As the person wanted the fountain to be the same distance from each edge of the pond and the incenter of the triangle is equidistant
How to illustrate the distance?From the information, the person is placing a fountain in a triangular koi pond and want the fountain to be the same distance from each edge of the
pond.
The intersection of all three of the triangle's interior angle bisectors is where a triangle's incenter is located. It can be thought of as the intersection of the triangle's internal angle bisectors. The fountain is equally spaced from each edge of the pond because the person wanted it to be, and the triangle's incenter is also evenly spaced.
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a square and a rectangle have the same area. the length of the rectangle is 196x196 centimeters, and the width of the rectangle is 44 centimeters. what is the length, in centimeters, of a side of the square?
The length in centimeters of the side of the square is 8 cm.
What is the area of a rectangle and a square?The surface of a shape's surface is measured by its area. The length and width of a rectangle or square must be multiplied to determine their respective areas. A has a perimeter of x by y. Find the side of the square if the rectangle's length and width are 27 cm and 3 cm, respectively. Given, the area of a square equals the area of a rectangle. The first step is to calculate the rectangle's area using the specified length and width values.
The area of a rectangle and a square are -
A{R} = Length x Breadth
A{S} = Side x Side
Given is that a square and a rectangle have the same area. The length of the rectangle is 32 cm and the width of the rectangle is 2 cm.
It is given that -
A{R} = A{S}
Length x Breadth = Side x Side
32 x 2 = (Side)²
(Side)² = 64
Side = 8
Therefore, the length in centimeters of the side of the square is 8 cm.
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Mitch's pool can hold 10,000 gallons of water. At noon, the pool is 80% full. Unfortunately, the pool has a leak, and it loses 120 gallons of water every hour. Mitch turns on a house at noon that fills the pool at a rate of 225 gallons per hour. He checks the water level in the pool every hour, starting at 1 PM. At what time does Mitch first see the pool overflowing?
Step-by-step explanation:
He starts at 8000 gallons when he adds 2000 gals it will overflow
120 gal go out each hour 225 gal goes in each hour net : 105 gal per hour IN
105 x = 2000 gal
x = 19.048 hours until overflow
1 pm + 19 .048 hours = 8.048 AM = ~~8 :03 AM Since he checks every hour, he will first see the overflow at 9:00 AM
Find the vertex, focus, directrix, and focal width of the parabola.
x2 = 28y
Vertex: (0, 0); Focus: (0, -7); Directrix: x = -7; Focal width: 112
Vertex: (0, 0); Focus: (7, 0); Directrix: x = 7; Focal width: 7
Vertex: (0, 0); Focus: (0, 7); Directrix: y = -7; Focal width: 28
Vertex: (0, 0); Focus: (7, 0); Directrix: y = 7; Focal width: 112
These are the vertex, focus, directrix, and focal width
Vertex: (0, 0), Focus: (0, 7), Directrix: y = -7, Focal width: 28
The vertex, focus, directrix, and focal width of the parabola described by the equation x^2 = 28y are:
Vertex: (0, 0)
Focus: (0, 7)
Directrix: y = -7
Focal width: 28
The vertex of a parabola is the midpoint of the directrix and the focus, which in this case is (0, 0). The focus is the point on the parabolic curve that is closest to the directrix, which in this case is (0, 7).
The directrix is the line along which the distance between the parabolic curve and its focus is minimized, which in this case is y = -7. The focal width is the distance between the focus and the directrix, which in this case is 28.
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Give me the answer, please
3x° - 3° = 2x° + 13°
They are vertically opposite angle...
3x° - 2x° = 13° + 3°
1x = 16°
x = 16°
hence...the value of x is 16°
Re-write the quadratic function below in Standard Form
y=-2(x-3)(x+4)
Answer:
[tex]\boxed{-2x^2 -2x +24\\}\\\\[/tex]
Step-by-step explanation:
The standard form of a quadratic function is:
[tex]y = ax^2 + bx + c\\[/tex]
where a, b and c are constants
[tex]\textrm{The given expression is $y=-2\left(x-3\right)\left(x+4\right)$}[/tex]
Expand the right side of this expression
[tex]-2\left(x-3\right)\left(x+4\right)[/tex]
First expand (x-3)(x+4) using the FOIL method:
[tex](x-3)(x+4)[/tex]
[tex]=x\cdot x+x\cdot \:4-3x-3\cdot \:4\\\\= x^2+x-12[/tex]
[tex]-2\left(x-3\right)\left(x+4\right)\\\\= -2(x^2+x-12)\\\\= \boxed{-2x^2 -2x +24\\}\\\\[/tex]
ANSWER
How do you write and graph linear inequalities in two variables?.
Now, According to the question:
Linear inequalities are defined as a mathematical expression in which two expressions are compared using the inequality symbol. The expression can be an algebraic expression or numerical expression or a combination of both.
Graph Linear Inequalities in Two Variables:
Identify and graph the boundary line. If the inequality is ≤ or ≥, the boundary line is solid. Test a point that is not on the boundary line. (If not on the boundary line, (0,0) is usually a convenient test point.) Shade in one side of the boundary line.Learn more about Linear Inequalities at:
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A craft store recieved the following amounts of colored beads in today's shipment. The beads are sold in bags that weigh 1/10 of a pound. How many full bags of pink beads can be made from today's shipment?
The number of bags of pink beads that can be made from today's shipment is given as follows:
5 bags.
How to obtain the number of bags?The number of bags is obtained applying the proportions in the context of this problem.
We have that each bag weights 1/10 of a pound.
The shipment was of 4/7 pounds of pink beads, hence the total number of bags of pink beads that can be made from today's shipment is calculated as follows:
4/7/(1/10) = 4 x 10/7 = 40/7 = 5.
(rounded down, as the number of bags is a countable amount).
Missing InformationThe problem is given by the image presented at the end of the answer.
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Solve for b.
29b = 290
Answer: 10
Hope this helps :)
Step-by-step explanation:
29b = 290
/29 /29
b = 10
Answer:
b = 10
Step-by-step explanation:
29b = 290
----- ------
29 29
b = 10
Erika is 12 years older than her friend Nick. She is also 3 times as old as Nick. Let x represent Nick’s current age.
Answer:
Nick is 6 years old.
Erica is 18 years old.
Step-by-step explanation:
Hello!
We know that Erica is 12 years older than Nick, which also means she is 3 times older than Nick. We can represent this situation as two equations.
Let E be Erica's age, and x be Nick's age.
E = x + 12, and E = x* 3
Since E is equal to E, we can say that x + 12 = 3x.
Solve for xx + 12 = 3x12 = 2x6 = xThe value of x is 6. Nick is 6 years old, and Erica is 18 years old.
PLS HELP what is the slope
Y=_x +_
Answer:
it's a little blurry but i think the slope is 2/3 and the y-intercept is -2
Step-by-step explanation:
hamid has gained weight
he now weighs 88kg which is 10% higher than his normal weight
what is hamids normal weight
Answer:
Let's say Hamid's normal weight is x.
88kg = 110%x
88kg=11/10x
Divide by 11 on each side
8kg=1/10x
Multiply by 10 on each side
80kg=x
Hamid's normal weight is 80kg
What i the eaiet way to combine a imilar file that are all located in the ame folder?
The easiest way to combine a similar file that are all located in the same folder are:
Using the command line.Using a script.Using a text editor.Using a file manager.Specify your file.Combine A Similar File
There are several ways to combine similar files that are located in the same folder, depending on the type of files and the operating system you are using. Some options include:
Using the command line: On Windows, you can use the "copy" command to combine all the files into one, while on Mac or Linux, you can use the "cat" command.Using a script: You can write a script in a language such as Python or JavaScript that reads all the files in a directory and concatenates their contents into a single file.Using a text editor: Some text editors, such as Sublime Text and Visual Studio Code, have a feature that allows you to combine multiple files into one.Using a file manager: Some file managers, such as Windows Explorer and Finder, have an option to select multiple files, right-click and select "combine" or "merge".Please specify your file type and the OS you are using for a more specific solution.Learn more about Combine a similar file here:
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Which equation describes the same line as y-6=-4(x+1)
Answer:
y = -4x + 2
Step-by-step explanation:
y-6=-4x+4
y = -4x - 4 + 6
y = -4x + 2
What angle is 360 degree?.
The angle 360 degree is called as complete angle.
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
A form of angle that measures 360° is known as a full angle. When two lines meet at a point, an angle is created, and the angle is the width of the space created.
The angle generated in this case is referred to be the complete angle if, after one complete revolution, the final ray corresponds with the incident or initial ray. A round angle and a complete angle are the alternate names. The angle, which corresponds to the center of a circle, is 2 radians, or 360 degrees. A complete angle is made up of four right angles or two straight angles. The amount of rotation makes the angle different from a zero angle.
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Two campers are traveling. One camper is 5 miles East and 4 miles north, represented by the
coordinates (5, 4). The other camper is 7 miles South and 3 miles East, represented by the
coordinates (3,-7). If each unit represents 1 mile, how far apart are the two hikers, to the
nearest mile?
The hikers are approximately
15 miles
from each other.
The two bikers are 11.18 miles apart from each other according o the coordinate plane.
What is coordinate plane?A surface with two dimensions made of two number lines is referred to as a coordinate plane. When the origin, the place where the X- and Y-axes intersect, is reached, it is produced. A coordinate grid's numbers are used to find points. For graphing points, lines, and many other things, a coordinate plane is helpful. It functions as a map and gives precise directions on how to get from one place to another.
Distance between two coordinates is given by
d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Here, (x₁, y₁) is (5, 4) and (x₂, y₂) is (3,-7)
Putting the values in formula
d = [tex]\sqrt{(3-5)^2+(-7-4)^2}[/tex]
d = [tex]5\sqrt{5}[/tex]
d = 11.18 miles
Thus, The two bikers are 11.18 miles apart from each other according o the coordinate plane.
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What are the side lengths of a 45 45 90 triangle are in the ratio 1 1 2?.
The ratios in a 45-45-90 triangle are as follows: 1 : 1 : 2 for angles (45 degrees: 45° : 90°); and. 1 : 1 : 2 on the sides (a: a : a√2).
The 45-45-90 triangle is what?In addition, the 45-45-90 triangle is an isosceles triangle, which indicates that each of its legs is the same length.
In a triangle, the trigonometric ratio Tan Theta is the same as opposite or adjacent.
A 45-45-90 triangle has side lengths that are 1: 1: .
As a result, tan45 has a value of 1.
How long are the sides of a 45-degree, 90-degree triangle?According to the 45 45 90 triangle theorem, special right triangles with sides whose lengths are in a special ratio of 1: 1 : 2 1:1:sqrt2 1:1:2, two angles of 45 degrees, and one right angle of 90 degrees.
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A baeball team ha won 25 game and lot 12 game. If the baeball team' rate continue through a 148 game eaon then how many game will they have won
They will win 100 games if the team rate continues through a 148-game season.
We will solve our question with the help of the Multiplication rule.
As per the question, the baseball team has won 25 games and lost 12 games. This will give us a total of 25+12= 37 games.
It is given that if the baseball team rate continues through a 148-game season which is 37*4 = 148 games.
So, we should multiply our initial won matches by 4 to get the final won matches as per the given condition, we will get:
25*4 = 100 matches.
We can also find the answer by:
You would multiply 25 by 148 divided by 37 to determine the number of games won if you were comparing the 25 of the 37 games won to the total of 148 games played.
(148*25)/(25+12)
= 3700/37 = 100
Therefore if the baseball teams' rate continues through a 148-game season, then they will win 100 matches.
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A rectangle’s length is 8 more than it’s width. Express its perimeter in terms of its width.
Answer:
length= 8x
width= x
perimeter of a rectangle= 2L+2W
=2(8x) + 2(x)
=16x + 2x
perimeter=18x
20.) Margaret, Justin and Leigh are babysitting for the neighbor's children during the summer. Each week they make a total of $72.00, and they split the money evenly. At the end of 4 weeks, how much money did Justin make? **Show your work! a) $130.00 b) $144.00 c) $72.00 d) $96.00
Using multiplication, Correct option is B, Justin earned $144 in 4 weeks.
One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.
What components make up multiplication?The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product. Let's examine a few various forms of multiplication sentences and discover how to finish them.
As per the question,
Each week they make a total of $72.00,
Money earned in 4 weeks = 72 × 4 = $288
They split in equal halves,
⇒ $288 / 2 = $144
∴ Justin earned $144 in 4 weeks.
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You must show your work for each
Answer:
1. 8
2.3
Step-by-step explanation:
This for num 2
[tex] \sqrt{8} = \sqrt{2 \times 4} = 2 \sqrt{4} = 2[/tex]
6÷2=3
1.
To solve [tex]\sqrt[n]{16}=2[/tex], you need to turn the question around and ask what value of n makes [tex]2^n=16[/tex].
n = 4
2.
To simplify this, your teacher could mean two things, either "just simplify the radical" or "rationalize the denominator."
For the first option, [tex]\sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2\cdot\sqrt{2}[/tex], so your overall expression becomes:
[tex]\dfrac{6}{2\cdot\sqrt{2}} = \dfrac{3}{\sqrt{2}}[/tex]
Now if your teacher also wants the denominator rationalized, then you keep going and multiply that by [tex]\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]:
[tex]\dfrac{3}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3\sqrt{2}}{2}[/tex]
how do i solve? im studying so please be detailed
Answer:
26. Scale Factor of A to B: [tex]\boxed{\dfrac{3}{4}}[/tex]
27. Scale factor of B to A: [tex]\boxed{\dfrac{4}{3}}[/tex]
Step-by-step explanation:
If two triangles are similar, the ratios of the side length to the corresponding side length of the other must be the same for all sides
The first challenge is to figure out which side of triangle A corresponds to which side of triangle B
If you flip triangle A counterclockwise by 90° the angles will be aligned with each other and it is easier to see the corresponding sides of A and B
We see that ....
side length 24 of A matches with side length 18 of B
side length 36 of A matches with side length 27 of B
side length 32 of A matches with side length 24 of B
B is of smaller size than A so the scale factor of A to B is less than 1
26.
Therefore the scale factor of A to B is
[tex]\dfrac{18}{24} = \dfrac{27}{36} =\dfrac{24}{32}\\\\\\\dfrac{18}{24}= \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 6}[/tex]
[tex]\dfrac{27}{36} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 9}\\\\\\\dfrac{24}{32} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 8}\\\\\\[/tex]
So the scale factor of Figure A to Figure B is [tex]\dfrac{3}{4}[/tex]
----------------------------------------------------------------------------------------------
27.
The scale factor of Figure B to Figure A is the reciprocal of
[tex]\dfrac{3}{4}[/tex]
Reciprocal of
[tex]\dfrac{3}{4} \; is \; \dfrac{4}{3}[/tex]
So scale factor of B to A is
[tex]\dfrac{4}{3}[/tex]
if f(x) = x^3 -12x^2 + 29x + 42 and f(7) = 0, then find all zeros of f(x) algebraically
The zeroes of the polynomial f(x) are 7, 6 and -1. The solution is obtained by the method of polynomial long division.
What is polynomial long division?
A long division polynomial is a formula for dividing one polynomial by another of the same degree or lower. The divisor, quotient, dividend, and remainder are all components of the long division of polynomials, just like they are for long division of numbers.
We are given f(7) = 0.
This means that (x-7) is one factor of f(x).
Using Polynomial Long Division,
Dividing : x^3 -12x^2 + 29x + 42 ("Dividend")
By : x-7 ("Divisor")
Dividend x^3 - 12x^2 + 29x + 42
- divisor * x2 x^3 - 7x^2
Remainder - 5x^2 + 29x + 42
- divisor * 5x - 5x^2 + 35x
Remainder - 6x + 42
- divisor * (-6) - 6x + 42
Remainder 0
Quotient : x^2-5x-6
Remainder: 0
Now, factoring x^2-5x-6 , we get
⇒x^2-6x+x-6
⇒x(x-6)+1(x-6)
⇒(x+1)(x-6)
Thus, the factors are (x+1), (x-6) and (x-7).
Hence, the zeroes of the polynomial f(x) are 7, 6 and -1.
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How to solve a three variable system of equations on a calculator?.
The 3-Systems of Equations Calculator is an online tool that provides the answer for the unknown variables after solving three equations with three different variables each utilizing a different approach.
To resolve equations involving the three variables x, y, and z, use the 3 systems of equations calculator. A group of three equations with three variables make up the three systems of equations. Three equations are entered, the equations are rearranged, and the values of x, y, and z are solved for.
This calculator can also calculate equations of the second and third degree, which result in complex solutions for the variables x, y, and z. Three actual solutions are provided by the calculator if the equation system is linear.
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what is 2 divided by 3/7 PLS HELP MEEEEEEEEEEEEEEEEEE
Answer:
2 / 3/7
2/1 x 3/7
Cross Multiply
14/3
The ratio of girls to boys in the school play is 5:2. There are 49 kids in the school play.How many are boys?
Answer:
14 boys
Step-by-step explanation:
We know
The ratio of girls to boys is 5:2, which means for every 7 kids, there are 5 girls and 2 boys
So, 49 kids there are
2 x 7 = 14 boys
So, there are 14 boys
The cost of breakfast cereal is R35 for 1kg calculate how much 25kg of breakfast cereal will cost
Answer:
R875
Step-by-step explanation:
We know
R35 = 1kg of breakfast cereal
? = 25kg of breakfast cereal
35 times 25 = R875
So, 25kg of breakfast cereal will cost R875.
i need help with this
The measure of ∠V of the parallelogram is = 150.5°
What is a Parallelogram?A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure
The four types are parallelograms, squares, rectangles, and rhombuses
Properties of Parallelogram
Opposite sides are parallel
Opposite sides are congruent
Opposite angles are congruent.
Same-Side interior angles (consecutive angles) are supplementary
Each diagonal of a parallelogram separates it into two congruent triangles
The diagonals of a parallelogram bisect each other
Given data ,
Let the measure of the angle ∠Y = 10x + 27
Let the measure of the angle ∠W = 2x + 29
Now , for a parallelogram the opposite sides are congruent and opposite angles are congruent
Substituting the values in the equation , we get
10x + 27 = 2x + 29
Subtracting 2x on both sides of the equation , we get
8x + 27 = 29
Subtracting 27 on both sides of the equation , we get
8x = 2
Divide by 8 on both sides of the equation , we get
x = 1/4
Let the measure of the angle ∠Y = 10 ( 1/4 ) + 27
Let the measure of the angle ∠Y = 2.5 + 27
Let the measure of the angle ∠Y = 29.5°
Now , same-side interior angles (consecutive angles) are supplementary
Substituting the values in the equation , we get
angle ∠Y + angle ∠V = 180°
29.5° + m∠V = 180°
Subtracting 29.5 on both sides of the equation , we get
m∠V = 150.5°
Hence , the measure of m∠V = 150.5°
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The mass
a cube, M (kg),
is proportional to the cube of
the length of its edge,
L (m).
The mass
the cube is 40
kg when the length of its
edge is 35 cm.
Work out M (to 2 DP) when L
=
0.6 m
Thanks
The mass when L = 0.6 is given as follows:
M = 68.57 kg.
How to obtain the mass of the cube?The mass of the cube is modeled according to a proportional relationship, as follows:
M = kL.
In which k is the constant of proportionality.
The mass the cube is 40 kg when the length of its edge is 35 cm = 0.35 m, hence the constant is obtained as follows:
0.35k = 40
k = 40/0.35
k = 114.28.
Hence the mass when L is of 0.6 m is given as follows:
M = 114.28 x 0.6
M = 68.57 kg.
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Question 4 of 6 What larger conclusion can you reach by stringing together the sentences given below? If Henry goes to the library, he reads a book. D If Henry reads a book, he becomes smarter. 0 If Henry becomes smarter, he becomes happier. • If Henry becomes happier, the world is a better place. D A. If the world is a better place, Henry becomes smarter. B. If Henry goes to the library, the world is a better place. C. If the world is a better place, Henry goes to the library. D. If Henry goes to the library, he looks for books on tape. ← PREVIOUS
The conclusion we can reach is D. If Henry goes to the library, he looks for books on tape.
What is mathematical induction?
An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.
Given, If Henry goes to the library, he reads a book.
If Henry reads a book, he becomes smarter.
If Henry becomes smarter, he becomes happier.
If Henry becomes happier, the world is a better place.
Now, The only statement that is valid is If Henry goes to the library, he looks for books on tape.
As reading books only by henry won't make the world a better place.
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NEED IT VERY URGENT PLEASE!!!!!!
at a right angle. Sidewalk B extends 500 feet on either side of the intersection with
Reason Four sidewalks form two right triangles. Sidewalk A and Sidewalk B intersec
Sidewalk A. Sidewalk C and Sidewalk D start at the ends of Sidewalk B and intersect
Sidewalk A at the same point. Do you have enough information to prove that the two
right triangles are congruent? Explain your reasoning.
A pair of right triangles are said to be congruent if the lengths of their respective sides and angles are the same.
Are two right angle triangles congruent?If the size and shape of two right triangles match, they are said to be congruent. Alternatively said, two right triangles are said to be congruent if the length of their respective sides and angles are equal. Fig. 1 shows that ABC = RPQ since A = R, C = Q, and B = P.
No, not every right triangle has a congruent angle. If the hypotenuse and the leg of one right-angled triangle match the hypotenuse and the corresponding leg of the other triangle, the two triangles are said to be congruent. This circumstance, known as RHS congruence of two triangles, only applies to right angled triangles. An isosceles triangle is one that possesses two congruent sides.
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