Consider the function f(x)=−23x+2f(x)=−23x+2 . What is f(12)f(12) ? Enter your answer, as a simplified fraction, in the box
Answer:
If the function is [tex]f(x)=-23x+2[/tex], then the value of f(12) is -274.
Note: If the function is [tex]f(x)=-\frac{2}{3}x+2[/tex], then the value of [tex]f(\frac{1}{2})[/tex] is [tex]\frac{5}{3}[/tex].
Step-by-step explanation:
The given function is
[tex]f(x)=-23x+2[/tex]
Put x=12,
[tex]f(x)=-23(12)+2=-274[/tex]
It is not a fraction value.
Note: If the given function is
[tex]f(x)=-\frac{2}{3}x+2[/tex]
We have to find the value of [tex]f(\frac{1}{2})[/tex].
Put [tex]x=\frac{1}{2}[/tex] in the given function.
[tex]f(\frac{1}{2})=-\frac{2}{3}(\frac{1}{2})+2[/tex]
[tex]f(\frac{1}{2})=-\frac{1}{3}+2[/tex]
[tex]f(\frac{1}{2})=\frac{-1+6}{3}[/tex]
[tex]f(\frac{1}{2})=\frac{5}{3}[/tex]
Therefore the value of [tex]f(\frac{1}{2})[/tex] is [tex]\frac{5}{3}[/tex].
Sunitha is 24 years older than her daughter kavitha. 6 years ago Sunitha was thrice as old as Kavitha. Find their present ages
What are the x and y-intercepts of the line described by the equation?
−6x+3y=18.9
Enter your answers, in decimal form, in the boxes.
x-intercept =
y-intercept =
What is the point slope form of the line with slope −14 that passes through the point (−2, 9) ?
A. y−2=−14(x+9)
B. y+2=−14(x−9)
C. y−9=−14(x+2)
D. y+9=−14(x−2)
which ordered pairs are solutions to the inequality y− 4x ≥−5 ?
Select each correct answer.
(4, 0)
(1, −1)
(−4, 2)
(−2, 1)
(5, −2)
The x-intercept of the line −6x+3y=18.9 is −3.15, and the y-intercept is 6.3. The point-slope form of the line with slope −14 passing through (-2, 9) is y−9=−14(x+2). The ordered pairs that solve the inequality y∓4x≥−5 are (1, −1), (−4, 2), and (−2, 1).
Explanation:To find the x-intercept and y-intercept of the line described by the equation −6x+3y=18.9, we can set each variable to zero in turn and solve for the other:
For the x-intercept, set y = 0:Therefore, the x-intercept is −3.15 and the y-intercept is 6.3.
For the point-slope form of the line with slope −14 that passes through the point (−2, 9), we use the formula y – y1 = m(x – x1), where m is the slope and (x1, y1) is the point the line passes through. This gives us:
y – 9 = −14(x – (−2)) → y – 9 = −14(x + 2)
The correct option is C. y – 9 = −14(x + 2).
To determine which ordered pairs are solutions to the inequality y – 4x ≥ −5, we test each pair by substituting the x and y values into the inequality:
(4, 0): −4 – 4(4) ≥ −5 → −4 – 16 ≥ −5 is false.(1, −1): −1 – 4(1) ≥ −5 → −1 – 4 ≥ −5 is true.(−4, 2): 2 – 4(−4) ≥ −5 → 2 + 16 ≥ −5 is true.(−2, 1): 1 – 4(−2) ≥ −5 → 1 + 8 ≥ −5 is true.(5, −2): −2 – 4(5) ≥ −5 → −2 – 20 ≥ −5 is false.The ordered pairs that are solutions to the inequality are (1, −1), (−4, 2), and (−2, 1).
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What is the most precise classification of the quadrilateral?
F(-13, 7), I(1, 12), N(15, 7), E(1, -5)
The most precise classification of the quadrilateral defined by the points F(-13, 7), I(1, 12), N(15, 7), and E(1, -5) is a kite.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral. That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We are given that;
The points F(-13, 7), I(1, 12), N(15, 7), E(1, -5)
Now,
To determine the most precise classification of the quadrilateral defined by the points F(-13, 7), I(1, 12), N(15, 7), and E(1, -5), we need to use the properties of quadrilaterals and their classifications.
One way to classify a quadrilateral is by its sides and angles. Based on this classification, the quadrilateral can be classified as a kite. A kite is a quadrilateral with two pairs of adjacent sides that are equal in length, and the diagonals of a kite are perpendicular.
