The inverse of the logarithmic function f x log9x is f-1(x)=9^x.
The inverse of a logarithmic function is the exponential function. To find the inverse of the logarithmic function f x log9x, we can use the following equation: f-1(x)=9^x. This equation states that the inverse of the logarithmic function f x log9x is the exponential function f-1(x)=9^x.
The inverse of the logarithmic function f x log9x is f-1(x)=9^x, which is the exponential function.This means that for any value of x, the inverse of the logarithmic function f x log9x is equal to 9 raised to the power of x. For example, if x=2, then the inverse of the logarithmic function f x log9x is 9^2, or 81. Similarly, if x=3, then the inverse of the logarithmic function f x log9x is 9^3, or 729. In general, the inverse of the logarithmic function f x log9x is 9 raised to the power of x, for any value of x.
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Answer: f –1(x) = 9x
Step-by-step explanation:
The density function of the continuous random variable x, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is given below: f(x) = { x, 0 < x < 1 8 − x, 1 ≤ x < 2 0, otherwise Find the average number of hours per year that families run their vacuum cleaners?
Answer:
1000 hours
Step-by-step explanation:
∫xf(x)dx = ∫x*xdx (1,0) + ∫x*(8-x)dx (2,1)
∫xf(x)dx = ∫x²dx (1,0) + ∫8x - x²dx (2,1)
∫xf(x)dx = ∫x²dx (1,0) + ∫8xdx (2,1) - ∫x²dx (2,1)
∫xf(x)dx = x³/3(1,0) + 8x²/2 (2,1) - x³/3(2,1)
∫xf(x)dx = 1/3 + 8(4/2 - 1/2) - (8/3 - 1/3)
∫xf(x)dx = 1/3 + 8(2-0.5) - (7/3)
∫xf(x)dx = 1/3 + 8(1.5) - 7/3
∫xf(x)dx = 1/3 + 12 - 7/3
∫xf(x)dx = - 6/3 + 12
∫xf(x)dx = - 2 + 12
∫xf(x)dx = 10
The average number of hours the family runs their vacuum cleaner in units of 100 hours
100 * 10 hours = 1000 hours
Rewrite the radical by extracting all possible roots and write your answer in radical form 75x4y7−−−−−−√
Answer:
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{75x^4y^7[/tex]
Required
Rewrite
Express 75 as 25 * 3
[tex]\sqrt{75x^4y^7} = \sqrt{25 * 3x^4y^7}[/tex]
Split
[tex]\sqrt{75x^4y^7} = \sqrt{25} * \sqrt{3x^4y^7}[/tex]
This gives:
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3x^4y^7}[/tex]
Express y^7 as y^6 * y
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3*x^4 * y^6 * y}[/tex]
Split
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} *\sqrt{x^4} * \sqrt{y^6} * \sqrt{y}[/tex]
Express square roots as exponents
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^{(4 * \frac{1}{2})} * y^{(6* \frac{1}{2})} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5 * \sqrt{3} * x^2 * y^3 * \sqrt{y}[/tex]
Rewrite the factors
[tex]\sqrt{75x^4y^7} = 5 * x^2 * y^3* \sqrt{3} * \sqrt{y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3} * \sqrt{y}[/tex]
Combine roots
[tex]\sqrt{75x^4y^7} = 5x^2y^3* \sqrt{3y}[/tex]
[tex]\sqrt{75x^4y^7} = 5x^2y^3\sqrt{3y}[/tex]
In a circle with radius 5.1, an angle intercepts an arc of length 30.3. Find the angle in
radians to the nearest 10th.
