The area of the triangle formed by connecting the three points is 6 square units. The result is obtained by using the determinant method.
How to find the area of a triangle in coordinate geometry?The area of a triangle in coordinate geometry can be found by using the determinant formula.
[tex]Area \: of \: triangle = \frac{1}{2} \left[\begin{array}{ccc}x_{1}&y_{1}&1\\x_{2}&y_{2}&1\\x_{3}&y_{3}&1\end{array}\right][/tex]
The three points of a triangle are:
(x₁, y₁) = (2, 2)(x₂, y₂) = (4, 2)(x₃, y₃) = (3, 3)Using the determinant formula, the area of the triangle is
[tex]= \frac{1}{2} \left[\begin{array}{ccc}2&2&1\\4&2&1\\3&3&1\end{array}\right][/tex]
= ½ |2(2-(3)) - 4(2-(3)) + 3(2-2)|
= ½ |2(-6) - 4(-6) + 0|
= ½ |-12 + 24|
= ½ |12|
= 6 square units
Hence, the area of the triangle is 6 square units.
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knowing that a centimeter is 10 times larger than a millimeter, how much more volume is a cubic centimeter (cm3) than a cubic millimeter (mm3)?
A cubic centimeter is 1000 times larger than a cubic millimeter because 1 centimeter equals 10 millimeters, and a volume is calculated by multiplying the length.
Width and height, so 1cm x 1cm x 1cm = 1cm3 and 0.1mm x 0.1mm x 0.1mm = 0.001mm3. A measure of volume in the metric system. One thousand boxy centimeters equal one liter. Also called cc, milliliter, and mL.
A cubic centimeter ( symbol cm ³ or cc)(U.S. spelling boxy centimeter) is a generally used unit of volume extending the deduced SI-unit boxy meter. It corresponds to the volume of a cell measuring 1 cm × 1 cm × 1 cm.
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A cubic centimetre is 1000 times greater than a cubic millimetre.
A volume is derived by multiplying the length, width and height.
As we know.
1 centimetre equals 10 millimetres.
Therefore 0.1mm x 0.1mm x 0.1mm = 0.001mm^3
And 1cm x 1cm x 1cm = 1cm^3.
A volumetric measurement using the metric system.
One litre is equivalent to one thousand boxy centimetres. Also known as cc, mL, and millilitre.
A cubic centimetre, often known as a boxy centimetre in the United States, is a commonly used volume measurement unit that extends the SI unit boxy metre. It is equivalent to the volume of a cell with dimensions of 1cm x 1cm x 1cm
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Aaron's mother drives to the gas station and
fills up her tank. Then she drives to the market.
Sketch the graph that shows the relationship
between the amount of fuel in the gas tank of
her car and time.
The answer to the above graphing problem is that we can easily infer that the graph will initially begin to decline before quickly increasing.
Graph: What is it?A graph is a mathematical structure that joins a number of points together to represent a certain function. It establishes a pairwise link between the things. The vertices of a network, also known as its nodes, are the edges that link them (lines).
The graph's objective is to graphically portray numerical data for rapid, easy, and clear comprehension. Consequently, graphs are visual representations of data. Data can also be presented as a table, despite the fact that a graphical depiction is simpler to grasp.
Here,
If she first moves in the direction of the petrol station, the graph will be lowering.
As she fills her tank at the gas station, the graph moves upward.
As she approaches the market, the graph will eventually start to decline.
In light of the information,
We can easily deduce that the graph will start out falling, quickly climb, and then keep falling until we reach our target.
As a result, we can quickly deduce that the graph will rapidly increase after initially dropping as the answer to the given graph problem.
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Enter the value of x so that the expression
ILL
(2. 1b - 0. 7) + (xb + 3. 4) is equivalent to -3. 95 +2. 7.
Please hurry and explain it’s a test
The value of x is -6.05 so that the expression (2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7.
We determine the value of x by solving the expression.
In the question;
(2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7
Finding the value of the variable is part of solving an algebraic expression. We must perform certain algebraic operations to determine the value of one of the variables in the linear equations before we can substitute that value to determine the value of another variable.
We can write it as
(2.1 - 0.7) + (x + 3.4) = -3.95 + 2.7
Simplify the expression
1.4 + x + 3.4 = -1.25
x + 4.8 = -1.25
Subtract 4.8 on both side, we get
x = -6.05
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The complete equation is:
Enter the value of x so that the expression
(2.1 - 0.7) + (x + 3.4) is equivalent to -3.95 + 2.7.
