Given:
The equation of parallel line is [tex]y=-\dfrac{1}{4}x+5[/tex].
Required line passes through (2,-3).
To find:
The equation of line.
Solution:
We have,
[tex]y=-\dfrac{1}{4}x+5[/tex]
On comparing this equation with [tex]y=mx+b[/tex], where m is slope, we get
[tex]m=-\dfrac{1}{4}[/tex]
Slope of two parallel lines are always same. So, slope of required line is [tex]m=-\dfrac{1}{4}[/tex].
The required line passes through the point (2,-3) having slope [tex]m=-\dfrac{1}{4}[/tex], so the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-3)=-\dfrac{1}{4}(x-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)-\dfrac{1}{4}(-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)+\dfrac{1}{2}[/tex]
Subtracting 3 from both sides, we get
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1}{2}-3[/tex]
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1-6}{2}[/tex]
[tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex]
Therefore, the equation of required line is [tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex].
Christina has 50 coins consisting of quarters and dimes. The coins combined value is $9.50. Write a system of equation to determine how many quarters and dimes Christina has.
Answer:
Christina has 30 quarters and 20 dimes.
Step-by-step explanation:
Given that a quarter is worth 0.25 dollars and a dime is worth 0.10 dollars, if Christina has 50 coins and these add up to a total of $ 9.50, to determine the number of quarters and dimes that she has in her possession, the following calculation must be carried out, taking into account that the difference between a quarter and a dime is 0.15 dollars:
50 x 0.25 = 12.5
12.5 - 9.5 = 3
Thus, the difference between the value that Christina has and the value that she would have if all of her coins were quarters is 3 dollars. Thus, since 0.15 x 20 equals 3, of the 50 coins Christina has, 30 are quarters and 20 are dimes.
This is confirmed through the following equation:
30 x 0.25 + 20 x 0.1 = X
7.5 + 2 = X
9.5 = X
HELP!!! STATS!!!
A random sample of 100 felony trials showed a sample mean waiting time between arrest and trial = 173 days with a population standard deviation of waiting times = 28 days. Find a 99% confidence interval for the population mean waiting time.
Stats question, I'm really stck please help me!
Answer:
The 99% confidence interval is [tex] 165.776 < \mu < 180.224 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 100
The sample mean is [tex]\= x = 173 \ days[/tex]
The population standard deviation is [tex]\sigma = 28 \ days[/tex]
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58 [/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
[tex]E = 2.58 * \frac{28 }{\sqrt{100} }[/tex]
=> [tex]E = 7.224 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex] 173 -7.224 < \mu < 173 + 7.224 [/tex]
=> [tex] 165.776 < \mu < 180.224 [/tex]
The largest prime number that is a factor of 35 is multiplied by the smallest prime number
Answer:
the largest factor of 35 is 35 and the smallest prime number is 2 so 35 times two is 70
Step-by-step explanation:
Given
f
(
x
)
=
−
x
−
3
f(x)=−x−3, solve for
x
x when
f
(
x
)
=
−
2
f(x)=−2.
Answer:
-5
Step-by-step explanation:
Substitute every part of the equation where x appears with the value of x, which is -2
f(-2)=-2-3
f(-2)=-5
So, f(x)=-5
Plzzz answer it :( :
All fraction or mixed number answers are in simplest form or reduced form .
True or false
Answer:
false it is not always reduced form
9.6x10^85/3x10^63 in scientific notation
Answer:
3.27*10^22
Step-by-step explanation:
Given the expression 9.6x10^85/3x10^63, we are to write it on scientific notation as shown:
9.6x10^85/3x10^63
= (9.8/3) * (10^85/10^63)
= (9.8/3) * 10^{85-63}
= (9.8/3) *10^22
= 3.27 *10^22
Hence the expression in scientific notation is 3.27*10^22
whats 7, −6, 4, −10, 3 least to greatest
Answer:
-10, -6, 3, 4, 7
Step-by-step explanation:
Hope it helps ^^
what is wswssssssssss 4+4?
Answer: 4+4=8
Hope this helps :)
Step-by-step explanation:
Say you have four apples, and your friend gives you four more. You put together the amount of apples you have and you get 8.
Look at the equation. y=2x−2 Which situation is best described by the equation?
A. The temperature at 2.00AM 2°c and rises 2°C each hour for x hours
B. The temperature at 2.00AM is -2°C and rises 2°C each hour for x hours
C.The temperature at 2:00AM is 2°C and drops 2°C each hour for X hours
D. The temperature at 2:00AM is -2°C and drops 2°C each hour for x hours.
Answer: A
Step-by-step explanation:y=2x−2 2.00AM 2°c and rises 2°C each hour for x hours
Juanita earns $36 for 3 hours of work. At that rate, how long would she have to work to earn $720?
Answer:
She has to work for 60hours in order to earn $720.
Step-by-step explanation:
Amount of money earned in 1hour=36÷3
=12$
Total time required=720÷12
=60hours
Applesauce recipe for 8 uses 3 quarters of water. How much water for 12 people
Answer:
4.5 quartsStep-by-step explanation:
We use a proportion to solve this.
8/3 = 12/x
Cross-multiply to get:
8x = 36
x = 4.5
The answer to the question is 4.5
0.5= x djdododododododdodod
Answer:
25
Step-by-step explanation:
cuz
Least to greatest 0.4, 5/8, 74%, 3/5
Answer:
0.4,3/5,5/8,74%
Step-by-step explanation:
Change them all into decimals.
Get 0.4,0.625,0.74,0.6
Then reorder and see what their original values were
For a Biology assignment, Lisa collected data on plant growth of a sunflower every week for 9 weeks. When Lisa first planted the sunflower, it was 10 centimeters tall. The time (in weeks) is plotted against the height (in centimeters) as shown below. Using the best-fit line, approximately how tall was the sunflower plant during the fifth week? 33 centimeters 34 centimeters 35 centimeters 30 centimeters
Answer:
I think it was 34 cm because it should be not too long
Step-by-step explanation:
this is from my logic perspective
Explain how to graph 8 is greater than it equal to y
Answer:
t w e n t y c h a r e c t e r s l o n g
One of the Confederation's accomplishments was an arrangement for
{currency to be created}
{foreign troops}
{new states in the West}
{the military}
MY HRW ‼️ Solve the equation. You may find using algebra tiles helpful in solving this problem.
X +6=-X-6
Answer:
x=-6
Step-by-step explanation:
x+6=-x-6
(-6)+6=(6)-6
0=0
Answer:
Solve the equation. You may find using algebra tiles helpful in solving this problem. X +6=-X-6 X= -6
8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to explain.
Answer:
Yes
Step-by-step explanation:
Lisa and Frank type at the same rate.
They both type 1 page every six minutes.
Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get
[tex]\frac{36}{6} = 6[/tex]
And Frank types 5 pages ever 30 minutes, when we divide we get
[tex]\frac{30}{5} = 6[/tex]
need this done quick pls
Answer:
50 degrees
Step-by-step explanation:
40+50=130
130-180
50
Answer:
50
I have not done this in years!
1/13 times 1/2.54 show your work
Answer:
0.03028467595
Step-by-step explanation:
calculator?
simplifyyyyyyyyyyyyyyyyyy
Answer:
Step-by-step explanation:
x^2 - 11x + 30 = (x - 6)(x - 5)
x^2 - 4 = (x + 2)(x - 2)
x^2 + 3x - 40 = (x + 8)(x - 5)
x - 2 = x - 2
Invert and multiply the right fraction.
(x - 6)(x - 5) (x - 2)
=========== x =======
(x - 2)(x + 2) (x + 8)(x - 5)
x - 5 on the top cancels with x - 5 on the bottom
x - 2 on the top cancels with x - 2 on the bottom left
So what's left?
(x - 6)
===============
(x + 2)(x + 8)
This is likely the answer.
Answer:
[tex]\frac{x-6}{x^{2} +10x+16}[/tex]
Step-by-step explanation:
to much to explain
1) -1 = x – 5
2) -5x + 2 = 17
PLS ANSWER PLS PLS PLS
What’s 2/2 x 5/6 plz help me
Answer:
5/6
Step-by-step explanation:
2/2 = 11 × 5/6 = 5/6I hope this helps!
Maggie is participating in her school reading challenge. She reads 80 books in 6 months. If 40 of the books are fiction, then what percent of the books that she read are fiction?
Answer:
50%
Step-by-step explanation:
*In this question, the 6 does not matter*
If 40/80 books are fiction, and if you simplify that fraction, you get 1/2.
Percentages are just fancy fractions and decimals. 50% means 1/2.
Thus, the answer is 50%
Delete this already.
Need help geometric sequences see pic for details
Given:
The recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex]
[tex]a_1=-3[/tex]
To find:
The explicit formula of the given geometric sequence.
Solution:
We know that, first term of geometric sequence is [tex]a_1=-3[/tex].
Recursive formula of a geometric sequence is
[tex]a_n=a_{n-1}\times r[/tex] ...(i)
where, r is common ratio.
We have,
[tex]a_n=a_{n-1}\cdot (\dfrac{1}{8})[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]r=\dfrac{1}{8}[/tex]
The explicit formula of a geometric sequence is
[tex]a_n=a_1r^{n-1}[/tex]
Putting [tex]a_1=-3[/tex] and [tex]r=\dfrac{1}{8}[/tex], we get
[tex]a_n=-3\left(\dfrac{1}{8}\right)^{n-1}[/tex]
Therefore, the correct option is D.
Put these numbers in order from least to greatest.
3 4/5 3 3/4 3.5
Answer:
3/4, 4/5, 3, 3, 3.5
Answer:
3.5,3 3/4,3 4/5
Step-by-step explanation:
plz help! will give brainliest! really easy!
Answer:
C
Step-by-step explanation:
I explained it in the comments of the other one
Find the area of the circle use 3.14 for pi with a radius of 6ft
The formula for the area of a circle (A) is A =Πr2.
r = 6 ft Π = 3.14,
A = 3.14 x 62
A = 113.04 (which is an estimated answer because Π is estimated in this case).
Therefore, the answer would be D. If you can use a calculator, then your answer will be more exact. Just realize that the estimate will put you close enough to your answer in a multiple choice setting if a calculator is not available.
A = 3.14 x 36
Step-by-step explanation:
Help me with this plz!?!? I will mark brainliest!!!
Consider this function.
(r) = -3r + 3
Which graph represents the inverse of function ?
9514 1404 393
Answer:
C. graph Y
Step-by-step explanation:
Starting with f(r) = -3r +3, the inverse function can be found from ...
r = f(y)
r = -3y +3
r -3 = -3y
(r -3)/-3 = y
y = -1/3r +1
The inverse function will have a slightly negative slope and a y-intercept of 1. This matches graph Y.