To express the number of miles driven, y, in terms of the number of hours driven, t, we first find the speed and then use it to formulate the equation of the line as y = 60t. However, to accurately represent the entire trip, we must include the initial 100 miles driven in 2 hours, leading to y = 60t - 20 as the final equation.
To write an equation that gives the number of miles driven, y, in terms of the number of hours driven, t, we can use the relationship between distance and travel time. Given that after two hours you had gone 100 miles and after 8 hours, you reached your destination, which is 460 miles away, we establish two points on our distance-time graph: (2, 100) and (8, 460).
Using the two points, we can find the slope of the line, which represents the speed:
Slope (speed) = (change in distance) / (change in time) = (460 - 100) miles / (8 - 2) hours = 360 miles / 6 hours = 60 miles/hour.
We can now express the equation of the line as y = mx + b, where m is the slope and b is the y-intercept. The y-intercept represents the distance at time zero, which for most driving scenarios we assume to be 0 miles. Thus, the equation becomes y = 60t. However, this equation would not accurately represent the entire trip since it doesn't account for the initial 100 miles driven in the first 2 hours.
To adjust for that, we'll introduce an offset for the initial 100 miles traveled in the first 2 hours. The y-intercept would be 100 miles less than if we had started from 0 miles at 0 hours. The corrected equation for the entire trip would be of the form y = 60t + b, where b = y - 60t and y are the miles covered in the initial 2 hours, which is 100 miles. Substituting the values, we get b = 100 - 60 x 2 which equals -20.
The final equation, accounting for the first 2 hours of travel, would therefore be: y = 60t - 20.
Scott bought three bags of candy with 75 pieces in each one. He plans to divide all the candy evenly among seven friends. How many pieces of candy will Scott have left for himself?
Answer:
The answer is only one piece of candy
Step-by-step explanation:
Firstly, we have to determine the total amount of pieces of candy:
There are three bags with 75 pieces in each one, so the total is:
[tex]75+75+75=225[/tex]
Then, in order to determine the amount of pieces of candy for every friend,
we have to divide the total amount by 7, where the remainder of the division is the answer.
[tex]\frac{225}{7}=32*7+1[/tex]
Remainder=1
Finally, every friend of Scott receive 32 pieces of candy evenly and Scott is left with only one piece of candy.
What is the remainder obtained by dividing x7 x5 1 by the generator polynomial x3 1?
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
Given:
The generator polynomial is [tex]{x^3} + 1.[/tex]
The polynomial is [tex]{x^7} + {x^5} + 1[/tex]
Explanation:
There are two methods of dividing the two polynomials.
(1). Synthetic division
(2). Long division method
The fraction can be expressed as,
[tex]{\text{Fraction}}= \dfrac{{{x^7} + {x^5} + 1}}{{{x^3} + 1}}[/tex]
The denominator of the fraction is [tex]{x^3} + 1[/tex] and the numerator of the fraction is [tex]{x^7} + {x^5} + 1.[/tex]
Divide [tex]{x^7} + {x^5} + 1[/tex] by [tex]{x^3} + 1[/tex] to obtain the remainder and the quotient of the polynomial.
The remainder obtained by dividing on [tex]{x^7} + {x^5} + 1[/tex] the generator polynomial [tex]{x^3} + 1[/tex] is [tex]\boxed{{-x^2} + {x} +1}[/tex]
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Long division method
Keywords: division, binomial synthetic division, long division method, coefficients, quotients, remainders, numerator, denominator, polynomial, zeros, degree, cubic polynomial, quadratic equation.
Final answer:
To find the remainder of the polynomial division of x^7 + x^5 + 1 by x^3 + 1, one would perform polynomial long division or synthetic division, continuing until the degree of the remainder is less than the divisor.