Answer:
5.9 radian
Step-by-step explanation:
Applying,
S = 2πrФ/360°................. Equation 1
Where s = length of the arc, r = radius, Ф = angle.
make Ф the subject of the equation
Ф = 360S/(2πr)........... Equation 2
From the question,
Given: S = 30.3, r = 5.1
Constant: π = 3.14
Substitute into equation 2
Ф = (360×30.3)/(2×5.1×3.14)
Ф = 340.58°
Ф = (340.58×2×3.14)/360
Ф = 5.9 radian
Write a rule to calculate 1% of any number
find the area of the shaded regions below. give your answer as a completely simplified exact value in terms of π (no approximations)
Answer:
Step-by-step explanation:
the area of the hemisphere is 1/2 [tex]\pi[/tex][tex]r^{2}[/tex]
the radius is 1/2 the diameter,
the diameter is also the hypotenuse of the isosceles triangle
[tex]d^{2}[/tex] = [tex]4^{2}[/tex]+[tex]4^{2}[/tex]
[tex]d^{2}[/tex] = 32
d =[tex]\sqrt{32}[/tex]
r = 1/2[tex]\sqrt{32}[/tex]
1/2[tex]\pi[/tex](1/2[tex]\sqrt{32}[/tex])^2
1/2[tex]\pi[/tex](1/4*32)
(32/8 )*[tex]\pi[/tex]
4[tex]\pi[/tex] ( the entire upper hemisphere )
area of the triangle is 1/2* 4 *4 = 8
then the exact area of the parts of the circle would be
4[tex]\pi[/tex] - 8
For what value of n is n-2] + 2 equal to 0?
Answer:
n=0
Step-by-step explanation:
0 - 2 = -2
-2 + 2 = 0
Can anyone help explain this math equation like I gotta turn this math in by midnight tonight!! I will give brainlist btw!!
Answer: 1) 288 inch^3
2) 960 inch^3
3) 188 cm^3
4) 44 inch^3
5) 396 ft^3
6) 552 inch^3
Step-by-step explanation:
1) (2*3)(3*2)(2*4)=288 inch^3
2) (4*5)(4*3)(4*1)=960 inch^3
3) 4*4*8+3*4*5=188 cm^3
4) 2*2*8+2*6*1=44 in^3
5) 4*6*6+6*6*7=396 ft^3
6) 8*6*10+4*3*6=552 in^3
What is the sum of the measures of the exterior angles of the polygon shown below if necessary round to the nearest 10th
Answer:
24
Step-by-step explanation:
Number of sides = 15 (counted and it was a pain the a*s)
The total measure of the exterior angle = 360
= 360/15
= 24 degree
Each angle is measured 24 degree
The sum of the exterior angles of the polygon shown in the image is: 360°.
What is the Sum of Exterior Angles of a Polygon?Regardless of the number of sides or angles a polygon has, the sum of exterior angles of any polygon is always 360 degrees.
Thus, the polygon given has 15 sides, however, the sum of all its exterior angles will still give 360 degrees.
Therefore, the sum of the exterior angles of the polygon shown in the image is: 360°.
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Convert one three fifths to a percent find that percent of 30 Divide your answer by 25% of 16
Answer:
40%
Step-by-step explanation:
1 and 3/5 as a fraction is 8/5 which as a percent is 160%.
25% of 16 is 4
160%/4 = 40%
A rectangle frame needs to be constructed so that its width and length are in a ratio of 3:4 and its diagonal is 25 inches. What is the perimeter of the frame?
Answer:
70 inches
Step-by-step explanation:
From the diagram attached,
Assuming the width, lenght and diagonal of the rectangle forms a right angle triangle.
Applying pythagoras theorem,
a² = b²+c²................... Equation 1
Where a = diagonal = 25 inches, b = width = 3x inches, c = length = 4x inches
Substitute these values into equation 1 and solve for x
25² = (4x)²+(3x)²
625 = 14x²+9x²
625 = 25x²
25x² = 625
x² = 625/25
x² = 25
x = √25
x = 5 inches.
Therefore,
Width(w) = 3×5 = 15 inches
Length(l) = 4×5 = 20 inches
Perimeter (P) = 2(l+b)
P = 2(15+20)
P = 2(35)
P = 70 inches
Hence the perimeter of the frame is 70 inches
The integral 1 π(y2−y4) dy 0 represents the volume of a solid. Describe the solid.
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y2 and x = y4 around the y axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the x axis
O The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The correct option is (d). The solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y2 around the y axis
The difference between the areas beneath the two curves that form a boundary is the area between the curves. You will then have the area between the two curves, or the difference, between them.
