Need some help! Graph the equations y=3x-5 and x+3y=6 on the same xy-plane. What is significant about these two lines? (Explain your answer)
Thanks!
Answers
y=3x-5 is already in SIF, so we only need to work on the other one.
x+3y=6
-x -x
3y=-x+6
/3 /3
y=-1/3x+2
Now we have both equations in slope intercept form, so we can start graphing from the y-intercepts and just follow the slopes.
When we do this, we will see that the lines meet at an exactly 90° angle. When a pair of lines does this, it means they are perpendicular.
Below I have attached an image that has both lines graphed so that you may visualize it. The green dots show the slopes, while the highlighted areas show the y-intercepts. Note that the lines intersect at a 90° angle, making them perpendicular.
Related Questions
Collecting data from a sample that does not represent the population is called
Answers
The answer in the given statement above is sample bias, this is considered to be a sampling error because this type of technique uses a sample in which they don’t represent the population, causing error in which could be eliminated with the use of methods.
The sum of 4 consecutive even integers is 20. what are the integers?
Answers
2x + 2x+2 + 2x+4 + 2x+6 = 2O
8x + I2 = 2O
8x = 8
x = I
Therefore integers are; 2, 4, 6, 8
The given four consecutive even integers are 2, 4, 6, 8
What are even numbers and how can we write consecutive even numbers?Even numbers are numbers which are divisible by two.
Any even number can be written as 2n , where n is any integer
If we increase n by 1 then next even number will be obtained. Then the consecutive even numbers be 2n , 2 (n+1), 2(n +2) , 2 (n+3), ....... so on.
Given that the sum of four consecutive even integers is 20
Let the four consecutive even integers are :
2n , 2(n+1) , 2(n+2), 2( n+3)
Then
⇒2n + 2(n+1) + 2(n+2) + 2( n+3) = 20
⇒ 2n + 2n +2 +2n +4 + 2n +6 =20
⇒ 8n + 12 =20
⇒ 8n = 20-12
⇒ 8n = 8
⇒ n =8/8 = 1
Therefore, the given four consecutive even integers are 2, 4, 6, 8
Also, Learn more about the even numbers from the link below:
brainly.com/question/4184435
#SPJ2
Use the properties of logarithmic functions to simplify the expression on the left side of the equation and determine the values of x and y. Then evaluate the simplified expression.
The value of x is , and the value of y is. The value of the expression, rounded to nearest hundredth, is
Answers
Properties of exponents tell us that:
log7(2) / log7(5) = log5(2)
x = 5
y = 2
Answer = 0.43
By using the logarithmic property the solution of the given function will be 0.43.
What is Logarithm?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division
The solution of the given expression is given as:-
Log7(70) - log7(35) = log7(70/35) = log7(2)
Properties of exponents tell us that:
log7(2) / log7(5) = log5(2)
x = 5
y = 2
Answer = 0.43
Therefore using the logarithmic property the solution of the given function will be 0.43.
To know more about Expression follow
https://brainly.com/question/723406
#SPJ2
how to solve for literal equations with multiple variables
Answers
What would you do if ST were not equal to TU when you checked the problem?
Answers
the sum of four consecutive integers os -18. what is the greatest of these integers?
Answers
Answer:
-3
Step-by-step explanation:
-3+(-4)+(-5)+(-6)=-3-4-5-6=-18
-3 is the greatest because the smaller the number behind the negative sign, the larger the number that's larger than that but behind a negative sign is smaller. e.g. -4 is less than -3
What is the r (common ratio) for the geometric sequence: -3, -15, -75, -375, -1875...
Answers
Please vote my answer brainliest. thanks!
A dreidel is a top with four sides, used in a Hanukah game. The sides are labeled with the Hebrew letters, nun, gimel, hay, and shin. A dreidel is spun 100 times, with the following results: nun 10 gimel 45 hay 24 shin 21 A player wins tokens if the dreidel lands on either gimel or hay. What is the probability of winning tokens? a. 0.54 c. 0.69 b. 0.63 d. 0.87
Answers
45 gimmel and 24 hay
total is 45+24=69
69/100 or 69% chance of winning or 0.69
answer is C (confusing because C is 2nd option)
The probability of winning tokens is 0.69. Therefore, the option C is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favorable outcomes/Total number of outcomes.
Given that, dreidel is spun 100 times, with the following results: nun =10, gimel =45, hay =24 and shin =21.
A player wins tokens if the dreidel lands on either gimel or hay.
Here, probability of getting gimel is 45/100
The probability of getting hay is 24/100
So, the probability of an event is 45/100 +24/100
= 69/100
= 0.69
Therefore, the option C is the correct answer.
To learn more about the probability visit:
https://brainly.com/question/11234923.
#SPJ7
The length of a rectangle is 3 times the width.the permitted of the rectangle is 72ft find the dimensions of the rectangle
Answers
l = 3w
Using this, we can make all the variables the same by substitution:
2l + 2w = perimeter
2l + 2w = 72
2(3w) + 2w = 72
6w + 2w = 72
8w = 72
w = 9
The width is 9, to the length must be 9*3, or 27.
Hope this helped!
What percent of 225 is 180
Answers
which term best describes the intersection of two lines?
a) angle
b) line segment
c) point
d) ray
Answers
When two lines intersect, you will get a coordinate which makes a point. It might be confused with the angle. To make an angle, you need two rays, not two lines. In fact, when 2 lines intersect the angle made will be 4 angles. But intersecting lines should only make 1 point.
Use the chart to multiply the binomial by the trinomial.
What is the product?
A.y3 + 27
B.y3 – 27
C.y3 – 6y2 + 27
D.y3 + 6y2 + 27
Answers
y(y^2 - 3y + 9) + 3(y^2 - 3y + 9) =
y^3 - 3y^2 + 9y + 3y^2 - 9y + 27 =
y^3 + 27 <==
Answer:
option (1) is correct.
the product of the binomial by the trinomial is [tex]y^3+27[/tex].
Step-by-step explanation:
Binomial is the term having two different term and trinomial having three different terms.
Here, Binomial is [tex]y+3[/tex] and trinomial is [tex]y^2-3y+9[/tex]
We have find the product of the binomial by the trinomial.
[tex](y+3)(y^2-3y+9)[/tex]
Multiply each term of binomial with trinomial,
[tex]\Rightarrow y(y^2-3y+9)+3(y^2-3y+9)[/tex]
[tex]\Rightarrow y^3-3y^2+9y+3y^2-9y+27[/tex]
Combining like term, we get,
[tex]\Rightarrow y^3+(3-3)y^2+(9-9)y+27[/tex]
[tex]\Rightarrow y^3+27[/tex]
Thus, the product of the binomial by the trinomial is [tex]y^3+27[/tex].
Hence, option (1) is correct.
A rectangular picture frame measures 10 cm by 12 cm. Do you want to triple the frames area by adding the same distance "x" to the length and the width. Write and solve an equation to find the value of "x". What are the new dimensions of the picture frame?
Answers
x(x+30)-8(x+30)=(x-8)(x+30). To make the expression equal to 0, since 0 multiplied by anything is 0, we have to figure out when x-8 and x+30 equal 0, which is when x=8 and -30 respectively (To do this, you could add 8 from both sides to turn x-8=0 to x=8, and something similar to -30). Plugging each one in, we get (10+(8))*(12+(8))=18*20=360. To make sure there aren't 2 solutions, we get that the new width is 10-30=-20, which clearly can't be negative , making x equal to 8.
A equilateral triangle is rotated around an axis bisecting the triangle. what shape is formed
Answers
Answer:
A right cone. If an equilateral triangle were to be cut in half then it would form a right triangle then if this right triangle were rotated 360 degrees it would form a right cone
Step-by-step explanation:
Which of the following is not part of the job search preparation checklist
A- self assessment
B-resume
C-fact sheet
D- follow up plan
Answers
Answer:
c). Fact sheet
Step-by-step explanation:
A). Self assessment
Self assessment is analyzing oneself or examining oneself. This is important for job search as to it provides a clear idea in our mind that what we actually want to do and want we are interested in.
B). resume
Resume is very important in job search. It is basic bio data or a brief summary of our education and past employment experience if any. It also showcases our strength and weakness and our main objective in our life.
C). fact sheet
Fact sheet is a list of facts or events listed in a chart and it has no connection to any job search. It may be good to have knowledge about facts but it is not necessary and compulsory for job search.
D). follow up plan
Follow up plan is a routine check to be done when searching for jobs. Searching for vacancies, contacting the company and following up with the employer is a necessary thing in job search.
Therefore, C). fact sheet is not a part of job search preparation checklist.
A rectangular field is nine times as long as it is wide. If the perimeter of the field is 1600 feet, what are the dimensions of the field?
Answers
Final answer:
The width of the field is 80 feet, and the length is 720 feet, calculated using the perimeter formula and the given ratio of length to width.
Explanation:
To determine the dimensions of the rectangular field, we need to set up two equations based on the given information that the field's length is nine times its width and that the perimeter is 1600 feet. We'll let w represent the width of the field and l represent the length.
Since the field's length is nine times its width, we can express this as l = 9w. The perimeter P of a rectangle is given by P = 2l + 2w. Since we know the perimeter is 1600 feet, we can use this to create the equation 1600 = 2(9w) + 2w, which simplifies to 1600 = 18w + 2w.
Combining like terms gives us 1600 = 20w, and solving for w gives us w = 1600 / 20, so w = 80 feet. Knowing w, we can find l by multiplying the width by 9: l = 9w = 9 × 80 = 720 feet.
Therefore, the dimensions of the field are a width of 80 feet and a length of 720 feet.
Thirty-one books are arranged from left to right in order of increasing prices. The price of each book differs by $2 from that of each adjacent book. The price of the book at the extreme right is equal to the price of the middle book plus a book adjacent to the middle one. Give an expression for the cost of the $n$th book in terms of $n$.
Answers
Case 1: The last book costs the same as the middle book and one to its right. Then
x + (x+2) = x + 30
x = 28
However, this means the leftmost book costs x-30 = -2 dollars, which is unlikely.
Case 2: The last book costs the same as the middle book and one to its left. Then
x + (x-2) = x + 30
x = 32
In this case, the costs of the books are
$2, $4, $62.
The nth book costs 2n dollars.
A company bought a total of 4 1/2 feet of cable to connect 3 computers to the wall outlet. Each computer needs the same amount of cable. How many feet of cable are needed to connect each computer?A.1 1/2 ft B.1/3 ft C.1 1/3 ft D.1/2 ft please help i will mark brainliest
Answers
Answer:
A Hope this helps
Step-by-step explanation:
Eight plus the quotient of a number and 3 is -2
Answers
Which unit rates would be appropriate for describing the rate of growth of a tree?
Select each correct answer.
inches per year
millimeters per week
milliliters per minute
miles per hour
Answers
Inches per year
Hope i helped!
The second answer is millimeters per week. You're welcome!
h(x) = x^2 + 1 k(x) = x – 2
(h + k)(2)=?
Answers
To add polynomials, we add terms whose variables are alike, for example:
we add the coefficients of x^2 together, the coefficients of x together and so on.
Therefore:
h + k = x^2 + 1 + x - 2 = x^2+x-1
Now, we will multiply this answer by 2 to get the final answer:
2(h+k) = 2(x^2+x-1) = 2x^2 + 2x -2
Answer: the answer is 5
Step-by-step explanation: edge 2020
PLZ HELP I NEED HELP!!!!!
Which names are other ways to name angle 2?
Select each correct answer.
HKG
G
H
K
HGK
GHK
KGH
Answers
How many days between 09/26/16 and 10/04/2016?
Answers
There are 7 days between September 26, 2016, and October 4, 2016.
To find the number of days between 09/26/16 and 10/04/16, you can follow these steps:
Start Date: September 27, 2016End Date: October 3, 2016Count the days from September 27 to October 3 as the question asks for days between 26 September and 4 October, i.e., days belonging to the interval (26 September,4 October).Let's break it down:
September 27 to September 28: 1 daySeptember 28 to September 29: 1 daySeptember 29 to September 30: 1 daySeptember 30 to October 1: 1 dayOctober 1 to October 2: 1 dayOctober 2 to October 3: 1 dayWhen you add these, the total is 7 days.
Therefore, there are 7 days between 09/26/16 and 10/04/16.
Of all the students enrolled at Anderson High School, 9, percent are in the band. The band has 1801members.How many students are enrolled at Anderson?
Answers
Which is a stretch of an exponential decay function? f(x) = 4/5(5/4)^x f(x) =4/5(4/5)^x f(x) =5/4(4/5)^x f(x) =5/4(5/4)^x
Answers
Answer:choice three
Step-by-step explanation:
Answer:
The correct option is 3. The function [tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex] is a stretch of an exponential decay function.
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is the initial value and b is the growth factor.
If b<1, then it represents a decay function and if b>1, then it represents a growth function.
Let k be a stretch and compression factor.
[tex]g(x)=kf(x)[/tex]
If k<1, then it represents vertical compression and if k>1, then it represents vertical stretch.
In third function
[tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex]
[tex]k>1[/tex]
[tex]b<1[/tex]
Therefore the function [tex]f(x)=\frac{5}{4}(\frac{4}{5})^x[/tex] is a stretch of an exponential decay function.
Round 26502.9085923 to the nearest hundredth
Answers
What is 64.48 rounded to the nearest whole number?
Answers
2x - y - 4 = 0
3x + y - 9 = 0
What is the solution set of the given system?
(A.) {(6/5, 13/5)}
(B.) {(13/5, 6/5)}
(C.) {(5, 6)}
(D.) {(6, 5)}
Answers
3x+y=9
5x=13
x=13/5
3(13/5)+y=9
39/5+y=45/5
y=45/5-39/5
y=6/5
the answer is b
what are 3 consecutive integers that have a sum of 234
Answers
77,78,79
Which statement describes the translation of . y= -1/2(x-2) ^2 from standard position? A) Moved up and to the right. B) Moved up and to the left. C) Moved down and to the left. D) Moved down and to the right. .
Answers
Answer: The correct option is
(D) Moved down and to the right.
Step-by-step explanation: We are given to select the statement that best describes the translation of the following function from the standard position.
[tex]y=-\dfrac{1}{2}(x-2)^2~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
This is an equation of a parabola.
The standard position of a parabola of this type is
[tex]y=x^2,[/tex]
where the vertex is at (0, 0). Since the coefficient of x² is positive, so the parabola opens upwards.
Now, from equation (i), we have
the vertex of the parabola is at (2, 0) and since the coefficient of x² is negative, so the parabola opens downwards.
Also, the vertex (0, 0) has been shifted to (2, 0), so the parabola is moved 2 units to the right.
Therefore, the given parabola is moved down and 2 units to the right as compared to the standard position.
The images of the given parabola (i) and the standard parabola are shown in the attached figure below.
Thus, (d) is the correct option.