The expression (xy)z can be simplified as;
[tex]\begin{gathered} (xy)z=xyz \\ \text{Therefore xyz;} \\ xyz=x(yz) \end{gathered}[/tex]The correct answer is option C
Deck PlanOutside* EdgeWall A10 feetDoorway13 feet-10 feetWall BThe deck will have the shape of one fourthof a circle. What is the best estimate of thearea (A) of this deck?(Area of circle = tr2)πr)(Use 3.14 for it.)
18) the best estimate will be 75 square feet (option G)
Explanation:18) radius = 10ft
let π = 3.14
We are told the deck will have 1/4 the area of a circle. We need to first find the area of a circle.
Area of circle = πr²
[tex]\begin{gathered} Area\text{ of circle = 3.14 }\times\text{ 10}^2 \\ Area\text{ of circle = 314 ft}^2 \end{gathered}[/tex]Next, we will divide the area by 4:
[tex]\begin{gathered} Area\text{ of the deck = }\frac{area\text{ of circle}}{4} \\ Area\text{ of the deck = }\frac{314}{4} \\ \\ Area\text{ of the deck = 78.5 ft}^2 \end{gathered}[/tex]From the options, the one close to the result we got is 75 square feet
Hence, the best estimate will be 75 square feet (option G)
A new statue in a local park has a length (L), width (W), and height (H) (all in feet) that can be expressed by a system of equations. L+W=28L+H=26W+H=22What is the width of the statue?
To determine the width of the statue:
[tex]\begin{gathered} L+W=28\ldots\ldots..(1) \\ L+H=26\ldots\ldots\ldots(11) \\ W+H=22\ldots\ldots..(111) \end{gathered}[/tex]A local park has a length (L), width (W), and height (H) (all in feet)
Solve equation 1 and 2 simultaneously,
[tex]\begin{gathered} L+W=28 \\ L+H=26 \\ \text{Subtract equation (1) - (11)} \\ W-H=2\ldots\ldots\ldots(IV) \end{gathered}[/tex]Solve equation 3 & 4 simultaneously, make W the subject of formular
[tex]\begin{gathered} W+H=22 \\ W-H=2 \\ \text{Add the two equation} \\ 2W=24 \\ \text{divide both side by 2} \\ \frac{2W}{2}=\frac{24}{2} \\ W=12 \end{gathered}[/tex]Therefore the value of width of the statue = 12 feet
Araceli filled a cone-shaped container with a variety of colored sand to give as a gift to a friend. The volume of a cone is represented by the expression below, where r is the radius of the base of the cone and h is the height of the cone.radius = 3 1/23 5/3 is the height
The volume of the cone is 45.28 cubic inches.
The amount of sand inside the cone is measured by its volume.
Based on the numbers for the radius and height, the cone's volume is 45.28 cubic inches.
The volume of a cone is the measure of how much space a cone takes up. Cone height and base radius both affect how much space the cone takes up.
The volume of the cone is given by V = [tex]\frac{1}{3}\pi r^{2} h[/tex]
The value of the radius is r = [tex]3\frac{1}{23} = \frac{70}{23}[/tex]
The value of Height is h = [tex]3\frac{5}{3} = \frac{14}{3}[/tex]
So, the Volume of the cone =[tex]V =\frac{1}{3}\pi r^{2} h[/tex]
[tex]V =\frac{1}{3}\pi r^{2} h\\\\V = \frac{1}{3}\pi (\frac{70}{23}) ^{2} \frac{14}{3} \\\\V = 45.28[/tex]
The volume of the cone is 45.28 cubic. inches
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A pizza is to be cut into halves. Each of these halves is to be cut into fourths. What fraction of the pizza is each of thefinal pieces?
Given:
Each of these halves is to be cut into fourths.
So:.
A pizza is to be cut into halves
since half is represented by 1/2.
