1. Refer to the equation 3x − 5y = 15. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line. Work for Point 1 Work for Point 2 Work for Point 3 Work for Point 4
Answers
Answer:
We have the equation:
3x - 5y = 15
a) We want to create a table with at least 4 points.
To do this, first, let's write the equation as a function: We must isolate one of the variables. Let's isolate y.
5y = 3x - 15
y = (3/5)*x - 3.
Then we have a linear equation.
Now, we can input different values of x, and see what value takes y in each case, then in this way we can be sure that the points will be on the line.
x = 0.
y = (3/5)*0 - 3
y = -3
Then we have the point (0, -3).
x = 1.
y = (3/5)*1 - 3 = 3/5 - 15/5 = -12/5
y = -12/5
Then we have the point (1, -12/5)
x = 5
y = (3/5)*5 - 3 = 3 - 3 = 0
y = 0
then we have the point (5, 0)
x = 10
y = (3/5)*10 - 3 = 6 - 3 = 3
y = 3
Then we have the point (10, 3).
Now we can create the table
[tex]\left[\begin{array}{ccc}x&y\\0&-3\\1&-12/5\\5&0\\10&3\end{array}\right][/tex]
Below you can see a graph, where the blue dots are our 4 points, and the green line is the line that represents the equation.
Related Questions
Express each of these statements using quantifiers. Then form the negation of the statement so that no negation is to the left of a quantifier. Next, express the negation in simple English. In each case, identify the domain and specify the predicates.
a. No one has lost more than one thousand dollars playing the lottery.
b. There is a student in this class who has chatted with exactly one other student.
c. No student in this class has sent e-mail to exactly two other students in this class.
d. One student has solved every exercise in this book.
e. No student has solved at least one exercise in every section of this book.
Answers
Answer and Step-by-step explanation:
Not p = ¬p
P or q = p ∨ q
P and q = p ∧ q
If p then q = p → q
P if and only if q = p ↔ q
Existential quantification: There exist an element x in the domain such that p(x).
Universal quantification: p(x) for all values of x in the domain.
(a) No one has lost more than one thousand dollars playing the lottery.
Let A(x) means ‘x has lost more than one dollars playing the lottery’
It can also write as “there does not exists a person that lost more than one thousand dollars playing”
¬Ǝ x A (x)
Negation of this statement:
By using double negation law:
¬ [¬Ǝ x A (x)] ≡ Ǝ x A(x)
(b) There is a student in this class who has chatted with exactly one other student.
Let B(x,y) means “ x has chatted with y” and domain is all students of this class.
We can write the given sentence as:
“There is a student in the class who has chatted with one student and this student is not himself and for all people the student chatted with, this student has to be himself or the one student he chatted with”
Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x,y) → ( z = x v z = y))]
The negation:
¬ Ǝ x Ǝ y[B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]
By using De Morgan’s law for quantifiers:
≡∀x ¬ Ǝ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]
≡∀x ∀ y [B ( x, y) ∧ x ≠ y ∧ ∀ z (B(x ,y) → ( z = x v z = y))]
De Morgan’s law:
≡∀x ∀ y [¬ B ( x, y) v ¬ ( x ≠ y) v ∀ z (B(x ,y) → ( z = x v z = y))]
By using De Morgan’s law for quantifiers:
≡∀x ∀ y [¬ B ( x, y) v x= y v Ǝ z¬ (B(x ,z) → ( z = x v z = y))]
(c) No student in this class has sent e-mail to exactly two other students in this class
Let c(x, y) means “ x has sent email to y” and the domain is all student of class.
Using double negation law:
Ǝ x Ǝ y Ǝ z [c(x, y) ∧c(x ,z) ∧ x≠ y ∧ x ≠z ∧ y ≠ z ∀ w (c(x,w) → ( w = x v w = y v w = z)]
There is a student in class that has sent email to exaxtly two other students in class.
(d) One student has solved every exercise in this book
Let D(x , y) mean student x has solved exercise y in this book.
The negation:
Ǝx∀yD(x,y)
Use De Morgan’s law for qualifiers:
≡∀ x Ǝ y ¬D(x, y)
(e). No student has solved at least one exercise in every section of this book.
Let E(x, y,z) be student x has solved exercise y in section z of this book.
We can write “there does not exist a student that solved at least one exercise in all sections of this book”
¬Ǝ x Ǝ y ∀ Z E(x, y, z)
Negation:
≡¬ [¬ Ǝ x Ǝ y ∀ Z E(x, y, z) ]
Use double negation law:
≡ Ǝ x Ǝ y ∀ Z E(x, y, z)
find the value of x
need to show work
Thank you guys
Answers
Answer:
Since they are vertical angles (or angles opposite each other), you set them equal to each other.
5x + 4 = 74
5x = 70
x = 15
-1/2(6t+2)?simplify the expressions by disturbing the negatives and combining like terms
Answers
Answer:
-3t-1
Step-by-step explanation:
The adjacent supplementary angle to any of the interior angles of a triangle is called an exterior angle of a triangle.
Answers
Answer:
Correct
Step-by-step explanation:
The supplementary angle to any of the interior angles of a triangle is called an exterior angle, they are supplementary because they form a 180º angle when you extend a straight line from the adjacent side of the angle and any straight angle is a 180º angle, so supplementary angles added up would make 180º.
Plzz answers its easy points!!!! im just really dumb!!!!
Answers
Answer:
see below
Step-by-step explanation:
V = Bh where B is the area of the base and h is the height
Divide each side by h
V/h = Bh/h
V/h = B
36/6 = B
6 = B
The area of the base is 6 in^2
PLEASE HELP ASAP!!
There are 800 students who attend Park Middle School. There are 1.5 times as many boys as there are girls.
x is boys
y is girls
800=1.5x=y
Determine how many boys and girls attend Park Middle School. Round to the nearest whole number if necessary. Show your work.
Answers
Answer:
320 boys; 480 girls
Step-by-step explanation:
Here is the correct system of equations you can write for this equation:
1.5x=y
x+y=800
x+1.5x=800
2.5x=800
x=320
320+y=800
y=480
What line is perpendicular to y=2/7x+11/7 travel through (-3,8)
Answers
Answer:
y=−7/2x−5/2
Step-by-step explanation:
Find the negative reciprocal of the slope of the original line and use the point-slope formula
y−y1=m(x−x1) to find the line perpendicular to y=2/7x+11/7.
sub to astronaut gaming i have 27 subs if you need help finding i will help
Answers
Answer:
i subbed :P
Step-by-step explanation:
hope this helps </3
The answer is 118 as well right??
Answers
Answer: 118 is the correct degree
Step-by-step explanation:
Which are vertical angles?
Answers
What is the value of x?
Answers
Answer:
Step-by-step explanation:
where are the other variables?
-9(-2x-3) simplified
Answers
Answer:
18x +27
Step-by-step explanation:
-9(-2x-3)
Distribute
-9 * -2x -9*(-3)
18x +27
Find the slope of f(x)=5x-4
Answers
Answer:
5
Step-by-step explanation:
Answer:
slope, m = 5
Step-by-step explanation:
Recall that the slope-intercept form of a linear equation can be written:
y = mx + b or f(x) = mx + b
where m is the slope of the line.
in our case, we are given
f(x) = 5x - 4
if we compare this with the general equations above, we can see that
slope = m = 5
hence the slope is 5
Which two numbers have a product of −18 and a sum of −7?
Answers
Answer:
2 and -9
Step-by-step explanation:
2 times -9 is -18
2 plus -9 is -7
Hope this helped!
Solve 2y - 3 = 4y +6.
у
DONE
Answers
Answer:
y= -4.5
Step-by-step explanation:
2y - 3 = 4y +6
subtract 2y from both sides: -3 = 2y +6
subtract 6 from both sides: -9 = 2y
divide both sides by 2: -4.5 = y
Answer:
y= -4.5
Step-by-step explanation:
2y - 3 = 4y + 6
+3 + 3
2y = 4y + 9
-4y -4y
-2y = 9
divide by -2 to get -4.5
Planes S and R both intersect plane T Which statements are true based on the diagram? Select three options OPlane S contains points B and E. The line containing points A and B lies entirely in plane T B ULine v intersects lines x and y at the same point ULine z intersects plane S at point C OPlanes R and T intersections at line y.
Answers
Answer:
Options (2), (4) and (5)
Step-by-step explanation:
Option (1).
Planes S contains points B and F.
False.
(Point B lies on plane S and point F lies on plane R)
Option (2).
The line containing points A and B lie on the plane T.
True.
(points A and B lie on plane T)
Option (3).
Line v intersects lines x and y at the same plane.
False.
Option (4).
Line z intersects plane S at point C.
True.
Option (5).
Planes R and T intersect at line y.
True.
Answer:its b d e
Step-by-step explanation:
factorise 3x^3-4x^2-28x-16
Answers
Answer:
i just saw that on google, but i'm not sure if that's what you are looking for
Answer: -2
Step-by-step explanation:
Hope it help you
Stayhomestaysafe
REAL NAME - SHRESTH DUBEY
Help pls it’s urgent
Answers
Answer:
d. -2
Step-by-step explanation:
they're telling you those lines are parallel there are specific knowns about the angles
since it's urgent I won't go into it, but PLS look it up it's super simple and makes sense
nonetheless this means angle 1 and angle 5 are the same value so we can set them equal
3x + 24 = 7x + 32
substract 32 from both sides
3x - 8 = 7x
substract 3x from both sides
-8 = 4x
divide 4 from both sides
-2 = x
Find the equation of a parabola with a focus at (–2,–3) and a directrix at y = –5.
A)
y = 1∕4(x – 2)2 – 4
B)
y = –1∕16(x + 2)2 – 4
C)
y = 1∕4(x + 2)2 – 8
D)
y = 1∕4(x + 2)2 – 4
Answers
Answer:
It"s (C) byeeee and ur welcome
What is the value of p?
Answers
What integers are the closest to the square root of 11
Answers
Answer:
-3, 3.
Step-by-step explanation:
3^2 = 9 and 4^2 = 16.
Also -3 and -4 give the same results.
Since 9 is closer to 11 than 16 the answer is 3 and -3.
Ten less than a number is twice the same number
Answers
Meaning lees 10 from 20 and multiply
Hi there!
First of all, let the unknown number be z.
Now, subtract 10:
z-10
This expression is equal to twice the same number:
z-10=2z
Solve this equation:
z-2z=10
-z=10
Divide both sides by -1 in order to get rid of the minus sign:
z=-10
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Larry picked 8 pounds of strawberries. If each jar of jam takes 38 of a pound of strawberries, how many jars of jam can Larry make?
Answers
Answer:
21 Jars
Step-by-step explanation: Divide 8 by 0.38 (38/100ths) and the answer is 21.052631578947368421052631578947 but you just round to 21.
Find the area of the circle look no
Answers
Area of a complete circle is area = pi x r ^2
Area = 3.14 x 4^2
Area = 3.14 x 16
Area = 50.24 square units.
1/4 of the circle is missing, so multiply the area of the full circle by 3/4:
50.24 x 0.75 = 37.68 cubic units.
Please answer this correctly without making mistakes
Answers
Answer:
the answser is 8%.
PLS I NEED THIS ASAP 100 POINT ---------The shoe store’s clerks are paid on commission. If the clerk receives a 12% commission on total purchase amounts before tax is applied, how much would the commission be for Isaac’s purchase with and without a coupon? 100 POINTS
Answers
Answer:
12%
Step-by-step explanation:
You never gave any numbers than 12% and you asked how much the commission would be...
If he gets 12% commission then he would have to pay 12% commission.
The left and nght page numbers of an open book are two consecutive integers whose sum is 447. Find these page numbers
Answers
Answer:
223 and 224
Step-by-step explanation:
Divide 447 by 2. It gives a decimal of 223.5, but obviously you don't have half pages. So the page number would be 223 and 224.
Answer:
223,224
Step-by-step explanation:
page 1-x
page 2-x+1
2x+1=447
2x=446
x=223
page 1=223
page 2=224
Brainliest is Very Appreciated!
z=b+ m/a, solve for a
Answers
A machine in a factory produces 25 gismos a day. After a $174 repair job, the machine improves its gizmo output by 16%.If the sale of a gizmo makes a profit of 75cents, the number of days it will take to recover the machine's repair is???
PLEAS HELP ME!!!
Answers
Answer:
Around 10 days ( 9.28 days: 9 days 6 hours 43 minutes 12 seconds).
Step-by-step explanation:
Given that 25 gizmos are produced each day, and 75 ¢ are made off of each one, a 174$ repair job will take away money that will need to be paid off.
We can create the following equation by using the amount of gizmos earned per day(x or time) multiplied the money made off of each one(in cents ¢), is equal to the repair job since it will be paid off once it is canceled out.
25x(75¢) = 174$.
Since the money made by each gizmo is in cents and not dollars, it is best to convert this into dollars since the repair job is in this form. Because 100¢ are in each dollar, 75¢ = 75/100 dollars = 3/4 dollars.
3/4 * 25 x = (3/4) * (25x) = (25*3) / 4 = 75/4x
(75/4)x = 174$
(75/4x) * (4/75) = (174$) * (4/75)
x = (174 * 4) / 75
x = 696 / 75
x = 9.28
We are multiplying by the reciprocal (numerator and denominator are switched) since it will make your coefficient 1 which is the variable itself. anything times it's reciprocal is equal to one.
75/4x = 174$
×4 ×4
(cancel out the denominator)
____________
75x = 696$
÷ 75 ÷ 75
(cancel out 75 to get the variable by itself)
___________
x = 696/75
x = 232/25
x = 928/100
x = 9.28
___________
Using a system of equation, the number of days it will take to recuvwr the repair cost is 58 days.
The increase in amount of gizmo produced after repair :
0.16) × 25 = 4 gizmos per dayPrize per gizmo = 75 cent = $0.75
Repair cost = $174
The number of days it will take to recover the repair fee can be calculated thus :
(Increase on gizmo per day × cost per gizmo)× number of days = repair fee
(4 × 0.75)d= 174
3d = 174
d = 174 / 3
d = 58
Therefore, it will take 58 days to recover the repair fee.
Learn more : https://brainly.com/question/18796573
Kenya went to the convenience store to buy some candy bars for her friends. She spent a total of $6.00 on candy bars. Each candy bar cost $1.50.
How many candy bars did Kenya buy?
Answers
Answer:
4
Step-by-step explanation:
Answer:
4
Step-by-step explanation: