The inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
The given function is:
f(x) = 7x - 1
Make x the subject of the formula
[tex]f(x) = 7x - 1\\\\7x = f(x) + 1\\\\[/tex]
Divide through by 7
[tex]\frac{7x}{7}= \frac{f(x)}{7} + \frac{1}{7}\\\\x = \frac{f(x)}{7} + \frac{1}{7}[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and replace f(x) by x:
[tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
Therefore the inverse of the function f(x) = 7x - 1 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{1}{7}[/tex]
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Solve the simultaneous equations 2x+3y=13
4x-y=-2
The value of x and y are 0.5 and 4 respectively.
2x+3y=13 ..... i
4x-y=-2 ...... ii
Multiply equation i by 4
Multiply equation ii by 2
8x + 12y = 52 ..... iii
8x - 2y = -4 ...... iv
Subtract iv from iii
14y = 56
Divide both side by 14
14y/14 = 56/14
y = 4
Since 4x-y=-2
4x - 4 = -2
4x = -2 + 4.
4x = 2
x = 2/4 = 0.5
Therefore, x = 0.5 and y = 4
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A consumer group claims that the mean annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. A random sample of 120 people in the U.S. has a sample mean annual consumption of high fructose corn syrup of 49.5 pounds. Assume the population standard deviation is 3.6 pounds. evidence to support the group’s claim? 1). State the hypothesis: H0 : Ha : 2). Specify the level of significance 3). Sketch the sampling distribution 4). Calculate the test statistic At = 0.05, is there enough 5). Find the P-value and shade this in the distribution in (3): 6). Decision (using the P-value): 7). Write a statement to interpret the decision in the context of the original claim 2
your bakery is in a large shopping center. The entrie shopping center is 4,500 square feet. Your bakery takes up only 1/10 of that space.How many square feet is your bakery
The bakery takes up 1/10 of the total shopping center space. Since the shopping center is 4,500 square feet, the bakery is 450 square feet.
To determine the size of the bakery in square feet, we need to calculate 1/10th of the total shopping center's area. The shopping center is 4,500 square feet in total. So, the calculation would be:
Divide the total area by 10 to find 1/10 of the area.Multiply that number by 1 to get the exact area for the bakery.Here's the step-by-step calculation:
4,500 square feet / 10 = 450 square feetTherefore, the bakery takes up 450 square feet of space within the shopping center.
China's population is 1.446×10^9 . Marshall Islands's population is 6.025×10^4 . How many times larger is China's population than Marshall Islands's population? Drag and drop the values into the boxes to represent the answer in scientific notation.
China's population is 2.4 x 10^4 times larger than Marshall Islands's population.
How does scientific notations work?The number is written in the form [tex]a \times 10^b[/tex] where we have [tex]1 \leq a < 10[/tex]. The number b shows the order, which is the most important figure for which scientific notation is used. It tells us how much order large or small a value is in powers of 10. Scientific notations have some of the profits as; Better readability due to compact representation. Its value in terms of power of 10 is known, which helps in easy comparison of quantities differing by a large value.
We have given that
China's population = 1.446 × [tex]10^9[/tex]. Marshall Islands's population is 6.025× [tex]10^4[/tex]).
Then ;
(1.446 × [tex]10^9[/tex]) ÷ (6.025 × [tex]10^4[/tex])
= 0.24 x 10 power of 5
= 2.4 x [tex]10^4[/tex]
Therefore, China's population is 2.4 x 10^4 times larger than Marshall Islands's population.
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Help asap pleaaaaaaaaase
The base of a pyramid has n sides.
Write an EXPRESSION for the number of faces of the pyramid.
Answer: The expression for number of faces of a pyramid =1+n
Step-by-step explanation:
A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .
Its base describe the number of other faces of it.
For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....
So the total number of faces in a pyramid = base + lateral faces
If a pyramid has n sides therefore it give rise to n lateral faces such that
The total number of faces in a pyramid= 1+n .
The total number of faces of the pyramid is [tex]n+1[/tex].
A pyramid is a three-dimensional structure whose lateral sides converge to a single step at the summit, roughly forming a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any other polygon shape.
For a pyramid having triangular base then, the total number of faces will be [tex]3+1=4[/tex].
In a similar way, if a pyramid has four sides at the base then, the total number of faces will be [tex]4+1=5[/tex].
Hence, in the given question the pyramid has [tex]n[/tex] sides at the base so, the total number of faces of the pyramid is [tex](n+1)[/tex].
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how much water will it take to simmer 1 3/4 quarts of barley using a water to barley ratio of 4 to 1
Answer:
The water will be 4 times more as compared to the original.
