In rectangle , The domain of A is: 0 ≤ l ≤ 5
To express the area of the rectangle as a function of the length of one of its sides, we first need to use the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.
In this case, we know that the perimeter is 20 m, so we can write:
20 = 2l + 2w
Simplifying this equation, we can solve for the width:
w = 10 - l
Now we can use the formula for the area of a rectangle, which is A = lw, to express the area as a function of the length:
A(l) = l(10 - l)
Expanding this expression, we get:
A(l) = 10l - l^2
To find the domain of A, we need to consider what values of l make sense in this context. Since l represents the length of one of the sides of the rectangle, it must be a positive number less than or equal to half of the perimeter (since the other side must also be less than or equal to half the perimeter). Therefore, the domain of A is:
0 ≤ l ≤ 5
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Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the result when 2 x 3 − 9 x 2 + 11 x − 6 2 x 3 - 9 x 2 + 11 x - 6 is divided by x − 3 x − 3 ? Show your work.
Answer:
2x^3 -9x^2 +11x-6 divided by x-3
Step-by-step explanation:
2x^2 - 3x + 2
------------------------------
x - 3 2x^3 - 9x^2 + 11x - 6
2x^3 - 6x^2
--------------------------------------subtract
-3x^2 + 11x
-3x^2 + 9 x
----------------------------------------subtract
2x - 6
2x - 6
-----------------------------subtract
0
- 2x^2 - 3x + 2
:/
The figure below is a right rectangular prism.
X
W
Intro
M
N
x
Y
N
O
12
2-
T
Which expression represents the volume of the prism?
01
(1²
01/1²
27
4
Done
the volume of the rectangular prism is 1/2 x³.
What is rectangular prism?
The normal's length from the prism's base to its top base serves as a gauge for the structure's height. At their base, certain prisms have an angle. Prism's top end is referred to as the "base" since the word "base" can refer to either end of a prism. The area (A) of the base of a prism's base times its height (H) equals the prism's volume (V). Since A is the base area and H is the prism's height, the volume of the prism is therefore A H cubic units.
The base area is A = x*x =x²
The height is 1/2 x
The volume of the rectangular prism is A*H = 1/2 x³.
Hence the volume of the rectangular prism is 1/2 x³.
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How much horsepower is a 160hp engine using at 65% efficiency
Answer:
The power is 15 watts.
Step-by-step explanation:
It is equivalent to:
0.02012 mechanical horsepowers
0.02039 metric horsepowers
0.02011 electrical horsepowers
0.001529 boiler horsepowers
16. Write the equation of a linear function and define one point that lies on this function. Write the equation of your function translated 4 units to the left and 5 units down. What are the coordinates of
your new point?
The original linear function is:
y = 2*x + 4 with the point (1, 6)
The translated function is:
y = 2x + 7
And the translated point is (-3, 1)
How to translate the linear function?First, we want to write a random linear function, I will use:
y = 2*x + 4
To find a point on that line, we can just evaluate the function in x = 1, we will get:
y = 2*1 + 4
y = 2 + 4
y = 6
So we have the point (1, 6)
Now we want to translate it 4 units to the left and 5 units down.
To translate it 4 units to the left, we need to add 4 to the argument.
y = 2*(x + 4) + 4
And to translate it 5 units down, we just need to subtract 5, we will get:
y = 2*(x + 4) + 4 - 5
Now we can simplify this to get:
y = 2*x + 2*4 + 4 - 5
y = 2x + 8 + 4 - 5
y = 2x + 7
The new coordinates of the point are the same as the last ones, but we subtract 4 to the x-value and 5 to the y-value:
(1 - 4, 6 - 5) = (-3, 1)
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What are the 9 formulas of algebra?
There are both numbers and letters in algebra. Numbers are constant, i.e. e. The unknown quantities in the algebraic formula are represented by letters or alphabets. The 9 formulas of algebra are explained further.
Define algebra and its 9 formulas?Algebra is a mathematical tool that we use to calculate distances, volumes, and perimeters of spaces as well as to calculate costs, rent things out, and understand time relationships.
Algebraic equations come in five main categories. We can tell them apart by the variables' positions, the types of operators and functions being used, and the behavior of the graphs. Each equation has a different probable input and generates a different result based on analysis.The 9 formulas of algebra are explained as:
a² – b² = (a-b)(a+b)(a+b)² = a² + 2ab + b²(a-b)² = a² – 2ab + b²a² + b² = (a-b)² +2ab.(a+b+c)² = a²+b²+c²+2ab+2ac+2bc.(a-b-c)² = a²+b²+c²-2ab-2ac+2bc.a³-b³ = (a-b) (a² + ab + b²)a³+b³ = (a+b) (a² – ab + b²)(aⁿ)(aˣ) = aⁿ⁺ˣ (ab)ⁿ = aⁿˣTo know more about the algebra, here
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Write a system of equations for the coefficients of a polynomial of degree 2 that passes through (1, - 2), (- 2, 7) and (- 5, - 2) Solve the system.
The system of equations is:
-2 = a + b + c
7 = 4a - 2b +c
-2 = 25a + 5b + c
The polynomial is:
y = (1/3)*x^2 - 6x - 1/3
How to write and solve the system of equations?The general polynomial of degree 2 can be written as:
y = a*x^2 + b*x +c
If we use the fact that it passes through the 3 given points, then we can write the 3 equations:
-2 = a*1^2+ b*1 + c
7 = a*(-2)^2 + b*-2 + c
-2 = a*5^2 + b*5 + c
We can simplify these to get the system of equations:
-2 = a + b + c
7 = 4a - 2b +c
-2 = 25a + 5b + c
First, isolate c on the first equation to get:
c = -2 - a- b
Replace it on the other two:
7 = 4a - 2b + (-2 - a - b)
-2 = 25a + 5b + (-2 - a - b)
9 = 3a - 3b
0 = 24a + 4b
Using the second equation we can rewrite:
-24a = 4b
-24a/4 = b
-6a = b
Ande replace that in the other equation:
9 = 3a - 3*(-6a)
9 = 3a + 18a
9/21 = a
1/3 = a
And the value of b is:
-6*(1/3) = b
-2 = b
And the value of c is:
c = -2 - (-2) - 1/3
c = -1/3
The polynomial is:
y = (1/3)*x^2 - 6x - 1/3
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SOMEONE HELP PLSSSS
Which equation does the graph below represent?
(image below)
Answer:below
Step-by-step explanation:
y=1/3x
Which of the following illustrates the truth value of the given conditional statement? If 5 = 3 + 2, then 3 + 2 = 5. F T → T F F → F T T → T T F → F
The option that illustrates the truth value of the given conditional statement is; T T → T
How to interpret Truth conditional statements?A conditional statement is considered to be true when the antecedent and consequent statements are both true or if the antecedent is false. When the antecedent is false, it means that the truth value of the consequent does not matter; the conditional will always be true.
We are given the conditional statements at;
If 5 = 3 + 2, then 3 + 2 = 5
Now, a conditional statement, signified by t f which means true and false, is an if-then statement with t being a hypothesis and f being an inference. The statement that illustrates the truth value is T T → T because 5 = 3 + 2 which is true and 3 + 2 = 5 which is also true.
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Select all the equations where z=5z=5z, equals, 5 is a solution.
All the equations in which z = 5 are a solution are given as follows:
A. 8 = z + 3.
D. 12z = 60.
E. 12 + z = 17.
How to solve the equations?The first equation is defined as
8 = z + 3.
Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:
z = 8 - 3
z = 5.
The second equation is given as follows:
z - 1 = 6.
Applying the addition operation, which is the inverse of the subtraction, the solution is given as follows:
z = 7.
The third equation is given as follows:
20 = 40z
Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:
z = 20/40
z = 0.5.
The fourth equation is given as follows:
12z = 60.
Applying the quotient operation, which is the inverse of the multiplication, the solution is given as follows:
z = 60/12
z = 5.
The fifth equation is defined as
12 + z = 17.