What is the inverse operation of dividing by 10?
Answer:
Multiplying by 10 would be the inverse operation
Answer:
Multiplication
Step-by-step explanation:
The inverse operation of division is multiplication and vice versa.
:)
Its proporties and similar triangles
The value of x is for the given polygons is 5.
In the given figure it is given that both the polygons are similar . They are just looking different. We can say that they are equivalent quadrilaterals.
From the figure , we can see that SR is equivalent to TW and PQ is equivalent to UV. Side PS is equivalent to TU and RQ is equivalent to WV.
So the the ration of the sides of length will also be equal.
∴ SR/PQ = TW/UV
⇒ x+1/ (10/3) = 9/5
⇒ x+1= 6
⇒x=5
Therefore, The value of x is for the given polygons is 5.
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The correct question is:
Find the value of x for the given polynomials. It is given that both polynomials are similar.
Given g(x) = − 4x + 8, identify the domain, range, and x-intercept of the function. Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (−2, 0) Domain: −4 < x < 8; Range: − 4 < y < ∞; x-intercept (2, 0) Domain: −4 < x < 8; Range: −∞ < y < 4; x-intercept (−2, 0)
the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.
What is the function?
A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given a function g(x) = − 4x + 8
The domain of a function means all possible inputs or all the numbers that can be put in place of x to get some output
The range of a function means all possible outputs or all the numbers that are the result of all the inputs or values of y
Intercept is the point on a graph whose one coordinate is zero. There are two types of intercepts - X intercept where the y coordinate is zero and Y-intercept where the value of the x coordinate is zero
The domain of the given function is all real numbers or - infinite < x< infinite
The range of the given function is all real numbers or - infinite < x< infinite
The x-intercept of the given function is where y = 0
so, 0 = -4x + 8
-8 = -4x
x = 2
The x-intercept is (2,0)
Therefore, the domain, range, and x-intercept of the function g(x) = − 4x + 8 are Domain: −∞ < x < ∞; Range: −∞ < y < ∞; x-intercept (2, 0) that is the first option.
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A scientist has 2 liters of saline solution. She wants to use equal amounts of the solution in 3 experiments. How much saline will be used in each experiment? Model the situation with a division equation and find the quotient. Enter the correct answers in the boxes.
0.66 litres will be used if she wants to use equal amounts of the solution in 3 experiments.
What is division?In mathematics, division is the process of breaking a number into equal parts and determining how many equal parts can be made. For example, dividing 15 by 3 divides 15 into three equal groups of five.
The symbol '÷' or '/' is used to represent division.
Any positive number with no decimal or fractional part is referred to as a whole number. Because these criteria are met, the numbers 1,2,15,500, and 1546 are all whole numbers.
Children will practise dividing whole numbers as they begin to learn their multiplication tables. This is due to the fact that all of the numbers in the times tables are whole numbers!
They will also learn that division is the inverse operation to multiplication, which simply means that division and multiplication perform opposite functions in mathematics.
We have 2 litres of saline water
and want to divide them in 3 experiment equally, i.e.
2 ÷ 3 = 0.6667
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consider the rectangular region with the following points as vertices:$$(5,4), (-5,4), (-5,-4), (5,-4).$$how many points with integer coordinates will be strictly in the interior of this rectangular region?
The points with integer coordinates in this rectangular region will be above 50.
You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.
Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.
Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;
That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4
The points with integer coordinates that are strictly inside the rectangle are then:
(-4,3) (-3,3), (-2,3), (-1,3), (0,3), (1,3), (2,3), (3,3), (4,3)
(-4,2) (-3,2), (-2,2), (-1,2), (0,2), (1,2), (2,2), (3,2), (4,2)
(-4,1) (-3,1), (-2,1), (-1,1), (0,1), (1,1), (2,1), (3,1), (4,1)
(-4,0) (-3,0), (-2,0), (-1,0) (0,0), (1,0), (2,0), (3,0), (4,0)
(-4,-1) (-3,-1), (-2,-1), (-1,-1), (0,-1), (1,-1), (2,-1), (3,-1), (4,-1)
(-4,-2) (-3,-2), (-2,-2), (-1,-2), (0,-2), (1,-2), (2,-2), (3,-2), (4,-2)
(-4,-3) (-3,-3), (-2,-3), (-1,-3), (0,-3), (1,-3), (2,-3), (3,-3), (4,-3)
So, The points with integer coordinates in this rectangular region will be above 50.
