A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
When a linear equation is graphed, it always produces a straight line since each term in the equation has an exponent of 1 or 0. A linear equation is an algebraic equation. If an equation has the formula y=mx+b, with m representing the slope and b the y-intercept, it is said to be linear.
The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.
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What is a 3 sided called?
A triangle is a polygon with 3 sides, and the sum of its interior angles is 180 degrees.
The properties of a triangle are:
A triangle has three sides, three angles, and three vertices.The sum of the length of any two sides of a triangle is greater than the length of the third side.The side opposite the largest angle of a triangle is the largest side.There are several types of triangles, including:
Equilateral triangle: This is a triangle with three sides of equal length and three angles of 60 degrees.
Isosceles triangle: This is a triangle with two sides of equal length and two angles of equal measure.
Scalene triangle: This is a triangle with three sides of different lengths and three angles of different measure.
Right triangle: This is a triangle with one 90-degree angle.
Acute triangle: This is a triangle with three angles that are all less than 90 degrees.
Obtuse triangle: This is a triangle with one angle that is greater than 90 degrees.
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Find the inverse of y = √x + 8, y ≥ 8
To find the inverse of a function, you can follow these steps:
Swap the variables x and y in the original function. For example, if the original function is y = √x + 8, you would swap the variables to get x = √y + 8.
Solve the equation for y. In this case, you would get:
x = √y + 8
y = x - 8
Replace y with f^-1(x) to denote the inverse function. The inverse function is defined as f^-1(x) = y, so you would get:
f^-1(x) = x - 8
This is the inverse function of y = √x + 8.
Note that the inverse function is only defined for values of x such that y ≥ 8. This is because the original function y = √x + 8 is only defined for y ≥ 8.
What is Polya's 4 step method?
Polya's 4 step method is a process designed to help problem solvers become better at tackling difficult problems.
It was developed by the mathematician George Polya in 1945 and consists of four basic steps:
1. Understand the problem: The first step is to read and understand the problem. This means understanding the problem and identifying what information is given and what is required.
2. Devise a plan: The second step is to identify a strategy or plan of attack. This involves breaking the problem down into smaller parts, identifying the key elements, and using logical reasoning to identify a solution.
3. Carry out the plan: The third step is to execute the plan. This involves following the steps of the plan in order to solve the problem.
4. Look back: The fourth and final step is to take a look back at the solution and evaluate it. This involves checking to make sure the solution is correct and making any necessary adjustments.
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Liz is watching a film at the cinema. The film started at 14 30. The film is 105 minutes long. When the film ends, Liz takes 20 minutes to get to the bus stop. Does Liz get to the bus stop in time to get this bus? You must show all your working
The answer is yes, she does and she still has 10 minutes free.
What is time ?
Time can be defined as the sequence on which particular event exists and time can measured in minutes , seconds, and hours.
Given,
The film started at 14 30. The film is 105 minutes long.
When the film ends, Liz takes 20 minutes to get to the bus stop.
105min=1h 45min
14h 30min + 1h 45min= 16h 15min
16h 15min + 0h 20min=16h 35min
16h 45min - 16h 35min= 10min
Hence, the answer is yes, she does and she still has 10 minutes free.
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im 12 and struggling help me please i need my grades up
Answer:
you would multiply 17% by 228,000
Step-by-step explanation:
you would get 177840
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have from 1 to 23 members. How many committees can be formed
The total number of such committees that may be created, divided by the prime numbers that divide N, is 81.
What is the prime numbers that divide N?In the scenario presented in this question, a club with 11 men and 12 women must elect a committee from among its members in order for there to be one more woman on the committee than males.
The committee might consist of only 1 person or up to 23 people.
Let N represent the maximum possible number of such committees.
The total number of prime numbers that divide N must be determined.
The number of ladies chosen will be m.
The number of guys who were not chosen would thus be:
11 - (m - 1) = 12 - m
Each pairing of men who were not chosen and women who were chosen represents a committee choice.