So each piece is now
[tex]\frac{1}{2}\text{ of the original.}[/tex]If each of these halves is to be cut into fourths, then the fraction of final pieces is:
[tex]\begin{gathered} =\frac{1}{2}\times\frac{1}{4} \\ =\frac{1}{8} \end{gathered}[/tex]
Answer:
1/8
Step-by-step explanation:
Fractions
We have 1/2
!/2 is to be cut in 1/4
1/2 * 1/4 = 1/8
Determine weather it is a function, and state it’s domain and range.
Find the inverse of:
[tex]f(x)=(3x-24)^2[/tex]The variable x can take any real value and the function f(x) exists. This means
the domain of f(x) is (-∞, +∞).
Now find the inverse function.
[tex]\begin{gathered} y=(3x-24)^2 \\ \pm\sqrt[]{y}=3x-24 \\ \pm\sqrt[]{y}+24=3x \\ x=\frac{\pm\sqrt[]{y}+24}{3} \\ x=\pm\frac{1}{3}\sqrt[]{y}+8 \end{gathered}[/tex]Swapping letters, we get the inverse function:
[tex]y=\pm\frac{1}{3}\sqrt[]{x}+8[/tex]For each value of x, we get two values of y, thus this is not a function.
The domain of the inverse is restricted to values of x that make the square root exist, thus the domain is x ≥ 0, or [0, +∞)
The range of the inverse is the domain of the original function, that is, (-∞, +∞)
Function: No
Domain: [0, +∞)
Range: (-∞, +∞)
The choice to select is shown below.
100 POINTS AND BRAINLY FOR THE CORRECT ONLY ANSWER IF U UNDERSTAND THE QUESTION!
A line includes the points (10,6) and (2,7). What is its equation in point-slope form?
Use one of the specified points in your equation. Write your answer using integers, proper fractions, and improper fractions. Simplify all fractions.
PLEASE AND THANK U
Answer:
[tex]y-6=-\dfrac{1}{8}(x-10)[/tex]
Step-by-step explanation:
To find the equation of a line that passes through two points, first find its slope by substituting the given points into the slope formula.
Define the points:
(x₁, y₁) = (10, 6)(x₂, y₂) = (2, 7)Substitute the points into the slope formula:
[tex]\implies m=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-6}{2-10}=\dfrac{1}{-8}=-\dfrac{1}{8}[/tex]
Therefore, the slope of the line is -¹/₈.
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
To find the equation in point-slope form, simply substitute the found slope and one of the given points into the point-slope formula:
[tex]\implies y-6=-\dfrac{1}{8}(x-10)[/tex]
The confidence interval on estimating the heights of the students is given as (5.5, 6.5). Find the sample proportion of the confidence interval.
Answer:
Step-by-step explanation:
Why would a person pay property taxes?
An example of an experiment that leads to a uniform probability distribution is...Choose one answer. 1. the sum of rolling two dice 2. measuring the heights of all the students in a school 3. tossing a coin ten times and recording the number of heads 4. selecting a card from a deck of 52 cards
Solution
A probability distribution in which all of the values of the random variable occur with equal probability is called a uniform probability distribution. Describe an example of an experiment that would produce a uniform distribution. Then find the theoretical probabilities that would result from this experiment. Include a table and graph of the distribution.
Answer:
The theoretical probability experiment of rolling a die would result in a uniform distribution because the probabilities of rolling a 1,2,3,4,5,6 are all equally likely to occur.
Therefore the sum of rolling two dice is an option
Hence the correct answer is
Option 1
Isolate one radical on one side of the equation.Raise each side of the equation to a power equal to the index of the radical and simplify. Check all proposed solutions in the original equation.
