The best estimate of the volume of the stack once it has been bumped/shifted is 4πt³ cubic centimeters.
Describe Volume of cylinder?A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases connected by a curved surface. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula:
Volume = πr²h
where π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the circular base, and h is the height of the cylinder.
Assuming that the coins have the same dimensions and are perfectly circular, the original stack of 15 coins formed a cylinder with a height of 15 times the thickness of a single coin, and a radius equal to the radius of a single coin.
The volume of this cylinder can be calculated using the formula V = πr²h, where r is the radius and h is the height.
Since the volume of the original stack is 8 cubic centimeters, we can set up the equation:
8 = πr²(15t)
where t is the thickness of a single coin.
Solving for r, we get:
r = √(8/15πt)
When the stack is bumped and shifts to a leaning position, the new shape will still be a cylinder, but the height will be shorter than before. Let's say that the new height is h2. We can calculate the new volume using the same formula:
V2 = πr²h2
To estimate the new height, we can use the fact that the coins are now leaning against each other, so the new height will be less than 15t. Let's say that the new height is approximately 12t.
Substituting in the values, we get:
V2 = π(√(8/15πt))²(12t)
Simplifying, we get:
V2 = 4πt³
Therefore, the best estimate of the volume of the stack once it has been bumped/shifted is 4π³ cubic centimeters.
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A little help here please !!
Answer:
Step-by-step explanation:
a) Determine whether the following set of vectors inR4is linearly independent or linearly dependent.S={(1,0,−1,0),(1,1,0,2),(0,3,1,−2),(0,1,−1,2)}b) Write the vectoru=(10,1,4)as a linear combination of the vectorsv1=(2,3,5),v2=(1,2,4) and v3=(−2,2,3)
The given set of vectors in R4 is linearly independent and the vector u as a linear combination of the vectors v1, v2, and v3 can be written as u = (7,12,22)
a) To determine if the set of vectors in R4 is linearly independent or linearly dependent, we can use the rank of the matrix formed by these vectors. If the rank of the matrix is equal to the number of vectors, then the set is linearly independent. Otherwise, it is linearly dependent.
First, let's form the matrix using the vectors:
| 1 0 -1 0 |
| 1 1 0 2 |
| 0 3 1 -2 |
| 0 1 -1 2 |
Next, let's find the rank of the matrix. We can do this by using Gaussian elimination to reduce the matrix to row echelon form:
| 1 0 -1 0 |
| 0 1 1 -2 |
| 0 0 4 -6 |
| 0 0 0 4 |
The rank of the matrix is 4, which is equal to the number of vectors. Therefore, the set of vectors is linearly independent.
b) To write the vector u as a linear combination of the vectors v1, v2, and v3, we need to find the scalars a, b, and c such that:
u = av1 + bv2 + cv3
This gives us the following system of equations:
10 = 2a + b - 2c
1 = 3a + 2b + 2c
4 = 5a + 4b + 3c
We can use Gaussian elimination to solve this system of equations:
| 2 1 -2 | | a | = | 10 |
| 3 2 2 | | b | = | 1 |
| 5 4 3 | | c | = | 4 |
After reducing the matrix to row echelon form, we get:
| 1 0 1 | | a | = | 2 |
| 0 1 -2 | | b | = | 3 |
| 0 0 0 | | c | = | 0 |
From the third equation, we can see that c can be any value. Let's choose c = 0. Then, from the first two equations, we get:
a = 2
b = 3
Therefore, the vector u can be written as a linear combination of the vectors v1, v2, and v3 as follows:
u = 2v1 + 3v2 + 0v3
u = (2)(2,3,5) + (3)(1,2,4) + (0)(-2,2,3)
u = (4,6,10) + (3,6,12) + (0,0,0)
u = (7,12,22)
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Nicole has 15 nickels and dimes. If the value of her coins is $
1.10how many of each coin does she have?
Nicole has 8 nickels and 7 dimes.
