Three points can define a plane in a three-dimensional space.
Because a plane can be defined as a flat surface that extends infinitely in all directions, three points in space are sufficient to specify a plane. A plane can be determined by any three non-collinear points, i.e., points that are not on the same straight line, as long as they are not on the same line. Imagine three points in space, A, B, and C. We draw straight lines from A to C to create a plane. The triangle formed by these lines is a flat surface. A plane can be made by endlessly extending the flat surface in all directions.
The triangle formed by the three points A, B, and C, which are not collinear, extends in all directions to form a plane. A plane is therefore defined by three points. It's crucial to remember that any new point that lies on the same plane as A, B, and C will also be connected to the three defining points by the same straight line.
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What are the 3 types of multiplication?.
Answer: Commutative, associative, distributive
Step-by-step explanation: I hope this helped!
What is the factored form of x² +8x +16?.
To find the factored form of the quadratic equation x^2 + 8x + 16, we can use the technique of factoring by grouping.
First, we write the equation in the form of (x^2 + ax + b) + (x + c) = 0
x^2 + 8x + 16 = 0
Next, we find two numbers that multiply to b and add to a, in this case, b = 16 and a = 8
We can factor out a common factor of x from the first two terms and x + 4 from the last two terms: x^2 + 8x + 16 = (x^2 + 8x) + (16)
Finally, we can factor out a common factor of x + 4 from both terms:
x^2 + 8x + 16 = x(x + 8) + 4(4)
So the factored form of x^2 + 8x + 16 is (x+4)^2.
You can also find the factored form of the quadratic equation x^2 + 8x + 16 by using the difference of squares method:
x^2 + 8x + 16 = (x+4)^2
It's worth noting that this is a perfect square trinomial, which means that it can be factored into the square of a binomial.
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A linear expression is in ___ when it is expressed as the product of its factors.
A linear expression is in polynomials when it is expressed as the product of it's factor
What is linear expression?A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power. In other words, none of the exponents can be greater than 1. For example, x² is a variable raised to the second power, but x is a variable raised to the first power.
When two linear factors are expressed together the result forms a polynomial.
A polynomial is an expression in which the power of it's variable is higher than 1. quadratic expression is also an example of polynomial.
For example if an expression is given as (x+2)(x+3). The result of the expression will give x²+5x+6 which is a quadratic expression and a polynomial.
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Find an equation of a line with a slope of -4 and having the point (2, 0) on the line. Then graph the line.
Answer: Hi there! Your equation would be y = −4x + 8
Step-by-step explanation: I hope this helps!
Write a function of the form f(x) = A sin (Bx-C) for the given graph.
The sine function graphed is given as follows:
y = 0.5sin(x - π/4).
How to define the sine function?The sine function for this problem is defined as follows:
y = Asin(Bx - C).
For which the parameters are given as follows:
A is the amplitude.The period is of 2π/B.C is the phase shift.The difference between the highest value and the lowest value is of 1, hence the amplitude of the function is givne as follows:
2A = 1
A = 1/2
A = 0.5.
The period of the function is of 2π, hence the parameter b is obtained as follows:
2π/B = 2π
B = 1.
The sine function, without phase shift, should pass through the origin, while the function here was shifted right π/4 units, hence the parameter C is given as follows:
C = π/4.
Hence the function is:
y = 0.5sin(x - π/4).
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Alisha wants to enlarge a photograph to make into a poster for her room. The photograph is 6 inches tall.The poster will be created using a scale of 4n5 inches=2inches.How tall would the poster be?
The enlarged size of the poster will be 13.5 inches.
What is a scale factor?A scale factor is defined as the ratio of the scale of a given original object to the scale of a new object that is its representation but of a different size (bigger or smaller).
The scale factor is defined as the proportion of the new image's size to that of the previous image.
Given that Alisha wants to enlarge a photograph to make into a poster for her room. The photograph is 6 inches tall. The poster will be created using a scale of 4.5 inches = 2 inches.
