According to the given information the formula for f(x) in term of x is f(x) = (4/5)x - 4.
What is a function, exactly?A function is a relationship between a number of inputs and outcomes. Simply described, a function is an association between inputs where each input is linked to exactly one output. There is a range, codomain, as well as domain for every function. A function is commonly referred to as f(x), where x is in fact the input.
How can a math function be identified?When looking at a graph, we use a procedure known as the Vertical Line Test to determine whether a function is indeed a function. Simply drawing a vertical line will reveal if the graph is a function if it touches it once.
4x - 5y = 20
Subtracting 4x from both sides
-5y = -4x + 20
Dividing 5 from the both sides
y = (4/5)x - 4
The formula for f(x) in terms of x is:
f(x) = (4/5)x - 4
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(8,12) and (x,9) where m = -1/2
Answer:
Step-by-step explanation:
The slope of a line between two points (x1, y1) and (x2, y2) is given by:
m = (y2 - y1) / (x2 - x1)
In this case, we are given that m = -1/2, so substituting in the two points we have:
-1/2 = (9 - 12) / (x - 8)
Expanding and simplifying the equation:
-1/2 = -3 / (x - 8)
Multiplying both sides by -2:
1 = 3 / (x - 8)
Multiplying both sides by (x - 8):
x - 8 = 3
Adding 8 to both sides:
x = 11
So the x-coordinate of the second point is x = 11.
Writing Find the length of the hypotenuse of the right triangle. Use pencil and paper. Explain how you can interpret the Pythagorean Theorem using the areas of squares.
Answer:
The length of the hypotenuse is 17.
Longitude and latitude can be easily calculated by observing the direction that the fish are swimming.
True
False
Answer:
False.
Step-by-step explanation:
Longitude and latitude are geographical coordinates used to determine the location of a place on the earth's surface. They are not easily calculated by observing the direction that fish are swimming. Latitude is determined by observing the position of the sun relative to the earth's equator and longitude is determined by observing the position of the sun relative to the Prime Meridian. To accurately calculate latitude and longitude, one would need to use specialized instruments, such as a sextant, or rely on GPS technology. Observing the direction that fish are swimming would not provide enough information to accurately determine latitude and longitude.
False
the longitude and latitude can be easily calculated and determined with using a map not by observing the direction that the fish are swimming.
A taxi driver records the time required to complete various and the distance for each trip. The best-given fit line by the equation y=0.467x + 0.417, where y represents the distance miles, and x represents the time for the trip in minutes.
use the best fit line to estimate the time for a trip that is 6 miles long
By using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.
What is line of best fit?A line of best fit is a graphical representation of straight line which gives the best approximation of the given data set.
A taxi driver records the time required to complete various and the distance for each trip.
The best-given fit line by the equation y=0.467x + 0.417.---(1)
where y represents the distance miles, and x represents the time for the trip in minutes.
To find the time for a 6 miles:
i.e., substitute y=6 in the equation(1)
6=0.467x+0.417
⇒x=11.96 minutes.
Hence, by using line of best fit, the time for a trip of 6 miles long is 11.96 minutes.
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if 0 < 0 < pi/2, as 0 increases, the value of cos0 and the value of sin0
As the angle increases from 0 to π/2, the value of sine increases, and the value of cosine decreases.
Trigonometry is a branch of mathematics that deals with the relationships between angles and sides of triangles.
Let us first understand the concept of sine and cosine. In a right-angled triangle, the sine of an angle is defined as the ratio of the length of the side opposite to the angle and the length of the hypotenuse. Similarly, the cosine of an angle is defined as the ratio of the length of the adjacent side and the length of the hypotenuse.
As the angle θ increases from 0 to π/2, the length of the opposite side (the numerator in sine) of the triangle increases, and the length of the hypotenuse (the denominator in sine) remains the same. Therefore, the value of sine increases as θ increases.
On the other hand, as the angle θ increases from 0 to π/2, the length of the adjacent side (the numerator in cosine) decreases and the length of the hypotenuse (the denominator in cosine) remains the same. Therefore, the value of cosine decreases as θ increases.
This behavior is consistent with the fact that sine is an increasing function, while cosine is a decreasing function within this range of angles.
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Complete Question:
If 0< θ <π/2, as Theta increases, the value of
cos(θ) [Decreases/Increases/Remains The Same]
and the value of sin(θ) [Decreases/Increases Remains The Same]
Write the exponential function that describes the situation.
The initial amount of the function is 12, and then it decreases by a factor of 7/9
with each unit increase in x.
