The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
What is the equation of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let r be the radius of the circle and the location of the center of the circle be (h, k). Then the equation of the circle is given as,
(x - h)² + (y - k)² = r²
The equation of the semicircle upper side of the x-axis will be given as,
(x - h)² + (y - k)² = r²
x - h = √[r² - (y - k)²]
x = √[r² - (y - k)²] + h
The equation of the semicircle upper side of the x-axis will be x = √[r² - (y - k)²] + h.
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Complete the equation of the line through
(
−
8
,
−
2
)
(−8,−2)left parenthesis, minus, 8, comma, minus, 2, right parenthesis and
(
−
4
,
6
)
(−4,6)left parenthesis, minus, 4, comma, 6, right parenthesis
The linear function through the points (-8,-2) and (-4,6) is given as follows:
y = 2x + 14.
How to define a linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the linear function.The intercept b represents the value of y when x = 0.Given two points, the slope is calculated as the change in y divided by the change in x, hence:
m = (6 - (-2))/(-4 - (-8))
m = 8/4
m = 2.
Hence:
y = 2x + b.
When x = -8, y = -2, hence the intercept b is obtained as follows:
-2 = 2(-8) + b
b = 14.
Hence the equation is:
y = 2x + 14.
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What is the value of 300m in miles
Answer:
Step-by-step explanation:0.18
8x - 7y = 56
plot on the graph
Answer: put tow points, 1 on the x-axis (horizontal) and the other 1 on y-axis (vertical).
x = 7
y = -8
and you make a straight line , connecting them
Which function will approach positive infinity the fastest?
O f(x)= 100(1.5)*
O f(x) = 100x5 + 200x³ + 100
Of(x) = 200(1.45)*
O f(x) = 200x3 + 100x² + 100
Answer:
Step-by-step explanation:
fx
Gracie deposited $20,000 into an account that compounds interest weekly at a rate of 1.56%. Each week, her bank withdraws $200 from the account and puts that amount into her mortgage account. How long will it take until the account has a balance of $0? Round to the nearest tenth of a year.
It takes 2 years for the account balance to come down to 0.
What is the compound interest?Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
The formula used to find the compound interest = [tex]A=P(1+\frac{r}{100})^{nt}[/tex].
Given that, principal =$20,000, rate of interest =1.56%, n=52 and W=$200.
Use the formula, [tex]P=W\frac{1-(1+\frac{r}{n})^{-nt} }{\frac{r}{n} }[/tex]
[tex]20000=200\frac{1-(1+\frac{0.0156}{52})^{-52t} }{\frac{0.0156}{52} }[/tex]
[tex]100=\frac{1-(1+0.0003)^{-52t}}{0.0003}[/tex]
[tex]0.03=1-(1.0003)^{-52t}[/tex]
[tex]0.97=(1.0003)^{-52t}[/tex]
Take log on both the side, we get
-52t·log(1.0003)=log0.97
So, t=2 years
Therefore, it takes 2 years for the account balance to come down to 0.
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A charge 5. 00 nc is placed at the origin of an xy-coordinate system, and a charge -2. 00 nc is placed on the positive x-axis at x = 4. 00 cm. A third particle, of charge 6. 00 nc is now placed at the point x = 4. 00 cm , y = 3. 00 cm.
The x-component of the total force exerted on the third charge by the other two charges is equal to k * (30.00 nC * 4.00 cm / 5.00 cm + 12.00 nC).
Force is a physical quantity that measures the influence of one object on another. It is a vector quantity, meaning it has both magnitude and direction.
Let's use Coulomb's Law to calculate the x-component of the total force exerted on the third charge by the other two charges. The x-component of the total force is just the sum of the x-components of the forces exerted by each of the two charges.
First, we'll calculate the force exerted by the 5.00 nC charge at the origin. The direction of this force will be towards the third charge, so the angle θ is the arctangent of the ratio of the y-coordinate of the third charge and the x-coordinate of the third charge. That is, θ = arctan(3.00 cm / 4.00 cm). Using Coulomb's Law, we have:
F = k * q1 * q2 / r²,
where k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. For this case,
=> r = √(4.00 cm² + 3.00 cm²) = 5.00 cm.
Thus,
F = k * 5.00 nC * 6.00 nC / 5.00 cm^2 = k * 30.00 nC.
Fx = F * cos(θ) = k * 30.00 nC * cos(arctan(3.00 cm / 4.00 cm))
Fx = k * 30.00 nC * 4.00 cm / 5.00 cm.
Next, we'll calculate the force exerted by the -2.00 nC charge on the x-axis. This force will be in the negative x-direction, so the angle θ is 180 degrees. Thus,
F = k * -2.00 nC * 6.00 nC / 4.00 cm^2 = -k * 12.00 nC.
Fx = F * cos(180) = -k * 12.00 nC * cos(180) = k * 12.00 nC.
Finally, we add up the x-components of the forces exerted by each charge to get the total x-component of the force:
Fx = k * 30.00 nC * 4.00 cm / 5.00 cm + k * 12.00 nC
Fx = k * (30.00 nC * 4.00 cm / 5.00 cm + 12.00 nC).
Complete Question:
A charge of 5.00 nC is placed at the origin of the xy - coordinate system, and a charge of -2.00 nC is placed on the positive x-axis at x = 4.00 cm. A third particle, of charge 6.00 nC is now placed at the point x = 4.00 cm, y = 3.00 cm.
Find the x-component of the total force exerted on the third charge by the other two.
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can someone help me with this question the letter a b or c or d
Answer:
The answer is D
Step-by-step explanation:
because u need to divide the y and x and when u do it to all of them u will get the same ratio which is 4
what should a good residual plot look like if the regression line fits the data well?
A good residual plot should have the points randomly scattered around the horizontal line with no discernible pattern.
This indicates that the model is well fit to the data. The residuals should also be equally distributed on either side of the horizontal line. This can be seen as the sum of the residuals being equal to 0, or mathematically expressed as the sum of the residuals (e) being equal to 0, where [tex]e = y - ŷ[/tex], where y is the observed value and ŷ is the predicted value. The equation can be expressed as Σe=0.
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Each student in a math class has to buy the items in the table. Write an expression in simplest form that represents the
total cost for x students.
Item
Calculator
Notebook
Pack of pencils
11.55
9.65x+0.65x+1.25x
11.55x
x(9.65+0.65+1.25)
Cost
$9.65
$0.65
$1.25
The expression in simplest form that represents the total cost for x students is 11.55x, the correct option is C.
What is an expression?Expression in mathematics can be defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that a student in a math class has to buy the items in the table.
Now,
x(9.65+0.65+1.25)
=9.65x+0.65x+1.25x
=11.55x
Therefore, the expression in simplest form will be 11.55x.
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Here’s another…23+18w=-21+14w
Answer: -11
Step-by-step explanation:
using diagonals from a common vertex, how many triangles could be formed from a 21-gon?
Total 816 triangles that can be formed using diagonals from a common vertex of a 21-gon.
What are Diagonals?In mathematics, a diagonal is a line joining two vertices of a polygon or solid whose vertices do not lie on the same edge. Diagonals are generally defined as oblique lines or slanted lines connecting the vertices of a shape. A diagonal is defined as a horizontal shape with sides/edges and corners.
Solution of the given problem:
Firstly, choose 3 vertices of 21-gon which are not adjacent to each other.
Secondly, connect all three vertices to a common vertex.
Now, there are 18 vertices that are not adjacent to common vertex and there are now 18 diagonals that can be drawn to the common vertex up to these vertices.
To form a triangle using these diagonals, we need to choose 3 of these 18 vertices, this can be calculated using the binomial coefficient formula:
18 choose 3 = 18! / (3! * (18 - 3)!) = (18 * 17 * 16) / (3 * 2 * 1) = 816
Thus, total 816 triangles can be formed.