Isolating the variable z, applying the subtraction operation, which is the inverse of the addition, the solution is given as follows:
z = 17 - 12
z = 5.
Missing InformationThe equations are given by the image presented at the end of the answer.
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What is the difference between 2D coordinate system and 3D coordinate system?
The main difference between the 2D and 3D coordinate systems is that the 3D coordinate system adds a third axis (Z) to the two axes of the 2D coordinate system.
What is coordinates system?A coordinate system is a two-dimensional or three-dimensional system which is used to identify the location of a point or object in the space. It is represented by a set of axes, which are perpendicular and equally spaced from each other to form a grid-like structure. The coordinates of a point or object are determined by the intersection of the two or three axes. Common coordinate systems used in mathematics and science include the Cartesian, polar, and spherical coordinate systems.
A 2D coordinate system is a system in which two axes (X and Y) are used to define a point in a two-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the two axes. The two axes form a coordinate plane, which provides a visual representation of the system.
A 3D coordinate system is a system in which three axes (X, Y, and Z) are used to define a point in a three-dimensional space. This system is used to describe the position of a point in relation to the origin, which is located at the intersection of the three axes. The three axes form a coordinate space, which provides a visual representation of the system.
This third axis allows points in the 3D coordinate system to be represented in the third dimension. Additionally, the 3D coordinate system provides a more detailed representation of points, as it can represent points in all three dimensions.
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Find the margin of error
11.13 < μ < 15.03
The margin of error of the intervals 11.13 < μ < 15.03 is 1.95
How to solve for the margin of errorIn order to get the margin of error, we would first have to find the samole mean.
The sample mean x = the upper limit + lower limit / 2
the upper limit = 15.03
The lower limit = 11.13
Then we would have: 15.03 + 11.13 / 2
= 26.16 / 2
= 13.08
Then the margin of error would be
upper limit - sample mean
= 15.03 - 13.08
= 1.95
The margin of error is given as 1.95
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Pls helppppppppppppppppp
Answer:
x=8
Step-by-step explanation:
11x+2=90
11x=88
x=8
Answer:
19. X=8
20. x=7
Identify the slope, and y -intercepts and graph the linear equation.
4. y=1-3
5. 5x +3y = 15
6. y = 3
The slope, and the y-intercepts are
Slope = 0, y-intercept = -2Slope = -5/3, y-intercept = 5Slope = 0, y-intercept = 3How to determine the slope and the intercept of the equationsA linear equation can be represented as
y = mx + c
Where
slope = m
y-intercept = c
Using the above as a guide, we have the following:
Slope of (4) = 0 and the y-intercept is -2Slope of (5) = -5/4 and the y-intercept is 5Slope of (6) = 0 and the y-intercept is 3See attachment for the graph
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the sum of two numbers is 49 and the difference between the numbers is 1
The values of x and y are 24 and 25 when the sum of two numbers is 49 and the difference between the numbers is 1
What is Linear equation ?
linear equation can be defined as the equation in which the highest degree is one.
Given ,
the sum of two numbers is 49 and
the difference between the numbers is 1
Let the two numbers be x and y .
so x+y = 49
x-y = 1
x = 1+y
from two equations ,
Substitute x = 1+y in x+y = 49
we get,
1+y+y = 49
2y = 49 - 1
2y = 48
y = 24
substitute y =24 in x=1+y ,
we get
x = 24+1
x = 25
Hence , the values of x and y are 24 and 25 .
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On the blueprints of their new home, Paul and Gretha notice the balcony is 9 inches long and 4 inches wide. They know
that the actual balcony will be 11.7 ft long. How wide will the balcony be?
The wideness of the actual balcony would be = 5.2 feet.
What is a scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object.
The actual size = scale factor × blueprint
where actual length = 9 inches
blueprint = 11.7 = 140.4 inches
scale factor = actual size/blue print
= 140.4/9 = 15.6
If the blue print width size = 4
the actual size = 4× 15.6 = 62.4 inches = 5.2 feet
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At a certain high school, the distribution of backpack weight is approximately normal with mean 19. 7 pounds and standard deviation 3. 1 pounds. A random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded.
