11. Using the equation: y + 2 = 3(x - 1).
a) Identify the slope and y-intercept.
b) Graph the equation.
c) Does the point (0,0) satisfy the equation?
Justify your answer.
Answers
For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.
Linear Function
An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex].
m= the slope.
[tex](x_1,y_1)[/tex]= the coordinate of a point.
For the given example: m=1 and b=19.
The question gives: y + 2 = 3(x - 1). Therefore,
y + 2 = 3(x - 1)
y=3x-3-2
y=3x-5
Letter A - Identify the slope and y-interceptIf y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:
m= the slope. It can be calculated for Δy/Δx.
b= the constant term that represents the y-intercept
Thus, the slope is 3 and the y-intercept is -5.
Letter B - Graph the equation.For this, you should do a table with points
x y= 3x-5
-2 y=3*(-2)-5=-6-5= -11
-1 y=3*(-1)-5=-3-5= -8
0 y=3*(0)-5=0-5= -5
1 y=3*(1)-5=3-5= -2
2 y=3*(2)-5=6-5= 1
Draw a graph from these points, see the attached image.
Letter C - Does the point (0,0) satisfy the equation?The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.
y= 3x-5, for x=0
y=3*0-5
y=0-5
y=-5
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Related Questions
What is an equation of the line that passes through the points (-2, -7) and
(-1, -3)?
Answers
m= (6- 3)/ (-5 -1)
2x - y + 11= 0
Explanation
Double points. Please help!
Answers
which equals 20.21433097
or 20.2 to 1 dp
A group of students are at a library.
6 of them leave. 7 students are left. Which part-part-whole
model shows how many students were at the library to start?
Answers
The total number of students at library using part part whole model is 13.
What is part part whole model ?
The idea that numbers may be divided into parts, often known as the part-whole model or part-part-whole reasoning, is one that can be used to the study of mathematics. The relationship between the entire number and its component components will be clear to children utilising this model, which will aid learners in connecting addition and subtraction.
Here Number of student who leave library = 6
Number of students who stay at library = 7
Here we have to take Number of student who leave library as one part and Number of students who stay at library as another part . Then
Total number of students at library at start = 6+7 = 13.
The part part whole model like,
=> Total = 13
Part=6 Part=7
Hence the Total number of students is 13.
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If two fair dice are rolled, find the probability that the sum of the dice is 9, given that the sum is greater than 3.
The probability is
Answers
The probability that the sum of the dice is 9 is, 4/33.
What is dice?
Dice are little, thrown-away devices with marked sides that can rest in various locations. They are frequently employed in tabletop games including dice games, board games, role-playing games, and games of chance to provide random values.
Let two fair dice are rolled.
So the possible number of outcomes are,
(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)
(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)
(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)
(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4,6)
(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)
(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)
There are total 36 outcomes.
There are 33 outcomes with sum greater than 3.
The outcomes with sum greater than 9 are, 4 which are (3, 6), (4, 5), (5, 4) and (6, 3).
Hence, the probability that the sum of the dice is 9 is, 4/33.
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Directions: Match the situation provided to the correct equation/inequa
Situation:
Wyatt is saving up
money for a new
game. It costs $60,
including tax. He has
already saved $20.
At least how much
more money, X,
does he need to
save?
Inequality/Equation:
Innquality/Equation:
Solution
Graphed Solution:
Solution
Answers
The equation can be given as X+20 = 60
Wyatt needs to save $40 to buy the new game.
What is an equation?
An equation is an expression which has an equality symbol in it.
We are given that, Wyatt is saving up money for a new game. It costs $60,
including tax.
He has already saved $20. At least how much more money, X, does he need to save
Hence the equation can be given as
X + 20 = 60
On solving the equation X = 40
Hence Wyatt needs to save $40 to buy the new game
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f(-10) = 4, ƒ(8) = -5
Answers
Answer: f(x)=-.5x-1
Step-by-step explanation:
I believe this is the answer you are looking for. Because if you plug in -10 for x and it gives you 4. Do the same with 8 and you get -5
Hope this helps :)
A survey of the worlds nation in 2004 shows a strong positive correlation between percentage of the country using cell phones and life expectancy and years at birth
Answers
1. No This survey does not mean that cell phones are good for your health.
2. The factor that can be used as the best explanation for the strong correlation would be the general economic conditions of the people.
What is meant by a strong correlation?When one variable's value rises, the other variable's value also rises in a similar way. For instance, a student's exam score tends to be greater the more hours they study. Exam results and study time have a significant positive link.