What is system of equations?A system of equations is simply two or more equations that share the same variables.
Let's use a system of equations to solve this problem:
Let x be the number of nickels, and y be the number of dimes.
From the problem, we know that:
x + y = 15 (equation 1) (the total number of coins is 15)
0.05x + 0.1y = 1.1 (equation 2) (the total value of the coins is $1.10)
To solve for x and y, we can use substitution or elimination. Let's use elimination:
Multiply equation 1 by 0.1:
0.1x + 0.1y = 1.5 (equation 3)
Subtract equation 3 from equation 2:
0.05x = 0.4
x = 8
Substitute x = 8 into equation 1:
8 + y = 15
y = 7
Therefore, Nicole has 8 nickels and 7 dimes.
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I really need help with this quickly, will mark brainiest and give most points.
After taking a dose of medication, the amount of medicine remaining in a person's
bloodstream, in milligrams, after a hours can be modeled by the function
f(x) = 95(0.84)^x. Find and interpret the given function values and determine an
appropriate domain for the function.
Round your answers to the nearest hundredth.
To find the function values, we need to substitute the given values of x into the function:
a) f(2) = 95(0.84)^2 ≈ 66.96
This means that after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.
b) f(6) = 95(0.84)^6 ≈ 35.33
This means that after 6 hours, there are approximately 35.33 milligrams of medicine remaining in the person's bloodstream.
To determine an appropriate domain for the function, we need to consider the context of the problem. The function represents the amount of medicine remaining in a person's bloodstream after taking a dose of medication, so the domain should be the set of non-negative real numbers, since the amount of medicine cannot be negative and time cannot be negative. Therefore, an appropriate domain for the function is [0, ∞).
Interpretation: The function f(x) = 95(0.84)^x models the amount of medicine, in milligrams, remaining in a person's bloodstream after x hours of taking the medication. For example, after 2 hours, there are approximately 66.96 milligrams of medicine remaining in the person's bloodstream.
After taking a dose of medication, the amount of medicine remaining in a person's bloodstream, in milligrams, after x hours can be modeled by the function
To find:
Interpret the given function values and determine an appropriate domain for the function.
Solution:
The general form of an exponential function is
Where, a is the initial value, 0<b<1 is decay factor and b>1 is growth factor.
We have,
Here, 110 is the initial value and 0.83 is the decay factor.
It means, the amount of medicine in the person's bloodstream after taking the dose is 110 milligrams and the amount of medicine decreasing in the person's bloodstream with the decay factor 0.83 or decreasing at the rate of (1-0.83)=0.17=17%.
We know that an exponential function is defined for all real values of x but the time cannot be negative. So, x must be non negative.
We know that for any value of x. So, for all values of x.
Therefore, domain of the function is and the range is .
Hope this helps!!!
GTPex-
HELP ME PLEASE THIS IS DUE TOMORROW PLEASE USE ANY STRATEGIE
Answer:
C
Step-by-step explanation:
The equation that shows the whole amount of pizza Miah ate on Saturday is 3/32 of the whole pizza
What is word problem?A word problem is a math problem written out as a short story or scenario. Basically, it describes a realistic problem and asks you to imagine how you would solve it using math.
This word problem are interpreted to mathematical equation
The left over is calculated is 3/8
therefore 5/8 of the pizza is left for Saturday
On Saturday she ate 1/4 of the pizza
= 1/4 × 3/8
= 3/32
therefore Miah ate 3/32 of the whole pizza on Saturday.
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The following expressions are polynomials. What is the sum of the expressions (8x^(5)-5x^(3)+x^(2)) and (4x^(5)+3x^(4)-6x^(2))?
The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).
To find the sum of the two polynomials, we need to add the coefficients of the like terms. Like terms are terms that have the same variable and exponent.
Step 1: Identify the like terms in the two polynomials.
- The like terms are 8x^(5) and 4x^(5), -5x^(3) and 0 (since there is no x^(3) term in the second polynomial), x^(2) and -6x^(2).
