The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.
Two triangles are congruent if and only if they have the same three sides and angles.
SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.
SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.
ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.
AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.
HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.
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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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When can we say that the two triangles are congruent?
Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
What is congruent?
Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.
Here,
we have to prove when can we say that the two triangles are congruent.
SSS, SAS, ASA, AAS, and HL.
These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.
Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
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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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where is the incenter of any given triangle
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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Whats the width of her head
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
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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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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A five-card hand is dealt at random from a standard deck. (A five-card hand is any set of five different cards, chosen without replacement.)
What is the probability that the hand contains exactly three face cards?
Round your answer to the nearest hundredth.
The value of the solution is 6.6%
What is permutation explain with example?An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order. For instance, the set A=1,6 has a permutation of 2, which is 1,6,1. There is no other way to arrange the components of set A, as you can see.
How do you know if it's a permutation or combination?Combinations exist when the order doesn't matter, but permutations exist when it does. A permutation might be described as an ordered combination. The following formula determines how many permutations of n objects, taken r at a time: P(n,r)=n!
According to the above question :-
= (3 × 4)C3 × (52 — 3 × 4)C(5 — 3) / 52C5
= 12C3 × 40C2 / 52C5
= 12! × 40! × 47! × 5! / (52! × 9! × 3! × 38! × 2!)
= 12!/9! × 40!/38! × 47!/52! × 5!/(3!2!)
= ((10 × 11 × 12) × (39 × 40) / (48 × 49 × 50 × 51 × 52)) × (5 × 4 / 2)
= 10 × (1 × 11 × 1 × 3 × 40) / (4 × 49 × 5 × 51 × 4)
= (10 × 40 / (4 × 5 × 4)) × (11 × 1 / (49 × 17))
= 5 × 11 / (49 × 17)
= 55 / (17 × (50 — 1))
= 55 / (850 — 17)
= 55 / 833
≈ 6.6%
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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.
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%.
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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How do you know if a triangle is ASA or AAS?
The difference between 2 parts of congruency is as follows.
What is congruent?
Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’
Main Body:
ASA vs AAS:
ASA stands for “Angle, Side, Angle”,
AAS means “Angle, Angle, Side”
ASA ===
two triangles are congruent if they need associate equal aspect contained between corresponding equal angles. If the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the enclosed aspect of 1 triangle are congruent, severally, to the 2 angles and therefore the enclosed aspect of the second triangles, then it satisfies the condition that the triangles are congruent.
AAS===
two angles and an opposite facet. AAS is one amongst the 5 ways that to see if 2 triangles are congruent. It states that if the vertices of 2 triangles are in matched correspondence such 2 angles and therefore the facet opposite to at least one of them in one triangle are congruent to the corresponding angles and therefore the non-included facet of the second triangle, then the triangles are congruent.
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If <1=<2"
Definition of congruence
Angle addition postulate
Linear Pair Theorem
Vertical Angles Theorem
A. Congruence means the same.
B. Angle addition postulate states that two angles side by side sum the measure of the two angles.
C. Linear pair theorem states that linear pair angles add up to 180 degrees.
D. Vertical angles theorem states that vertical angles are congruent.
What is congruence?
Congruence in angles simply means the same or equals to. Two angles are congruent when they are the same.
What is angles addition postulate?The angle addition postulate states that the measure of an angle formed by two angles side by side is the sum of the measures of the two angles.
What is linear pair theorem?The Linear Pair Theorem states that two angles that form a linear pair are supplementary. They add up to 180 degrees.
What is vertical angles theorem?The Vertical Angle Theorem says the opposing angles of two intersecting lines must be congruent, or identical in value
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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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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..
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
Find and graph the linear regression equation and the quadratic regression equation. Determine which model best fits the given data. Round your answers to the nearest hundredth.
Y = 1x – 2 is the equation for linear regression.
Explain about the linear regression equation?
A linear regression line is represented by the equation Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of a line, b, is equal to the intercept of that line, which is the value of y when x = 0.
Based on the value of another variable, linear regression analysis can be used to predict the value of a variable. You want to be able to predict the dependent variable. You create a forecast about the value of the other variable using the independent variable.
A positive linear relationship exists if the slope of the line is positive, meaning that when one rises, the other rises as well.
Y = -2 -1 x
Y= -2 -1x
Y = 1x - 2
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what is the sum 2x24x2
Answer: 96
Step-by-step explanation:
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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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 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 ;>
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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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
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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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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.
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
Express each of the following ratios in the form 1:N
8:13
Answer:
Step-by-step explanation:
i just need the points bro
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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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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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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