The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)
The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.
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the number of telephone lines in each country in central america and the caribbean is shown above in a dot plot. the number of telephone lines in each country has been rounded to the nearest 250250250 thousand. according to the dot plot, what is the median number of telephone lines in thousands?
The median number of telephone line in thousands is 0
The number of telephone lines in each country = 250000
From the given dot plot
The data set will be
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 250, 250, 250, 250, 250, 500, 750, 750, 1000, 1000, 1250, 1750
The median of the data set is the middle term of the ordered data set. The order of the data set maybe ascending or descending order
There are 28 terms in the data set the middle terms will be 14th and 15th
Both 4th and 15 terms are 0
Therefore, the median is 0
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I cant put the Problem here But just look up "PUZZLE TIME 7.3 What Kind Of Ship Can Last Forever?"
If both pairs of opposite sides of a quadrilateral are ___________, then the quadrilateral is a parallelogram.
If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram
What is a quadrilateral?A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.
A parallelogram is formed when both pairs of opposite sides of a quadrilateral are congruent. A parallelogram is formed when one pair of opposite sides of a quadrilateral are parallel and congruent.
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find the flux of f = xy i yz j zxk out of a sphere of radius 6 centered at the origin.
The flux = 0
Divergence Theorem: What is it?According to the divergence theorem, the volume integral of the divergence of a vector point function "F" taken over the volume "V" encompassed by the surface "S" is equal to the surface integral of the normal component of F taken over the closed surface "S." As a result, the divergence theorem is symbolically represented as:∬ v ∫ ▽ F → .
The sphere is presumably closed, so we can use the divergence theorem.
▽ F =d(xy)/dx + d(yz)/dy + d(zx)/dz
▽ F =x + y + z
Now convert to spherical coordinates:
x=ρsinφcosθ,
y=ρsinφsinθ,
z=ρcosφ
The flux is then given by the volume integral for the radius 6
[tex]\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} = 36 }[/tex] f.ds = [tex]\int\limits\int\limits\int\limitsx_{x^{2} +y^{2}+z^{2} < =36 }[/tex] (x+y+z) dv
Thus the flux = 0
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The graph below displays the wrist circumferences and heights of six students in Alyssa’s classroom.
A graph titled Wrist Circumference versus Height has wrist circumference (centimeters) on the x-axis and height (centimeters) on the y-axis. Points are at (13.8, 151), (14.2, 151), (15.2, 156), (15.6, 159), (16, 162) and (16, 165).
Is the height of these students a function of their wrist circumference?
Yes because as wrist circumference increases height also increases.
Yes because a line can be fit to these data to predict other pairings.
No because the height of 151 cm is paired with two wrist circumferences.
No because the wrist circumference of 16 cm is paired with two heights.
Option D (No, as there are two heights associated with the wrist circumference of 16 cm.
What is meant by graph?An illustration of a relation is a function graph. In set theory and modern mathematical foundations, a function is truly equal to its graph.
The wrist circumferences and heights of six kids in Alyssa's class are represented by a collection of points in the graph that is shown.
The height is represented by the y axis, and the wrist circumference by the x axis.
Any relation is referred to as a function if there is only one value of y for any given value of x. The graph is referred to as a function if it passes the vertical line test, which requires that a vertical line be drawn and only touch the graph once.
There are two y values (162 and 165) on the above graph for the x value of x=16.
The graph is not a function as a result.
Among the possibilities The correct response is option D, "No," since the wrist circumference of 16 cm pairs with two heights.
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Mei Mei spends a winter day recording the temperature once every three hours for science class. At 9 am, the temperature was -10.2°F. Between 9am and noon, the temperature rose 1.9°F. Between noon and 3pm, the temperature dropped 16.4°F. Between 3pm and 6pm, the temperature dropped 15.5°F. What was the temperature at 6pm?
The temperature at 6 pm is given as follows:
-40.2 ºF.
How to obtain the temperature at 6 pm?To obtain the temperature at 6 pm, we keep looking at the temperature for each interval given in the problem.
At 9 am, the temperature is given as follows:
-10.2ºF.
