticket = 1
Selecting 1 ticket from 100 = [tex]\left[\begin{array}{ccc}100\\1\\\end{array}\right][/tex]
= 100
Selecting 1 ticket from 10 = [tex]\left[\begin{array}{ccc}10\\1\\\end{array}\right][/tex]
= 10
Selecting 1 ticket from 5 = [tex]\left[\begin{array}{ccc}5\\1\\\end{array}\right][/tex]
= 5
Probability = favorable outcome/total outcome
Probability of George winning = [tex]\frac{10}{100}[/tex]
= 0.1
Probability of Julia winning = [tex]\frac{5}{100}[/tex]
= 0.05
Hence, probabilities are 0.1 and 0.05 respectively.
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Given m=-1/2 and n= -1/3 which is greater
Answer: n is greater than m
Step-by-step explanation:
if m=-1/2 then that means its -.50 and n=-1/3 meaning its -.333(...)
so n is greater (remember its negative so higher numbers are actually lesser in value)
Hope this helped... :)
What 1+2
Apparently that wasn’t enough info…
Answer:
3???
Step-by-step explanation:
Helppp it’s due tomorrow…
Evaluate the given function for f (2).
The value of f(2) is 2.
What is graph function?
The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. We may alternatively say that the graph of f is the graph of y = f. (x). As a result, the graph of an equation is a particular instance of the graph of a function.
All y-coordinates of the graph function are an output of the graph function.
All x-coordinates of the graph function are an input of the graph function.
f(2) is an output of the function.
Here find the y-coordinates of the point on the graph when the value of x is 2.
(2,3) is a point on the graph.
Thus f(2) = 3
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Which of the following has a graph that is wider than the graph of y = 5x² - 3?
-
y = 8x² - 10
y = 5x² + 2
y=-6x² + 1
y = 3x² + 4
The equations y = -6x² + 1 and y = 3x² + 4 both have graphs that are wider than the graph of y = 5x² - 3.To determine which equation has a graph wider than the graph of y = 5x² - 3, we need to compare the coefficients of x² in each equation.
A wider graph indicates a smaller coefficient in front of x², which means the parabola will be less steep and have a broader shape.Let's compare the coefficients:y = 8x² - 10: The coefficient is 8, which is larger than 5. Therefore, this equation does not have a wider graph than y = 5x² - 3.
y = 5x² + 2: The coefficient is 5, which is equal to the coefficient in y = 5x² - 3. Therefore, the graphs of these two equations will have the same width.
y = -6x² + 1: The coefficient is -6, which is smaller than 5. Hence, this equation has a wider graph than y = 5x² - 3.
y = 3x² + 4: The coefficient is 3, which is smaller than 5. Hence, this equation also has a wider graph than y = 5x² - 3.
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Please Help!!!!
Kim and Tracy are collecting data for their final project in their psychology
class, in which they are conducting a survey about people’s overall job
satisfaction. They decide to go to the local mall to collect their data. To get a
more varied sample, Kim surveys shoppers coming out of store A, a discount
clothing store, while Tracy surveys shoppers coming out of store B, a high-end
boutique.
A. Identify a possible problem with this type of sampling method. (6 points)
B. How might Kim and Tracy improve on their sample design so as to get more
accurate information from the shoppers at the mall?
Answer:
below
Step-by-step explanation:
A problem would be that they are not surveying people from multiple places. They are doing it at 2 opposite stores, at the same times. They should try multiple different stores at other days and times to get more objective data.
How many solutions does the equation have?
12x + 6 = 14(2x – 24) because when simplified we get?
a) 6=-6
a) infinitely many solutions
b) x=-6
b) one solution
c) 6=6
c) no solution
Answer:
One solution: x =21.6
Step-by-step explanation:
Equation
12x + 6 = 14(2x – 24) Remove the brackets
Solution
12x + 6 = 28x - 336 Add 336 to both sides.