Step 2: Add the coefficients of the like terms.
- 8x^(5) + 4x^(5) = 12x^(5)
- -5x^(3) + 0 = -5x^(3)
- x^(2) + -6x^(2) = -5x^(2)
Step 3: Combine the terms to get the sum of the two polynomials.
- 12x^(5) + -5x^(3) + -5x^(2)
Step 4: Simplify the expression if possible.
- There are no like terms that can be combined, so the expression is already simplified.
The sum of the two polynomials is 12x^(5) - 5x^(3) - 5x^(2).
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9. Simplify each expression: a. √(1 + cos 76° / 2) b. (sin 158.2°) / (1 + cos 158.2°) 10. Verify that each equation is an identity. a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2 b. tan θ/2 = csc θ – cot θ
LHS ≠ RHS and the equation is not an identity.
9. Simplify each expression:
a. √(1 + cos 76° / 2)
b. (sin 158.2°) / (1 + cos 158.2°)
10. Verify that each equation is an identity.
a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
b. tan θ/2 = csc θ – cot θ
Answer:
9. a. √(1 + cos 76° / 2) = √(1 + 0.2419 / 2) = √(1 + 0.12095) = √(1.12095) = 1.0589
b. (sin 158.2°) / (1 + cos 158.2°) = (0.12088) / (1 + (-0.9927)) = 0.12088 / 0.0073 = 16.566
10. a. sin 2x / 2 sin x = cos^2 x/2 – sin^2 x/2
LHS = sin 2x / 2 sin x = 2 sin x cos x / 2 sin x = cos x
RHS = cos^2 x/2 – sin^2 x/2 = (cos x + sin x)(cos x - sin x) / 4 = (1)(cos x - sin x) / 4 = cos x - sin x / 4
Therefore, LHS ≠ RHS and the equation is not an identity.
b. tan θ/2 = csc θ – cot θ
LHS = tan θ/2 = sin θ/2 / cos θ/2
RHS = csc θ – cot θ = 1 / sin θ - 1 / cos θ = (cos θ - sin θ) / (sin θ cos θ)
Therefore, LHS ≠ RHS and the equation is not an identity.
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Jordan's football team gained 12 yards on their first play. On the second play, the team lost 8 yards. Which expression could be used to describe the total yards gained by Jordan's team?
The total yards gained by Jordan's team is 4.
What is Expression ?
Mathematical statements called expressions must contain a minimum of two terms with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are terms with an addition operator between them. Mathematical expressions can be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.
On first day, Jordan's football team gained 12 yards.
On second day, Jordan's football team lost 8 yards.
So, The total yards(net) would be :
= total yards gained by team - total yards lost by team
= 12 - 8
= 4 yards.
Here, total yards gained by team is the first expression while total yards lost by team is the second expression.
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I NEED HELPP ASAP!!!!!!!!!!!!!!!!!
The measure of center that would best summarize the plot is given as follows: Median of 11.
The measure of variability is given as follows: IQR of 1.5.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.From the plot, these features are given as follows:
Minimum non-outliter value of 6.Q1 of 10.Median of 11.Q2 of 11.5.Maximum non-outlier value of 16.The median is the best measure of center of the data-set.
There is an outlier at 16, hence the best measure of variability is the IQR, given by the difference between the Q3 and the Q1, hence:
IQR = 11.5 - 10
IQR = 1.5.
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A scatterplot showing a relationship between x and y is shown below. Which equation represents the line of best fit for the graph? Responses y=x+5 y = x + 5 y=x−5 y = x − 5 y=x+15 y = x + 15 y=2x−15
Plotting the data and visually examining the connection between x and y equation is often the best method for identifying which equation best describes the line of best fit.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions.
Based on the above equations, y = x + 5 or y = x - 5 would be the most plausible contenders. Both of these equations have the typical slope for a linear connection, which is a straight line slope of 1.