Between 9am and noon, the temperature rose 1.9°F, hence the temperature at noon is given as follows:
-10.2 + 1.9 = -8.3ºF.
Between noon and 3pm, the temperature dropped 16.4°F, hence the temperature at 3 pm is given as follows:
-8.3 - 16.4 = -24.7ºF.
Between 3pm and 6pm, the temperature dropped 15.5°F, hence the temperature at 6 pm is given as follows:
-24.7 - 15.5 = -40.2 ºF.
(subtracting the decline from the previous temperature, as we did for previous intervals).
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a caterer made a sandwich 6ft6in long for a party. by request, 3ft8in were added to the sandwich. what was the total length of the sandwich?
If a caterer made a sandwich 6feet 6inches long for a party and 3 feet 8 inches added to the sandwich The total length of the sandwich is 122 inches
The height of the sandwich = 6 feet 6 inches
Convert to the inches
We know 1 feet = 12 inches
6 feet 6 inches = 6 × 12 + 6
= 72 + 6
= 78 inches
The height added to sandwich = 3 feet 8 inches
Convert to inches
3 feet 8 inches = 3 × 12 + 8
= 36 + 8
= 44 inches
The new height of the sandwich = 78 + 44
= 122
Therefore, the final height of the sandwich is 122 inches
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The shadow of the moon during a solar eclipse travels 2300 miles in 1 hour in the first 20 minutes the shadow traveled 7662/3 miles how long does it take for the shadow to travel 1150 miles
The time that it will take for the shadow to travel 1150 miles is; 30 minutes
How to solve linear equations?Let y represent the distance in miles
Let x represent the time in minutes
The shadow travels 2300 miles in 1 hour or 60 minutes and in the first 20 minutes the shadow traveled 766 ²/₃ miles or 2300/3 miles
Thus, the coordinates are;
(60, 2300) and (20, 2300/3)
The slope is;
m = (2300 - 2300/3)/(60 - 20)
m = 115/3 mi/min
Thus, the linear equation in point slope form is;
y - 2300 = (115/3)(x - 60)
This gives;
y = (115/3)x
When y = 1150 miles, we have;
1150 = (115/3)x
x = 30 minutes
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An isosceles triangle has side lengths of 3x, (4x − 7), and (1/2x+9)
Write an expression in
simplest form to represent the perimeter of the triangle. (Show your work on another paper)
The perimeter of the isosceles triangle with side lengths 3·x, (4·x - 7), and (1/2·x + 9) is 51[tex]\frac{1}{14}[/tex]
What is an isosceles triangle?An isosceles triangle is a triangle that has a pair of congruent sides and according to the triangle inequality theorem, a pair of congruent angles.
The lengths of the sides of the isosceles triangle are;
3·x, 4·x - 7, and 1/2·x + 9
Let the sides, 3·x and 4·x - 7 represent the congruent sides of the triangle, we get;
3·x = 4·x - 7
4·x - 3·x = x = 7
x = 7
The length of the sides of the triangle, found by plugging in x = 7 in the specified expressions for the lengths of the sides of the triangle are therefore;
Length of the first side; 3·x = 3 × 7 = 21
The length of the second specified side; 4·x - 7 = 4 × 7 - 7 = 21
Length of the third specified side; (1/2×x) + 9 = (1/(2 × 7)) + 9 = 1/14 + 9
The perimeter of the triangle is the sum of the lengths of the sides of the triangle, therefore;
The perimeter of the triangle is; 21 + 21 + 1/14 + 9 = 51 [tex]\frac{1}{14}[/tex]
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The company Larry works for charges $10 for each service call, plus an additional $5 for each hour spent on the call Larry created the graph below to model this relationship Service Call Charges. Which statement about the graph and charges is true? A. The graph that Larry created is a correct representation of his company's charges. B. The rate of change on Larry's graph is correct, but the y-intercept is incorrect C. The rate of change on Larry's graph is less than the rate his company charges. D. The rate of change on Larry's graph is greater than the rate his company charges.