Step-by-step explanation:
The temperature is changing every day by negative 7 over 18 degrees Fahrenheit. What will be the change in the temperature after 3 days? 21 over 6 degrees Fahrenheit negative 21 over 6 degrees Fahrenheit negative 7 over 6 degrees Fahrenheit 7 over 6 degrees Fahrenh
-7
6
taking teeeeesststt not sure id corryect
A money market fund advertises a simple interest rate of 88%. Find the total amount received on an investment of $4000 for 15 months.A money market fund advertises a simple interest rate of 88%. Find the total amount received on an investment of $4000 for 15 months. The total amount received on an investment of $4000 for 15 months is $ . (Do not round until the final answer. Then round to the nearest cent as needed.)
Sergei says that 10%10% of a number will always be less than 20%20% of any other number. Complete one inequality to support Sergei's claim and one to show that he is incorrect
Answer:
Step-by-step explanation:
The library is 0.96 mile away from Theo’s home. Write this distance as a fraction in simplest from.
evaluate each expression if y=2 Question 8y to the power of -4
What is 9 (3 x 4)??????
Find the average value of the function f(x) = 9 sin2(x) cos3(x) on the interval [−π, π].
The average value of f(x) = 9 sin²(x) cos³(x) over the interval [-π, π] is 0.
Explanation:Integrate and Divide: To find the average value of a function f(x) over an interval [a, b], we calculate the definite integral of f(x) over the interval and divide by the interval's width:
Average value = (1/(b-a)) * ∫a^b f(x) dx
In this case, a = -π and b = π, so b - a = 2π.
Integrate f(x): Unfortunately, integrating f(x) = 9 sin²(x) cos³(x) directly is quite complex. However, we can use the trigonometric identity sin²x = (1 - cos²x) to rewrite the function:
f(x) = 9 sin²(x) cos³(x) = 9 (1 - cos²x) cos³(x)
Integrating this form of f(x) is more manageable, although it still involves integration by parts due to the product of three terms.
Zero Integral: After integrating and simplifying, the definite integral of f(x) over [-π, π] evaluates to 0.
Average Value: Dividing the integral by the interval's width (2π) confirms the average value of f(x) on [-π, π] is 0:
Average value = (1/2π) * 0 = 0
Therefore, the average value of f(x) = 9 sin²(x) cos³(x) on the interval [-π, π] is 0, despite the function's non-zero values within the interval.
A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1800 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Number 26 on a b and c pls I need the answer
which regular polygon has a minimum rotation of 45 to carry the polygon onto itself
What is the nth term for 1 13 33 61 97 141
What is the solution to the proportion 6-10 = 9-x
Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply.
f(n) = –6.5n + 14.5f(n) = –1.5n + 9.5f(n) = 6.5n + 1.5f(1) = 8, f(n + 1) = f(n) – 6.5f(1) = 8, f(n + 1) = f(n) – 1.5f(1) = 8, f(n + 1) = f(n) + 6.5
Answer:
f(n)= -6.5n +14.5
f(1)= 8, f(n+1) = f(n) - 6.5
Step-by-step explanation:
the arithmetic sequence 8, 1.5, –5, –11.5 . . .
First term is 8
Now we find difference between the terms
1.5 - 8= -6.5
-5-1.5= -6.5
difference is -6.5
The formula is f(n)= a1 + (n-1)d
where a1 is the first term and d is the difference
f(n)= 8 + (n-1)(-6.5)
f(n)= 8 -6.5n+6.5
f(n)= -6.5n +14.5
To get recursive formula we use
f(n+1) = f(n)+ difference
f(1)= 8, f(n+1) = f(n) - 6.5
The functions that represent the arithmetic sequence is given by:
f(n) = –6.5n + 14.5
f(n+1) f(n) – 6.5, f(1) = 8
------------------
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the nth term is given by:
[tex]f(n) = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term.The sequence can also be represented by a recursive sequence, given by:
[tex]f(1) = a_1[/tex]
[tex]f(n+1) = f(n) - d[/tex]
In this sequence:
The first term is [tex]a_1 = -[/tex]The common difference is [tex]d = 1.5 - 8 = -6.5[/tex].Thus, the possible representations are:
[tex]f(n) = a_1 + (n-1)d[/tex]
[tex]f(n) = 8 - 6.5(n-1)[/tex]
[tex]f(n) = 8 - 6.5n + 6.5[/tex]
[tex]f(n) = -6.5n + 14.5[/tex]
And
[tex]f(1) = a_1[/tex]
[tex]f(n+1) = f(n) - d[/tex]
[tex]f(1) = 8[/tex]
[tex]f(n+1) = f(n) - 6.5[/tex]
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Assume ABC=DEF. if AB=18, BC=10, and AC=25, what is the length of DF?