While the y-intercept of the equation y = x + 15 has a significantly bigger value than would be predicted based on the other possibilities, the slope of the equation is 1. Similar to that, the slope of the equation y = 2x - 15 is 2.
Plotting the data and visually examining the connection between x and y is often the best method for identifying which equation best describes the line of best fit.
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Adam is rewriting the expression 8^5/8^2 in equivalent form. His steps
The correct equivalent form of 8⁵/8² is Adam made an error in step 2. The denominator should be 1, not 8¹. Option B is correct.
In step 2, Adam used the property of exponents that states: [tex]a^{(m-n)}[/tex] = [tex]a^{m}[/tex] / [tex]a^{n}[/tex]. However, he made a mistake by writing 8¹in the denominator instead of 1.
The correct expression after step 2 should be:
[tex]8^{5-2}[/tex] /1 = 8³
Then, in step 3, Adam used the property of exponents that states: [tex]a^{m}[/tex] / a = [tex]a^{m-1}[/tex]. This step is correct, and the expression becomes:
[tex]8^{3/8}[/tex]
Finally, in step 4, Adam simplified the expression by dividing 8³ by 8². This step is also correct, and the expression simplifies to:
8¹ = 8
Therefore, the correct equivalent form of 8⁵/8² is 8.
Hence, B. Adam made an error in step 2. The denominator should be 1, not 8¹ is the correct option.
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--The given question is incomplete, the complete question is
"Adam is rewriting the expression 8^5/8^2 in equivalent form. His steps are shown: step 1: 8^5/8^2, step 2: 8^(5-2)/8^1, step 3: 8^3/8, step 4: /8^2. which statement describes the step and the error Adam made in that step? A) Adam made an error in step 2. The exponent in the numerator should be 5+2 B) Adam made an error in step 2. The denominator should be 1, not 8^1 C) Adam made an error in step 3. The value of 8^1 is 1, not 8."--
Could someone please explain how to do this? My teacher wasn't clear, so I don't know how.
Check the picture below.
[tex]\boxed{4} \\\\\\ (x+3)^2~~ = ~~[(x-1)+10](x-1)\implies x^2+6x+9~~ = ~~(x+9)(x-1) \\\\\\ x^2+6x+9~~ = ~~x^2+8x-9\implies 6x+9=8x-9\implies 9=2x-9 \\\\\\ 18=2x\implies \cfrac{18}{2}=x\implies 9=x[/tex]
Help!!!!
I’m on the last question
Answer:
The area of the whole rectangle is 28 cm^2
Step-by-step explanation:
since both triangles are congruent, they have the same area. 14 x 2 = 28
How do you do c) really need help!!
DBA QUESTION #1 (Lesson 1.03)
Explain what terms and degrees are.
How are they used to classify polynomials?
Give an example.
The degree and terms of the polynomial are explained and an example is also discussed.
What are polynomials?
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. It is a mathematical expression made up of exponents, constants, and variables that are mixed using addition, subtraction, multiplication, and division (No division operation by a variable).
The expression's components that are divided up by the operators "+" or "-" are referred to as polynomial terms. In polynomials, like terms are ones that share the same variable and power. Unlike terms are those that have dissimilar variables and/or dissimilar powers.
The degree of a polynomial is the highest or biggest exponent of the variable in the polynomial. A polynomial equation's maximum number of solutions can be calculated using the degree.
The different types of polynomials based on terms are:
Monomial - Single termBinomial - Two termsTrinomial - Three termsThe different types of polynomials based on the degree are:
Constant polynomial - Zero degreeLinear polynomial - Degree is oneQuadratic polynomial - Degree is twoCubic polynomial - Degree is 3Example,
Consider a polynomial 3x² + 5x + 4
Number of terms = 3 (Trinomial)
Degree = 2 (Quadratic polynomial)
Therefore the degree and terms of the polynomial are explained and an example is also discussed.