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Given an integer representing a 10-digit phone number, output the area code, prefix, and line number using the format (800) 555-1212.
Here we have a program written in C++ language. Each // symbol is a relative comment explaining the reason for each command line (and is not included during the program execution).
The Program:
#include <iostream>
//c++ build in library
using namespace std;
//main code body starts here
int main()
{
//declare variable to store phone numbers,its area code, prefix and line number.
long pnumber; //declare long variable
int ac, prefix, lnumber;
//declare integer variables, where ac: Area Code and lnumber is the Line Number
cout<<"Enter a 10-digit Phone Number: "<<endl;
//cout command prints on screen the desired message
cin>>pnumber;
//cin command enables the user to interact with the programm and enter information manually
//main body to obtain the desired output starts below
//each 'division' is used to allocate the correct value at the correct
//since prefix is used to get the desired output of ( ) -
ac = pnumber/10000000;
prefix = (pnumber/10000)%1000;
lnumber = pnumber%10000;
//main body ends here
cout<<"Based on your 10-digit number"<<endl;
cout<<"below you have (AreaCode), Prefix, and - line number "<<endl;
cout<<"("<<ac<<")"<<""<<prefix<<"-"<<lnumber<<endl;
//Prints on screen the desired output of the long 10 digit Number
return 0; //ends program
}
-------------------------------------------------------------------------------------------------------
The Output Sample:
Enter a 10-digit Phone Number:
8019004673
Based on your 10-digit number
below you have (Area Code), Prefix, and - line number
(801) 900-4673
....Programm finished with exit code 0
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What type of graph is shown, and what is the growth factor?
linear function; growth factor of 2
linear function; growth factor of 4
exponential function; growth factor of 2
exponential function; growth factor of 4
The graph is a linear function with a growth factor of 4
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
The graph has the shape of a straight line, so it is linear.
The graph starts at point (0, 0). It passes through point (1, 4).
slope = 4/1 = 4
The slope is 4. Growth factor is the same as slope for a linear function.
Hence, the graph is a linear function with a growth factor of 4
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The average of your first 6 tests is 82. If your test average after your seventh test is an 80. 5, what did you score on the seventh test?.
The score on the seventh test is 71.5
"Information available from the question"
The average of your first 6 tests is 82.
If your test average after your seventh test is an 80. 5
To find the score on the seventh test.
Now, According to the information:
Average of 6 test is 82
We know that :
Average = Sum of all test / Total no. of test => 82 = Sum of all test / 6
Sum of all test = 492
Let the seventh test be 'x'
So, Sum of seventh test is = 492 + x
Average = [tex]\frac{492+x}{7}[/tex]
80.5 = [tex]\frac{492+x}{7}[/tex]
=> 80.5 × 7 = 492 + x
x = (80.5 × 7) - 492
=> x = 563.5 - 492
x = 71.5
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What are the 5 most common Pythagorean triples?
The 5 most common Pythagorean triples are ( 3 , 4 , 5 ) , ( 5 , 12 , 13 ) ,
( 6 , 8 , 10 ) , ( 9 , 12 , 15 ) , and ( 15 , 20 , 25 ) .
Pythagorean triples:
Any three positive integers that completely satisfy the Pythagorean theorem is considered a Pythagorean triple number. According to the theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a right triangle. A Pythagorean triple consists of the three sides of a right triangle. In this article, you will learn how to create multiple Pythagorean triples.
A Pythagorean triple consists of the three natural numbers a, b, c such that a² + b² = c². These triples are usually written as (a, b, c), examples
(3, 4, 5) are well known. If (a, b, c) is a Pythagorean triple, then (ka, kb, kc) is also a Pythagorean triple for all natural k. A primitive Pythagorean triplet is a triplet in which a, b, and c are coprime (i.e., have no common divisor greater than 1). For example, (3, 4, 5) is a basic Pythagorean triple, but (6, 8, 10) is not.
A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is necessarily a right triangle.