Answer:
A. The graph that Larry created is a correct representation of his company's charges.
Step-by-step explanation:
The equation for the services charges, y, is made up of the $10 initial service call fee plus $5 times the number of hours, x.
y = 5x + 10
Try any 2 values for x to see if they fits the graph.
x(hr) y($)
0 10
1 15
4 30
This is the line already drawn on the graph. Larry did everything correctly, so options B, C, and D are all false/incorrect.
Solve the following compound inequality.
9x + 6 > 132 and -7x + 19 < -128
The solution of the inequality 9x + 6 ≥ 132 and -7x + 19 < -128 is x ≥ 14 and x > 21.
How to solve compound inequality?Compound inequalities are a type of inequality that has two or more parts.
In other words, a compound inequality is an inequality that combines two simple inequalities.
Therefore, let's solve the compound inequality as follows:
9x + 6 ≥ 132 and -7x + 19 < -128
Let's solve them independently.
9x + 6 ≥ 132
subtract 6 from both sides of the inequality
9x + 6 ≥ 132
9x + 6 - 6 ≥ 132 - 6
9x ≥ 126
divide both sides by 9
x ≥ 126 / 9
x ≥ 14
-7x + 19 < -128
subtract 19 from both sides of the inequality
-7x + 19 - 19 < - 128 - 19
-7x < - 147
divide both sides by - 7
x > - 147 / -7
x > 21
Therefore, the solution is x > 21 and x ≥ 14
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Which of the following number lines represents the solution to the inequality 4x + 10 < 6?
The solution to the inequality 4x + 10 < 6 is x < -1.
What is the solution to the given inequality?Given the inequality;
4x + 10 < 6
Solve for x.
Move all terms not containing x to the right side of the inequality by subtracting 10 from both sides of the inequality.
4x + 10 < 6
4x + 10 - 10 < 6 - 10
4x < 6 - 10
Subtract 10 from 6
4x < -4
Divide each term by 4 and simplify
4x < -4
4x/4 < -4/4
Simplify the left-hand side
x < -4/4
Simplify the right-hand side
x < -1
The result in inequality form is x < -1.
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the ________ function does the same thing as using the mathematical operator.
The power or pow() function achieves the same result as the operator "^" in mathematics.
The power of an integer is calculated using the pow() function. The power raised to the base number is returned by the pow() function, which takes two parameters (the base value and the power value). This is denoted by "^". This function in computer programming helps to determine the value of an integer raised to a certain power. This is written as,
pow = power = ^ (Power operator)
In mathematics, it also helps to calculate the number raised to power. For instance, 3^2 = 3²=9. The blank can be filled with the pow() function.
The complete question is -
The ________ function does the same thing as using the mathematical ^ operator.
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please help me do this I've been stuck for over an hour
Find the missing length indicated. Leave your answer in simplest radical form.
when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one. Check the picture below.
so the longest leg of the larger triangle will be "z" and the shorter leg of it will be "y", so let's find those fellows using proportions
[tex]\cfrac{x}{16}=\cfrac{9}{x}\implies x^2=144\implies x=\sqrt{144}\implies \boxed{x=12} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{x}=\cfrac{25}{16}\implies \cfrac{y}{12}=\cfrac{25}{16}\implies y=\cfrac{(12)(25)}{16}\implies \boxed{y=\cfrac{75}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y}{z}=\cfrac{9}{x}\implies \cfrac{~~ \frac{75 }{4 } ~~}{z}=\cfrac{9}{12}\implies \cfrac{75}{4z}=\cfrac{3}{4}\implies 300=12z \\\\\\ \cfrac{300}{12}=z\implies \boxed{25=z}[/tex]
What is 11/32 - 2/8?
Answer:
= 3/32
Step-by-step explanation:
What is 11/32 - 2/8?
11/32 - 8/32 = 3/32
The coordinates of point A are (-3a,4b). If point A' is the image of point A reflected over the line y = x, what
are the coordinates of A?
Answer: (4b, -3a)
Reason:
When reflecting over the line y = x, we swap the positions of the x and y coordinates.
The reflection rule is [tex](\text{x},\text{y}) \to (\text{y},\text{x})[/tex]
As an example: [tex](2,3) \to (3,2)[/tex]
Billy’s Crystal Stores Inc. has assets of $5,960,000 and turns over its assets 1.9 times per year. Return on assets is 8 percent. What is the firm’s profit margin (return on sales)?
