Answers
to get the equation of any straight line, we simply need two points off of it, let's use those points from the picture below.
[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{4}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{4 +2}{3 -1} \implies \cfrac{ 6 }{ 2 }\implies 3[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{3}(x-\stackrel{x_1}{1}) \implies y +2= 3 (x -1) \\\\\\ y+2=3x-3\implies {\LARGE \begin{array}{llll} y=3x\underset{(0~~,~~-5)}{\stackrel{\stackrel{y-intercept}{\downarrow }}{-5}} \end{array}}[/tex]
Related Questions
Keith has $500 in a savings account at the beginning of Summer. He wants to have at least $300 in the account by the end of the summer. He withdraws $25 each week for food, clothes and movie tickets how many weeks can Keith withdraw money from his account?
Answers
Answer: 8 weeks
Step-by-step explanation: 25x4 =100 double it that makes 25x8=200 then 500 - 200 = 300
Answer:
12
Step-by-step explanation:
500 is what we are starting with and 300 is the endpoint.
if he spends 25 a week, we can multiply 25 12 times and we get 300
25•12= 300
What is the value of x?
Answers
Answer: x = 7
Step-by-step explanation:
1. Set line PS equal to QR
2x - 3 = 11
2. Add 3 to both sides:
2x = 14
3. Divide both sides by two:
2x/2 = 14/2
4. Simplify
x = 7
What is the midpoint of the segment shown below
Answers
holaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answers
Answer:
Hello.
Step-by-step explanation:
Help me, please for my Maths Homework I don't understand I need answers
Answers
The resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)
Translating coordinates ofa triangleThe triangle is a shape that has three sides and angles. Given the coordinate points of the triangle given as:
A(-2, 3)
B (-2, 5)
C (-4, 5)
If the coordinate points is translated by the vector (2, -7), hence the resulting coordinate points will be:
A' = (2+2, 3-7) = (4, -4)
B' = (-2+2, 5-7) = (0, -2)
C' = (-4-2, 5-7) = (-6,-2)
Hence the resulting coordinate points after translation is (4, -4), (0, -2) and -6,-2)
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which of the following is an advantage of a cumulative frequency polygon over a histogram or frequency polygon?
Answers
The significant benefit of a cumulative frequency polygon above a histogram and frequency polygon is that it can demonstrate the total number of observations that are less than the upper limit of a specific class.
What is cumulative frequency polygon?A line segment-joined plot of a cumulative frequency against by the upper class boundary. An ogive would be any continuous cumulative frequency curve, along with a cumulative frequency polygon.
Some main points related to cumulative frequency polygon are-
The cumulative frequency graph can graphically represent data organized in the pattern of a cumulative frequency distribution. The method for drawing cumulative frequency polygons as well as cumulative frequency curves and perhaps ogives is similar. The only distinction in that a cumulative frequency polygon is formed by connecting points with line segments, whereas the cumulative frequency polygon is formed by connecting points with a free hand smooth curve.The cumulative frequency polygon is primarily a line graph drawn on graph paper by projecting the actual lower and upper limits of a class intervals on the x-axis and their respective cumulative frequencies on the y-axis.To know more about the cumulative frequency polygon, here
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Bryar gathered 10 eggs from the chickens. When he got to the house, he discovered all of the eggs were broken. Write an expression to represent this situation.
Answers
The expression when Bryar gathered 10 eggs from the chickens is 10 - x = 0.
How to calculate the expression?Let the eggs that are broken be represented by x.
Therefore, from the information, Bryar gathered 10 eggs from the chickens. When he got to the house, he discovered all of the eggs were broken.
Therefore, the expression will be:
10 - x = 0
This illustrates that there are zero left.
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solve the system by using any method. if a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 2(3x y)
Answers
By solving the equations, We get
[tex](\frac{34}{31} ,\frac{10}{31} )[/tex]
Explain Unique solution?
