Hello! Can someone please help me with this question ? I’ll mark brainly thanks ! :)
Answers
Answer:
[tex]\Large\boxed{\text{Perpendicular Equation:} \ y = -\frac{2}{7}x + \frac{22}{7}}[/tex]
[tex]\Large\boxed{\text{Parallel Equation:} \ y = \frac{7}{2}x -12}[/tex]
Step-by-step explanation:
In order to find the equations that are parallel/perpendicular to the line [tex]y = \frac{7}{2}x - 4[/tex], we need to note a couple things about the relationships between lines and their parallel/perpendicular lines.
A) If a line is perpendicular to another, the slopes will be opposite reciprocals (for instance [tex]-2[/tex] and [tex]\frac{1}{2}[/tex] - multiplied, they equal -1.)B) If a line is parallel to another, they will have the exact same slope.Perpendicular:We know that the slope of a perpendicular line will be the the opposite reciprocal of the line we're comparing it to.
Since the slope of our base line is [tex]\frac{7}{2}[/tex], we can find the reciprocal, then the opposite of that.
Reciprocal of [tex]\frac{7}{2} = \frac{2}{7}[/tex] Opposite of [tex]\frac{2}{7} = -\frac{2}{7}[/tex]So the slope of this line will be [tex]-\frac{2}{7}[/tex], making our equation [tex]y = -\frac{2}{7}x+ b[/tex]
However, y-intercepts will not stay the same. In order to find this, we can substitute the point (4, 2) into our equation to solve for b.
[tex]2 = -\frac{2}{7} \cdot 4 + b[/tex] [tex]2 = -\frac{8}{7} + b[/tex] [tex]b = 2+\frac{8}{7}[/tex] [tex]b = 2 \frac{8}{7}[/tex] [tex]b=\frac{22}{7}[/tex]Now we know the y-intercept of this equation is [tex]\frac{22}{7}[/tex]. We can now finish off our equation of the line by substituting that in to what we already have, [tex]y = -\frac{2}{7}x+ b[/tex].
[tex]y = -\frac{2}{7}x+ \frac{22}{7}[/tex]
Parallel:As mentioned earlier, parallel lines will have the exact same slope but not the same y-intercept. Since the slope of our original equation is [tex]\frac{7}{2}[/tex], the slope for this one will also be [tex]\frac{7}{2}[/tex].
So we now know the equation looks something like [tex]y = \frac{7}{2}x + b[/tex].
In order to solve for b, we apply the same logic we did in the perpendicular line and substitute in the point (4, 2) into the equation.
[tex]2 = \frac{7}{2} \cdot 4 + b[/tex] [tex]2 = \frac{28}{2}+b[/tex] [tex]2 = 14+b[/tex] [tex]b = 2-14[/tex] [tex]b =-12[/tex]Now that we know the slope and the y-intercept, we can finish off our equation as [tex]y = \frac{7}{2}x -12[/tex].
Hope this helped!
Related Questions
What is this question?
Answers
Answer:
A
Step-by-step explanation:
So timing a fraction with a fraction smaller by 1 means its a proper fraction.
And it can't get bigger than it already is because it's timing a less than 1 itself.
So it's A, it will be smaller
ABCD is a parallelogram. AB = x + 16, AD = 4y – 4, CD = 2x + 8. If the perimeter of ▱ABCD is 80, find the value of y.
Answers
Answer:
Coronavirusss
Step-by-step explanation:
Stay at home :D
Wilson is 6 years older than Mary. Wilson's age is 10 years less than five times Mary's age. The equations below model the relationship between Wilson's age (w) and Mary's age (m):
w = m + 6
w = 5m − 10
Which is a possible correct method to find Wilson's and Mary's ages?
Solve w + 6 = 5w − 10 to find the value of w.
Write the points where the graphs of the equations intersect the x axis.
Solve m + 6 = 5m − 10 to find the value of m.
Write the points where the graphs of the equations intersect the y axis.
Answers
Answer:
no 4=f
Step-by-step explanation:
dwfn sdv and it appers to be marys age ;)
think before you do something rude
Answer:
C. Solve m + 6 = 5m - 10
Step-by-step explanation:
Wilson is 6 years older than Mary.
(MARY's age + 6 = WILSON's age)
Wilson's age is 10 years less than five times Mary's age.
(MARY's age * 5 - 10years = WILSON's age)
(Mary is 4 years old and Wilson is 10:
4 + 6 = 10
4(5) = 20 - 10 = 10
just in case you were curious)
Good luck!!
