Answer:
The cost of putting in the flooring is $493.20
Step-by-step explanation:
First you have to find the area
area = length times width
area = 5 x 18
a = 90 feet
The cost will be 90 x 5.48 = 493.20
Helping in the name of Jesus.
4.02 Lesson check ! (9)
Hence, in response to the provided question, we can say that As a result, arithmetic progression the usual difference is d = -30.
what is arithmetic progression?The difference between subsequent terms in a string will never vary, and this is referred like an arithmetic progression. The sequences 5, 7, 9, 11, 13, through 15 are examples of arithmetic progressions with a tolerance of 2. Arithmetic progression (A.P.) is a progression that has a set tolerance between any 2 consecutive values. Numerical progression may fall into one of two main types: finite-length arithmetic series A finite geometry progression is a series with just a fixed number of terms. The series' terms can be used to calculate the early, late, leniency, and number of term.
A) The sequence is, indeed, arithmetic.
We can find the common difference by subtracting any two consecutive terms:
109 - 9 = 100
209 - 109 = 100
309 - 209 = 100
As a result, the typical difference is d = 100.
A) The sequence is, indeed, arithmetic.
We can find the common difference by subtracting any two consecutive terms:
-32 - (-2) = -30 \s-62 - (-32) = -30 \s-92 - (-62) = -30
As a result, the usual difference is d = -30.
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When customers buy a book from an online bookstore,
they pay a $6 shipping fee in addition to the cost of the
book.
The total cost is the book price plus $6.
Let x=book price
Let y = total cost
Which equation represents the situation?
A. y = 6x
B. y=x+6
C. y =
D. y=x-6
The equation that represents the situation is y = x + 6.
What is equations ?An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides separated by an equal sign (=) and can involve numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
According to given information :The equation that represents the situation is B. y = x + 6.
The problem states that the total cost, y, is the book price, x, plus a $6 shipping fee. We can express this as:
y = x + 6
Option A, y = 6x, suggests that the total cost is only determined by the book price multiplied by 6, which is not what the problem states.
Option C, y = , is not a valid equation as it does not include any terms to determine the value of y.
Option D, y = x - 6, suggests that the total cost is the book price minus $6, which is not what the problem states either.
Therefore, the equation that represents the situation is y = x + 6.
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A shop owner had three boxes, containing a total of 1500 plastic cups. The number of plastic cups in Box A to the total number of plastic cups was 3:10. He sold 330 plastic cups from Box B and sold 1/3 of the plastic cups in Box C. The number of plastic cups left in Box B to the number of plastic cups left in Box C was 3:1. How many plastic cups were there in Box B at first?
The initial number of cups in Box B at first is given as follows:
810 cups.
How to obtain the initial number of cups?The initial number of cups in box B is obtained solving a system of equations, for which the variables A, B and C represents the amounts of each box.
A shop owner had three boxes, containing a total of 1500 plastic cups. The number of plastic cups in Box A to the total number of plastic cups was 3:10, hence the initial amount of Box A is given as follows:
0.3 x 1500 = 450 cups.
Then:
B + C = 1500 - 450
B + C = 1050.
He sold 330 plastic cups from Box B and sold 1/3 of the plastic cups in = Box C. The number of plastic cups left in Box B to the number of plastic cups left in Box C was 3:1, hence:
(B - 330)/(2C/3) = 3
B - 330 = 2C
C = 0.5B - 165
Replacing into B + C = 1050, the value of B is given as follows:
B + 0.5B - 165 = 1050
B = 1215/1.5
B = 810.
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Please Help!!!!!
Type the inverse of the matrix. Use decimals. If no inverse exists type "none".
In response to the question, we may say that Therefore, the inverse of the given matrix is: [ 0.0 1.5 -1.0 ], [ 1.0 -2.0 2.0 ] and [-1.0 1.5 -2.0 ]
what is matrix?An arrangement of integers in rows and columns is known as a matrix. learns about matrices' components and dimensions and first presents them. A matrix is a rectangular grid with integers arranged in rows and columns. For example, Matrix A contains two rows and three columns. The origin of its moniker is due to its single row and 1 n row matrix arrangement. For example, a row matrix of order 1 by 4 is A = [1 2 4 5]. The row matrix P = [-4 -21 -17] of order 1-by-cubic is another example.
Let's begin by calculating the determinant of the matrix:
[tex]det(A) = 1(41 - 30) - 2(40 - 20) + 3(10 - 21)\\det(A) = 4 - 0 - 6\\det(A) = -2\\[/tex]
Since the determinant is not zero, an inverse exists. Let's find the adjugate matrix:
[tex]adj(A) = [dof(A)]^T\\[/tex]
where dof(A) is the matrix of cofactors of A.
[tex]dof(A) = [(-1)^(1+1)0, (-1)^(1+2)2, (-1)^(1+3)(-2),\\(-1)^(2+1)(-3), (-1)^(2+2)4, (-1)^(2+3)(-3),\\(-1)^(3+1)2, (-1)^(3+2)(-4), (-1)^(3+3)*4]\\dof(A) = [0, -2, 2, 3, 4, -3, 2, -4, 4]\\[/tex]
Therefore,
[tex]adj(A) = [0 -3 2; -2 4 -4; 2 -3 4]\\[/tex]
Finally, we can find the inverse matrix by multiplying the adjugate matrix by the reciprocal of the determinant:
[tex]A^(-1) = (1/det(A)) * adj(A)\\A^(-1) = (-1/2) * [0 -3 2; -2 4 -4; 2 -3 4]\\A^(-1) = [0.0 1.5 -1.0; 1.0 -2.0 2.0; -1.0 1.5 -2.0]\\[/tex]
Therefore, the inverse of the given matrix is:
[ 0.0 1.5 -1.0 ]
[ 1.0 -2.0 2.0 ]
[-1.0 1.5 -2.0 ]
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Answer
[ 1.25 -0.75
-0.5 0.5 ]
Step-by-step explanation:
what is (3-4i)+(3+4i)
Answer:
6
Step-by-step explanation:
.
Answer:
6
Step-by-step explanation:
look above
The ministry of health was interested in the relationship between office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 555 years they gathered and analyzed the entire data
The data collected by the ministry of health denotes C) Observational Study
The degree of movement along or opposite that may occur in one of the data values when another data value is increased or lowered, respectively, is shown by the correlation of two pairs of data values. An observational study selects participants from a sample of the community, but the independent variable is not controlled due to moral considerations, outside influence, and occasionally, restrictions.
To gather data on office employment and worker health concerns, the health ministry only provides questionnaires to employees every five years. They are only keeping an eye on the employees, and the survey enables them to evaluate and draw a connection between working in an office and health issues among employees. This makes the study an observational one.
Complete Question:
The ministry of health was interested in the relationship between the office habits of workers and health issues. Each year, they distributed a survey to all workers in the public sector that contained various questions on work habits as well as a standard health questionnaire. After 5 years they gathered and analyzed the entire data.
A) Sample study
B)Experiment
C) Observational Study
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350=(4/3)πr2^2
Find r
Answer:
see below
Step-by-step explanation:
350=[tex]\frac{4}{3}[/tex][tex]\pi[/tex]r[tex]2^{2}[/tex]
^ is this correct. i will edit my answer to be the solution.
if a = 2.4 units, b = 4 units, c = 6 units, and d = 8 units, what is the volume of the figure above?
A) 162.56
B) 111.36
C) 256
D) 130.56
I neeeeeed help, this is due tomorrow!!!!
10 points to whoever gives the correct answer!
Sphere A has a radius of 2 cm. Sphere B has a radius of 4 cm.he radius of Sphere B is doubled that of sphere A. How many times greater is the volume of B? times
Volume of Sphere B is 8 times greater than the volume of Sphere A
What does sphere refer to?
A sphere is symmetrical and round in form. All of its surface points are equally spaced from the centre, making it a three-dimensional solid. Depending on the radius, it has a surface area and a volume. No faces, corners, or edges exist on it.
It is sometimes referred to as the second cousin of a circle, the sphere is a three-dimensional form. Round, without boundaries, and solid in shape, a sphere is spherical. Examples of spherical shapes include a playing ball, a balloon, and even light bulbs.
Sphere A: V = 4π (2³)/3 = 32π/3
Sphere B: V = 4π (4³)/3 = 4π(64)/3 = 256π/3
volume of Sphere B / volume of Sphere A = (256π/3)/(32π/3) = 8
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true/false. the basic calculation for obtaining a response bias is to the number of legitimately completed questionnaires returned divided by the total number of sample members provided a chance to participate.
The statement "The basic calculation for obtaining a response bias is not to divide the number of legitimately completed questionnaires returned by the total number of sample members provided a chance to participate." is False
Instead, the basic calculation for obtaining a response bias is to subtract the response rate from 100%. The response rate is calculated by dividing the number of legitimately completed questionnaires returned by the total number of sample members provided a chance to participate.
So, the formula for calculating response bias is:
Response bias = 100% - (number of legitimately completed questionnaires returned / total number of sample members provided a chance to participate)
In other words, response bias is the percentage of sample members who did not participate or did not complete the questionnaire legitimately. It is important to calculate response bias in order to understand how representative the sample is of the population.
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Write in expanded form
Alex had an income of $7,000. He got 9% of his income from tips. How much of his income
was not from tips?
well, Not from tips that'd be 100% - 9% = 91%, so 91% of $7000.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{91\% of 7000}}{\left( \cfrac{91}{100} \right)7000}\implies \text{\LARGE 6370}[/tex]
On a map, two cities are 2.8 inches apart. The map has a scale of 1 inch to 25 miles. How far apart, in inches, would the same two citites on a map that has a scale oof 1 inch to 40 miles
The distance on the map where the scale is 1 inch to 40 miles is 1.75 inches.
How far will be the two cities on the other map?First we know that the cities are at 2.8 inches apart on a map whose scale is 1 inch to 25 miles, then the real distance between the two cities is:
[tex]D = (2.8)\times25\text{mi}= 70 \ \text{mi}[/tex]
Now we move to a map where each inch is 40 miles, to find the distance in inches, we can take the quotient between the real distance and the scale, it gives:
[tex]D = (\dfrac{70\text{mi}}{40\text{mi}} ) \ \text{inches}[/tex]
[tex]D = 1.75 \ \text{inches}[/tex]
The distance on the other map is 1.75 inches.
Tammy’s water bill is automatically deducting $160 from her bank account every other month. How
much will the deductions total for two years?
Step-by-step explanation:
Every-other-month for two years ( 24 months) is 12 deductions
12 * $ 160 = $ 1920
Three students are comparing how fast their social media posts spread the results are on the table.
1. Write an exponential function to represent the spread of Ben's social media post.
2. Write an exponential function to represent the spread of Carter's social media post.
3. Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
4. Using the functions for each student, predict how many shares each student's post
will be received on Day 3 and then on Day 10. Justify your answers.
5. If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of
Amber's photo share?
6. Based on your results, which students' post travels the fastest? How is this shown
in the equation form of the functions?
7. If you had to choose, would you prefer a post with fewer friends initially but more
shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from
previous questions.
The spread of Carter's social media post is f(x) = 3(3)x. On Day 3, Ben's post will be received 8 shares and Carter's post will be received 27 shares. On Day 10, Ben's post will be received 524 shares and Carter's post will be received 729 shares.
What is exponential function?Amber's new function of f(x) = 3(4)x + 45 will produce a graph with a steeper slope than the original graph of Amber's photo share. Carter's post travels the fastest, as his equation form has the highest exponential rate. Depending on the goal of the post, one might prefer a post with fewer friends initially but more shares, such as Amber, or more friends initially but fewer shares, such as Ben.
Exponential function is a mathematical function that increases or decreases exponentially. It is an equation of the form y = ax^b, where a is the base and b is the exponent, and x is the independent variable.
1. The exponential function to represent the spread of Ben’s social media post is f(x) = 3(2)x.
2. The exponential function to represent the spread of Carter’s social media post is f(x) = 3(3)x.
3. The graph of Ben’s post will have a curve that increases exponentially as the x-values increase, while the graph of Carter’s post will have a curve that increases exponentially faster than Ben’s as the x-values increase. Three points that can be used to graph each curve are (0, 3), (1, 9), and (2, 27) for Ben’s post and (0, 3), (1, 9), and (2, 27) for Carter’s post.
4. On Day 3, Ben’s post will have 81 shares (f(3) = 3(2^3) = 81), and Carter’s post will have 243 shares (f(3) = 3(3^3) = 243). On Day 10, Ben’s post will have 59049 shares (f(10) = 3(2^10) = 59049), and Carter’s post will have 59049 shares (f(10) = 3(3^10) = 59049). This is shown in the equation form of the functions because each function is in the form of a(b^x). For Ben’s post, a = 3, b = 2, and for Carter’s post, a = 3, b = 3. As the x-values increase, the value of b increases exponentially and so the total number of shares increases exponentially.
5. Amber’s new function representing her photo shares is f(x) = 3(4)x + 45. The graph of this function will be different from the original graph of Amber’s photo share because it is no longer an exponential function - it is a linear function. The graph will have a constant rate of increase as the x-values increase, reflecting that the number of shares is increasing by a constant number with each additional day.
6. Based on the results, Carter’s post travels the fastest. This is shown in the equation form of the functions because Carter’s post has a larger value of b (3) than Ben’s post (2), indicating that Carter’s post is increasing exponentially faster than Ben’s post.
7. It would depend on the situation, but generally speaking it would be preferable to have more friends initially and fewer shares, like Amber. This is because if a post has few friends initially and more shares, the post will spread faster, but there is no guarantee that the post will continue to spread after it reaches its peak. If a post has more friends initially and fewer shares, the post will spread more slowly, but it is more likely to continue to spread for a longer period of time.
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The amount of shore at a local beach changes an average of -3/4 foot each year. What is the change in the amount of shore after 7 years and 4 months ( 7 1/3)
The change in the amount of shore after 7 years and 4 months is -5.4975 feet.
First, let us convert the values into the same quantities
7 1/3 years = 7 + 1/3 years = 7.33 years
The change in shore after 7 years and 4 months can be calculated as
Change in amount of shore = (average change per year) x (number of years)
Change in amount of shore = (-3/4 foot/year) x (7.33 years)
Change in amount of shore = -5.4975 feet.
Therefore, the change in the amount of shore after 7 years and 4 months is approximately -5.4975 feet.
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The school library has 35 biology books, 17 chemistry books, and 33 physics books. What is the ratio of chemistry books to the number of books in the library written in the simplest form
Answer:
17:85
Step-by-step explanation:
Muffy ordered 3 muffins and 2 lattes for $7. Sammy ordered 4 muffins and a latte for $6. Create a system of equations.
The system of equations created from the statements is 3m + 2l = 7 and 4m + l = 6
Creating the system of equations. Let's define the variables:
m = cost of one muffinl = cost of one latteUsing these variables, we can create the following system of equations to represent the given information:
Equation 1: 3m + 2l = 7
Muffy ordered 3 muffins and 2 lattes for $7.
Equation 2: 4m + l = 6
Sammy ordered 4 muffins and a latte for $6.
Hence, the system is 3m + 2l = 7 and 4m + l = 6
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Can someone help with this fast!?!
Solve the equation 2(4x - 1) = -10(x - 3) + 4. Show each step in the solving process separately, please. Also in order what would this be in like properties wise? Been trying to get better at this I just need a little help so I can get better.
Answer:
x=2
Step-by-step explanation:
2(4x - 1) = -10(x - 3) + 4
First, we distribute the 2 on the left side and -10 on the right side using the distributive property of equality:
8x - 2 = -10x + 30 + 4
Next, we combine like terms on the right side:
8x - 2 = -10x + 34
We add 10x to both sides using the addition property of equality:
8x - 2 + 10x = -10x + 34 + 10x
Simplifying:
18x - 2 = 34
We add 2 to both sides:
18x - 2 + 2 = 34 + 2
Simplifying:
18x = 36
Finally, we divide both sides by 18:
18x / 18 = 36 / 18
Simplifying:
x = 2
In each step, we used a different property of equality:
Distributive property of equalityCombining like termsAddition property of equalitySimplifyingAddition property of equalitySimplifyingDivision property of equalityPlease hit brainliest if this helped! Comment if you have a question.
At a scout jamboree, dinner is served from tinned food. each tin of soup is shared between 2 scouts. each tin of frankfurters is shared between 3 scouts and each tin of fruit is shared between 4 scouts. if 117 tins are opened to feed all the scouts, how many scouts attended the jamboree
By answering the above question, we may state that As a result, there equation were 108 scouts who attended the jamboree.
What is equation?A math equation is a mechanism for connecting two claims by using the equals sign (=) to indicate equivalence. A mathematical statement that establishes the equivalence of two mathematical expressions is known as an equation in algebra. The equal symbol, for example, splits the numbers 3x + 5 and 14. A mathematical formula can be used to describe the relationship between two phrases written on opposite sides of a letter. The logo and programme are frequently the same. 2x - 4 Equals 2, for example.
Because each tin is divided by four scouts, the number of fruit tins necessary will be one-fourth of the number of scouts. As a result, the quantity of tins of fruit required is x/4.
The total number of tins opened, according to the query, is 117. Based on the preceding data, we can construct the following equation:
x/2 + x/3 + x/4 = 117
To remove the denominators, multiply both sides by 12 (the LCM of 2, 3, and 4).
6x + 4x + 3x = 1404
When we simplify, we get:
13x = 1404
By multiplying both sides by 13, we get:
x = 108
As a result, there were 108 scouts who attended the jamboree.
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A rectangle has a height of 555 and a width of 4x^2-2x-64x
2
−2x−64, x, squared, minus, 2, x, minus, 6.
Express the area of the entire rectangle.
Expression should be expanded.
The area of the entire rectangle is 20x^2 - 10x - 30
How to determine the area of the entire rectangleFrom the question, we have the following parameters that can be used in our computation:
Height = 5
Width = 4x^2 - 2x - 6
Using the above as a guide, we have the following:
The area of a rectangle is the product of its dimension
So, we have
Area = Height * Width
Substitute the known values in the above equation, so, we have the following representation
Area = 5 * (4x^2 - 2x - 6)
Evaluate
Area = 20x^2 - 10x - 30
Hence, the area is 20x^2 - 10x - 30
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Point P has coordinates (3, -4). If P is reflected across the x-axis, what are the coordinates of the P'
In response to the query, we can state that Hence, P"s coordinates are coordinates (3, 4).
what are coordinates?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
A point's y-coordinate changes sign when it is reflected across the x-axis, but its x-coordinate stays the same.
Hence, we must modify the sign of the y-coordinate while leaving the x-coordinate unaffected in order to reflect point P(3,-4) across the x-axis. The reflected point P' will therefore have coordinates (3, 4).
Hence, P"s coordinates are (3, 4).
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let f(x)=6x-2 and g(x)=5x-kx+15. if k=3, what is the value of f(g(10))?
Answer:
We need to find the value of f(g(10)) when k = 3, where f(x) = 6x - 2 and g(x) = 5x - kx + 15.
First, we need to evaluate g(10) when k = 3:
g(x) = 5x - kx + 15
g(10) = 5(10) - 3(10) + 15
g(10) = 50 - 30 + 15
g(10) = 35
Now that we know g(10) = 35, we can evaluate f(g(10)):
f(x) = 6x - 2
f(g(10)) = 6(35) - 2
f(g(10)) = 208
Therefore, when k = 3, f(g(10)) = 208.
A car is stopped at a red light.when the light turns green,the car speed up to 80m/s in 5s.what is the acceleration of the car
Given
Required
Equation
solution
Answer
Answer:
Given:
Initial velocity, u = 0 (since the car is stopped)
Final velocity, v = 80 m/s
Time taken, t = 5 s
Required:
Acceleration, a
Equation:
We can use the following equation to calculate the acceleration:
a = (v - u) / t
where u is the initial velocity, v is the final velocity, and t is the time taken.
Solution:
Substituting the given values, we get:
a = (80 - 0) / 5
a = 16 m/s²
Answer:
The acceleration of the car is 16 m/s².
(^2 is just another version of ²)
Hope this helped! Sorry if it didn't. If you need more help, ask me! :]
n is an integer greater than 1
Prove algebraically that n²-2-(n-2)2 is always an even number.
Answer:
Starting with the expression n² - 2 - (n - 2)², we can simplify it by expanding the second term using the formula for the square of a binomial:
n² - 2 - (n - 2)² = n² - 2 - (n² - 4n + 4)
Next, we can combine like terms:
n² - 2 - (n² - 4n + 4) = n² - n² + 4n - 6
Simplifying further, we get:
n² - 2 - (n - 2)² = 4n - 6
To prove that this expression is always even, we can show that it can be written in the form 2k, where k is an integer.
So, let's rewrite the expression as:
4n - 6 = 2(2n - 3)
Since 2n - 3 is an integer (because n is an integer greater than 1), we have shown that 4n - 6 can be written in the form 2k, where k is an integer.
Therefore, we have proved algebraically that n² - 2 - (n - 2)² is always an even number.
Anyone know how to solve these both? Ik it’s a lot but I really need help bc I’m like super tired.
(please separate each question from each other so I can actually read it)
a. If Kayla runs on the inside she would run for about 400.96 meters
b. If Emi runs on the outer edge, in one lap, she would run for about 463.76 meters
c. The difference = 62.80 m
we have to find the perimeter of the outer edgeThis is = 200 + (2π * 42 / 2) + (2π * 42 / 2)
= 200 + 84 π
= 200 + 84 * 3.14
= 463.76 meters
Next we have to solve for the perimeter of the inside edge
200 + (2 π * 32 / 2) + (2 π * 32 / 2)
= 200 + 64π
= 400.96
The difference is given as 463.76 - 400.96
= 62.80 m
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I NEED HELP ON THIS ASAP! PLEASE HELP!! I WILL GIVE YOU BRAINLIEST!!
A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.
A graph of the system of inequalities is shown on the coordinate plane below.
How to write the required system of linear inequalities?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of HD Big View television produced in one day.Let the variable y represent the number of Mega Tele box television produced in one day.Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox television takes 3 person-hours to make, a linear equation to describe this situation is given by:
2x + 3y = 192.
Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;
x + y = 72
For the constraints, we have the following system of linear inequalities:
x ≥ 0.
y ≥ 0.
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A rental car company charges $37. 93 per day to rent a car and $0. 11 for every mile driven. Taylor wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $300 to spend.
Which inequality can be used to determine dd, the maximum number of days Taylor can afford to rent for while staying within her budget?
The inequality 5.5+37.93d ≤ 300 should be used to calculate the number of days.
The relationship between two non-equal expressions, denoted by a symbol such as 'not equal to, 'greater than' or 'less than' is known as inequality.
She drives 50 miles and per mile, it costs $0.11.
So, for 50 miles, cost = 50 x $0.11 = $5.5
and per day cost = $37.93
Thus, the inequality that must be used to calculate the number of days is
5.5+37.93d ≤ 300 .
the complete question is-
A rental car company charges $37.93 per day to rent a car and $0.11 for every mile driven. Taylor wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $300 to spend.
Which inequality can be used to determine dd, the maximum number of days Taylor can afford to rent for while staying within her budget?
5.5d + 37.93 ≥ 300
5.5 + 37.93d ≤300
5.5 + 37.93d ≥ 300
5.5d + 37.93 ≤ 300
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Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, –7). Which system of equations can be used to determine whether the paths of the boats cross?
StartLayout Enlarged Left-Brace 1st Row y = negative one-ninth (x minus 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = one-ninth (x + 8) squared + 1 2nd Row y = Negative one-eighth (x + 8) squared + 1 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative StartFraction 9 Over 49 EndFraction (x + 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative 17 (x minus 1) squared + 10 2nd Row y = 17 x squared minus 7 EndLayout
A system of equations can be used to determine whether the paths of the boats cross include the following:
A. y = -1/9(x - 1)² + 10.
y = 1/8x² - 7
How to determine the required system of equations?Based on the information provided about the first boat, the x-coordinate of the vertex can be determined as follows;
x = -b/2a
1 = -b/2a
b = -2a
Additionally, the standard form of the equation of a parabola (quadratic function) is given by;
y = a(x - h)² + k.
y = ax² - 2ax + c.
Therefore, the y-coordinate of the vertex is given by:
y = ax² - 2ax + c
10 = a(1)² - 2a(1) + c
c - a = 10 .......equation 1.
Since the parabola passes through the point (-8, 1), we have:
y = ax² - 2ax + c
1 = a(-8)² - 2a(-8) + c
80a + c = 1 .......equation 1.
Solving equations 1 and 2 simultaneously, we have:
81a = -9
a = -9/81 = -1/9
b = -2a = -2(-1/9) = 2/9
c = 10 + a = 10 - 1/9 = 89/9
Rewriting the equation for the first boat, we have:
y = -1/9x² + 2/9x + 89/9
y = -1/9(x - 1)² + 10.
For the second boat, the x-coordinate of the vertex can be determined as follows:
y = ax² + bx + c
x = -b/2a
0 = -b/2a
b = 0
Additionally, the y-coordinate of the vertex is given by:
y = ax² + c
-7 = a(0)² + c
c = -7
Since the parabola passes through the point (-8, 1), we have:
y = ax² + c
1 = a(-8)² - 7
a = -1/8
b = 0
c = -7
Rewriting the equation for the second boat, we have:
y = ax² + c
y = 1/8x² - 7
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Answer: A
Step-by-step explanation:
edge 2023
What is the area of a sector with a central angle of 30° and a radius of 12.5 cm?
Use 3.14 for pi and round your final answer to the nearest hundredth.
Enter your answer as a decimal in the box.
Therefore , the solution of the given problem of area comes out to be section has a size of about 164.07 square centimetres.
What exactly is area?Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.
Here,
The following algorithm determines a sector's area:
=> A = (θ/360°) * π * r²
where is the mathematical constant pi, r is the radius, and is the centre angle (approximately 3.14).
If we substitute the numbers provided, we get:
=> A = (30/360) * 3.14 * (12.5)^2
By condensing and computing, we arrive at:
=> A ≈ 164.06
To the closest hundredth, we have the following:
=> A ≈ 164.06 ≈ 164.07
Consequently, the section has a size of about 164.07 square centimetres.
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