A ball with radius r, lying inside a glass described by the function y = x^2, has its center at (0, F(r)) units above the bottom of the glass. (F(r) is a function of r) Compute f(2) - f(1/4)?
Pick one of the choices
-2
0
2
4
d). A ball with radius r, lying inside a glass described by the function y = x^2, has its center at (0, F(r)) units above the bottom of the glass. f(2) - f(1/4)=4.
To solve this problem, we first need to find the function F(r). We can do this by finding the y-coordinate of the center of the ball when its radius is r.
Since the ball lies inside the glass described by the function y = x2, the y-coordinate of the center of the ball when its radius is r is equal to the y-coordinate of the point (r,r2).
Thus, the function F(r) is given by F(r) = r2. Now, we can calculate f(2) - f(1/4) = F(2) - F(1/4) = 22 - (1/4)2 = 4 - 1/16 = 4 - 0.0625 = 3.9375 ≈ 2. Therefore, f(2) - f(1/4) = 2.
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can you help m with this?
Cody sells sourdough bread by weight. He cuts a 1-lb loaf into 12 equal slices. What is the weight of one slice of Cody’s bread?
Answer:
ewd
Step-by-step explanation:
ewddew
How do you divide division?
The division is performed by dividing the dividend by the divisor. This helps to find the quotient and remainder.
Along with addition, subtraction, and multiplication, the fourth main operation in mathematics is division. There are five main division techniques used in arithmetic calculations: long division, short division, dividing fractions, dividing exponents, and dividing decimals.
For example, to divide 500 by 5 we use the following steps using short division. Here, the divisor is 5 and the dividend is 500. Doing the division we get, the quotient is 100, and the remainder is 0. This is represented in the attached image. Here, the answer for the division of 500 by 5 is 100.
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13. Consider the system of equations.
y = 6.9x + 4.3
y = 4.7x + 8
What is the solution of the system?
Round your answer to the nearest
hundredth, if necessary. (Lesson 6-1)
A. 1.06
B. 1.68
C. 2.14
D. 5.59
If the equations be y = 6.9x + 4.3, y = 4.7x + 8 then the solution of the system is 2.14.
What is meant by system of equations?A system of equations, usually referred to as an equation system or a set of simultaneous equations, is a finite set of equations for which common solutions are sought.
Multiple equations in algebra must be solved concurrently (i.e., the solution must satisfy all the equations in the system). There must be an equal number of equations and unknowns for a system to have a singular solution. As was said earlier, a system of equations is a group of equations that attempt to find a common solution for all of the variables.
Let the system of equations be
y = 6.9x + 4.3
y = 4.7x + 8
then the solution of the system be 2.14.
Therefore, the correct answer is option C. 2.14.
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Which of the following are propositions? Give the truth value of each proposition.
(a) What time is dinner?
(b) It is not the case that π is not a rational number.
(c) x / 2 is a rational number.
(d) 2x + 3y is a real number.
(e) Either π is rational and 17 is a prime, or 7 < 13 and 81 is a perfect square.
(f) Either 2 is rational and π is irrational, or 2π is rational.
(g) Either 5π is rational and 4.9 is rational, or there are exactly four primes less than 10.
(h) −3.7 is rational, and either 3π < 10 or 3π > 15.
(i) It is not the case that 39 is prime, or that 64 is a power of 2.
(j) There are more than three false statements in this book, and this statement is one of them.
The Propositions from the given data are All Statements except Statement A.
(a) What time is dinner? This is not a proposition because it is a question and does not have a definite truth value.
(b) It is not the case that π is not a rational number. This is a proposition and its truth value is True because pi is not a rational number.
(c) x / 2 is a rational number. This is not a proposition because it is a statement about a variable, and the truth value depends on the value of x.
(d) 2x + 3y is a real number. This is not a proposition because it is a statement about variables, and the truth value depends on the values of x and y.
(e) Either π is rational and 17 is a prime, or 7 < 13 and 81 is a perfect square. This is a proposition and its truth value is False, because neither pi is rational nor 17 is prime.
(f) Either 2 is rational and π is irrational, or 2π is rational. This is a proposition and its truth value is False, 2 is rational and π is irrational.
(g) Either 5π is rational and 4.9 is rational, or there are exactly four primes less than 10. This is a proposition and its truth value is False because 5π is not rational and 4.9 is not rational and also there are four primes less than 10.
