The common denominator of the complex fraction is (1/a - 1/b)/(1/a + 1/b) is a²b² which is option D.
The provided complex fraction is (1/a - 1/b)/(1/a + 1/b).
Now, to find the common denominator,
Solving this complex fraction.
First multiplying each component of every bracket to every component of the other bracket,
= 1/a² + 1/ab - 1/ab - 1/b²
Now, simplifying the equation,
= 1/a² + 1/b²
= (a²+b²)/a²b²
The denominator is the lower part of the fraction.
Hence, the common denominator of the complex fraction is a²b².
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Complete question - What is the common denominator of 1/a + 1/b in the complex fraction (1/a - 1/b)/(1/a + 1/b)?
A)a2 b2
B)a – b
C)a + b
D)ab
Problem:
The perpendicular bisector of line segment AB is the line that passes through the midpoint of AB and is perpendicular to AB
What is an equation for the perpendicular bisector of the line segment joining (1,2) and (-5,12) ? Write your equation in point-slope form, standard form, or slope-intercept form.
The equation of the perpendicular bisector, in slope-intercept form, is: y = 3/5x + 7/5.
How to Find the Equation of a Perpendicular Line?The equation of a line can be expressed:
In slope-intercept form is y = mx + b.In point-slope form is y - b = m(x - a).In standard form, it is Ax + By = C.First, find the slope of the line that is bisected perpendicularly that passes through (1, 2) and (-5, 12):
Slope (m) = change in y / change in x = (12 - 2) / (-5 - 1) = 10/-6
Slope (m) = -5/3
The negative reciprocal or -5/3 is 3/5. Therefore, the slope (m) of the perpendicular bisector would be: 3/5.
To write the equation of the line in point-slope form, substitute m = 3/5 and (a, b) = (1, 2) into y - b = m(x - a):
y - 2 = 3/5(x - 1)
Rewrite in slope-intercept form:
y - 2 = 3/5x - 3/5
y = 3/5x - 3/5 + 2
y = 3/5x + 7/5
Rewrite the equation in standard form:
-3/5x + y = 7/5.
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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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Whats the width of her head
Answer: 12 inches
Step-by-step explanation:
Answer: 15 cm
Step-by-step explanation:
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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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
A firm has the marginal-demand function where D(x)=-1400x÷√25-x² is the number of units sold at x dollars per unit. Find the demand function given that D=17,000 when x=3 per unit.
The demand function is D(x)=
The equation of the demand function is D(x) = 1400√(25-x²) + 11400
How to determine the demand function?From the question, we have the following parameters that can be used in our computation:
Marginal demand function, D'(x) = -1400x÷√25-x²
Also, we have
D = 17000, when the value of x = 3
To start with, we need to integrate the marginal demand function, D'(x)
So, we have the following representation
D(x) = 1400√(25-x²) + C
Recall that
D = 17000 at x = 3
So, we have
17000 = 1400√(25-3²) + C
Evaluate
17000 = 5600 + C
Solve for C
C = 17000 - 5600
So, we have
C = 11400
Substitute C = 11400 in D(x) = 1400√(25-x²) + C
D(x) = 1400√(25-x²) + 11400
Hence, the function is D(x) = 1400√(25-x²) + 11400
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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 ;>
Sample Test 4: Cartesian Graphing
Score: 38 / 200 \quad 4 / 20 answered
Question 14
Determine the slope of the line represented by the equation: 3 x+1 y=3
Slope DO NOT USE 1 AS THE DENOMINATOR!
Write answer as an integer or a reduced fraction.
The slope of the line is - 3
How to calculate the slope of a line?The equation of the line is given by,
3x + 1y = 3
y = -3x + 3 ---(1)
The slope- intercept form of a line is given by ,
y = mx + c ---(2)
where ,m is the slope
c is the y intercept
Comparing (1) and (2)
The slope of the line is , m = -3
What is a slope?A value known as slope can be used to define a line's direction and steepness. It is represented by the letter m in variable format. The gradient or rate of change of a line is another name for its slope. The line gets steeper as the slope's magnitude goes up. The line grows less steep as the slope's magnitude diminishes, which is the opposite of what happens. A line's direction can also be determined by a slope. A line that extends from left to right and has an upward slope is said to be growing.To learn more about slope, refer:
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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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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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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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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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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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Marley's daughter has a toy box in the shape of a cuboid. The box measures 90cm x 50 cm by 40 cm Marley wants to paint the outside of the box with red sparkly paint A 2 litre sin of red sparkly paint costs £8.99 Each tin covers an area of 7500cm² How much will it cost Marley to paint the toy box?
