The total area of the sandbox is given by 6x^2-11x+5
Width of the sandbox = (x-1)
Length of the sandbox = (6x-5)
Rectangle area in geometry refers to the area that a rectangle occupies on a two-dimensional plane. A quadrilateral, a form of a two-dimensional object with four sides and four vertices, is what a rectangle is. The rectangle's four angles are all right angles or exactly 90 degrees. The rectangle's opposing sides are equal and parallel to one another.
The formula for the area of a rectangle:
Area of rectangle = Length*Width
Substituting the value in the formula we get:
Area of rectangle = (x-1)*(6x-5)
= 6x^2-5x-6x+5
= 6x^2-11x+5
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What is 44 millimeters converted to m
Solve a³ = 11.
Solve c² = 27.
Answer: A: A = 2.2240 B: C = 3
Hope this helped! :)
What is the slope of the line that passes through the points (6, -5)(6,−5) and (6, -4)(6,−4)?
Answer:
Undefined
Step-by-step explanation:
The x-coordinates are ths same, so this is a vertical line. Vertical lines have undefined slope.
is the sum rational or irrational drag the labels
The rational sums are:
√16 + (-21/5)
√4 + 5
√36 + ∛27
The irrational sums are:
π + 24
√8 + π
3/4 + √27
What are rational and irrational numbers?Irrational numbers cannot be stated as a fraction, although rational numbers can be expressed as ratios (such as P/Q and Q≠0). Additionally, an irrational number's decimal expansion neither repeats nor terminates. Terminating and repeating decimals are rational numbers.√16 + (-21/5)
= 4 + (-21/5)
= 4 - (21/5)
= (20 - 21) / 5
= - 1/5
= -0.2
Hence, the sum can be expressed as p/q so it is a rational number.
π + 24
= 3.1428571429 + 24
= 27.1428571429
The sum is non-terminating, so it is an irrational number.
√8 + π
= 2.82842712 + 3.1428571429
= 5.97128426
The sum is non-terminating, so it is an irrational number.
√4 + 5
= 2 + 5
= 7
The sum is an integer so it is a rational number.
√36 + ∛27
= 6 + 3
= 9
The sum is an integer so it is a rational number.
3/4 + √27
= 3/4 + 5.1961524227
= 0.75 + 5.1961524227
= 5.9461524227
The sum is non-repeating so it is an irrational number.
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The complete question is: "The table has a set of expressions representing the sums of rational and irrational numbers. Find each sum, and indicate whether the sum is rational or irrational. Drag the labels to the correct locations on the table. Each label can be used more than once."
Simplify a raised to the negative third power over quantity 2 times b raised to the fourth power end quantity all cubed
Here is the answer
I hope it helped you
A statement is given below:
"The number of square units in the area of a square is greater than or equal to the number of units in the perimeter of the
square
Which side length of a square provides a counterexample to the given statement?
o 10 units
O 2 units
o 6 units
Previos
The side length of the square that provides a counterexample to the statement square units in the area of a square is greater than or equal to the number of units in the perimeter is 2 Units.
What is a square?A square is a kind of a 2D figure in which all the sides are equal.
We know that the absolute perimeter of a square is the sum of the lengths of all the total sides and as we see the area of a square is (side)².
Assuming that the whole square has four units completed for each side.
The square's circumference can be calculated as is 4 sides plus 4 fours, or as seen as 16 units.
Now the area of the square will be calculated as (4) ² = 16 sq units.
Now assuming that the total side length of the square about is 2 units.
The square's perimeter is calculated as (24) = 8 units, while its total area is calculated as (22) = 4 units.
∴ 2 units make up the side length that serves as a counterexample.
Basically, herein we have to determine the absolute numbers that when are multiplied by 4 are seen to be greater than it's square such numbers are 1, 2, 3.
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4. Write an equation of the line that passes through (1,3) and has a slope of 5/4
5. Write two equivalent equations for a line with x-intercept (3,0) and y-intercept (0, 2).
The equation of the first line is y = -1/3x - 4, while the equivalent equations of the second line are y = -2/3(x - 3) and y = -2/3x + 2
How to determine the equation of the line?The given parameters are
Slope, m = 5/4
Point, (x1, y1) = (1, 3)
A linear equation is represented as
y = m(x - x1) + y1
So, we have
y = 5/4(x - 1) + 3
This gives
y = 5/4x + 7/4
Hence. the linear equation is y = 5/4x + 7/4
The equivalent equationsHere, we have
(x, y) = (3, 0) and (0, 2)
A linear equation is represented as
y = m(x - x1) + y1
Where
m = (y2 - y1)/(x2 - x1)
So, we have
m = (2 - 0)/(0 - 3)
m = -2/3
So, we have
y = -2/3(x - 3)
The above equation can be rewritten as
y = -2/3x + 2
Hence, the equations are y = -2/3(x - 3) and y = -2/3x + 2
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Events A and B are mutually exclusive. Suppose event A occurs with probability 0.23 and event B occurs with probability 0.21.
a. Compute the probability that A occurs but B does not occur.
b. Compute the probability that either A occurs without B occurring or B occurs without A occurring.
