Answer:
Step-by-step explanation:
8 :)
1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 8
:0
inverse functionf(x)= 1/2 (3-3x)
f(x)= 1/2 (3-3x)
First, write as a linear equation: (replace f(x) by y)
y= 1/2 (3-3x)
Swap x and y variables:
x = 1/2 (3-3y)
Solve for y:
x = 1/2(3)+1/2(-3y)
x= 3/2 -3/2y
x-3/2 = -3/2y
(x-3/2) / -3/2 = y
-2/3x+1=y
Write in inverse notation
f-1(x) = -2/3x+1
14) The angle of elevationfrom a point 116 meters fromthe base of the Eiffel Towerto the top of the tower is68.9°. Find the approximateheight of the tower to thenearest meter.
Given data:
The given angle of elevation is θ= 68.9°.
The horizontal distance is d=116 m.
The expression for tanθ is,
[tex]\begin{gathered} \tan \theta=\frac{h}{d} \\ \tan (68.9^{\circ})=\frac{h}{116\text{ m}} \\ h=300.62\text{ m} \\ \approx301\text{ m} \end{gathered}[/tex]Thus, the height of the tower is 301 m.
which anwser shows the best approximation of [tex] \sqrt[]{26} [/tex]
Solution
[tex]\begin{gathered} \sqrt[]{26} \\ \text{simplifying }to\text{ decimal form} \\ =5.09901\ldots \end{gathered}[/tex]Answer: the best approximation is 5.1
can someone please help me find the value degree of 33-gon
the sum of exterior angles of any n-gon is 360.
Sum of exterior angles of a 33-gon is 360°
Direction. Write the letter of the correct answer on a separate answer sheet.
1. The composite functions are two o more functions combining within another to create a new function.
So the correct notion is:
a. h(p(x))
b. ( s o t) (x)
c. f(g(x))
So the b. f(x) g(x) is not a notation of a composite function.
sugar cookies require 2 cups of flour for every 2/3 cups of sugar. how much sugar for 5 cups of flour
Billy, this is the solution to the exercise:
For answering it, we will use the Direct Rule of Three, this way:
Sugar (cups) Flour (cups)
2/3 2
x 5
____________________________
x * 2 = 5 * 2/3
2x = 10/3
Dividing by 2 at both sides:
2x/2 = 10/3 / 2
x = 10/3 * 1/2
x = 10/6
x = 1 2/3 (simplifying)
We will need 1 2/3 cups of sugar for 5 cups of flour
The hydrogen ion concentration of a solution is 0.0001mol/L. Calculate the pH (given pH = -log[H]+
Given:
The hydrogen ion concentration of a solution is 0.0001 mol/L
we will find the value of pH
The relation between pH and the hydrogen ion concentration H will be:
[tex]pH=-\log H^+[/tex]Given H = 0.0001 mol/L
so, the value of pH will be as follows:
[tex]pH=-\log (0.0001)=-\log 10^{-4}=-(-4\log 10)=4[/tex]so, the answer will be pH = 4
Dan’s income can be calculated as $20 times the number of hours worked (h) added to his overtime wages of $300. If you subtract $600 to pay a bill, his income totals $500. Which expression represents dance income?
Income:
$20 x number of hours = 20h
Add the overtime wages of $300
Dan's income= 2h+300
Subtract 600 to pay a bill:
2h+300-600
His income totals $500
2h+300-600 =500
Combine like terms:
2h-300 = 500
find the slope of the equation. y=-(-x+1)
The form of the linear equation is
[tex]y=mx+b[/tex]m is the slope
b is the y-intercept
Since the given equation is
[tex]y=-(-x+1)[/tex]Simplify it by multiplying each term in the bracket by (-)
[tex]\begin{gathered} y=-(-x)+-(1) \\ y=x+-1 \\ y=x-1 \end{gathered}[/tex]Compare it with the form above to find the value of m
[tex]m=1[/tex]The slope of the equation is 1
what is the perimeter of a triangle with vertices located at (1,3), (2,6), (0,4)
ANSWER
EXPLANATION
The perimeter of a triangle is the sum of the length of its three sides. For this triangle we know the location of the vertices. The length of each side is the distance between each pair of points:
you are visiting new Orleans, la and a taxi company charges a flat fee of $2.75 for using the taxi and $0.35 per mile write an equation
We have a fixed fee of $2.75, independent of the miles.
