cory earns 52.50 in 7 hours. find the unit rate
divide them:
52.50 / 7 = 7.50 dollars per hour
—
Is 1.0227 a rational number?
A town's population has been growing linearly. In 2003, the population was 60000, and the population has been growing by 2700 people each year.
Write an equation for the population x years after 2003.
James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during the first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed ti
Answer:
n = 6.2f
Step-by-step explanation:
Find the derivative of the function y = sin(tan 4x)
Hi guys can I plz get some help I don't understand and can I plz get the answers so I can get a 4 on this paper thx
The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is s(t) = -16t2 - 64t + 80, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? (2 points)
Select one:
a. 256 ft/sec
b. -96 ft/sec
c. 0 ft/sec
d. 112 ft/sec
The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r)=2πrh+2πr2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 4. (2 points)
Select one:
a. 24π
b. 16π
c. 64π
d. 20π
The instantaneous velocity of the ball when it hits the ground is found by deriving the height function and solving for the time of impact. The instantaneous rate of change of the surface area of a cylinder with respect to its radius when r = 4 is found by differentiating the surface area function and evaluating at r = 4.
The student's question involves two separate parts of physics and calculus related to kinematics and surface area calculations.
Part 1: Instantaneous Velocity of the Ball
The height, s, of a ball thrown straight down with initial speed 64 ft/sec from a cliff 80 feet high is given by s(t) = -16t2 - 64t + 80. The instantaneous velocity when the ball hits the ground is the derivative of position with respect to time, s'(t), evaluated at the time t when s(t) = 0 (when the ball hits the ground).
First, we find t by solving -16t2 - 64t + 80 = 0. Then, we find the derivative s'(t) = -32t - 64 and evaluate it at the found time, which gives us the instantaneous velocity.
Part 2: Rate of Change of Surface Area
The surface area of a right circular cylinder of height 4 feet and radius r feet is given by S(r) = 2πrh + 2πr2. The instantaneous rate of change of the surface area with respect to the radius, when r = 4, is the derivative dS/dr evaluated at r = 4. This is done by differentiating S(r) with respect to r and substituting r = 4 into the resulting expression.
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A.x = 15, y = 10
B.x = 20, y = 50
C.x = 50, y = 10
D.x = 50, y = 20
Answer is C x=50 y=10
Answer:
C. [tex]x=50[/tex], [tex]y=10[/tex]
Step-by-step explanation:
We have been given an image of two intersecting lines. We are asked to find the value of x and y for our given diagram.
We know that when two line intersect each other, then vertical angles are congruent.
Using vertical angles theorem, we will get a system of equations as sown below:
[tex]3y=x-20...(1)[/tex]
[tex]5x-100=y+140...(2)[/tex]
From equation (1), we will get:
[tex]x=3y+20[/tex]
Upon substituting this value in equation (2), we will get:
[tex]5(3y+20)-100=y+140[/tex]
[tex]5*3y+5*20-100=y+140[/tex]
[tex]15y+100-100=y+140[/tex]
[tex]15y=y+140[/tex]
[tex]15y-y=y-y+140[/tex]
[tex]14y=140[/tex]
[tex]\frac{14y}{14}=\frac{140}{14}[/tex]
[tex]y=10[/tex]
Therefore, the value of y is 10.
To find the value of x, we will substitute [tex]y=10[/tex] in equation (1) as:
[tex]3*10=x-20[/tex]
[tex]30=x-20[/tex]
[tex]30+20=x-20+20[/tex]
[tex]50=x[/tex]
Therefore, the value of x is 50 and option C is the correct choice.
Answer:
Option C) x = 50, y = 10
Step-by-step explanation:
We are given a two pairs of vertically opposite angle in the image.
Vertically opposite angle is formed when two lines intersect anf they are always equal.
Thus, we can write:
[tex]3y = x -20\\\Rightarrow x - 3y = 20\\5x-100 = y +140\\\Rightarrow 5x - y =240[/tex]
Solving the two equations in two variable, we get:
[tex]x - 3y = 20\\5x - y =240\\\text{Multiplying first equation by 5}\\5x - 15y = 100\\\text{Subtracting the equations}\\5x - 15y-(5x-y) = 100-240\\-14y = -140\\y = 10\\ x - 3(10) = 20\\x = 20 + 30\\x =50[/tex]
The value of x is 50 and y is 10.
Please someone help me this is the second time I posted this question....
What is the equation, in point-slope form, for a line that goes through (8, −4) and has a slope of −5/6 ?
A. y−4=−5/6(x−8)
B. y+4=−5/6(x−8)
C. y−4=−5/6(x+8)
D. y+4=−5/6(x+8)
Please provide an explanation on how to do this.
