Answer:
156 cm³
Step-by-step explanation:
The solid is a prism with a trapezoid base.
volume = (area of base) × height
V = (8 cm + 5 cm)(1/2)(4 cm) × 6 cm
V = 156 cm³
A dairy farmer wants to mix a 45% protein supplement and a standard 15% protein ration to make 1200 pounds of a high-grade 40% protein ration. How many pounds of each should he use?
A dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
Given that, a dairy farmer wants to mix a 45% protein supplement.
What is percentage?Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".
Let x be number of pounds farmer wants to mix a 45% protein supplement.
Here,
0.45x + 0.15(1200-x) = 0.40(1200)
⇒ 0.45x +180-0.15x = 480
⇒ 0.30x=480-180
⇒ 0.30x=300
⇒ x=300/0.30
⇒ x=1000
Here, 45% of 1000
= 450 pounds
15% of (1200-100)
= 0.15×200
= 30 pounds
40% of 1200
= 480 pounds
Therefore, a dairy farmer needs to mix 450 pounds of protein supplement, 30 pounds of protein ration and 480 pounds of high-grade protein ration.
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What is the solution to this system of linear equations 2x 3y 3?
The solution to this system of linear equations is x = 3 & y = -1.
Given linear equations are
2x + 3y = 3 ---- 1
7x - 3y = 24 ---- 2
By dividing both the equations, we get
9x = 27
x = 27/9
x = 3
Now substituting x = 3 in the equation 1, we get
2(3) + 3y = 3
6 + 3y = 3
3y = 3 - 6
y = -3/3
y = -1
Hence the answer is the solution to this system of linear equations is x = 3 & y = -1.
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The product of 5 and the sum of 3 and a number is 20.
Answer:
The product of 5 and the sum of 3 and 1 is 20
Step-by-step explanation:
Equation:
5*(3+x)=20
15+5x=20
5x=5
x=1
please I need help on question 8
Answer:
BM = 20m
YZ = 13m
m∠B = 39
m∠M = 34
m∠Y = 107
Step-by-step explanation:
CM = 16m
BM = 20m
YZ = 13m
m∠B = 39
m∠M = 34
m∠Y = 107
May I please have a brainliest? Thank you!
GREETINGS NEED HELP ASAP!
Think about wether the diagram shown represents a function. then use the drop down menus to complete the statement about the diagram.
This_____represent a function because the_____ has two different _____
choices for first blank- does or does not
choices for second- x value 7, 11, -5, 2
choices for third- x values or y values
It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.
Given that,
In the picture we have a diagram
We have to find if the diagram is a function or not.
We know that,
What is a function?Mathematical calculus' core component is functions. The unique types of relationships are the functions. When it comes to math, a function is represented as a rule that produces a different result for each input x.
Function is satisfy one-to-one and many-to-one.
So,
In the picture we can see
Input -2 to output 7 it is one-to-one
Input 7 to output 8 and 2 it is one-to-many
Input 11 and 2 1/3 to output 5 it is many-to-one
Therefore, It is not a function because it has one-to-many function when it also has one-to-one and many-to-one.
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find the domain and range of 1 - x^2
The range and the domain of the function f(x) = 1 - x^2 is less than or equal to 1 and all values of x are a real number (R).
Domain: x ∈ R
Range: f ( x ) ≤ 1, ∈ R
f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).
x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.
Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.
So, the range of f(x)≤ 1, and the domain is all real values ( R ).
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What type of triangle is def?
An isosceles triangle therefore has both two equal sides and two equal angles.
What is traiangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. 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.
What is isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides. It can be stated as having exactly two equal-length sides or at least two equal-length sides, with the latter definition containing the equilateral triangle as an exception.
Any triangle with (at least) two equal sides is said to be isosceles. The remaining side in the previous illustration has length in addition to the two equal sides. This characteristic equates to the triangle's two angles being equal. Therefore, an isosceles triangle has two equal sides as well as two equal angles. The Greek words iso (same) and skelos are the source of the name (leg).
An equilateral triangle is one in which all of its sides are equal, whereas a scalene triangle is one in which none of its sides are equal. Therefore, an equilateral triangle is a specific example of an isosceles triangle that has equal sides and angles on all three of its faces. The isosceles right triangle is yet another unique instance of an isosceles triangle.
The Pythagorean theorem can be used to determine the height of the isosceles triangle shown in figure:
[tex]h = \sqrt{b^2-\frac{1}{4}a^2 }[/tex]
Consequently, the region is given by:
A=1/2ah
A = [tex]\frac{1}{2}a\sqrt{b^2-\frac{1}{4}a^2 }[/tex]
[tex]A = \frac{1}{2}a^2\sqrt{\frac{b^2}{a^2}-\frac{1}{4} }[/tex]
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Applying the exterior angles and triangle sum theorems, the statements that are true are:
C. m∠5 + m∠6 = 180°
D. ∠2 + m∠3 = m∠6
E. m∠2 + m∠3 + m∠5 = 180°
What is the Exterior Angles and Triangle Sum Theorems?All three interior angles of a triangle is equal to a sum of 180 degrees, based on the triangle sum theorem, while the exterior angle theorem states that the exterior angle of a triangle is equal to the two remote interior angles of the triangle.
Given the image showing the triangles and its exterior angles, the following can be deduced:
m∠2 + m∠3 + m∠5 = 180° [based on the triangle sum theorem]
m∠2 + m∠3 = m∠6 [based on the exterior angles theorem]
m∠5 + m∠6 = 180° [based on the triangle sum theorem]
Therefore, the true statements are:
C. m∠5 + m∠6 = 180°
D. ∠2 + m∠3 = m∠6
E. m∠2 + m∠3 + m∠5 = 180°
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Sample Test 4: Cartesian Graphing
Score: 38 / 200 \quad 4 / 20 answered
Question 14
Determine the slope of the line represented by the equation: 3 x+1 y=3
Slope DO NOT USE 1 AS THE DENOMINATOR!
Write answer as an integer or a reduced fraction.
The slope of the line is - 3
How to calculate the slope of a line?The equation of the line is given by,
3x + 1y = 3
y = -3x + 3 ---(1)
The slope- intercept form of a line is given by ,
y = mx + c ---(2)
where ,m is the slope
c is the y intercept
Comparing (1) and (2)
The slope of the line is , m = -3
What is a slope?A value known as slope can be used to define a line's direction and steepness. It is represented by the letter m in variable format. The gradient or rate of change of a line is another name for its slope. The line gets steeper as the slope's magnitude goes up. The line grows less steep as the slope's magnitude diminishes, which is the opposite of what happens. A line's direction can also be determined by a slope. A line that extends from left to right and has an upward slope is said to be growing.To learn more about slope, refer:
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Help with my math please
Answer:
$27,000 at 8%$3,000 at 7%Step-by-step explanation:
You want the amounts invested in each of two accounts, one earning 7% and the other earning 8% simple interest, when the total investment of $30,000 earns total interest of $2370.
SetupLet x represent the amount invested at 8%. Then the amount invested at 7% is 30000-x. The total interest earned is ...
0.08(x) +0.07(30000-x) = 2370
Solution0.01x +2100 = 2370 . . . . simplify
0.01x = 270 . . . . . . . . subtract 2100
x = 27000 . . . . . . . multiply by 100
30000-x = 3000
Deshaun invested $27,000 at 8% and $3,000 at 7%.
What is 6\9 reritten.
Answer:
Simplied:
2/3
Step-by-step explanation:
So basically so look at the factors and find that 6 and 9 both divided by 3 so 6/3=2 and 9/3=3
so 2/3
But if you are looking for equivalent:
8/12
6/9= 0.66 repeating which is 60/90 (I think)
HOPE THIS HELPS!!
Willy Wonka makes a 13 metre chocolate bar as he believes that chocolate is best made as a giant piece rather than small packaged pieces. The chocolate bar is then cut into 4/11 of a metre. How many bars does this make?
There will be 35 chocolate bar cut out from the 13-meter chocolate bar.
What is division?Division is breaking a number up into an equal number of parts.
Given that, Willy Wonka makes a 13-metre chocolate and the chocolate bar is then cut into 4/11 of a metre.
Number of bars made = 13/4/11 = 35.75 ≈ 35
Hence, There will be 35 chocolate bar cut out from the 13-meter chocolate bar.
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How do you find the missing side of a congruent triangle?
Triangles that are exactly the same in size and shape are said to be congruent. Two triangles are said to be congruent when their corresponding sides and angles are also congruent.
What is Traingle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Using the Triangle Sum Theorem, we can determine the third angle in a triangle when only two angles are known.
The two angles' combined angles are subtracted from 180 degrees.
The diagram needs a third angle. Try to match the angles and sides of two triangles with the provided information if the congruence statement is not provided in the problem.
List the corresponding vertices in the same order once the vertices of the two triangles have been matched. The congruence assertion reads as follows if vertex A relates to vertex D, vertex B to E, and vertex C to F:
△ABC≅△DEF
Congruent triangles are two triangles that are the same size and shape. Two congruent triangles are still congruent even if we flip, spin, or otherwise alter one of them.
Two triangles must have the same angles and, as a result, must be congruent if their sides are the same. If two triangles are congruent or not, we may determine this simply by looking at their sides.
These two triangles are also equivalent if we know that two sides of one triangle and the angle between them are congruent to two sides and the angle between them of another triangle.
Likely, these two triangles are congruent if we know that two angles and the side between them in one triangle are congruent with two angles and the side between them in another triangle.
When two angles and a non-included side in a triangle are congruent to one another, this is the final scenario that results in congruent triangles.
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The equation of line T, shown below, can be written in the form y=mx+c.
What are the values of m and c?
Give each of your answers as an integer or as a fraction in its simplest form.
The straight line has the equation, y = 5x - 4.
What is the equation of a straight line?A straight line is made up of an infinite number of points that are joined on both sides of the point.
Any straight line's slope 'm' is given by:
m = y2 - y1 / x2 - x1
In slope-intercept form, a linear equation has the formula y = mx + b. The variables in the equation are X and Y. The values m and b represent the slope (m) of the line and the value of y when x = 0.
The obtained points from the graph are (0,-4) and (1,1)
The slope is ,
m = 1-(-4) / 1-0
= 5/1
= 5
Because it intersects the y-axis at the point where the intercept C = -4,
The line's equation will be:
⇒ y = mx + c
⇒ y = 5x + (-4)
⇒ y = 5x - 4
As a result, the equation for the straight line shown below is y = 5x - 4.
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A rectangular parking lot has an area of 2/3 of a square kilometer. The width is 1/2 of a kilometer. What is the length, in kilometers, of the parking lot?
Group of answer choices
5/3 km
2/3 km
1/3 km
4/3 km
Answer:
Step-by-step explanation:
2/3 = 1/2x
2/3 / 1/3 = x
x = 4/3
Answer: The answer is 4/3
Step-by-step explanation: I have my ways ;>
Express each of the following ratios in the form 1:N
8:13
Answer:
Step-by-step explanation:
i just need the points bro
Function and function notation
Please help asap
The value of function f(1/2) = 9.
What is function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between input variables in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x seems to be the input. A function is typically represented as y = f. (x). In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) as well as their outputs (also referred to as the codomain), where each input does have exactly one output and the output could be linked to its input.
Given function f(x) = (4+x)/x
put x = 1/2,
f(x) = (4+1/2)/1/2
f(x) = 9/2/1/2
f(1/2) = 9
Now f(3) = (4+3)/3
=7/3
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percent proportions and equations what do you call a destroyed angle
The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
Given, a destroyed angle
A destroyed angle is called a figure in Geometry also known as Rectangle.
A rectangle is a quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
So, A destroyed angle is the quadrilateral which is specifically a parallelogram also having all the angles equal and equal to 90 degree.
Therefore, the destroyed angle is a rectangle.
Hence, The destroyed angle is a rectangle specifically a parallelogram also having all the angles equal and equal to 90 degree.
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A box is 36 inches long,18 inches wide, and 6 inches deep. How many
cubic feet are in the box?
A 2.25 cubic feet
B) 4.5 cubic feet
C) 5 cubic feet
D) 3 cubic feet
Answer:
A
Step-by-step explanation:
The volume in cubic inches is [tex](36)(18)(6)=3888[/tex].
This is equal to [tex]3888/12^3=2.25[/tex] cubic feet.
Identify the recursive formula for the sequence 900, 850, 800, 750,...
C (3rd Answer)
1st term is 900 and as n increases (number of terms increase), each time it goes down by 50 if n is greater than 1.
For each function, select whether it’s inverse is a function or not a function. refer to the attached picture.
Function
y=x⁴
y=x⁹
y=x⁸
y=x¹¹
The inverses of the functions y= x⁹ and y= x¹¹ are functions.
The inverses of the functions y = x⁴ and y= x⁸ are not functions.
How is the functionality of the given functions determined?(a )Consider ,the inverse of the function is a function
(2 ) y= x⁹
The inverse of the function is given by,
x = [tex]\sqrt[9]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
So, this is a function.
(4) y= x¹¹
The inverse of the function is given by,
x = [tex]\sqrt[11]{y}[/tex]
Here y is an element of the real numbers.
i.e. y ∈R
Similarly , this is a function.
(b ) Consider ,the inverse of the function is a not a function
(1 )y = x⁴
The inverse of the function is given by,
x = [tex]\sqrt[4]{y}[/tex] (y ≥0)
It is of one- one correspondence,
when y = 4 ,
x = ±√2
Thus, it is not a function.
(3) y= x⁸
The inverse of the function is given by,
x = [tex]\sqrt[8]{y}[/tex]
Likewise , this is not a function.
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7. Choose the graph below that best represents the equation: x-y = -2
Answer: B
Step-by-step explanation:
First, we will turn this equation into slope-intercept form as it is easier to view in terms of a graph.
Given:
x - y = 2
Add y and subtract 2 from both sides of the equation:
y = x - 2
We can see that this equation has a y-intercept of -2, so it must intercept the graph at (0, -2). The answer option that meets these requirements is B.
Answer: it is graph A
Step-by-step explanation:
It is pretty easy to tell when x-y= -2
Let's say x is 0 then we have left is -y=-2
So y= 2
And we have [0,2] so graph A is correct
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 7 to 4. If there were
10,164 total votes, how many yes votes were there?
Answer:
There are 6468 yes votes
Step-by-step explanation:
10164÷(7+4)×7
=10164÷11×7
=924×7
=6468
Functions are in the world all around us. You have used functions to model phenomena and to make predictions. Mathematically, you can add, subtract, multiply, and divide functions, and you can also create a composition of functions.
A composition of functions occurs when you evaluate one function using another function, or even with the same function. A composition of functions is useful when a change in one function will create a change in another function, which, in turn, affects a third function. For example, suppose that humans build a housing development on land that was previously used as a corn field. This change in land usage causes the number of birds in the area to decrease, which causes the number of mosquitos to increase. You could model the increase in the number of mosquitoes as a function of the number of birds in the area, which is a function of the number of humans that live on that land.
You can also use the composition of functions to show that one function is the inverse of another function. Recall that the graphs of inverse functions are reflections of each other over the line. Think about these ideas as you read through the scenario below.
Last night it started raining as Hiba was closing up the store where she works. By 3 am, the roof of the store developed a small hole and water began to leak onto the sales floor. The water created a circular puddle on the floor. At any time, t, in minutes, the radius of the puddle increases by 0.1 cm. The rain continued through the night, but stopped by the time the morning shift arrived at the store at 7 am.
When the employees arrived at work, the leak and water puddle were discovered. The employees cleaned up the water puddle and placed a tall circular bucket underneath the leak, which was still slowly dripping. The capacity of the bucket can be expressed as. By 10 am, the amount of water in the bucket is.
Function composition is only one way to combine existing functions. Another way is to carry out the usual algebraic operations on functions, such as addition, subtraction, multiplication and division.
What is composition function ?The procedure known as "function composition" in mathematics takes two functions, f and g, and creates a function, h = g f, such that h(x) = g(f(x)). The combination of two functions to create a third function is known as function composition. Simply using the first function's output as the input for the second function is how it works.The function g is applied in this operation on the outcome of applying the function f to x. In other words, a function that maps x in domain X to g(f(x)) in codomain Z is produced by composing the functions f: X Y and g: Y Z. It makes sense that z would be a function of x if z were a function of y and y was a function of x. The resulting composite function is designated as (g f )(x) = g(f(x)) for all x in X, and is written as g f: X Z. [nb 1]Find the attachment of answer
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What is root domain example?
The root domain in the DNS system of the Internet is a domain that is indicated by an empty name (i.e., containing no characters).
Each domain is split from the next when you enter a domain name, and there may also be a dot at the end of the name to demarcate the empty name for the root domain. If this dot is present and in its proper location, such as "www.example.com," the domain name is regarded as full (absolute). The name is regarded as relative if there isn't a dot at the end ("www.example" or "www.example.com").
Even if the phrase "root domain" was frequently used, the primary domain name of the website is the one that must be purchased or registered with a TLD extension.
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How do you know △ ABC ≅ △ DEF explain?
We know that △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.
According to the question,
We have the following information:
△ ABC ≅ △ DEF
Now, we know that this sign is used to show that the two triangles are congruent.
Now, we also know that in these two triangles, their corresponding sides will be equal. So, all the three sides of one triangle will be corresponding to the same sides in another triangle.
Hence, we know that △ ABC ≅ △ DEF are congruent because AB corresponds to DE of another triangle, BC corresponds to EF and AC corresponds to DF.
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What is the point of concurrence of perpendicular bisectors of a triangle?
The points of concurrency of perpendicular bisectors of triangle is circumcenter.
A point of concurrency shared by three or more lines is referred to as a single point of concurrency. Constructed lines in triangle interiors are excellent places to look for points of convergence.
When you construct a triangle's medians, perpendicular bisectors, angle bisectors, or altitudes, you create a point of concurrency for each of them.
Because the triangle can have four distinct types of line segments, it can have four distinct points of convergence. Each point of concurrency represents the intersection of a particular type of line segment: centroid, circumcenter, incenter, and orthocenter.
The centroid of the triangle is the point of convergence shared by the three medians.The point at which the triangle's three angle bisectors intersect is known as the incenter.The three perpendicular bisectors will intersect at the circumcenter, which is a point of convergence.The orthocenter is the point at which the three altitudes/heights of a triangle intersect.Thus, the points of concurrency of perpendicular bisectors of triangle is circumcenter.
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Twenty members of a health club who jog were asked how many miles they jog per week. The responses are to the right. Construct a stem-and-leaf display. For single digit data, use a stem of 0. 14 26 8 14 14 22 26 25 4 34 44 34 6 18 24 17 11 6 19 17
The steam-leaf display is shown as follows
How do stem and leaf displays work?A stem and leaf plot resembles a bar graph in appearance. The term stems from the fact that each number in the data is divided into a stem and a leaf. The number's final digit is not part of the stem. The number's leaf will always be one digit.
What are the advantages of stem and leaf display?Pencil and paper can be used to quickly create the plot. The plot can be used to determine the values of each individual data point. Since the stem is not repeated across multiple data points, the data is organized compactly.
The stem-and-leaf display for the given data is shown below followed by a detailed explanation.
0|358
1|25179476
2|73823
3|44
4|0
Note that it is often customary to organize the "leaf" values from lowest to highest as follows:
0|3578
1|12456779
2|23378
3|44
4|0
Each row's initial number is referred to as the stem, and the group of numbers that come after it as the leaves. The tenth position of the numerals is indicated by the stem. Therefore, a stem of 0 indicates a single-digit number, a stem of 1 indicates a number between 10 and 19, and so on. The leaves identify the numerals' unit position. If the number is 28, for instance, the stem and leaf are each two.
The data for stem 0 contains four one-digit numbers, which are 3, 5, 8 and 7 in appearance order. Therefore, the stem 0's leaves are 3, 5, 8, and 7.
Eight values between 10 and 19 may be found in the data for stem 1, and they are 12, 15, 11, 17, 19, 14, and 16 in that sequence. Therefore, 2, 5, 1, 7, 9, 4, and 6 make up the stem 1's leaves.
Five values between 20 and 29 may be found in the data for stem 2, and they are 27, 23, 28, 22, and 23 in that sequence. As a result, the stem 2's leaves are 7, 3, 8, and 3.
For stem 3, the data contain two integers between 30 and 39 that, in the order of appearance, are 34 and 34. The leaves for the stem 3 are therefore formed by 4 and 4.
For stem 4, the data only contains the number 40, which falls within the range of 40 to 49. Consequently, 4 creates the leaf for stem 2.
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what is the center of a circle whose equation is x2 y2 12x 2y 12 0
The center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
What are circles?Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve.
A circle is a closed shape that can be created by following a moving point in a plane while maintaining a constant distance from another point.
The Greek word kirks, which means hoop or ring, is whence the word circle gets its form.
So, we have the equation: x²+y²-12x-2y+12=0
Compared to the circle's basic equation:
2 + y² + 2gx + 2fy + c = 0
2g = -12, 2f = -2, c = 12
g = -6, f = -1
Centre = (-g, -f)= (6, 1)
Now, fill in the square:
x² - 12x + 36 + y² - 2y + 1 = -12 + 36 + 1
(x - 6)² + (y - 1)² = 25
(x - 6)² + (y -1)² = 52
When compared to the equation for a circle with the centers at (h, k) and radius "r," Centre = (h, k) = (6,1).
Therefore, the center is (6, 1) of the given circle with the equation x²+y²-12x-2y+12=0.
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Correct question:
What is the center of a circle whose equation is x²+y²-12x-2y+12=0?
Answer:
6,1
Step-by-step explanation:
trust me
what is the value of this expression when w 5 w2 3w 11 a 51 b 36 c 16 d 1
The value of this expression when w = -5 in w² + 3w - 11 is -1
Algebraic expressions comprises of at least one variable and one operation, it is an expression built up from integer constants, variables, and the algebraic operations
We need to find the value of this expression when w = -5 in w² + 3w - 11
After substituting the value of x as 5, we get the expression as
5² + 3(-5) - 11
25 - 15 - 11
25 - 26
= -1
Therefore, the value of this expression when w = -5 in w² + 3w - 11 is -1
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