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The answer is:
⇨ belowWork/explanation:
Here's how we classify polynomials based on the number of terms:
monomial - has only one term
binomial - has two terms
trinomial - has three terms
polynomial - has four terms or more
As for degrees, those are the highest exponents the polynomial.
Example: Classify [tex]\bf{2p^2+p}[/tex].
It has 2 terms so it's a binomial.
Its highest exponent is 2 so it's a second degree binomial.
Hence, that's how we classify polynomials.HELP ME!! i don't really understand this!
Answer:
Step-by-step explanation:
lol sorry I know it but don’t know how up to right it sorry
Can someone help with this please?
According to the Synthetic Division, the Quotient is equal to 7x² -4x + 5 and the Remainder is equal to 8.
Synthetic Division: What is it?Synthetic division can divide two polynomials more quickly than the standard long division algorithm.
With this method, the dividend and divisor polynomials are reduced to a set of numerical numbers.
Given:
(7x³-25x² +17x -7) ÷ (x-3).
So, Synthetic Division for this is as follows:
(x-3) | (7x³-25x² +17x -7) | 7x² -4x + 5
7x³-21x²
_________
-4x² + 17x
-4x² + 12x
_______________
5x - 7
5x - 15
________
8
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A student needs 8 more classes to complete her degree. If she has met 5 pre-requisites for all the courses, how many ways can she take 4 classes next semester?
There is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.
Since the student needs to take 8 more classes to complete her degree and has already taken 5 pre-requisites, she has 8 - 5 = 3 classes that she can choose from for next semester.
To calculate the number of ways she can take 4 classes next semester, we can use the combination formula:
nCr = n / (r × (n-r))
where n is the number of classes she can choose from (which is 3), and r is the number of classes she will take next semester (which is 4).
Plugging in the values, we get:
3C4 = 3 / (4 × (3-4)) = 0
Since we cannot choose 4 classes from a set of 3 classes, the answer is 0.
Therefore, there is no way for the student to take 4 classes next semester, given that she needs 8 more classes to complete her degree and has already met 5 pre-requisites.
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Milo sets sail from a dock and heads in a straight line for 7 miles. The wind then picks up momentarily and he is forced to change direction by 5pi/36. He then sails in a straight line in this new direction for another 4 miles. At this point, how far is he from the dock? Round to 2 decimal places.
Milo is 8.09 miles from the dock.
Here we can use the Law of Cosines,
which states that c² = a² + b² - 2abcos(C),
Where c is the side opposite the angle C in a triangle.
Call the distance from the dock to the point where Milo changes direction "a", the distance Milo sails in the new direction "b", and the angle between these two sides "C".
We know that a = 7 miles and b = 4 miles.
To find C, we can use the fact that Milo changes direction by 5π/36 radians.
Since he turned to the right, we can say that he turned by,
⇒ 360 - 5π/36 = 355π/36 radians.
This is the angle between the two sides of the triangle.
Now we can plug these values into the Law of Cosines to find the distance from Milo to the dock:
⇒ c² = a² + b² - 2abcos(C)
⇒ c² = 7² + 4² - 2(7)(4)cos(355π/36)
⇒ c² = 49 + 16 - 56cos(355π/36)
⇒ c² = 65.47
Taking the square root of both sides, we get:
c = 8.09 miles (rounded to 2 decimal places)
Therefore, Milo is 8.09 miles from the dock.
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Select the correct answer. Which graph represents this equation? A. A parabola declines through (negative 4, 10), (negative 3, 4), (negative 2, 0), (negative 0 point 5, negative 4), (0, negative 6), (2, negative 8), (4, negative 6), (6, 0), (8, 10) on the x y coordinate plane. B. A parabola declines through (negative 12, 10), (negative 11, 8), (negative 10, 0), (negative 8, negative 6), (negative 4, negative 10), and rises through (0, negative 6), (2, 0) and (3, 6) on the x y coordinate plane. C. A parabola declines through (negative 3, 8), (negative 2, 0), (0, negative 6) and (4, negative 10) and rises through (8, negative 6), (10, 0) and (11, 6) on the x y coordinate plane. D. A parabola declines through (negative 8, 10), (negative 7, 4), (negative 6, 0), (negative 4 negative 6) and (negative 1, negative 8) and rises through (1, negative 4), (2, 0), (3, 4) and (4, 8) on the x y coordinate plane.