This name comes from the Pythagorean theorem, which states that the side lengths of each right triangle satisfy the formula a² + b² =c². A Pythagorean triple gives the length of three integers of the sides of a right triangle. However, right triangles whose sides are not integers do not form a Pythagorean triple. For example, a triangle with sides a = b = 1 and c = √2 but, (1,1,2) is not a Pythagorean triple because √2 is not an integer. Also, the numbers 1 and √2 do not have a common multiple because √2 is irrational.
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The table shows the height of water in a pool as it is being filled. A table showing Height of Water in a Pool with two columns and six rows. The first column, Time in minutes, has the entries, 2, 4, 6, 8, 10. The second column, Height in inches, has the entries, 8, 12, 16, 20, 24. The slope of the line through the points is 2. Which statement describes how the slope relates to the height of the water in the pool? The height of the water increases 2 inches per minute. The height of the water decreases 2 inches per minute. The height of the water was 2 inches before any water was added. The height of the water will be 2 inches when the pool is filled.
The correct statement that describes how the slope relates to the height of the water in the pool is: The height of the water increases 2 inches per minute, the correct option is A.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
We are given that;
The time in minutes: 2, 4, 6, 8, 10
Height in inches: 8, 12, 16, 20, 24
Now,
The slope of the line through the points is 2, which means that for every 1 unit of time (in minutes) that passes, the height of the water in the pool increases by 2 units (in inches).
Therefore, by the given slope answer will be height of the water increases 2 inches per minute.
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Suppose ABC is a right triangle, and cos (B) =a/c, which of the following much also be true ?
Answer:
option 1 --> sec A = c/a
option 3 --> sin(b) = b/c
option 4 --> Sin(A) = a/c
Step-by-step explanation:
Since cos is adjacent, we know the legs are a and b and the hypotenuse is c
For angle B
sin (opposite over hypotenuse) = b/ctan (opposite over adjacent) = b/acsc (hypotenuse over opposite) = c/bsec (hypotenuse over adjacent) = c/bcot (adjacent over opposite) = a/bFor Angle A
sin = a/ccos = b/ctan = a/bcsc = c/asec = c/bcot = b/aThe original cost of a shirt is $40. A store manager marks up the cost by 20% to get
the selling price. During a sale, the store manager marks down the cost of the shirt
by 20%. What is the percent change from the original cost to the sale price? Is this
a percent increase or a percent decrease? Show your work.
Answer:
Step-by-step explanation:
Ans:percentage increased by 20
Gross profit/Cost of sales=20percent
Gross profit=20percent x cost of sales
Sales=120percent x cost of sales
Sales=120x40
=$48
48-40=$8
8/40x100percent=20percent
Answer: Decrease? not 100% sure
Step-by-step explanation:
4 divided by an eighth
Answer:
32
Step-by-step explanation:
select all expressions that are equivalent to 2to the power of 4 / ((3.2 x 0.8) + 1.44)
The value of the given expression will be 4.
Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
Given that the expression is 2⁴ / ( 3.2 x 0.8 0 + 1.44 ). SOlve the expression as below,
E = 2⁴ / ( 3.2 x 0.8 ) + 1.44 )
Solve the denominator by mathematical operation.
E = 16 / ( 2.56 + 1.44 )
Divide the numerator by denominator,
E = 16 / 4
E = 4
Therefore, the solution of the expression is 4.
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Someone please help me!!
Answer:
84 units
Step-by-step explanation:
The darkest shaded face has 12 full units. Times that by the width or the lightest shade area (7) you get the answer 84 units.
12(7) = 84
(-2,1) (-8,-5) round nearest tenth
The slope of line from the points given is 1
What is the slope of lineThe slope of a line is a measure of how steep the line is and the direction it is going. In mathematical terms, it is defined as the ratio of the change in the y-coordinate (rise) to the change in the x-coordinate (run) between two points on the line. Slope is often represented by the letter "m". If (x₁, y₁) and (x₂, y₂) are two points on the line, the slope can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
In this problem, we can take the two points and calculate the slope.