(h) −3.7 is rational, and either 3π < 10 or 3π > 15. This is a proposition and its truth value is False because −3.7 is not rational.
(i) It is not the case that 39 is prime, or that 64 is a power of 2. This is a proposition and its truth value is True because 39 is not a prime and 64 is a power of 2.
(j) There are more than three false statements in this book, and this statement is one of them. This is a proposition and its truth value is False because it is self-referential and also it's not true that there are more than three false statements in this book.
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Why do you think you succeeded (or failed) at making money in the stock market?
Answer:
Succeeded because you did the correct research and made educated investments in a reliable company.
Failed because you did not do good and deep research and invested in an unreliable company.
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), D(4, 4) is dilated using a scale factor of one fourth to create polygon A′B′C′D′. Determine the vertices of polygon A′B′C′D′.
A′(−0.8, 1.2), B′(−0.4, 0.4), C′(0.8, −0.4), D′(0.8, 0.8)
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)
A′(−2, 3), B′(−1, 1), C′(2, −1), D′(2, 2)
A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3)
After dilatation, the vertices of polygon ABCD with vertices at A (4, 6), B (2, 2), C (4, 2), and D (4, 4) will be
A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (1, 1)How to determine the image's coordinatesDilation is a transformation technique that can either enlarge or reduce the preimage depending on the scale factor.
The following is the dilation transformation rule:
(x, y) with r as the scaling factor (rx, ry)
Using a similar process for the given issue, we have for r = one fourth
preimage dilation image
A(-4, 6) → (1/4 * -4, 1/4 * 6) → A'(-1, 1.5)
B(−2, 2) → (1/4 * -2, 1/4 * 2) → B'(-0.5, 0.5)
C(4, −2) → (1/4 * 4, 1/4 * -2) → C'(1, -0.5)
D(4, 4) → (1/4 * 4, 1/4 * 4) → D'(1, 1)
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The graph shows the distance y (in miles) that a bus travels in x hours. Find and interpret the slope of the line.
A line graph titled "Bus Trip"
The x-axis is labeled time, in hours. The y-axis is labeled distance, in miles. A line begins at ordered pair (0, 0 )and goes through ordered pair (1, 60) and ordered pair (2, 120).
The slope of the line is __ The bus is traveling at a speed of __ miles per hour.
The slope of the line is 60 The bus is traveling at a speed of 60 miles per hour.
What is the slope?A line's steepness is determined by its slope. Slope can be computed mathematically as "rise over run" (change in y divided by change in x). In the slope-intercept form, the equation for the line is expressed as follows: y = mx + b, where m denotes the slope and b the y-intercept. When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). Its y value of the y intercept point is represented by b in the equation.
Given that,
A line begins at ordered pair (0, 0) and goes through ordered pair (1, 60) and ordered pair (2, 120).
Slope of the line (m) = (y₂ - y₁) / (x₂ - x₁)
m = 120 - 60 / 2 - 1
m = 60
thus, slope of the line = 60
The bus is travelling at a speed of 60 miles per hour.
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Luca decided to walk to a new park in town and estimated how long it would take. When he arrived, it had taken him 20 minutes to walk to the park. His estimate was 25% more than that. How long did Luca estimate it would take him to walk to the park
Answer: If it took Luca 20 minutes to walk to the park and his estimate was 25% more than that, we know that the estimate was 20 * 1.25 = 20 + (20 * 0.25) = 20 + 5 = 25 minutes.
So Luca estimated that it would take him 25 minutes to walk to the park.
Step-by-step explanation:
6-4 Additional Practice Proving a Quadrilateral Is a Parallelogram Is there enough information to prove each quadrilateral is a parallelogram? Explain: For what values of and b is each quadrilateral parallelogram? (I2b 26 + 45 2u + 14 Understand Margaret says there is not enough information to show that WXYZ is parallelogram: Explain why Margaret is incorrect: 10. Apply A hazard sign has_ identical parallelogram-shaped stripes as shown: Charles must outline each stripe with reflective tape: Is one roll of 144 inches of tape enough to finish the job? Explain: 6I_3n 6n enVision" Geometry * Teaching Resources'
Margaret is incorrect because the given information does not include enough details to determine if the quadrilateral WXYZ is a parallelogram.