Explanation:
The student is asking how to find the remainder of a polynomial division. Specifically, they want to know the remainder when dividing x^7 + x^5 + 1 by the polynomial x^3 + 1. To solve this, one would typically use long division of polynomials or synthetic division. The process is similar to long division with numbers. We would start by looking at the highest degree terms of both polynomials and divide them, then multiply the divisor by the result and subtract from the dividend. Repeat this process until the degree of the remainder is less than the degree of the divisor. Since finding the remainder requires us to consider terms up to x^2, we are essentially looking for the result of division that does not perfectly divide, similar to how 7 divided by 3 leaves a remainder.
( 10x-20) (6x + 8) what is the value of x
The solution is, the value of x is 7.
What is simplification?Simplify simply means to make it simple. In mathematics, simply or simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.
here, we have,
given that,
(10x-20)=(6x+8)
We simplify the equation to the form, which is simple to understand
(10x-20)=(6x+8)
Remove unnecessary parentheses
10x-20=(6x+8)
Remove unnecessary parentheses
10x-20=6x+8
We move all terms containing x to the left and all other terms to the right.
+10x-6x=+8+20
We simplify left and right side of the equation.
+4x=+28
We divide both sides of the equation by 4 to get x.
x=7
Hence, The solution is, the value of x is 7.
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A machine laying underground cable can place 125 meters of cable in 5 minutes
The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.
To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.
We calculate the rate as follows:
Divide the total length of cable by the total time: 125 meters / 5 minutes = 25 meters per minute.This means the machine lays cable at a rate of 25 meters per minute.
Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?
A pizza parlor has 8 different toppings and 3 different cheeses to choose from on the menu. How many pizza combinations are possible if each pizza has 1 topping and 1 cheese
Final answer:
To find the number of pizza combinations available using 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, one multiplies the number of topping choices by the number of cheese choices, giving 8 x 3 = 24 possible combinations.
Explanation:
Calculating Pizza Combinations
When calculating the number of possible pizza combinations with 1 topping and 1 cheese from 8 different toppings and 3 different cheeses, we use basic counting principles. Each pizza can be thought of as a combination of one topping and one cheese. Since these choices are independent, we multiply the number of options for toppings by the number of options for cheeses to find the total combination possibilities. This results in 8 toppings multiplied by 3 cheeses, giving 24 possible combinations.
The formula used is straightforward: Number of combinations = Number of toppings × Number of cheeses.
Pizza Combination Calculation Example
For instance, if you were at a pizza parlor where you could choose from pepperoni, mushrooms, onions, and 5 other toppings, along with mozzarella, cheddar, and one other cheese, you could create 24 unique pizzas. Just pick one topping and one cheese, and that's your combination.
If $850 is deducted each month for 12 months from your checking account to pay your mortgage, what impact will it have on your checking account balance?
A) $10,200
B) $850
C) -$10,200
D) -$850
Graph the line for y+1=−35(x−4) on the coordinate plane.
Just write what the coordinates would be
Answer:
(0, 139) and (139/35, 0)
Step-by-step explanation:
To graph a line, two points are needed. Taking x = 0 and replacing this value in the equation, we get:
y+1=−35(0−4)
y = 140 - 1
y = 139
Then, the point (0, 139) is on the line.
Taking y = 0 and replacing this value in the equation, we get:
0+1=−35(x−4)
1/(-35) = x -4
1/(-35) + 4 = x
139/35 = x
3.971 = x
Then, the point (139/35, 0) is on the line.
Which fraction is equivalent to 4 over negative 9?
A.) -4 over 9
B) 4 over 9
C) -4 over -9
D) 9 over 4
Answer:
A) -4 over 9
Step-by-step explanation:
We have the fraction [tex]\frac{4}{-9}[/tex] the equivalent of this fraction is [tex]\frac{-4}{9}[/tex]
[tex]\frac{4}{-9}= \frac{-4}{9} =-\frac{4}{9}[/tex]
Both fractions are the same and equivalent, the negative sign makes the whole fraction negative regardless of whether it is in the numerator or denominator.
Ms. Winter makes homemade bath soaps and bottles of lotion. In her inventory, she had 48 bath soaps and 64 bottles of lotion. She wants to use all of her inventory to make as many gift baskets as she can use using the same number of bath soaps and the same number of lotion bottles in each gift basket. She will be able to make at most ? gift baskets. Each basket will contain ? bath soaps and ? bottles of lotion.
