A rectangle is graphed on the coordinate grid.
Which represents the equation of the side that is parallel to side s?
Answers
So, the line parallel to s is q, which has these two points: (3,6) and (6,3)
There are different ways to get the line. For instance, this one:
y = a*x+b,
a = slope = difference_y/difference_x = (3-6)/(6-3) = -1,
y = -x + b,
Now use any point, say (3,6) to get b:
6 = -3+b-> b = 9,
line is y = -x + 9,
It checks out in the other point: (6,3) --> 3 = -6+9 = 3. Good.
Other method could be:
y-y2 = a*(x-x2), where (x2,y2) is one of the two points and a is the slope as defined before.
Hope it helps!
The side that is parallel to side s is side q. The equation of side q is: y = -x + 9.
What is the Equation of a Line?We can represent the equation of a line as, y = mx + b, where m is the slope of the line and b is the y-intercept.
The side that is parallel to side s is q.
Slope (m) of q = change in y / change in x = (6 - 3) / (3 - 6) = 3/-3 = -1.
Substitute m = -1 and (3, 6) = (a, b) into y - b = m(x - a):
y - 6 = -1(x - 3)
y - 6 = -x + 3
y = -x + 3 + 6
y = -x + 9
Equation of the side that is parallel to side s is: y = -x + 9.
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Related Questions
How many 6-digit numbers can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, if repetitions of digits are allowed?
Answers
Final answer:
There can be 900,000 unique 6-digit numbers formed using the digits 0-9 with repetitions allowed, considering the first digit cannot be 0.
Explanation:
Calculating 6-Digit Numbers with Repetitions
The question pertains to the number of unique 6-digit combinations that can be made from the digits 0-9 when repetitions are allowed. Since the first digit of a 6-digit number cannot be 0 (as it would make the number a 5-digit number), there are 9 possibilities for the first digit (1-9). For each of the five remaining positions, all 10 digits (0-9) are possibilities because we are allowing repetitions. Therefore, the total number of combinations is calculated by multiplying the possibilities for each digit place.
The solution is as follows: 9 possibilities for the first digit times 10 possibilities for each of the second, third, fourth, fifth, and sixth digits.
9 (first digit) * 10 (second digit) * 10 (third digit) * 10 (fourth digit) * 10 (fifth digit) * 10 (sixth digit) = 900,000 unique 6-digit numbers that can be formed.
The slope of a line running through points (2, 3) and (1, 7) is:
4.
-4.
2.
-2.
Answers
You need to buy 5 notebooks for your classes at school. Each notebook costs $2.79. What is the total costs of 5 notebooks Before tax?
Answers
multiply 2.79 x 5
2.79*5 = 13.95 before tax
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim t → −2 t4 − 3 2t2 − 3t + 3
Answers
Final answer:
To evaluate the limit of the given function, substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get 0.7647.
Explanation:
To evaluate the limit of the given function, we can substitute the value that t is approaching into the expression. In this case, t is approaching -2. Plugging -2 into the function, we get:
lim t → -2 t^4 - 3 / 2t^2 - 3t + 3 = (-2)^4 - 3 / 2(-2)^2 - 3(-2) + 3 = 16 - 3 / 8 + 6 + 3 = 13 / 17 = 0.7647
Therefore, the limit is approximately 0.7647.
What is 35 minus 3 times 8
Answers
Evaluate multiplication first (order of operations).
35-24
Then subtract
35-24=11
Final answer: 11
First you would multiply 8•3 which gives you 24.
Then you would subtract 24 from 35
35 - 24 = 11
Final answer: 11
:)
Find an explicit rule for the nth term of a geometric sequence where the second and fifth terms are 20 and 2500, respectively.
Answers
The formula for geometric sequence is given by:
nth=ar^(n-1)
where:
a=1st term
r=common ratio
n=nth term
thus the 2nd term is:
20=ar^(2-1)
20=ar......i
the 5th term is:
2500=ar^(5-1)
2500=ar^4.......ii
from i
a=20/r
from ii
a=2500/r^4
therefore:
20/r=2500/r^4
multiplying through by r^4 we get:
20r^3=2500
dividing both sides by 20 we get:
r^3=125
hence;
r=5
substituting the value of r in i we get:
20=ar
20=5a
thus;
a=4
the formula for the sequence will therefore be:
nth=ar^(n-1)
nth=4*5^(n-1)
Answer:
The explicit formula of the geometric sequence is:
[tex]a_n=4\times 5^{n-1}[/tex]
Step-by-step explanation:
The explicit formula is the expression where the nth term is given in terms of the first term of the sequence.
We know that the explicit formula for a geometric sequence is given by:
[tex]a_n=(a_1)^{r-1}[/tex]
Here we are given:
The second and fifth terms as: 20 and 2500 respectively.
i.e.
[tex]a_2=20[/tex] and [tex]a_5=2500[/tex]
i.e.
[tex]ar=20\ and\ ar^4=2500[/tex]
Hence,
[tex]\dfrac{ar}{ar^4}=\dfrac{20}{2500}\\\\\\\dfrac{1}{r^3}=\dfrac{1}{125}\\\\\\(\dfrac{1}{r})^3=(\dfrac{1}{5})^3\\\\\\\dfrac{1}{r}=\dfrac{1}{5}\\\\\\r=5[/tex]
Also,
we have:
[tex]ar=20\\\\i.e.\\\\a\times 5=20\\\\i.e.\ a=4[/tex]
Hence, the explicit formula is given by:
[tex]a_n=4\times 5^{n-1}[/tex]
Raina wants to paint the ceiling of her restaurant. The ceiling is in the shape of a square. Its side lengths are 55 feet. Suppose each can of paint will cover 275 square feet. How many cans will she need to paint the ceiling?
Answers
area of the ceiling = 55 x 55 = 3025 square feet
3025/275 = 11 cans
HELP PLEASE ASAP !!!! 80 POINTS !!!!!!!
There are 975 birds in an aviary. Each month, the number of birds decreases by 7%. There are 350 trees in the aviary. Each month, 7 trees are removed.
Part A: Write functions to represent the number of birds and the number of trees in the aviary throughout the months. (4 points)
Part B: How many birds are in the aviary after 12 months? How many trees are in the aviary after the same number of months? (2 points)
Part C: After approximately how many months is the number of birds and the number of trees the same? Justify your answer mathematically. (4 points)
Answers
Part A
months = m
since birds decrease by 7%, there will be 93% left. 93% = 0.93
birds: 975 x 0.93^m
trees: 350 - 7m
Part B
birds: 975 x 0.93^12 = 408
trees: 350-7(12) = 266
Part C
350 - 7m = 0.93^m(975)
We have intersection points at approximately 22.21 and 44.4781. round off to whole numbers, we have 22 and 44 months.
LAW ENFORCEMENT: A police accident investigator can use the formula S=25L‾‾‾√S=25L to estimate the speed s of a car in miles per hour based on the length l in feet of the skid marks it left. How fast was a car traveling that left skid marks 109 feet long?
Answers
sqrtS=25L
where:
L is the length in feet of skid marks it left.
Thus the speed of a car with skid marks L=107 ft =107/5280=0.02 miles, will be:
sqrtS=25*0.02=0.5
thus the speed will be given by:
S=(0.5)^2=0.25 miles per hour
What is the tangent ratio for angle f
Answers
hope it helps
tan(f)=8/6=4/3
The table shows the estimated number of lines of code written by computer programmers per hour when x people are working.
Which model best represents the data?
A.) y = 47(1.191)x
B.) y = 34(1.204)x
C.) y = 26.9x – 1.3
D.) y = 27x – 4
Answers
Answer:
Hence, the model that best represents the data is:
[tex]y=26.9x-1.3[/tex]
Step-by-step explanation:
We are given a table that shows the estimated number of lines of code written by computer programmers per hour when x people are working.
We are asked to find which model best represents the data?