Scale factor = 4.5 / 2 = 2.25
The enlarged size of the poster will be calculated as:-
Size = 6 x 2.25
Size = 13.5 inches
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Explain one concept that you’ve learned in geometry. Please answer in at least two complete sentences
One concept that I have learnt in geometry is the congruency of triangles.
What is a concept in geometry?We know that in geometry, the core of the study is the shapes. We have studied several shapes and the properties of the shapes and there are a lot of concepts that have been discussed.
One of the important concepts of geometry that we have discussed is the congruency of the triangles. There are several reasons why we can say that the triangles are congruent such as;
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yo help i dont get this at all pls
[tex]x~~ : ~~(x+5)~~ = ~~4~~ : ~~5\qquad \implies \qquad \cfrac{x}{x+5}=\cfrac{4}{5} \\\\\\ 5x=4x+20 \implies x=20[/tex]
URGENT!
find the value of x in each supplementary angle pair
[tex] \frac{x}{3° } + 49° = 180° \\ [/tex]
Cross multiply
[tex]x + 147° = 180°[/tex]
simplify
x = 180° - 147°
answer : x = 33°
How do you write 10 more than a number?.
To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.
To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.
In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.
This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.
Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.
Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.
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The grocery store has bulk pecans on sale, which is great since you're planning on making 6 pecan pies for a wedding. How many pounds of pecans should you buy?
First, determine what information you need to answer this question, then click here to display that info (along with other info).
You will need to buy ____ pounds of pecans.
Give your answer accurate to at least one decimal place.
Answer:
2.29 pounds.
Step-by-step explanation:
The following is the analysis for the response to this query:
There must be some relationship among both the volume and the weight.
According to the given label's information, one cup weighs 99 grams. Given that there are 99/453.6 pounds for every cup as well as you require 7*1 1/2 cups, multiplying 10.5 cups by 99/453.6 pounds for every cup results in 2.3 pounds. A pound (avoirdupois) is defined as 453.6 grammes.
Another way to write this would be:
7 (pecan pie) * 1.5 (cup/pecan pie) * 99 (gram/cup) * 0.0022 (pounds/gram) = 2.292 pounds
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What are the 3 methods in solving system of nonlinear equations?.
There are several methods that can be used to solve a system of nonlinear equations, but three common ones are: substitution method, elimination method and graphing method.
Substitution method: This involves isolating one variable in one equation and substituting it into the other equation to eliminate that variable. You can then solve for the remaining variable and substitute it back into the original equation to find the solution.
Elimination method: This method involves adding or subtracting the equations in such a way as to eliminate one of the variables. Then you can solve for the remaining variable and substitute it back into the original equation to find the solution.
Graphical method: This method involves graphing both equations on the same coordinate plane and finding the point of intersection of the two lines. The coordinates of this point will be the solution to the system of equations.
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A veterinarian's scale weighs animals to the nearest one eighth pound. The list below shows the weights, in pounds, of the last 14 dogs that the veterinarian saw. 15⅛, 19, 17½, 15⅛, 16¼, 17½, 17½, 18¼, 16⅝, 14¼, 19, 17⅜, 17⅛, 18 Create a line plot to show the data. How should the line plot's scale be labeled to show these data?
Answer:
A line plot is the most appropriate way to visualize these data. The scale should be labeled starting at 14 and going up to 19, with increments of 1/8 pound. For example, the x-axis labels could be 14, 14⅛, 14¼, 14⅜, 14½, 14⅝, 14¾, 14⅞, 15, 15⅛ and so on up to 19.
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Point A represents a positive number. Which point represents the opposite of that number?
A number line. Point E is 5 units to the left of zero. Point D is 3 units to the left of zero. Point C is 2 units to the right of zero. Point A is 2 units to the right. Point B is 4 units to the right.
The point opposite to point A is not labeled in the number line.
What is a number line?A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.
Given a number line,
for any number line points left of zero are negative numbers and points right to the zero are positive numbers,
Given points, Point A is 2 units to the right = +2
Point B is 4 units to the right = +4
Point C is 2 units to the right of zero = +2
Point D is 3 units to the left of zero = -3
Point E is 5 units to the left of zero = -5
so the point opposite to +2 is -2 which is 2 units left of zero,
but it is not given on the labeled points.
Therefore, the opposite point of A is not labeled.
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(a) this is part of thr fibonacci sequence;21,34,55
what is the next term of the sequence
a 68
b 76
c 88
d 89
Answer:
89
Step-by-step explanation:
fibonacci sequence is a famous sequence where each number is the sum of the last two.
Therefore :
34+55 will give us the next number which is 89
Jake is buying baseball cards for his brother in college. The price of a card is based on its condition. The table shows the total cost of x number of cards for each condition.
Condition Total Cost
Poor x
Fair 1.75x
Good 9.5x
Excellent 20.5x
Like New 45.65x
He buys 6 that are in fair condition, 5 that are in good condition, and 2 that are in excellent condition. The shipping cost for the baseball cards is $4.00. What expression represents the total cost of buying and shipping the baseball cards?
The expression that represents the total cost of buying and shipping the baseball cards,
= 6(1.75) + 5(9.5) + 2(20.5) + 4
What is addition?Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.
Given:
Jake is buying baseball cards for his brother in college.
The price of a card is based on its condition.
The table shows the total cost of x number of cards for each condition.
He buys 6 that are in fair condition, 5 that are in good condition, and 2 that are in excellent condition.
The shipping cost for the baseball cards is $4.00.
The expression that represents the total cost of buying and shipping the baseball cards,
= 6(1.75) + 5(9.5) + 2(20.5) + 4
= 10.5 + 47.5 + 41 + 4
= 103
Therefore, the total cost is $103.
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What is the Cartesian product of AxB of A ={ 1 2 and B ={ a/b }?.
The Cartesian product of A(1, 2) and B(a, b) is the set A × B, i.e., {(1, a), (1, b), (2, a), (2, b)}.
Given sets are:
A(1, 2)
B(a, b)
A × B = {1, 2} × {a, b}
= {(1, a), (1, b), (2, a), (2, b)}
The Cartesian product, which consists of all ordered pairs of items with the first element coming from the first set and the second element coming from the second set, and so on, is a set created from two or more given sets. Once more, an ordered pair set results from the Cartesian product of sets.
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Determine whether the triangle is similar
true or false?
Answer:
True
Step-by-step explanation:
from the figure they have an equal angle and an opposite angle, consequently also the third angle is congruent, therefore they are congruent, therefore also similar
Please help I need answers asap please show your work
Answer:
#1) [tex]\frac{1}{7}[/tex]
#2) 4
Step-by-step explanation:
#1) 37x=9x+4
37x=9x+4
-9x
28x=4
28 28
answer: [tex]\frac{4}{28} = \frac{1}{7}[/tex]
#2) 2x+3=11
2x+3=11
-3
2x= 8
2 2
answer: [tex]\frac{8}{2} =4[/tex]
I need some help please
Answer:
x = 39
m ∠1 = 63°
m ∠2 = 117°
Step-by-step explanation:
m∠1 + m∠2 = 180° since they are adjacent linear angles lying on the same straight line
Therefore x + 24 + 3x = 180
4x + 24 = 180
4x = 180-24 = 156
x = 156/4 = 39
Therefore x = 39 (a)
FOr (b) substitute this value of x = 39 into each equation
m∠1 = x + 24 = 39 + 24 = 63°
m∠2 = 3x = 3(39) = 117°
Larry and Bonny began saving money the same week. The table below shows the
models for the amount of money Larry and Bonny had saved after x weeks.