The graph of the quadratic function y = 1.5x² + 4x - 2 is given by the image shown at the end of the answer.
How to obtain a graph of a quadratic function?The function for this given problem is defined as follows:
y = 1.5x² + 4x - 2.
a 1.5, b 4, c -2.
By Solving the equation we get these values,
x = -3.09, hence function passes through the point (-3.09, 0).
x = 0.43, hence function passes through the point (0.43, 0).
The y-intercept of this function is given by coefficient c = -2, hence the function also passes through the point (0, -2).
The x-coordinate vertex is given as follows:
x = -b/2a = -4/3 = -1.33.
Hence the y-coordinate vertex is of:
y = 1.5(-1.33)² + 4(-1.33) - 2 = -4.67.
Missing Information
The problem asks for the graph of the following function is given below:
y = 1.5x² + 4x - 2.
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Please help this is Algebra
According to this data, 36 people selected their favorite colors, fill in the blanks below:
the product (2x^(4)y)(3x^(5)y^(8))is equivalent towhat polynomial must be added to x^(2)-2x+6 so that the sum is 3x^(2)+7x
The polynomial that must be added to x^(2)-2x+6 is 2x^(2) + 9x - 6.
To find the product of the two polynomials (2x^(4)y)(3x^(5)y^(8)), we need to use the distributive property and combine like terms.
The distributive property states that a(b+c) = ab+ac. So, we can distribute the first polynomial to each term in the second polynomial:
(2x^(4)y)(3x^(5)y^(8)) = (2x^(4)y)(3x^(5)) + (2x^(4)y)(y^(8))
Next, we can combine like terms by adding the exponents of the variables:
= 6x^(4+5)y^(1+8)
= 6x^(9)y^(9)
So, the product of the two polynomials is 6x^(9)y^(9).
To find the polynomial that must be added to x^(2)-2x+6 so that the sum is 3x^(2)+7x, we can set up an equation:
x^(2)-2x+6 + (a+bx+cx^(2)) = 3x^(2)+7x
Then, we can rearrange the equation to solve for the polynomial:
a+bx+cx^(2) = 3x^(2)+7x - x^(2) + 2x - 6
a+bx+cx^(2) = 2x^(2) + 9x - 6
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solve the system of linear equation by elimination 8x+3y=-5
3y=x+4 please show work
The solution of linear equations is (x, y) = (-0.8905, 0.708).
To solve this system of linear equations by elimination, first multiply both equations by the same number so that when you add the equations together, one of the variables is eliminated. In this case, we'll multiply the first equation by 3 and the second equation by 8.
8(8x+3y=-5)
3(3y=x+4)
24x + 9y = -15
24y = 8x + 32
Now add the two equations together:
24x + 24y = -15 + 32
24x + 24y = 17
Simplifying this equation, we get:
24y = 17
y = 17/24
y = 0.708
Now, plug in the value of y into one of the original equations to solve for x. We'll use the first equation:
8x + 3(0.708) = -5
8x + 2.124 = -5
8x = -7.124
x = -7.124/8
x = -0.8905
Therefore, the solution to the system of linear equations is (x, y) = (-0.8905, 0.708).
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What is the largest possible value x could take given that it must be an integer? x < 2
The largest possible value x could take given that it must be an integer for x < 2 is 1.
Difference between an inequality and an equation?The key distinction between an inequality and an equation is that an inequality describes a connection of inequality between two expressions, whereas an equation expresses equality between two expressions. In other words, an inequality shows that one expression is more or less than the other expression, but an equation shows that two expressions have the same value.