The given equation is
[tex]\sqrt[]{3\text{ - 2x}}\text{ - 4x = 0}[/tex]The first step is to add 4x to both sides of the equation. We have
[tex]\begin{gathered} \sqrt[]{3\text{ - 2x}}\text{ - 4x + 4x = 0 + 4x} \\ \sqrt[]{3\text{ - 2x}}\text{ = 4x} \\ \text{Squaring both sides of the equation, we have} \\ (\sqrt[]{3-2x)}^2=(4x)^2 \\ 3-2x=16x^2 \end{gathered}[/tex]3 - 2x = 16x^2
Adding 2x to both sides of the equation, we have
3 - 2x + 2x = 16x^2 + 2x
3 = 16x^2 + 2x
Subtracting 3 from both sides of the equation, we have
3 - 3 = 16x^2 + 2x - 3
0 = 16x^2 + 2x - 3
16x^2 + 2x - 3 = 0
This is a quadratic equation. We would solve for x by applying the method of factorisation. The first step is to multiply the first and last terms. We have 16x^2 * - 3 = - 48x^2. We would find two terms such that their sum or difference is 2x and their product is - 48x^2. The terms are 8x and - 6x. By replacing 2x with with 8x - 6x in the equation, we have
16x^2 + 8x - 6x - 3 = 0
By factorising, we have
8x(2x + 1) - 3(2x + 1) = 0
Since 2x + 1 is common, we have
(2x + 1)(8x - 3) = 0
2x + 1 = 0 or 8x - 3 = 0
2x = - 1 or 8x = 3
x = - 1/2 or x = 3/8
We would substitute these values in the original equation to check. We have
[tex]\begin{gathered} For\text{ x = }-\text{ }\frac{1}{2} \\ \sqrt[]{3\text{ - 2}\times-\frac{1}{2}}\text{ - 4}\times-\text{ }\frac{1}{2}\text{ = 0} \\ \sqrt[]{3\text{ - - 1}}\text{ + 2 = 0} \\ \sqrt[]{4}\text{ + 2 = 0} \\ 2\text{ + 2 }\ne0 \end{gathered}[/tex][tex]\begin{gathered} \text{For x = }\frac{3}{8} \\ \sqrt[]{3\text{ - 2}\times\frac{3}{8}}\text{ - 4}\times\frac{3}{8}\text{ = 0} \\ \sqrt[]{3\text{ - }\frac{3}{4}}\text{ - }\frac{3}{2}=\text{ 0} \\ \sqrt[]{\frac{9}{4}}\text{ - }\frac{3}{2}\text{ = 0} \\ \frac{3}{2}\text{ - }\frac{3}{2}\text{ = 0} \end{gathered}[/tex]The solution is x = 3/8
Suppose that y varies inversely with x, and y = 5/4 when x = 16.(a) Write an inverse variation equation that relates x and y.Equation: (b) Find y when x = 4.y =
In general, an inverse variation relation has the form shown below
[tex]\begin{gathered} y=\frac{k}{x} \\ k\to\text{ constant} \end{gathered}[/tex]It is given that x=16, then y=5/4; thus,
[tex]\begin{gathered} \frac{5}{4}=\frac{k}{16} \\ \Rightarrow k=\frac{5}{4}\cdot16 \\ \Rightarrow k=20 \end{gathered}[/tex]Therefore, the equation is y=20/x
[tex]\Rightarrow y=\frac{20}{x}[/tex]2) Set x=4 in the equation above; then
[tex]\begin{gathered} x=4 \\ \Rightarrow y=\frac{20}{4}=5 \\ \Rightarrow y=5 \end{gathered}[/tex]When x=4, y=5.
Given the formula for the perimeter of a rectangle, p=2l+2wwhich answer would you get if you solve for l? p−2w 2 p/w-2 p/2−2w p−2l/2
If we have:
[tex]p=2w+2l[/tex]To solve for l we can start by inverting the sides and substracting 2w from both sides so that the term with l becomes alone in the left side:
[tex]\begin{gathered} p=2w+2l \\ 2w+2l=p \\ 2w-2w+2l=p-2w \\ 2l=p-2w \end{gathered}[/tex]Now, we can divide both sides by 2 so thay the 2 in 2l gets canceled:
[tex]\begin{gathered} 2l=p-2w \\ \frac{2l}{2}=\frac{p-2w}{2} \\ l=\frac{p-2w}{2} \end{gathered}[/tex]So, the answer we would get is
[tex]\frac{p-2w}{2}[/tex]if 3x +6 = 18 what is 10x -2
38
1) Starting from the first equation
3x +6 = 18 Subtract 6 from both sides
3x = 18 -6
3x = 12 Divide both sides by 3
x =4
2) Since x =4, let's plug that into the second expression 10x -2 to find out "what is 10x -2"
10x -2 Replace x, by 4
10(4) -2 Effectuate the multiplication
40 -2
38
Hence, the answer is 38
Factor the following polynomials completely.(x + y)³ + 1 =
Given the equation (x + y)³ + 1 , we can assume we have two terms here. These are (x + y)³ and 1. Since both terms are perfect cubes, we can use the sum of cubes formula which is:
[tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex]where a = (x+y) and b = 1.