When all seats are filled, a Ferris wheel can take 72 people for a rude. There are 313 people waiting to ride the wheel. Which drawing represents the number of rides with all the seats filled. Is the answer B?
Find the maximum and minimum values of f(x,y,z)=3x+3y+3zf(x,y,z)=3x+3y+3z on the sphere x2+y2+z2=1x2+y2+z2=1.
Sue traveled 96 miles in 12 hours. A unit rate to describe Sue's travel is 8 miles per hour. What is another unit rate in this situation? (1 point) 1/8 mile per hour, 1/8 hour per mile, 1 mile per hour, 8 hours per mile
Answer:
I believe the answer is 1/8 hour per mile
Step-by-step:
I don't know. I just believe that that is the most reasonable answer to this question and I have this question as well, it might seem hard it's really not.
Polygon ABCDE rotates 52º about the origin to create polygon A′B′C′D′E′. If measure of angle BCD equal 31 º , what is the measure of angle B'C'D' ?
sorry cant give answers not a multiple choice question
Answer:
Answer is 31,
Step-by-step explanation:
PLATO Confirmed
Choose the constant term that completes the perfect square trinomial x 2 - 18x
The correct answer should be +18
will the standard form 3.2 x 10 -4 be more or less than 1 Explain what effect the negative exponent has
Please help me!
A pair of shoes is on sale for $29.95. What will the sales tax on the shoes be if the sales tax rate is
7 1/2%?
$1.99
$2.10
$2.25
$2.99
Option C)The sales tax will be $2.25.
Convert the sales tax rate from a percentage to a decimal,
7.5% becomes 0.075.
Multiply the decimal by the total cost of the shoes,
0.075 × 29.95
= 2.24625.
$2.25.
Therefore, the sales tax on the shoes will be $2.25,Option C
Lulu buys a dress for $67, a hat for $35, and shoes for $49. How much did Lulu spend?
If y =18 and x=60 what is the constant of proportionality
Final answer:
The constant of proportionality when y = 18 and x = 60 is calculated by dividing y by x, which results in a constant of 0.3.
Explanation:
To find the constant of proportionality when y = 18 and x = 60, we must assume that the relationship between y and x is directly proportional. This means that as x increases, y increases at a constant rate, and vice versa. If the relationship is directly proportional, we can write y = kx, where k is the constant of proportionality.
To calculate k, we simply divide y by x. So we have:
k = y / x
k = 18 / 60
k = 0.3
Therefore, the constant of proportionality is 0.3.
Find the solution of the differential equation 3e^(3x)dy/dx=â9x/y^2
To solve the given differential equation, variables need to be separated, followed by integration of both sides. Since the equation involves both exponential and inverse square terms, separation of variables and integration are key steps. A specific solution also requires substituting a given function of y into the found general solution to determine any integration constants.
Explanation:The question involves solving a differential equation 3e^(3x)dy/dx = -9x/y^2. First, we need to recognize this as a separable differential equation, which can be solved by isolating all terms involving y on one side and all terms involving x on the other side. After separation, we integrate both sides with respect to their respective variables.
Step 1: Separate the variables. We get dy/y^2 = -3x e^(-3x) dx.
Step 2: Integrate both sides. The integration of dy/y^2 with respect to y is -1/y, and the integration of -3x e^(-3x) with respect to x requires integration by parts or a table of integrals.
Step 3: Upon integration, we would find an implicit solution involving y and x, combined with an integration constant that needs to be determined based on initial conditions or additional information. Since specific initial conditions are not provided in the initial question, we'd include a constant C in our final expression.
For a specific solution when y(x) = cos(3x), additional steps are required to substitute this y expression into our general solution and solve for the constant.
Sam gets $1000 dollars per month. She has to spend $20 a day on transportation, she also needs to buy groceries each week and have $30 extra spending money per week. How much money should be spent on food per day?