The length of DF is equal to 25 units. Then the correct option is D.
What is a triangle?Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.
The two triangles ABC and DEF are congruent to each other and all the sides of one triangle will be the same as all the sides of the other triangle. The value of DF is equal to AC. AC is 25 so DF is equal to 25.
Hence, option D is correct.
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Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 − 4x − 2, x2 + y2 ≤ 16
The minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
[tex]f(x,y)=2x^2+3y^2-4x-2, g(x,y)=x^2+y^2-16.[/tex]
[tex]f_x (x,y)=4x+0-4-0=4(x-1)[/tex]
[tex]f_y (x,y)=0+6y-0-0=6y[/tex]
[tex]4(x-1)=0, x=1[/tex]
[tex]6y=0, y=0.[/tex]
So, critical points of [tex]f(x,y)[/tex] is [tex](1,0)[/tex].
Put this in [tex]g(x,y)=x^2+y^2-16[/tex].
[tex]g(1,0)=1^2+0^2-16=-15<0[/tex].
So, critical point is in the interior point of the given region.
[tex]g_x (x,y)=2x+0-0=2x[/tex]
[tex]g_y (x,y)=0+2y-0=2y[/tex]
Let there is a parameter [tex]\lambda[/tex] such that [tex]f_x = \lambda g_x[/tex] and [tex]f_y = \lambda g_y[/tex].
[tex]4(x-1)=\lambda (2x)[/tex] and [tex]6y=\lambda (2y)[/tex]
So, [tex]2(x-1)=x\lambda[/tex] and [tex]\lambda=3[/tex]
So, [tex]2(x-1)=3x[/tex]
So, [tex]-2=x[/tex]
Put [tex]x=-2[/tex] in [tex]x^2+y^2=16[/tex], to determine the value of [tex]y[/tex].
[tex](-2)^2+y^2=16[/tex]
[tex]y^2=12[/tex]
[tex]y=\pm 2\sqrt{3}[/tex]
So, the obtained possible extrema are [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
Now, find [tex]f(x,y)[/tex] at [tex](1,0), (-2, -2\sqrt{3}),[/tex] and [tex](-2, 2\sqrt{3})[/tex].
[tex]f(1,0)=2(1)^2+3(0)^2-4(1)-2[/tex]
[tex]=2-4-2[/tex]
[tex]=-4[/tex]
[tex]f(-2,-2\sqrt{3})=2(-2)^2+3(-2\sqrt{3})^2-4(-2)-2[/tex]
[tex]=8+36+8-2[/tex]
[tex]=50[/tex]
[tex]f(-2,2\sqrt{3})=2(-2)^2+3(2\sqrt{3})^2-4(-2)-2[/tex]
[tex]=8+36+8-2[/tex]
[tex]=50[/tex]
So, the minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
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What is the volume of the pyramid?
11*11*12 are the missing dimensions
A. 420 cm3 B. 139 cm3 C. 142 cm3 D. 484 cm2
Convert the decimal number 625 to binary using addition/subtraction method
The owners of a business must spend less than $140 on supplies. They have already spent $60. Now they want to buy chairs that cost $20 each. Let x represent the number of chairs they can buy. Select True or False for each statement.
They can buy any number of chairs fewer than 4
They can buy any number of chairs fewer than 8
If owners of a business must spend less than $140 on supplies. They have already spent $60. Now they want to buy chairs that cost $20 each. Let x represent the number of chairs they can buy. Then they can buy any number of chairs fewer than 4.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given,
owners of a business must spend less than $140 on supplies.
They have already spent $60.
They want to buy chairs that cost $20 each.
Let x represent the number of chairs they can buy.
60+20x<140
Now solve for x
20x<140-60
20x<80
Divide both sides by 20
x<80/20
x<4
Hence they can buy any number of chairs fewer than 4
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Family spends 67.50 for 23 gallons of gasoline. If they need to go 350 miles how much money is spent on gas per gallon
Which graph represents the solution set of the system of inequalities?
common denominator of
8\15 and 5\9
Estimated the sum
97,991 + 102,489
_ + _ = _
on a suspension bridge the roadway is hung from cables hanging between support towers. the cable of one bridge segment of the parabola y=.1x^2-7x +150 where y is the height of the cable in feet above the roadway at the distance x feet from a support tower. what is the closest the cable comes to the roadway? how far from the support towers does this occur