Quiz 3-3 Parallel and Perpendicular Lines on the Coordinate Plane (Gina Wilson All Things Algebra 2014-2019) need these for a quiz please!
Answers
Answer:
14. [tex]y = -2x -1[/tex]
15. [tex]y = -\frac{3}{4}x +3[/tex]
16. [tex]y= 4x + 9[/tex]
17. [tex]y = -\frac{5}{3}x -2[/tex]
18. [tex]y= -\frac{2}{3}x -5[/tex]
19. [tex]y = 4x -3[/tex]
20. [tex]y = -3x -7[/tex]
Step-by-step explanation:
Solving (14):
Given
[tex](x_1,y_1) = (-7,13)[/tex]
[tex]Slope (m) = -2[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 13 = -2(x -(-7))[/tex]
[tex]y - 13 = -2(x +7)[/tex]
[tex]y - 13 = -2x -14[/tex]
Collect Like Terms
[tex]y = -2x -14 + 13[/tex]
[tex]y = -2x -1[/tex]
Solving (15):
Given
[tex](x_1,y_1) = (-4,6)[/tex]
[tex]Slope (m) = -\frac{3}{4}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 6 = -\frac{3}{4}(x - (-4))[/tex]
[tex]y - 6 = -\frac{3}{4}(x +4)[/tex]
[tex]y - 6 = -\frac{3}{4}x -3[/tex]
Collect Like Terms
[tex]y = -\frac{3}{4}x -3 + 6[/tex]
[tex]y = -\frac{3}{4}x +3[/tex]
Solving (16):
Given
[tex](x_1,y_1) = (-5,-11)[/tex]
[tex](x_2,y_2) = (-2,1)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{1 - (-11)}{-2 - (-5)}[/tex]
[tex]m = \frac{1 +11}{-2 +5}[/tex]
[tex]m = \frac{12}{3}[/tex]
[tex]m = 4[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x -(-5))[/tex]
[tex]y +11 = 4(x+5)[/tex]
[tex]y +11 = 4x+20[/tex]
Collect Like Terms
[tex]y= 4x + 20 - 11[/tex]
[tex]y= 4x + 9[/tex]
Solving (17):
Given
[tex](x_1,y_1) = (-6,8)[/tex]
[tex](x_2,y_2) = (3,-7)[/tex]
First, we need to calculate the [tex]slope\ (m)[/tex]
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{-7 - 8}{3- (-6)}[/tex]
[tex]m = \frac{-7 - 8}{3+6}[/tex]
[tex]m = \frac{-15}{9}[/tex]
[tex]m = -\frac{5}{3}[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - 8 = -\frac{5}{3}(x -(-6))[/tex]
[tex]y - 8 = -\frac{5}{3}(x +6)[/tex]
[tex]y - 8 = -\frac{5}{3}x -10[/tex]
Collect Like Terms
[tex]y = -\frac{5}{3}x -10 + 8[/tex]
[tex]y = -\frac{5}{3}x -2[/tex]
18.
Given
[tex](x_1,y_1) = (-6,-1)[/tex]
[tex]y = -\frac{2}{3}x+1[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = m_2[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m = -\frac{2}{3}[/tex]
and
[tex]m_1 = m_2 = -\frac{2}{3}[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1
[tex]y - (-1) = -\frac{2}{3}(x - (-6))[/tex]
[tex]y +1 = -\frac{2}{3}(x +6)[/tex]
[tex]y +1 = -\frac{2}{3}x -4[/tex]
[tex]y= -\frac{2}{3}x -4 - 1[/tex]
[tex]y= -\frac{2}{3}x -5[/tex]
19.
Given
[tex](x_1,y_1) = (-2,-11)[/tex]
[tex]y = -\frac{1}{4}x+2[/tex]
Since the given point is parallel to the line equation, then the slope of the point is calculated as:
[tex]m_1 = -\frac{1}{m_2}[/tex]
Where [tex]m_2[/tex] represents the slope
Going by the format of an equation, [tex]y = mx + b[/tex]; by comparison
[tex]m_2 = -\frac{1}{4}[/tex]
and
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{-1}{4}[/tex]
[tex]m_1 = -1*\frac{-4}{1}[/tex]
[tex]m_1 = 4[/tex]
Equation in [tex]slope\ intercept\ form[/tex] is:
[tex]y - y_1 = m(x-x_1)[/tex]
[tex](x_1,y_1) = (-2,-11)[/tex]
Substitute values for y1, m and x1
[tex]y - (-11) = 4(x - (-2))[/tex]
[tex]y +11 = 4(x +2)[/tex]
[tex]y +11 = 4x +8[/tex]
Collect Like Terms
[tex]y = 4x + 8 - 11[/tex]
[tex]y = 4x -3[/tex]
20.
Given
[tex](x_1,y_1) = (-10,3)[/tex]
[tex](x_2,y_2) = (2,7)[/tex]
First, we need to calculate the slope of the given points
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{7 - 3}{2 - (-10)}[/tex]
[tex]m = \frac{7 - 3}{2 +10}[/tex]
[tex]m = \frac{4}{12}[/tex]
[tex]m = \frac{1}{3}[/tex]
Next, we determine the slope of the perpendicular bisector using:
[tex]m_1 = -\frac{1}{m_2}[/tex]
[tex]m_1 = -1/\frac{1}{3}[/tex]
[tex]m_1 = -3[/tex]
Next, is to determine the coordinates of the bisector.
To bisect means to divide into equal parts.
So the coordinates of the bisector is the midpoint of the given points;
[tex]Midpoint = [\frac{1}{2}(x_1+x_2),\frac{1}{2}(y_1+y_2)][/tex]
[tex]Midpoint = [\frac{1}{2}(-10+2),\frac{1}{2}(3+7)][/tex]
[tex]Midpoint = [\frac{1}{2}(-8),\frac{1}{2}(10)][/tex]
[tex]Midpoint = (-4,5)[/tex]
So, the coordinates of the midpoint is:
[tex](x_1,y_1) = (-4,5)[/tex]
Equation in [tex]slope- intercept[/tex] form is:
[tex]y - y_1 = m(x-x_1)[/tex]
Substitute values for y1, m and x1: [tex]m_1 = -3[/tex] & [tex](x_1,y_1) = (-4,5)[/tex]
[tex]y - 5 = -3(x - (-4))[/tex]
[tex]y - 5 = -3(x +4)[/tex]
[tex]y - 5 = -3x-12[/tex]
Collect Like Terms
[tex]y = -3x - 12 +5[/tex]
[tex]y = -3x -7[/tex]
Related Questions
US
Find the value of x.
es
les
2x - 4
10
Answers
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 2x-4=10 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=10+4 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2x=14 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac {14}{2}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=7 [/tex]
What is the answer for -3(4x-2)<18
Answers
Answer:
[tex]x>-1[/tex]
Step-by-step explanation:
I used guess and check - anything above -1 works!
Answer:
x>-1
Explanation:
4x-2>-6
4x>-6+2
4x>-4
4x>-4
=x>-1
What are the domain and the range of this function?
Answers
!!HELP ME PLEASE!!
Which describes the graph of y = (x + 6)2 + 1?
A. Vertex at (−6, 1)
B. Vertex at (6, −1)
C. Vertex at (−6, −1)
D. Vertex at (6, 1)
Answers
Answer:
answers
Step-by-step explanation:
A. Vertex at (−6, 1)
PLEASE HELP
1. Select ALL expression(s) has a value less than 4?
A) |-8|
B) |6|
C) -10
D) |-2|
Answers
|-2| means that it’s 2 units away from 0. -10 is also less than 4. |-8| is 8 and |6| is 6 which are both higher than 4. Thus, the correct answers are C and D.
What is the equation of the line perpendicular to y=-1/5x -2 and contains the point (2, -10)?
Answers
Answer:
y= 5x-20
Step-by-step explanation:
I didn't understand if I had to find the perpendicular line or parallel haha.
You’re welcome :)
Answer:
y = 5x -20
Step-by-step explanation:
for the line to be perpendicular it must have the inverse slope
therefore m = 5
no substitute the point (2, -10) in for (x, y) respectively to find the y intercept
-10 = 5(2) + b
-10 = 10 + b
b = -20
the equation will be y = 5x -20
The complex numbers z and w are graphed. Which expression represents z + w? (2 + i) + (3 + i) (2 – i) + (3 + i) (2 – i) + (3 + 2i) (2 + i) + (3 + 2i)
Answers
Answer:
(2 - i) + (3 + 2i)
Step-by-step explanation:
got it right on edge 2020
Answer:
C. (2 – i) + (3 + 2i)
Step-by-step explanation:
In 2003, the average attendance per game for a football team was about (1 × 104) + (9 × 103) + (9 × 102). What is this number in standard form?
show work
Answers
Answer:
1.99 * 10^4
Step-by-step explanation:
Here, we want to write the addition in standard form
= (1 * 10^4) + (9 * 10^3) + (9 * 10^2)
= 10,000 + 9000 + 900
= 19,900
so the number in standard form is;
1.99 * 10^4
There are 48 students in a school play. The ratio of boys to girls is 5:7. How many more girls than boys are in the play? Explain how you found your answer
Answers
The ratio of boys to girls is 5:7. 5 + 7 = 12 5/12 of the students are boys. 7/12 of the students are girls. The number of boys is (5/12)48 = 20. The number of girls is (7/12)48 = 28. 28 - 20 =8. Therefore, there are 8 more girls than boys in the play.
