The triangles are congruent if all three sets of comparable sides are present. The side-side-side shortcut is a congruence technique (SSS). Side-angle-side (SAS), which uses two sets of sides and an angle between them that is known to be congruent, is another shortcut.
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. The triangles are congruent if two pairs of corresponding angles and the included sides are both true. This standard is called angle-side-angle (ASA).
Angle-angle-side (AAS) is another criterion that takes into account the congruence of two pairs of angles as well as the non-included side. SSS stands for "side, side, side," which signifies that we have two triangles with equal sides on all three sides. SAS, ASA, and AAS are acronyms for these rules. "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal.
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If f(x) = 5 + 3x and g(x) = 5 - 9x, find f(g(2)).
If the function f(x) = 5 + 3x and g(x) = 5 - 9x. The value of f(g(2)) is -34
The given functions are
f(x) = 5 + 3x and g(x) = 5 − 9x.
a. We plug-in 2 in the function g(x) and then the obtained image in the function
f(x)g(2) = 5 − 9 × 2
= 5 - 18
= -13
f(g(2)) = f(-13)
= 5 + 3 × (−13)
= 5 - 39
= -34
b. We find the composite function by replacing x in f(x) by
g(x) f(g(x)) = 5 + 3g(x)
= 5 + 3 × (5−9x)
= 5 + 15 − 27x
f(g(x)) = 20 − 27x
f(g(2)) = 20 − 27 × 2
= 20 − 54
= -34
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Why does AAS congruence work?
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle. AAS congruence may be demonstrated with a few simple methods.
When two triangles in geometry are the same size and shape, they are said to be congruent. The Angle-Angle-Side (AAS) congruence theorem is one of several approaches to demonstrate that two triangles are congruent.
According to the AAS congruence theorem, triangles are congruent if two angles and the side that connects them in one triangle are congruent with two angles and the side that connects them in another triangle. This is how this theorem is expressed:
If ∠A = ∠E, ∠B = ∠F, and AB = EF, then ∆ABC ≅ ∆DEF
In other terms, triangles ABC and DEF are congruent if two angles and the side between them in triangle ABC are equivalent to two angles and the side between them in triangle DEF.
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What is the set of all x values?
The range is the set of all "y" values in an ordered pair, while the domain is really the set of all "x" values.
What is defined as the term called domain?Keep in mind which ordered pairs are represented by the following symbols: (x, y).
List all the x values first from relation to determine the domain when examining a set of ordered pairs. List each of the y values first from ordered pairs to determine the range. Repeated values that fall inside the domain or range need only be listed once. Each x value in a relation must have a unique value for the y value for it to be a function.A collection of ordered pairs isn't a function if an x value has had more than one y value associated with it, as as in the relation (4, 1), (4, 2), where the x value of 4 has y values of 1 and 2.
Thus, If there is only one y-value for every x-value, then the relation is called a function.
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Consider the following equation.
-16p + 37 =49 - 21 the equation that has the same solution
The equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p
We are given the equation;
-16p + 37 = 49 - 21p
We are supposed to identify the equation that has similar solution with the equation given;
The solution for the equation given is;
-16p + 37 = 49 - 21p
Combining the like terms;
-16p + 21p = 49 - 37
5p = 12
p = 2.4
Solution for the choices given;
A. -14 + 6p = -9 - 6p
6p + 6p = -9 +14
12p = 5
p= 0.417
B. -55 + 12p = 5p + 16
12p - 5p = 16 + 55
7p = 71
p = 10.14
C. 2 + 1.25p = 3.75p + 10
1.25p - 3.75p = 10 - 2
-2.5p = 8
p = -3.2
D. 3/2p - 5 + 9/4p = 7 - 5/4p
3/2p +5/4p +9/4p = 7 + 5
5p =12
p = 2.4
Therefore, the equation that has similar equation with the one given is D. 3/2p - 5 + 9/4p = 7 - 5/4p
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How do you know if a function is positive or negative?
A function is positive if the output values are greater than the input values and negative if the output values are less than the input values.
