Answers
The value of the variable x and the measures of each side of the triangle ΔDEF found using the definition of an isosceles triangle are;
x = 9
DE = 13
EF = 28
DF = 28
What is an isosceles triangle?An isosceles triangle is a triangle that has two angles in the triangle that are congruent and two congruent sides.
The specified parameters are;
∠D is congruent to ∠E in triangle ΔDEF
The length of the segments of ΔDEF are;
DE = x + 4
EF = 4·x - 8
DF = 7·x - 35
The (base) angles ∠D and ∠F of ΔDEF are congruent, therefore, ΔDEF is an isosceles triangle (definition)
Therefore;
EF = DF (Definition of an isosceles triangle)
4·x - 8 = 7·x - 35
7·x - 4·x = 3·x = 35 - 8 = 27
3·x = 27
x = 27 ÷ 3 = 9
x = 9
DE = x + 4
Therefore;
DE = 9 + 4 = 13
EF = 4·x - 8
Therefore;
EF = 4 × 9 - 8 = 28
DF = 7·x - 35
Therefore;
DF = 7 × 9 - 35 = 28
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Related Questions
One integer is 2 times another. If the product of the two integers is 32, then find the integers
Answers
Answer:
The integers could be 8 and 4, just checked with a calculator
if the diagonals of a parallelogram bisect each other then it must be a rhombus
Answers
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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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
Answers
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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What are the types of inverse?
Answers
The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions
If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.
A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.
The various types of inverse function are:
Inverse Trigonometric Functions : The inverse trigonometric functions are also known as arc function as they produce the length of the arc.Inverse Hyperbolic Function : Just like inverse trigonometric functions, the inverse hyperbolic functions are the inverses of the hyperbolic functions. There are mainly 6 inverse hyperbolic functions exist which include sinh⁻¹ , cosh⁻¹, tanh⁻¹, csch⁻¹, coth⁻¹, and sech⁻¹Inverse Logarithmic Functions and Inverse Exponential Function : The natural log functions are inverse of the exponential functions.To know more about The inverse of function here
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What are the 4 types of properties?
Answers
There are four basic properties of numbers: commutative, associative, distributive, and identity.
1.Commutative Property
a. Addition
. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.
3 + 5 = 8 or 5 + 3 = 8
b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.
3 x 5 = 15 or 5 x 3 = 15
2.Associative Property
a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.
6 + (4 + 3) = 13 or (6 + 4) + 3 = 13
b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.
6 x (4 x 3) = 72 or (6 x 4) x 3 = 72
3.Distributive Property
The sum of two numbers times a third number is equal to the sum of each addend times the third number.
5 x (7 + 2) = 45 or 5 x 7 + 5 x 2 = 45
4.Identity Property
a. Addition. The sum of any number and zero is that number.
12 + 0 = 12
b. Multiplication, The product of any number and one is that number.
18 x 1 = 18
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Select the correct answer.
What is the approximate solution to this equation?
19 + 2 ln x= 25
Answers
Answer:
3
Step-by-step explanation:
Hope this helps..
Whats the width of her head
Answers
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
write 3/5 as a fraction or as a whole or mixed number
Answers
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
What is the quadrant of 0 6?
Answers
Answer:
it depends im pretty sure that you mean y and x cord so answer is 0 x 6 y
Step-by-step explanation:
or 0 X so width or y height 6 Y
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?
Answers
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.
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?
Answers
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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What type of triangle is def?
Answers
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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Determine the length of the line segment shown 4 units
18 units
19 units
21 units
Answers
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.
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)=____
Answers
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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Write the function for the graph of
g(x)
g(x)=[2x]
g(x)= [x]+2
g(x)= [x-2]
g(x)=[x]-2
Answers
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
Answers
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
What is the upfront cost to secure this apartment?
A) $1,876
B) $1,225
C) $2,105
D) $1,025
Answers
B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)
1000 + 25 + 200 = 1225
How do you solve an isosceles triangle problem?
Answers
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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How do you make an exponential decay model?
Answers
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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A line with a slope of 1 passes through the point (5, 3). What is its equation in slope "-intercept" form?
Answers
Answer: y=x−2 y = x − 2
Step-by-step explanation:
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
Answers
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.
percent proportions and equations what do you call a destroyed angle
Answers
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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Does 15 36 39 form a right triangle?
Answers
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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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?
Answers
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
find the domain and range of 1 - x^2
Answers
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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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?
Answers
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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A toy maker is putting multicolored sand in transparent cubes. Each cube measures 10 millimeters on each side. A coworker remarks that, for the cubes to be completely filled, each cube will need no more than 30 cubic millimeters of sand. Is the coworker correct? The coworker is correct. The volume of each cube is 20 cubic millimeters. The coworker is correct. The volume of each cube is 30 cubic millimeters. The coworker is not correct. The volume of each cube is 100 cubic millimeters. The coworker is not correct. The volume of each cube is 400 cubic millimeters. The coworker is not correct. The volume of each cube is 1,000 cubic millimeters.
Answers
The true statements are
The co-worker is not correct. The volume of each cube is 1,000 cubic millimetresHow to determine the true statement about the volume?The side length of the transparent cube is given as
Length = 10 millimetres
The volume of the cube is calculated as
Volume = Length³
Substitute the known values in the above equation, so, we have the following representation
Volume =10³
Evaluate
Volume = 1000 cubic millimetres
1000 cubic millimetres and 30 cubic millimetres do not have the same value
So, the co-worker is incorrect.
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How do you find the degree of a polynomial in precalculus?
Answers
Answer:
add up the exponents of each term and select the highest sum.
What is the volume of the following rectangular prism? 4/3units 23/4units2 Volume ==equals units^3 3 cubed
Answers
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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Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula 1 w, where I represents
the length, and w represents the width. The floor of the shed will have measurements of either / = 9 and w =
= 7 or/= 8 and
w = 8. What is the area of the larger floor?
O63
O 64
O 56
O 72
Answers
The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).
To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.
If w = 7 and l = 9
A = l × w = 8 × 6 = 48
If w = 8 and l = 8
A = l × w = 8 × 8 = 64
So, the second case would obtain a larger area.
Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.
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