Answers
9514 1404 393
Answer:
a. y = -1/3x +7/3
b. f(6) = 1/3
Step-by-step explanation:
The two given points are (1, 2) and (4, 1). The slope of the line between them is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (1 -2)/(4 -1) = -1/3
The point-slope form of the equation of the line is ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
We can add k to both sides of this equation and substitute for our slope (-1/3) and the first point (1, 2). This gives ...
y = m(x -h) +k
y = -1/3(x -1) +2
y = -1/3x +7/3 . . . . eliminate parentheses
__
b. The value of y when x=6 is ...
y = -1/3(6) +7/3 = (-6 +7)/3
y = 1/3
That is, for f(x) = -1/3x +7/3, ...
f(6) = 1/3
Related Questions
SOLVE PLZ I give brainlest
17+ -9
A. 26
B. 8
C. -8
D.-26
Answers
Answer:
B: 8
Step-by-step explanation:
When you add a negative number, it means you subtract that number.
[tex]17+-9=17-9=8[/tex]
Last year, Derek's mother gave him 53 blue stamps and 36 red stamps to start a stamp collection. Now Derek has 4 times as many stamps in his collection How many stamps does Derek have in his collection? Complete the bar diagram to show your work.
Answers
Answer:
At present he has x stamps
Every month he adds 6 numbers, for 8 months
So total added 8x6=48
The total will be x+48 which is expected to be twice of x
x+48=2x
Solving x=48
At present he has 48 stamps
Step-by-step explanation:
Answer:
356
Step-by-step explanation:
53 + 36 = 89
89 x 4 = 356
and where is the bar diagram????
Find the equation of the line through P=(8,7) such that the triangle bounded by this line and the axes in the first quadrant has the minimal area.
Answers
The area of the triangle is given by the product of 0.5 and the distances of the x and y intercepts from the origin.
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]Reasons:
The area of the triangle, A = 0.5·x·y
Where;
x and y are the values of the line at the intercepts
The equation of the line is; (y - 7) = m·(x - 8)
At the y-intercept, x = 0, therefore;
(y - 7) = m·(0 - 8) = -8·m
At the y-intercept, y = 7 - 8·m
At the x-intercept, y = 0, therefore;
(0 - 7) = m·(0 - 8) = -8·m
At the x-intercept, -7 = m·x - 8·m
8·m - 7 = m·x
[tex]\displaystyle x = \mathbf{8 - \frac{7}{m}}[/tex]
Therefore;
[tex]\displaystyle A = 0.5 \times \left(7 - 8 \cdot m\right) \times \left(8 - \frac{7}{m} \right) = \mathbf{\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}}[/tex]
When the area is minimal, we have;
[tex]\displaystyle \frac{dA}{dm} =0 = \frac{d}{dm} \left(\frac{-32 \cdot m^2 +56 \cdot m - 24.5}{m}\right) = \mathbf{-\frac{32 \cdot m^2 - 24.5}{m^2}}[/tex]
m² × 0 = 24.5 - 32·m²
[tex]\displaystyle m^2 = \frac{24.5}{32} = \frac{49}{64}[/tex]
[tex]\displaystyle m = \sqrt{\frac{49}{64}} = \frac{7}{8}[/tex]
[tex]\displaystyle m = \pm \frac{7}{8}[/tex]
The equation of the line when [tex]\displaystyle m = + \frac{7}{8}[/tex] is therefore;
(y - 7) = m·(x - 8)
[tex]\displaystyle (y - 7) = \mathbf{\frac{7}{8} \cdot (x - 8)}[/tex]
[tex]\displaystyle (y - 7) = \frac{7}{8} \cdot (x - 8) = \frac{7}{8} \cdot x - \frac{7}{8} \times 8 = \frac{7}{8} \cdot x - 7[/tex]
[tex]\displaystyle y = \frac{7}{8} \cdot x - 7 + 7 = \frac{7}{8} \cdot x[/tex]
[tex]\displaystyle y = \mathbf{\frac{7}{8} \cdot x}[/tex]
The x and y intercept of the above line are 0
When [tex]\displaystyle m = - \frac{7}{8}[/tex], we have;
[tex]\displaystyle (y - 7) = -\frac{7}{8} \cdot (x - 8) = -\frac{7}{8} \cdot x + \frac{7}{8} \times 8 = -\frac{7}{8} \cdot x + 7[/tex]
Which gives;
[tex]\displaystyle y = \frac{7}{8} \cdot x + 7 + 7 = \frac{7}{8} \cdot x + 14[/tex]
[tex]\mathrm{The \ equation \ of \ the \ line \ is, }\displaystyle \ y = \mathbf{14 - \frac{7}{8} \cdot x}[/tex]
The equation of the line through P = (8, 7) such that the triangle bounded by the line and the axes in the first quadrant has minimal area is therefore;
[tex]\displaystyle \ \underline{ y = 14 - \frac{7}{8} \cdot x}[/tex]
Learn more here:
https://brainly.com/question/4032024
https://brainly.com/question/1621381
Find the lengths of the sides of the triangle formed by the coordinates below. Then classify the triangle by sides.