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the values into the formula to find the slope;
m = -5 - 1 / -8 - (-2)
m = 1
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Complete Question; Calculate the slope of the line (-2, 1) and (-8, -5)
Help for those questions please
The evaluation of the expressions are shown below
How to evaluate the expressionsTo determine the solution to the expressions, we make use of laws of indices and exponents
Expression 1 (a) and (b)
(27)^(-4/3) ÷ (1/64)^(2/3) = (3^3)^(-4/3) ÷ (1/4^3)^(2/3)
(27)^(-4/3) = (3)^(-4) ÷ (1/4)^(2)
(27)^(-4/3) = 1/81 ÷ 1/16
So, we have
(27)^(-4/3) = 16/81
Next, we have
(32)^(2/5) - (-125)^(-1/3) = (2^5)^(2/5) - (-5^3)^(-1/3)
(32)^(2/5) - (-125)^(-1/3) = (2)^(2) - (-5)^(-1)
(32)^(2/5) - (-125)^(-1/3) = 4 + 1/5
(32)^(2/5) - (-125)^(-1/3) = 21/5
Equation (2)
Here, we have
3(8/27)^(-2/3) = 2^x/3^y
So, we have
3(3/2)^(2) = 2^x/3^y
So, we have
3^3/2^2 = 2^x/3^y
By comparison, we have
x = -2 and y = 3
Equation (3)
Here, we have
3^x(9^[1 - x]) = 27^[x + 2]
So, we have
3^x(3^2[1 - x]) = 27^[x + 2]
This gives
3^(x + 2[1 - x]) = 3^3[x + 2]
By comparison, we have
x + 2[1 - x] = 3[x + 2]
So, we have
x + 2 - 2x = 3x + 6
Evaluate
4x = -4
x = -1
Equation (4)
Here, we have
(5^x)^2x = 25(1/125)^x
So, we have
(5)^2x^2 = 5^[2 - 3x]
By comparison, we have
2x^2 = 2 - 3x
So, we have
2x^2 + 3x - 2 = 0
Evaluate
x = -2 and x = 1/2
Equation (5)
Here, we have
2^x+1 + 2^3-x = 10
Here, we make use of a graphing tool
So, we have
x = 0 and x = 2
Expression (6)
Here, we have
√16^x+2
Express 16 as 2^4
So, we have
√16^x+2 = √2^4[x+2]
Take the square roots
√16^x+2 = 2^2[x+2]
Open the bracket
√16^x+2 = 2^2x+4
Hence, the expression is 2^2x+4
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In many classes, a passing test grade is 60 (A = 60). Using the formula A = 10 R,
what raw score (R) would a student need to get a passing grade after her score is
adjusted?
A student need a raw score of 36.
How to determine the raw score (R) of the student?
We can find the raw score (R) of the student by substituting A = 60 into the the formula and then solve for R. That is:
A = 10√R
√R = 60/10
√R = 6
R = 6²
R = 36
Thus, a student need a raw score of 36 to get a passing grade after her score is adjusted.
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how to find focus of parabola
(h, k+1/4a) are the coordinates for the focus of parabola. And the standard form is (x - h)2 = 4p (y - k).
To get the focus of a parabola, you must be aware that the equation of a parabola in a vertex form is y=a(xh)2+k, where a denotes the slope of the equation. The center of the parabola is at (h, k+1/4a), according to the formula. The focal point of the parabola is its axis. The centre of a parabola is 'a' units away from the vertex. The vertex and the focus are positioned on the parabola's axis, which you may identify using the equation for the parabola.
The axis of the parabola with a second-degree x equation is the y axis, or a line parallel to it, whereas the axis of the parabola with a second-degree y equation is the x axis, or a line parallel to it.
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i don’t understand how to get answer
Answer:
You probably know that it is a good idea to brush your teeth every day. What does this do that helps prevent tooth decay?
Step-by-step explanation
What is the value of root 216?
Answer: The square root of 216 is equal to approximately 6.485281.