Since selecting 12 people from a total of 23 would result in m women and 12 - m males, the committee chose:
making use of a combination formula
N = 23C12
N = 23!/12!(23 - 12)!
N = 1352078
These are the main components of 1352078: 2, 7, 13, 17, 19, and 23.
Consequently, the prime number total would be,
2 + 7 + 13 + 17 + 19 + 23 = 81
The total of the prime numbers is thus 81.
The complete question is:
A club consisting of 11 men and 12 women needs to choose a committee from among its members so that the number of women on the committee is one more than the number of men on the committee. The committee could have as few as 1 member or as many as 23 members. Let N be the number of such committees that can be formed. Find the sum of the prime numbers that divide N.
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The admission fee to the carnival is $4. 50 for children and $7. 25 for adults. If a large group purchased 28 tickets and paid $159 how many adult tickets did they purchase?
The number of adult tickets purchased is 12.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
Let no. of adult = x
No. of children = 28 -x
So, 7. 25 * x + (28 - x) *4. 50 = 159
⇒2.75x +126=159
⇒2.75x =33
⇒x=33/2.75
x=12
Hence, the number of adult tickets purchased is 12.
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the graph represents the piecewise function
The piecewise function represented by the graph is:
f(x) = 2x when -3 ≤ x < 0
f(x) = 3 When 1/2 < x < 3/2
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Let f(x) = y = mx + c
From the graph, when -3 ≤ x < 0.
(-3, -6) and (-1, -2)
m = (-2 + 6) / (-1 + 3) = 4 / 2 = 2
(-1, -2) = (x, y)
-2 = 2 x (-1) + c
-2 = -2 + c
c = 0
f(x) = 2x
From the graph, When 1/2 < x < 3/2.
It is a horizontal line of y = 3.
f(x) = 3
Thus,
f(x) = 2x when -3 ≤ x < 0
f(x) = 3 When 1/2 < x < 3/2
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Need some help with these trigonometry questions
Answer: 11, 23, 166
Step-by-step explanation:
Hiya! From the drawings, I'm assuming all of the triangles are right-angled triangles. If they aren't though, tell me and I'll tell you how to solve them.
Anyways, assuming they are right angled-triangles, you can use Pythagoras' Theorem (aka a² + b² = c²)
c is the hypotenuse or the side opposite the right angle.
a and b are just the other two sides (doesn't really matter which is which)
Question 7:
c² = a² + b²
12² = a² + 5²
144 = a² + 25
144 - 25 = a²
119 = a²
a = 10.908712114635714411502154487373
(To the nearest whole number: 11)
Question 8:
c² = a² + b²
24² = 7² + b²
576 = 49 + b²
576 - 49 = b²
527 = b²
b = 22.956480566497992703585747092065
(To the nearest whole number: 23)
Question 9:
c² = a² + b²
c² = 90² + 140²
c² = 8,100 + 19,600
c² = 27,700
c = 166.43316977093238068928214785346
(To the nearest whole number: 166)
Hoped this helped! Tell me if there's something you don't understand. :)
A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount spent on lunches. The variance of the cost of nine business dinners was and the variance on 12 lunches was . What test value should be used in an F test
Why 1 [infinity] is not defined?
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
1. Infinity is an abstract concept and cannot be used in the same way as numeric values.
2. Infinity is not a number or a numerical value.
3. Therefore, it cannot be used in equations or arithmetic operations.
4. Therefore, 1 [infinity] is not defined.
1 [infinity] is not defined because infinity is an abstract concept and cannot be used in the same way as numeric values. Infinity is not a number or a numerical value, and therefore it cannot be used in equations or arithmetic operations.
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Marcus is shopping for pants. The available styles are boot cut (B), skinny (S), and relaxed fit (R). Make an organized list to show all possible outcomes if he buts two new pair of pants.