In the cartesian coordinate system, a plane is divided into four areas by the X-axis, a horizontal line, and the Y-axis, a vertical line. The term "quadrant" refers to these four areas.Use washer method:The washer method enables us to use cylindrical discs with holes to compute the volume of solids in a rotation.
As we have mentioned, the washer method is an extension of the disk method. This technique is established so that we can also calculate for the volume of the solid returned by rotating the region bounded by two curves over the x and y axis.[tex]$$\begin{aligned}& V=\int_a^b \pi\left(x_1^2-x_2^2\right) d y \\& =\int_0^1 \pi\left(y^2-\left(y^2\right)^2\right) d y \\& =\int_0^1 \pi\left(y^2-y^4\right) d y\end{aligned}$$[/tex]
Therefore, the solid obtained by rotating the region in the first quadrant bounded by the curves x = y and x = y² around the y axis.
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4r= -36
-72
-40
-9
9
Answer:
4r=-36
-36/4=r
-9=r
Therefore
r=-9
Answer: r=−9
Step-by-step explanation: Hope this help :D
Let's solve your equation step-by-step.
4r=−36
Step 1: Divide both sides by 4.
4r/4=−36/4r
=−9
hello please help i’ll give brainliest
Answer:
ocean crust is thinner
Step-by-step explanation:
Answer:
Oceanic crust is thinner
hope this helped
Step-by-step explanation:
The absolute value function graphed below can also be represented by a piecewise function.
Determine which function is represented by the graph.
please help!!!
Answer:
Step-by-step explanation:
Trust me
In ΔABC, M∠A = 56°and M∠B = 73°. what is M∠C?
Answer:
51
Step-by-step explanation:
triangles equal to 180, 56+73+51 equals 180 :)
brainliest pls
Answer:
m∠C = 51°
Step-by-step explanation:
By definition of interior angles of a triangle, the ∑ΔABC's interior angles = 180°.
It is given that m∠A = 56° & m∠B = 73°. Set the equation:
56 + 73 + m∠C = 180
First, combine like terms:
(56 + 73) + m∠C = 180
m∠C + 129 = 180
Next, isolate the term, m∠C. Note the equal sign, what you do to one side, you do to the other. Subtract 129 from both sides:
m∠C + 129 (-129) = 180 (-129)
m∠C = 180 - 129
m∠C = 51°
51° is your answer for m∠C.
~
)8th grade math, Pls help, will mark Brainliest (For the FIRST AND CORRECT answer)
please help me!!10points
Answer:
167 feet
Step-by-step explanation:
Please see the attached image.
(90-42)°=48°
The tangent of an angle is the opposite side relative to that angle divided by the adjacent side.
tan(48°)=x/150
x=tan(48°)*150
x≈167
Answer: 167 feet
Please help me with this homework question. No silly answers please and no bots, links, etc! I will mark brainliest to whoever gets this right. Thank you!
Answer:
T = (m × 20) + 25
(2.5 × 20) + 25 = 75
75 minutes
110 - 25 = 85
85 ÷ 20 = 4.25
4.25 kilograms
What properties does the shape below have? Why is it not a parallelogram?
Answer:
Parallelograms have two symmetries but this kite had only one symmetry
Define symmetry-The symmetry that a figure has if it can be divided by a line into two parts that are mirror images.
Observe my example why its not a parallelogram...
Hope this helps plz like and brainly :D
Much would be appreciated <3
helppp PLEASEE !!! lol
Answer:
3.14 x 3.8^2 = 45.3416
* find the surface area
hope this helped
Step-by-step explanation:
Answer:
if your going by 3 as pie you would do this:
Step-by-step explanation:
3*3.8*3.8=43.32
Please help I will give 15 points
Answer:
THE FIRST ONE
Step-by-step explanation:
How do you write 5 more than a number?
x+5 is the way we can write 5 more than a number.
In a formula or equation involving mathematical operations, the representation of numbers by alphabet is referred to as algebra.