Determine the slope and y-intercept of the line. y = 8.5x + 6
Answer: Slope = 8.5 and y-intercept = 6
Step-by-step explanation:
The intercept form of a linear equation is given by :_
[tex]y=mx+c[/tex], where m( coefficinet of x ) is the slope and c (constant term) is the y-intercept.
The given equation in intercept form : [tex]y = 8.5x + 6[/tex]
Here , the coefficient of c = 8.5
thus , the slope = 8.5
Also, the constant term = 6
Thus, the y-intercept =6
How many yards equals 765 inches?
Enter your answer, as a decimal.
How do you simplify sqrt of x^20?
the calendar shows the number of days carlota rides her bike each month. each time ahe rides her bike, she travels 10 miles.is it rwasonable to say that carlota will bike more than 500 miles in 6 months?
During a certain period of time, a car can cover the distance of 120 miles, going at an average speed of 55 mph. What distance over the same period of time would cover a truck, going at an average speed of 44 mph
5.5-x=-4.5-x. how do you solve this?
The equation 5.5 - x = -4.5 - x has no solution. After cancelling out the variable x, we are left with 5.5 = -4.5, which is a contradiction.
Explanation:To solve the equation 5.5 - x = -4.5 - x, we first notice that the variable x is present on both sides of the equation. We can simply subtract or add x to both sides to cancel it out. This will give us an equation without variables:
5.5 - x + x = -4.5 - x + x
5.5 = -4.5
This equation suggests that 5.5 is equal to -4.5, which is not true. Therefore, we can conclude that there is no solution to the equation since the two sides of the equation do not balance.
Moreover, this type of equation is an example of a contradiction, meaning that it presents a statement that is inherently false regardless of the value of x. As there is no value of x that can make the equation true, we say that the equation has no solution.
Final answer:
The equation 5.5 - x = -4.5 - x simplifies to 5.5 = -4.5 when the x terms are cancelled out. Since 5.5 does not equal -4.5, the equation has no solutions.
Explanation:
To solve the equation 5.5 - x = -4.5 - x, we can first try to simplify it by adding or subtracting the same value from both sides. This method is based on the principle that whatever you do to one side of the equation, you must do to the other to maintain balance.
In this case, if we add x to both sides of the equation, the x terms will cancel out on both sides, which leaves us with 5.5 = -4.5. Here, we notice that both sides of the equation represent constant values and no longer contain the variable x.
Therefore, since 5.5 and -4.5 are not equal, we can conclude that there is no value of x that can satisfy this equation. This equation is a contradiction, which means there are no solutions.
You purchased 8 pounds 10 ounces of candy from a candy shop. You want to split it equally among 3 classrooms at a local school./7425116/3d9f02b9?utm_source=registration
Jordan is playing a video game. For every 35 stars she collects, she gets 4,000 points. Her record is 86,000 points. Which of the following proportions could she use to determine x, the number of stars she needs to tie her record?
A polygon has an area of 144 square inches and one of its sides is 10 inches long. If a second similar polygon has an area of 64 square inches, what is the length of the corresponding side in the second polygon?
Steven bagged 52 pounds of potatoes. About what is that measure in kilograms? Round to the nearest hundredth
write a trinomial expression equivalent to (2x+5)(3x-2)
The required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
According to the question, we have to determine the trinomial expression that is equivalent to the (2x+5)(3x-2).
A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax+b is a polynomial.
Here,
Given expression in the question,
= (2x+5)(3x-2)
Following the distributive property
= 2x (3x - 2) + 5 (3x - 2)
= 6x² - 4x + 15x - 10
= 6x² - 11x - 10
Thus, the required trinomial expression that is equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
Learn more about polynomial function here:
https://brainly.com/question/12976257
#SPJ2
Final answer:
The trinomial expression equivalent to (2x+5)(3x-2) is calculated using the FOIL method, resulting in 6x² + 11x - 10.
Explanation:
To write a trinomial expression equivalent to the product of two binomials, (2x+5)(3x-2), we perform the multiplication by using the distributive property (also known as the FOIL method).
Multiply the first terms: 2x × 3x = 6x²
Multiply the outside terms: 2x × (-2) = -4x
Multiply the inside terms: 5 × 3x = 15x
Multiply the last terms: 5 × (-2) = -10
Combine like terms:
6x² + (15x - 4x) - 10 = 6x² + 11x - 10
The trinomial expression equivalent to (2x+5)(3x-2) is 6x² + 11x - 10.
Solve for y: 10y + 3.8 = 38.8
The solution for ( y ) is ( y = 3.5 ).