Larry's Savings
f(x)=8x+15
Bonny's Savings
g(x)=5,5x+25
After how many weeks will Larry and Bonny have the same amount of money saved?
Equation:
Answer:
Answer:
4
Step-by-step explanation:
8x + 15 = 5.5x +25
so 2.5x =10
x=4
What type of graph is used for two variable analysis?.
A scatter plot or scattergram chart will show the relationship between two different variables or reveals distribution trends.
Now, According to the question:
A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
Use a scatter plot to determine whether or not two variables have a relationship or correlation. Are you trying to see if your two variables might mean something when put together? Plotting a scattergram with your data points can help you to determine whether there's a potential relationship between them.
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What does the subtraction of 7 from 9 mean?
Answer: it mean 7-9.
Step-by-step explanation:
7 is smaller than 9, so the answer is going to be negative. I like to do
7-9
Is basically just 9-7, just put a negative label
So 7-9 can be solved as 9-7=2 slap on a negative sign and -2! Hope this helps!
What is the value of X? 3 ,4,5,6,8
Answer:
but it is not possible to determine the value of X with the information provided. The numbers 3, 4, 5, 6, and 8 are all different values, and without any additional context or information, it is impossible to determine which one is X.
It would be helpful if you could provide more information such as an equation or some context, to help determine the value of X.
Painter A can paint the house in 50 hours. Painter B can paint the same house in 35 hours. If they work together, about how many hours should it take them to paint the house?
It will take 20.6 hours to paint the house if both painter A and painter B worked together.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p: q : : r : s.
This is same as p : q = r : s or p/q = r/s
Let F represent the house fully painted.
Painting done by painter A in 50 hours = F
Painting done by painter A in 1 hour = F/50
Painting done by painter B in 35 hours = F
Painting done by painter B in 1 hour = F/35
If they both paint together,
Painting done by painter A and painter B in 1 hour = F/50 + F/35
= 85/1750 F
= 17/350 F
Time taken to paint 17/350 F = 1 hour
Time taken to paint F = 1 / (17/350)
= 20.588
≈ 20.6 hours
Hence time taken to paint the house by both working together is 20.6 hours.
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How do you solve 2nd degree equations with 2 variables?.
The solution is the set of values for the two variables (x, y) that satisfy both equations.
To solve a system of two equations with two variables that are both quadratic (2nd degree), you can use the following steps:
Write the two equations in standard form, which is ax² + bx + c = 0 for each equation, where a, b, and c are coefficients.
Solve each equation separately for one variable by factoring or by using the quadratic formula.
Substitute the value of one variable from one equation into the other equation, and solve for the other variable.
Substitute the value of the other variable from the previous step back into one of the original equations to find the value of the first variable.
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What dose quantity mean
Answer: Quantity is the indefinite amount of any material item. It's a measurement of something.
Step-by-step explanation:
I hope this helps!
y divided by -8 = 8
Giving 10 points for correct answer
Answer:
y = -64
Step-by-step explanation:
y / -8 = 8
y = -64
Answer:
y= -64
Step-by-step explanation:
I don't understand the question but
y/-8 = 8
y = 8×-8
y = -64
Can someone please help solve this math problem? There are two boxes underneath the graph. I have to find the domain/range in this math problem, it is listed in the picture below, Thanks!
Domain:
Range:
Answer:
Domain: is -4 ≤ x ≤ 1
which can be expressed in interval notation as
[-4, 1]
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
Step-by-step explanation:
The domain is the set of x values from minimum to maximum
The range is the set of y values again from minimum to maximum
Minimum value of x = -4
Maximum value = 1
So range is -4 ≤ x ≤ 1 which can be expressed in interval notation as
[-4, 1]
Minimum y-value is -3 and maximum y-value is 2
Range is -3 ≤ y ≤ 2
or in interval notation: [-3, 2]
Mr. Berry had $120,000 in a retirement account. The account paid 4.25% simple interest. How much money was in the account at the end of 10 years?