Therefore, the factors of (x + y)³ + 1 is:
[tex]\begin{gathered} \mleft(x+y\mright)^3+1=(x+y+1)\lbrack(x+y)^2-(x+y)(1)+1^2) \\ (x+y)^3+1=(x+y+1)(x^2+2xy+y^2-x-y+1) \end{gathered}[/tex]The factor of (x + y)³ + 1 is (x + y + 1)(x² + 2xy + y² - x - y +1).
Use the definition of the derivative to find the derivative of the function with respect to x. Show steps
The derivative of the function y = -1/x-2 is 1/(x-2)².
Given, the function is y = -1/x-2
Differentiate the function with respect to x.
dy/dx = d/dx (-1/x-2)
the function is in the form of :
d/dx [f(x)g(x)] = f(x)d/dx((x)) + g(x)d/dx(f(x))
here d/dx [f(x)g(x)] = d/dx [(-1)(1/x-2)]
therefore, d/dx [(-1)(1/x-2)] = (-1)d/dx(1/x-2) +(1/x-2)d/dx(-1)
⇒ d/dx [(-1)(1/x-2)] = (-1)(-1)(x-2)⁻¹⁻¹ + (1/x-2)d/dx(0)
⇒ d/dx [(-1)(1/x-2)] = 1(x-2)⁻² + 0
⇒ d/dx [(-1)(1/x-2)] = 1/(x-2)²
Hence the derivative of the function is 1/(x-2)²
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Exponential Regression
The table below shows the population, P. (in thousands) of a town after 12 years.
0
72
P 2400
3
2801.27
7
3608.71
12
14
4974.15 5426.17
19
6898.37
(a) Use your calculator to determine the exponential regression equation P that models the set of
data above. Round the value of a to two decimal places and round the value of b to three decimal
places. Use the indicated variables.
P =
(b) Based on the regression model, what is the percent increase per year?
96
(c) Use your regression model to find P when n = 13. Round your answer to two decimal places.
The population of the town after
P =
thousand people
(d) Interpret your answer by completing the following sentence.
years is
thousand people.
Considering the given table, it is found that:
a. The exponential regression equation is: P(t) = 2408.80(1.059)^t.
b. The yearly percent increase is of 5.9%.
c. P(13) = 5075.
d. The population of the town after 13 years is of 5075.
How to find the exponential regression equation?The exponential regression equation is found inserting the points into a calculator.
The points are given as follows:
(0, 2400), (3, 2801.27), (7, 3608.71), (12, 4974.15), (14, 5426.17), (19, 6898.37).
Using a calculator, the function is:
2408.80(1.059)^t.
The yearly percent increase rate is calculated as follows:
1 + r = 1.059
r = 1.059 - 1
r = 0.059
r = 5.9%.
Then in 13 years, the population will be given as follows:
P(13) = 2408.80(1.059)^13 = 5075.
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Find area and perimeter of the shape identify the shape
Part A
The dimensions of the shape shown are given as
length, l = 12 in
breadth (b) = width, w = 4 in
The area of the shape is given as;
[tex]\begin{gathered} A=l\times b \\ A=12\times4 \\ A=48in^2 \end{gathered}[/tex]Therefore, the area of the shape is 48 square inches.