To prove that a quadrilateral is a parallelogram, the four sides must be equal in length and the opposite angles must be congruent. The given information does not include any measurements or angles, so it is not possible to determine if the quadrilateral is a parallelogram.
No, 144 inches of tape is not enough to finish the job. The hazard sign has two identical parallelogram-shaped stripes, and each stripe will require more than 144 inches of tape to outline. The area of a parallelogram can be calculated using the formula A = bh, where b is the base and h is the height. In order to determine how much tape is needed to outline the stripes, the base and height of the parallelograms must be known.
There is not enough information to prove that a quadrilateral is a parallelogram, as all four sides must be equal in length and the opposite angles must be congruent. Additionally, 144 inches of tape is not enough to outline the hazard sign's two identical parallelogram-shaped stripes, as the base and height of the parallelograms must be known in order to calculate the area.
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What is 2x2x2 in exponential form?
Answer: 8
Step-by-step explanation:
2 x 2 = 4 2 x 4 = 8
Match each fraction to a reasonable estimate
7.3 revised quiz part 1
Given DF bisects
On solving the provided question, we can say that angle are given a 9n - 3 + 8n +9 = 60; angle 1 = 24 and angle 2 = 33
what are angles?In Euclidean geometry, an angle is a shape made up of two rays, referred to as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays can generate an angle that is in the plane where the rays are located. The meeting of two planes also creates an angle. They are referred to as dihedral angles. An angle is the shape created by two rays or lines that have a shared termination in plane geometry. The Latin word "angulus," which meaning "horn," is the source of the English term "angle." The vertex is the common terminal of the two rays, which are referred to as the sides of the angle.
here,
angle are given as
9n - 3 + 8n +9 = 60
17n = 60-6
17n = 54
n = 3.1764705882 = 3
n = 3
angle 1 = 24
angle 2 = 33
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2. What is the value of the median?
Answer:
median = 4
Step-by-step explanation:
On the box plot the median is represented by the vertical line inside the box.
That is the median = 4
How many combinations of 8 are there?
There are one combination of choosing all 8 from 8 items when the order does not matter.
Therefore the answer is 1.
The number of combinations of 8 items is given by the formula:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items and k is the number of items in each combination.
In this case, we want to find the number of combinations of 8 items, so n = 8 and k = 8.
Plugging these values into the formula, we get:
C(8, 8) = 8! / (8!(8-8)!) = 8! / (8!(0!))
= 8! / 8! = 1.
So, there is only 1 combination of 8 items when k = 8.
It's important to note that a combination is a set of items in which the order doesn't matter, so the order of the items in the set doesn't affect the number of combinations. If you want to find the number of permutations, in which order matters, it would be 8! (8 factorial) = 8x7x6x5x4x3x2x1 = 40320.
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graph 2y – 4x < 8 thanksss
The solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.
What is the graph of a function?
The graph of a function is a visual representation of the relationship between the input values (x-coordinates) and the output values (y-coordinates) of the function. In other words, it is a visual representation of the function's rule.
The graph of a function can take many different forms, depending on the function's rule. Linear functions, for example, will produce a straight line on the graph.
To solve the inequality 2y – 4x < 8, we can start by isolating y by adding 4x to both sides:
2y < 4x + 8
then divide both sides by 2:
y < 2x + 4
This is the solution in slope-intercept form (y = mx + b), where the slope is m = 2 and the y-intercept is b = 4.
To graph the solution, you can pick a few x-values and substitute them into the inequality to find the corresponding y-values.
You can use x = -2, x = -1, x = 0, x = 1, x = 2, for example and find the y-values for each x, y < 2* -2 + 4 = 0, y < 2* -1 + 4 = 2, y < 20 + 4 = 4, y < 21 + 4 = 6 and y < 2*2 + 4 = 8.
Then plot those points on a coordinate plane and draw the line that goes through them, and shade the half-plane that is below the line
Hence, the solution is the set of all points (x,y) that satisfy the inequality y < 2x + 4.
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slope=7;(4,-30)
what is the y-intercept
and what is the equation
Answer:
The y-intercept is -58
The equation is y=7x-58
Step-by-step explanation:
We'll look for an equation of the form y=mx+b, where m is the slope and b the y-intercept (the value of y when x is 0).
We are given the slope and one point on a line. The slope, m, of 7 leads us to:
y=7x+b
We need a value for b that will force the line to go through point (4,-30). Enter that point in the above equation and solve for b:
y = 7x+b
-30 = 7(4)+b for point (4,-30)
-30 = 28 + b
b = -58 [b is the y-intercept]
The equation is y = 7x-58
See the attached graph.
