Answer: 13
Step-by-step explanation:
Given : The equation [tex]d=\dfrac{1}{2}n(n-3)[/tex] gives the number of diagonals d for polygon with n sides.
To find the number of sides n for a polygon that has 65 diagonals, we substitute the value of d= 65 in the given equation, we get
[tex]65=\dfrac{1}{2}n(n-3)[/tex]
Multiply 2 on both sides , we get
[tex]n(n-3)=130\\\\\Rightarrow\ n^2-3n-130=0\\\\\Rightarrow\ n^2-13n+10n-130=0\\\\\Rightarrow\ n(n-13)+10(n-13)=0\\\\\Rightarrow\ (n-13)(n+10)=0\\\\\Rightarrow\ n= -10\ or\ n= 13[/tex]
But number of sides cannot be negative, so the number of sides n for a polygon that has 65 diagonals = 13
Which has smallest value 0.79 or 0.425
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.
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.
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:
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.
Can someone help me with this question, please?
Find the shaded area of the basketball court to the nearest foot.
5:36, 2:9, 3:18 , 1:3 which ratio is the largest?
6 + 12 ÷ 3 – 2 × 2 =
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]
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.
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
The front wall of your shed is in the shape of a trapezoid. The bottom measures 22 feet, the top measures 20 feet, and the height is 10 feet. Calculate the area of the front wall of your shed.
Answer:
the answer on edge is D. 66^2
Step-by-step explanation:
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,
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what percent of 28 is 21
Hey can you please help me posted picture of question
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 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.
PLEASE HELP ME ILL GIVE U A BRAINLIST a man who is 6 feet tall cats a shadow that is 15 feet long.A tree casts a similar shadow is 22 FT how tall is the tree?
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
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HELP ASAP How do I find the answer to this
Given that KJ = MN and that L is the midpoint of JN, prove JKL = NML.
20 points Easy question
what is 5/20 simplify
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
The circumference of a circle is 28 pi inches. What is the length of the radius of this circle?
Answer:
The length of the radius of this circle is 14 inches.
Step-by-step explanation:
Circumference of the circle = [tex]28\pi[/tex]
Let's take the length of the radius of the circle as [tex]a[/tex]
Circumference of a circle = [tex]2\pi r[/tex]
Where,
r is the radius of the circle.
Therefore,
[tex]2\pi a=28\pi[/tex]
[tex]2a=28[/tex]
[tex]a=14[/tex]
Therefore, the length of the radius of this circle is 14 inches.
the length of johns patio is 5 feet less than 3 times the length of howards patio .johns patio has a length of 40 feet . what is the length of howards patio
Easy 20 points!
Which expression finds the length of side y in this right triangle?
The Last one is your answer
Answer:
The last one i did this before
Step-by-step explanation:
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
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.
find the slope of the line. -7 , - 1/7, 7, 7/1