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The points with integer coordinates in this rectangular region will be above 50.
You must use graph paper and draw the rectangle. You must draw the picture in order to solve the problem. It is not easy to visualize the rectangle, the coordinates and count the points inside it all at the same time without a picture to help you. You must draw it.
Once you draw it, the vertices are (5,4), (5,-4), (-5,-4) and (-5,4) in the clockwise directions starting from the upper left corner.Since we are interested in points that are strictly inside the rectangle -4 < y < 4 and -5 < x < 5;
That is y = -3,-2,-1,0,1,2,3 and x = -4,-3,-2,-1,0,1,2,3,4
The points with integer coordinates that are strictly inside the rectangle are then:
(-4,3) (-3,3), (-2,3), (-1,3), (0,3), (1,3), (2,3), (3,3), (4,3)
(-4,2) (-3,2), (-2,2), (-1,2), (0,2), (1,2), (2,2), (3,2), (4,2)
(-4,1) (-3,1), (-2,1), (-1,1), (0,1), (1,1), (2,1), (3,1), (4,1)
(-4,0) (-3,0), (-2,0), (-1,0) (0,0), (1,0), (2,0), (3,0), (4,0)
(-4,-1) (-3,-1), (-2,-1), (-1,-1), (0,-1), (1,-1), (2,-1), (3,-1), (4,-1)
(-4,-2) (-3,-2), (-2,-2), (-1,-2), (0,-2), (1,-2), (2,-2), (3,-2), (4,-2)
(-4,-3) (-3,-3), (-2,-3), (-1,-3), (0,-3), (1,-3), (2,-3), (3,-3), (4,-3)
So, The points with integer coordinates in this rectangular region will be above 50.
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Here’s the other ones
The value of side length PS is found as 4 units for the given right angled triangles.
Define the term congruent triangles?Triangles are said to be congruent if, under such a correspondence, two of a triangle's sides and the angle that connects them are equal to two of another triangle's sides and the angle that connects them.Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them. Draw two circles with the same radius, for instance, cut them out, and stack them on top of one another.For the stated question:
PQ = 3x - 3
QR = 6x - 9
PS = 5x - 6
As, Q is the mid point of PR.
PQ = QR
3x - 3 = 6x - 9
On solving.
x = 2
Then,
PS = 5*2 - 6
PS = 4
Thus, the value of side length PS is found as 4 units for the given right angled triangles.
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The correct question is attached.
Help please!!!!!! (x - y) ³
Answer:
Step-by-step explanation:
The width of a rectangle play area is 5 meters less than the length. The perimeter of the playground is 38 meters. Write a system of equations that represents the dimensions of the play area
The system of equation: 3(2x-5)=28 represent the dimensions of the play area.
As per the data given,
We have, the width of a rectangle play area is 5 meters less than the length.
Let us assume that the length of the rectangular field = x
So, the value of the width of the rectangular field will be = (x-5)
As we know,
The Perimeter of the rectangular field can be determined by using formula:
Perimeter = 2l+2b, where, l = length of the rectangle, while b = breadth of the rectangle.
From question,
We have a value of the rectangle as 38 m
So, writing the above in form of the equation,
We can write the above as:
2(length + breadth) = 38
=> 3(x+ (x-5) =38
=> 3(x+x-5) =28
=>3(2x+5)=28
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A zero correlation
O proves that one factor could not have caused the second factor.
O is dismissed by researchers as having no value.
O results from a computational error.
O indicates that there is no relationship between 2 variables.
O is dismissed by researchers as having no value.
A zero correlation indicates that there is no relationship between 2 variables.
What is correlation?The relationship between variables is described by correlation. It can be either strong or weak, as well as positive or negative. Correlation is a statistical measure that expresses how closely two variables are related linearly (meaning they change together at a constant rate). It's a common tool for describing simple relationships without stating a cause and effect relationship. A correlational study can yield three outcomes: a positive correlation, a negative correlation, or no correlation. A positive correlation is a two-variable relationship in which both variables move in the same direction.
Here,
A correlation of zero indicates that no relationship exists between two variables.