You spent $34 for 8.5 gallons of gasoline. At
the same price per gallon, how many gallons
could you buy for $51?
Answers
which expression shows the correct way to expand (6x-6)^2?
Answers
Answer:
[tex](6x -6)^{2} = (6x +6)(6x +6) = 36x^{2} -72x + 36[/tex]
Step-by-step explanation:
Even if I don't know the options I can give all the option that will be right for expending this. Just look at each step and see which one is one of the options.
[tex](6x -6)^{2} = (6x +6)(6x +6) = 36x^{2} -72x + 36[/tex]
If your first first oil changes 5000 miles and then every three hundred three thousand miles after if you drive your car 250 miles a week how many oil changes will you need the first year
Answers
Answer:
4 oil changes
Step-by-step explanation:
Given that:
Distance after first oil change = 5000 miles
Subsequent oil changes = 3300 miles
If distance in miles moved per week = 250 m
Number of weeks per year = 52
Total miles moved per year = (250 * 52) = 13000 miles
Let Number of oil change per year = n
Difference between successive oil change = d = 3300 miles
Using the relation :
Total miles = Ist change + (n - 1)d
13000 = 5000 + (n - 1)3300
13000 = 5000 + 3300n - 3300
13000 = 1700 + 3300n
13000 - 1700 = 3300n
11300 = 3300n
n = 3.424
Hence, number of oil. Changes in first year = 4
How can you use the coordinates of two points on a line to determine the slope of the line?
Answers
Answer:
you can use the slope intercept formula!
y2-y1/x2-x1
Step-by-step explanation:
lets take an example!
the coordinates of 1 point are (2,4) and the other point is (4,6)
so lets plug in (x1,y1) (y1,y2)y2 is the y intercept of second point so it is 6 minus y1 which is 4.
6-4/x2-x1
lets do same for x!
6-4/4-2
lets solve
2/2
=1
the slope is 1
What is the amount of INTEREST paid on this loan: Principal: $3,500 Rate: 14% Term: 2 years
Answers
Answer:
Annual interest rate for this loan. Interest is calculated monthly on the current outstanding balance of your loan at 1/12 of the annual rate.
Monthly loan payment is $400.76 for 60 payments at 7.5%.
Step-by-step explanation:
Calculate:PaymentAmount
?Loan amount:*Enter an amount between $0 and $100,000,000
$20,000
?Monthly payment:
$401
?Interest rate:*Enter an amount between 0% and 25%
7.5%
?Term in months:*Enter an amount between 1 and 480
60
Total interest paid:$4,045.51
Total payments:$24,045.51
Abdul can type 23 words per minute. Abdul has a 500-word essay to type for his English teacher. How long will it take him to type it? Round your answer to the nearest minute.
pleaseeee
Answers
Answer:
22 minutes. (rounded)
Step-by-step explanation:
Ok so what your going to do is just divde.
You divide and get 21.7
So round it and you will get 22 minutes.
help pls !!!! order them from least to greatest
Answers
Answer: 3.5 , 2 1/2 , 5, 7, 11, π
Step-by-step explanation:
i hope i said those right
the number of members in 20 families in a village is given as 6,8,6,3,2,5,7,8,6,5,5,7,7,8,6,6,7,7,6,5
how many families have more than 5 members
step by step explanation please answer this... don't spam
Answers
Answer:
2
6,6,6,6,6,6=more than 5
7,7,7,7,7=has exactly 5 members
If the sum of the measures of the interior
angles of a polygon is 1930°, how many sides
does it have?
Answers
Answer:
Thus, the number of sides: n ≈ 13 (rounded to the nearest whole number).
Step-by-step explanation:
We know that the formula of the sum of the measures of the interior angles of a polygon
Sum = (n-2) × 180°
where
n is the number of sides
In your case, since the sum of the interior angles is 1930°, then
1930° = (n-2) × 180°
so we can determine the number of sides n, such as
1930 / 180 = n-2
[1930 / 180] + 2 = n
n ≈ 12.7
If 12.7 rounded to the nearest whole number, then
n ≈ 13
Thus, the number of sides: n ≈ 13 (rounded to the nearest whole number).
MATH LOVERS!!! Can u send me a pic of you filling this out plz!!!!