How many radians are contained in a central angle that is 2/3 of a circle?
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The central angle that is 2/3 of a circle will be given as,
⇒ 2π × (2 / 3)
Simplify the expression, then we have
⇒ 2π × (2 / 3)
⇒ 4π / 3 radian
The radians that are contained in a central angle that is 2/3 of a circle will be 4π / 3 radians.
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Solve this quadratic equation using the quadratic formula. 5 - 10x - 3x2 = 0
Answer:
Since, by the quadratic formula,
The solution of a quadratic equation [tex]ax^2+bx+c=0[/tex] is,
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Here, the given quadratic equation,
[tex]5-10x-3x^2=0[/tex]
[tex]-3x^2-10x+5=0[/tex]
By the above formula,
[tex]x=\frac{-(-10)\pm \sqrt{(-10)^2-4\times -3\times 5}}{2\times -3}[/tex]
[tex]=\frac{10\pm \sqrt{100+60}}{-6}[/tex]
[tex]=\frac{10\pm \sqrt{160}}{-6}[/tex]
[tex]=\frac{5\pm 2\sqrt{10}}{-3}[/tex]
[tex]\implies x=-\frac{5+2\sqrt{10}}{3}\text{ or }x=-\frac{5-2\sqrt{10}}{3}[/tex]
You purchased xyz common shares for $45 per share one year ago. one year later aftering receiving $4 dividend per share, you sold your stock at $48 per share. what is your total return for the one year period?
a. 14.58%
b. 8.89%
c. 15.56%
d. 6.67%
A restaurent sold 350 less hotdogs than hamburgers. Altogether, the restaurant sold 700 hotdogs and hamburgers. How many of each did they sell?
A computer can sort x objects in t seconds, as modeled by the function below: t=0.007x^2+0.003x. How long, in seconds, will it take the computer to sort 15 objects? Round your answer to the nearest hundredth of a second.
As modeled by the function below: t=0.007x^2+0.003x. The time it will take the computer to sort 15 objects is 1.62sec
What is Time?
Time is the ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future.
Given:
t = 0.007x^2+0.003x
x = 15
Substituting the value in the equation we get,
t = 0.007(15)^2+0.003(15)
t = 0.007(225) + 0.045
t = 1.575 + 0.045
t = 1.62sec
Hence, It will take 1.65sec to sort 15 objects
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Which of the following is an example of a proper fraction?
A. 7⁄6
B. 4⁄3
C. 3⁄4
D. 4⁄4
0/1 points | previous answers devorestat9 4.e.041. ask your teacher my notes question part points submissions used the automatic opening device of a military cargo parachute has been designed to open when the parachute is 200 m above the ground. suppose opening altitude actually has a normal distribution with mean value 200 and standard deviation 31 m. equipment damage will occur if the parachute opens at an altitude of less than 100 m. what is the probability that there is equipment damage to the payload of at least one of five independently dropped parachutes? (round your answer to four decimal places.)
Each box holds 10 cartons of milk.there are 300 cartons of milk.how many boxes are there?
determine whether each equation is a linear equation. write yes or no. if yes, write the equation in standard form. if the answer is no, circle the part that makes it no
1. y = 4 - 2x
The given equation y = 4 - 2x is a linear equation, however, it is not in standard form. The standard form is 2x + y = 4.
Explanation:The equation y = 4 - 2x is indeed a linear equation. A linear equation is an equation that represents a straight line when graphed. It generally has the form 'y = mx + b' where 'm' represents the slope of the line, and 'b' represents the y-intercept. Here, 'm' is -2 and 'b' is 4.
However, it is not currently in standard form. The standard form of a linear equation is 'Ax + By = C', where A, B, and C are integers, and A and B are not both zero. To write the equation in standard form, we can re-arrange it as 2x + y = 4.
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Jackson earned $60 and put 1 5 of those earnings into his savings account. How much did he put into his savings account?
Answer:
12
Step-by-step explanation:
=1x60
5x1
=60
5
12