Answer
It will take David 18.67 hours or 18 hours, 40 minutes to paint 8 rooms.
Explanation
We are asked to calculate the number of hours it'll take David to paint 8 rooms.
Let the number of hours David will take to paint 8 rooms be x
David can paint 3 rooms in 7 hours.
3 rooms = 7 hours
8 rooms = x hours
We can form a mathematical relationship by cross multiplying
3 × x = 8 × 7
3x = 56
Divide both sides 3
(3x/3) = (56/3)
x = 18.67 hours = 18 hours, 40 mins
Hope this Helps!!!
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:
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
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.
I need help with this problem it says find the missing value in the raitio table then write the equivalent ratios the table says boys:1 then □ girls 5 ! 10 . what's the equivalent ratios of 1 :□ and □ :□
Answer:
Equivalent ratios are 1:5 and 2:10
Step-by-step explanation:
We have the following ratios, and we can use proportional relationships to find the missing value:
[tex]\begin{gathered} \frac{1}{5}=\frac{x}{10{}} \\ x=\frac{10}{5} \\ x=2 \end{gathered}[/tex]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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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°
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.
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 values of c and d make the equation true?3/162x2y3 –3x+y{VoyaO c = 2, d = 2O c = 2, d = 4O c = 6, d = 2O c= 6, d = 4
we have the expression
[tex]\sqrt[3]{162x^cy^5}=3x^2y(\sqrt[3]{6y^d)}[/tex]Verify for each option
1) For c=2 and d=2
substitute
[tex]undefined[/tex]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°
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
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 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
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]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
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.
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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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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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
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
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
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:
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.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
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
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]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
Pls Pls Pls can you pls tell me what the parent function is?
The parent function of the given graph is y = |x| .
Let us consider finding the equation of the given graph.
the graph of the function is from the vertex is translated to the right by 2 units and the graph is translated downwards by 5 units.
So the graph of the function is : y = |x-2| - 5
The parent function of the graph will be y=|x| which is the basis of the given graph.
The absolute value of a number or variable is determined by a modulus function, which is defined. It produces the variable count's size. It is also known as an absolute value function. Whatever input was given to this function, the results are always positive.
Y = |x| is the formula. Similar to other simple processes, plotting these graphs involves defining the domain as all input values, such as x (all real numbers), and the range as all function values, such as y = f(x), which is equal to all input values and all positive real numbers other than 0.
Hence the parent function of the given graph is y = |x| .
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Which of the following is the graph of f(x) = |x+2|-3?
Answer:
Option D.
Explanation:
To know which is the correct graph, we need to replace one point of each graph and determine if the equation for f(x) is satisfied.
Then, for option A, point (-2, -1), we get:
f(x) = |x+2|-3
-1 = | -2 + 2| - 3
-1 = |0| - 3
-1 ≠ - 3
Since 1 and 3 are distinct, this is not the correct graph.
For option B, point (1, -2), we get:
f(x) = |x+2|-3
-2 = |1 + 2| - 3
-2 = |3| - 3
-2 ≠ 0
Since -2 and 1 are distinct, this is not the correct graph.
For option C, point (2, 3), we get:
f(x) = |x+2|-3
3 = |2 + 2| - 3
3 = |4| - 3
3 = 4 - 3
3 ≠ 1
Since 3 and 1 are distinct, this is not the correct graph.
For option D, point (-3, -2), we get:
f(x) = |x+2|-3
-2 = |-3 + 2| - 3
-2 = |-1| - 3
-2 = 1 - 3
-2 = -2
Therefore, option D is the correct answer.
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