Answers
Answers
Located In The Following Attachments
High Hopes
Barry-
Answer:
you would just do 2/3*-6-1= -5
and you would fill in the numbers in the x column and solve
5-1/2*-2=6
and you would replace x with the number in the x column
(ik i already helped you on this lol)
have a great day/night
In the picture I need the answers to the questions.
Answers
Answer:
a) [tex]\mathbf{ f(g(x))=x+2\sqrt{x} +1}[/tex]
b) [tex]\mathbf{f(g(9))=16}[/tex]
Step-by-step explanation:
We are given:
[tex]f(x)=(x-2)^2\\g(x)=\sqrt{x} +3[/tex]
We need to find [tex]a) f(g(x))\\b) f(g(9))[/tex]
a) First finding: [tex]f(g(x))[/tex]
It can be found by putting the value of g(x) into f(x)
We are given:
[tex]f(x)=(x-2)^2\\Put\:x=g(x)\:i.e. \: x= \sqrt{x} +3\\f(g(x))=(\sqrt{x} +3-2)^2\\Now\: solving:\\f(g(x))=(\sqrt{x} +1)^2\\Using\:formula\:\mathbf{(a+b)^2=a^2+2ab+b^2}\\f(g(x))=(\sqrt{x})^2+2(\sqrt{x} )(1)+(1)^2\\ f(g(x))=x+2\sqrt{x} +1[/tex]
SO, we get: [tex]\mathbf{ f(g(x))=x+2\sqrt{x} +1}[/tex]
b) Now finding: [tex]f(g(9))[/tex]
It can be found by putting x=9 in f(g(x))
We have:
[tex]f(g(x))=x+2\sqrt{x} +1\\Put\:x=9\\f(g(9))=9+2\sqrt{9}+1\\We\:know\: \sqrt{9}=3\\ f(g(9))=9+2(3)+1\\f(g(9))=9+6+1\\f(g(9))=16[/tex]
So, we get: [tex]\mathbf{f(g(9))=16}[/tex]
Stanley has a collection of seashells. He found 35% of his collection on Florida beaches. If Stanley has 49 seashells from Florida, how many seashells does he have in his collection all together?
A) 90
B) 120
C) 140
D) 160
Answers
Answer:
140 shells. So, C
Step-by-step explanation:
Let x equal the total number of shells in Stanley's collection. Then,
.35 x = 49
x = 49 / .35
x = 140
The temperature was 80 °F and then fell 20 °F. What is the new temperature?
Answers
Hope this helps have a nice day :) !!!
y=2x+2 y+4=2(x-3)
What is the solution of the system of equations?
Answers
Answer: y = 2x + 2
y + 4 = 2 (x − 3)
Note sure but hope this helped!!!
If the elevator ascends or GOES UP 80 meters, is
that represented by 80 or -80?
Answers
Answer:
80
Step-by-step explanation:
Under her cell phone plan, Hannah pays a flat cost of $65.50 per month and $4 per
gigabyte, or part of a gigabyte. (For example, if she used 2.3 gigabytes, she would
have to pay for 3 whole gigabytes.) She wants to keep her bill under $70 per month.
What is the maximum whole number of gigabytes of data she can use while staying
within her budget?
Answers
Answer:
1 gigabyte
Step-by-step explanation:
70-65.50=4.5
The maximum whole number of gigabytes of data she can use while staying within her budget 2 gigabytes.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now given that,
Flat cost per month = $65.50
Cost per gigabyte = $4
Let x be the total gigabytes she uses in a month.
Thus, Cost of gigabytes of month = 4x
So, total bill of the month = 65.50 + 4x
Now since, Hannah wants to keep her bill under $70 per month
⇒ 65.50 + 4x ≤ 70
Subtracting 65.50 both the side we get,
4x ≤ 70 - 65.50
⇒ 4x ≤ 4.50
Dividing 4 both the side we get,
⇒ x ≤ 1.125
Since she has to pay for the whole gigabytes
⇒ x ≤ 2
which is the required gigabytes she can use to keep her bill $70.
Thus, the maximum whole number of gigabytes of data she can use while staying within her budget is 2 gigabytes.
To learn more about inequality :
https://brainly.com/question/13363104
#SPJ2
Guy looks at his checking account balance and sees that it is less than −10 dollars.
Select from the drop-down menu to correctly complete the statement.
An account balance less than−10 dollars represents a debt
Choose...
10 dollars. is t greater less or = to
Answers
Answer:
greater than
Step-by-step explanation:
Steve decreased the number of miles he ran from 25 to 18. By what percent did the number of miles decrease?