Answer:
48 students total in the school play
Ratio of boys to girls is 5:7
How many more girls are there than boys in the play?
Let's let "5x" represent the number of boys in the school play and "7x" represent the number of girls in the school play.
5x = boys
7x = girls
If we know that the total number of students in the play equals 48, then that must me that both the number of boys and girls combined must equal 48:
5x + 7x = 48
12x = 48
x = 4
Now, take your x-value and plug it into both the boys' and girls' values to figure out how many boys and girls there are in the play:
5x = 5 (4) = 20 boys
7x = 7 (4) = 28 girls
To find out how many more girls there are than boys in the play, just subtract the number of girls minus the number of boys:
# girls - # boys = 28 - 20 = 8
This means that there are 8 more girls than boys in the school play.
Step-by-step explanation:
Hope this helped
The slope of a line is -4, and the y-intercept is -3. What is the equation of the line written in slope-intercept form?
y = -4x - 3
y = 4x - 3
y = -4x + 3
Answers
Answer:
y= -4x+-3 = y=-4x-3
The rest are wrong.
Hi there! :)
We are given the slope of the line and its y-intercept.
So, we write the equation in slope-intercept form (y=mx+b)
m is the slope of the line, and b is the y-intercept.
y=mx+b
y=-4x-3
Hence, that's the equation (Option A)
Hope it helps. Use the comment section to clarify your doubts.
Answered by
~A cheerful gal who helps others and smiles
Good luck.
Does anyone know how to find the area to this I really need help?!
Answers
Help!!!!!!! Meeee plead I’ve already out this question down but nobody answers it:(
Answers
Answer:
1. Y = 6
2. Y = 8
3. Y = 1
4. Y = 3
Step-by-step explanation:
1. Y = -(-1) + 5 = 1 + 5 = 6
2. Y = -(-3) + 5 = 3 + 5 = 8
3. Y = -4 + 5 = 1
4. Y = -2 + 5 = 3
Hope this helps you!
Answer: hold up, the answer is 4, 2, 9, and 7. Don't worry I help you to answer this question. Wrong answer the answer is 1. Y = 6
2. Y = 8
3. Y = 1
4. Y = 3
Step-by-step explanation:
Hi. ITS URGENT.
I need help with No 5 and 7 (see image)
Please show workings
Answers
Answer:
5. a^3 + b^3 = (a+b)^3 - 3ab(a+b)
Step-by-step explanation:
(a+b)^3
= (a+b) (a+b) (a+b)
={(a+b) (a+b)} (a+b)
={a(a+b) + b(a+b)} (a+b)
=(a^2 + ab + ab + b^2) (a+b)
=(a^2 + b^2 + 2ab) (a+b)
=a^2(a+b) + b^2(a+b) + 2ab(a+b)
=a^3 + a^2b + ab^2 + b^3 + 2a^2b + 2ab^2
=a^3 + b^3 + 3a^2b + 3ab^2
=a^3 + b^3 + 3ab(a+b)
(a+b)^3 = a^3 + b^3 + 3ab(a+b)
(a+b)^3 - 3ab(a+b) = a^3 + b^3
a^3 + b^3 = (a+b)^3 - 3ab(a+b)
Hope this helped!
Answer:
I am just giving the expansion, so that you can substitute the values and solve it
Stephan has a dog that weighs 5 times as much as Ian's dog. The total weight of both dogs is 72 pounds. how much does Stephans dog weigh??
Answers
Answer:
Stephan's dog weighs 60 pounds.
Step-by-step explanation:
Which can be used to expand the expression below?
5 3x
associative property
O commutative property
O distributive property
O subtracting
Answers
Answer:
the answer is disributive!
Step-by-step explanation:
hiii so my parents just finally agreed to let me get a puppy so could you list some boy and girl name ideas? tyyyy
pls say at least 3
Answers
Answer:
abby
frisk
mimi
Step-by-step explanation:
Answer:
Mochi, Athena, and Oreo ^^
Step-by-step explanation:
Congrats! :D
Combine like terms to simplify each expression.
1) -3x + 7x
Answers
Answer:
4x
Step-by-step explanation:
-3x + 7x
(-3 + 7)x
4x
Answer:
4x
Step-by-step explanation:
to make it easier, remove the x:
-3+7
Add:
4
Put the X back:
4x
This method will not always work for every problem.
can you solve what is 5 x 1 2/3
Answers
Answer:
8.33333333
Step-by-step explanation:
(x,3) and (7,-5) given m= -8/7
Answers
Answer:
(0, 3)Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
[tex]m[/tex] - slope
[tex]b[/tex] - y-intercept
Given
[tex]m=-\dfrac{8}{7}[/tex]
and point [tex](7;\ -5)[/tex]
Substitute the value of the slope and the coordinates of the point ot the equation of a line:
[tex]-5=-\dfrac{8}{7\!\!\!\!\diagup}\cdot7\!\!\!\!\diagup+b[/tex] cancel 7
[tex]-5=-8+b[/tex] add 8 to both sides
[tex]-5+8=-8+8+b[/tex]
[tex]3=b\to b=3[/tex]
Therefore we have the equation of the line:
[tex]y=-\dfrac{8}{7}x+3[/tex]
Substitute (x, 3) to the equation:
[tex]3=-\dfrac{8}{7}x+3[/tex] subtract 3 from both sides
[tex]3-3=-\dfrac{8}{7}x+3-3[/tex]
[tex]0=-\dfrac{8}{7}x[/tex] divide both sides by (-8/7)
[tex]0=x\to x=0[/tex]
Is this graph a function?
Answers
Answer:A
Step-by-step explanation:
Answer: a
Step-by-step explanation:
Help plz Brainliest if I can gave u cuz sometime I can’t
Answers
Answer:
3 1/2 * 4 = 14
Step-by-step explanation:
To find your answer, which is 14, one side is 3 1/2, and to find cm you need to multiply. 3 1/2 times 4 (Prisms have 4 sides) which is 14!
If you need points or just want points u can answer this very simple question:
What is 2 + 2?
Answers
Answer:
2 + 2 is 4
Step-by-step explanation:
thanks!!!!!!!
Judah's mother gave him a certain amount of money for doing his chores last week. This week she gave him two times the amount because he did a few more chores. After counting the money his mother gave him for the two weeks of chores and the $15 that was already in his wallet, Judah had $52.50. How much did he earn for one week of chores?
Answers
Answer:
He earned $37.50
Step-by-step explanation:
Just subtract the $15 that he already had and you’ll get the answer
If log (100ab^2) is expressed as a function of log b, the result would be:
1). 2 log a + 2 log b
2). 100 log a + 2 log b
3). 2 + log a + 2 log b
4). 2 + 2 log a + 2 log 6
Answers
Answer: Choice (3)
2 + log(a) + 2*log(b)
======================================================
Work Shown:
The log rules we'll use are
log(xy) = log(x)+log(y)log(x^y) = y*log(x)log(10) = 1, where the log is base 10So,
c = log(100ab^2)
c = log(100) + log(a) + log(b^2) ......... use log rule 1
c = log(10^2) + log(a) + log(b^2)
c = 2*log(10) + log(a) + 2*log(b) ......... use log rule 2
c = 2*1 + log(a) + 2*log(b) .................... use log rule 3
c = 2 + log(a) + 2*log(b)
Note: The use of rule 3 assumes that all logs shown are in base 10, which is the default assumed base. Rule 3 doesn't work for any general base. The more generalized rule is [tex]\log_b(b) = 1[/tex]. If b = 10, then we get rule 3 above.
I have no use for my points
Answers
Answer: patronaged by the church
Step-by-step explanation:
frre black Friday points to you guyyysssss!
Have a nice day :)
I think I give brainliest to the person who can tell me the 100 decimal places of Pi!
[tex]\pi[/tex]
3.xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Answers
Answer:
Thanks, hope you have a nice day!
Step-by-step explanation:
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679
What is the equation of this line?
y = 2x
y=12x
y=−2x
y=−12x
Answers
Looking at the line you can see that it is moving up from left to right, making it positive. So -2X and -12X are incorrect.
Next we can find the slope by putting rise over run. Chose a point on the line, I’ll use (2,4).
On this point we rise to 4 and run over to 2.
So for rise over run we have 4/2 which is 2.
So y=2x is correct.
Thi is a venn diagram or set question
In a village all the people speak Hausa or English or both. If 97% speak Hausa an 64% speak English, what percentage speak both languages?
please help me
please
Answers
Answer: The answer is 33% of people spoke Hausa and English language.
Step-by-step explanation:
if the original is 12 units and the scale factor is 1/4 what is the size of the scale drawing?
Answers
What is another way to write the absolute value inequality lp|<1 2?
Answers
Answer:
|p| ≤ 12
Step-by-step explanation:
The absolute value of p less than or equal to 12
Answer:
its A
Step-by-step explanation:
yes