[tex]\frac{1 }{8*a^{9}*b^{12}}[/tex].
Step-by-step explanation:1. Write the expression.[tex](\frac{a^{-3} }{2b^{4} } )^{3}[/tex]
2. Solve the parenthesis by multiplying the exponents with each part of the fraction.[tex]\frac{a^{(-3*3)} }{2^{(3)} b^{(4*3)} } \\ \\\frac{a^{(-9)} }{8b^{(12)} }\\ \\\frac{a^{-9} }{8b^{12} }[/tex]
3. Move a to the denominator (the negative sign of the exponent vanishes).[tex]\frac{1 }{8b^{12} *a^{9}}\\ \\\frac{1 }{8*a^{9}*b^{12}}[/tex]
4. Express your result.[tex](\frac{a^{-3} }{2b^{4} } )^{3}=\frac{1 }{8*a^{9}*b^{12}}[/tex].
translate the following verbal statement into an algebraic equation and solve. Paid 24,998 for a car which was 1,815 less than sticker price what was the sticker price of the caruse x for your vairableequation_______x=______
paid price = 24,998
it is the amount that is 1815 less than the sticker price,
so the sticker price or price of the car is x
so x = 24,998 + 1815
x =26,813
so the price of car is x = 26,813.
I need help please. I don’t know what to do.Number 6
By definition, a relation is a function if each input value (x-value) has one and only one output value (y-value).
In this case, you have the following relation:
[tex]\mleft(1,5\mright)\mleft(3,1\mright)\mleft(5,0\mright)\mleft(-2,6\mright)[/tex]Notice that each ordered pair has this form:
[tex](x,y)[/tex]Where "x" is the input value and "y" is the output value.
You can identify that each input value has one and only output value. Therefore, you can conclude that this relation is a function.
Hence, the answer is: It is a function.
The total payroll for a baseball team is 2.44 × 109 dollars, and the total payroll for a football team is 2.9 × 1011 dollars. How many more dollars is the football team's total payroll than the baseball team's total payroll?
0.46 × 109 dollars
2.8756 × 109 dollars
4.6 × 1011 dollars
2.8756 × 1011 dollars
Answer: I belive it would be 4.6 x 10^11 dollars. I hope this helps you :)
Step-by-step explanation:
Answer:it would be 4.6x10^11
Step-by-step explanation:
Where are the minimum and maximum values for f(x)A. min: x =2¹ 2Reset Selectionmax:z = = 0, π, 2πOB. min:z = π max:x = 0, 2OC. min:z = 0, 2π max:x = πOD. min:z = ,,max:x = 0, 3, 4,2=- 3 cos z - 2 on the interval [0, 2π]?2P
Given:
The function f(x) = 3cos(x) - 2.
Required:
What are the minimum and maximum value of function?
Explanation:
To check maximum and minimum value of function.
First derivate the original function.
After putting first derivative equal to zero, critical points can be found.
Then, do second deritvative to check points of maxima and minima.
The critical points at which second derivative greater than zero. Point will be of minima.
The critical points at which second derivative less than zero. Point will be of maxima.
So,
[tex]\begin{gathered} f(x)=3cos(x)-2 \\ \text{ First derivative} \\ f^{\prime}(x)=-3sinx \\ \text{ Put }f^{\prime}(x)=0 \\ sinx=0 \\ x=0,\pi,2\pi \end{gathered}[/tex]Now, do second derivative test for maximum and minimum points
[tex]\begin{gathered} f^{\prime}^{\prime}(x)=-3cosx \\ \text{ At }x=0 \\ f^{\prime}^{\prime}(0)=-3\times1=-3<0 \\ \text{ At }x=\pi \\ f^{\prime}^{\prime}(\pi)=-3\times cos(\pi)=-3\times-1=3>0 \\ At\text{ }x=2\pi \\ f^{\prime}^{\prime}(2\pi)=-3\times1=-3<0 \\ \end{gathered}[/tex]Answer:
[tex]\text{ The points }0,2\pi\text{ are points of maxima and }\pi\text{ giving minima.}[/tex]
fine one value of x for which f(x) = 4 and find f(0)look at the graph below
To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]To find the value of x for which f(x) = 4 we must find the point (x, 4), first, let's draw a horizontal line at y = 4:
As we can see the horizontal line touches the graph, then it touches the graph we draw a vertical line until we reach the x-axis, where we reach it, it's the value of x:
As we can see, the vertical line reaches x = -4, therefore, f(-4) = 4
[tex]f(-4)=4[/tex]Our final answer will be x = -4
b)
Now for f(0) = ?, we must do the same logic, but now we start with a vertical line at x = 0, and goes up until we reach the graph
As we can see it touches the graphic at y = 2, hence, f(0) = 2
[tex]f(0)=2[/tex]which is the new equation written in the slope-intercept form
he slope-intercept form is
y = mx + c
here, m = slope of the line and C is intercept on y axis.
Please help me and explain to me these questions step by step. Thank youQuestion 8: Use simple interest
Given:
Amount Nicole borrowed = $1100
Annual interest rate = 7%
Duration = 6 months
Let the amount of interest be x
The amount after t years can be calculated using the formula:
[tex]\text{Amount = }P(1\text{ }+\text{ rt)}[/tex]The interest that she would pay can be calculated using the formula:
[tex]\text{Interest = Amount - Principal}[/tex]The amount after 6 months is:
[tex]\begin{gathered} \text{Amount = 1100(1 + 007 }\times\frac{6}{12}) \\ =\text{ 1138.5} \end{gathered}[/tex]Hence, the interest:
[tex]\begin{gathered} \text{Interest = 1138.5 - 1100} \\ =\text{ 38.5} \end{gathered}[/tex]Answer: $38.5
I'm graphing and I need to find out how mutch it costs for 4.5 inches of the construction. and the construction is $25.50 per inch
You have to determine the cost for 4.5 inches of the construction using the graph.
The height is on the y-axis, and the cost is on the x-axis.
First, locate 4.5 in the y-axis, which is the value in the midpoint between 4 and 5.
Draw a horizontal line until you intersect with the line, then draw a vertical line from the function until the x-axis:
The line crosses the x-axis at the midpoint between values 102 and 127.5 to determine the value at this point you have to average both costs:
[tex]\frac{127.5+102}{2}=\frac{229.5}{2}=114.75[/tex]The cost of 4.5 inches of construction is $114.5
How many fourteenths are there in 3/ 7 ?
Help on math question precalculus Match the description with the correct base for the logarithm.-LOG without a subscript has a base of -Ln has a base of Choices =10,e
The formal way of writing a logarithm is the following:
[tex]\log _ab[/tex]Where "a" is the base of the logarithm and "b2 is the argument.
If "a = 10", then the base is not written, like this:
[tex]\log _{10}b=\log b[/tex]In the case that the base is the constant number "e" then the logarithm is called a "natural logarithm" and it is written as follows:
[tex]\log _eb=\ln b[/tex]Which of the following values have 3 significant figures? Check all that apply.A. 10.1B. 100.05C. 120D. 129
The number of significant figures in 10.1 is 3 as there are two digits before the decimal and one digit after the decimal.
The number of significant digit in 100.05 is 5 as there are 3 digits before the decimal and two digits after the decimal.
The number of significant digits in 120 is 2.
The number of significant digits in 129 is 3.
Hence, the correct answers are (A) and (D)digit
Convert the polar equation r=3 to a Cartesian equation.x^2+y^2=√3x^2+y^2=3x^2+y^2=9
For the given equation:
[tex]\begin{gathered} \text{Polar form: } \\ r=3 \\ \\ \text{Cartesian form:} \\ x^2+y^2=3^2 \\ x^2+y^2=9 \end{gathered}[/tex]If a = (3.2) and b=(-5. 3), what is a +b?
Given the value of a and b
[tex]\begin{gathered} a=3.2 \\ b=-5.3 \end{gathered}[/tex]To get a+b
[tex]a+b=3.2-5.3[/tex]Thus
[tex]a+b=-2.1[/tex]Thus, a + b = -2.1
Consider the polynomial function q ( x ) = − 2 x 8 + 5 x 6 − 3 x 5 + 50
The function has an end behaviour of x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
How to determine the end behaviour of the function?The equation of the polynomial function is given as
q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
To determine the end behaviour of the function, we calculate
q(∞) and q(-∞)
So, we have
q(∞) = -2(∞)⁸ + 5(∞)⁶ - 3(∞)⁵ + 50
Evaluate the exponents
q(∞) = -2(∞) + 5(∞) - 3(∞) + 50
This gives
q(∞) = -∞ + ∞ - ∞ + 50
q(∞) = -∞
Also, we have
q(-∞) = -2(-∞)⁸ + 5(-∞)⁶ - 3(-∞)⁵ + 50
Evaluate the exponents
q(-∞) = -2(∞) + 5(∞) - 3(-∞) + 50
This gives
q(-∞) = -∞ + ∞ + ∞ + 50
q(-∞) = -∞
Hence, the end behaviour of the graph is x → ∞, q(x) → -∞ and x → -∞, q(x) → -∞
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Complete question
Consider the polynomial function q(x) = -2x⁸ + 5x⁶ - 3x⁵ + 50
Calculate the end behaviour
Which equivalent equation results when completing the square to solve x^2-8x+7=0?
Using complete the square method:
[tex]\begin{gathered} x^2\text{ - 8x + 7 = 0} \\ x^2\text{ - 8x = -7} \\ \text{Add half the square of the coefficient of x to both sides:} \\ \text{half the coefficient = -8/2 = -4} \\ \text{square half the coefficient = (-4)}^2 \end{gathered}[/tex][tex]\begin{gathered} x^2-8x+(-4)^2=-7+(-4)^2 \\ \text{making it a p}\operatorname{erf}ect\text{ square:} \\ (x-4)^2\text{ = -7 }+(-4)^2 \end{gathered}[/tex][tex]\begin{gathered} (x-4)^2\text{ = -7 + 16} \\ (x-4)^2\text{ = 9 (option D)} \end{gathered}[/tex]The table displays the mean name length for seven samples of students.Sample1Mean Name Length5.47.1236.345.2566.04.976.2What can be said about the variation between the sample means?The variation between the sample means is small.The variation between the sample means is large.The variation shows that the values are far apart.The variation cannot be used to make predictions.
First option is correct.
For all the sample sizes, the sample mean is close to 6, give or take (
Which statements about the graph of the exponential function f(x) are TRUE?The x-intercept is 1.The y-intercept is 3.The asymptote is y = -3The range is all real numbers greater than -3The domain is all real numbers.f(x) is positive for all x-values greater than 1As x increases, f(x) approaches, but never reaches, -3.
1 The x-intercept is the value of x where the graph intersects the x-axis. The graph crosses the x-axis at x = 1. This statement is true.
2 The y-intercept is the value of y where the graph intersects the y-axis. The graph crosses the y-axis at y = -2. This statement is false.
3 The horizontal asymptote is the value of y to which the graph approaches but never reaches. This value seems to be y = -3, thus this statement is true.
4 The range is the set of values of y where the function exists. The graph exists only for values of y greater than -3. This statement is true.
5 We can give x any real value and the function exists, i.e., any vertical line would eventually intersect the graph. This statement is true.
To find the domain of a function when we are given the graph, we use the vertical line test. This consists of drawing an imaginary vertical line throughout the x-axis. If the line intersects the graph, that value of x is part of the domain.
This imaginary exercise gives us the centainty that there is no value of x that won't intercept the graph, thus the domain is the set of all the real values.
6 We can see the graph is positive exactly when the function has its x-intercept, thus This statement is true.
7 As x increases, y goes to infinity. The value of -3 is not a number where f(x) approaches when x increases, but when x decreases. This statement is false.
select all reasons that support one or more statements in ghe proof.
Answer:
B, C, D and E.
Explanation:
The proof and reasons for each step is given below:
Step 1:
Statement: RSTU is a parallelogram.
Reason: Given
Step 2:
Statement: RS is parallel to TU and RU is parallel to TS
Reason: (B)Definition of a parallelogram
Step 3:
Statement: ∠RSU≅∠TUS and ∠RUS≅∠TSU.
Reason: (C)Alternate Interior angles are congruent
Step 4:
Statement: SU≅US.
Reason: (E)corresponding parts of congruent triangles are congruent.
Step 5:
Statement: Triangle RSU≅Triangle TUS.
Reason: AAS Congruence Theorem
Step 6:
Statement: RS≅TU and RU≅TS
Reason: (D)Opposite sides of a parallelogram are congruent.
The reasons that support the proof are B, C, D and E.
Inequality-x less than or equal to 18
Answer: x[tex]\leq[/tex]18
Write a explicit formula for the given recursive formulas for each arithmetic sequence
9,15,21,27 and 7,0,-7,-14
In arithmetic progression, 9,15,21,27,33,39 is a₅ and a₆ .
What is arithmetic progression?
A series of numbers is called a "arithmetic progression" (AP) when any two subsequent numbers have a constant difference. It also goes by the name Arithmetic Sequence.a₁ = 9
a₂ = 15
a₃ = 21
Notice that a₂ - a₁ = 6 and a₃ - a₂ = 6
We can deduce that aₙ₊₁ = aₙ + 6
We can test this on the 4th term : a₄ should equal 21 + 6 = 27
Since this checks out we can say that the sequence is an arithmetic progression with a common difference of 6.
a₅ = 27 + 5 = 33
and
a₆ = 33 + 6 = 39
7,0,-7,-14
find the common difference by substracting any term in the sequence from the term that comes after it.
a₂ - a₁ = 0 - 7 = -7
a₃ - a₂ = -7 - 0 = -7
a₄ - a₃ = -14 - -7 = -7
the difference of the sequence is constant and equals the difference between two consecutive terms.
d = -7
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How would the fraction71-√√√5using difference of squares?OA. 7-7√56OB. 7+7√56O c. 7+7√5OD. -7+7√5← PREVIOUSbe rewritten if its denominator is rationalizedSUBMIT
1) Examining that ratio, we can perform the following:
[tex]\begin{gathered} \frac{7}{1-\sqrt{5}} \\ \\ \frac{7\left(1+\sqrt{5}\right)}{\left(1-\sqrt{5}\right)\left(1+\sqrt{5}\right)} \\ \\ \frac{7+7\sqrt{5}}{1^2-(\sqrt{5})^2} \\ \\ \frac{7(1+\sqrt{5})}{-4} \\ \\ -\frac{7(1+\sqrt{5})}{4} \end{gathered}[/tex]2) Note that when we multiply that ratio by their conjugates, that yields a difference between two squares. Note that on the top, there is the expanded version of this expression.
Thus, the answer is D
Points that lie on the same line are called: a) opposite rays b) coplanar and non-collinear c) non-collinear and non-coplanar d) collin ear and coplanar
Given:
Points that lie on the same line.
Opposite rays
8ftÜ4ft7ft5ftA right angle is removed from a rectangle to create the shaded region shown below find the area of the shaded region be sure to include the correct unit in your answer
First, we need to find the sides of the triangle.
The base of the triangles is 8ft - 5ft = 3ft.
The height for the triangle is 7ft - 4ft = 3ft
Now, we need to find the area of the triangle:
[tex]A_t=\frac{base\cdot height}{2}[/tex]Replacing the values:
[tex]A_t=\frac{3ft\cdot3ft}{2}[/tex]Then
[tex]A_t=4.5ft^2^{}[/tex]Now, we need to find the area for the rectangle:
Area for a rectangle = Length * Width
In this case:
Length = 8ft
Width = 7ft
Therefore:
[tex]A_r=8ft\cdot7ft[/tex]Then
[tex]A_r=56[/tex]Finally, to find the area of the shaded region we need to subtract the triangle area from the rectangle area:
[tex]A=A_r-A_t[/tex]Therefore:
[tex]A=56ft^2-4.5ft^2[/tex][tex]A=51.5ft^2[/tex]Hence, the area for the shaded region is 51.5 ft².
