The diameter , radius and area of the circle is 126cm, 63cm, 12474cm² respectively.
What is circumference of a circle?The circumference of a circle is the perimeter of the circle. It is the total length of the boundary of the circle.
The circumference of a circle is given as;
C = π d
where d is the diameter of the circle
therefore 396 = 22/7 × d
22d = 396× 7
22d = 2772
divide both sides by 22
d = 2772/22
d = 126 cm
the diameter of a circle is 2 times it's radius
d = 2r
126 = 2r
r = 126/2
r = 63cm
The area of the circle is
A = πr²
A = 22/7× 63× 63
A = 22×9× 63
A= 12474cm²
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Unit 5: Sytem of Equation & Inequalitie Homework 3: olving ytem by elimination
For math equation, To eliminate a variable, it must have the same coefficient. So if the coefficients of the variables are not the same then first equate the coefficients by multiplying or dividing them.
Problems exampleDetermine the set of solutions to the following system of equations using the elimination method, if x and y are variables in the set of real numbers.
Completion:
1. x + y = 1 and x + 5y = 5
Step I (eliminate variable y)To eliminate the y variable, remember that the coefficients of y must be the same, so the equation x + y = 1 times 5 and the equation x + 5y = 5 times 1, then:
x + y = 1 │× 5 => 5x + 5y = 5
x + 5y = 5 │× 1 => x + 5y = 5
5x + 5y = 5
x + 5y = 5
--------------- –
4x + 0 = 0
x = 0
Step II (eliminate variable x)Same as step I, there is no need to equate the coefficients to eliminate variable x because the coefficients are the same, then:
x + y = 1
x + 5y = 5
--------------- –
0 + –4y = –4
y = 1
So, the solution set is {(0, 1)}.
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Where is the vertex of the parabola y X² 2x 3?.
The vertex of the equation y = x² + 2x -3 is (-1, -4).
The term vertex in math is known as a point on a polygon where the sides or edges of the object meet or where two rays or line segments meet.
Here we have the expression y = x² + 2x -3
As we all know that the given equation of parabola is written as,
=> y = ax² + bx + c
As we all know that the vertex of the parabola is given by (h, k).
Here we have calculated the value of the x coordinate of vertex as ,
=> h = -b/2a
And the value of y coordinate of vertex k by using the formula,
=> k = y(h)
Through the given equation we have identified the value of a = 1, b = 2 and c = -3
Then the value of x coordinate is calculated as,
=> h = -2/(2 × 1)
Therefore, the value of h is -1
Then the value of y coordinate is calculated as,
=> k = y (-1)
Here we have to substitute -1 in the equation, then we get
=> k = (-1)2 + 2(-1) - 3
=> k = 1 - 5 = -4
Hence the coordinate of the vertex is (-1, -4).
Complete Question:
Where is the vertex of the parabola of the equation y = x² + 2x -3?
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Determine whether the next pair of triangles is similar. If the triangles are similar, give a reason: write AA, SSS, or SAS.
The two triangles in this problem are not similar, as they do not have congruent angle measures.
What are similar triangles?Similar triangles are triangle that share these following two features:
Congruent angle measures.Proportional side lengths.The angle measures for each triangle are given as follows:
25º, 75º and 180 - 100 = 80º.25, 70º and 180 - 95 = 85º.As the triangles have different angle measures, they are not similar.
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the number of nickels exceeds the number of dimes by 7. the total value of the coins is $1.55. How many coins of each type are there?
Answer:
15 nickels and 8 dimes
Step-by-step explanation:
Let N = number of nickels and D = number of dimes
N - D = 7 (the number of nickels exceeds the number of dimes by 7.)
or
N = D + 7
Total value of N nickels = 5N
Total value of D nickels = 10D
Combined total value => 5N + 10D = 155
Substitute for N in terms of D
==> 5(D + 7) + 10D = 155
5D + 35 + 10D = 155
15D + 35 = 155
15D = 155 - 35
15D = 120
D = 120/15
D = 8
N = D + 7 = 8 + 7 = 15
15 nickels and 8 dimes
What is linear inequality in two variables and linear equation in two variables?.
A linear inequality in two variables is an inequality that can be written in the form "ax + by < c" or "ax + by > c" or "ax + by = c", where a, b, and c are constants and x and y are variables. This inequality represents a boundary line and all the solutions of the inequality make up a region of the xy-plane.
For example, the inequality "2x + 3y < 6" represents the region of the xy-plane that is on one side of line 2x + 3y = 6. To graph this inequality, one can find the boundary line by setting the inequality equal to zero and then shading in the region that satisfies the inequality.
A linear equation in two variables is an equation that can be written in the form "ax + by = c", where a, b, and c are constants and x and y are variables. This equation represents a straight line in the xy-plane and all the solutions of the equation are the coordinates of the points on that line.
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Question 6 of 25
f(x) = 5x + 3. Find the inverse of f(x).
O A. f-¹(x)=3-5x
OB. f-¹(x) = x-5/3
OC. f-¹(x) = 5x - 3
OD. f-¹ (x) = x-3/5
It is option D (f-¹ (x) = x-3/5
Find the unknown measures.
3.
A
50°
B
?
?
C
The measure of angle B is 50 degrees and angle C is 80 degrees.
What is the angle sum property of a triangle?The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°.
In the given triangle, we can use the concept of triangle angle sum to find the unknown measures.
We know that the sum of the angles in a triangle is always 180 degrees.
Therefore, if we know two angles in a triangle, we can find the third angle by subtracting the sum of those angles from 180.
We are given that angle A is 50 degrees. We are also given that angles B and C are unknown. Therefore,
we can use the following equation to find the measure of angles B and C:
A + B + C = 180
50 + B + C = 180
B + C = 180 - 50
B + C = 130
So the sum of angles B and C is 130 degrees. Therefore, we can't find individual measures of angles B and C.
Alternatively, we can use the property of the angle pair which states that if two parallel lines are intersected by a transversal, the alternate interior angles are congruent.
If we know that angle A and angle B are congruent, we can find the measure of angle B as 50 degrees. As a result, angle C will be 180 - 50 - B = 130-50 = 80 degrees.
Hence, the measure of angle B is 50 degrees and angle C is 80 degrees.
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Graph 16x - 4y = 12
(You can only graph on the given points)
*NO IN BETWEEN*
16x - 4y = 12
4x - y = 3
4x = 3+y
x= 3+y/4
for y = 1
x= 3+1/4 = 1
y = 2
x=3+2/4 = 5/4 = 1.25
y = 3
x = 3+3/4 = 6/4 = 1.5
Tiana hare a granola bar with her brother. They each get one piece of the bar. What fraction name one part?
A fraction share that Tiana share with her brother called half part. This because the part is split into two where the first part is called first half and other called as second half.
How to name a piece that split into several part?To name a piece of an object that split into several you have to:
Determine how many part that the object splitDetermine the name the total part that created such as half for two, one third for three, quarter for four, etc. The name always following by the order of the split like the first part of quarter part called the first quarter.Learn more about fraction of a set here
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A store owner typically sells hats for $34. 99. During a sale he prices them at $29. 99. What is the approximate percent discount on a hat?.
Based on the price of the hats and the new price after the discount, the percent discount is 15%.
What is the Percentage discount?
Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and its par value.
Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
To find the discount, use the formula:
= (Difference between price before discount and price after discount) / Initial price of hat x 100%
According to the given values,
Solving gives:
= (34.99 - 29.99) / 34.99 x 100%
= 15%
In conclusion, the approximate percent discount is 15%.
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please i need help. what is the answer???
ok
0 is the smallest value or X is the smallest value
Can someone please help me with this math problem? I can't use letters, the square box where I type doesn't allow it. Only numbers and infinity symbols, etc...
The math problem is in the picture, Thanks!
Answer:
Step-by-step explanation:
-4,+ infinity symbol which I can’t find
How do you plot a point?.
An x-y (or bivariate) plot is any graph or plot with two axes. The "x-axis" is typically the horizontal axis, whereas the "y-axis" is typically the vertical axis.
Your plot's axes should be identified, and the scale should be chosen (if the graph is not already labeled). Plot the first two pairs of numbers first (the top row of numbers).
Finding the number a on the horizontal, or x-, axis and tracing up or down from there while maintaining a parallel path to the vertical, or y-, axis, will allow you to draw the point at (a, b) on the Cartesian plane.
The position of the point is this area (a, b). The intersection of the two axes defines the plane's center. It is referred to as the beginning or point (0,0).
Each axis is further subdivided into equal units starting at the origin: rising, positive numbers on the x-axis and up the y-axis; falling, negative numbers on the x-axis and down the y-axis.
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PLEASE HURRY, LIMITED TIME EARLY!!!
Question-The center of circle A with equation (x – 7)2 + (y – 1)2 = 16 is mapped to the center of circle B with equation (x + 8)2 + (y – 2)2 = 16. Determine the translation needed for this mapping.
Answers-
A. (x, y) ⟶ (x - 15, y + 1)
B. (x, y) ⟶ (x - 12, y + 9)
C. (x, y) ⟶ (x - 8, y + 2)
D. (x, y) ⟶ (x + 15, y - 1)
The solution is Option A.
The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
What is a Circle?A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle
The circumference of circle = 2πr
The area of the circle = πr²
where r is the radius of the circle
The standard form of a circle is
( x - h )² + ( y - k )² = r²,
where r is the radius of the circle and (h,k) is the center of the circle.
Given data ,
Let the equation for the circle A be represented as
( x - 7 )² + ( y - 1 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )
Let the equation for the circle A be represented as
( x + 8 )² + ( y - 2 )² = 16
Now , the equation is of the form ( x - h )² + ( y - k )² = r²
So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )
So , the translation of circle A to B is given by
( 7 , 1 ) to ( -8 , 2 )
So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up
Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )
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explain how you could write a quadratic function in factored form that would have vertex with an x-coordinate of 3 and two roots
Last week, Russell bought 11 books and 12 movies for a total of
$245. Today, Russell bought 10 books and 26 movies for a total of $434. Assuming neither item has changed in price, what is the cost of a book in dollars?
The cost of a book bought by Russell is found in in dollars is $7.
What is meant by the term equation?The description of an equation in algebra is a statistical 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.For the stated question-
Let the price of the each book be 'x'.
Let the price of movie be 'y'.
Then,
11x + 12y = 245 ...eq 1
10x + 26y = 434 ...eq 2
Solving both eq 1 and 2 using calculator.
x = 7 and y = 14
Thus, the cost of a book bought by Russell is found in in dollars is $7.
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If Jenna Owen 15% of the stock in a business that has 50,000 shares, how many shares does she own?
Answer:
7500
Step-by-step explanation:
15/100×50000
750000/100
=7500
Which is the shortest side of the triangle?
What is the line y =- 7?.
A horizontal straight line at the -7 point.
A straight line can be formed between two points also but both ends extend to infinity.
A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined on both sides of a point.
A straight line does not have any curve in it. It can be horizontal, vertical, or slanted. If we draw an angle between any two points on a straight line, we will always get a 180-degree.
With no other values other than -7, the only value possible must be -7. Thus, we get a straight line.
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Find the angle e between vectors u and v to the nearest tenth of a degree
u = <5, 2> and v = <4, -3>
The angle e between vectors u and v to the nearest tenth of a degree is
≈ 3.14°.
What is an angle?An angle in plane geometry is a shape created by two rays or lines that have a shared termination. The name "angle" originates from the Latin word "angulus," which means "corner. "The common terminus of two rays is known as the vertex, and the two rays are known as sides of an angle.
According to the given information:When u and v's two vectors are at an angle, if, then cosθ = (u·v) / [llull llvll]
u·v = (5)(4) + (2)(-3)
= 20 - 6
= 14
llull = √[(5)2 + (2)2]
= √29
llvll = √[(4)2+(-3)2]
= √25
So, cosθ = 14 / [√725]
= 0.51
θ = cosθ-(0.51) ≈ 3.14°
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Which of the following is the quotient of the rational expressions shown below?
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
Which is rational expressions?The quotient of the rational expressions is
4(x+2) / 5(x-1) (x-1)
The quotient of the rational expressions shown below
Explanation in detail:
Two expressions are shown here.
Expression 1 : 2x/x-1
Expression II for 5x/2x+4.
The product of expressions I and II must be calculated.
(2x / x-1 ) ÷ (5x / 2x+4)
applying the upcoming regulation
a ÷ b = a× 1/b
(2x/x-1)×( 2x+4 / 5x)
(2x) (2x+4) / (x-1)(5x) (5x)
(2) (2) (x+2) / (x-1)(5) (5)
The solution to the previous question is 4(x+2) / 5(x-1).
The quotient of the rational expressions is 4(x+2) / 5(x-1) (x-1)
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How will the area of the circle change if it i dilated by a cale factor of One-half?
A circle with radiu 8 centimeter. The area will be 2 time greater than the original. The area will be 4 time greater than the original. The area will be One-fourth the original. The area will be One-half the original
The area will be 1/4 of the original.
The area is the region defined by an object's shape. The area of a shape is the space covered by a figure or any two-dimensional geometric shape in a plane.
The area of all shapes is determined by their dimensions and attributes. Different shapes have various areas. The perimeter of a shape is defined as the total distance around the shape.
Given that,
[scale factor]=1/2
[dilated area of circle]=[original area of circle]*[scale factor]²
so
[dilated area of circle]=[original area of circle]*[1/2]²
[dilated area of circle]=[original area of circle]*[1/4]
Thus, The area will be 1/4 of the original.
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How do you solve linear and nonlinear systems?.
To see the steps of linear and non linear system of equation.
Now, According to the question:
Steps to solve non linear equation are:
Identify the graph of each equation. Sketch the possible options for intersection.Graph the first equation.Graph the second equation on the same rectangular coordinate system.Determine whether the graphs intersect.Identify the points of intersection.Check that each ordered pair is a solution to both original equations.To solve a system of linear equations using substitution:
Isolate one of the two variables in one of the equations.Substitute the expression that is equal to the isolated variable from Step 1 into the other equation. This should result in a linear equation with only one variable.Solve the linear equation for the remaining variable.Use the solution of Step 3 to calculate the value of the other variable in the system by using one of the original equations.Learn more about Linear and non linear Equation at:
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How do you find the domain and range of a square root of a quadratic function?.
Domain and range of a square root of a quadratic function is as [ 0, ∞ ) , and [ 0 ,∞ ) respectively which is find by simplification.
Let us consider a square root quadratic function y = √x.
Domain of a square root quadratic function is :
All input values of x are domain of a function.
y = √x
⇒ x = y²
⇒ x ≥ 0
All the input values representing the domain are x > 0.
This implies domain is [0 , ∞ ).
And range of a square root quadratic function is:
All output values of y are range of a function.
y = √x
As we know x = y²
√y² = y > 0 .
Range is [ 0, ∞ ).
Therefore, domain and range of square root of a quadratic function is calculated by simplifying the function.
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Determine whether each scenario is best represented by a discrete or continuous domain.
1. The distance a woman walks and runs during her morning workout. Discrete or continuous?
2. The local candy store sells ring pops for 5 cents each. Discrete or continuous?
3. The baseball’s height compared to it’s horizontal distance after being thrown by a player. Discrete or continuous?
4. The market sells grapes by the pond. Discrete or continuous?
5. The amount paid when purchasing cans of peas. Discrete or continuous?
The scenario is best represented by a discrete or continuous domain is
a. discrete
b. continuous
c. discrete
d. continuous
e. discrete
What is discrete?Constituting a distinct entity being unique in one's own right. divided into multiple independent portions; made up of separate or unrelated components: having a limited or countably infinite range of values is referred to as being noncontinuous. continuous probabilities. having a separate existence or form from other entities with a similar nature; separate.There are four distinct neighborhoods in this area, all clustered around a school. different from others; distinct; set apart: six separate pieces. containing or characterized by separate or different components; discontinuous."Discrete" means separately separate, different, or unconnected, whereas "discreet" means to do anything in a clandestine, low-profile, or cautious manner.opposite of cautious and sensible in words or behavior. Indiscreet, ill-advised, hasty, and unwise.To learn more about Discrete refer to:
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How many angles is 5 Rays?.
Five rays from common endpoints or vertex form 10 distinct angles.
Angles are constructed when two lines intersect at a point. The measurement of the 'opening' between these two rays is called an 'angle'. The symbol represents it ∠. Angles are usually measured in degrees and radians, which is a measurement of circularity or rotation.
In geometry, an angle is constructed when two rays are joined at their endpoints. These rays are named the sides or arms of the angle.
The arms and the vertex are two primary parts of an angle.
The two rays which converge at a common point to create the angle are called the arms of the angle.
Vertex is a common endpoint that is shared by the two sides.
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Lance and Alberto cycled along the same 75 km route.
It took Lance 3 hours to cycle the 75 km.
Alberto started to cycle 4 minutes after Lance started to cycle.
Alberto caught up with Lance when they had both cycled 10 km.
Lance and Alberto both cycled at constant speeds.
Work out Alberto's speed.
Lance and Alberto cycled along the same 75 km route. Speed of Alberto is 30 km/ hr
Calculating the problem:Since, Lance takes 3 hours to complete 75km, his speed will be
v= [tex]\frac{75}{3}[/tex]
v= 25 km/hr
The amount of time taken by Lance to complete 10 km is
t= 10/25
t =0.4 hr
t= 0,4×60 min
t=24 min.
Since Alberto started 4 min late and time taken by Alberto to complete 10 km is
t= 24-4
t=20 min.
Hence, speed of Alberto is v=10/0.33
v=30 km/hr.
In math, what is speed?A measure of how quickly something is moving is speed. The distance an object travels in a single time unit is its speed. The speed formula is: Distance times speed. Meters per second (m/s), kilometres per hour (km/h), and miles per hour (mph) are the most common units of speed.
What is distance and speed of time?Speed is calculated by dividing distance by time. You must be familiar with the distance and time units in order to determine the units of speed. The units will be measured in meters per second (m/s) because distance is measured in meters (m) and time is measured in seconds (s).
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Cindy is 6 years older than half her
mother's age. Cindy's mom is 70 years old.
How old is Cindy?
Answer:
cindy is 51
Step-by-step explanation:
70 divided by 2 is 45
45+ 6 is 51
Solve the system by using elementary row operations on the equations or on the augmented matrix. Follow the systemic elimination procedure.
x1+5x2=7
−2x1−7x2=−5
The solution of the system by using elementary row operations on the equations or on the augmented matrix following systemic elimination procedure is x1 = −8 and x2 = 3.
The complexity of the algebra required to solve a linear system rises as the number of equations and unknowns grows. By streamlining the nomenclature and standardizing processes, the necessary computations may be made easier to handle.
The procedures listed below should be followed in order to solve a system of linear equations using the row operations:
1. As a matrix equation, write the equations as AX = B.
2. Create an augmented matrix by converting the matrix equation to the following form: [A | B] (the word "augmented" refers to the vertical line we create to remind us where the equals sign belongs).
3. Reduce the augmented matrix using row operations to arrive at the answer.
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What is the solution of the equations 8x +3y 5 and 3x 2y 5?.
The solution of the given linear equations is (x,y) = (1,-1).
The given linear equations are
8x + 3y = 5 - - - ( 1 )
3x - 2y = 5 - - - ( 2 )
As the RHS of both equations is equal, equating the LHS of both equations, we get,
8x + 3y = 3x - 2y
⇒ 8x - 3x = - 2y - 3y
⇒ 5x = - 5y
⇒ x = - 5y ÷ 5
⇒ x = - y
By substituting x = - y in equation ( 1 ), we get,
8x + 3y = 5 - - - ( 1 )
⇒ 8 ( - y ) + 3y = 5
⇒ - 8y + 3y = 5
⇒ - 5y = 5
⇒ y = - 5 ÷ 5
⇒ y = - 1
Now,
x = - y
⇒ x = - ( - 1 )
⇒ x = 1
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