To determine if a function is positive or negative, you must first look at the output values of the function. If the output values are greater than the input values, then the function is positive. This means that the output values increase as the input values increase. Conversely, if the output values are less than the input values, then the function is negative. This means that the output values decrease as the input values increase. For example, if a function has an input value of 3 and an output value of 5, then the function is positive because the output is greater than the input. On the other hand, if the same function had an output value of 1, then the function would be negative because the output is less than the input. In summary, a function is positive if the output values are greater than the input values and negative if the output values are less than the input values.
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During the day, a patient had her temperature measured at 37.3C, 38C, 37.8C and 38.5C. So what was her average temperature?
If the distance between the points A(2, -2) and B(-1, x) is equal to 5, then the value of x is: (a)2 (b)-2 (c)1 (d)-1
Answer:
(a) 2
Step-by-step explanation:
We can assume this is a 3-4-5 triangle from the two given sides, 5 and 3(2--1) so then we know the y difference of the y coordinate should be + or - 4 from -2 giving us two solutions of 2 and -6 since this is a multiple choice and a is 2 he answer is 2
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What are the two function used to form the rational function?
The two functions used to form the rational function are the ratio of two rational polynomial expression p and q.
A function is called a rational function if it can be expressed in terms of the ratio of p and q.
f( x ) = p( x ) / q( x )
They generally are made up of more than one part.
Each function has a domain and a co - domain , they generally tells us about the limits of the function. We can use the rational function to calculate the domain.
Rational function asymptotes are of 3 types which are known as ,
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What is the best approximation of the solution to the system to the nearest integer values?
(7, 1)
(7, 0)
(1, 7)
(0, 6)
Answer:
7,0
Step-by-step explanation:
How do you find the missing number in an integer array of 1 to 100?
The missing number in an integer array of 1 to 100 can be found by summing the numbers 1-100 and subtracting the sum of the given array. The difference between the two sums will be the missing number.
To find the missing number, first sum the numbers 1-100 to get the total sum. Then sum the given array and subtract this sum from the total sum. The difference between the two sums will be the missing number. This method works because the total of the array should be equal to the sum of 1-100 if all the numbers are present. By subtracting the sum of the given array from the total sum, any missing numbers will be accounted for in the difference.
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Could you please find X and show me how
Answer:
[tex]x=13\cos 25^{\circ}[/tex]
Step-by-step explanation:
[tex]\cos 25^{\circ}=\frac{x}{13} \\ \\ x=13 \cos 25^{\circ}[/tex]
Saha ue 3 teapoon of hot chocolate mix for every 8 ounce of milk. How many teapoon of hot chocolate mix doe he need for 48 ounce of milk?
Saha uses 3 teaspoons of hot chocolate mix for every 8 ounces of milk. for 48 ounces of milk, he needs 18 teaspoons of hot chocolate.
The problem can be solved using unitary method or using ratio.
- Unitary method
Using this method, first, compute how many teaspoons of chocolate needed for 1 ounce of milk.
8 ounces of milk need 3 teaspoons of hot chocolate. Hence,
1 ounce of milk need 3/8 teaspoons of hot chocolate
48 ounce of milk need 3/8 x 48 = 18 teaspoons of hot chocolate
- Using ratio
Let p = number of teaspoons of hot chocolate needed for 48 ounces of milk. Then,
3 : 8 = p : 48
8p = 3 x 48
p = 3 x 48/8 = 3 x 6 = 18 teaspoons
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How do you solve an equation using the substitution method?
Solution of the equation using substitution method is given by following steps:
1. Get the value of one variable in the other variable form using one equation.
2. Substitute the value of that variable in the second equation and get the value of both the variables.
Let us consider the system of equation to explain the solution of substitution method:
x + y = 0 __(1)
2x + 3y = 6 ___(2)
Get the value of y in the x form and substitute the value of y in equation (2) we get,
y = -x
2x + 3(-x) = 6
⇒2x - 3x = 6
⇒ -x = 6
⇒ x = -6
Now substitute the value of x in equation (1) we get,
y = -( -6)
⇒ y = 6
Therefore, the solution of the equation using substitution method is given by following way:
1. Get the value of one variable in the other variable form using one equation.
2. Substitute the value of that variable in the second equation and get the value of both the variables.
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Which of the following statements about dilations are true? Select all that apply.