A strong correlation, also known as a high correlation, indicates that two or more variables have a significant relationship with one another, whereas a weak or low correlation indicates that the variables are rarely associated.
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complete question
A survey of the world's nations in 2004 shows a strong positive correlation (hence, a positive association) between percentage of the country using cell phones and life expectancy in years at birth.
a. Does this mean that cell phones are good for your health? select one: ____ yes ____ no
b. What might best explain the strong correlation (as a lurking variable)?
Select one:
_____ Percent of young people
____ General economic conditions of the country
____ Percent of pop. living in cities
18. Write three valid congruency statements given the triangles below.
Answers
QR = ST
TU = PQ
Triangle PQR = Triangle STU reason=ASA
The three valid congruency statements are; Triangle PQR = Triangle STU
What are congruent angles?Angles who are of same measurement are called congruent.
Suppose that two angles ∠A and ∠B are of same measure, then
[tex]m\angle A = m\angle B[/tex] is the notation to say that they are of same measurement, where the small m shows that its the measurement of the angles they're preceding.
Congruence statement states that a statement used in geometry that simply says that two objects are congruent, or has the same shape and size.
Also, we can make congruence statements in words or in symbols. Using symbols we use the congruence symbol i,e ≅ to indicate that two objects are congruent.
In the given triangles;
Angle T = Angle Q
QR = ST
TU = PQ
Triangle PQR = Triangle STU reason=ASA
Therefore, the three valid congruency statements are;
Triangle PQR = Triangle STU
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The angles of elevation of the top of a tower with respect to points A and B are 30° and 75°respectively. Points A and B are 175 feet apart and at equal elevations, and the base of the tower lies on the line between them. Find the height of the tower. Round your final answer to the nearest ten thousandth.
Answers
The height of the tower is 87.4870 feet
What is Angle of elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.
The body of the calculation is contained in the attached file.
In conclusion, the height of the tower to the nearest ten thousandth is 87.4870 feet
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raina swam 8 kilometers against the current in the same amount of time it took her to swim kilometers with the current. the rate of the current was kilometer per hour. how fast would raina swim if there were no current?
Answers
The speed at which raina can swim if there is no current is 3 km/hor 3 kilometers per hour.
Given that,
In the same length of time it took raina to swim kilometers with the river, she was able to swim 8 kilometers against it. The current flowed at a kilometer per hour rate.
Distance 1 * (Raina's velocity - current velocity) = Distance2 * (Raina's velocity + current velocity)
16 * (Raina's velocity - 1) = 8 * (Ivan's velocity + 1)
(16 * Raina's velocity) - 16 = (8 * Ivan's velocity) +8
8 * Raina's velocity = 24
Raina's velocity = 3 kilometers per hour
As a result, Raina can swim at a speed of 3 km/hr in the absence of a current.
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Can someone please help me this is due tomorrow!
Answers
Answer:
I can use the given (algebraic expression) 24c+12 to find the total cost of the order
The expression has two (terms). They are 24c and 12
In 24c the number 24 is the (coefficient) and the letter c is the (variable).
The term 24c represents a (product)
To find the total cost of the order I can (evaluate) the given expression
I have to (substitute) the given value for the variable then I can follow the (order of operations) to simplify the expression
24c+12
24(6)+12
144+12
156
The total cost is 156
Hope this helps :)
A 100-gallon fish tank fills at a rate of x gallons per minute. The tank has already been filling for 5 minutes. The
function f(x)=100/x-5 represents the remaining time in minutes needed to fill the tank. How is the graph of the parent function f(x)=1/x
transformed to create the graph of the function f(x)=100/x-5?
Answers
Answer:
The parent graph has been dilated by a scale factor of 100 and has been moved to the right by 5 units
Step-by-step explanation:
The change made to f(x) = 1/x to f(x) = 100/x is a dilation by a scale factor of 100(the function has been multiplied by 100) .
The transformation of function f(x) = 100/x to f(x) = 100/x-5 is moving o the right 5 units (whenever a constant, let's call it "c", is being subtracted from the x when graphing, it means the graph has moved "c" units to the right, and vice versa--if "c" was added to x, then the graph would be moved "c" units to the left.).
TL;DR: f(x-c) means c units to the right, f(x+c) means c units to the left. f(x)*c means a dilation of c units.
Find the vertex of the parabola y=2(x-1)2+4.
Answers
Answer:
(1, 4)
Step-by-step explanation:
You want the vertex of the parabola y=2(x-1)²+4.