For all samples of 5, there is a 0.05 probability that the sample mean would be higher than 22 pounds.
The selection of bags weights, on average, 19.7 pounds.
The standard variation is 3.1 pounds.
Both the normal probability density function and the sampling distribution theorem were used.
When dealing with issues involving samples of data that are regularly distributed, the z-score algorithm is applied.
The z-score of a measure X is calculated as follows:
z = (x - μ) ÷ σ
The number of standard deviations is calculated using the Z-score. The average is the metric employed.
We examine the p-value linked with the Z-score in the z-score table after computing the Z-score.
The chance that the measure's value is less than X, or what proportion of X, is represented by this p-value.
We may calculate the likelihood that the metric exceeds X by subtracting 1.
The Central Limitation Theorem also holds for skewed variables when n is at least 30.
The sample mean will remain constant regardless of sample size.
The standard error, though, will alter.
The probability that the sample means will be higher than 22 is shown by P(a > 22).
For all samples of size 5, the possibility that they will weigh more than 22 pounds is about 0.05.
Your question is incomplete but most probably your full question was
at a certain high school, the distribution of backpack weight is approximately normal with a mean of 19.7 pounds and a standard deviation of 3.1 pounds. a random sample of 5 backpacks will be selected, and the weight, in pounds, of each backpack will be recorded. what is the probability that my next five samples will average 22 pounds?
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A triangle has side lengths measuring 20 cm, 5 cm, and n cm. Which describes the possible values of n?5 < n < 155 < n < 2015 < n < 2015 < n < 25.
After using the triangle inequality theorem, the possible values of the unknown side of the triangle is 15 < n < 25.
In this case, we are given that:
The lengths of the sides of a triangle are 20, 5, and n centimeters.
The theorem of triangle inequality stated that the lengths of any two of a triangle's sides added together must be bigger than the length of the third side. Given two sides, x and y, we can use the triangle inequality theorem to predict that the length of the third side will be between x + y and x - y.
Therefore,
x - y < n < x + y
20 - 5 < n < 20 + 5
15 < n < 25
As the result, the possible value of the unknow side of the triangle would be 15 < n < 25.
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!PLEASE HELP! 35 POINTS!
How does the total amount of work used to move a storage box 10 meters across the floor with a force of 20-N compare to moving the same storage box 8 meters with the same amount of force?
How much work is required to move each box? How do those numbers compare with one another? Which requires more work?
Answer: By 40J
Step-by-step explanation:
20*10 = 200J in Newton meter (nm)20*8 = 160J in Newton meter (nm)Storage Box 1 (20*10J) needs more work as compared to Storage Box 2 (20*8J)And 200-160=40 or 20*10-20*810-8=2, Hence the difference is (20*2) or 40pls mark it as brainliest
In mixed fraction please
Question is the picture.
Answer:
in decimal it is 36.72, in fraction it is 918/25
Step-by-step explanation:
The cost in dollars to produce x shovels in a factory is given by the function C(x) = 26x +400. The number of shovels that can be produced in h hours is
given by the function N(h) = 20h.
7. Find the rule for C(N(h)).
8. Find the cost when h=6 hours.
The amount of shovels that can be produced in h hours is 960 shovels
What is an equation example?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
What is the full meaning of the equation?A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7.
In the given equation,
The number of shovels produced are
C(x)=26*20+400
=520+400
=920 shovels
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Nicky said, “You’ll never guess my numbers! Their sum is 12 and their difference is 26.” What numbers is she thinking of?
Answer:
She's thinking of 19 and -7.
Step-by-step explanation:
x+y=12
x-y=26
-----------
2x=38
x=38/2
x=19
19+y=12
y=12-19=-7
What is the area of the triangle having sides 3 cm 4 cm and 5 cm?
The area of the triangle having sides 3 cm 4 cm and 5 cm is calculated to be 6 cm².
Given that,
The sides of the triangle are said to be 3 cm, 4 cm and 5 cm.