A quadratic equation has zero real number solutions. Which could be the discriminant value associated with this equation?
–5
0
1
6
The discriminant value associated with this quadratic equation when it has zero real number solutions is -5.
Option A is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
In a quadratic equation when the discriminant is 0 we get one real solution.
In a quadratic equation when the discriminant is positive we get two real solutions.
In a quadratic equation when the discriminant is negative we get a complex solution.
A complex solution is not a real solution.
So,
The discriminant value must be -5.
Thus,
The discriminant value associated with this equation is -5.
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Answer: It’s A: -5
Step-by-step explanation:
on edge 2020
(Took test)
Points P, Q, and R are collinear, with PQ=5, PR=7, and QR=12. Complete the statement.
Point P lies between Q and R
What are collinear points?Collinear points are the points that lie on the same straight line or in a single line. If two or more than two points lie on a line close to or far from each other, then they are said to be collinear, in Euclidean geometry.
Given here: Points P, Q, and R are collinear, with PQ=5, PR=7, and QR=12
Clearly we can observe that QR = PQ+PR
12=5+7
And the three points are collinear therefore we can deduce that Point P must lie between the two points Q,R.
Hence, Point P lies between Q and R
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Harry the hippo collected change from the bottom of the pond but he only kept the quarters and nickels if he collected 100 coins and has 17.40 how many of each coin does he have
Algebra is a branch of mathematics that deals with mathematical statements and relationships in which symbols (such as x, y, and z) represent numbers or other unknown values. Harry has 62 quarters and 38 nickels.
How many of each coin does he have?
To find out how many of each coin Harry has, we need to use algebra. Let x be the number of quarters and y be the number of nickels. We know that:
x + y = 100 (because Harry collected 100 coins in total)
0.25x + 0.05y = 17.40 (because that's the total value of the quarters and nickels in dollars)
We can use the first equation to solve for one of the variables in terms of the other. For example, we can subtract y from both sides to get:
x = 100 - y
Then we can substitute this value of x into the second equation and solve for y:
0.25(100 - y) + 0.05y = 17.40
25 - 0.25y + 0.05y = 17.40
25 = 17.40 + 0.20y
0.20y = 7.60
y = 38 (the number of nickels)
Now that we know the value of y, we can use the first equation to find the value of x:
x + 38 = 100
x = 62 (the number of quarters)
So Harry has 62 quarters and 38 nickels.
These symbols are used to represent quantities, and the operations and relationships between them are studied through the use of mathematical laws and rules.
Algebraic equations and formulas allow one to solve a wide variety of problems, including problems in physics, engineering, and other sciences, as well as in everyday life.
Algebraic concepts include variables, expressions, equations, and functions. It is the study of mathematical symbols and the rules for manipulating these symbols. Algebra is a powerful tool for solving problems by using mathematical models.
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What are 2 types of images?
In mathematics, the image of a function is the algebraic set of all output values it may generate. Real image and Virtual Image.
More generally, evaluating a given function
f at each element of a given subset
A of its domain produces a set, called the "image of
A under (or through) f
f". Likely, the inverse image (or preimage) of a given subset.
B of the codomain of f
f, is the set of all elements of the domain that map to the members of B.
Both Image and inverse image may also be defined for general binary relations, not just functions.
Image In common language an image is a picture or other visual way of showing something. But in mathematics it is another name for Range of a Function
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-4>n or 3n+1>-2 solve equation or inequality
graph it too
The value of n is -1 < n < -4.
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
-4>n or 3n+1>-2
now, solving the above inequality
3n+1>-2
3n > -2-1
3n > -3
n > -1
So, the value of n varies -1 < n < -4.
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Doris Schutt earns a weekly gross salary of $1,500.00. When she receives her
raise from her job at Precision Doors and Windows next year, she will be earning
an annual salary of $83,500.00. How much more money will she make next year
than this year?
Your answer
Answer:239.583
Step-by-step explanation:
First you have to divide 83500 by 12 because there is 12 months in a year which gives you 6958.3
Second you have to divide 6958.3 by 4 because there is 4 weeks in a month and that gives you 1739.583
Finally you have to subtract 1739.583 by 1500 giving you 239.583
what is 1/2 x 1/3 i could never get this answer its to hard!!!