There are 9 possible outcomes to buy two new pair of pants.
What is combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.
Given:
we have the following Styles
Boot cut (B), Skinny (S), and Relaxed fit (R).
So, if her buys two paints then the possible combination he can take as
Boot cut x Boot cut
Skinny x Skinny
Relaxed fit x Relaxed fit
Boot cut x Skinny
Boot cut x Relaxed fit
Skinny x Relaxed fit
Skinny x Boot cut
Relaxed fit x Boot cut
Relaxed fit x Skinny
Hence, there are 9 possible ways.
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Yara is 8 years old. Yara's mother is 4n times older than Yara. How old
was Yara's mother 5 years ago in terms of n?
Yara's mother was 32n-5 years old 5 years ago in terms of n.
Yara's mother is 4n times older than Yara, and Yara is 8 years old, so we can set up the equation:
Mother's age = 4n * 8 years
We are also told that Yara's mother is 5 years older than she is now, so we can add 5 to the equation above:
Mother's age 5 years ago = 4n * 8 years - 5 years
Now we can simplify this equation:
Mother's age 5 years ago = 32n - 5 years
Now we can substitute the value of n to find the mother's age in terms of n.
To find the age of Yara's mother 5 years ago in terms of n, we need to know the value of n. But we don't have the value of n so we can't find the exact age but we can find it in terms of n which is 32n-5 years.
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When the equations 3x 5y 9 and 5x 3y 7 are solved then the value of x y 2?
When these equations are solved, the value of x is 4 and the value of y is 3. Therefore, the value of x + y = 7.
To solve the system of equations, we will use the elimination method.
First, we multiply the first equation by 3 and the second equation by 5.
3(3x + 5y = 9)
5(5x + 3y = 7)
Then, we add the equations together:
9x + 15y = 27
25x + 15y = 35
Now, we subtract the second equation from the first to eliminate the x terms:
-16y = -8
y = 0.5
Next, we plug this value for y into one of the original equations and solve for x:
3x + 5(0.5) = 9
3x = 8.5
x = 2.83
Finally, we plug the values of x and y into the original equation to verify that they are correct:
3(2.83) + 5(0.5) = 9
So, the value of x is 2.83 and the value of y is 0.5. Therefore, the value of x + y = 2.83 + 0.5 = 3.33.
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.A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
This equation can be used to determine how long the car was traveling at each speed. You can solve for one of the variables by using algebraic techniques. For example, you could subtract 35y from both sides to get:
55x = 200 - 35y
Then divide both sides by 55 to get:
x = (200 - 35y)/55
This equation shows that the value of x (the time spent traveling at 55 mph) is determined by the value of y (the time spent traveling at 35 mph). If you know the value of y, you can use this equation to calculate the value of x.
To find the values of x and y that satisfy the equation, you will need to use additional information. For example, you could set up a system of equations and solve for x and y using techniques such as substitution or elimination.
Step-by-step explanation:
find the values of x, z and y
The values of x is 82° , z is 98°and y is 69°. in the given triangle.
Is the sum of all triangle angles always 180 degrees?Because one outside angle of a triangle is equal to the total of the other two angles in the triangle, the angles of a triangle add up to 180 degrees. In other words, the third angle must join with the other two angles in the triangle to generate a 180-degree angle (the two angles that add up to form the outside angle).
we know that the sum of angle of triangle = 180
so,
x+ 60 +38=180
x=180-8
x=82°
and also
x+z = 180
z= 98°
for value of y
13 + 98 +y = 180
y= 69°
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PLEASE HELP ASAP
Which is the following is not an attribute of a right rectangular prism?
1 apex
12 edges
rectangular faces
square bases
Square bases is not an attribute of a right rectangular prism. Option D
What is a right rectangular prism?A right rectangular prism can be described as a three-dimensional solid shape with 6 faces, 12 edges, and 8 vertices.