The firm's profit margin is 4.17%.
To calculate the firm's profit margin, also known as the return on sales, you need to divide the firm's net income by its total sales. In this case, you are given the firm's return on assets (ROA), which is equal to the firm's net income divided by its total assets.
You can use this information to set up the following equation:
ROA = [tex]\frac{net \ income}{total \ assets}[/tex]
Plugging in the given values, you get:
8%= [tex]\frac{net \ income} {5,960,000}[/tex]
Solving for net income, you find that the firm's net income is
8% × 5,960,000 = 476,800.
Now that you know the firm's net income, you can calculate its profit margin by dividing its net income by its total sales. To do this, you need to know the firm's total sales.
You can use the firm's asset turnover ratio, which is equal to its total sales divided by its total assets, to calculate its total sales. In this case, the asset turnover ratio is 1.9, so you can set up the following equation:
asset turnover ratio = [tex]\frac{total \ sales}{total \ assets}[/tex]
Plugging in the given values, you get:
[tex]1.9 =\frac {total \ sales }{5,960,000}[/tex]
Solving for total sales, you find that the firm's total sales are
1.9 × 5,960,000 = 11,444,000.
Now that you know the firm's total sales, you can calculate its profit margin by dividing its net income by its total sales:
[tex]profit \ margin = \frac{net \ income}{total \ sales}[/tex]
[tex]= \frac{476,800}{11,444,000}= 4.17%[/tex]
Therefore, the firm's profit margin is 4.17%.
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How many total atoms are in 1.0 moles of H₂O?
Answer:
Below
Step-by-step explanation:
There are three ATOMS in each MOLECULE H2 O
(two hydrogen one Oxygen)
Each mole of MOLECULES = 6.022 x 10^23
6.022 X 10^23 X 3 = 1.81 x 10^24 atoms
Evaluate the expression 5x^3 for x=2
PLS HELP!!!
Answer: 40
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
5x^2
5 ( 2 )^2 (substituting the value of x)
5 ( 2 x 2) (working out the exponents of x)
5 (4) (solving the brackets)
20
Without graphing, determine whether the function represents exponential growth or exponential decay.
y = 129(1.63)x
The exponential growth of three sections is given below.
What is exponential growth?Exponential growth means whose growth more rapid in proportion.
An exponential function is of the form , where b is a positive number not equal to 1.
The value of b determines whether tha function is an exponential growth or an exponential decay.
An exponential function is an exponential growth if b > 1 and an exponential decay if b <1.
Given the function= y 4(5/6)^x
B= 5/6 < 1
Therefore, the function is an exponential decay.
Given the function
Therefore, the function is an exponential growth.
Therefore, the function is an exponential growth is y= 129(1.63)^x is an exponential growth.
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If t= 9 m, what is the area of the triangle?
71
Enter the answer in the box
Answer: 1134 m^2
Step-by-step explanation:
First, you would plug in "9" to replace the variable. It would be 7(9) and 4(9). Parenthesis means multiplication.
Then, you would multiply. 7 x 9 = 63, 4 x 9 = 36
The area of a triangle is bh/2. So, 63x36=2268, 2268/2=1134.
I believe the answer is 1134 m^2.
cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation. how many ways are there to line up all of the tas such that each ta with recitation partner(s) is standing next to them?
504 ways are there to line up all of the tas such that each tas with recitation partner(s) is standing next to them
Given :
cs 2050 has 9 recitation sections. 6 of the recitation sections are led by a pair of tas, and 3 recitation sections are led by a trio of tas. there are also 5 tas who do not teach recitation.
Number of ways = 9P6 * 9C3 * 1 / 5!
= 9! / ( 9 - 6 ) ! * 9! / ( 9 - 3 ) ! * 1 / 5!
= 9! / 3! * 9! / 6! * 1/5!
= 9 * 8 * 7 * 6 / 3 * 2 * 9 * 8 * 7
= 9 * 8 * 7
= 504 ways
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the number of trees in a forest is decaying by 1% every year if in one year it has 10 million trees how many million trees win be there in 8 years round to the nearest hundredths
As it is given, 1% of left tree is decaying every year.
Number of tree left after 8 years.
A = P{1-R/100}^[tex]^{T}[/tex] = 10M{1-1%/100}^ [tex]^{8}[/tex]
= 10M *(0.99)[tex]^[/tex]^[tex]^{8}[/tex]
= 9227446
If round at hundredth, then,
Number of tree = 9227400.
How can you compute depreciation mathematically?Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).
How does depreciation work?Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.
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How do you divide 56.87 by 14 with explanation?
find the percentage change of the first quantity with
reference to the second quantity: 480 units, 560 units.
The percentage change of the first quantity with reference to the second quantity: 480 units, 560 units is: -14.29%.
How to find the percentage change?First step is to find the difference between the two numbers
Difference = New Number - Original Number
Difference = 480 -560
Decrease = -80
Now let find the percentage change
Percentage change = Decrease / Original Number × 100
Percentage change = -80 /560 × 100
Percentage change = -14.29%
Therefore we can conclude that the percentage change is -14.29%.
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To the nearest tenth, what is the BEST estimate of the value of √24?
A 2.4
B 4.1
C 4.9
D 5.1
Answer: C: 4.9
The original answer is 4.8989, so I rounded 8 to the nearest hundredth and got the answer of 4.9. Having a Mathematics calculator also helps with math like this.
How are the rational and radical related?
Any expression that contains the square root of a number is a radical expression it was in my DoNow but I got this wrong so my teacher told me it was this .
Which of the following is the value of discriminant for √ 2x² − 5x+ √ 2 = 0?
17 is the value of discriminant for quadratic equation.
What in mathematics is a quadratic equation?
A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.
The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.
General form of a quadratic equation is
ax² + bx + c = 0
The Discriminant of the quadratic equation is denoted by D and defined as
D = b² - 4ac
The given Quadratic equation is
√2x² - 5x + √2 = 0
Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get
a = √2 , b = - 5 , c = √2
Value of Discriminant
= b² - 4ac
= (-5)² - 4 * √2 * √2
= 25 - 8
= 17
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in the following expression, the variable truckweight has the value 70000 and the variable weightlimit has the value 80000.truck weight < weight limit what value does the expression evaluate to?
The expression evaluates because the variable truck weight's true value is present. The correct answer is (C).
Define expression.Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Given,
In the following expression, the variable truck weight has the value 70000 and the variable weight limit has the value 80000.truck weight < weight limit.
Expression,
Truck weight < Truck limit
The value of expression evaluate,
It is true.
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What is the solution of this compound inequality?
Answer: -27≥x OR x>7
Step-by-step explanation:
[tex]\displaystyle\\a)\ -7\geq \frac{x}{3}+2 \\\\\-7-2\geq \frac{x}{3}+2-2\\\\ -9\geq \frac{x}{3} \\\\[/tex]
Multiply both parts of the equation by 3:
[tex]\displaystyle\\-9(3)\geq \frac{x}{3}(3)\\\\\boxed {-27\geq x}[/tex]
[tex]\displaystyle\\b)\ \frac{3x+1}{2} > 11[/tex]
Multiply both parts of the equation by 2:
[tex]\displaystyle\\\frac{3x+1}{2}(2) > 11(2)\\\\3x+1 > 22\\\\3x+1-1 > 22-1\\\\3x > 21[/tex]
Divide both parts of the equation by 3:
[tex]\boxed{x > 7}[/tex]
Lawson planted a tree when it was 14 inches tall and it will grow 3 inches per year. Ezra planted a tree when it was 8 inches tall and it will grow 5 inches per year. Determine how many years it will take for the trees to be the same height. Person right gets brainlyest
Answer:
3 years
Step-by-step explanation:
Let x = number of years, and let y = height at x years.
Lawson:
Initial height: 14
Annual growth: 3
equation: y = 3x + 14
Ezra:
Initial height: 8
Annual growth: 5
equation: y = 5x + 8
We want to know the number of years, x, when the heights are equal.
y = y
3x + 14 = 5x + 8
-2x = -6
x = 3
