What is the area of a regular hexagon with a side of 5 and an apothem of 4.33
you have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friends to have the same balance?
The demand function for an auto parts manufacturing company is given by f(x) = 100000 - 2500x , where x represents price and f(x) represents quantity. f^-1 (x) = _______. In the inverse function, the variable X represents _____
Answer:
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
The variable X represents the quantity.
Step-by-step explanation:
We are given that
The demand function for an auto parts manufacturing company is fiven by
f(x)=100000-25 x
Where x=Represents price
f(x)= Represents quantity
We have to find inverse function [tex]f^{-1}(X)[/tex]
Let f(x)=X
[tex]X=100000-2500 x[/tex]
[tex]2500x=100000-X[/tex]
[tex]x=\frac{100000-X}{2500}[/tex]
Substituting the value of x then we get
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Therefore, the inverse function
[tex]f^{-1}(X)=\frac{100000-X}{2500}[/tex]
Where X= Represents the quantity
[tex]f^{-1}(X)[/tex]=Represents price
Explain why two similar right triangles will have the same cosine ratios.
You invest $3,756.00 and buy 100 shares of a company's stock. Their value increases by 12%. How much is each share worth?
Answer:
Each share worth is $42.0672 .
Step-by-step explanation:
As given
You invest $3,756.00 and buy 100 shares of a company's stock.
Their value increases by 12%.
12% is written in the decimal form
[tex]= \frac{12}{100}[/tex]
= 0.12
Share value increase = 0.12 × Investment cost
= 0.12 × 3756
= $450.72
Total value of shares becomes after increases of 12% = Share value increase + Investment cost .
Total value of shares becomes after increases of 12% = $3756+ $450.72
= $4206.72
[tex]Each\ shares\ worth = \frac{Total\ value\ of\ shares\ after\ increase\ of\ 12\%}{Number\ of\ shares}[/tex]
[tex]Each\ shares\ worth = \frac{4206.72}{100}[/tex]
Each shares worth = $42.0672
Therefore the each share worth is $42.0672 .
A line passes through (−2, 5) and has slope 13 . What is an equation of the line in point-slope form
SOMEONE PLEASE HELP!!!!
Which area formula or formulas show(s) a joint variation?
I A=s^2
II A=pir^2
III A=l*w
Select one:
a. III only
b. II and III
c. II only
d. I, II, and III
Answer:
Step-by-step explanation:
Evaluate p(7,5) can someone help
Find the area of a regular hexagon with a 48-inch perimeter.
48√3 in2
96√3 in2
192√3 in2
in2 means inches squared
twice a number added to 4 is 28
John's Coffee Shop makes a blend that is a mixture of two types of coffee. Type A coffee costs John $4.70 per pound, and type B coffee costs $5.90 per pound. This month, John made 181 pounds of the blend, for a total cost of $967.10 . How many pounds of type A coffee did he use?
A +B = 181
A=181-B
4.70A+5.90B= 967.10
4.70(181-B) +5.90B =967.10
850.70-4.70B+5.90B=967.10
850.70+1.2B =967.10
1.2B=116.40
B =116.40/1.2 = 97
A=181-97 = 84 pounds of type A coffee
The diagram below shows equilateral triangle ABC sharing a side with square ACDE. The square has side lengths of 4. What is BE? Justify your answer.
BE is [tex]7.73[/tex]
What is Square?
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
What is equilateral triangle?
In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
According to question, The diagram below shows equilateral triangle ABC sharing a side with square ACDE.
We have to find BE.
Now, AB [tex]= 4[/tex] and AE [tex]= 4.[/tex]
The angle EAB is [tex]90+60 = 150[/tex]°
Using the law of the cosines, we get
[tex]BE^2 = AE^2 + AB^2 - 2(AB)(AE)cos(150)[/tex]
[tex]=4^2 + 4^2 -[/tex][tex]2(4)(4)[/tex]×[tex]\frac{\sqrt{3} }{2}[/tex]
⇒[tex]BE=7.73[/tex]
Hence, we can conclude that BE is [tex]7.73[/tex]
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which angles are corresponding angles? check all that aply
The circle shown below has ab and bc as its tangents: ab and bc are two tangents to a circle which intersect outside the circle at a point
b. if the measure of arc ac is 160°, what is the measure of angle abc? 80° 40° 60° 20°
Answer:
Answer: 20°
Step-by-step explanation:
I need help with this problem and a few others
The data set shows the ages of the members of a book club. What is the shape of the distribution of this data set?
19, 21, 18, 19, 16, 21, 20, 17, 16, 17, 20, 18.
Answers: symmetrical, uniform, skewed to the left, skewed to the right.
which of the following could be the equation of the graph shown below
Answer:
-4x+2y+-6 and y=3x-2
What is the average rate of change from x = 2 to x = 3?
2
3
0
5
Answer:
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
Step-by-step explanation:
The average rate of a function f(x) on the interval [a,b] is defined as
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
The average rate of change from x = 2 to x = 3 is
[tex]m=\frac{f(3)-f(2)}{3-2}[/tex] .... (1)
From the given graph it is clear that the value of the function is -3 at x=2 and -1 at x=3. It means f(2)=-3 and f(3)=-1.
Put f(2)=-3 and f(3)=-1 in equation (1).
[tex]m=\frac{-1-(-3)}{3-2}[/tex]
[tex]m=\frac{-1+3}{1}[/tex]
[tex]m=\frac{2}{1}[/tex]
[tex]m=2[/tex]
The average rate of change from x = 2 to x = 3 is 2. Therefore first option is correct.