Answers
Answer:
28%
Step-by-step explanation:
1) 25-18=7(your decreased value)
2) 7(decreased value of miles ran)/25(overall number of miles ran)
3) 7/25*4/4 (this will make the denominator 100)=28/100=28%
Algebra 1 Honors
BUSINESS a printing press valued at $120,000depreciates 12% per year. What will be the approximate value for the printing press in 7 years?
A. $19,200 B. $265,282 C. $49,041 D. $55,728
Answers
Answer:
19200
brainliest if correct
Explanation
12% of 120,000 = 14400
14400x7 = 100800
120,000 - 100800 = 19200
5x^2-12=88 solve algebraically
Answers
Answer:
x = 2sqrt(5) or x = -2sqrt(5)
Step-by-step explanation:
5x^2 - 12 = 88
5x^2 = 100
x^2 = 20
x = +/- sqrt(20)
x = 2sqrt(5) or x = -2sqrt(5)
Answer:
[tex]x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
Step-by-step explanation:
Given equation: [tex]5x^2-12=88[/tex]
Step 1: Add 12 to both sides.
[tex]\\\implies 5x^2-12+12=88+12\\\\\implies 5x^2=100[/tex]
Step 2: Divide both sides by 5
[tex]\\\implies\dfrac{5x^2}{5}=\dfrac{100}{5}\\\\\implies x^2=20[/tex]
Step 3: Take the square root of both sides (positive and negative roots).
[tex]\\\implies \sqrt{x^2}=\sqrt{20}\\\\\implies x=\pm\ \sqrt{20}[/tex]
Step 4: Simplify.
[tex]\\\implies x=\pm\ \sqrt{4\times5}\\\\\implies x=\pm\ 2\sqrt{5}[/tex]
Step 5: Separate into two cases.
[tex]\implies x_1=-2\sqrt{5},\ x_2=2\sqrt{5}[/tex]
Another example:
https://brainly.com/question/20778317
What is the value of x?
(2x + 15)°
to
2x
A. 24
B. 33
C. 72
D. 75
Answers
Answer:
D. 75
Step-by-step explanation:
Andre’s school orders some new supplies for the chemistry lab. The online store shows a pack of 10 test tubes costs $4 less than a set of nested beakers. In order to fully equip the lab, the school orders 12 sets of beakers and 8 packs of test tubes.
Write an equation that shows the cost of a pack of test tubes, , in terms of the cost of a set of beakers, .
Answers
Answer:
70
Step-by-step explanation:
Which property is illustrated? 8(a + c) = 8a+ 8c
Answers
Answer:
Distributive property
Step-by-step explanation:
Here, we want to evaluate the property illustrated
From what we can see, we have that each of the inner values are multiplied by the outside value
This is simply a display of distributivity
We can conclude that we have a right distributive property in place here
Why does the narrator state that taking the road less traveled has made all the difference?
Answers
Answer:
See below
Step-by-step explanation:
The phrase itself is a famous few lines extracted from "The Road Not Taken" by poet Robert Frost. The statement "taking the road less traveled" means that someone is acting independently, freeing themselves from the conformity of others (who choose to take 'the road more often traveled.'), generally making their own choices, and perhaps leaving a new trail that will become the road more often traveled
all the multiples of 5 are multiples of 10
Answers
Answer:
False
Step-by-step explanation:
This is the answer because:
1) All the multiples of 5 are not multiples of 10 because multiples of 10 end in zeros and not all the multiples of 5 end in a zero.
Therefore, the answer is false.
Hope this helps! :D
Answer: false
Step-by-step explanation: say for instance 25 (5•5) is not a multiple of 10
HELP ASAP!!!!!!!
PLS I NEED THIS TURNED IN IN 10 MINS
Answers
Answer:
slope = 2
y-int = 3
Step-by-step explanation:
y-intercept can be determined by the coordinate (0,3) which is 3 units up from origin on the y-axis
slope can be determined by taking the difference of a pair of y-values and dividing it by the difference of the x-values
ex, 3 - 1 = 2
0 - (-1) 1
or: 5 - 3 = 2
1 - 0 1
ﾟ+*:ꔫ:*
A. (2, 1)
B. (1, -2)
C. (1, 2)
D. (-1, 2)
♡━━━━━━━━━♡
︎thank you! ♡´･ᴗ･`♡
Answers
Answer:2,1
Step-by-step explanation:
Answer:
C
Step-by-step explanation: