The incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
we know that
The incenter is the point where the angle bisectors intersect. The incenter is also the center of the triangle's incircle.
therefore
Is the point of concurrency of the angle bisectors of the triangle
Part 2)
we know that
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side
therefore
Is a segment drawn from a vertex to the midpoint of the opposite side
Therefore, the incenter of any given triangle s the point of congurrency of the angle bisectors of the triangle
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Determine the length of the line segment shown 4 units
18 units
19 units
21 units
The length of the line segment will be 4 units. Then the correct option is A.
What is the distance between two points?The line joining the two points is known as a line segment. Let one point be (x, y) and another point be (h, k).
Then the distance between the points will be
D² = (x - h)² + (y - k)²
From the graph, the two points are (2, -2) and (2, 2). Then the distance between the points is calculated as,
D² = (2 - 2)² + (2 + 2)²
Simplify the equation, then we have
D² = (2 - 2)² + (2 + 2)²
D² = (4)²
D = 4 units
The length of the line segment will be 4 units. Then the correct option is A.
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The missing diagram is attached below.
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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Select the correct answer.
What is the approximate solution to this equation?
19 + 2 ln x= 25
Answer:
3
Step-by-step explanation:
Hope this helps..
write 3/5 as a fraction or as a whole or mixed number
Answer:
Step-by-step explanation:
1) 4 1/4 + 5 1/2
= 9 3/4
2) 10 4/5 - 6 1/5
= 4 3/5
3) 3 1/4 - 1 3/4
= 1 1/2
4) 3 2/5 + 7 7/10
= 11 1/10
5 ) 10 3/13 + 2 10/13
= 13
Answer:
1
Step-by-step explanation:
Its for sure 1
Toby created a sculpture for art class using different-sized cubes. The smallest cube is 1.5 inches along each edge. The largest cube is 7.5 inches along each edge.
How many of the smallest cubes would it take to fill the largest cube?
Write your answer as a whole number or decimal. Do not round.
There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume
Volume of cubeThe volume of cube is calculated by using a × a × a = a³ where "a" is the edge.
The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches
The volume of the smallest cube = 3.375inches³
The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches
The volume of the largest cube = 421.875inches³
Thus, the number of the smallest cubes it would take to fill the largest cube is derived by
421.875inches³/3.375inches³ = 125.
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The graph of F is shown below evaluate each integral by interpreting it in terms of area
The answer to this question is after solving definite integration 0,1,-4,-10
What is Definite integration?
It is just basically Simple Integration with limits. In other words it is completely same as area under curve
Solution:
We will proceed by finding area under curve
Here we have to consider the area above x axis as positive and area under x axis as negative area
In First part +ve area and -ve area cancels each other hence answer is 0
In second part after cancellation only 1 square block above x axis remains whose area is 1 hence answer is 1
remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative
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if the diagonals of a parallelogram bisect each other then it must be a rhombus
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
What is rhombus?Due to the fact that it is a quadrilateral with two pairs of parallel sides, a rhombus can be considered a particular parallelogram.A rhombus also has equal sides on all four sides, exactly like a square. Because of this, it is often referred to as a tilted square.To comprehend the relationship between the rhombus shape, parallelogram, and square, look at the graphic below.
All parallelograms are parallelograms, however not all parallelograms are rhombuses or rhombi.All squares are rhombuses, but not all rhombuses are squares.There are three additional names for a rhombus:
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When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle it means that we are going to use what postulate?
The used postulate is explained below.
What is congruent triangles?
Two triangles are stated to be congruent if the 3 facets and the 3 angles of each the angles are same in any orientation.
When angles and facet blanketed in among those angles of 1 triangle are identical as any other one, each those triangle are Congruent.
This standards of congruency is is aware of as ASA criterion as a facet blanketed among angles are all identical.
Two triangles are congruent, if angles and the facet blanketed among them in a single triangle is same to the 2 angles and the facet blanketed among them of the alternative triangle.
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What is the volume of the following rectangular prism? 4/3units 23/4units2 Volume ==equals units^3 3 cubed
The volume of the rectangular prism with length of 5 units, width of 4 units and height of 3 units is 60 unit³
What is an equation?An equation is an expression that is used to show the relationship between two or more numbers and variables.
Volume is the amount of space occupied by a three dimensional side or object.
Let us assume that the rectangle prism have length of 5 units, width of 4 units and height of 3 units. Hence:
Volume of prism = length * width * height
Volume = 5 units * 4 units * 3 units = 60 unit³
The volume is 60 unit³
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What is the upfront cost to secure this apartment?
A) $1,876
B) $1,225
C) $2,105
D) $1,025
B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)
1000 + 25 + 200 = 1225
Represent the following statement on a number line: I have anywhere from $5 to $8 in my pocket.
The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.
What is a number line?In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).
Translating the statement, we have the following inequality:
Let the variable x represent the amount of money in pocket.
From $5 to $8 in my pocket = 5 ≤ x ≤ 8.
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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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Write the function for the graph of
g(x)
g(x)=[2x]
g(x)= [x]+2
g(x)= [x-2]
g(x)=[x]-2
The function of the graph is g(x) = [x]+2
What is linear function?A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of terms
y = output variable
x = input variable
m = slope
c = y intercept
The c from the graph is +2
m for points (1, 3) and (-3, -1)
= (-1 - 3) / (-3 - 1)
= -4/-4
= 1
substituting to the equation y = mx + c
y = x + 2
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Ameekah is working with consecutive integers. If she uses x to represent her first number, what should she use to represent her second number?
A x
B x + 1
C x + 2
D 2x
Answer:
B) x + 1
Step-by-step explanation:
Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.
Eg: 5 , 6 , 7 ,.....
6 = 5 + 1
7 = 6 + 1
So, if first number is x, then the next number will be x + 1
How do you find the equidistant point of a triangle?
The equidistant point of the triangle is point O , which is shown below.
In the question ,
we have to find the equidistant point in the triangle ,
We know that the equidistant point from the vertices of the triangle is the circumcenter ,
let the circumcenter be point O .
The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .
We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .
So ,we draw OA ,OB and OC .
we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.
that means , OA = OC and OC = OB .
which means OA = OB .
we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.
So, we can say that point O is on the perpendicular bisector of AB .
and
Since OA = OB = OC , the point O is equidistant from A , B and C .
Therefore , the equidistant point of the triangle is the circumcenter (point O) .
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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.
What is the quadrant axis of 6 8?
The I quadrant will contain the point (6, 8). The number is in the I quadrant as a result.
What is Quadrant?
A quadrant is any one of the four divisions of the coordinate plane. Additionally, we refer to the sections as they are divided by the coordinate axes when we talk about the sections. The y-axis is situated on this up-down axis, and the x-axis is situated here. As you can see, it divides the coordinate space into four parts.
A point can be mathematically expressed as:
A(x, y )
The intersection of the coordinate axes divides the cartesian plane into four quadrants (x and y-axis).
(x, y )
In the first quadrant, the x and y coordinates are both positive.
(x, y)
Y is positive while x is negative in the second quadrant.
(-x, y)
The point will be located in the third quadrant if both x and y are equally negative.
(-x, -y)
The point will be located in the fourth quadrant if both x and y are positive.
(x, -y)
pointed out; A(6, 8)
The y-coordinate in the highlighted position is positive at (8), while the x-coordinate is negative at (6).
Remember that if the x-coordinate is negative and the y-coordinate is positive, the point is in the I quadrant.
As a result, the provided point (6, 8) is said to be in the I quadrant.
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Does 15 36 39 form a right triangle?
1521=1521 therefore a triangle has sides with lengths of 15 inches, 36 inches, and 39 inches form a right triangle.
What is Right traingle?
A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
When we enter the values of the triangle's legs (15 and 36) and hypotenuse (39),
assuming it is a right triangle, into the Pythagoras theorem, the values of each side of the equation will be equal;
The Pythagoras Theorem is:
[tex]a^2+b^2=c^2[/tex]
Making substitutions and applying the math results in:
[tex]15^2 + 36^2= 39^2[/tex]
225 + 1296 = 1521
1521 = 1521
Therefore, it is a right traingle.
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How do you make an exponential decay model?
The exponential decay formula can take one of three forms:
f (x) = abˣ , f (x) = a (1 – r)ˣ , P = P₀[tex]e^{-kt}[/tex]
Where,
a (or) P₀ = Initial amount ,b = decay factor, e = Euler’s constant, r = Rate of decay (for exponential decay), k = constant of proportionality
What is Exponential Decay ?
Exponential decay occurs in mathematical functions when the pace by which changes are occurring are decreasing and must thus reach a limitation, which is the horizontal asymptote of an exponential function.
The amount drops gradually, followed by a quick reduction in the speed of change and increases over time. The exponential decay formula is used to determine the decrease in growth. The exponential decay formula can take one of three forms:
f (x) = abx
f (x) = a (1 – r)x
P = P0 e-k t
Where,
a (or) P0 = Initial amount
b = decay factor
e = Euler’s constant
r = Rate of decay (for exponential decay)
k = constant of proportionality
x (or) t = time intervals (time can be in years, days, (or) months, whatever you are using should be consistent throughout the problem).
In exponential decay, the quantity decreases very rapidly at first, and then more slowly. The rate of change decreases over time. The rate of decay becomes slower as time passes. Hence, the exponential decay graph is denoted as
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How do you solve an isosceles triangle problem?
Isosceles triangle problem can be solved by given steps
what is isosceles triangle ?
An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.
explanation:
In isosceles triangle
1. Two sides of the triangle are congruent
2. The angle opposite those sides are congruent
x + 72 +72 = 180
x = 180 -144
x = 36
Hence the isosceles triangle problem can be solved by above steps and explanation
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Whats the width of her head
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
at a field trip for every 8 students there is 1 chaperone. if the teacher purchased 108 total tickets, how many tickets were for students?
First, 108/9=12
This means that are 12 groups of people.
If there are 8 students in each group, 12 x 8 = 96.
96 should be your answer.
The box-and-whisker plots below (sometimes called boxplots) summarize the noon temperatures for each city.
Use the box-and-whisker plots to answer the questions.
Comparing the box-and-whisker plots for both data of each city, we have:
a. City B had more noon temperatures above 76°F
b. Both had the same interquartile range.
c. City B had a larger median noon temperature
d. City A had the largest noon temperature.
How to Analyze a Box-and-whisker Plot?The box-and-whisker plot has the following values it displays about a data distribution:
Minimum value: This is the value at the beginning of the left whisker.Lower quartile (Q1): This is indicated by the beginning of the edge of the box, 25% of the data are below this point.Median value: the line that divides the box is the median value which is 50% of the data.Upper quartile (Q3): This is indicated by the end of the edge of the box, 75% of the data are below this point.Maximum value: This is the largest data point and is located at the end of the right whisker.Interquartile range = Q3 - Q1
Analyzing the box-and-whisker plots given above, we have the following to conclude:
a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.
b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7
Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7
Both had the same interquartile range.
c. Median for City A = 70
Median for City B = 78
City B had a larger median noon temperature
d. City A had the largest noon temperature of 85.
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There are 28 students in the classroom. Each student needs 2 pencils for the exam. How many pencils in all are needed for the exam?
Total 56 pencils are needed for the exam.
What is Multiplication?Multiplication is one of the arithmetic operation used to find total numbers of items or things.
Given,
Total students in the classroom = 28
Total number of pencils needed by each student for the exam=2 pencils
Total number of pencils needed for the exam are,
= Total student × Number of pencils needed by each student
= 28 × 2
= 56 pencils
Hence , The total number of pencils needed by the students for the exam would be 56 .
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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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In a clothing store, a shirt that sells for $15 is marked “10% off.” What is the discount? What is the sale price of the shirt?
Answer:
$13.50
Step-by-step explanation:
If the shirt is 10% off, that means the shirt is 90% of the original cost, which is $15.
If the shirt is 90% of the original cost which is 15, that means that we must turn the percentage into a decimal (0.9) and multiply it by 15.
0.9*15 = 13.5
The sale price of the shirt is $13.50
The graph shows g(x), which is a translation of f(x)=|x|. Write the function rule for g(x).
Write your answer in the form a|x-h| + k, where a, h, and k are integers or simplified fractions.
g(x)=____
From the graph it can be calculated that Function rule for g(x) g(x) = |x - 7|
What is graph of a function?
The collection of ordered pairs with the (x,y)(x,y) sign is known as the graph of the a function in mathematics, where f(x)=y. x and f seem to be Cartesian coordinates of pts in two-dimensional space, and in the typical case where they are real numbers, they form a subset of the this plane.
Instead of the pairs "((x,y),z)" and "((x,y),z)" as in the definition above, the graph for functions of two variables, i.e. functions for whom the domain consists of pairs "(x,y)," "(x,y)," is typically the set of ordered triples "(x,y,z)" and "(x,y,z)" where "A surface for a constant real-valued function of the two real variables, this set is indeed a sub - set of three-dimensional space.
Graph of a function f(x) is the collection of points of the form (x, f(x))The given graph is a translation of |x| only,
So value of a is 1
Now since the tip of the graph lies on x- axis, k = 0So the value of g(x) is
g(x) = |x - h|g(7) = 0|7 - h| = 07 - h = 0h = 7
Function rule for g(x) g(x) = = |x - 7|
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Directions: Find the value of each variable.
11) x=?
y=?
12) x=?
y=?
13) x=?
y=?
14) x=?
y=?
15) x=?
y=?
z=?
The value of the variables x and y are,
11) x = 13, y = 18.4
12) x = 6.9, y = 8.
What is right angle triangle?
A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.
11)Let the given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]
Using this to find the value of y.
[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]
So, the values of x and y are x = 13 and y = 18.4.
12) The given triangle is a right angle triangle.
So we can use trigonometric ratio,
[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]
Now to find the value of x.
[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]
Hence, the values of x and y are, x = 6.9 and y = 8.
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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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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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