Therefore exact coordinates of Centroid = (0,3/2)
Define Centroid.The centroid of a flat figure or solid figure, also known as the geometric center or center of figure, in mathematics and physics, is the arithmetic mean position of all the points on the figure's surface. Any n-dimensional Euclidean object is included by the same definition.
What is Triangle?A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
This region is a parabola opening downward, with vertex at (0, 49) and a range of y values from 0 to 49. The region is symmetric about the y-axis, This means that the x-coordinate of the centroid is at 0.
To find the y-coordinate:
Integral from -√(49) to √(49) of (49-x²) x dx = [x²(49-x²)/3] from -√(49) to √(49) = (492√(49))/3 = (98√(49))/3
The area is integral from -√(49) to √(49) of (49-x²) dx = [x(49-x²)/2] from -√(49) to √(49) = (49*(2√(49)) - (2/3)(49^(3/2)))/2 = (49*(2*√(49)) - (98√(49))/3)/2
Therefore Centroid = (0, (98√(49))/(49*(2*√(49)) - (98√(49))/3)) = (0,3/2)
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Find the product.
(6t²-8bs) (t² + bs)
Enter the correct answer.
The product of given equation is [tex]6t^{4} + 6t^{2} bs-8bst^{2} -8b^{2} s^{2}[/tex] .
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's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
[tex]=(6t^{2} -8bs) (t^{2} + bs)[/tex]
[tex]=6t^{2} (t^{2} + bs) -8bs(t^{2} + bs)[/tex]
[tex]=6t^{4} +6t^{2}bs -8bst^{2} -8b^{2} s^{2}[/tex]
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how to horizontally stretch a cubic fucnction
Answer:
Steps for How to Transform the Graph of a Cubic Function
Step 1: The standard form of a cubic function is y=a(x−h)3+k y = a ( x − h ) 3 + k , where a indicates a stretch or a shrink, h indicates a vertical shift, and k indicates a horizontal shift.
Step-by-step explanation:
(36)^-2 x (9)^-2 i need help
Answer: 1/104976
Step-by-step explanation:
You can get rid of negative exponents by flipping the number. So in this case, the expression would change to: 1/(36)^2 x (9)^2.
From there, simplify the expression. 36 squared is 1296. 9 squared is 81. Multiply those together to get 104,976.
1/104976 is your answer!
evaluate - [tex]6^{2}- 2(5+1+3[/tex]
The expression 6² - 2(5 + 1 + 3) after evaluation gives 18.
What is BODMAS rule?BODMAS rule is rule for operation of numbers in a specific order when more than one type of operations is involved.
BODMAS is the abbreviated form for Brackets, Order including powers and exponents, Division, Multiplication, Addition and Subtraction.
Given expression is, 6² - 2(5 + 1 + 3).
First we should do the operation in brackets.
6² - 2(5 + 1 + 3) = 6² - 2 (9)
Now we should do the power operations.
6² - 2 (9) = 36 - 2 × 9
Now we do multiplication.
36 - 2 × 9 = 36 - 18
Now we do subtraction.
36 - 18 = 18
Hence the answer of the expression given is 18.
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Bob's Gift Shop sold 550 cards for Mother's Day. One salesman, Anand, sold 4% of the cards sold for Mother's Day. How many cards did Anand sell?
22 cards were sold by the Anand.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Bob's Gift Shop sold 550 cards for Mother's Day.
One salesman, Anand, sold 4% of the cards sold for Mother's Day.
We need to find the number of cards sold by Anand
Convert 4% to decimal by dividing 4 by 100
4/100=0.04
Now multiply 0.04 with 550
0.04×550
22
Hence, 22 cards were sold by the Anand.
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(30 points) write the equation of line a that goes through points (3,2) and has a y-intercept of 1
Use the equation that you wrote for line a to write an equation for line b which is perpendicular to line 8 and goes through the point (-4,2)
To write the equation of a line that goes through the point (3,2) and has a y-intercept of 1, we can use the point-slope form of a line. The point-slope form is:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line, and m is the slope of the line. The slope is a measure of the steepness of the line, and it is calculated as the rise (the change in y) over the run (the change in x).