Using the knowledge provided above, we must translate the mathematical statement provided in the question into an algebraic expression. Let's say that number is "x". The result of adding 5 to the provided number is a number that is 5 greater than this number. Thus, a number that is 5 more than x is equal to x+5. As a result, "5 more than a number" is represented by the algebraic expression "x+5".
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What do () mean in math?
Parentheses are employed to indicate changes to the usual order of operations.
Define round brackets.The well-known () symbols, often known as "round brackets," are used in pairs to group things together or designate the order of operations in an equation. You will frequently need to employ brackets in math when forming or resolving equations. They support number grouping and operation definition.
Mention other brackets as well.{}, [] are other type of brackets.
In mathematical expressions, parentheses are employed to indicate changes to the usual order of operations (precedence rules). In an expression like, the portion of the expression enclosed in parentheses,, is first assessed, and the outcome is then incorporated into the remaining portions of the expression.
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Determine the missing angle measure.
Answer:
Step-by-step explanation:
Since you already know that one of the angles is 21 degrees, this helps you A LOT. In total the line is 180 degrees so to find x you just do 180-21 which equals 159
x+ 159 degrees
80 board game is on sale for 20 percent off
How much is the board game?
Answer:
the answer is 64 dollars or pounds or whichever currency
Answer:
The bord game is 64$.
Step-by-step explanation:
80/10=8
8*(8-2)=
64$
On a negatively skewed curve, which is true?
The statistical model is not good, and this is true for a negatively skewed curve.
What means negatively skewed curve?It is a statistical term implies that a curve is skewed at the left side.
In a statistical data for a certain distribution, we can get a negatively skewed curve when most of the data values are located on the right side of the distribution graph. The high concentration of values on the right side of distribution curve forms a long tail in the negative direction.
Which is true for negatively skewed curve?In general, negatively skewed curve is not good because it expresses the tendency of left tail events. Negatively skewed curves indicate a poor return from an investment. That means a person might be earn lower or no profit from his business. In case of an exam scores, negative skewed data value implies the question was too easy to perform better than usual.
In a word, left skewed or negatively skewed curve or data values inform us to be aware about the current statistical model and inspire us to take proper steps for wellbeing.
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Jak starts to save at age 40 for a vacation home that he wants to buy for his 50th birthday. He will contribute $1000 each quarter to an account, which earns 2.1% interest, compounded annually. What is the future value of the investment, rounded to the nearest dollar, when jak is ready to purchase the vacation home?
Answer:
[tex]P=\$40840[/tex]
Step-by-step explanation:[tex]I=840[/tex]
From the question we are told that:
Time interval [tex]t=50-40=>10years[/tex]
Annual contribution [tex]X= 4*1000=>\$4000[/tex]
Annual interest rate [tex]r=2.1\%[/tex]
Generally the 10 years interest I is mathematically given by
[tex]I=X*t*r[/tex]
[tex]I=4000*0.021*10[/tex]
[tex]I=840[/tex]
Generally the equation for the future value of the investment [tex]P[/tex] is mathematically given by
[tex]P=X*t+840[/tex]
[tex]P=(4000*10)+840[/tex]
[tex]P=\$40840[/tex]
Find the value of x.
x+16
9
Answer:
x = - 7
Step-by-step explanation:
given that the 3 angles in the triangle are congruent, then the triangle is equilateral with the 3 sides congruent , then
x + 16 = 9 ( subtract 16 from both sides )
x = - 7
Answer:
x=-7
Step-by-step explanation:
The triangles sides are all the same in length, therefore, you need all the sides to be equal to 9.
-12+16=4 This addition problem does not equal to 9 so it is not correct.
-7+16=9 This is correct because -7+16 or 16-7 = 9.
-9+16=7 This addition problem does not equal to 9 so it is not correct.
-11+16=5 This addition problem does not equal to 9 so it is not correct.
So, x = -7.
Find the missing side lengths. Leave your answers as radicals is simplest form.
The reputation of a city has been decreasing exponentially since 1990. In 1990, the population was 1,000,000. In 2010, the population was 560,000. If t represents time in years since 1990, which of the following equations
best models the decay of the population?
Answer:
i think you have to soleve that srry