We also have to add a variable fee, the depends on the number of miles (lets call them x), that is $0.35 per mile.
Then, we can write the total fee as:
[tex]C(x)=2.75+0.35\cdot x[/tex]What linear equation represents the graph of a horizontal line, parallel to the x-axis, that travels through the point (0,4)? Use the grid or a piece of paper if needed. LY 2 1 X 5 2 2 0 1 2 3 4 1 -2
It's important to know that all horizontal lines can be represented as y = k, where k is a real number.
In this case, we know that the horizontal line passes through (0,4).
Therefore, the equation of the line is y = 4.what is the value of a in the function's equation? please help asap.
The general equation for a quadratic function is,
[tex]f(x)=cx^2+bx+a[/tex]The zeros of equation is -8 and 4, means that f(-8) = 0 and f(4) = 0.
Determine the equation for a, b and c.
[tex]\begin{gathered} f(-8)=c(-8)^2+b(-8)+a \\ 0=64c-8b+a \\ a=-64c+8b \end{gathered}[/tex][tex]\begin{gathered} f(4)=c(4)^2+b(4)+a \\ 0=16c+4b+a \\ a=-16c-4b \end{gathered}[/tex]So equation is,
[tex]\begin{gathered} -16c-4b=-64c+8b \\ 48c=12b \\ b=4c \end{gathered}[/tex]Differentiate the function
Solve: Show your work.
-2-(-5)=
Answer:
3
Step-by-step explanation:
First you turn the two negatives/minuses in -(-5 into a plus (you will get it later)
Next you have -2 + 5 which is 3
Or is you want to do it the less lazy way
First you gotta know that subtracting a negative number means you are adding to the first number
You have -2 Minus -5 so you add five to -2 which is 3
Find the 12th term of the arithmetic sequence whose common difference is d = -7 and whose first term is a 1 = 30 .(Picture is more understandable)
T12 = -47
Explanations:The nth term of an arithmetic sequence is expressed as:
[tex]T_n=a+(n-1)\cdot d[/tex]where:
• a is the, first term
,• n is the ,number of terms
,• d is the ,common difference
Given the following parameters
a = 30
n = 12 (12th term)
d = -7 (common difference)
Substitute the given parameters into the formula
[tex]\begin{gathered} T_{12}=30+(12-1)\cdot(-7) \\ T_{12}=30+11(-7) \\ T_{12}=30-77 \\ T_{12}=-47 \end{gathered}[/tex]Hence the 12th term of the arithmetic sequence is -47
Find the value of the following logarithms without using a calculator.(a) log319(b) log51(c) lne5(d) log0.00001
For this part, we can use the following properties:
[tex]\begin{gathered} \frac{1}{a^n}=a^{-n}\Rightarrow\text{ Property of the exponents} \\ \log _aa^x=x\Rightarrow\text{ Property of logarithms} \end{gathered}[/tex]So, applying the above property of exponents, we have:
[tex]\begin{gathered} \frac{1}{9}=\frac{1}{3\cdot3} \\ \frac{1}{9}=\frac{1}{3^2} \\ \frac{1}{9}=3^{-2} \end{gathered}[/tex]Now, applying the above property of logarithms, we have:
[tex]\begin{gathered} \log _3\frac{1}{9}=\log _33^{-2} \\ $$\boldsymbol{\log _3\frac{1}{9}=-2}$$ \end{gathered}[/tex]Part b)For this part, we can apply the following property of logarithms:
[tex]\log _a1=0[/tex]Then, in this case, we have:
[tex]\begin{gathered} a=5 \\ \log _a1=0 \\ \boldsymbol{\log _51=0} \end{gathered}[/tex]Part c)For this part, we can apply the following property of logarithms:
[tex]\ln e^x=x[/tex]So, we have:
[tex]\begin{gathered} x=5 \\ \ln e^x=x \\ $$\boldsymbol{\ln e}^{\boldsymbol{5}}\boldsymbol{=5}$$ \end{gathered}[/tex]Part d)For this part, we can rewrite 0.00001 like this:
[tex]\begin{gathered} 0.00001=\frac{0.00001}{1} \\ 0.00001=\frac{0.00001\cdot100,000}{1\cdot100,000} \\ 0.00001=\frac{1}{100,000} \\ 0.00001=\frac{1}{10\cdot10\cdot10\cdot10\cdot10} \\ 0.00001=\frac{1}{10^5} \\ 0.00001=10^{-5} \end{gathered}[/tex]Now, applying the above property of logarithms, we have:
[tex]\begin{gathered} a=10\text{ and }x=-5 \\ \log _aa^x=x \\ \log 0.00001=\log _{10}10^{-5} \\ $$\boldsymbol{\log 0.00001=-5}$$ \end{gathered}[/tex]What is the solution to the equation 7c+5= 9(c- 3)?ROc=2Oc=4Oc=11Oc= 16
ANSWER:
16
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]7c+5=\: 9\mleft(c-\: 3\mright)[/tex]We solve for c:
[tex]\begin{gathered} 7c+5=9c-27 \\ 9c-7c=27+5 \\ 2c=32 \\ c=\frac{32}{2} \\ c=16 \end{gathered}[/tex]The solution of the equation is that c equals 16
For the image above, find the following:
x =
ACB =
Answer:
x = 25
m∠ACB = 115°
Step-by-step explanation:
A full circle measures 360°: 92 + (4x+15) + (6x+3) = 360
10x + 110 = 360
10x = 250
x = 25
Central angles have the same measure as the intercepted arc:
ACB = 4x + 15 = 4(25) + 15 = 115°
Answer:
Answer:
x = 25
m∠ACB = 115°
Step-by-step explanation:
ACB = 4x + 15 = 4(25) + 15 = 115°
The total volume of a tree increases 8% each year. What will its volume be after 7 years if it’s volume is 5 m³ now?
The volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
In the given question we have to find the volume be after 7 years if it’s volume is 5 meter cube now.
The increment in tree each year = 8%
At now the volume is 5 meter cube.
Time = 7 years
So the formula is used to find the volume after 7 years
A=P(1+ r/100)^n
A=volume after 7 years
P=now the volume of tree
n=time
Putting the values
A=5(1+ 8/100)^7
A=5((100+8)/100)^7
A=5(108/100)^7
A=5(1.08)^7
A=5×1.714
A=8.57
Hence, volume of trees after 7 years if it’s volume is 5 m cube now is 8.57 m cube.
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Which describes the transformation shown below?AAdc4b1af2565e7f59d96219e110571cd3.webm 11988O aOьReflection over the y-axisRotation 270 clockwiseRotation 90' clockwiseTranslation leftOd
Looking at the picture. the image, A' is on the left hand side of the object A. This could mean rotation about the origin or reflection about the y axis. Since the positions of the coordinate changed, it means that it is rotation. For 270 degrees, an object with coordinates, (x, y
Calculate the second and third derivative of y =9x-1/x
y = 9x - 1/x
I like to rewrite 1/x as x^-1
y = 9x - x^-1
Taking the derivative
dy/dx = 9 - -1 x^-2
= 9 + 1/x^2
That is the first derivative
Now we do it again
dy^2/dx^2 = d/dx ( 9 + 1/x^2)
= d/dx( 9 + x^-2)
= 0 -2x^-3
=-2/x^3
The second derivative is -2 / x^3
How many lines are determined by 18 points, no 3 of which are collinear?
First, consider the 3 points, no 3 of which are collinear; as shown in the diagram below
As one can see, we can form 3 different lines, lines 12, 13, and 23 (this is 2+1=3).
Similarly, in the case of 4 points,
There are 6 possible lines when considering 4 points on the plane (3+2+1=6).
Finally, in the case of 5 points on the plane,
4+3+2+1=10 lines when 5 points.
Therefore, for 18 points, there are 17+16+15+14+...+3+2+1=153
in the interactive below, fill out five products for a company and sells in column A and their respective prices in column B. Inter five as the quantity in cells C2 through C6. write an expression in column D to find the value of each cell by multiplying the corresponding B and C cells. for example the cell D2 should use the formula =B2*C2. The cell D7 should be determined by writing an expression to add cells D2 through D6.type in the items you’re purchasing in column A, type in the price of the items in column B. Enter an expression using an asterisk in columb D to multiply two cells together. For example in D2, type “=B2*C2” without the quotation marks.
We are tasked to complete a table by providing information on the prices of 5 items and finding their total cost.
To do this, we must first think of 5 items and find out (or at least estimate) their unit prices.
