Unit 4 linear equations homework 9 parallel and perpendicular lines (day1) activity
Directions if segments AB and CD are parallel,perpendicular, or neither
Answers
The lines that are parallel continuously have equal distances from each
other and perpendicular lines form 90° angle at their intersection.
The correct responses are;
Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel. ║Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neitherSegment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular, ⊥Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neitherThe equations are parallel, ║The equations are perpendicular, ⊥The equations are perpendicular, ⊥The equations are neither parallel or perpendicularReasons:
Segment [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel where; Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex]
[tex]\displaystyle \overline{AB} \ and \ \overline{CD} \ are \ perpendicular\ where; \ Slope \ of \ \overline{AB} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex]
[tex]1. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{13 - 3}{-2 - 0}} = \frac{10}{-2} = -5[/tex]
[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{3 - 0}{10 - (-5)} = \frac{1}{5}[/tex]
[tex]\displaystyle \mathbf{Slope \ of \ \overline{AB}} = -\frac{1}{Slope \ of \ \overline{CD}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]2. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{\frac{7- 1}{3 - (-6)}} = \frac{6}{9} =\frac{2}{3}[/tex]
[tex]\geq \displaystyle Slope \ of \ \overline{CD} = \frac{-5 - (-1)}{-6 - 0} = \frac{-4}{-6}=\frac{2}{3}[/tex]
Slope of [tex]\mathbf{\overline{AB}}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel
[tex]3. \ \displaystyle Slope \ of \ \overline{AB} = \mathbf{ \frac{2- 4}{-6 - (-2)} = \frac{-2}{-4}} =\frac{1}{2}[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{11 - (-7)}{-1 - 5} = \frac{18}{-6}=-3[/tex]
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
[tex]4. \ \displaystyle Slope \ of \ \overline{AB} = \frac{8- 3}{-3 - 2} = \frac{5}{-5} =-1[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \frac{6 - 2}{-4 - (-8)} = \frac{4}{4}=1[/tex]
[tex]\displaystyle Slope \ of \ \overline{AB} = \mathbf{-\frac{1}{Slope \ of \ \overline{CD}}}[/tex], [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are perpendicular
[tex]5. \ \displaystyle Slope \ of \ \overline{AB} = \frac{-1 - 2}{-8 - (-4)} = \frac{-3}{-4} =\frac{3}{4}[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-3 - 6}{0 - 12}} = \frac{-9}{-12}=\frac{3}{4}[/tex]
Slope of [tex]\overline{AB}[/tex] = Slope of [tex]\overline{CD}[/tex] , [tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are parallel
[tex]6. \ \displaystyle Slope \ of \ \overline{AB} = \frac{5 - (-1)}{6 - 3} = \frac{6}{3} =2[/tex]
[tex]\displaystyle Slope \ of \ \overline{CD} = \mathbf{\frac{-5 - 7}{2 - (-4)}} = \frac{-12}{6}=-2[/tex]
[tex]\overline{AB}[/tex] and [tex]\overline{CD}[/tex] are neither parallel or perpendicular
Directions: To determine if the equations are parallel or perpendicular
Solution:
The equations are parallel if when expressed in the form, y = m·x + c, the value of m are equal
The equations are perpendicular, when we have;
[tex]\displaystyle The \ value \ of \ \mathbf{m} \ in \ one \ equation = -\frac{1}{The \ value \ of \ \mathbf{m} \ in \ the \ other\ equation }[/tex]
7. First equation
3·x + 2·y = 6
Therefore; [tex]\displaystyle y = -\frac{3}{2} \cdot x + 3[/tex]
Second equation; [tex]\displaystyle y = \mathbf{-\frac{3}{2} \cdot x + 5}[/tex]
The value of m which is the coefficient of x are both equal to [tex]\displaystyle -\frac{3}{2}[/tex]
Therefore, the equations are parallel
8. Equation 1; 3·y = 4·x + 15
Therefore;
[tex]\displaystyle y = \frac{4}{3} \cdot x + 5[/tex]
Equation 2; 9·x + 12·y = 12
[tex]\displaystyle y = -\frac{9}{12} \cdot x + 1 = 1 - \frac{3}{4} \cdot x[/tex]
The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular
9. Equation 1: 8·x - 2·y = 4
Therefore;
y = 4·x - 2
Equation 2: x + 4·y = -12
Therefore;
[tex]\displaystyle y = -\frac{1}{4} \cdot x - 3[/tex]
The slope of the equation 2 is the negative inverse of the slope of equation 1, therefore, the equations are perpendicular.
10. Equation 1: 3·x + 2·y = 10
Therefore;
[tex]\displaystyle y = -\frac{3}{2} \cdot x - 5[/tex]
Equation 2: 2·x + 3·y = -3
[tex]\displaystyle y = -\frac{2}{3} \cdot x -1[/tex]
The slopes of the equation 1 and 2 are not equal, and are not the negative inverse of each other, therefore, the equations are neither parallel nor perpendicular.
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Related Questions
When finding a critical T value for 95% confidence and a sample size of 30, how many degrees of freedom are there?
Answers
Answer:
29
Step-by-step explanation:
The formula for calculating degrees of freedom in a t-test is n-1 where n is the sample size. Therefore, there are 30-1=29 degrees of freedom if the sample size is n=30.
What is the answer to n?
Answers
Answer:
n = 108
Step-by-step explanation:
The three medians of a triangle intersect at the same point inside the triangle.
The segment from a vertex to the point in the center is 2 times as long as the
other part of the median line. So OC is 2 times KC.
KC =108
OC = 2(108)
2n + 10 = 216
2n = 206
n = 108
In ΔABC , Value of [tex]n= 31[/tex] as per given condition of median of a triangle .
What is median of a triangle?" Median of a triangle is defined as the line segment passing the vertex of a triangle and intersect at mid point of its opposite side.Intersecting point of three medians is known as Centroid."
Property used
Centroid divides the median in the ratio of [tex]2:1[/tex] from vertex side.
According to the question,
Given,
In ΔABC,
BL, AM, CK are the medians of a triangle ABC.
'O' represents the Centroid
[tex]KC = 108\\\\OC = 2n +10[/tex]
Ratio of [tex]KC : OC = 3: 2[/tex]
Substitute the value of KC and OC we get,
[tex]108 : (2n + 10) = 3:2\\\\\implies 3 (2n+ 10) = 2(108)\\\\\implies 6n + 30 = 216\\\\\implies 6n = 186\\\\\implies n = 31[/tex]
Hence, in ΔABC , Value of [tex]n= 31[/tex] as per given condition of median of a triangle .
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James deposited $575 into a bank account that earned 5.5% simple interest each year. No money was deposited into or withdrawn from the account.
How much money was in the account after 212 years?
Round your answer to the nearest cent.
Answers
Answer:
Answer:it's 654.06I just did the test
Step-by-step explanation:
Like terms can be ________
this is fill - up question
Answers
Answer:
.the same variables and same powers
Step-by-step explanation:
In algebra, like terms are terms that have the same variables and powers. The coefficients do not need to match. Unlike terms are two or more terms that are not like terms, i.e. they do not have the same variables or powers.
HOPE IT HELPS...............
A gym is offering a deal to members. Customers can sign up by paying a registration fee of $100 and $28 per month. The function that models this situation is c(m) = 28m + 100, where m is the number of months and c(m) is the cost of becoming a member.
Determine:
6. the shape of the graph
7. the independent and dependent variables
8. the domain and range
9. Interpret the slope and y-intercept values
10. How much will the membership cost for a whole year?
Answers
6) The equation given is written in standard form of writing the equation of a line y = mx + b
Hence the shape of the graph that denotes the equation c(m) = 28m + 100 is a straight line
7) The independent variable is a variable that can stand alone while the dependent variable is depending on all other variables in an expression.
From the given equation c(m) = 28m + 100, the independent variable is (m) while the dependent variable is c(m)
8) The domain is the input value for which the equation exists while the rage is the output value for which the equation exists. For the given expression, the value of the expression will exist at a point where c(m) > 0
28m + 100 > 0
28m > -100
m > -100/28
m > --25/7
The domain is m > -25/7 while the range is c(m) > 0
9) The comparing the equation with y = xm+ b
where x is the slope
28m = mx
x = 28
This shows that the rate of change of cost per member is $28
The y-intercept is the point where the number of months is 0
If m = 0
c(0) = 28(0) + 100
c(0) = 100
The initial cost of membership in the first month is $100
10) Given the formula c(m) = 28m + 100
For a whole year, m = 12
c(12) = 28(12) + 100
c(12) = 336 + 100
c(12) = 436
Hence the membership will cost $436 for the whole year
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Which expression shows the number 19.65 correctly decomposed?