Step-by-step explanation:
The square root of 216 is equal to the number that, when multiplied by itself, gives 216. The value of the square root of 216 can be found using several methods, including estimation, the long division method, and a calculator. Here, I'll provide a step-by-step explanation using estimation.
Step 1: Estimate the value of the square root.
One way to estimate the value of the square root of 216 is to find two perfect squares that are close to 216, and whose square roots are therefore close to the square root of 216. In this case, the perfect squares closest to 216 are 144 (12^2) and 225 (15^2). Since 216 is closer to 144, the square root of 216 is likely to be closer to 12 than to 15.
Step 2: Refine the estimate.
To refine the estimate of the square root of 216, we can average the two closest perfect squares and their square roots. In this case, the average of 12 and 15 is 13.5, and this is a better estimate of the square root of 216 than either 12 or 15 alone.
Step 3: Improve the estimate using a more precise method.
One method for finding an even more precise estimate of the square root of 216 is to use the Newton-Raphson formula for finding square roots. This formula involves repeatedly applying the following equation:
x_n+1 = (x_n + n/x_n) / 2,
where x_n is the nth estimate of the square root, and n is the number whose square root we are trying to find (in this case, n = 216). We can start with an initial estimate, such as x_0 = 13.5, and iterate the formula until the estimate converges to a desired level of precision.
Step 4: Use a calculator or other tools to find the exact value.
Finally, we can use a calculator or computer program to find the exact value of the square root of 216 to as many decimal places as desired. The exact value of the square root of 216 is equal to approximately 6.485281.
Please help me. I am inept when it comes to math. thx
Note that the proof required is given based on the AA Similarity Postulate.
Similar triangles: If two triangles are similar then their corresponding angles are equal.
By the transitive property of equality if a = b, and b= c then a = c.
AA postulate of similarity states that when two corresponding angles of two triangles are equal then they are called similar to each other.
Given ΔABC ~ ΔRST; and
ΔDEF ~ ΔRST
To Prove: ΔABC ~ DEF Note that:
ΔABC ~ ΔRST - Given
ΔDEF ~ ΔRST
- Given
∠A = ∠R, ∠D = ∠R - Definition of Similar Triangles
∠C = ∠T, ∠F = ∠T
∠A= ∠C, ∠D = ∠F - Transitive property of Equality; Thus,
ΔABC ~ Δ DEF (AA Similarity Postulate)
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Find the volume.
(Pls help…. I’ve tried many times but ain’t near the answer)
The volume of the composite figure is equal to 1395 square inches.
How to determine the volume of the composite figure
In this problem we need to determine the volume of a composite figure, which is the result of combining the volumes of a right prism and a pyramid, whose volume formulas are listed below:
Pyramid
V = (1 / 3) · w · l · h
Prism
V = w · l · h
Where:
w - Width, in inchesl - Length, in inchesh - Height, in inchesNow we proceed to determine the volume of composite solid:
V = (9 in) · (15 in) · (7 in) + (1 / 3) · (15 in) · (9 in) · (10 in)
V = 1395 in³
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015 Chapter 1: Perimeter and Area in the Coordinate Plane > Section Exercises 1.4> Exercise 8
8
Find the perimeter of the polygon with the vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2)
The perimeter is
units
The perimeter of the polygon with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2) is 16 units.
What is the perimeter?Perimeter is a circumferential measure of the figure, for example, the perimeter of a square is the sum of all its sides.
Here,
To find the perimeter of a polygon, we need to add up the lengths of all its sides. In this case, we have a quadrilateral with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2).
We can use the distance formula to find the lengths of each side:
Length of QR = √[(1 - (-3))² + (2 - 2)²] = 4
Similarly,
Length of RS= 4
Length of ST= 4
Length of TQ= 4
Therefore, the perimeter of the polygon is 4 + 4 + 4 + 4 = 16
So the perimeter of the polygon with vertices Q(-3, 2), R(1, 2), S(1,-2), and T(-3,-2) is 16 units.
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