What is the solution to the following system?
3x+2y+z=20
x-4y-z=-10
2x+y+2z=15
A. (2, 3, 4)
B. (4, 3, –2)
C. (4, 3, 2)
D. (6, 7, –2)
Answer:
C. (4, 3, 2)
Step-by-step explanation:
Given : [tex]3x+2y+z=20[/tex]
[tex]x-4y-z=-10[/tex]
[tex]2x+y+2z=15[/tex]
To Find: Solution:
[tex]3x+2y+z=20[/tex] -1
[tex]x-4y-z=-10[/tex] --2
[tex]2x+y+2z=15[/tex] --3
Substitute the value of z from 1 in 2 and 3
So in 2 , [tex]x-4y-(20-3x-2y)=-10[/tex]
[tex]x-4y-20+3x+2y=-10[/tex]
[tex]4x-2y=-10+20[/tex]
[tex]4x-2y=10[/tex] ---4
So, in 3 , [tex]2x+y+2(20-3x-2y)=15[/tex]
[tex]2x+y+40-6x-4y=15[/tex]
[tex]-4x-3y=15-40[/tex]
[tex]-4x-3y=-25[/tex] -5
Now solve 4 and 5
Substitute the value of x from 4 in 5
[tex]-4(\frac{10+2y}{4})-3y=-25[/tex]
[tex]-1(10+2y)-3y=-25[/tex]
[tex]-10-2y-3y=-25[/tex]
[tex]-10-5y=-25[/tex]
[tex]-5y=-15[/tex]
[tex]y=3[/tex]
Now substitute the value of y in 4
[tex]4x-2(3)=10[/tex]
[tex]4x-6=10[/tex]
[tex]4x=10+6[/tex]
[tex]4x=16[/tex]
[tex]x=4[/tex]
Now substitute the value of x and y in 1 to get value of z
[tex]3(4)+2(3)+z=20[/tex]
[tex]12+6+z=20[/tex]
[tex]18+z=20[/tex]
[tex]z=20-18[/tex]
[tex]z=2[/tex]
Thus The solution is (4,3,2)
Hence Option c is correct.
What is 8q+3(10q^2+2)+8
What are the solutions of the equation z2-12z+36=0
What is the solution set of the following equation? -5x + x + 9 = -4x + 12
How old is molly if she was 52 years old when she was fourteen years ago?
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
For a 30-60-90 triangle with a hypotenuse of length x, the perimeter would be defined by the formula x(3 + √3)/2.
Explanation:In terms of mathematics, the question discusses a right triangle, specifically a 30-60-90 triangle. When it comes to a 30-60-90 triangle, certain ratios of sides exist. In this triangle, the ratio of the lengths of the sides opposite the 30°, 60° and 90° angles are 1:√3:2. Given that the length of the hypotenuse is x, the sides opposite the 30° and 60° angles would be x/2 and x√3/2, respectively. So, the perimeter of the triangle could be determined by adding up the lengths of all three sides i.e., x + x/2 + x√3/2. The simplified form of this equation indicates that the
perimeter
of the triangle = x(1 + 1/2 + √3/2), which can also be written as x(3 + √3)/2.
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help factoring trinomial
need 2 numbers when added = 5 and when multiplied = -24
answer is D
-3+8 = 5
-3*8 = -24
Find the probability that 4 randomly selected people all have the same birthday. Ignore leap years. Round to eight decimal places.
The probability that 4 randomly selected people all have the same birthday, ignoring leap years, is 0.00000002 when rounded to eight decimal places.
Explanation:The problem is asking about the probability that 4 people, selected at random, all have the same birthday. Since we're ignoring leap years, each person can have a birthday on any of 365 days of the year. The probability that the first person has a birthday on any day of the year is 1, because there's no restriction on when their birthday can be. However, the probability that the second, third, and fourth people share this same birthday becomes much less.
Given that we've selected a specific day for the first person, the second person has a 1 in 365 chance (or approximately a 0.00274 chance) of having that same birthday. The same applies for the third and fourth person. Since each of these events is independent (meaning the outcome of the first event doesn't change the probability of the next event), we can find the total probability by multiplying the individual probabilities together: 1 (for the first person) * 0.00274 (for the second person) * 0.00274 (for the third person) * 0.00274 (for the fourth person) = 0.000000020500. To the eight decimal place, this becomes 0.00000002.
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The area of a rectangular lot that is 50 feet wide by 100 feet deep is:
The area of a rectangle can be directly calculated using the formula:
A = l * w
Where l is the length or the depth while w is the width
Therefore,
A = 50 feet * 100 feet
A = 5000 square feet
A delivery truck uses $375 in gasoline during a 3 week period. if the truck is driven 5 days per week, how much is spent on gas each day?
Final answer:
Approximately $17.86 is spent on gas each day.
Explanation:
To find out how much is spent on gas each day, we need to divide the total amount spent on gas by the number of days in the 3-week period.
First, let's calculate the number of days in 3 weeks. Since there are 7 days in a week, there are 3 × 7 = 21 days in 3 weeks.
Next, we divide the total amount spent on gas, $375, by the number of days: $375 ÷ 21 = $17.86
Therefore, approximately $17.86 is spent on gas each day.
Relations and functions need help please.
87 less than the quotient of an unknown number and 43 is -75.
What is the value of the unknown number?