The true statement on dilations are that :
A. Dilations have the same shape as the original shape C. Dilations can be reductions of the original image What are dilations ?Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or shrink. A square of side 5 units can be widened to a square of side 15 units using dilation math, but the square's shape doesn't change.
Dilation therefore allows for the same shape as the original shape, but it is a reduction of the original shape and so cannot be the same size.
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Is it true a 0 or 1?
Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.
Describe a binary number.Binary code, the foundation of everything binary utilised in computing systems, provides a numbering system in which there are only two potential values for each digit: 0 or 1.
Here,
In this case, binary logic has two states: false and true. "binary" – It's critical that there be two of them.
If you want to, you can refer to them as 0 and 1, yes and no, or off and on if you're an electrical engineer. They function as intended.
Therefore, In the binary number 0 comes out to be false and 1 comes out to be true.
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Did zero is prime number?
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer, so it is not considered a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
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How many terms are there in the expression 3 }- 3p 2 }+ 4p 7?
There are four terms in the expression –2p³ – 3p² + 4p + 7. The first term is –2p³, the second term is –3p², the third term is 4p, and the fourth and final term is 7.
What is terms?Terms in math are individual components of equations or expressions, which can consist of constants, variables, and operators. A term can also be a single number or variable, or several numbers or variables multiplied together. Terms are separated by addition or subtraction operators. Terms can also be used to describe an algebraic expression such as the sum of two terms, or the product of two terms.
The expression can be written as –2p³ – 3p² + 4p + 7 = 0. This expression is a polynomial equation with degree three, meaning the largest exponent of the variables is 3.
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What are the 3 steps to finding an inverse function?
Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.
What is multiplicative inverse ?A number that, when multiplied by a number x, produces the multiplicative identity 1, or 1/x or x1, is known as a multiplicative inverse or reciprocal in mathematics. B/a is the multiplicative inverse of the fraction a/b. Divide 1 by the real number to find its multiplicative inverse. As an illustration, the reciprocal of 5 is 1/5 (1/5 or 0.2), whereas the reciprocal of 0.25 is 1 divided by 0.25 (1 divided by 0.25 = 4) One of the most straightforward instances of a function that is its own inverse is the reciprocal function, or f(x), which transfers x to 1/x (an involution).Since no real number multiplied by 0 yields 1, zero does not have a reciprocal in the real numbers (the product of any number with zero is zero). The reciprocals of all real numbers, except zero, are real; the reciprocals of all rational numbers, except zero; and the reciprocals of all complex numbers, save zero.Hence, Rewrite f(x)= as y in step one, Swap X and Y in step one, then solve for y in step three.
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What equation is perpendicular to Y =- 3x 4?
Equation y = -3x is perpendicular to Y =- 3x - 4.
Describe perpendicular.A perpendicular is a straight line in mathematics that forms a right angle (90 degrees) with another line. In other words, two lines are perpendicular to one another if they connect at a right angle. In every case, perpendicular lines cross or intersect. Any two perpendicular lines will always have an angle of 90 degrees.
Given
y = -3x - 4
Using slope intercept form.
y = mx + b
The reciprocal of the slope of the perpendicular line is negative.
By doing this, you alter the slope's sign to the opposite, in this case to 3. The slope of the perpendicular line is then equal to 1/3 by finding the reciprocal by flipping the denominator and numerator.
Equation y = -3x is perpendicular to Y =- 3x - 4.
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What ratio does the point 1 a divided the join of (- 1/4 and 4 1 )? Also find the value of a?
Using the provided values for the points and the slope, With the formula of slope we can calculate the value of a = 14/5 =2.8 and the ratio as
1:1.49 .
What do you mean by slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.
What do you mean by ratio?A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the total amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
point (1,a) divided line joined by (-1,4) and (4,1).
Since, The slope between these points are same as they all line in a single line, we can ,
[tex]\frac{a-4}{1+1} = \frac{1-a}{4-1}[/tex]
3a-12=2-2a
5a=14
a=14/5 =2.8.
distance between (-1,4) and (1,2.8),
[tex]d1 = \sqrt{(1--1)^2 +(2.8-4)^2}\\=\sqrt{5.44}\\=2.33[/tex]
distance between (1,2.8) and (4,1),
[tex]d2= \sqrt{(4-1)^2 + (1-2.8)^2}\\=\sqrt{12.24}\\=3.49\\\\[/tex]
ratio = d1/d2
= 1: 1.49
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Calculating length of the curve
Can somebody give me a detailed description how we did the last three steps?