Using it's concept, the probabilities for this problem are given as follows:
a) A occurs and B does not: 0.1817 = 18.17%.
b) Either occurs: 0.3434 = 34.34%.
What is a probability?A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.
In the context of this problem, we have two mutually exclusive events, meaning that they cannot happen together.
For item a, we have that:
The probability of A occurring is 0.23.The probability of B not occurring is of 1 - 0.21 = 0.79.The events are mutually exclusive, hence we can multiply the probabilities as follows:
p = 0.23 x 0.79 = 0.1817 = 18.17%.
For item b, we add the probability in item with the probability of B occurring and A not, found as follows:
The probability of B occurring is 0.21.The probability of A not occurring is of 1 - 0.23 = 0.77.Hence:
p = 0.1817 + 0.21 x 0.77 = 0.3434 = 34.34%.
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r(x) = 4x² + 2x - c(x) = 10x + 25
(r-c) (x)
The most appropriate choice for function and subtraction of function will be given by-
(r-c)(x) = [tex]4x^2-8x-25[/tex]
What is function and subtraction of function?
A function from A to B is a rule that assigns to each element of A a unique element of B
A is the domain set and B is the co-domain set.
Subtraction of function
Suppose f(x) and g(x) are two functions. Then
(f - g)(x) = f(x) - g(x)
Here,
r(x) = [tex]4x^2 + 2x[/tex]
c(x) = [tex]10x+25[/tex]
(r-c)(x) = r(x) - c(x) = [tex](4x^2+2x)-(10x +25)[/tex]
= [tex]4x^2+2x -10x-25[/tex]
= [tex]4x^2-8x-25[/tex]
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Graph the function f(x)=-3x+1.
Use the line tool and select two points to graph.
+Move Line
Undo
Redo
x Reset
The y-intercept is (0, 1).
Substituting [tex]x=-3[/tex] yields [tex]f(x)=-\frac{1}{3}(-3)+1=2[/tex].
So, draw the line through (0, 1) and (-3, 2).
the area of lake Okeechobee is 7.3 * 10 to the second power square miles. how many square miles is the area of lake Okeechobee?
Lake Okeechobee has a surface area of 5329 square miles, as determined by solving the given values.
How do you compute a square mile?The area of a square unit, such as a square mile, is calculated by multiplying two lengths. Each length in the case of square miles is measured in miles.
Given: The Okeechobee lake is 7.3 * 10 to the second power square miles in area.
We need to figure out how many square miles Lake Okeechobee covers.
Area covered in square miles = (7.3 × 10)²
= 73²
= 5329 square miles
Therefore, Lake Okeechobee covers an area of 5329 square miles which was calculated by solving the given values.
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50-100 points + brainliest
Construct a perpendicular bisector to AB
Step-by-step explanation:
In order to construct a perpendicular from a point to a given line segment: Draw two arcs crossing the line segment. Make two more arcs which intersect. Join the point where the arcs intersect to the original point.
The. median, range, and mode for the following numbers:8,7,12,7,11,10,7,12
Answer:
median = 9
range = 5
mode = 7
Step-by-step explanation:
median = 9 is in the middle of 10 and 8
range = 12 - 7
mode = there are 3 7s
Mode : the quantity that appears the most in a sequence
Because 7 is the number that appears the most ( 3 times ), it is the mode.
Range : the difference between the largest number and the smallest number
In this case, 12 is the biggest and 7 is the smallest -> Range = 5.
Median : the "middle number" (for example, if the sequence has 7 numbers, the 4th number will be the median. if the sequence has 8 numbers, the median will be the average of the 4th and 5th number, and of course from increasing order.)
There are 8 numbers in the sequence, from lowest to highest : 7,7,7,8,10,11,12,12.
So, the median = (8+10)/2 = 9.