12x + 6+336 = 28x - 336 Combine
12x + 342 = 28x -336+336
12x + 342 = 28x Subtract 12x from both sides.
12x-12x + 342 = 28x - 12x Combine
342 = 16x Divide by 16
342/16 = 16x/16
21.6=x
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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What is 3 inches above average written as an integer
The integer +3 describes the statement, 3 inches above average.
What is an average?
A single number chosen to represent a group of numbers is called an average, and it is typically calculated by dividing the total number of numbers in the group by the number of numbers in the group. As an illustration, the sum of the integers 2, 3, 4, 7, and 9 is 5.
One point in the average refers to the amount of 1 inch.
If the average is above 3 inches, it means that the value of the average is above 3 inches. It further implies that the total value has gained 3 inches on that average.
Inches mainly describe the gains and losses in short-time investments. A positive sign (+) shows the above average, and a negative sign (-) represents the below average.
Therefore, the integer +3 describes the statement, 3 inches above average.
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Josh loves to visit his aunt's house. When there, his two favorite activities are walking the dog and playing darts. Let A represent the event that he walks his dog at his aunt's house and B represent the event that he plays darts at his aunt's house. If A and B are independent events with P(A)=0.9 and P(B)=0.4, find P(A AND B).
The probability of P(A AND B) when Josh visit his aunt's house is 0.36.
What is probability?Probability is the likelihood that an event will occur or take place.
Let A = the event that he walks his dog at his aunt's house
Let B = the event that he plays darts at his aunt's house.
When A and B are independent events with P(A)=0.9 and P(B)=0.4, the probability of P(A AND B) will be:
= P(A) × P(B)
= 0.9 × 0.4
= 0.36
The probability is 0.36.
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Find the exact arc length of f(x)=√2x+1 0≤x≤4
The exact arc length of f(x)=√2x+1 is 4.5.
The arc length is the separation between two points along a curve segment. The arc length of a function f(x) is given by the formula,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx[/tex]
Where f'(x) is derivative of function f(x). The arc length is, to put it simply, the distance that passes across the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.
Finding the arc length of f(x)=√2x+1 0≤x≤4, using the formula,
First finding the derivative of function,
[tex]f'(x)=\frac{d(\sqrt{2x+1})}{dx} \\\\=\frac{2}{2\sqrt{2x+1}} \\\\=\frac{1}{\sqrt{2x+1}}[/tex]
Now, putting the derivative of function f(x) in the formula of arc length L,
[tex]L=\int\limits^a_b {\sqrt{1+f'(x)^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+(\frac{1}{\sqrt{2x+1}})^2}} \, dx\\\\L=\int\limits^4_0 {\sqrt{1+\frac{1}{2x+1}}}\\\\L=\int\limits^4_0 {\sqrt{\frac{2x+1+1}{2x+1}}}\\L=\int\limits^4_0 {\sqrt{\frac{1}{2x+1}}}\\\approx4.5[/tex]
Therefore, the exact arc length of f(x)=√2x+1 is 4.5.
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ALGEBRA 1 HW!! PLEASE HELP I WILL GIVE BRAINLYEST
The value of constant C is 50.
Explain linear equation.Equations with a maximum degree of one are referred to as linear equations. According to this rule, a variable in a linear equation cannot have an exponent greater than 1.
A linear equation's graph is always depicted as a straight line. There are linear equations for one variable and two variables, respectively.
Given, the linear equation is 12.5x+5y = C
Here, constant C.
Consider one points from given table x = -2 and y = 15,
Putting the value of x and y,
C = 12.5×(-2) + 5×15
= -25 + 75
= 50
For point, x = 0 and y = 10,
Putting the value of x and y,
C = 12.5×0 + 5×10
= 50
For point, x = 2 and y = 5,
Putting the value of x and y,
C = 12.5×2 + 5×5
= 25 + 25
= 50
Given, x = 4 and y = 0,
Putting the value of x and y,
C = 12.5×4 + 5×0
= 50
Therefore, the value of constant C was found to be 50.
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