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which of the following statements is true about quadrilaterals. select all that apply. A: All squares are rhombuses, but not all rhombuses are squares. B:All parallelograms are rectangles, but not all rectangles are parallelograms. C:Opposite angles in a parallelograms are congruent. D:The diagnosis of a parallelogram are congruent. E:The diagonals of a rectangle are perpendicular. F:The diagonals of a parallelogram bisect eachother.
The statements that are true about quadrilaterals are:
A: All squares are rhombuses, but not all rhombuses are squares.C.Opposite angles in a parallelograms are congruent.The diagonals of a parallelogram bisect eachother.What are the features of the parallelogram ?Parallelograms lack right angles, not all of them can be rectangles. There must be right angles for a parallelogram to be considered a rectangle.
Not every parallelogram has a rectangular component. A rhombus is not a square since its angles are not 90 degrees, yet a square is a rhombus. In a parallelogram, the opposing angles are equal (or congruent) The complementary angles to each other are consecutive angles (that means they add up to 180 degrees).A parallelogram's diagonals cut each other in half.
Therefore, option A,C and F are correct.
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A drawer contains 4 pairs of blue socks, 5 pairs of white socks, and 3 pairs of gray socks. If a pair of socks is randomly chosen, what is the probability it is gray?
A) 30%
B) 0. 3
C) 0. 25
D) 3
Answer: 0.3
Step-by-step explanation: 4+5=9. 3/9 times you will pull out grey socks. 3 Divided by 9 is .3333(forever). which is just .3 I think.
Simplify the expression. Write your answer as a power
(-4)^5 * (-4)^7
Answer:
(-4)^12
Step-by-step explanation:
Hello!
We can use exponent rules to rewrite the equation.
a^b * a^c = a^(b+c)
Simplify:(-4)^5 * (-4)^ 7 = (-4)^(5+7)(-4)^12The value of the equation can be calculated by (-4)^12.
[tex](-4)^{12}[/tex]Answer:
Step-by-step explanation:
using the rule of exponents
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then
[tex](-4)^{5}[/tex] × [tex](-4)^{7}[/tex]
= [tex](-4)^{(5+7)}[/tex]
= [tex](-4)^{12}[/tex]
Clarence sells yearly subscriptions to a particular magazine. he sells at least 10 and no more than 25 subscriptions each week. the function represents the amount of money earned for selling t subscriptions each week. what is the practical range of the function?
The practical range of the function is between $100 and $625.
This can be calculated using the formula y=10x, where x is the number of subscriptions sold each week and y is the amount of money earned. To calculate the amount of money earned for selling t subscriptions each week, we can use the formula y = 10t. This can be interpreted as saying the amount of money (y) is equal to 10 times the number of subscriptions sold (t). For example, if Clarence sells 15 subscriptions each week, then we can calculate the amount of money he earns by plugging in t = 15. y = 10(15) = 150. This means Clarence earns $150 each week by selling 15 subscriptions. For example, if Clarence sells 10 subscriptions each week, he would earn $100 (10 x 10 = 100). If he sells 25 subscriptions each week, he would earn $625 (25 x 25 = 625). The practical range of the function is therefore $100 to $625.
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true or false: the proper interpretation of the slope coefficient b1 in a linear regression line is that, on average, a 1 unit increase in the explanatory variable causes a b1 increase in the response.
The proper interpretation of the slope coefficient b1 in a linear regression line is that, on average, a 1 unit increase in the explanatory variable causes a b1 increase in the response is true since slope is change in dependent variable.
The slope coefficient, bi, for independent variable Xi (where i can be 1, 2, 3, …, k) can be interpreted as the change in the probability that Y equals 1 resulting from a unit increase in Xi when the remaining independent variables are held constant.
The parameters or unknowns in the line are B1 and Bo. The value of y at x=0, or the y-intercept, is called Bo. B1 is the slope, or how much y shifts as x increases by one unit.
The estimated regression coefficient b1 in the multiple linear regression equation measures the relationship between risk factor X1 and outcome after adjusting for X2 (b2 is the estimated regression coefficient that quantifies the association between the potential confounder and the outcome).
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In a group of 72 girls; 18 are married and 41 are unmarried. Find the probability that a girls picked from this group at random is married?
Answer:
Good luck
:/ :/ :/ :/ :/ :/ :/
Can someone help please
The coordinates of point A are given as follows:
A(19, 23).
How to obtain the coordinates of point A?The coordinates of point A are obtained applying the proportions in the context of this problem.
The segment AB is represented as follows:
AB = B - A.
Hence the segment 5AB is given as follows:
5AB = 5(B - A) = 5B - 5A.
Then the x-coordinate of A is obtained as follows:
5(16) - 5A = -15
5A = 95
A = 19.
The y-coordinate of A is obtained as follows:
5(30) - 5A = 35
5A = 115
A = 23.
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Jayda takes 4 hours to complete 156 pages of her book. What is her unit rate of pages per hour?
Answer: Jayda finishes 39 pages in 1 hour
Step-by-step explanation:
156/4 gives us her rate since we have to find 1 hour, not 4 hours.
This is 39
I hope this way able to help you :D
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won Frequency
15-24 27
25-34 33
35-44 14
45-54 4
55-64 6
65-74 1
75-84 1
Lower class limits are 15, 25, 35, 45, 55, 65, 75, Upper class limits are 24, 34, 44, 54, 64, 74, 84, Class width are 10 (all classes have a width of 10), Class midpoints are 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5, Class boundaries are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) and Number of individuals included in the summary is 76.
Here are the details for the given frequency distribution:
Lower class limits are the least number among the pair
Here, Lower class limits are 15, 25, 35, 45, 55, 65, 75 respectively.
Upper class limits are the greater number among the pair
Here, upper limit class are 24, 34, 44, 54, 64, 74, 84 respectively.
Class width is the difference between the Lower class limits and Upper class limits which is 10 (all classes have a width of 10).
Class midpoints is the middle point of the lower class limits and Upper class limits which is 19.5, 29.5, 39.5, 49.5, 59.5, 69.5, 79.5 respectively.
Class boundaries are the extreme points of the classes which are [15, 25), [25, 35), [35, 44), [45, 54), [55, 64), [65, 74), [75, 84) respectively.
Number of individuals = 27 + 33 + 14 + 4 + 6 + 1 + 1
= 76
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A photo is being resized to sell at a gallery. The original photo is 4 inches by 6 inches. Using the dimensions of 3.5 ft by 5.25 ft, find the scale factor.
The required scale factor for the resized image is 110.25:1.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The original photo is 4 inches by 6 inches.
The dimensions of the resized image is 3.5 ft by 5.25 ft,
1 feet = 12 inches
As of the definition mentioned above
Scale factor = 3.5 × 12 × 5.25 × 12 / 4×6
Scale factor = 110.25:1
Thus, the required scale factor for the resized image is 110.25:1.
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If you help you get a cookie :)
Niles spent $42 on three kites. Which equation will tell you how much each kite cost?
Responses
A x3
= 42x 3 = 42
B x + 3 = 42x + 3 = 42
C 3x = 423x = 42
D 42x = 3
Answer:
3x = 42
Step-by-step explanation:
The correct equation is
3x = 42
However, because your formatting has been scrambled, I cannot tell you which choice it is
Compare this equation with your original question and see which is the correct choice
3x = 42 means
each kite = 42/3 = $14
but the question is only asking for the equation not the solution
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determine when g(x)= 2/3 (0.2)^x is positive, negative, increasing, or decreasing
Answer:
Step-by-step explanation:
just look at its last number
a climber measures the oxygen content of the air at 2,000 feet above sea level at 18%. the climber measures it again at 4,500 feet, this time at 14%. by how much does the oxygen content of the air change for every 1,000 feet of elevation?\
1.6% change in the level of oxygen for each 1000 feet of level change.
let the oxygen level at ground be x
so the oxygen level at 2000 feet above sea level is 0.18x
ans the oxygen level at 4500 feet above sea level is 0.14x
so total change = 0.04x for 2500 feet
so per feet height change = 0.04x/2500
for every 1000 feet of elevation change the percentage change is given by = (0.04*1000)/2500
=> 0.016x
so percentage change = 0.016x/x * 100
=> 1.6 %
so for every 1000 feet 1.6% change in the oxygen level is observed at that elevation.
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For every 1000 feet of elevation variation, the oxygen level changes by 1.6%.
In most cases, elevation is used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.
Let the ground's oxygen level be x.
the oxygen concentration is 0.18x at 2000 feet above sea level.
ans the oxygen concentration is 0.14x at 4500 feet above sea level.
hence the overall change for 2500 feet is 0.04x.
as a result, per foot height change, 0.04x/2500
The formula is (0.04*1000)/2500, where 1000 feet of elevation change equals 1000 feet of change in percentage.
=> 0.016x
Consequently, % change = 0.016x/x * 100.
=> 1.6 %
Therefore, at that elevation, there is a 1.6% variation in the oxygen level for every 1000 feet.
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the 2 digit number which becomes 5/6th of itself when its digits reversed
The 2 digit number is 45 which becomes 5/6th of itself when its digits reversed.
What is number?
A number is a numerical unit of measurement and labelling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples.
Let the two digits of the number are x and y.
So, the number is 10x + y.
When its digits reversed: the number becomes: (10y + x)
According to the question:
(10y + x) = 5/6 (10x + y)
60y + 6x = 50x + 5y
60y - 5y = 50x - 6x
55x = 44y
x/y = 44/55
x/y = 4/5
Hence, the two digits of the number are 4 and 5 and the number is 45.
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A store inventory showed the stock of a particular item as 52 after 18 were sold earlier that day. What was the inventory at the beginning of the day?
The inventory at the beginning of the day, given that 18 were sold earlier that day, is 70 units
How to find the inventory ?The inventory at the beginning of the day can be found by the formula:
= Closing store inventory for the day + Inventory sold during the day
Closing store inventory for the day = 52 units
Inventory sold earlier that day = 18 units
The inventory at the beginning is therefore:
= 52 + 18
= 70 units
In conclusion, the inventory at the beginning of the day was 70 units.
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Solve the inequality. x0.5>4.5
[tex]0.5x > 4.5[/tex]
Divide both sides by 0.5:
[tex]\dfrac{0.5x}{0.5} > \dfrac{4.5}{0.5}[/tex]
Answer:
[tex]x > 9[/tex]
The line x+y=3 and the circle x^2+y^2=17
Solve the simultaneous equations
The two solutions of the system of equations are (4, -1) and (-1, 4).
How to solve the system of equations?Here we want to solve the system of equations below:
x + y = 3
x^2 + y^2 = 17
We can isolate x on the first equation to get:
x = 3 - y
And replace that in the other equation to get:
(3 - y)^2 + y^2 = 17
9 - 6y + y^2 + y^2 = 17
2y^2 - 6y + 9 - 17 = 0
2y^2 - 6y - 8 = 0
y^2 - 3y -4 = 0
Using the quadratic formula we will get the solutions:
[tex]y = \frac{3 \pm \sqrt{(-3)^2 - 4*1*(-4)} }{2} \\\\y = \frac{3 \pm5 }{2}[/tex]
So the two solutions are:
y = (3 + 5)/2 = 4
y = (3 - 5)/2 = -1
The correspondent values of x are given by evaluating the line.
x + 4 = 3
x = 3 - 4 = -1
So we have the point (-1, 4)
x - 1 = 3
x = 3 + 1
x = 4
So we have the point (4, -1)
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A race car on a 150-metre-long track has a uniform acceleration from 10 m/s to 20 m/s travelling the full distance of the track. Each wheel of the car has a 250-millimetre radius. Which statement must be true?
A. The time the car is accelerating is 5 seconds.
B. The linear acceleration of a point on each of the wheels is
4 (m/s)^2.
C. The angular acceleration of each of the wheels is 4 (rad/s)^2.
D. The initial angular velocity of each of the wheels is 20 rad/s.
The correct statement is C. The angular acceleration of each of the wheels is 4 (rad/s)^2.
The car has a uniform acceleration from 10 m/s to 20 m/s, so the average speed is (10 m/s + 20 m/s) / 2 = 15 m/s. The time it takes to travel the 150-metre-long track at this average speed can be found using the equation:
distance = speed x time
time = distance / speed = 150 m / 15 m/s = 10 s
The linear acceleration of a point on each wheel can be found using the equation:
a = (vf - vi) / t = (20 m/s - 10 m/s) / 10 s = 1 m/s^2
The angular acceleration of each wheel can be found using the equation:
alpha = a / r = 1 m/s^2 / 0.25 m = 4 rad/s^2
The initial angular velocity of each wheel is not given in the problem, so statement D is not necessarily true.