So for finding this we will put the value of x in each of the functions and check which hold true that which gives the value of y i.e. f(x) as is given in the table:
We are given 4 functions as:
A)
[tex]y = 47(1.191)^x[/tex]
B)
[tex]y=34\times (1.204)^x[/tex]
C)
[tex]y=26.9x-1.3[/tex]
D)
[tex]y=27x-4[/tex]
We make the table of these values at different values of x.
x A B C D
2 66.66 49.3 52.5 50
4 94.57 71.44 106.3 104
6 134.14 103.57 160.1 158
8 190.27 150.14 213.9 212
10 269.91 217.64 267.7 266
12 382.85 315.5 321.5 320.
Hence, the function that best represents the data is:
Option C.
y=26.9x-1.3
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches?
Answers
what is the question ?????
What is the approximate difference in the amount of wax needed to make a candle from each of these molds? use π = 3.14. 16.75 cubic inches 20.93 cubic inches 24.25 cubic inches 33.49 cubic inches? what are we taking the diffference from
You pick 3 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 3 digits of your phone number? assume there are no repeats of digits in your phone number.
Answers
P = 1/720
The required probability of the numbers picked of the first three digits of the mobile number is 0.037.
Given that,
Pick 3 digits (0-9) at random without replacement, and write them in the order picked. what is the probability that you have written the first 3 digits of your phone number? assume there are no repeats of digits in your phone number is to be evaluated.
Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
From 0 to 9 we have 10 numbers,
For the number to be picked,
There must be no repetition,
So the number of ways to 1 pick 1st number is 10,
The number of ways to pick 2nd number is 9
The number of ways to pick 3rd number is 8
Total number of ways = 10 + 9 + 8 = 27
Now probability, that this three-digit would be a mobile number,
= 1 / 27
= 0.037
Thus, the required probability of the numbers picked of the first three digits of the mobile number is 0.037.
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Based on the chart, which would be considered the dependant variable?
Answers
Answer:
u didn't provide a chart but the dependent variable is the y axis, or the vertical line
Step-by-step explanation:
It's always the y axis (the vertical line)
If a circle has a diameter of 30 meters, which expression gives its area in square meters?
A.15^2 x π
B. 30 x π
C. 30^2 x π
D. 15 x π
Answers
Radius of a circle is half of the diameter
We have the diameter 30 meters, so the radius is 30÷2=15 meters
Area of the circle = [tex] \pi (15)^{2} [/tex]
Note: The option given doesn't show the [tex] \pi [/tex] symbol but it seems like the correct answer is option A
Answer:
A.15^2 x π (APEX)
Step-by-step explanation:
convert this percent into decimal form
3
82-- % same as 82 3/4%
4
Answers
82% = 0.82
823/4% = 0.8275
if z=2.5, x=102 and x=100, what is s?
Answers
I believe the problem ask for s which is the standard deviation. We must recall that the formula for z statistic is stated as:
z = (x – x over bar) / s
Where,
z = z statistic = 2.5
x = sample value or sample score = 102
x over bar = the sample mean or sample average = 100
s = standard deviation = unknown
Rewriting the equation in terms of s:
s = (x – x over bar) / z
Substituting the given values into the equation:
s = (102 – 100) / 2.5
s = 0.8
Therefore the standard deviation s is 0.8
What is the slope of a line that is parallel to the graph of y=3x-2
Answers
[tex]\bf y=\stackrel{slope}{3}x-2[/tex]
Which is the equation of the trend line that can be generated by using the data from year 1 and 5?
Answers
y = 6.75x + 81.25
you can double check by plug in x values (year) into the equation to find out y values (# of participants)
For those looking for the letter the answer is C
Your welcome :)
At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
Answers
a=2c
6.2c+9.8a=593.4, using a from above in this equation gives you:
6.2c+9.8(2c)=593.4 perform indicated multiplication on left side
6.2c+19.6c=593.4 combine like terms on left side
25.8c=593.4 divide both sides by 25.8
c=23
So 23 child tickers were sold that day.
He measures of the angles of a triangle are in the extended ratio 4 : 5 : 6. what is the measure of the smallest angle?
Answers
4x + 5x + 6x = 180
15x = 180
x = 180/15
x = 12
the measure of the smallest angle = 4x = 4*12 = 48°
$5.50 markup 75% what is the selling prize
Answers
To calculate the selling price with a 75% markup on a $5.50 item, multiply the original cost by 0.75 to find the markup amount and then add it to the original cost. The final selling price is $9.63.
Calculating the Selling Price with a Markup
To determine the selling price of an item with a 75% markup, follow these steps:
Determine the original cost of the item, which is $5.50 in this case.Calculate the markup amount by multiplying the original cost by the markup percentage. Express the percentage as a decimal:Markup Amount = Original Cost × Markup Percentage
Markup Amount = $5.50 × 0.75 = $4.125Add the markup amount to the original cost to get the selling price:
Selling Price = Original Cost + Markup Amount
Selling Price = $5.50 + $4.125 = $9.625Optionally, round the selling price to two decimal places (if necessary):
Selling Price ≈ $9.63
Therefore, the selling price for the item with a 75% markup on an original cost of $5.50 is $9.63.
I just need the answers for this.im really confused
Answers
We have weekly saving of $2.50, the target amount of $85.98 and the amount carried forward from birthday present of $35, We want to work out the number of weeks we need to save to buy season pass
By working backwards, the steps are
[tex]85.98-35=50.98[/tex] ⇒ We subtract the birthday money from the season-pass fee
[tex]50.98/2.50 = 20.392[/tex] ≈ 21 Weeks ⇒ We divide by the amount we save every week
The answer is rounded up to 21 weeks
Question b)
Let the number of weeks be '[tex]x[/tex]' and the season-pass fee be '[tex]y[/tex]'
The equation that represents the context is
[tex]y=35+25x[/tex]
In words: To achieve the value [tex]y[/tex] we need to multiply [tex]x[/tex] by $2.50 (saving) and add $35 (birthday money)
We know that [tex]y=85.98[/tex] as this is the amount we aim to achieve by saving $2.50 per week. Substituting this into the equation we formed earlier we have
[tex]85.98=35+2.5x[/tex] ⇒ Subtract 35 from both sides
[tex]85.98-35=35-35+2.5x[/tex]
[tex]50.98=2.5x[/tex] ⇒ Divide both sides by 2.5
[tex] \frac{50.98}{2.5}= \frac{2.5x}{2.5} [/tex]
[tex]x=20.392[/tex] ≈ 21
We round the answer to 21 weeks. We achieve the same answer with part a)
Question c)
This time, we aim to save $85.98 by the end of 11th week. We might need to adjust the amount we save per week. We will use the same equation we form in part b) but this time we will use the variable [tex]'s'[/tex] to represent the amount of weekly saving.
[tex]y=35+11s[/tex] ⇒ where [tex]y[/tex] is the season pass fee, '35' is the birthday money, '11' is the number of weeks, and [tex]'s'[/tex] is the amount of saving
We have [tex]y=85.98[/tex]
[tex]85.98=35+11s[/tex]
[tex]85.98-35=11s[/tex]
[tex]50.98=11s[/tex]
[tex]s= \frac{50.98}{11}=4.6345 [/tex] ≈ 5
The answer is $5 to be saved for 11 weeks to achieve $85.98
----------------------------------------------------------------------------------------------------------------
Use the same equation to work out the number of weeks we need to save $2.50 per week if we have to pay the higher price of season pass fee of $120.98
[tex]y=35+2.50x[/tex]
[tex]120.98=35+2.5x[/tex]
[tex]120.98-35=2.5x[/tex]
[tex]85.98=2.5x[/tex]
[tex]x= \frac{85.98}{2.5}=34.392 [/tex]≈ 35 weeks
-----------------------------------------------------------------------------------------------------------
If we can start saving as early as possible, then 21 weeks of $2.50/week would work for the cheaper price of season-fee and we don't need to adjust the budget. However, if we still want to aim for $85.98 season pass fee, but only have fewer weeks to save, then adjusting budget is necessary. We can perhaps decide not to go bowling every week so we can use the budget for saving instead, or we can alternate between bowling and movie every week.
Question d)
Using the original budget, we work out a third of $2.50 which is 2.5÷3 = 0.83
It means we have 2.5-0.83 = 1.6 left to save weekly.
Using the same equation with part b)
[tex]y=35+1.6x[/tex] ⇒ Notice that we adjust the constant 2.5 to 1.6
[tex]85.98 = 35+1.6x[/tex] ⇒ We still aim to save for the cheapest season-pass
[tex]85.98-35=1.6x[/tex]
[tex]50.98=1.6x[/tex]
[tex]x= \frac{50.98}{1.6}=31.8625 [/tex] ≈ 32 weeks
We will have 32 weeks × $0.83 = $26.56 to buy gift for Mother.
Question e)
From information from part a) to part d), there are many different ways to adjust the budget.
Indicate a general rule for the nth term of this sequence. 12m, 15m, 18m, 21m, 24m,...
a. = 3mn + 9m
b. = -3mn - 9m
c. = -3mn + 9m
d. = 3mn - 9m
Answers
12m, 15m, 18m, 21m, 24m, ...,
The 1st term is a₁ = 12m
The 2nd term is a₂ = 15m = a₁ + 3m = a₁ + (2-1)*3m
The 3rd term is a₃ = 18m = a₂ + 3m = a₁ + (3-1)*3m
Because each successive term is 3m more than the previous term, we have an arithmetic sequence with a common difference of 3.
Answer:
The n-th term is
[tex]a_{n} = a_{1} + (n-1)*(3m),\\for\, n=1,2,3,\,...,[/tex]
In recursive form,
[tex]a_{n+1}=a_{n}+3m[/tex]
Use the Remainder Theorem to determine which of the following is a factor of p(x) = x 3 - 2x 2 - 5x 6.
Answers
Answer:
x-3
Step-by-step explanation:
The coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1).
Find the midpoint of FJ
A) (0,4)
B) (1, -2)
C) (-4, 0)
D) (5, 2)
This is a question from my math chapter 20: Figures in the Coordinate Plane
Answers
i think that is C i had that one but i forget
hope that help
BMK
Answer:
B. [tex](1,-2)[/tex]
Step-by-step explanation:
We have been given that coordinates of quadrilateral FGHJ are F(-5, -3), G(-3, 3), H(3, 5), and J(7, -1). We are asked to find the coordinates of mid-point of segment FJ.
We will use mid-point formula to solve our given problem.
[tex]\text{Mid-point}=\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}[/tex]
Upon substituting the coordinates of points F and J in mid-point formula we will get,
[tex]\text{Mid-point}=\frac{-5+7}{2},\frac{-3+-1}{2}[/tex]
[tex]\text{Mid-point}=\frac{2}{2},\frac{-4}{2}[/tex]
[tex]\text{Mid-point}=1,-2[/tex]
Therefore, the coordinates of mid-point of segment FJ are [tex](1,-2)[/tex] and option B is the correct choice.
Melinda has 1 seashell, and Jun has 9 seashells. If Melinda and Jun put their seashells together and then divide them up equally, how many will each one of them have? 3 5 8 10
Answers
Answer:
B.) 5
Step-by-step explanation:
Just did this :3
Evaluate the expression m + o for m = 9 and o = 7.
Answers
o = 7
m + 0 = 9 + 7 = 16
Hence, the answer is 16.
The drawing below is an example of what kind of perspective?
One-point
Two-point
Three-point
Four-point
Five-point
Answers
Answer:
Two-point
Step-by-step explanation:
"Orthogonal" lines intersect the horizon at two points. This is an example of 2-point perspective.
What is the point-slope equation of a line with slope -4 that contains the point (-2, 7)?
A. y + 7 = -4(x + 2)
B. y + 7 = -4(x - 2)
C. y - 7 = -4(x - 2)
D. y - 7 = -4(x + 2)
Answers
y - y1 = m(x - x1)
m = -4
(-2, 7)
y - 7 = -4(x + 2)
answer is D