I don't see the picture. Can you send it in the message.
H(x)=3x^4+2x-5/x+9x^3-7 is it polynomial? If so write in standard form, degree, type, and leading coefficient. (20 points)
Answer:
yes its a polynomial espero te sirva
Write an equation for the line in slope-intercept form
Answer: y=2/5x +5
Step-by-step explanation: slope is 2/5 y intercept is 5
How do you find the mean of 5?
The mean of given data is 5.
To find: Mean of the given data
Given data: 5
Mean: Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Mean=Sum of observations / Number of observationsHere sum of observation is 5
Arithmetic mean refers to the average amount in a given group of data. It is defined as the summation of all the observation is the data which is divided by the number of observations in the data
Total number of observation is 1
The number of observations provides information on the total number of values that are contained in the Dataset. This property is intended to provide an indication of the size of a Dataset
Now substitute the values in above formula
=[tex]\frac{5}{1}[/tex]=5
Therefore, the mean is 5.
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How do you find the base area of a pyramid?
The base of a solid, three-dimensional, or shaped item. What the thing "rests" on is the base. Polygons, forms, and solids all employ base.
Explain the term base area of a pyramid?Any pyramid's surface area can be calculated by multiplying the base's surface area by the lateral faces' surface areas.
If you know how to calculate the area of the pyramid's base, you may use a formula to determine the surface area of a normal pyramid. Knowing how to calculate the area of forms like pentagons and hexagons is useful because the basis can be any polygon. However, when dealing with the usual, standard square pyramid, figuring out the total surface area is straightforward.Pyramid's slant height and the square base's side length.
Thus, base area of the square pyramid is length x width.
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By what number must you multiply each side of the equation 45x=8 to produce the equivalent equation x = 10?.
Answer:
5
Step-by-step explanation:
For this case, we have the following equation:
4/5x = 8
We must find a number that when multiplied on both sides of the equation, as a result:
x = 10x
So, if we multiply 8 * 5 = 40
Now, the left side must also be multiplied by 5 to not alter the equation:
(4/5)x*5=4x
x∗5=4x
Finally we have 4x=40
Clearing "x":
\begin{gathered}x = 40/4
x=10
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Santa take 8 minutes to build 1 train and 6 minutes to built I car. How much minutes will it take him to build 100 train and 100 cars?
Answer:
800 and 600
Step-by-step explanation:
1 train = 8 minutes
100 trains =8×100
= 800 minutes
1 car= 6 minutes
100 cars = 6×100
= 600 minutes
Answer:
1400 minutes / 23 hrs
Step-by-step explanation:
William works at a tire shop and earns 6.75% commission on everything he sells. He also earns a base salary of $300 per week. How much will he earn for the week if he sells $5,385 worth of tires?
Answer: 363.49
Step-by-step explanation:
6.75%=.0675
5385*.0675+300=363.4875
round up
$363.49
A college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses. Choose the correct answer from the drop-down menu to complete the statement.
As per the concept of linear equation, the college student took 13 courses of 3 credit hours.
An equation in math is defined as a mathematical statement with an 'equal to' symbol between two expressions that have equal values
Here we have given that college student completed some courses worth 3 credits and some courses worth 4 credits. The student earned a total of 59 credits after completing 18 courses
And we need to find number of students in each category.
While we looking into the given question, we have given the values like the following,
Here the total credits = 59
And the total courses = 18
Then let us consider the number of 3 credit hour courses is referred as x and the number of 4 credit hour courses referred as y
Then based on the given statement, we have written the equation as
=> x + y = 18 ----------------------------(1)
=> 3x+4y=59 --------------------------(2)
Here we have to eliminate y to find the number of 3 credit hour courses, by multiplying Equation 1 by 4
Then we get,
=> 4x + 4y = 72
Then we have to subtract Equation 2 from Equation 3
Then we get,
=> x = 13
Therefore, the resulting value is 13.
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