A unique solution to a set of linear simultaneous equations exists if and only if,
(A) There are the same number of equations and unknowns.
(b) Each equation is valid.
(c) All equations are independent and there is no linear connection between any two or more equations.
Given:
[tex]2(3x+y)=y-x+8[/tex]
[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]
Solving the equations,
[tex]2(3x+y)=y-x+8[/tex]
[tex]6x+2y=y-x+8[/tex]
[tex]7x+y=8\;\;\;\;\;------equation(1)[/tex]
[tex]x-\frac{4}{3}\;y=\frac{2}{3}[/tex]
[tex]\frac{3x-4y}{3}=\frac{2}{3}[/tex]
[tex]3x-4y=2 \;\;\;\;\;------equation(2)[/tex]
By solving equation(1) and (2), We get
[tex]x=\frac{34}{31}[/tex]
Substitute the value of x in equation(1),
[tex]7\;(\frac{34}{31}) +y=8[/tex]
[tex]y=8-7(\frac{34}{31} )[/tex]
[tex]y=8-\frac{238}{31}[/tex]
[tex]y=\frac{248-238}{31}[/tex]
[tex]y=\frac{10}{31}[/tex]
Therefore, The points (x, y) is,
[tex](\frac{34}{31} ,\;\frac{10}{31} )[/tex]
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Given the rule (x,y) --> (x-4, y+8), describe what transformation occurs to any given point.
Answers
For any given point, the transformation that occurs is
The x - coordinate is translated 4 units to the right and the y - coordinate is translated 8 units up. What are transformations?Transformations are mathematical operations that are performed on a function or object to change is shape or orientation or value.
The types of transformations that can be performed on an object or function include
TranslationDilationReflection andRotationHow to describe the trnasformation that occurs given the rule (x,y) --> (x - 4, y + 8).Given the transformation rule (x,y) --> (x - 4, y + 8), we see that both the x and y coordinated are shifted or translated.
The x - coordinate is translated 4 units to the right and the y - coordinate is translated 8 units up.So, for any given point, the transformation that occurs is
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what is inverse of matrix
Answers
Answer:
linear algebra, an n-by-n square matrix A is called invertible, if there exists an n-by-n square matrix B such that \mathbf {AB} =\mathbf {BA} =\mathbf {I} _{n}\ where Iₙ denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.
Answer:
Brainliest pls
Step-by-step explanation:
The inverse of a square matrix A, denoted by A-1, is the matrix so that the product of A and A-1 is the Identity matrix.
if 10 customers show up between 9:00 am and 10:00 am and 25 customers show up between 10:00 am and 11:00 am, then there is a variability in customer
Answers
if 10 customers show up between 9:00 am and 10:00 am and 25 customers show up between 10:00 am and 11:00 am, then there is a variability in customer Arrivals.
What is variability?The term "variability" (also known as "spread" or "dispersion") describes how dispersed a set of data is. You may use statistics to compare your data to other sets of data by using the term "variability" to indicate how much the data sets differ from one another.
In a data collection, there are four major approaches to describe variability:
Range: The difference between your smallest and largest piece in the set called the range.Interquartile range: The interquartile range is virtually identical to the range, with the exception that you only give the value for the "middle fifty" as opposed to the range for the whole data set.Variance: A data set's variance offers you a general indication of how evenly distributed your data is.Standard deviation: You may determine how closely your data is grouped around the mean using the standard deviation (the average).To learn more about variability , visit:
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a swimming pool has the shape of a right circular cylinder with radius 20 feet and height 10 feet. suppose that the pool is full of water weighing 62.5 pounds per cubic foot.
Answers
Answer:
The water required to pump all the water to a platform 2 feet above the top of the pool is is 6061310.32 foot-pound.
Step-by-step explanation:
Sam gets $6.00 each week for allowance. he wants to purchase a toy that costs $24.00. he also wants to purchase a movie that costs $6.00. label your drawings with toy
Answers
Answer:
$36
Step-by-step explanation:
$6.00+$24.00+$6.00
x+2)4x²+10x+2(
SOLVE THIS QUADRATIC EQUATION PLS
Answers
Step-by-step explanation:
4x^2 +10+ 2(2x+4)
4x^2 + 10x+4x+8
4x^2 +14x+8
4x^2+16x-2x -8
4(x+4)+2(x+4)
4+2(x+4)
6(x+4)
Solve for x in the equation x2-10x+25= 35-
X=5+2√ √5
O x=5± √√35
x=10+2√√/5
x = 10+ √√√35
0 0 0 0
Answers
The solution of the quadratic equation is x=5±√35 .
A quadratic equation is given by the equation which can be written in the form ax²+bx +c.
There are two solution of x for a quadratic equation. the graph of a quadratic equation is in the shape of a parabola in the cartesian plane.To solve a quadratic equation various methods are used:Completing of squaresMiddle term factorizationusing the quadratic formulathe given quadratic equation is :
x²-10x+25=35
Simplifying the equation we get:
or, x²-10x+25-35=0
or, x²-10x-10=0
Now we will solve the equation by completion squares method:
x²-10x-10=0
or, x²-2×x×5+5²-5²-10=0
or, (x-5)²=35
or, x-5=±√35
or, x= 5±√35
Therefore the solution of the quadratic equation is 5+√35 and 5-√35 .
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what is the arcsin of 3
Answers
The value of the arcsin of 3 is 90 - 100.998i
Inverse of Trigonometric functions
From the question, we are to determine the inverse sine or arcsine of the given number
The given number is 3
All the values for the sine of angles are less than or equal to 1
That is,
Given an angle θ,
sinθ ≤ 1
From this, we can infer that the arcsine of 3 will be an imaginary number.
The arcsine of 3 is
sin⁻¹(3) = 90 - 100.998i
Hence, the value of the arcsin of 3 is 90 - 100.998i
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Which of these fractions is equal to 1? A 31/31 B 17/18 C 1/5 D 7/4
Answers
Answer:
A
Step-by-step explanation:
31 divided by 31 is 1 (Since fractions are basically division)
B is incorrect because 17 is one number less than 18.
C is incorrect because 1 is four numbers less than what would equal a whole.
D is incorrect because the numerator is greater than the denominator, which would mean that the fraction 7/4 is greater than a whole.
A, however, is correct; 31 = 31, meaning they are the same number. If the numerator and denominator are equal, we know that we have a whole. Therefore, A is correct.
Please answer number one and two.
[tex]\sqrt{40+9}[/tex]
[tex]\frac{\sqrt[3]{125+3} }{2}[/tex]
Answers
The simplified forms of the given expressions are
7[tex]2\sqrt[3]{2}[/tex]Evaluating an expressionFrom the question, we are to evaluate the given radical expressions
The given radical expressions are
[tex]\sqrt{40+9}[/tex]
and
[tex]\frac{\sqrt[3]{125+3} }{2}[/tex]
Evaluating [tex]\sqrt{40+9}[/tex]
[tex]\sqrt{40+9}[/tex]
= [tex]\sqrt{49}[/tex]
= 7
Evaluating [tex]\frac{\sqrt[3]{125+3} }{2}[/tex]
[tex]\frac{\sqrt[3]{125+3} }{2}[/tex]
= [tex]\frac{\sqrt[3]{128} }{2}[/tex]
= [tex]\frac{\sqrt[3]{64 \times 2} }{2}[/tex]
= [tex]\frac{\sqrt[3]{64 } \times \sqrt[3]{2} }{2}[/tex]
= [tex]\frac{4\times \sqrt[3]{2} }{2}[/tex]
= [tex]\frac{4 }{2} \times \sqrt[3]{2}[/tex]
= [tex]2\times \sqrt[3]{2}[/tex]
= [tex]2\sqrt[3]{2}[/tex]
Hence, the simplified forms of the given expressions are
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calculate the percent of population each situation represents b) 90 out of a population of 450 people
Answers
The percent of population in the situation is 20 %.
Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.
We have to find the percentage of population 90 out of a population of 450 people represents.
We know that, the formula for percentage will be:-
(Given people/ Total people)*100
Here,
Given people = 90
Total people = 450
Hence, the percentage will be :-
= (90/450)*100 = (1/5)*100 = 20 % .
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7th GRADE SCIENCE QUESTION PLEASE ANSWER AS FAST AS YOU CAN I NEED IT (it can be 1 day late is fine... Ok I'll give you today like this minute and you can answer it when it is posted about 1-2 days but if you can answer it now that will be great)!!!
Question #1: State the role of a nucleus in a cell.
Answers
The longest side of a triangle is twice the length of the shortest side. The remaining side is 20 cm longer than the shortest side. The perimeter of the triangle is 132 cm. What is the length of each side?
Answers
Answer:
The triangle has sides lengths 28, 56, 48
Step-by-step explanation:
Let x = the shortest side
So then the longest side will be 2x, because the question said that "the longest side... is twice the length of the shortest side" Then the third side would be x + 20.
The perimeter was given so add all the sides and set it equal to 132.
x + 2x + x + 20 = 132
Combine like terms.
4x + 20 = 132
Subtract 20
4x = 112
Divide by 4.
x = 28
Then use x = 28 to find the lengths of all the sides.
Shortest Side:
x = 28
Longest Side:
2x
= 2(28)
= 56
Third Side:
x + 20
= 28 + 20
= 48
f(x)=7/3x -9 for f(-3)
Answers
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable. If f(x)=7/3x -9 then f(-3) is -88/9.
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
Given function is
f(x)=7/3x -9
where x=-3.
Subtract x=-3 in the above function.
f(-3)=7/3(-3) - 9
f(-3)=7/-9 - 9
f(-3)=-7/9-9
f(-3)=(-7-81)/9
f(-3)=-88/9
Therefore f(-3) is -88/9.
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40) SHOPPING Stevenson's Market is selling 3 packs of stylus pens for $5.00. How
much will 10 packs of stylus pens cost at this price?
Answers
The cost of ten pack of stylus pen is $(50/3).
This problem can be solved by unitary method and can be understood by the following process.
In this method we have to determine the cost of a unit of product and then the total amount by multiplying the unit cost by the desired quantity what we want.
Here, it is given that three packs of stylus pen costs $5.
Cost of one pack of stylus pen = $ 5/3
Therefore cost of 10 packs of stylus pen = $(5/3)*10
= $(50/3)
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what number can u multiply 8 by to get 120 how can you use this number to solve part of the problem
Answers
Answer: 15
Step-by-step explanation:
n=number
8*n=120
n=120/8
n=15
Help! factoring out the gcf from the equation 4w with an exponent of 3 subtracted from 12w with an exponent of 2
Answers
The GCF of [tex]12w^{2} - 4w^{3}[/tex] is [tex]4w^{2}[/tex].
The Greatest Common Factor (GCF) of two or more numbers is defined as the factors which is common and highest .
For Example The GCF of 6 and 8
express 6=2*3
8=2*2*2. since 2 is common in both the GCF is 2.
In the given question
we need to factor out gcf from [tex]12w^{2} - 4w^{3}[/tex]
first express both terms in prime factors
[tex]12w^{2} =3*4*w*w[/tex]
and
[tex]4w^{3} =4*w*w*w[/tex]
the equation becomes
[tex](3*4*w*w-4*w*w*w)[/tex]
we can see that [tex]4*w*w[/tex] is common in both the terms .
So we can write [tex]4w^{2} (3-w)[/tex]
Therefore [tex]4w^{2}[/tex] is the gcf by factoring of [tex]12w^{2} - 4w^{3}[/tex].
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Students were surveyed about what summer camp they would be attending.
Camp Name Number of Students
Camp Arrowhead 130
Camp Kern 220
Camp Redwood 170
Of the students that stated they would be going to Camp Redwood, 20% did not go to camp. Of the students that stated they would be going to Camp Kern, 15% did not go to camp. How many more students went to Camp Kern than Camp Redwood?
Answers
If the students that stated they would be going to Camp Redwood, 20 percentage did not go to camp and the students that stated they would be going to Camp Kern, 15 percentage did not go to camp, then 51 more students went to camp kern than camp redwood
The total number of students in Camp redwood =170
Number of students who didn't attend the camp redwood = 170×(20/100)
=34 students
Number of students who went to camp redwood =170-34
=136 students
Total number of students in Kern camp = 220
Number of students who didn't attend the camp Kern=220×(15/100)
=33 students
Number of students who went to camp kern =220-33
=187 students
How many more students went camp Kern than Camp Redwood= 187-136
=51
Hence, 51 more students went to camp kern than camp redwood
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Angelo drove home from college traveling an average speed of 71.7 mph and drove back to the college the following week at an average speed of 64.1 mph. if the total round trip took 5 hours, how much time did it take angelo to drive from home back to college? express the time in hours and minutes. round to the nearest minute.
Answers
When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip then the time taken to travel from home to college is 2.63 hours
Given,
The average speed from college to home = 71.7 mph
The average speed from home to college = 64.1 mph
We know,
Speed = Distance / Time
Consider the total distance as x
Time taken = Distance / Speed
Then the time taken to travel from college to home = [tex]\frac{x}{71.7}[/tex] hours
time taken to travel from home to college = [tex]\frac{x}{64.1}[/tex] hours
Total time taken = 5 hours
Then the equation will become
[tex]\frac{x}{71.7}+\frac{x}{64.1}=5[/tex]
Cross multiply the terms
[tex]\frac{64.1x+71.7x}{(71.7)(64.1)}=5\\ \frac{135.8x}{4595.97}=5[/tex]
135.8x= 5×4595.97
135.8x=22979.85
x=169.21
Time taken to travel from home to college =[tex]\frac{169.21}{64.1}[/tex]
=2.63 hours
Hence, When Angelo drove home from college with an average speed of 71.7 mph and back to college with an average speed of 64.1 mph, she took 5 hours for full trip, then the time taken to travel from home to college is 2.63 hours
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Solve for y 11x+y= 18x
Answers
Answer: y = 7x
Step-by-step explanation:
11x + y = 18x
-11x -11x
y = 7x
How many 1 3/4-inch long machine bolt blanks can be cut from a 5-foot length of stock? allow 7/32 inch for waste on each blank.
Answers
The number of the 1(3/4) inch blocks will be 34 out of the 5 feet of stock.
What is an expression?The mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.
Given that 1 3/4-inch long machine bolt blanks can be cut from a 5-foot length of the stock. The number of the blocks will be calculated as below:-
Number = 5 foot / ( 1(3/4)
Number = 60 / ( 7/4)
Number = 34.2
Therefore, the number of the 1(3/4) inch blocks will be 34.
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What is the solation to the equation?
√x+7= -2
Answers
√x+7 The solution to the equation is x=-3.
Square root: If we take the square root of a number and then take the square of the outcome, we get the original number back again.
e.g. 4 = 2 and 22 = 4.
We can say that the square root and the square cancel each other out. They are the inverse of each other.
If we have a number written with the index 2 ( squared) then taking the square root simply means that we leave out the 2 ( this only applies to positive numbers ).
We can therefore take any squared numbers that are under the square root sign out from under the root sign by leaving out the power 2.
The solution to the equation√x+7= -2.
√x+7= -2
First we take Squaring on both sides
(√x+7)2= (-2)2
x+7 = 4
x=-3.
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