NEED AN ANSWER QUICKLY PLEASE I WILL GIVE BRAININEST
Hi. I need 8 expressions that are equivalent to 31(2760q - d)
Answer: is 1 of them 31(2760)q -d)
A survey was conducted among a group of employees to find the average time they spent online each day. The answers of the employees (in minutes) are shown in the box. 25, 45, 60, 30, 35, 20, 40, 45, 15, 30 Which of these scales would be most appropriate on the y -axis to represent this data on a bar graph? Responses
An appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Since the data represents the average time employees spent online, the y-axis of the bar graph should represent time in minutes.
To choose an appropriate scale for the y-axis.
we need to consider the range of values in the data set.
The lowest value is 15 minutes
and the highest value is 60 minutes
Range of values is 60 - 15 = 45 minutes.
It's best to choose a scale that divides the range of values into equal intervals.
One possible option is to use a scale where each unit represents 5 minutes of time. This would allow us to represent the data accurately without making the bars too small or too large.
Therefore, an appropriate scale for the y-axis would be to have each unit represent 5 minutes of time.
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What is the slope of the line that contains these points?
xxx 888 111111 141414 171717
yyy 363636 121212 -12−12minus, 12 -36−36minus, 36
The slope of the given straight line passing through the coordinates given would be -8.
What is the general equation of a straight line?The general equation of a straight line is → Ax + By + C = 0Rearranging the equation, we can write -By + C = - Ax
By = - Ax - C
y = -(A/B)x - (C/B)
Given are the coordinate points lying on the line.
Slope of a line measures the rate of change of {y} with respect to {x}.Mathematically, we can write the slope as → m = (y₂ - y₁)/(x₂ - x₁)We can write the slope as -
m = (y₂ - y₁)/(x₂ - x₁)
m = {12 - 36}/{11 - 8}
m = -24/3
m = -8
Therefore, the slope of the given straight line passing through the coordinates given would be -8.
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6 unit squares each have 3/5 of their area shaded. What is 3/5 of 6?
Answer: 3.6
Step-by-step explanation:
3/5 is equal to 20% (3 divided by 5 times 100)
1.2 is 20% of 6
So, 3.6 is 3/5 of 6
There are eight groups of students, each working on a science project in the gym. Each group has the same number of students. Mr. Davids asks for 44 students from each group come with him to get more supplies. Now there are a total of 5656 students in the gym.
a. Write an equation to represent this situation, where xx represents the number of students in each group.
Preview
b. How many students are in each group? Simplify your answer completely.
Answer:
58585
Step-by-step explanation:
i know
Write a matrix to represent the following system: -x+5y=7, 7x-2y=3
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
The system of linear equations
-x + 5y = 7
7x - 2y = 3
can be represented in matrix form as:
[tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex]
The matrix on the left represents the coefficients of the variables x and y, and the matrix on the right represents the constants on the right-hand side of each equation.
The vector on the left contains the variables x and y, and the vector on the right contains the constants.
Hence, [tex]\left[\begin{array}{ccc}-1&5\\7&-2\end{array}\right]\left[\begin{array}{ccc}x\\y&\end{array}\right] =\left[\begin{array}{ccc}7\\3&\end{array}\right][/tex] is the representation of system of equation x+5y=7, 7x-2y=3
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7. A storage shed is shown below. How many cubic feet will the storage shed hold? 13 ft 13.6 ft 5 8 ft 13.6 ft 6 ft
The amount of cubic feet that the storage shed can hold is 168 ft³
What is an equation?An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.
The volume of the storage shed is the product of the base area and the height. It is given by:
Volume = base area * height
From the diagram, the base is a triangle. Hence:
Area of base = (1/2) * base * height = (1/2) * 8 ft * 7 ft = 28 ft²
Volume = base area * height = 28 ft² * 6 ft. = 168 ft³
The volume of the storage shed is 168 ft³
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please help if answered correctly ill give the brainiest and all stars and ill cavxsh avxpp u 15 if it's correct.
Hi there, here's your answer:
Before answering this question, we need to know the concept of 'End Behavior'.
What's "end behavior"?
The end behavior of a function [tex]f[/tex] describes the behavior of the graph of the function at the "ends" of the x-axis.
In other words, the end behavior of a function describes the trend of the graph if we look to the right end of the x-axis (as x approaches +∞) and to the left end of the x-axis (as x approaches -∞).
Thus, as V approaches negative infinity, V(x) approaches negative infinity.
And
As V approaches infinity, V(x) approaches infinity.
Hope it helps! Please mark as brainliest!
Answer:
Not enought information
Step-by-step explanation:
We need the function in question 1
However, If I had to guess I'd say
1. infinity
2. negative infinity
What are the coordinates of(D0.25∘rx-axis)(ABCD) for A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10)?
(express ordered pairs as decimal)
Answer: The coordinates of the image of a figure after a rotation of 0.25 degrees about the x-axis can be found using the following formulas:
x' = x
y' = y * cos(θ) - z * sin(θ)
z' = y * sin(θ) + z * cos(θ)
where (x, y, z) are the original coordinates and (x', y', z') are the new coordinates. In this case, we only need to find the y' coordinate because the rotation is about the x-axis and the x coordinate will not change.
For each point, we can use the formula to find the y' coordinate:
A (2, 6) -> y' = 6 * cos(0.25) - 0 * sin(0.25) = 5.99911... ~ 6
B (0, 0) -> y' = 0 * cos(0.25) - 0 * sin(0.25) = 0
C (-5, 8) -> y' = 8 * cos(0.25) - 0 * sin(0.25) = 7.99823... ~ 8
D (-2, 10) -> y' = 10 * cos(0.25) - 0 * sin(0.25) = 9.99649... ~ 10
So, the new coordinates after rotating 0.25 degrees about the x-axis are:
A (2, 6) -> (2, 6)
B (0, 0) -> (0, 0)
C (-5, 8) -> (-5, 8)
D (-2, 10) -> (-2, 10)
The coordinates of the points have not changed after the rotation because the rotation angle is very small.
Step-by-step explanation:
Which model shows two equal expression when the value of x 2
The model that represents the two equal expression for the value x is 2 is given by :
option C. x 1 1 = 1 1 1 1
The correct model which represents the expression for the value x as 2 is given by :
A. x x x x = 1 1 1 1
On the left hand side substitute the value of x = 2 we get,
Left hand side
= 2 2 2 2
It is not equal to 1 1 1 1
Incorrect option.
B. x x x x = 1
On the left hand side substitute the value of x = 2 we get,
2 2 2 2
which is not equal to 1
Incorrect option.
C. x 1 1 = 1 1 1 1
On the left hand side substitute the value of x = 2 we get,
2 1 1
= 1 1 1 1
= Right hand side.
Correct option.
D. x x
On the left hand side substitute the value of x = 2 we get,
= 2 2
which is not equal to right hand side
Incorrect option.
Therefore, the correct model which represents the expression for the value of x = 2 is equal to option C. x 1 1 = 1 1 1 1 .
The above question is incomplete , the complete question is:
Which model shows two equal expression when the value of x is 2 ?
Attached model.
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help pls
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)n+1
n=1
Submit Answer
Which ratio is equivalent to 5:9
There are 250 people in a museum
2/5 of the 50 peoples are girls
3/10 of the 50 people are boys
The rest of the 250 people are adults
Work out the number of adults in museum
The number of adults in the museum, using the fractional value of girls and boys, is 75.
What is a fractional value?A fractional value refers to a portion of the total value.
A fractional value can be depicted in fractions, decimals, or percentages.
A fractional value can also be represented as a ratio or proportion.
In this situation, the fractional number of adults is determined using subtraction.
The total number of people in a museum = 250
The fraction of girls in the museum = 2/5
2/5 of 250 = 100 girls
The fraction of boys in the museum = 3/10
3/10 of 250 = 75
Alternatively:
2/5 + 3/10 = 7/10
7/10 of 250 = 175
Therefore, the number of adults = 75 [250 - (100 + 75)]
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Complete Question:There are 250 people in the museum.
2/5 of the 250 people are girls.
3/10 out of the 250 people are boys.
The rest of the 250 people are adults.
Work out the number of adults in the museum.
PLEASE HELP !!
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A university has 32,370 students. In a random sample of 180 students, 12 speak three or more languages. Predict the number of students at the university who speak three or more languages.
The expected number of students at the university who speak three or more languages is ___________ .
The institution anticipates having 2158 students who can speak three or more languages.
Describe proportion in simple terms.The two ratios given are equivalent to one another, as demonstrated by the proportional equation. The percentage expresses the equality of something like the two ratios as well as fractions.
How do you teach pupils about proportion?Comparing two integers that each stand for a component of a whole results in a percentage. In essence, a percentage declares that two fractions are equal, regardless of the difference in amount. For instance, the ratio of half of 10 marbles to half of 50 marbles is 10.
[tex]\frac{x}{32370}=\frac{12}{180}[/tex]
[tex]{x} = \frac{12}{180}\times32370\\{x}=2158[/tex]
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Find X then find angle NK
Using the two tangent exterior angle theorem:
x = 6
m(NK) = 153°
How to Apply the two tangent exterior angle theorem?According to the two tangent exterior angle theorem, when you draw two tangent lines from a point outside a circle, the angle formed between them is equal to half the difference between the measures of the arcs they intercept inside the circle.
Therefore, using the above theorem, we have:
7x + 6 = 1/2[(25x + 3) - (9x + 3)]
Solve for x:
2(7x + 6) = 25x + 3 - 9x - 3
14x + 12 = 16x
14x - 16x = -12
-2x = -12
x = -12/-2
x = 6
m(NK) = 25x + 3 = 25(6) + 3
m(NK) = 153°
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Solve the system of equations by graphing.
x+y = -7
4x + y = 19
Answer:
(8.666666667, -15.66666667)
or in fraction form
(26/3, -47/3)
Step-by-step explanation:
First we want to get both of the equations into y-intercept form
x + y = -7
subtract x from both sides
y = -x - 7
and the other
4x + y = 19
subtract 4x from both sides
y = -4x +19
now we can graph them
(See attached screenshot)
Reynold can make 4 baked zitis in 8 hours. With Donald’s help, they can bake the same amount of food in 4 hours. How long will it take Donald to make 4 baked zitis without help?
Donald and Reynold work at the same rate, the it also takes 8 hours for Donald to make 4 baked zitis.
How long will it take Donald to make 4 baked zitis without help?We know that Reynold can make 4 baked zitis in 8 hours, then his rate of work is:
R = (4 zitis)/(8 hours) = 0.5 zitis per hour.
Whit Donald's help they can make 4 zitis in 4 hours, if we define D as Donald's rate we can write:
(R + D)*4 hours = 4 zitis.
Replacing R we get:
(0.5 zitis/hour + D)*4 hours = 4 zitis
(0.5 zitis/hour + D) = (4 zitis)/(4 hours)
(0.5 zitis/hour + D) = 1 ziti/hour
D = 1 ziti/hour - 0.5 zitis/hour = 0.5 zitis/hour
So Donald works at the same rate than Reynold, then it will take 8 hours for Donald to make 4 baked zitis.
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hi can i have help with this question please i can’t figure out what c is
Answer: Decagon
Step-by-step explanation:
That would be a decagon because it has 10 sides. It does not matter if the shape looks wonky.
Hope this helps :)
draw a coordinate plane and find points A(-2;0) B(1;4) C(-5;-1) D(5;0) E(0;0)
pls help me
20 points
Gale will buy 9 total tickets.
Aquarium = $14.50 each
Wave pool = $16.75 each, but $12.25 each for groups larger than 4
What event will cost the least for 9 tickets?
Combine the like terms to simplify this expression: ( the 2 to the right of the x, is an exponent)
2x² + 3x-4-x² + x + 9
Answer:
x^2 +4x +5
Step-by-step explanation:
2x^2 -x^2 will be x^2
3x+x is 4x
-4+9 is 5
Points A,B, C and D lie on circle M. Line segment BD is a diameter. What is the measure of angle ACD?
The measure of angle ACD for the given circle is 67.5 degree.
What is inscribed triangle?A triangle is inside a circle when a circle encircles it, and each vertex of the triangle touches the circle.
When a circle encircles a triangle, the triangle lies outside the circle and the circle makes one point contact with each of the triangle's sides. The triangle's sides are perpendicular to the circle.
Given that,
The inscribed angle CDA = 1/2(arc AC).
arc AC = 90 degree.
Then:
∠ CDA = 90 / 2
∠ CDA = 45
Triangle ACD is isosceles, so:
∠ ACD + ∠ CAD + ∠ CDA = 180 degree
Here, ∠ ACD = ∠ CAD
∠ ACD + ∠ACD + ∠ CDA = 180 degree
∠ ACD = 180-45 / 2
∠ ACD = 67.5 degree
Hence, the measure of angle ACD for the given circle is 67.5 degree.
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The correct question is:
Points A, B, C, and D lie on circle M. Line segment BD is a diameter.
Triangle A C D is inscribed within circle M. Point B is on the circle between points C and B. A line is drawn to connect points D and B. Lines are drawn from points C and A to point M to form a right triangle. Arcs C D and A D are congruent.
What is the measure of angle ACD?
45.0°
67.5°
112.5°
135.0°
___ % of 20 is 3.2?
- 15%
-16%
- 18%
- 20%
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17.
Answer:
the iqr is the best measure of variability
The IQR is the best measure of variability, and it equals 4.
Option C is the correct answer.
What is the interquartile range?An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.
W can find the values of the upper and lower quartile and median from a box plot.
The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.
The formula used is Upper quartile - Lower quartile.
We have,
The appropriate measure of variability for the data is the interquartile range (IQR), which is the range of the middle 50% of the data.
In other words, it is the difference between the third quartile (Q3) and the first quartile (Q1).
From the box plot, we can see that the box extends from 17 to 21 on the number line, with a line at 19 inside the box.
This means that Q1 is 17 and Q3 is 21.
The IQR is:
IQR = Q3 - Q1 = 21 - 17 = 4
Thus,
The IQR is the best measure of variability, and it equals 4.
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