To find the slope of the line, we can use the two points (3,2) and (3,1). The rise is 1 - 2 = -1 and the run is 3 - 3 = 0, so the slope is -1/0, which is undefined. This means that the line is a vertical line and does not have a slope.
Since the line is a vertical line, we cannot use the point-slope form to write its equation. Instead, we can use the slope-intercept form, which is:
y = mx + b
Where m is the slope of the line and b is the y-intercept. In this case, the slope is 0 (since the line is vertical), and the y-intercept is 1, so the equation of the line is:
y = 0x + 1
To write the equation of a line that is perpendicular to line a and goes through the point (-4,2), we need to find the slope of line a. Since line a is a vertical line, its slope is undefined. However, we know that the slope of a line perpendicular to it must be 0.
Using the point-slope form, the equation of line b is:
y - 2 = 0(x - (-4))
Simplifying, we get:
y = 0x + 2
So, the equation of line b is:
y = 0x + 2
(2x+1)(x-3)(x+5) expand and fully simplify
Answer:
2x^3+5x^2−28x−15
Step-by-step explanation:
Simplify. -15 times the square root of y^2 if y>0
Answer:
-15y
Step-by-step explanation:
The square root of any squared number is always the number itself.
So in this case, it is -15y
Brainliest please. It'll help a lot.
Answer:
- 15y---------------------------------
Simplify the expression:
[tex]-15\sqrt{y^2}[/tex]We know the square root is never negative and since y is positive, we get:
[tex]-15\sqrt{y^2} =-15y[/tex]The area of the square is 25. The area of the circle is 39. What is the area of the shaded regions?
Answer:
c.
Step-by-step explanation:
First at all you need the half circle area formula:
(Pi*r2)/2 = 18Pi
After resolved this you have: r = 6, then diameter= 12
Then c) Its perimer is 40 because AB + CD + BC + AD = 40
3x+1
1. A function f: x →
X-1
(i)
Find the images of -1 and 3.
(ii)
Find the value of x for which f(x) = 7
2. The set P = {-2,-1,0,1,2} maps onto Q by the function f(x)=x²-2, where x E P.
(i)
Find the elements of Q.
(ii)
3. Given that f(x) = 2x - 1 and g(x) = x² +1:
Find f(1 + x):
Find the range of values of x for which f(x) < -3;
Simplify f(x) - g(x).
(i)
(ii)
(iii)
,x # 1, is defined on the set (-1, 0, 2, 3, 4, 5)
Draw a diagram showing the mapping between P and Q.
(i)
4. The function f and g are defined as follows: f:x →→ 2
x-1 and g:x→ 3x + 1
Evaluate f(-) +1
(ii)
Solve f(x) = g(-2)
5. Given that f(x) = px + q, find the values od p and q, if f(2)= 4 and f(4) == 10
The function f is defined as f:x→ 3x² - 5x.
6.
(i)
Evaluate f(--3)
(ii)
7. The functions f and g are defined as: f:xx-2 and g: x2x²-1. Solve:
(i) f(x) = g(-²/-) (ii) f(x) + g(x)= 0
4
Find the values of x for which f(x) = -² 3
On solving the provide the question, we can say that - the value of the following function is f(x) = -5x - 1.
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
[tex]x = -2, y = 9; x = -1 , y = 4; x =0, y = -1.[/tex]
x = 0 , y = -1 so c = -1.
slope of line [tex]= (4-9) / (-1-(-2)) = -5/ 1 = -5.[/tex]
function f(x) = -5x - 1.