Item Price
pencil $2
notebook $4
Chapstick $3
book $7
bookmark $1
Then, in column D, we need to type the following formulas:
=B2*C2
=B3*C3
=B4*C4
=B5*C5
=B6*C6
And finally, in cell D7, type in =D2+D3+D4+D5+D6 or =sum(D2:D6).
place and label the following numbers on the number line. draw your number line on paper
EXPLANATION
Drawing the numbers on the number line give us the following graph:
I know the first part not sure of the 2nd
Given
The shell looks are a cone
Diameter is 5
Radius is half diameter which 2.5in
Slant length is 10in
Solution
The formula for the surface area of a cone
[tex]=\pi r(r+l)[/tex]Now, substitute the given parameters into the formula
[tex]\begin{gathered} =\pi2.5(2.5+10) \\ =31.25\pi \\ =98.17477\text{ in}^2 \end{gathered}[/tex]Are [3/6 -4/5] and [5/-6 4/3] inverses? Why or why not?
Answer:
A.
Explanation:
Two matrices are inverses if when we multiply them, we get the identity matrix with 1 in the diagonal and 0 on the other entries.
In this case, we get that the multiplication of the matrices is equal to
[tex]\begin{bmatrix}{3} & {-4} \\ {6} & {5}\end{bmatrix}\begin{bmatrix}{5} & {4} \\ {-6} & {3}\end{bmatrix}=\begin{bmatrix}{3(5)-4(-6)} & {3(4)-4(3)} \\ {6(5)+5(-6)} & {6(4)+5(3)}\end{bmatrix}=\begin{bmatrix}{15+24} & {12-12} \\ {30-30} & {24+15}\end{bmatrix}=\begin{bmatrix}{39} & {0} \\ {0} & {39}\end{bmatrix}[/tex]Since
[tex]\begin{bmatrix}{39} & {0} \\ {0} & {39}\end{bmatrix}\ne\begin{bmatrix}{1} & {0} \\ {0} & {1}\end{bmatrix}[/tex]We get that the matrices are not inverses.
So, the answer is A.
what is this need to know Which model represents the product 6×34?
The model in the bottom-left represents the product 6×(3/4).
We are given two numbers. The first number is 6, which is a whole number. The second number is 3/4, which is a simple fraction. We need to represent the product of these two numbers in the form of the given models. The images of the models are attached below. The first number is already a whole number, so we can represent it with six whole horizontal blocks. The second number is a fraction, so we can represent it as 3 blocks out of 4, where 4 blocks combined represent the number 1. Hence, the bottom-left model represents the product.
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Annie has 13 yards of string. She uses 12 1 yards to fix her backpack. About how much string does she have left? 9 10
Annie will be left with 0.9 yd of string with her.
What is subtraction?In maths, to subtract means to take away from a group or a number of things.
Given that, Annie had a string of 13 yd, and she used 12.1 yd of the string for her backpack.
The length of string left with her after using for backpack = 13-12.1 = 0.9 yd
Hence, Annie will be left with 0.9 yd of string with her.
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how many cubic blocks with a side length of 1/6 cm are needed to fill the volume of this prism?
To answer this question we will compute the volume of the given rectangular prism, and the volume of a cube with a side of 1/6cm, and then we will divide the volume of the given prism by the volume of the cube.
The volume of the given rectangular prism is:
[tex]V_p=\frac{1}{6}cm\times\frac{1}{2}cm\times\frac{1}{2}cm.[/tex]Simplifying the above result we get:
[tex]V_p=\frac{1}{24}cm^3.[/tex]The volume of a cube with a side length of 1/6cm is:
[tex]V_c=(\frac{1}{6}cm)^3=\frac{1}{216}cm^3.[/tex]Therefore we need
[tex]\frac{V_p}{V_c}=\frac{\frac{1}{24}cm^3}{\frac{1}{216}cm^3}=\frac{216}{24}=9[/tex]cubic blocks with a side length of 1/6cm in order to fill the volume of the given prism.
Answer: 9.
Solve the equation. Enter the answer as an equation that shows the value ofthe variable, for example f = 7, or 6 = W.p+ 3 = 1
Let the given equation is p+3=1
The objective is to find the value of p.
[tex]\begin{gathered} p+3=1 \\ p=1-3 \\ p=-2 \end{gathered}[/tex]Hence the value of p is -2.