It is sometimes called a cuboid.
All the faces of the right rectangular prism are rectangular in shape.
Examples of right rectangular prisms are books, bricks and aquarium.
Some properties of a right rectangular prism include;
There are 12 edges There are 8 verticesAll the faces are rectanglesAll the angles formed at the vertices are of 90 degreesThese prisms have no square base(s)
Hence, the right option is square bases.
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Alberts double number line worked example find mistake
Albert has made mistake in double number line in step 3 and 4.
The best time to utilize a double number line diagram is when the quantities have various units. The existence of several, maybe indefinitely numerous pairs of numbers in the same ratio, including those with rational number elements, can be illustrated using double number line diagrams. Unit rates (R) appear in the pair, just like in tables (R, 1).
Numerous equivalent ratios can be discovered using a double number line diagram. For instance, "Mix 5 cups of cranberry juice with 2 cups of soda water," is how a recipe for fizzy juice is written. Cranberry juice and soda water are combined in a 5:2 ratio. Equivalent ratios are produced by multiplying each constituents by the same number.
Albert has made mistake in step 3 and step 4,
Firstly he has written wrong units for the respective number line,
If ratio of 2 parts of blue and 5 parts of red is used(2:5)
The equivalent ratio will be 10:25
We get the desired output by multiplying (2:5) by 5.
The Correct units will be 5 instead of 20
And the number corresponding to 25 will be 10.
The correct double number line is drawn below.
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Solve the following system of equations: −2x + 3y = 7 y = 3x + 7 (−5, −1) (−2, 1) (−1, 4) (1, 3)
Answer:
(-2, 1)
Step-by-step explanation:
−2x + 3y = 7
y = 3x + 7
Since the second equation is already solved for y, we can use the substitution method. Substitute y of the first equation with 3x + 7 and solve for x.
-2x + 3y = 7
-2x + 3(3x + 7) = 7
-2x + 9x + 21 = 7
7x = -14
x = -2
Now substitute x in the second equation with -2 and solve for y.
y = 3x + 7
y = 3(-2) + 7
y = 1
Answer: (-2, 1)
Is this a perfect square trinomial X² 6x 9?
x² + 6x + 9, this is a perfect square trinomial, which is expressed as
(x + 3)².
What is trinomial?Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."
An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.
A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.
Given that,
x² + 6x + 9
= (x)² + 2(3x) + 9
= (x)² + 2(x)(3) + 3²
This is similar to a² + 2ab + b² = (a + b)²
so, we can write:
= (x + 3)²
= (x +3) (x + 3)
so, this is a perfect square trinomial.
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What kind of triangle has 25 90 65?
25-90-65 is a right-angle triangle because one of the angles is 90°.
A right-angle triangle or orthogonal triangle is a triangle in which one angle is a right angle (that is, a 90-degree angle), and two sides are perpendicular. The relationship between the sides and angles of the right triangle is the basis for trigonometry.
The hypotenuse is the facing side to the right angle. Legs are the adjoining sides to the right angle.
Properties of right angle triangle:
The right angle is the largest angle in a right-angle triangle.The hypotenuse, the opposite of the right angle, is the longest side.There are no obtuse angles in a right-angle triangle.Read more about right-angle triangles:
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A falcon was recorded travelling 100 metres in 0. 93 seconds.
What was its average speed
a in m/s to 3 significant figures
The average speed of the falcon to 3 significant figures will be 107.526 m/s
Distance travelled by falcon = 100 meters
Time taken by falcon to travel the distance = 0.93 seconds
As we have the formula for finding the average speed:
Average speed is a pace defined as a quantity divided by the time required to obtain that quantity. Meters per second is the SI unit of speed. The formula S = d/t is used to compute average speed, where S is the average speed, d is total distance, and t is total time.
Average speed can be find by simply dividing the total distance covered by falcon by the total time taken by him to cover the distance.
