Can someone please help me with #14 and #15?
14.Given y=2(x - 10)+3, write an equation in point slope and slope intercept form that is:
a) Parallel and goes through (-4,1).
b) Perpendicular and goes through (-4,1).
15.Given 5x+2y=7
a.Find an equation parallel to the equation and through (0,10).
b.Find an equation perpendicular to the equation and through (0,10).
This picture is an example of what the answers should look like.
Answers
Problem 14, Part (a)
The given equation y = 2(x-10)+3 has a slope of m = 2. Anything parallel to this will also have the same slope, but a different y intercept.
Let's find the point slope form of the parallel line through (-4,1)
[tex]y-y_1 = m(x - x_1)\\\\y-1 = 2(x - (-4))\\\\y-1 = 2(x + 4)\\\\[/tex]
The point slope form is: y-1 = 2(x+4)Now solve for y to get the slope intercept form.
[tex]y-1 = 2(x + 4)\\\\y = 2(x + 4)+1\\\\y = 2x + 8+1\\\\y = 2x + 9\\\\[/tex]
The slope intercept form is: y = 2x+9============================================================
Problem 14, Part (b)
The original slope is m = 2. Apply the negative reciprocal to go from 2/1 to -1/2. The perpendicular slope is -1/2.
Using the same point (-4,1), we find that the point slope form is...
[tex]y-y_1 = m(x - x_1)\\\\y-1 = -\frac{1}{2}(x - (-4))\\\\y-1 = -\frac{1}{2}(x+4)\\\\[/tex]
The point slope form is: y-1 = (-1/2)*(x+4)Now solve for y
[tex]y-1 = -\frac{1}{2}(x+4)\\\\y = -\frac{1}{2}(x+4)+1\\\\y = -\frac{1}{2}x-2+1\\\\y = -\frac{1}{2}x-1\\\\[/tex]
The slope intercept form is: y = (-1/2)x - 1============================================================
Problem 15, Part (a)
Anything parallel to Ax+By = C will be in the form Ax+By = D. The only thing changes is the C becomes D, where [tex]C \ne D[/tex]. If C = D, then we'd be talking about the exact same line rather than two parallel lines.
We're given 5x+2y = 7. The answer is in the form 5x+2y = D. Plug in (x,y) = (0,10) to find the value of D
5x+2y = D
D = 5x+2y
D = 5(0)+2(10)
D = 20
The equation 5x+2y = D updates to 5x+2y = 20
Answer: 5x+2y = 20============================================================
Problem 15, Part (b)
If you are given Ax+By = C, then anything perpendicular to this is Bx-Ay = D. Here it's possible that C = D; however, it's likely that they'll be different.
The given equation 5x+2y = 7 is perpendicular to anything of the form 2x-5y = D. We'll plug in the given point to find D.
2x-5y = D
D = 2x-5y
D = 2(0)-5(10)
D = -50
Answer: 2x-5y = -50Related Questions
helppppppp pleaseeee again im sorry but i dont know any of itttttt.
Answers
Step-by-step explanation:
sqrt(5x)×(sqrt(8x²) - 2×sqrt(x)) =
sqrt(5x × 8x²) - 2×sqrt(5x × x) =
sqrt(40x) × x - 2x × sqrt(5) =
2x×sqrt(10x) - 2x×sqrt(5)
therefore, the last option is correct.
C plus 3/8 equals 1 1/3 what does C equal
ASAP
Answers
Answer:
Exact Form:
C=23/24
Decimal Form:
C=0.9583
Step-by-step explanation:
What are the zeros of the following function?
Answers
Answer:
Hence , (a,0) is a zeros of a function
Simplify 10^9 ÷ 10^7
Answers
Answer:
10^2
Step-by-step explanation:
10^9/10^7 is the same as 10^9*10^-7 if you multiply two same bases you can add there exponents. So, 9+(-7)=2. So, it’s 10^2
Answer:
100
Step-by-step explanation:
Hope it helps
PLS HELP WILL MARK BRAINLIEST
Answers
(a) A box contains 7 red balls, 6 white balls, and 7 black balls. Two balls are drawn at random from the box (with replacement of the first before the second is drawn). What is the probability of getting a red ball on the first draw and a white ball on the second
Answers
Answer:
Step-by-step explanation:
20=total marbles
7/20 × 6/20= 21/400 or 5.25%
red white
write an absolute value equation representing all numbers x whose distance from 0 is 6 units
Answers
Answer:
Answer:
Step-by-step explanation:
Step-by-step explanation:
You may use a calculator for this item,
Zach, Kolby, and Peyton are investing a total of $360,000 to open a cottee shop Their investments are in the radio
1:2:0.5, respectively
How much has Zach invested, in dollars?
Enter your answer in the space provided
Answers
Based on the investment ratio and the amount invested, the amount that Zach invested is $102,857.14.
First thing to do is to add up the numbers in the ratio:
= 1 + 2 + 0.5
= 3.5
The amount that Zach invested is:
= Zach's ration/ Sum of ratio x Amount invested
= 1 / 3.5 x 360,000
= $102,857.14
In conclusion, Zach invested $102,857.14.
Find out more at https://brainly.com/question/17061956.
Frank is going to buy some ties
at $7.50 per tie and some shirts
at $18.50 per shirt. If he buys
twice as many ties as shirts and
spends no more than $205, what is the greatest number of shirts he
can buy? [All prices include tax.]
Answers
Answer:
6 shirts
Step-by-step explanation:
The cost of a shirt and 2 ties is ...
$18.50 +2(7.50) = $33.50
For $205, Frank can buy $205/$33.50 = 6.12 sets of shirt and ties.
Frank can buy 6 shirts (and 12 ties) for an amount less than $205.
_____
Additional comment
Frank's cost will be $201 for that purchase.
Help me please! This is so confusing!
Answers
Answer:
a) yes, 2, 1/2
b) b = 2t; t = 1/2b
Step-by-step explanation:
a) The number of batteries is twice the number of toys. Using the variables of part B, this relation is ...
b = 2t
This is of the form required for a proportional relation: y = kx, with a value of k=2.
__
If we divide the above equation by 2 on both sides, we get ...
1/2b = t
This is also a proportional relation, with a constant of proportionality of 1/2.
Toys and batteries are in a proportional relationship. The constants of proportionality are 2 or 1/2.
__
b) As we saw above, the equations can be ...
b = 2t
t = 1/2b
pls help the will mean the world
Answers
Answer:
A: the area of the walls that are being painted
C: the cost per gallon of different paints
F: the number of square feet that can be painted per gallon of paint
Step-by-step explanation:
A rectangular poster has a area of 504 centimeters. The width of the poster is 14 centimeters. How long is the poster?
Answers
Answer:
36 cm
Step-by-step explanation:
504/14=36
2x-32=12
means they spent how much
Answers
Answer:
22
Step-by-step explanation:
Write 2 over 5 as a percent.
Answers
Answer:
40%
Step-by-step explanation:
2/5 = 40/100 = 40%
find the sum of 6/12+1/2
Answers
1/2 = 6/12
Answer:
1
Step-by-step explanation:
[tex] \frac{6}{12} + \frac{1}{2} \\ = \frac{1}{2} + \frac{1}{2} \\ = \frac{2}{2} \\ = \frac{1}{1} \\ = 1[/tex]
the table shows the pricing for four different types of gasoline which type cost the least per gallon a $20.20 for 10 galb $26.04 for 12 gal c $28.14 for 14 gal d $30.45 for 15 gal
Answers
Answer:
A is the cheapest deal.
Step-by-step explanation:
find unit rate; cost / quantity
20.20 / 10 = $2.02 per gallon
26.04 / 12 = $2.17 per gallon
28.24 / 24 = $2.01 per gallon
30.45 / 25 = $2.03 per gallon
Find the value of the expression 4a + 7 when a= 1/2.
plssss help quiiick
Answers
Answer:
The answer is 9
Step-by-step explanation:
1/2 of 4 is 2, so you plug that in
2+7=9
The price was reduced from two thousand, four hundred ninety-eight dollars to one thousand, nine hundred ninety- nine dollars. By how much was the price reduced?
Answers
Answer:
$499
Step-by-step explanation:
Since the price was reduced from an amount which is $2,498. You have to take that amount and the other amount which is $1999 and subtract them both.
2489-1999=499
(When you get your answer,make sure to add the dollar sign.)
The price was reduced by $499.
Henry is investing at a continuously compounded annual interest rate of 4.4%. How many years will it take for the balance to triple? Round your answer up to the nearest whole number, and do not include units in your answer.
Answers
The number of years it would take the amount to triple is 25 years.
The formula that would be used to determine the number of years it would take the balance to triple is:
FV = PV x [tex]e^{r}[/tex]N
Where:
n = number of years fv = future value PV = present value e = 2.7182818 r = interest rate3 = [tex]e^{0.044}[/tex]N
Take the log of both sides
log(3) / log(e) / (0.044) = 25 years
A similar question was answered here: https://brainly.com/question/7133042
A bag has 2 blue marbles, 3 red marbles, and 5 white marbles. Which events have a probability greater than One-fifth? Select three options. choosing 1 blue marble choosing 1 red marble choosing 1 red marble, not replacing it, and then choosing a blue marble choosing 1 white marble, replacing it, and choosing another white marble choosing 1 white marble
Answers
hi i know i'm late but might as well add my answer!
here's your answer: B D E or
B.choosing 1 red marble
D.choosing 1 white marble, replacing it, and choosing another white marble
E.choosing 1 white marble
hope i helped
Answer:
b d and e
Step-by-step explanation:
ya
A study was conducted that measured the total brain volume (TBV) (in) of patients that had
schizophrenia and patients that are considered normal. Table #9.3.5 contains the TBV of the normal
patients and table #9.3.6 contains the TBV of schizophrenia patients ("SOCR data oct2009." 2013). Is
there enough evidence to show that the patients with schizophrenia have less TBV on average than a
patient that is considered normal? Test at the 10% level.
Table #9.3.5: Total Brain Volume (in ) of Normal Patients
1663407 1583940 1299470 1535137 1431890 1578698
1453510 1650348 1288971 1366346 1326402 1503005
1474790 1317156 1441045 1463498 1650207 1523045
1441636 1432033 1420416 1480171
1360810 1410213
1574808 1502702 1203344 1319737 1688990 1292641
1512571 1635918
Table #9.3.6: Total Brain Volume (in) of Schizophrenia Patients
1331777 1487886 1066075 1297327 1499983 1861991
1368378 1476891 1443775 1337827 1658258 1588132
1690182 1569413 1177002 1387893 1483763 1688950
1563593 1317885 1420249 1363859 1238979 1286638
1325525 1588573 1476254 1648209 1354054 1354649
Answers
Using the t-distribution, it is found that since the test statistic is less than the critical value for the left tailed test, there is not enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal.
At the null hypothesis, we test if patients with schizophrenia do not have less TBV on average than a patient that is considered normal, that is, the subtraction is not negative, hence:
[tex]H_0: \mu_S - \mu_N \geq 0[/tex]
At the alternative hypothesis, we test if they have less, that is, if the subtraction is negative, hence:
[tex]H_1: \mu_S - \mu_N < 0[/tex]
Regarding each sample, the mean and standard deviation are found using a calculator.
[tex]\mu_N = 1463339.2, s_N = 125458.28 , n_N = 32[/tex]
[tex]\mu_S = 1445132.3, s_S = 171355.8, n_S = 30[/tex]
We have the standard deviation for each sample, hence, the t-distribution will be used.
The standard errors are given by:
[tex]Se_N = \frac{125458.28}{\sqrt{32}} = 22178.1[/tex]
[tex]Se_S = \frac{171355.8}{\sqrt{30}} = 31285.1[/tex]
The distribution of the difference has mean and standard error given by:
[tex]\overline{x} = \mu_S - \mu_N = 1445132.3 - 1463339.2 = -18206.9 [/tex]
[tex]Se = \sqrt{Se_N^2 + Se_S^2} = \sqrt{22178.1^2 + 31285.1^2} = 38348.7[/tex]
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{Se}[/tex]
In which [tex]\mu[/tex] is the value tested at the hypothesis.
Hence:
[tex]t = \frac{\overline{x} - \mu}{Se}[/tex]
[tex]t = \frac{-18206.9 - 0}{38348.7}[/tex]
[tex]t = -0.47[/tex]
The critical value for a left-tailed test, as we are testing if the mean is less than a value, with a significance level of 0.1 and 32 + 30 - 2 = 60 df is [tex]t^{\ast} = 2[/tex]
Since the test statistic is less than the critical value for the left tailed test, there is not enough evidence to show that the patients with schizophrenia have less TBV on average than a patient that is considered normal.
A similar problem is given at https://brainly.com/question/13873630
A local hamburger shop sold a combined total of 813 hamburgers and cheeseburgers on Saturday. There were 63 more cheeseburger sold than burgers. How many hamburgers were sold on Saturday?
Answers
9514 1404 393
Answer:
375 hamburgers
Step-by-step explanation:
Let h represent the number of hamburgers. Then h+63 is the number of cheeseburgers, and the combined total is ...
h +(h +63) = 813
2h = 813 -63 = 750
h = 750/2 = 375
375 hamburgers were sold on Saturday.
_____
Additional comment
In a "sum and difference" problem like this, the smaller number is half the difference between the sum and the difference. h = (813 -63)/2 = 375. This generic solution applies to all "sum and difference" problems.
What is 3 4/5÷(−1 1/10)?
Write the answer as a mixed number in simplest form.
Answers
I converted -11/10 to -1 1/10
Then I did 3 4/5 divided by it
Hope I help pls answer the quizzzz
Complete the equation for the line shown in the graph. (-1,-2) (0,1) (1,4)
Answers
Hope this helped you!! :)
WILL GIVE BRAINLIEST AND WORTH 20 POINTS! A train leaves Los Angeles at 2 p.m. heading north at 50 mph. If the next train leaves three hours later and also heads north at 60 mph, at what time will the second train catch up with the first?
Answers
Answer:
the second train will Cath up with the first after 15 hours hence time will be at (5pm+15hours= 8:00am
Step-by-step explanation:
Which inequality represents this sentence?
A number is no less than 48.
n < 48
n > 48
n < 48
n>48
Answers
The inequality that can be used to represent the information that a number is no less than 48 will be n > 48.
Inequality simply means a mathematical expression that is used in which the sides aren't equal to each other.
It should be noted that the expression that a number is no less than 48 means the number is greater than 48. Therefore, the inequality is n > 48.
Read related link on:
https://brainly.com/question/25701252
Answer: The correct answer is n≥48
Step-by-step explanation: Give me the brainiest
Find the equation of a line that passes through the point (2,5) and has a gradient of 2. Leave your answer in the form y = m x + c
Answers
Answer:
y=2x+1
Step-by-step explanation:
y-5/x-2=2
2x-4=y-5
y=2x+1
Seventy-nine ÷ nine and five
Answers
Answer:
13.77777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777777
1) Write a system of equations to describe the situation below, solve using any method, and
fill in the blanks.
)) Erin is training for a triathlon and needs to swim a certain distance for today's workout.
If she swims at the rec center pool, she will complete a 239-meter warmup and then swim
laps in a lane that is 32 meters long. If Erin swims at the indoor pool at her gym, she will
complete a 223-meter warmup, plus a main set that consists of 33 meters per lap. If Erin
swims the correct number of laps, she can complete the same distance in either pool. How
many laps will that take? How long will Erin's workout be in total?
Erin swims
meters
laps at either pool, she can complete a total workout of
Answers
y = 33x + 223
y = 32x + 239
I still like substitution, so let’s plug in 33x + 223 into the second equation
33x + 223 = 32x + 239
Move the terms into appropriate sides
33x - 32x = 239 - 223
Combine like terms
x = 16
Then plug in x for any equation
y = 32(16) + 239
y = 751
Erin will have to swim 16 laps for a total of 751 meters
Elliot ran 4 laps in 209.2 seconds. If he ran at the same
speed for each lap, what was his time for each lap?
Answers
Answer: 52.3 seconds
Step-by-step explanation:
209.2 divided by 4
which is 52.3 seconds