Part B
The perimeter of a shape is the sum of all the outer sides enclosing the shape
From the above shape, we add all four sides together
[tex]\begin{gathered} P=12+12+4+4 \\ P=32in \end{gathered}[/tex]Consequently, we can get the perimeter using formula method as well
[tex]\begin{gathered} P=2(l+b) \\ P=2(12+4) \\ P=2(16) \\ P=2\times16 \\ P=32in \end{gathered}[/tex]Therefore, the perimeter of the shape is 32 inches.
Part C
From the dimension given in the question, since the shape has a length and width, and the length and width are not equal, then the shape is a rectangle.
The shape, therefore, is a rectangle.
how do i use a graphing calculator to solve the system.
Given:
[tex]\begin{gathered} 0.4x\text{ + }\sqrt{2}y\text{ = 1} \\ \sqrt{5}\text{ x + 0.8y = 1} \end{gathered}[/tex]Using a graphing calculator, we have the graph shown below:
The point of intersection of the equations represents the solution to the system.
Hence, the solution to the system is:
x = 0.216
y = 0.646
What is the factor 24/28 in simplest form
Answer:
6/7
Step-by-step explanation:
24/28 they both are commonly divisible by 4,
making them 6/7
Solve the inequality and write the solution using:
Inequality Notation:
The answer of the given inequality is x < 16
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequality expression is ,
(1 * x) /4 < 4 or x/4 < 4
=> x < 4 * 4
=> x < 16
Therefore, the answer is x < 16.
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A batting cage charges a flat fee of $5 to practice and th Write an equation that models the charges (C) in terms of the number of bucket balls (b) that you use: O C = 1.50 b + 5 O C = 5 b + 1.50 6 Ob = 1.60 C + 5 Ob = 5 C + 1.50
we have
C -----> total charge
b -----> number of buckets of balls
Remmeber that
the equation of the line in slope intercept form is equal to
y=mx+b
where
m is the slope and b is the initial value or y-intercept
In this problem
m=$1.50 per buckey
b=$5
therefore
y=1.50x+5
or
C=1.50b+5
answer is first optionplease help me work through this homework problem! thank you!
Given:
Given the function
[tex]y=3+\frac{3}{x}+\frac{2}{x^2}[/tex]and a point x = 3.
Required: Equation of the line tangent to y at x = 3.
Explanation:
The derivative of a function is he slope of the tangent line of the function at a given point. So, finding the derivative gives the slope of the tangent line.
[tex]y^{\prime}=-\frac{3}{x^2}-\frac{4}{x^3}[/tex]Substitute 3 for x into the derivative.
[tex]\begin{gathered} y^{\prime}|_{x=3}=-\frac{3}{3^2}-\frac{4}{3^3} \\ =-\frac{31}{27} \end{gathered}[/tex]Therefore, the slope of the tangent line is -31/27.
Substitute 3 for x into y.
[tex]\begin{gathered} y|_{x=3}=3+\frac{3}{3}+\frac{2}{3^2} \\ =3+1+\frac{2}{9} \\ =4+\frac{2}{9} \\ =\frac{38}{9} \end{gathered}[/tex](3, 38/9) is the only point on the tangent line where it intersects the original graph.
Plug these coordinates along with slope into the general point-slope form to find the equation.
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-\frac{38}{9}=-\frac{31}{27}(x-3) \end{gathered}[/tex]Solving for y will give the equation in slope-intercept form.
[tex]\begin{gathered} y=-\frac{31}{27}(x-3)+\frac{38}{9} \\ =-\frac{31}{27}x+\frac{69}{9} \end{gathered}[/tex]Final Answer: The equation of the tangent line is
[tex]y=-\frac{31}{27}x+\frac{69}{9}[/tex]
Use the words to complete the sentences :1) Downards,2) 15,3) Ascending,4) does,5) upwards,6) Positive,7) Does not,8) Negative,9) Descending,10) 16,11) 3, 12) 3.51) The Graph a plane -----. 2) The line is slanting ------- and therefore has a ------ slope.3) It takes the plane ------ seconds to touch the ground.4) The plane starts at ------- kilometers in the sky .5) Graph ------ touch the origin (0, 0) .
According to the given graph, we have the following:
1) The graph represents a plane descending.
2) The line is slanting downwards and therefore has a negative slope.
3) It takes the plane 15 seconds to touch the ground.
4) The plane starts at 3 kilometers in the sky.
5) Graph does not touch the origin (0,0).
The given graph shows a decreasing line, starting at y = 3, and reaching y = 0 when x = 15.
help me please I love when I can get help
To determine in how many pices of 2/3ft can a 9ft long ribbon be cut, you have to divide 9 by 2/3:
[tex]9\div\frac{2}{3}[/tex]To divide both fractions, first turn the 9 into a fraction by adding 1 as a denominator
[tex]\frac{9}{1}\div\frac{2}{3}[/tex]Now you have to invert the fraction that is the denominator of the division
[tex]\frac{2}{3}\to\frac{3}{2}[/tex]And multiply it by the first fraction
[tex]\frac{9}{1}\cdot\frac{3}{2}=\frac{9\cdot3}{1\cdot2}=\frac{27}{2}\cong13.5[/tex]She can divide the ribbon in 13 pieces of 2/3ft each
Kayla has $37.99 in her checking account. she uses her debit card to make purchases of $26.29 and $22.98 which overdraws her account. her bank charges her account an overdraft fee of $25.00. She then deposits her paycheck for $55.07 from her part time job. what is the balance in her account?
Aye itz just me, this is the solution:
Initial balance = $ 37.99
Purchase 1 = ($ 26.29)
Purchase 2 = ($ 22.98)
Overdraft fee = ($ 25.00)
Deposit = $ 55.07
______________________
New balance = 37.99 - 26.29 - 22.98 - 25 + 55.07
New balance = $ 18.82
ABCD is a parallelogram
BE= 6x+44
ED= -6x-16
Find the length of BD
The line segment BD has a length of 18 units
How to calculate the length of BD?The possible figure is added as an attachment
From the question, we have the following parameters:
Name of shape = ABCDShape type = ParallelogramBE = 6x + 44ED = -6x - 16The lengths BE and ED implies that the point E is between the endpoints B and D
Since the shape is a parallelogram, then the point E is halfway between the endpoints B and D
So, we have
BE = ED
Substitute the known values in the above equation
6x + 44 = -6x - 16
Evaluate the like terms
So, we have
12x = -60
Divide both sides by 12
x = -5
Substitute x = -5 in BE = 6x + 44
So, we have
BE = 6 x -5 + 44
Evaluate
BE = 14
The length is then calculated as
BD = 2 x BE
So, we have
BD = 2 x 14
Evaluate
BD = 18 units
Hence, the length of BD is 18 units
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6 minus 3 times a number is less than 30. Find the number:
x > -8
Explanations:Let the number be represented by x:
Three times the number = 3x
Six minus three times the number = 6 - 3x
Six minus three times the number is less than 30:
That can be interpreted mathematically as:
6 - 3x < 30
To find the value of x:
Step 1: Collect like terms
- 3x < 30 - 6
-3x < 24
Step 2: Divide both sides by 3:
[tex]\frac{-3x}{3}=\text{ }\frac{24}{3}[/tex]-x < 8
Multiply both sides by (-1) and change the < sign to >
(-1) (-x) > 8 x(-1)
x > -8
I need to explain the mistake he made and show my work and I need the answer
The problem is;
-2(x-1) - 2 > 8 - 5x +4+ x
open the parenthesis
-2x + 2 -2 > 8- 5x + 4+ x
collect the like-term
-2x+5x-x > 8+4
2x > 12
divide both-side of the inequality by 2
x>6
The first mistake that was made is adding of the x-variables
It is 2x and not -6x
1 pointThe 5 consecutive integers below add up to 175. What is the value of x?x-3x-2X - 1ХX + 1
Then x=36.
Jenna bought a package of 2 chicken drumsticks. If the package weighed 0.232 kg, what is the average weight of
each drumstick?
Answer:
0.116
Step-by-step explanation:
[tex]\frac{0.232}{2}[/tex] = 0.116