Can someone help me with this question, please?
Yoshi is riding a bike-a-thon to raise money for his favorite charity The total distance of the bike-a-thon is 28.5 miles So far he has completed 1/10 of the bike-a-thon How many miles has Yoshi biked
Which expression is equivalent to 10x^6y^12/-5x^-2y^-6 ? Assume . –50x8y18 –2x8y18 –2x12y72 5x8y18
Answer:
Option B is correct, i.e. -2 x^8 y^18.
Step-by-step explanation:
To find the equivalent expression to (10)(x^6)(y^12) / (-5)(x^-2)(y^-6)
Step 1: simplify numerical terms
(10) / (-5) = -2
Step 2: simplify exponents of x-terms
(x^6) / (x^-2) = (x^6) * (x^2) = x^(6+2) = x^8
Step 3: simplify exponents of y-terms
(y^12) / (y^-6) = (y^12) * (y^6) = y^(12+6) = y^18
It means (10)(x^6)(y^12) / (-5)(x^-2)(y^-6) = -2 x^8 y^18
Hence, option B is correct, i.e. -2 x^8 y^18.
corey has 42 feet of fencing around his garden. The garden is rectangular in shape, and its length is equal to twice the width minus 3 feet. Define the variables, and write a system of equations to find the length and width of the garden
The variables as length are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
Area of rectangle = length × width.
As per the given total fencing = 42 feet
Let's say the length is L and the width is W.
As per the given,
L = 2W - 3
Perimeter = 2(length + width)
42 = 2(L + W)
21 = 2W - 3 + W
21 + 3 = 3W
W = 8 feet
And, L = 2(8) - 3 = 13 feet
Hence "The variables as lengths are L and width is W and the system of equations is L = 2W - 3 and 42 = 2(L + W) and the length and width are 13 feet and 8 feet respectively".
For more about rectangles,
https://brainly.com/question/15019502
#SPJ2
Which of the following functions has the largest value when x = 3? c(x) = 3x2 + 5x + 22 j(x) = 12x a(x) = 9x
To determine the function which has the largest value at x=3,
We will calculate the value of each function by substituting the value of x=3 in each of the given function.
Let us consider the first function,
[tex] c(x)=3x^{2}+5x+22 [/tex]
[tex] c(3)=3\times 3^{2}+5 \times 3+22 [/tex]
[tex] c(3)=27+15+22 [/tex]
[tex] c(3)=64 [/tex]
Let us consider the second function,
[tex] j(x)=12x [/tex]
[tex] j(x)=12 \times 3 =36 [/tex]
Let us consider the third function,
[tex] a(x)=9x [/tex]
[tex] a(x)=9 \times 3=27 [/tex]
Therefore, the function c(x) has the largest value at x=3.
The answer is 3
To determine which function has the largest value when x = 3, we need to substitute x with 3 into each function and calculate their values.
c(x) = 3x2 + 5x + 22 => c(3) = 3(3)2 + 5(3) + 22 = 27 + 15 + 22 = 64
j(x) = 12x => j(3) = 12(3) = 36
a(x) = 9x => a(3) = 9(3) = 27
The function c(x) has the largest value of 64 when x = 3.
Find the shaded area of the basketball court to the nearest foot.
Adam spent $3.42 on orange juice. It costs .12 per ounce. How many did Adam buy?
Adam bought 26.14 ounces of orange juice.
To solve the problem, we need to determine how many ounces of orange juice Adam bought with $3.42, given that the cost per ounce is $0.12. We can set up a simple proportion to find the answer.
First, we convert the cost of orange juice per ounce from a fraction to a decimal. The cost is $0.12 per ounce, which can also be written as [tex]$\frac{12}{100}$[/tex] dollars per ounce. Simplifying this fraction gives us [tex]$\frac{3}{25}$[/tex] dollars per ounce.
Next, we convert the total amount spent by Adam, $3.42, into a fraction. This is equivalent to [tex]$\frac{342}{100}$[/tex] dollars.
Now, we set up the equation to find the number of ounces (let's call it [tex]$x$[/tex]) that Adam bought:
[tex]\[ \frac{3}{25} \times x = \frac{342}{100} \][/tex]
To solve for [tex]$x$[/tex], we multiply both sides of the equation by the reciprocal of [tex]$\frac{3}{25}$[/tex], which is [tex]$\frac{25}{3}$[/tex]:
[tex]\[ x = \frac{342}{100} \times \frac{25}{3} \][/tex]
Multiplying the numerators and denominators separately, we get:
[tex]\[ x = \frac{342 \times 25}{100 \times 3} \][/tex]
Simplifying the right side of the equation by canceling out common factors (25 cancels with 100 to become 4, and 3 cancels with 342 to become 114), we have:
[tex]\[ x = \frac{114 \times 4}{4} \][/tex]
This simplifies to:
[tex]\[ x = 114 \][/tex]
However, we must remember that the original amount spent was $3.42, not $342. Therefore, we must divide our result by 100 to account for the cent conversion:
[tex]\[ x = \frac{114}{100} \][/tex]
[tex]\[ x = 1.14 \][/tex]
This result represents the number of ounces Adam bought in addition to the whole number of ounces he could buy with whole dollars. Since $3.00 would buy [tex]$\frac{3}{0.12}$[/tex] ounces, we need to add this to our 1.14 ounces to get the total:
[tex]\[ x_{total} = 1.14 + \frac{3}{\frac{12}{100}} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{3 \times 100}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + \frac{300}{12} \][/tex]
[tex]\[ x_{total} = 1.14 + 25 \][/tex]
[tex]\[ x_{total} = 26.14 \][/tex]
A 4-foot tall person standing with her back to the sun casts an 6-foot long shadow.
To the nearest degree, what angle does the sun make with the ground?
enter the ordered pair that is the solution to the system of equations graphed below please :]
Alice makes 8 bracelets. there are 4 red beads on each bracelets. witch number sentence shows the total number of beads used?
find the slope of the line. -7 , - 1/7, 7, 7/1
Given that KJ = MN and that L is the midpoint of JN, prove JKL = NML.
Hey can you please help me posted picture of question
Which has smallest value 0.79 or 0.425
Heather and Joel bought a house for $157,200 and know that the house appreciates every year. They keep track of their house value for 5 years and model their data with the exponential equation
The question relates to house appreciation and quality in mathematics. The house's value appreciates each year, an occurrence that Heather and Joel could monitor. House appreciation allows them to determine the annual interest rate and the value of their house after a particular period, and Ben and Freda's specifics help illustrate this situation.
Explanation:The question pertains to the concept of housing appreciation and equity in Mathematics. In this situation, Heather and Joel will observe that the value of their home increases annually due to appreciation. The value of their home after a certain period can be modeled using an exponential equation, taking the initial amount as the purchasing price, and the rate as the annual appreciation percentage.
For example, looking at Freda's situation, she bought a house for $150,000. Now, if she were to sell it, she would get $250,000. This increase in price from $150,000 to $250,000 would demonstrate the appreciation of her house over time. Similarly, Ben bought a house for $100,000 and borrowed the rest after a 20% down payment. As he pays the loan, his equity in the house increases and the house's increase in value also appreciates his equity.
Learn more about House Appreciation and Equity here:https://brainly.com/question/15073504
#SPJ12
A tank initially contains 40 ounces of salt mixed in 100 gallons of water. a solution containing 4 oz of salt per gallon is then pumped into the tank at a rate of 5 gal/min. the stirred mixture flows out of the tank at the same rate. how much salt is in the tank after 20 minutes ?
The amount of salt that is in the tank after 20 minutes is;
A(20) = 267.56 Oz
We are given;Initial amount of salt in tank; A(0) = 40 Ounces
A solution containing 4 oz salt per gallon is pumped into the tank at a rate of 5 gal/min.
This means rate in oz/min = 4/1 × 5/1 = 20 oz/min
Now, the rate at which the initial amount in the tank changes will be;A'(t) = 20 - [(A(t)/(100)) × 5/1]
A'(t) = 20 - A(t)/20
Rearranging gives;
A'(t) + A(t)/20 = 20
Since this is a linear equation, the integrating factor will be; [tex]e^{t/20}[/tex]Multiplying through by the integrating factor gives;
A'(t) [tex]e^{t/20}[/tex] + (A(t)/20) [tex]e^{t/20}[/tex] = 20[tex]e^{t/20}[/tex]
Thus, the solution will be;A(t) [tex]e^{t/20}[/tex] = 400[tex]e^{t/20}[/tex] + C
Divide through by [tex]e^{t/20}[/tex] to get;
A(t) = 400 + C [tex]e^{-t/20}[/tex]
At initial condition of A(0) = 40, we have;
40 = 400 + C
C = -360
Thus; at time (t), the amount of salt left is given by;
A(t) = 400 - 360 [tex]e^{-t/20}[/tex]
After 20 minutes;A(20) = 400 - 360 [tex]e^{-20/20}[/tex]
A(20) = 400 - 132.44
A(20) = 267.56 Oz
Read more at; https://brainly.com/question/17003995
How is the graph of y=^3√0.5x related to its parent function,y=^3√x ? A.It is horizontally stretched by a factor of 0.5 B. It is horizontally compressed by a factor of 0.5 C. It is translated left by 0.5 units D. It is translated right by 0.5 units
6 + 12 ÷ 3 – 2 × 2 =
***HELP***
Given that ABC ~ DEC, find the value of x. If necessary, round your answer to two decimal places.
find the least common multiple LCM of 10 and 5
Answer: I hope this is helpful
Step-by-step explanation:
10LCM of 5 and 10 is 10. LCM, also known as Least Common multiple or Lowest common multiple, is the smallest or the least positive integer that is divisible by the given set of numbers. In the given set of numbers 5 and 10, 10 is the least number that is divisible by both 5 and 10.
The average price of a gallon of milk at 5 supermarkets is $3.52. The prices at 4 of the supermarkets are $3.39, $3.82, $3.61, and $3.44, respectively. What is the price at the fifth supermarket?
Answer: B.)3.34
I did it on usatestprep
Step-by-step explanation:
Now that you have 3x=42, you need to isolate the variable so that you have an equation of the form "x= some number." what is the value of x (i.e., the amount you must pay)?
To solve the equation 3x = 42, divide both sides by 3, which results in x = 14. This means you would pay $14. The process is similar to isolating a variable in quadratic equations, where different methods may be employed.
Given the equation 3x = 42, we need to isolate the variable x to find its value. This is accomplished by dividing both sides of the equation by 3, which is the coefficient of x. Therefore, the equation becomes x = 42 / 3.
By performing this simple division, we find that x equals 14. So, if x represents the amount you must pay, then you would pay $14.
The process of isolating the variable is essential for solving not only simple equations but also more complex ones, such as quadratic equations which take the form ax² + bx + c = 0.
When dealing with quadratic equations, you can employ the quadratic formula or other methods like factoring or completing the square, depending on the nature of the coefficients and the terms present in the equation.
what percent of 28 is 21
What is the total surface area of the cone? 90π cm2 65π cm2 120π cm2 115π cm2
The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height. In this case, the correct answer is 115π cm².
Explanation:The total surface area of a cone can be found using the formula A = πr(r + l), where A is the total surface area, r is the radius of the base, and l is the slant height.
In this case, the correct answer is 115π cm². Let's calculate it:
Let's assume the radius of the cone is r.And let's assume the slant height of the cone is s.The total surface area of the cone is A = πr(r + s).We can substitute the given values into the formula: A = π(4)(4 + 7) = 115π cm².Therefore, the correct answer is 115π cm².
Mitch's father needs 1 1\2 tons of gravel.He bought 1,750 pounds of gravel.How many more pounds of gravel does he need
5:36, 2:9, 3:18 , 1:3 which ratio is the largest?
20 points Easy question
what is 5/20 simplify
Describe a reasonable sample space to model this experiment. (b) let n be the number of sample points that are inside the unit circle. find e(n). (c) use this to construct a random variable p with e(p) = π. this random variable will give your estimate of π.
ralph is a electrician he charges an initial fee of 24$ , plus 24 per hour. If ralph earned 144$ on the job , how long did the job take.
William made 1/2 gallon of lemonade to divide equally among 3 people. How much lemonade will each person?
a) 1/6 gallon
b)2/3 gallon
C) 1/5 gallon
d) 3/2 gallon