To see why the quadrilateral defined by F, I, N, and E is a kite, we can start by noting that FI and EN have equal length, as do IN and FE. Additionally, we can compute the lengths of the diagonals and check whether they are perpendicular.
The length of diagonal FN is sqrt(676+25)=sqrt(701), and
The length of diagonal IE is sqrt(256+49)=sqrt(305).
The product of the slopes of FI and EN is (12-7)/(1-(-13))*(1-(-5))/(1-15)=-5/4. This product is negative, indicating that the diagonals are perpendicular.
Therefore, the quadrilateral defined by F, I, N, and E is a kite.
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Final answer:
The most precise classification of the given quadrilateral formed by the coordinates (-13, 7), (1, 12), (15, 7), and (1, -5) is a parallelogram.
Explanation:
The given coordinates (-13, 7), (1, 12), (15, 7), and (1, -5) form a quadrilateral. To determine the most precise classification of the quadrilateral, we need to analyze its properties.
Based on the given coordinates, we can see that opposite sides of the quadrilateral are parallel. The vectors formed by connecting the consecutive points are FI = (14, 5), IN = (14, -12), and NE = (-14, -12). These vectors have equal magnitudes, indicating that the quadrilateral is a parallelogram.
Therefore, the most precise classification of the quadrilateral is a parallelogram.
Find the percent of change in altitude if a weather balloon moves from 100 ft to 103 ft. describe the percent of change as an increase or decrease. Round to the nearest tenth if necessary
A. 3% decrease
B.2.6% increase
C.3.4% decrease
D.3% increase
D. 3 is 3% of 100 and it increase by 3
Which is a secant?
CT
MH
CD
The secant in the given figure is:
CD
Step-by-step explanation:We know that in geometry a secant is a line that intersect the circle or any curve in atleast two distinct points.
Here we have a curve as a circle.
Hence, the secant is: CD
( Also MH is not a secant since it does not intersect the curve at any point.
Also CT is not a secant because it is not a line, it is a line segment although it intersect the curve at two distinct points )
Solve for x. 5x = -123
The sum of x and 8 is less than 72 find all possible values of x
after 5 points are subtracted from every score, the sample mean is found to be m = 24. what was the mean for the original sample?
Answer:
The mean of original sample is 29.
Step-by-step explanation:
After 5 points are subtracted from every score, the sample mean is found to be m = 24
So, the mean for the original sample was = [tex]24+5=29[/tex]
Here we are talking about mean so 5 points are subtracted from every score. when we are talking in terms of mean, 5 will be added to the mean, that will give 5 added to every score.
Solve the inequality 13x - 4 < 12x - 1.
x < 3
x > 3
x < 5
x > 5
Answer:
The answer is x<3
Step-by-step explanation:
The slope of a line is 2, and the y-intercept is 0. What is the equation of the line written in slope-intercept form?
A. y = x + 2
B. y = 2
C. y = 2x
Answer:
Equation of the line written in slope-intercept form y = 2x .
Option C is correct .
Step-by-step explanation:
As the equation of a line is represented by .
y = mx + c
Where m is the slope and c is the y - intercept .
As given
The slope of a line is 2, and the y-intercept is 0.
m = 2
c = 0
Put all the values in the above
y = 2x + 0
y = 2x
Therefore equation of the line written in slope-intercept form y = 2x .
Option C is correct .
A mail-order supplier of small electrical parts charges a shipping fee of $8, plus $5 for each pushbutton light switch ordered. If x is the number of pushbutton switches ordered, then the expression for the total cost of an order is 5x + 8 What is the total cost of six switches?
Answer:
B. Number of switches
x. 5x + 8
1. 13
2. 18
3. 23
Final answer:
The expression for the total cost of an order with x pushbutton switches is 5x + 8. For six switches, it amounts to 5(6) + 8, or $38.
Explanation:
The total cost of ordering a certain number of switches can be determined by the expression 5x + 8, where x is the number of pushbutton switches ordered. In this instance, to find the total cost for six switches, we substitute x with 6. Therefore, the calculation would be 5(6) + 8.
Calculating this, we get:
5(6) = 30Total cost = 30 + 8 = $38Thus, the total cost for ordering six switches is $38.
The cross-section of a beehive reveals it is made of regular hexagons. What is the measure of each angle in the regular hexagon ?
Each angle in a regular hexagon measures 60 degrees.
Explanation:A regular hexagon is a polygon with six equal sides and six equal angles. Since the cross-section of a beehive is made of regular hexagons, each angle in the regular hexagon would have the same measure.
To find the measure of each angle in the regular hexagon, we can use the formula:
Measure of each angle = (360 degrees) / (number of sides)
Substituting the value for a regular hexagon, we have:
Measure of each angle = (360 degrees) / (6 sides)
Therefore, each angle in a regular hexagon measures 60 degrees.
Tyler solved an inequality to determine the number of songs he can buy with a $20 credit at his favorite music website. The solution is graphed below
Which phrases accurately describe all the possible quantities of songs he can buy? Check all that apply.
no more than 8 songs
at least 8 songs
a minimum of 8 songs
at most 8 songs
fewer than 8 songs
a maximum of 8 songs
no fewer than 8 songs
Answer:
no more than 8 songs
at most 8 songs
Step-by-step explanation:
Answer: A & D
Step-by-step explanation:
please help
What is the perimeter of PQR? Show your work.
In which function is x = 2 mapped to 32?
A. f(x) = -3x^2-4
B. g(x) = 4(x+3)^2-68
C. h(x) = 3x
D. j(x) = 2x-62
Answer:
Option B - [tex]g(x) = 4(x+3)^2-68[/tex]
Step-by-step explanation:
Given : Function is x = 2 mapped to 32.
To find : Which function is it ?
Solution : We put x=2 in every function and which result to 32 is the answer.
A. [tex]f(x) = -3x^2-4[/tex]
[tex]f(2) = -3(2)^2-4[/tex]
[tex]f(2) = -3(4)-4[/tex]
[tex]f(2) = -12-4[/tex]
[tex]f(2) = -16[/tex]
B. [tex]g(x) = 4(x+3)^2-68[/tex]
[tex]g(2) = 4(2+3)^2-68[/tex]
[tex]g(2) = 4(5)^2-68[/tex]
[tex]g(2) = 4(25)-68[/tex]
[tex]g(2) = 100-68[/tex]
[tex]g(2) = 32[/tex]
C. [tex]h(x) = 3x[/tex]
[tex]h(2) = 3(2)[/tex]
[tex]h(2) = 6[/tex]
D. [tex]j(x) = 2x-62[/tex]
[tex]j(2) = 2(2)-62[/tex]
[tex]j(2) = 4-62[/tex]
[tex]j(2) =-58[/tex]
Option B -[tex]g(x) = 4(x+3)^2-68[/tex] gave you the result [tex]g(2) = 32[/tex]
Therefore, Option B is correct.
The distributive property between 48 and 72
48 + 72 = 120= 60*2
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Nicole deposits $2,136 in a savings account paying 5.36% interest. To the nearest dollar, how much money does Nicole have in total after nine years?
a.
$213
b.
$1,030
c.
$1,272
d.
$3,166
Answer:
its D (just did it)
Step-by-step explanation:
Mr. Hann is trying to decide how many new copies of a book to order for his students. Each book weighs 6 ounces. Which ordered pair is a viable solution if x represents the number of books he orders and y represents the total weight of the books, in ounces?
Answer:
Step-by-step explanation:
Y = total weight of books
X = number of books
6 = weight (in ounces) of 1 book
total weight of books = weight of books x number of books
Y = 6X
Answer:
Only 0,0 You don't order negative numbers of books which eliminates the first two pairs. And you don't order 1/2 a book which eliminates the last pair.
Step-by-step explanation:
If you order 0 shirts they will weight 0 ounces is the only viable solution.
What is the value of d? 0.5(6d+10)=17 Enter your answer in the box.
0.5(6d+10) = 17
3d+5 = 17
3d =12
d = 12/3
d = 4
Answer: it 5
Step-by-step explanation: 6d=6.5=10 = 16.5+0.5=17
A turtle swims at a speed of 1584 meters per hour. A girl swims at a speed of 1380 millimeters per second how much faster does the girl swim than the turtle in centimeters per minutes?
The girl swims 8280 centimeters per minute faster than the turtle.
Explanation:To calculate how much faster the girl swims than the turtle in centimeters per minute, we need to convert their speeds to a common unit of measurement.
The turtle swims at a speed of 1584 meters per hour, which is the same as 158400 centimeters per hour.
The girl swims at a speed of 1380 millimeters per second, which is the same as 138 centimeters per second.
To convert the girl's speed to centimeters per minute, we multiply her speed in centimeters per second by 60 (since there are 60 seconds in a minute). So, the girl swims at a speed of 138 * 60 = 8280 centimeters per minute.