So, the value of the average speed will be = (100 m/0.93 sec) =107.526 m/s
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What is the equation for the linear relationship in slope intercept form?
Answer:
y=1/2x-3
Step-by-step explanation:
y=mx+b
y=1/2x-3
What unit is equal to Avogadro's number ?
Avogadro's number is a unitless object. It represents a number.
What is unit?
The mass of a particular piece of metal or the length of a particular rod are examples of quantities (specific properties) of objects that have historically been used to define measurement units. An object that has no units is known as unitless.
The proportionality factor that connects the number of constituent particles (often molecules, atoms, or ions) in a sample with the amount of material in that sample is called the Avogadro constant, also known as NA or L. It has a precise value of 6.02214076 × 10²³ reciprocal moles and serves as a SI defining constant.
The value of Avogadro's number is 6.02214076 × 10²³.
One mole of the chemical compound consists of 6.02214076 × 10²³ atoms.
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please help quickly
The polygons are similar. x = ___ Write your answer as a decimal
By using the fact that the two images are similar, we can write and solve a linear equation to get x = 3/2.
How to find the value of x?We know that the two figures are similar, then, if we take the quotient between the adjacent sides for both figures, these quotients should give the same value.
Thus, we can write the equation:
14/10 = (x + 9)/(x + 6)
Now we can solve that equation for x, if we multiply both sides by (x + 6) we will get:
(14/10)*(x + 6) = x + 9
Now we can multiply both sides by 10 to get:
14*(x + 6) = 10*(x + 9)
14x + 84 = 10x + 90
Now we can solve this linear equation for x.
14x - 10x = 90 - 84
4x = 6
x = 6/4
x = 3/2
That is the value of x.
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prove that cos x = sin x cot x.
Answer:
can u give me the brainliest
the answer is in the attached documents
b. How should Kiran change the quantities that he used
so that his smoothie tastes
just like Clare's?
Answer:
Kiran's smoothie would be more chocolatey than Clare's. All ingredients are doubled, but there is an extra teaspoon of chocolate syrup in his smoothie.
Step-by-step explanation:
(aryan)
What is a 100 sided shape called?
Answer:
hectogon or hecatontagon or 100-gon
Step-by-step explanation:
It is a hundred - sided polygon ( shape ). The sum of all hectogon's interior angles are 17640 degrees.
Answer:
Regular exercise has been shown to aid in the prevention and management of noncommunicable illnesses such as diabetes, heart disease, stroke, and a number of malignancies. Additionally, it lowers blood pressure, supports healthy body weight, and enhances well-being through enhancing mental health.
Step-by-step explanation:
Evaluate the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1)
The gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1)
This gradient is a vector that points in the direction of the greatest rate of increase of the function f(x, y, z) = log(x2 + y2 + z2). To evaluate this gradient, the partial derivatives of the function with respect to x, y, and z must be calculated.
The partial derivative of the function with respect to x is (2x / (x2 + y2 + z2)). When x is 1, this simplifies to 2/1. Similarly, the partial derivative with respect to y is 0, and the partial derivative with respect to z is (2z / (x2 + y2 + z2)), which simplifies to 2/1 when z is 1. Therefore, the gradient of f(x, y, z) = log(x2 + y2 + z2) at (1, 0, 1) is (2/1, 0, 2/1).
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find the height of the two pillar with same height
Answer:
ED = AB = 25√3
Step-by-step explanation:
Let ED = AB = X
DC = 100 - BC
Tan 60 = [tex]\frac{\sqrt{3} }{1} = \frac{ED}{DC}[/tex] = [tex]\frac{X}{100-BC}[/tex]
[tex]\sqrt{3} (100-BC) = X[/tex]
Tan 30 = [tex]\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}[/tex]
[tex]\frac{BC}{\sqrt{3} } = X[/tex]
[tex]\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC[/tex]
X = [tex]\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\[/tex]
X = 25√3