Vertex formThe vertex form of the equation for a parabola is ...
y = a(x -h)² +k . . . . . . 'a' is the scale factor; (h, k) is the vertex
Comparing the given equation to the vertex form, we see that ...
a = 2
h = 1
k = 4
Then the coordinates of the vertex are (h, k) = (1, 4).
An animal shelter has 2 cats for every 3 dogs. If there are 45 animals in the shelter, how many dogs are there?
Answers
Answer: 27 dogs
Step-by-step explanation: 2 cats + 3 dogs= 5 in total for animals. 2/5x45=18 cats
3/5x45= 27 dogs
27+18=45 animals
There is 27 dogs in the shelter
3² × 3 = 3² Find the value of x.
Answers
The value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
According to the question,
We have the following information:
3² × [tex]3^{x}[/tex] = 3²
We know that when two numbers with the same base are in multiplication then the powers of the numbers are added. So, in this case, 2 will be added to x. And this expression of addition will be equal to the powers of the number on the right hand side.
Now, we have the following expression:
2+x = 2
x = 2-2
x = 0
Hence, the value of x in 3² × [tex]3^{x}[/tex] = 3² is 0.
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I don’t know the answer to this can you please help me
Answers
Answer:
The answer is 24 I think
Step-by-step explanation:
just multipy the numbers
There are approximately 420 national parks in the United States. A survey
showed that 85% of the national parks allow overnight camping. Based on
this information, how many national parks allow overnight camping?
Answers
420 times .85
Answer:
357 national parks
Step-by-step explanation:
420x85/100
420x17/20
21x17=
357
Find d, the distance across the lake.
Answers
how to solve/fhfhfhfhfhfhf
Answers
Answer:
b
Step-by-step explanation:
the right side base angle and 80° are vertically opposite angles and are congruent, both 80°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
123° is an exterior angle of the triangle , then
x + 80 = 123 ( subtract 80 from both sides )
x = 43
Lines m and n are parallel and are intersected by transversal p.
Which angle corresponds with angle 2?
3
5
6
8
Answers
The angle which corresponds with angle 2 given that; lines m and n are parallel and are intersected by transversal p is; angle 6.
What are corresponding angles?Corresponding angles by definition are any pair of angles each of which happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.
Therefore, it follows from the definition above that the angle which is corresponding to Angle 2 as required in the task content is; angle 6.
This follows from the fact that angles 2 and 6; each happens to be on the same side of one of two lines cut by a transversal and also on the same side of the transversal.
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a column contains phone numbers such as (801)-555-1234. what function should you use to extract the last four digits?
Answers
RIGHT function should be used to extract the last four digits from a column containing phone numbers.
The Excel TEXT functions section includes the RIGHT Function[1]. A predetermined number of characters from the end of a provided text string will be returned by the function.
The RIGHT function can be helpful in the financial analysis if we want to extract characters from a text string's right side. It is typically used in conjunction with functions like VALUE, SUM, COUNT, DATE, DAY, etc.
Formula is=RIGHT(text,[num chars])
The following arguments are used by the RIGHT function:
Text is the original text string (mandatory argument).
The number of characters to be returned from the end of the provided text is specified by the optional argument Num chars. It specifies how many characters will be taken, beginning on the right side of the text. If the argument is omitted, the value of 1 by default is used.
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3 quarts of blueberries for every 4 quarts of strawberries how many quarts of strawberries do they need for 9 quarts of blueberries?
Answers
Trevor is a high school quarterback. On
average, out of each 16 attempts, he
completes 5 out of 8 passes and throws 1
pass that is intercepted. If Trevor passes
40 times, how many completions would
he be expected to make? (setting up proportions )
Answers
The total number of completions Trevor be expected to make is 25.
Define the term proportions?Proportion is mostly discussed using ratios and fractions. A fraction is written as a/b, while a ratio is represented as a:b, and a proportion implies that two ratios remain equal. In this case, a and b can be any two integers. According to the notion of proportion, two ratios are in proportion when they are equivalent. It is a formula or statement that shows that two ratios and fractions are equivalent.For the given question.
Let the number of completion by Trevor be 'x'.
Trevor completes 5 out of 8 passes.
Total passes are 40
Then, proportions set up is-
5/8 = x/40
x = 25
Thus, the total number of completions Trevor be expected to make is 25.
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Solve:
2000(2000^2000)
(A) 2000^2001
(B) 4000^2000
(C) 2000^4000
(D) 4,000,000^2000
(E) 2000^4,000,000
PLEASE ANSWER ASAP!!!
Answers
Answer:
They all come out to be infinity
a javalina rancher wants to enclose a rectangular area and then divide it into 5 pens with fencing parallel to one side of the rectangle. there are 580 feet of fencing available to complete the job. what is the largest possible total area of the 5 pens?
Answers
When there is 580 feet of fencing available to complete the job, the largest possible total area of the 5 pens is 7008.33 feet.
What is an area?The quantity area expresses the extent of a region on a plane or curved surface.
STEP 1: We know that,
A=x y
The perimeter equals 580feet.
The equation is,
580=6x+2y
Step 2: Solving y terns with x,
y=-3x+290
This information will assist us in obtaining our Area equation in terms of a single variable (just in terms of x).
Step 3: Using the x-y relationship discovered in Step 2, write your Area equation in terms of x only. You should obtain
A=x y
A=x(-3x+290)
A=-3x²+290x
Step 4: Derive the area equation, A' = -6x+290
Step 5: Set A' = 0
-6x+290=0
x=290/6
x=48.33
Step 6: Find y by substituting 48.33 in x in the perimeter equation then,
y=-3(48.33)+290
y=145.01
Step 7: A=x y
A=(48.33)(145.01)
A=7008.33 feet
The largest possible total area of the 5 pens is 7008.33 feet
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A small publishing company is releasing a new book. The production costs will include a one-time fixed cost for editing an additional cost for each book printed. The total production cost C (in dollars) is given by the function C=650+17.95N, where N is the number of books.
The total revenue earned (in dollars) from selling the books is given by the function R=31.90N.
Let P be the profit made (in dollars). Write an equation relating P to N. Simplify your answer as much as possible.
P = ?
Homework help lolol
Answers
Answer: 67
Step-by-step explanation:
do the math
Nick bought a new car.
Each year the car depreciates in
value by 12%.
Work out the number of years it takes for the car to half in value.
Answers
1 year = 12%
4 years = 48%
5 years = 60%
per month = 1%
answer: it will take 4 years and 2 months for the car to half in value
Which ordered pairs is a solution to 5x+3y>12 Question 2 options: (3, 9) (-5, 5) (3, -6) (-2, -5) (2, 8) (-6, 0)
Answers
The solution to the expression given as 5x + 3y > 12 has the ordered pair of (3, 0)
How to determine the ordered pair of the solution?From the question, we have the following inequality that can be used in our computation:
5x + 3y > 12
Solving further, we need to collect the like terms
So, the expression becomes
3y > 12 - 5x
Next, we divide through the inequality by 3
So, we have the following representation
y > 12/3 - 5/3x
Evaluate
The equation becomes
y > 4 - 5/3x
At this point, we assume any value for x and then solve for y
Assume that the value of x is 3
So, we have the following representation
y > 4 - 5/3 * 3
Evaluate the products
y > -1
A value greater than -1 is 0
So, we have
x = 3 and y = 0
Express as ordered pairs
(x, y) = (3, 0)
Hence, the ordered pair of the solution is (3, 0)
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calculate the %cw for a sample of 1040 steel that has an original diameter of 12 mm and a final diameter of 10 mm.
Answers
The new yield strength of the 1040 steel will be the intercept on the curve for 30.56 %of cold work which is between700 to 800 MPA
Given original diameter do = 12 mm
Ao = [tex]\pi[/tex]/4 x 12² = 113.097 mm²
Deformed diameter d =10mm
Ad = [tex]\pi[/tex]/4 x 10² = 78.54 mm²
Degree of cold work %CW = (Ao - Ad/Ao)X 100
=(113. 097 - 78. 54/113.097) x 100
= 30.56%
% CW is 30.56 %
Therefore, the intercept on the curve for 30.56% of cold work, which is between 700 and 800 MPA, will represent the new yield strength of the 1040 steel.
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Which answer is correct?
(A) y = 3x − 2
y = 2x + 5
(B) y = −3x + 2
y = 2x − 5
(C) y = −3x − 2
y = −2x − 5
(D)y = 3x + 2
y = −2x + 5
Answers
Step-by-step explanation:
the slow of a line is the factor of x in a "y = ..." firm of equation.
the line going through (1, 5) has a slope of 3 (when x increases by +1, then y increases by +3, so the slope y/x = 3).
(B) and (C) are out, because there is no line with slope 3 (only -3).
the line going through (-2, 9) has a slope of -2 (when x increases by 1, y decreases by 2, so the slope y/x = -2/1 = -2).
(A) is out, as there is no line with the slope -2 (only +2).
so, (D) is the correct answer.