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Answer:
Step-by-step explanation:
1. (i) f(-1) = 3(-1) + 1 = -2 and f(3) = 3(3) + 1 = 10
(ii) To find the value of x for which f(x) = 7, we can set f(x) equal to 7 and solve for x:
3x + 1 = 7
3x = 6
x = 2
2. (i) Q = {x² - 2 | x E P} = {(-2)² - 2, (-1)² - 2, (0)² - 2, (1)² - 2, (2)² - 2} = {4, 0, -2, -1, 2}
(ii) As f(x)=x²-2, and P = {-2,-1,0,1,2} mapping into Q is {-2,-1,0,1,2} to {4,0,-2,-1,2}
3. (i) f(1 + x) = 2(1 + x) - 1 = 2x + 1
(ii) To find the range of values of x for which f(x) < -3, we can set f(x) equal to -3 and solve for x:
2x - 1 < -3
2x < -2
x < -1
so x can be any value less than -1
(iii) f(x) - g(x) = (2x - 1) - (x² + 1) = 2x - x² - 2
4. (i) f(-1) + 1 = 2(-1) - 1 + 1 = -1
(ii) To solve f(x) = g(-2), we can substitute the expressions for f(x) and g(x) into the equation:
2x - 1 = 3(-2) + 1
2x - 1 = -5
2x = -6
x = -3
5. f(x) = px + q, given that f(2)= 4 and f(4) == 10
so
4 = 2p + q
10 = 4p + q
solving for p and q we get p = 3 and q = -2
6. (i) f(--3) = 3(-3)² - 5(-3) = -27
7. (i) To solve f(x) = g(-2/-4), we can substitute the expressions for f(x) and g(x) into the equation:
x-2 = (1/4)x² - 1
x-2 = x²/4 - 1
4x-8 = x²-4
x²-4x+4 = 0
x = 2, -2
(ii) To solve f(x) + g(x) = 0
x-2 + x²-1 = 0
x²-2x+1 = 0
(x-1)² = 0
x = 1
for f(x) = -² 3 the expression does not make sense, but assuming the -² is just typo then we can solve for x by substituting f(x) = -3
into the expression of f(x) = 3x² - 5x
3x² - 5x = -3
3x² - 5
mr.jim would like to plant carrots all around base of the fence surrounding his square feet. the area of his garden is 100 sq feet. in feet what is tje perimeter
Identify the quotient and the remainder
(24x^3 - 14x^2 + 20x +6)÷(4x^2 - 3x +5)
The quotient is (6x + 1) and the remainder is (-7x + 1).
What is a factor of a polynomial?
We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.
To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.
Given A cubic polynomial 24x³ - 14x² + 20x + 6 divided by 4x² - 3x + 5.
So, (24x³ - 14x² + 20x + 6)/(4x² - 3x + 5).
= (4x² - 3x + 5)(6x + 1) + (-7x + 1)/(4x² - 3x + 5) in rhe form N = DQ + R.
The same applies to the division of polynomials.
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A trapezoid has interior angle measures of 95°, 97", 85° and X degrees. Find the measure of angle X in the trapezoid. Enter only the number of degrees in the answer
box.
The solution i:
As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.
The trapezoid is what?In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.
Given: When (-7,-2) to L, L becomes L' (-2,7)
You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).
The entire graphic is therefore rotated 90 degrees in a clockwise orientation.
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Polynomial in standard form
1.
7-3x^3+6x^2
2.
2y-3-8y^2
Answer:
[tex]-3x^3+6x^2+7[/tex][tex]-8y^2+2y-3[/tex]Step-by-step explanation:
The terms are ordered from greatest to least degree.
make x the subject of the formula in R = ax-p/q+bx
R = (ax - p)/(q + bx)
(ax - p) = R(q + bx)
ax - p = Rq + Rbx
ax - Rbx = Rq + p
x(a - Rb) = Rq + p
x = (Rq + p)/(a - Rb)
Convert:
30 quarts
=
bushels
Round to the nearest hundredths.