The highest number x might have is 1 if x must be an integer and x 2. This is due to the fact that any number higher than one would break the inequality x 2, and any number between one and two that is not an integer would also violate the stipulation that x must be an integer.
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Solving a rational equatic Solve for v. (3)/(4v)+(7)/(v)=1 If there is more than one solution, If there is no solution, click on "No s
There is only one solution for this equation. v = 31/4 is the only solution to this equation.
To solve for v in the equation (3)/(4v)+(7)/(v)=1, we need to get a common denominator and then solve for v.
Step 1: Get a common denominator. The common denominator for 4v and v is 4v. So, we will multiply the second fraction by 4/4 to get a common denominator:
(3)/(4v)+(7*4)/(v*4)=1
Step 2: Simplify the fractions:
(3)/(4v)+(28)/(4v)=1
Step 3: Combine the fractions:
(3+28)/(4v)=1
Step 4: Simplify the numerator:
(31)/(4v)=1
Step 5: Cross-multiply to solve for v:
31=4v
Step 6: Divide both sides by 4 to get v:
v=31/4
The solution is v=31/4.
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(Answer Quick) Can you show the work as well?
Giving 30 points!
Which expressions are equivalent to (a^2-16(a+4)? Select the three equivalent expressions
A.) a^3-64
B.) (a-4)^3
C.) (a+4)^3
D.) (a+4)^2(a-4)
E.) (a-4)^2(a+4)
F.) [(a)^2-(4^2)](a+4)
G.) (a-4)(a+4)(a+4)
Expressions A, B, and F are equivalent to (a²-16(a+4)).
What does equivalent mean?Equivalent is a term that means equal in value, measure, force, effect, or significance. It can be used to describe two or more things that are of the same value or having the same characteristics. For example, a 1:1 ratio is said to be equivalent because it has the same value on both sides. Equivalent can also mean having the same or similar effect, such as two different treatments for a disease that have the same outcome.
The expressions A, B, and F are equivalent to (a²-16(a+4)). Expression A is equal to a² - 16a - 64. This expression can be rewritten as a³ - 64, which is equal to A. Expression B is equal to (a - 4)³. This expression can be rewritten as a³ - 64, which is equal to A. Expression F is equal to [(a)²-(4^2)](a+4). This expression can be rewritten as (a² - 16)(a+4), which is equal to A. Therefore, expressions A, B, and F are equivalent to (a²-16(a+4)).
Expression C is equal to (a+4)³, which is not equivalent to (a²-16(a+4)). Expression D is equal to (a+4)²(a-4), which is not equivalent to (a²-16(a+4)). Expression E is equal to (a-4)²(a+4), which is not equivalent to (a²-16(a+4)). Expression G is equal to(a-4)(a+4)(a+4), which is not equivalent to (a²-16(a+4)). Therefore, expressions C, D, E, and G are not equivalent to (a²-16(a+4)).
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1. 1 8 Use the formula SA = 2πrh + 2πr2 to find is the surface area of the cylindrical food storage container. Use 3. 14 for π. Round your answer to the nearest hundredth of a square inch
The Surface Area of Container is 954. 56 inch².
What is Surface Area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area.
As, we Know the Surface Area of Cylinder
= 2πr² + 2πrh
Radius of the base = 8 inches
Height of the cylinder = 11 inches.
Now, putting the values we get
= 2πr² + 2πrh
= 2 x 3.14 x 8 x 8 + 2 x 3.14 x 8 x 11
= 401.92 + 552.64
= 954. 56 inch²
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Which graph models function m?
x- 0 1 2 3 4 5
m(x)- -9 -4 -1 0 -1 -4
The population of a city was approximately 450,000 in the year 2000 and was projected to grow at
an annual rate of 2.3%. Predict the population for the year 2006.
Answer: 515,783
Step-by-step explanation: f(x)= a(1+r)^x 450,000(1+0.023)^6