19 + 0.6 + 0.05
10 + 9 + 0.6 + 0.05
10 + 0.6 + 0.05
19 + 9 + 0.6 + 0.05
Answers
Answer: 10 + 9 + 0.6 + 0.05
Answer:
..............................................................
Step-by-step explanation:
..........................................................................
..........................................................................
Find the slope of the line
Answers
Slope is rise/run
So if you count the rise and run between two point on the graph you will know:)
It is negative because the line is heading down
Can you please help me
Answers
Answer:
11
Step-by-step explanation:
Find the slope of the line that passes through the point (-3,20), (12,15)
Answers
Which expression simplifies to 5√3?
Answers
Answer:
C.
[tex] \sqrt{75} [/tex]
Step-by-step explanation:
You can just enter it in the calculator to see which is equal to
[tex]5 \sqrt{3} [/tex]
I need help to divide fractions
BTW I'm in 5th grade
Answers
Erin finds 5% sales tax for a shirt that costs $21. She calculates the tax as
0.05 * 21 = 1.05 or $1.05.
Erin notices that she can add 21 + 1.05 = 22.05 to find the total cost, $22.05.
She uses the Distributive Property to write (1 * 21) + (0.05 * 21) = 1.05 * 21.
For each item, write the total cost of
the item as the product of two
numbers.
Tax
1.05 x 21
a.
b.
c.
d.
Item Name Price Tax Rate
shirt
$21.00 5%
bicycle $45.90 7%
shoes
$67.50 6%
laptop $299.99 8%
$39.95 4%
Credit Debit Subtotal
Check Cash
Tax
Order total
Print Receipt Cash
video game
$474.34
Answers
Answer:
Step-by-step explanation:
a. Bicycle (1.07 x 45.90)
b. Shoes (1.06 x 67.50)
c. Laptop (1.08 x 299.99)
d. Video Game (1.04 x 39.95)
make v the subject of the formula t=4v+3
Answers
Step-by-step explanation:
t=4v+3
t-3=4v
(t-3)/4=v
hope this helps you.
What is the equation of the line perpendicular to y = -4x + 3 that goes through (8, -3)?
Answers
-4 opposite and reciprocal = 1/4
Y = 1/4x + b
Plug in point
-3 = 1/4(8) + b
-3 = 2 + b, b = -5
Solution: y = 1/4x - 5
5p + 3 = 15
Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
Answers
The given expression represents a number whose 5 times is 3 less than 15 which is 12/5.
Given that,
An expression is given we have to discuss what the expression 5p + 3 = 15 implies.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
5p + 3 = 15
5p = 15 - 3
p = 12 / 5
Thus, the given expression represents a number whose 5 times is 3 less than 15 which is 12/5.
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what is the interest $5,200 at 4% for 3 years
Answers
Answer:
$624
Step-by-step explanation:
I =Prt I being interest paid, P is Principal, r is rate, t is term
I =5200x.04x3
I=624
Which linear equation represents the graph?
A) y = 7x + 3
B) y = 7x + 10
C) y = 1/7x+3
D) y = 1/7x+10
Answers
Answer:
y = 7x + 3
Step-by-step explanation:
A slope of 1/7 will give you a line that is not very steep. Therefore C and D is not the answer.
Now look at A and B. Check point (1, 10) into equations A and B because this point is on the given graph.
y = 7x + 3 y = 7x + 10
y = 7(1) + 3 y = 7(1) + 10
y = 7 + 3 y = 7 + 10
y = 10 (1, 10) y = 17 (1, 17)
ΔABC is an isosceles triangle with AB = AC, D is the midpoint of BC and AD is joined. Prove that ΔABD ≅ ΔACD
Answers
Answer:
ΔABD ≅ ΔACD
Step-by-step explanation: I took the quiz
Opps, forget to add picture. 6 minutes left. Pls help, thank you!
Answers
Answer:
I don't know sorry please forgive me
Answer:
D
Step-by-step explanation:
mean is 11.25 and midian is 10.50
Find the 75th term of the following arithmetic sequence.
2, 8, 14, 20,
..
Answers
Answer:
The 75th term is 446
Step-by-step explanation:
Using the explict formula you get an=6n-4
you plug in 75 for n which means 75 x 6 =450 and the subtract four which gets you 446
Answer:
446 is the 75th term
Step-by-step explanation:
This sequence increases by 6
2 8 14 20 26 32 38 44 50 56 62 68 74 80 86 92 98 104 110 116 122 128 134 140 146 152 158 164 170 176 182 188 194 200 206 212 218 224 230 236 242 248 254 260 266 272 278 284 290 296 302 308 314 320 326 332 338 344 350 356 362 368 374 380 386 392 398 404 410 416 422 428 434 440 446
mean: 7.3
median: 7.1
standard deviation: 1.1
Q1: 6.8
Q3: 7.4
when a tenth time is added to the list, the standard deviation increases to 1.5. is the tenth time likely an outlier
Answers
Answer:
Yes it is an outlier
Step-by-step explanation:
What is the discriminant of the quadratic equation 9x^2+5x-9=0
Answers
Answer:
Δ = 349
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is
Δ = b² - 4ac
9x² + 5x - 9 = 0 ← is in standard form
with a = 9, b = 5 , c = - 9 , then
b² - 4ac
= 5² - (4 × 9 × - 9)
= 25 - (- 324)
= 25 + 324
= 349
what part of 3 dollars are 25 nickels
Answers
Answer:
25 nickles are 5/12ths of a dollar
Step-by-step explanation:
25*5=125, or $1.25. Now we make this a fraction, we get 1.25/3, or 5/12
The 25 nickels are the 5/12 part of the 3 dollars.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We know that 1 nickel = 0.05 dollars.
Then the number of dollars in 25 nickels will be given as,
⇒ 25 x 0.05
⇒ $1.25
Divide the number 1.25 by 3. Then we have
⇒ 1.25 / 3
⇒ 5 / 12
The 25 nickels are the 5/12 part of the 3 dollars.
More about the Algebra link is given below.
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Math help because I forget
Answers
Answer:
R.I.P
Step-by-step explanation:
goodluck doing that
please help i dont understand this!
Answers
Answer:
Pmt Amt $12.50 $23.50 $64.00 $82.00
Fee $0.25 $0.47 $1.28 $1.64
Step-by-step explanation:
The top line is the payment amount.
The bottom line is the 2% fee.
Let's do the middle columns first.
For any payment amount, the fee is 2%.
To find a percent of a number, change the percent to a decimal by moving the decimal point of the percent to places to the left, and multiply the decimal by the number.
2% as a decimal is 0.02
To find 2% of a number, multiply 0.02 by the number.
The second column has payment amount of $23.50
We need to find 2% of $23.50
2% of $23.50 = 0.02 × $23.50 = $0.47
The third column has payment amount of $64.00
We need to find 2% of $64.00
2% of $64.00 = 0.02 × $64.00 = $1.28
Now we do the first and 4th columns. Here we know the fee, and we are looking for the payment amount.
Let the amount be x.
The fee is 2% of x, so the fee is
0.02x
We set the expression equal to the actual fee and solve for x.
The first column has a fee of $0.25
0.02x = $0.25
x = $0.25/0.02
x = $12.50
The 4th column has a fee of $1.64
0.02x = $1.64
x = $1.64/0.02
x = $82
Answer:
Pmt Amt $12.50 $23.50 $64.00 $82.00
Fee $0.25 $0.47 $1.28 $1.64
help asap for brainlist
Answers
Answer:
l=A/W
Step-by-step explanation:
Example:
Area = 500 m^2
w= 10m
L= Area/ W
L=500/10
L=50
To check this
A= L*W
500=50*10
Explanation: if your finding length you just have to get L by itself so you would divide by w to get w on the other side which would get you A divided by w
test ill give brainlist
Subtract.
7/8−4/8
Answers
Step-by-step explanation:
7/8 - 4/8.....find the common denominator
(7-4)/8 .....the common denominator is 8
3/8
hope this helps
Which of the following is equal to this expression? (254 * 64) 1/4
Answers
Answer:
4064
Step-by-step explanation:
254*64=16256*1/4=4064
HELP
One chocolate bar and two coconut bars contain 780 calories. Two chocolate bars
and one coconut bar contains 786 calories. Find the number of calories in each kind
of bar.
Answers
Answer:
Choc Bar: 258 cals
Coco Bar: 264 cals
Step-by-step explanation:
What we can do here is something called making a system of equations.
Let us name the choc. bars x and the coco. bars y.
Then, we can get:
x+2y=780
2x+y=786
Next, we solve for x in the first equation
x=780-2y
Now, we can substitute:
2(780-2y)+y=786
1560-3y=786
-3y=-774
y=258
x=780-516
x=264
find the nth term in the following sequesnce: 1, 3, 9, 27
Answers
Answer:81
Step-by-step explanation: it is skip by 3x so 21 x3 = 81
:)