Answer:
It will cost Marley £7.20 to paint the toy box. This is calculated by taking the total surface area of the toy box (180000 cm²) and dividing it by the area covered by each tin of paint (7500 cm²). This equals 24, so Marley will need 24 tins of paint. Twenty-four tins multiplied by the cost of each tin (£8.99) equals £215.76, which is the total cost of the paint.
Step-by-step explanation:
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?
The sale price is $13.5 and discount is $1.5.
What is discount?A price that is lower than the usual price.
Given that, a store sells a shirt at $15, and there is a discount of 10%.
Price reduced after discount = 10% of 15 = $1.5
Selling price = 15 - 1.5 = $13.5
Hence, The sale price is $13.5 and discount is $1.5.
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Steve inherited $100.000 from his grandmother and deposited it into an account that compounds interest monthlv at a rate of 4.8%. Each month he withdraws $500 from the account. How long will it take him until the account has a balance of $0? Round your answer to the nearest tenth of a year.
Using the compound interest formula, if the account compounds at 4.8% monthly and he withdraws $500 monthly, it will take Steve 33 years, 7 months (403 months) to reduce $100,000 to a balance (future value) of $0.
What is the difference between the future and present value?The future value is the compounded present value, while the present value is the discounted future value.
However, with periodic withdrawals, a present value that compounds at an interest rate into the future can become $0 (future value) after some periods.
The time (period) Steve reduces his inheritance to $0 can be computed using an online finance calculator as follows:
I/Y (Interest per year) = 4.8%
PV (Present Value) = $100,000
PMT (Periodic Payment) = $-500
FV (Future Value) = $0
Results:
N (# of periods) = 403.164
Sum of all periodic payments = $-201,581.83
Total Interest $101,581.83
Thus, after 403 monthly withdrawals, Steve's inheritance will be reduced to a $0 future value.
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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.
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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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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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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find the domain and range of 1 - x^2
The range and the domain of the function f(x) = 1 - x^2 is less than or equal to 1 and all values of x are a real number (R).
Domain: x ∈ R
Range: f ( x ) ≤ 1, ∈ R
f ( x ) = 1 − x^2 is defined for all Real values of x, and therefore the domain is all real values ( R ).
x^2 has a minimum value of 0 (for x ∈ R ) and therefore − x^2 has a maximum value of 0 and − x^2 + 1 = 1 − x^2 has a maximum value of 1.
Therefore f (x) has a maximum value of 1 and the range of f ( x ) is ≤ 1.
So, the range of f(x)≤ 1, and the domain is all real values ( R ).
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What 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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Yo pls help me anyone I really need help
Answer: 36 cm= 8, 112 cm=1.25, 183.75 cm= 12.25
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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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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Solve for m.
m+14<−125
Responses
m>−11320
m is greater than negative 1 and 13 over 20
m<−1320
m is less than negative 1 and 3 over 20
m<−11320
m is less than negative 1 and 13 over 20
m>−1320
The value of m in the inequality expression given as m + 14 < −125 is m < -139
How to calculate the value of m?In the question, the inequality expression is given as
m+14<−125
Express the inequality properly
So, we have the following representation
m + 14 < −125
To start with, we subtract 14 from both sides
This gives
m + 14 - 14 <−125 - 14
Evaluate the difference
m < -139
Hence, the solution is m < -139
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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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What is the name of concurrency for medians of a triangle?
The concurrency point for medians of a triangle is known as centroid.
A median is a line drawn from one of the vertices of a triangle that bisects the side opposite to the vertex. Since there are 3 vertices in a triangle, there are also 3 medians in a triangle. A median divides the triangle into 2 equal halves.
The 3 medians of a triangle intersect at a point inside the triangle. This point is known as the centroid of the triangle. It is the center point of a triangle and divides the medians in the ratio of 2 : 1.
Thus, the name of concurrency for medians of a triangle is centroid.
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Express each of the following ratios in the form 1:N
8:13
Answer:
Step-by-step explanation:
i just need the points bro