at a sale a desk is being sold for 24% of the regular price. the sale price is $182.40 what is the regular price
at a sale a desk is being sold for 24% of the regular price. the sale price is $182.40 what is the regular price
we have that
24% ------> represent $182.40
so
Applying proportion
Find out the 100%
Let
x ----> the regular price
182.40/24=x/100
solve for x
x=(182.40)*(100)/24
x=$760
therefore
The regular price is $760I only need part bb) A foam protector is covered with PVC material to make it waterproof. Find the total surface area of a protector which is covered by PVCmaterial.
Assuming all the parts are covered, inluding the internal part, we have to find the surface area of the whole protector.
So, let's list which areas we need:
- We need the lateral areas of the external parts, which are 4 rectangles.
- We need the top and bottom areas, which are both area of squares minus the area of the cicle of the hole.
- We need the interior aread, which is the same as the lateral area of a cylinder.
For the external part, we only need the dimensions of each rectangle. since they have the same length and the other sides are the sides of the squares, they are all the same.
The area of each of them is:
[tex]A_{\text{rectangle}}=300mm\cdot1.8m=0.3m\cdot1.8m=0.54m^2[/tex]Since we have 4, the total exterior lateral area is:
[tex]A_{\text{lateral}}=4\cdot0.54m^2=2.16m^2[/tex]For the top and bottom, both are the same, a square of 300 mm x 300 mm with a hole of 150 mm diameter.
First, let's get all to meters: 0.3 m x 0.3 m and 0.15 m diameter. The radius of the circle is half the diameter, so:
[tex]r=\frac{0.15m}{2}=0.075m[/tex]The area of a circle given its radius is:
[tex]A=\pi r^2[/tex]So, the area of both the top and bottom is the area of the square minus the area of the circle and double all of this:
[tex]\begin{gathered} A_{\text{top/ottom}}=2((0.3m)^2-\pi(0.075m)^2) \\ A_{\text{top/ottom}}=2(0.09m^2-0.005625\pi m^2) \\ A_{\text{top/ottom}}=2(0.09-0.005625\pi)m^2 \end{gathered}[/tex]We deal with π later on.
For the lateral area of the cylinder, we can remember that it is the same as the area of a rectangle with on dimension being the length of the cylinder and the other being the circumference of the top/bottom.
the circumference of a circle is:
[tex]C=2\pi r[/tex]The radius is the same as the hole, and the length is 1.8m, so the lateral area of the cylinder is:
[tex]\begin{gathered} A_{\text{cylinder}}=1.8m\cdot2\pi(0.075m) \\ A_{\text{cylinder}}=(1.8\cdot0.15\pi)m^2 \\ A_{\text{cylinder}}=(0.27\pi)m^2 \end{gathered}[/tex]So, the total surface area is the sum of all of these:
[tex]A=2.16m^2+2(0.09-0.005625\pi)m^2+(0.27\pi)m^2[/tex]Now, we just need to evaluate:
[tex]\begin{gathered} A=2.16m^2+2\cdot0.072328\ldots m^2+0.848230\ldots m^2 \\ A=2.16m^2+0.144657\ldots m^2+0.848230\ldots m^2 \\ A=3.152887\ldots m^2 \\ A\approx3.15m^2 \end{gathered}[/tex]So, the lateral area is approximately 3.15 m².
Determine the largest integer value of x in the solution of the following inequality.
Answer:
From the solution the largest possible integer value of x is;
[tex]-6[/tex]Explanation:
Given the inequality;
[tex]-x-1\ge5[/tex]To solve, let's add 1 to both sides of the inequality;
[tex]\begin{gathered} -x-1+1\ge5+1 \\ -x\ge6 \end{gathered}[/tex]then let us divide both sides of the inequaty by -1.
Note: since we are dividing by a negative number the inequality sign will change.
[tex]\begin{gathered} \frac{-x}{-1}\leq\frac{6}{-1} \\ x\leq-6 \end{gathered}[/tex]Therefore, From the solution the largest possible integer value of x is;
[tex]-6[/tex]
a positive integer is nice if there is a positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to . how many numbers in the set are nice?
Answer:
A positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
What is an integer?
Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of the equivalent positive numbers, which are additive, are the negative numbers. The boldface Z or blackboard bold "Z" is frequently used in mathematical notation to represent a collection of numbers.
Step-by-step explanation:
We know That total No. of factors
=product of (prime no′s power+1)
If N is the number of different divisors:
N=(p1+1)⋅(p2+1)⋅⋅⋅(pn+1)
100= 2^2 × 5^2
=2×2×5×5= (1+1)(1+1)(4+1)(4+1)
Then the integer n= a1^p1⋅a2^p2⋅⋅⋅⋅an^pn
For the smallest value: p1=4,p2=4,p3=1,p4=1
Then,
n=a1^4×a2^4×a3^1×a4^1
=24⋅34⋅51⋅71
=16⋅81⋅5⋅7
=45360
Hence, the positive integer with exactly four positive divisors (including and ) such that the sum of the four divisors is equal to The sum of four divisors is equal to 45360.
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The number of skateboards that can be produced by a company can be represented by the function f(h) = 325h, where h is the number of hours. The total manufacturing cost for b skateboards is represented by the function g(b) = 0.008b2 + 8b + 100. Which function shows the total manufacturing cost of skateboards as a function of the number of hours? g(f(h)) = 325h2 + 80h + 100 g(f(h)) = 3425h + 100 g(f(h)) = 845h2 + 2,600h + 100 g(f(h)) = 2.6h2 + 2,600h + 100
The function which shows the total manufacturing cost of skateboards as a function of the number of hours is; g(f(h)) = 845h2 + 2,600h + 100.
Which function shows the manufacturing cost as a function of number of hours?It follows from the task content that the function which shows the manufacturing cost as a function of the number of hours be determined.
Since, the number of skateboards is given in terms of hours as; f(h) = 325h and;
The manufacturing cost, g is given in terms of the number of skateboards, b manufactured;
The function instance which represents the manufacturing cost as a function of hours is; g(f(h)).
Therefore, we have; g(f(h)) = 0.008(325h)² + 8(325h) + 100.
Hence, the correct function is; g(f(h)) = 845h2 + 2,600h + 100.
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Plllssss help Select all equations that are also equivalent to0.6 + 15b + 4= 25.6 ( choose all the ones down below the equal the top)A . 15b+4 = 25.6B .15b+4=25 C. 3(0.6+ 15b +4) = 76.8 D. 15b = 25.6E. 15b= 21
The given equation is
[tex]0.6+15b+4=25.6[/tex]If we subtract 0.6 on each side, we get
[tex]\begin{gathered} 0.6+15b+4-0.6=25.6-0.6 \\ 15b+4=25 \end{gathered}[/tex]Therefore, the given expression is equivalent to B.
If we multiply the given equation with 3, we get
[tex]\begin{gathered} 3\cdot(0.6+15b+4)=25.6\cdot3 \\ 3(0.6+15b+4)=76.8 \end{gathered}[/tex]Therefore, the given expression is equivalent to C.
At last, if we subtract 0.6 and 4 on each side, we get
[tex]\begin{gathered} 0.6+15b+4-0.6-4=25.6-0.6-4 \\ 15b=21 \end{gathered}[/tex]Therefore, the given expression is equivalent to E.
The right answers are B, C, and E.
12345678912345678900[tex]11447 \times \frac{333}{999} \times {141}^{2} - x \times y = \sqrt[255]{33} [/tex]Jardin De Ronda. updtCHECK EQUATION in QUESTION ! UPDT 2 :) `!!!z
test
some text with formatting
0. primo
,1. secondo
,2. terzo
• good
,• better
,• the best
jiohoh oj; lkippomklok∛
yespl
lkp
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=)