To solve for y in the equation [tex]\( 10y + 3.8 = 38.8 \)[/tex], follow these steps:
Start with the given equation:
[tex]\[ 10y + 3.8 = 38.8 \][/tex]
Subtract 3.8 from both sides to isolate the term with y:
[tex]\[ 10y + 3.8 - 3.8 = 38.8 - 3.8 \][/tex]
[tex]\[ 10y = 35 \][/tex]
Divide both sides by 10 to solve for y :
[tex]\[ \frac{10y}{10} = \frac{35}{10} \][/tex]
y = 3.5
So, the solution for ( y ) is ( y = 3.5 ).
If point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9), what is the distance from a to b if the units of the coordinated system are meters?
The distance from a to b if the units of the coordinated system are meters is 10m.
What is a line segment?A line that has two endpoints and a fixed measurement is called a line segment.
It is given that point a is located at coordinates (5, 3) and point b is located at coordinates (-3, 9)
D = √[(x-p)² + (y-q)²]
Substituting the points we get;
D = √[(-3 - 5)² + (9 - 3)²]
D = √[(-8)² + (6)²]
D = √[(64) + (36)]
D = √100
D = 10
Hence, the distance from a to b if the units of the coordinated system are meters is 10 m.
To know more about the Line segment;
brainly.com/question/25727583
#SPJ5
Final answer:
The distance between point A (5, 3) and point B (-3, 9) is calculated using the distance formula, resulting in a distance of 10 meters.
Explanation:
The question is asking for the distance between two points in a coordinate system. To find the distance between point A (5, 3) and point B (-3, 9), we can use the distance formula which is derived from Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)² + (y2 - y1)²)
For point A and point B, we substitute the coordinates into the formula:
d = √((-3 - 5)² + (9 - 3)²)
= √(64 + 36)
= √100
= 10 meters
Therefore, the distance from A to B is 10 meters.
17,325 round to the nearest thousand
Rachel earned 34$, 34 in 4 hours at her job today
Witch set of orderd pairs contains only points that are on the graph of the function y=12-3x
A.(-3,-27),(0,0),(6,54)
B.(-18,10),(-6,6),(18,-2)
C(-5,27),(-1,15),(8,-12)
D(-7,-9),(-4,0)(2,18)
What can a doctor use to determine a patient's body fat percentage?
Bioelectrical impedance machine
MRI machine
Waist measurement
Weight measurement
Bioelectrical impedance machine can be used to determine a patient's body fat percentage
What is Fat percentage?The body fat percentage of a human or other living being is the total mass of fat divided by total body mass, multiplied by 100
A doctor can use a bioelectrical impedance machine to determine a patient's body fat percentage.
This machine works by sending a small electrical current through the body and measuring how quickly it travels through different types of tissue.
Since fat and muscle have different electrical conductivity, the machine can estimate the amount of fat in the body based on the resistance to the current.
Hence, Bioelectrical impedance machine can be used to determine a patient's body fat percentage
To learn more on Fat percentage click:
https://brainly.com/question/14457888
#SPJ2
Given right triangle def what is the value of sin e
Answer:
Step-by-step explanation:
From the given triangle DEF, we have
[tex](EF)^{2}=(ED)^{2}+(DF)^{2}[/tex]
[tex](10)^{2}=(8)^{2}+(DF)^{2}[/tex]
[tex]100-64=(DF)^2[/tex]
[tex]DF=6[/tex]
Now, we know that SinE=[tex]\frac{Perpendicular}{Hypotenuse}[/tex], thus
[tex]SinE=\frac{DF}{EF}[/tex]
[tex]SinE=\frac{6}{10}=\frac{3}{5}[/tex]
Therefore, the value of SinE is [tex]\frac{3}{5}[/tex].
The sum of two binomials is 3z-6. If one binomial is z+4, what is the other binomial?
What the answer to this
The formula A=P(1+r)t is used to show the total amount owed for a loan with a simple annual interest rate.
Solve for r.
Answer: [tex]r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex]
Step-by-step explanation
Compound interest is the addition of interest to the principal sum of a deposit or a loan.
Let P = principal amount which was taken as a loan then the accumulated amount A is given by
[tex]A=P(1+r)^t[/tex].......(1)
where, r is the rate of simple annual interest in decimal.
t is the time applied for interest.
For solving r divide both sides of equation by P in (1),we get
[tex]\frac{A}{P}=(1+r)^t\\\Rightarrow(\frac{A}{P})^{\frac{1}{t}}=1+r\\\Rightarrow\ r=(\frac{A}{P})^{\frac{1}{t}}-1[/tex].