3. What is the value of the expression -8-(-3)? -8-(-3) = -8____3 =
Answer:
+
Step-by-step explanation:
[tex]-8-(-3)=-8+3[/tex]
Consider the following expression.
5a+3+4b
Select all of the true statements below.
5a+3+4b is written as a product of three factors.
3 is a constant.
4 is a coefficient.
4b and 3 are like terms.
5a+3+4b is written as a sum of three terms.
None of these are true.
3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.
What is addition?The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. Mathematicians employ the action of addition to combine numbers. The sum of the given numbers is the outcome of addition, or the total of the inputted numbers.
Given that,
5a+3+4b
Select all of the true statements below.
5a+3+4b is written as a product of three factors.
3 is a constant.
4 is a coefficient.
4b and 3 are like terms.
5a+3+4b is written as a sum of three terms.
Therefore, 3 is a constant, 4 is the coefficient, 5a+3+4b is written as a sum of three terms are the true statements.
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Maxim raised $290.44 for charity. He divided the amount equally among his ten favorite
charities. How much did each charity receive (round to the nearest cent)?
Answer:
$29
Step-by-step explanation:
First you divide 290.44 by 10 which would equal 29.044, then you would round both 4's down to 0 which would get you $29.
Parallel lines are in the same ____? , but they do not____?
Answer: parallel lines are in the same slope? , but they do not intersect.
Step-by-step explanation:
because
Answer: slope, intersect
Step-by-step explanation:
As parallel lines never intersect
Graph the circle with center (2, −3) that passes through (2, 0). Find the area in terms of π and to the nearest tenth. Use 3.14 for π.
Circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).
As given in the question,
Circle with center C(2, -3)
Passes through point A(2,0)
Graph of the circle attached.
Radius of the circle 'r'
r =CA
CA = √(2-2)² +(0+3)²
= √9
= 3
Area of the circle = πr²
= π (3)²
= 9π units² (in terms of π)
= 9 ×3.14
= 28.26
= 28.3 units²
Therefore, circle with center (2,-3) that passes through (2,0) has an area of 9π units² in terms of π and 28.3 units² (nearest tenth).
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CARD #7:
Rectangle BCDE will be dilated by
3
a scale factor of
2°
Gabe says the
rectangle will
be reduced.
Gabi says the
rectangle will
be enlarged.
Gabi is correct to say that the rectangle will be enlarged when it will be dilated by a scale factor of 3/2.
What does the scale factor determine?The image's size will depend on the scale factor, which is used to dilate a mathematical entity (compared to the original object).An expansion happens when the scaling factor's absolute value exceeds one.Compression happens when the scale factor's absolute value falls below one.When the scale factor's absolute value is 1, neither expansion nor compression takes place.As it is given that the rectangle BCDE is dilated by the scale factor of 3/2 which is more than 1, so the rectangle will expand or enlarge.
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The complete question is: "Rectangle BCDE will be dilated by a scale factor of 3/2.
Gabe says the rectangle will be reduced.
Gabi says the rectangle will be enlarged."
2) Ashton left his house and ran 4 miles east and then 3 miles north. He then took the diagnol path back home. If he burned 105 calories every mile that he ran, how many total calories did he burn on his run? (just type in the number value and units)
1,470
Step-by-step explanation:
because if he 4 miles and than 3 miles you would add them and get 7. you would take that 7 and double the 7 and multiply it by 105 cause that's how many calories he burnt each miles he ran then you would get the total of 1470 calories
which equation represents the standard form of the equation y=(x+3)^2-4
A. y = x^2 + 3x - 4
B. y = x^2+ 6x - 4
C. y = x^2 + 3x + 5
D. y = x^2 + 6x + 5
Answer: y=x^2+6x+5 ==> D
Step-by-step explanation:
y=(x+3)^2-4
y=(x+3)(x+3)-4
y=x*x+3*x+3*x+3*3-4
y=x^2+3x+3x+9-4
y=x^2+6x+5 ==> D
two carts, a and b, are connected by a rope 39 ft long that passes over a pulley p. the point q is on the floor 12 ft directly beneath p and between the carts. cart a is being pulled away from q at a speed of 2 ft/s. how fast (in ft/s) is cart b moving toward q at the instant when cart a is 5 ft from q? (round your answer to two decimal places.)
The velocity of the cart b is found as 20/23 ft/s over the pulley.
What is defined as the rate of change?The momentum of a variable is represented by the rate of change, which is used to mathematically define the percentage change in value over such a defined period of time.For the given data in the question.
q's velocity is 2 feet per second.
Rope length is 39 feet.
Assume x is the distance between A and Q. (refer the image).
Assume y is the distance between Q and B. (refer the image).
As a result of the image,
x² + 12² = L²
Now, with respect to time t, differentiate the above equation.
2x(dx/dt) + 0 = 2L.(dL/dt)
For x = 5 ft and L = 13 ft
dL/dt = (5×2)/13 = 10/13
In the case of B,
y² + 12² = (39 - L)² ; from diagram.
Differentiating now,
2y(dy/dt) + 0 = -2(39 - L).(dL/dt)
At x = 5 ft and y = 23 ft.
dy/dy = -20/23
(A negative sign indicates the opposite direction)
Thus, the velocity of cart b is found as 20/23 ft/s.
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What is the value of |-3.25| And |-4.25|
The values are |-3.25| = 3.25 and |-4.25| = 4.25
How to determine the values of the expressions?The expressions are given as
|-3.25| and |-4.25|
The above expressions are absolute value expressions
And as a general rule, an absolute value expression, when evaluated must follow the following rule
|±a| = a
Using the above as a guide, we have
|-3.25| = 3.25
Also, we have
|-4.25| = 4.25
Hence, the values of the expressions are |-3.25| = 3.25 and |-4.25| = 4.25
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0.21 / 1.008. Pls helppp
the volume of a cylinder closed at one end is 2136cm³.. if its height is 14cm, find its diameter
diameter = 13.93771776cm
Can you please help me? Thank you!
The volume of the figure shown in the reference attachment, provided hereby with the question statement will be 6786 ft³.
As per the question statement and the reference attachment, we are provided with a figure and its dimensions.
We are required to calculate the volume of the concerned figure using the dimensional values provided.
To solve this question, we need to calculate the volumes of the bottom cuboidal part, and the top pyramidal part separately, and then add these volumes, to obtain our final desired answer.
Given, the dimensions of the bottom cuboidal part is (21ft by 18ft by 13ft).
We know that, volume of a cuboid = (length * breadth * height).
Therefore, volume of our concerned bottom cuboidal part
= (21 * 18 * 13) ft³
= 4914 ft³.
Also given, the dimensions of the top pyramidal part are as follows,
Base of the triangle = 18 ft,
Altitude of the triangle = 16 ft,
and length of the pyramid = 13 ft.
Therefore, Volume of the concerned pyramid
= [(1/2) * base * altitude * length]
= [(1/2) * 18 * 16 * 13] ft³
= (9 * 16 * 13) ft³
= 1872 ft³.
Therefore, Total volume of the concerned figure shown in the reference attachment, provided hereby with the question statement will be
(4914 + 1872) ft³ = 6786 ft³
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. If a number, when divided by 4,is reduced by 21, Find the number
Step by step please
Pls help
Answer:
n= -3
Step-by-step explanation:
The solution is attached
HELP ASAP I NEED THIS DONE BEFORE TONIGHT
PARALLEL LINES HAVE EQUAL GRADIENTS...MEANING THE GRADIENT OF THE NEW LINE IS ALSO
[tex] \frac{5}{6} [/tex]
I WILL USE THE GIVEN POINTS RO FIND THE VALUE OF c
[tex] 6= \frac{5}{6} ( - 1) + c \\ 6 = - \frac{5}{6} + c \\ c = 6 + \frac{5}{6} \\ c = \frac{41}{6} [/tex]
The equation now is
[tex]y = \frac{5}{6} x + \frac{41}{6} [/tex]
ATTACHED IS THE SOLUTION
Hello!
A line that is parallel to another line:
⇒ has the same slope
Thus the line: has a slope of 5/6
However, the line passes through (-1, 6):
==> let's set up the equation in point-slope form
[tex]y - y_1=m(x-x_1)[/tex]
m: slope(x₁, y₁): point on the line[tex]y - 6 = \dfrac{5}{6} (x -(-1))\\\\y -6 = \dfrac{5}{6} x + \dfrac{5}{6} \\\\y = \dfrac{5}{6} x +\dfrac{5}{6}+6\\\\ y=\dfrac{5}{6} x + \dfrac{5}{6} +\dfrac{36}{6} \\\\y=\dfrac{5}{6} x + \dfrac{41}{6}[/tex]<== Answer:
Hope that helps!
if a= 4 and b=b : 5a - b =
Answer:
20 - b
Step-by-step explanation:
5a - b
substitute a for 4 because a = 4
5(4) - b
20 - b