By looking at the lengths of the sides of the triangle, it is clear that they are the sides of a right angled triangle. The Pythagorean theorem can be used to verify this.
5² = 3² + 4²
25 = 25
So, 5 is said to be the hypotenuse side of the right triangle and 3, 4 are said to be the base and height of the right triangle.
The formula to find out the area of the triangle is given by,
Area A = 1/2 × Base b × Height h
A = 1/2 × b × h
From the above conclusion, b and h are found to be 3, 4.
So, A = 1/2 × b × h = 1/2 × 3 × 4 = 6 cm²
Thus, the area of the required triangle is calculated to be 6 cm².
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When there is a fixed factor and a variable factor the law would be Mcq?
When there are two factors—a fixed element and a variable factor—the law of variable proportions is created. According to the law of variable proportions, the marginal product of a factor will gradually decrease when its quantity is raised while the other elements remain constant.
We are aware that the relationship between the number of units of a variable factor and the entire physical product is shown by the law of variable proportions.
Additionally, the TPP increases initially at a rising pace, then at a falling rate, and finally declines if we maintain other parameters constant and increase the units of the variable factor.
According to the law of variable proportions, if a producer raises the units of a variable factor while keeping other elements constant, the total product will initially increase at an increasing pace, then it will increase at a diminishing rate, and finally it will begin to decline.
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What is x?
X= _______ degrees
Answer:
x = 149 degree
Step-by-step explanation:
First, we have to find the missing angle of the triangle
1 triangle = 180 degree
We know 2 angles, one is 63 degrees and one is 86 degrees.
63 + 86 = 149 degree
180 - 149 = 31 degree
So, the angle of the triangle is 31 degrees. Now we know that angle add with the x to get 180 degrees, so
180 - 31 = 149 degree
So, x = 149 degree
the vector sum of two or more other vectors is called the
Answer: resultant
Step-by-step explanation:
A Playstation 5 sells for $500. Today only, it is on sale for 30% off. What is the sale price of the PS5?
a: $30.00
b: $150.00
c: $350.00
d: $470.00
Answer:
c. $350.00
Step-by-step explanation
im sorry if this didn't help i wrote everything down on paper
Based on this graph, what is the BEST estimate of the number of toy cars Drew
must sell to break even?
A. 8000
B. 10,000
c. 20,000
D. 32,000
Solve the equation -4x+3y=12 for y.
5x+y=3,5x+y=2 by inspection
Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2. Either conditional solutions or identities are categories for equations.
what is equation ?Its simplest form is thought to be the number's smallest equivalent fraction. How to determine the simplest form. Look for shared factors in the denominator and numerator. A fractional number can be checked to discover if it is a prime number. A statement having two quadrilateral and an equal sign in the middle is referred to as a mathematical equation. Every variable's degrees are listed in descending order in the general form of any equation. The formula for a linear equation is x + b = 0. The general form of a two-variable linear equation is an x + b y + c = 0. (or something similar). Either conditional solutions or identities are categories for equations. An identity holds true for whatever value of the variables.
given
5x + y = 3
5x + y = 2
x = y-3/ 5
y - 3 +y = 2
2y = 5
y = 5/2
x = 3
Consequently, (3, 5/2) is the answer to the equations 5x+y=3 and 5x+y=2.
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Write an equation of a line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8
A line that is perpendicular to another line has a slope that is the negative reciprocal of the original line. The slope of the line y = 2/7x - 8 is 2/7. To find the slope of the line that is perpendicular to it, we take the negative reciprocal of 2/7 which is -7/2.
We know that the line we're trying to find passes through the point (-4, 2), so we can use this point and the slope to write the equation of the line in point-slope form:
y - y1 = m (x - x1)
where (x1, y1) is the point the line passes through, m is the slope, and y and x are the coordinates of any point on the line.
So the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is:
y - 2 = -7/2 (x + 4)
Simplifying this, we get
y = -7/2 x - 8
Therefore the equation of the line that passes through (-4,2) and is perpendicular to the line y= 2/7x - 8 is y = -7/2 x - 8