Answer:
30 quarts= 0.8057 bushels
rounded to the nearest hundredths = 0.81
Find the product. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar. 4/3*5/3
The solution to the product expression 4/3 * 5/3 is 20/9
How to evaluate the product expression?From the question, we have the following parameters that can be used in our computation:
The product 4/3*5/3
To start with, we need to represent the statement as an expression
So, we have the following representation
4/3 * 5/3
Using a calculator, we multiply the numerator
So, we have the following representation
4/3 * 5/3 = 20/3 * 1/3
Using a calculator, we multiply the denominator
So, we have the following representation
4/3 * 5/3 = 20/9
Hence, the solution is 20/9
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Jake has a floor that is 64 square feet. He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet. The tiles may be cut as needed. What is the fewest number of tiles required to fill the space while also requiring the fewest tiles to be cut? Show a diagram of the completed floor.
The number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .
What is area ?
Area can be defined as the total space taken by a 2-dimensional surface or shape of an object.
Given
Jake has a floor that is 64 square feet.
He wants to tile the entire floor using large tiles that measure 3 feet by 5 feet.
The area of 3 feet by 5 feet could be = 3 * 5 = 15 square meters.
number of tiles required to fill the space could be = 64 / 15
that is 4.3 (approx )
Hence , the number of tiles required to fill the space while also requiring the fewest tiles to be cut is 5 .
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7.89 divided by 2 step by step
Answer:
3.945
Step-by-step explanation:
hello i neeed help with my math question 5
Answer:
Add a file to it.
Step-by-step explanation:
We can't see anything.
Someone pls help!!
Construct a circle through points
X, Y, and Z.
By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.
What is a circle?It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)
How can you create a circumcircle?First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.
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This subtraction represents a translation of the
given triangle
——- and ——-
Answer:
right 2 unitsdown 4 unitsStep-by-step explanation:
You want to know the translation effected by subtracting -2 from the x-coordinate, and subtracting -4 from the y-coordinate of the vertices of a triangle.
TranslationYou have correctly observed that the triangle vertex (-2, 0) is translated to (0, -4) by the subtraction of the translation matrix. That is, the x-coordinate is increased by 2, moving the point 2 units to the right, while the y-coordinate is decreased by 4, moving the point 4 units down.
The translation is to the right by 2 units, and a translation down by 4 units.
Answer: 2 units right 4 units down
Step-by-step explanation: trust
Convert the degree measure to radians or the radian measure to degrees. Then find one positive angle and one negative angle that is coterminal with the given angle.
1. -560°
2. 170°
-560° in radian is -28π/9 radian and the positive and negative coterminals are 8π/9 and -10π/9 respectively.
170° in radian is 17π/18 radian and the positive and negative coterminals are 53π/18 and -19π/18 respectively
How to convert the degree measure of angle to radians?An angle can be converted from degree to radian by multiplying it by π/180.
1. -560°
-560° × π/180 = -28π/9 radian
2. 170°
170° × π/180 = 17π/18 radian
In general, if θ is any angle in radian, then θ + n(2π) is coterminal angle with θ, for all nonzero integer n.
coterminal of -28π/9:
positive: -28π/9 = -28π/9 + 2(2π) = 8π/9
negative: -28π/9 = -28π/9 + 2π = -10π/9
coterminal of 17π/18:
positive: 17π/18 = 17π/18 + 2π = 53π/18
negative: 17π/18 = 17π/18 - 2π = -19π/18
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Ashley and Saskia each think of a number.
1 less than Ashley's number is equal to 3 lots of Saskia's number.
4 lots of Ashley's number added to Saskia's number is 95.
Using the information above, write and solve two simultaneous equations to work out Ashley's and Saskia's numbers.
Based on the the information provided above, Ashley's and Saskia's numbers are equal to 22 and 7 respectively.
How to work out Ashley's and Saskia's numbers?In order to write a system of equations to describe this situation, we would assign variables to Ashley's number and Saskia's number respectively, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent Ashley's number.Let the variable y represent Saskia's number.Translating the word problem into an algebraic equation, we have the following:
x - 1 = 3y .....equation 1.
4x + y = 95 .......equation 2.
Making x the subject of formula in equation 1, we have:
x = 3y + 1 .......equation 3.
Substituting equation 3 into equation 2, we have:
4(3y + 1) + y = 95
12y + 4 + y = 95
13y = 95 - 4
13y = 91
y = 91/13
y = 7.
For the value of x, we have:
x = 3y + 1
x = 3(7) + 1
x = 21 + 1
x =22.
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Which of the following has kinetic energy?
O A. Food
O.B. Motion
OC. Gravity
OD. Light
Answer:
light
Step-by-step explanation:
it has kinetic energy
Answer:
Step-by-step explanation: Kinetic energy is made because of movement. So Motion would be the correct answer
What's the inches equivalent of 63.5 millimeters? A. 2.5, B. 24, C. 3.2. D 31
Answer: A
Step-by-step explanation: 2.5 inches = 63.5 millimeters
suppose you have a credit card debt of $6000. Last month, the bank charged you $55 interest on the debt. The solution to the equation 55= 6000/12 * r represents the annual interest rate in the credit card, r. Find the annual interest rate on the credit card
Answer: The formula for the interest charged on a credit card debt is:
Interest = (Principal * Annual Interest Rate) / 12
We know that the interest charged last month is $55, and the principal (the credit card debt) is $6000, so we can substitute these values into the formula and solve for the annual interest rate:
55 = (6000 * r) / 12
To find the annual interest rate, we will solve for r.
r = (55 * 12) / 6000
r = 0.09 which is a 9% annual interest rate.
So, the annual interest rate on the credit card is 9%.
Step-by-step explanation:
ln 4 - ln x = 2
Solve for x
Show all steps
Answer:
To solve this equation, we first need to isolate the ln term on one side of the equation. To do this, we can subtract ln 4 from both sides to get:
ln 4 - ln x - ln 4 = 2 - ln 4
This simplifies to:
-ln x = 2 - ln 4
Next, we can add ln 4 to both sides to get:
-ln x + ln 4 = 2
This simplifies to:
ln 4 - ln x = 2
Now, we can apply the identity ln a - ln b = ln(a/b) to both sides of the equation to get:
ln(4/x) = 2
To solve for x, we can apply the inverse logarithm function (exp) to both sides:
4/x = exp(2)
This simplifies to:
x = 4/exp(2)
Finally, we can evaluate this to get the value of x:
x = 4/exp(2) = 4/7.38905609893065
So the solution is x = 4/7.38905609893065.
Step-by-step explanation:
Fill in the blanks below in order to justify whether or not the mapping shown represents a function. Set A 5 0 7 Set B -2 9 -1 -3 The mapping diagram above a function since in where there .
The mapping does not represents a function
How to identify a function?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
In this case, for the mapping represent a function, every element in set A must be mapped to exactly one element in set B.
Since there is more than one arrow from set A (5) pointing to different values in set B (-2 and 9), then it is not a function. Also, the two different value (5 and 7) in set A has the same value (-2) in set B.
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Which values are possible rational roots of 9x3+14x2−x+18=0 according to the rational root theorem? Select each correct answer.
The possible roots of the cubic polynomial 9x³ + 14x² - x + 18 are 1, 2, and 3.
What is the rational root theorem?The rational root theorem explains how a polynomial's roots and coefficients are related. It explains the kind of rational roots that the polynomial might have in particular.
According to the rational root theorem, the possible roots of a polynomial of degree three and above are,
± (coefficient of the last term)/(coefficient of the first terms).
Given, A polynomial 9x³ + 14x² - x + 18 it is a cubic polynomial so it should have three roots they could be,
The factors of the constant term divided by the factors of the first terms,
So, 18 has factors ± (1, 2, 3, 6, 9, 18) and 9 has factors ± (1, 3, 9).
So, The possible roots are ± (1, 2, 3) and so on.
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