Answer: there
Step-by-step explanation:
0.16666666666
(01.02 MC)
The table gives a partial set of values of a polynomial h(x), which has a leading coefficient of 1.
If every x-intercept of h(x) is shown in the table and has a multiplicity of one, what is the equation of the polynomial function?
The function is given by: h(x) = -2(x³ - 2x² - 5x + 6).
What is meant by Factor Theorem?The factor theorem in algebra connects a polynomial's components and zeros. The polynomial remainder theorem has this particular special instance. A polynomial f(x) has a factor if and only if f=0, according to the factor theorem.
The Factor Theorem states that a polynomial function with roots [tex]$x_1, x_2, x_n$[/tex] is given by:
[tex]$$f(x)=a\left(x-x_1\right)\left(x-x_2\right) \cdots\left(x-x_n\right)$$[/tex]
In which a is the leading coefficient.
Looking at the table, considering the values of x when h(x)=0, the roots of h(x) are given as follows:
[tex]$$x_1=-2, x_2=1, x_3=3$$[/tex]
Then the rule is:
h(x) = a(x + 2)(x - 1)(x - 3)
h(x) = a(x² + x - 2)(x - 3)
h(x) = a(x³ - 2x² - 5x + 6)
The h-intercept is of -12, as when x = 0, h = -12, hence this is used to find a as follows:
6a = -12
simplifying the above equation, we get
a = -12/6
a = -2.
Therefore, the function is given by: h(x) = -2(x³ - 2x² - 5x + 6).
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Plssss helpppp!!!!!!
Proportionalit
26. Bonnie's Boutique had a T-shirt sale to make room for new inventory. At the end of
the sale, 16 T-shirts were left. Of these, 6 were blue. Write the ratio of blue T-shirts to
total T-shirts left as a fraction in simplest form.
ake it for abou
Answer:
3:8
Step-by-step explanation:
The total number of t-shirts is 16. Out of the 16 t-shirts, 6 are blue. We can write this as 6:16, or 6 out of 16. You can simplify this further by dividing the ratio by 2 to get 3:8. I hope this helps!
please answer quick!! thank you
Answer:
Question 2 :
[tex]\boxed{-35}[/tex]
Question 3:
[tex]\boxed{7}[/tex]
Question 4:
[tex]\boxed{-5}[/tex]
Question 5:
[tex]\boxed{-5}[/tex]
Step-by-step explanation:
The easiest points to take on the line are those where x =0, y = 35 (0,35) and x = 7, y =0 (7,0)
Question 2.
We can see that between these two points, the y value decreases linearly from 35 to 0. So the rise between (0, 35) and (7,0) = [tex]0 -35 = -35[/tex]
Question 3
[tex]\textrm{Between (0, 35) and (7,0) the x value increases from 0 to 7 so the run is 7}[/tex]
Question 4
[tex]\dfrac{rise}{run}= \dfrac{-35}{7}= -5}[/tex]
Question 5
Slope is the same as rise over run
We can also write this as
[tex]\dfrac{0-35}{7-0} = \dfrac{-35}{7} = -5[/tex]
Though not asked for, the equation of the line is
[tex]y = -5x + 35[/tex]
just a challenge. if 10 apples grew on a maple ctree and 3 were picked and 4 more grew
how many apples are thare
Answer:
apples don't grow on maple trees
Step-by-step explanation:
A decorator hangs a picture on a wall that is 48 inches wide. The width of the picture is 171 inches. The decorator hangs the picture exactly in the middle of the wall, as shown.
What is the value of x, in inches, on each side of the picture, written as an improper fraction (fraction greater than one)?
The value of x is 15.25 inches
What is subtraction?Subtraction is one of the four arithmetic operation along with addition, multiplication and division. Subtraction is an operation that represents removal of objects from a collection. For example, in the adjacent picture, there are 5 − 2 peaches, this means that 5 peaches with 2 taken away, resulting in a total of 3 peaches.
The frame is place in the Middle of the wall. The space left after the frame is hanged is calculated as 48inches - 17.5 inches = 30.5 inches.
Since the frame is at the middle of the wall , the space (x) at both sides is equal
therefore x+x = 30.5
2x = 30.5
divide both sides by 2
x = 30.5/2 = 15.25 inches
therefore the value of x is 15.25 inches.
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