Therefore, the girl swims 8280 centimeters per minute faster than the turtle.
Final answer:
The girl swims 150,120 centimeters per minute faster than the turtle.
Explanation:
To find out how much faster the girl swims than the turtle, we need to convert their speeds to the same units. First, we'll convert the turtle's speed from meters per hour to centimeters per minute. Since there are 60 minutes in an hour, we can multiply 1584 meters per hour by 100 to convert it to centimeters per minute. This gives us a speed of 158,400 centimeters per minute for the turtle.
Next, we'll convert the girl's speed from millimeters per second to centimeters per minute. Since there are 60 seconds in a minute, we can multiply 1380 millimeters per second by 6 to convert it to centimeters per minute. This gives us a speed of 8,280 centimeters per minute for the girl.
To find out how much faster the girl swims, we subtract the turtle's speed from the girl's speed. So the girl swims 8,280 - 158,400 = -150,120 centimeters per minute faster than the turtle. However, since we want the answer to be a positive value, we can take the absolute value of the difference, which gives us a final answer of 150,120 centimeters per minute.
A rectangular dog pen which is 5 times as long as it is wide
The domain for f(x) and g(x) is the set of all real numbers. let f(x) = 2x-3 and g(x) = 3x +8 find f(x)g(x)
Phineas is the lead research scientist in a lab and responsible for ordering supplies and equipment. The lab is out of petri dishes, so Phineas orders 185 of them. The lab uses 12 petri dishes each day.Explain how you would write a two-variable linear equation for this situation.
the equation for a two variable equation is ax +by = r
r would be the total number of petri dishes ordered
so you have ax + by = 185
ax would be the number of dished used times x number of days = 12x
so you now have 12x + by = 185
b is unknown so the equation becomes 12x +y = 185
Find equations for the lines through the point (a,
b.that are parallel to and perpendicular to the line y = mx + c, assuming m â 0.
A set of data that is made up of two paired variables is
Final answer:
A set of data that is made up of two paired variables is called bivariate data. These types of data reflect a one-to-one relationship between the paired variables and can be visualized using graphs with independent and dependent variables.
Explanation:
The set of data made up of two paired variables is known as bivariate data. This type of data includes pairs of related data where each data point in one set is matched with exactly one data point in the other set, establishing a one-to-one relationship between the two. Essentially, in a paired data set, both data sets are the same size, and there's an explicit connection between each point in one set to one in the other.
A common way to visualize the relationship between two properties of a system is by using a two-dimensional data plot. This graph will typically have two axes: a horizontal axis for the independent variable (often represented as 'x'), and a vertical axis for the dependent variable (often represented as 'y'). For example, if we know a relationship such as y = x² + 2, we can create a table of x and y values and then graph them to visualize the relationship.
When dealing with categorical variables, data is often represented in a two-way table, which is also based on bivariate data. In such a table, entries in the total row and total column are called marginal frequencies or marginal distributions.
Combine the like terms to make a simpler expression:
−3k−(−8)+2
Write 5^2 • 5^-1 • 5^3 as a single exponent,
Two sides of an equilateral triangle have lengths x+2 and -2x+20 Which could be the length of the third side: 14-x or 2x+4?
a. 2x + 4 only
b. both 14 - x and 2x + 4
c. 14 - x only
d. neither 14 - x nor 2x + 4
Part 1:Is it possible for a composite number to have more than one prime factorization? Is it possible for a number to have no prime factors? Why? Part 2: Give an example of how prime factorization could be used in the real world. Part 3: View and comment on the work of at least two other students. Explain why you agree or disagree with their ideas.
A composite number has only one prime factorization, and 1 is the only number without prime factors. Prime factorization plays a crucial role in cryptography. Peer work review would focus on understanding and accuracy but cannot be provided without specific student examples.
No, a composite number cannot have more than one prime factorization due to the Fundamental Theorem of Arithmetic, which states that every integer greater than 1 either is a prime number itself or can be factored into prime numbers in exactly one way, ignoring the order of the factors. On the other hand, the only number that has no prime factors is 1, as it is neither prime nor composite.
One real-world application of prime factorization is in cryptography, particularly in algorithms like RSA, which is used to secure data transmission over the internet. The difficulty in factoring large numbers into primes is what makes this method effective for encrypting sensitive information such as credit card numbers.
Without specific examples of the work of other students, it is not possible to provide a review. Typically, when reviewing peer work, one would assess the correctness of their understanding of prime factorization and its application in real-world scenarios, as well as the clarity and accuracy of their explanations.