A(1,1) B (4,1) C (4,5)
AB =
BC =
AC =
Number of congruent sides=
Then classify the triangle
Isosceles, scalene or equilateral
Answers
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{1}~,~\stackrel{y_1}{1})\qquad B(\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad AB = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(4-1)^2+(1-1)^2}\implies AB=\sqrt{3^2-0^2}\implies AB=3 \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{5})\qquad \qquad BC=\sqrt{(4-4)^2+(5-1)^2} \\\\\\ BC=\sqrt{0^2+4^2}\implies BC=4 \\\\[-0.35em] ~\dotfill[/tex]
[tex]C(\stackrel{x_1}{4}~,~\stackrel{y_1}{5})\qquad A(\stackrel{x_2}{1}~,~\stackrel{y_2}{1})\qquad \qquad CA=\sqrt{(1-4)^2+(1-5)^2} \\\\\\ CA=\sqrt{(-3)^2+(-4)^2}\implies CA=\sqrt{3^2+4^2}\implies CA=5[/tex]
well, how many congruent sides? none, all three sides differ, meaning is an scalene triangle.
what is the value of x
Answers
Answer:X= 41
Step-by-step explanation:
Alan will spend at most $30 on gifts. So far, he has spent $19. What are the possible additional amounts he will spend?
Answers
Answer:
$11
Step-by-step explanation:
This is because If you subtract 19 from 30 your answer will be 19.
9,962÷41. What dose it =
Answers
Answer:
242.975609756
Step-by-step explanation:
Answer:
242.975
Step-by-step explanation:
TIP: u can use a calculator if your teacher allows you, it would be faster :)
A number w increased by 6 is at most -30.
Answers
Could be -24 if you are raising the -30 by 6.
Caroline opens a savings account at her local
bank. She plans to put of her net paycheck
10
in her savings account every week. In June, her
paychecks are $164.69, $177.86, $187.74,
and $163.04. How much money did Caroline
put in her savings account in June?
Answers
Answer:
So she has $50–$43.85 = $6.15 in her pocket and $25 in her savings account
Step-by-step explanation:
7. Given that 16 watermelons cost $48, which of these are equivalent ratios of number of watermelons to cost in dollars? Choose all that apply. A) 16:48 B) 3:1 © 1:3 D) 48:16 E) 3:9
Answers
Answer:
c) 1:3
Step-by-step explanation:
Since 16 watermelons cost $48, the cost of 1 watermelon is 48 / 16 = $3.
Hence 1 : 3
h
A. 2x – 1 + 3x = 0
B.
5.2 -1=0
1) How can we get Equation B from Equation A?
Choose 1 answer:
Add/subtract the same quantity to/from both sides
B
Add/subtract a quantity to/from only one side
Rewrite one side (or both) by combining like terms
Rewrite one side (or both) using the distributive property
Answers
Answer:
A
Step-by-step explanation: :}
A circular garden has a diameter of 10 feet approximately how much edging trim is needed to surround the garden by placing the trim all along the gardens circumference
Answers
Answer: 31.4 feet
Step-by-step explanation:
For this, you basically need to calculate the perimeter of the circle. You do this using this formula:
diameter of the circle times Pie = the circumference of the circle
Since The number of Pie is infinite use the rounded version of pie to 2 decimal points which is 3.14(This is why the question asks for an approximate)
(Diameter = 10 Pie = 3.14 therefore circumference = 31.4)
10 times 3.14 = 31.4 feet
The amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is 31.4 ft.
The garden is circular in shape. Thereforem the trim that is needed to surround the garden is the circumfernce of the graden.
Circumference of a circleThe circumference of a circle is the perimeter of the circle. Therefore,
circumference = 2πr
where
r = radiusTherefore, the amount of edging trim needed to surround the garden by placing the trim all along the gardens circumference is as follows:
circumference = 2 × 3.14 × 5
circumference = 10 × 3.14
circumference = 31.4 ft
learn more on circumference here: https://brainly.com/question/25730499
The letter w represents a whole number such that 2021 + w is a multiple of 7. What is the smallest possible value of w?
Answers
Answer:
2
Step-by-step explanation:
2021/7 leaves a remainder of 5 so add 2 and that's the answer
Use the figure below to answer the questions. Unit 1 Test, Part 2: Basic Tools and Transformations
Answers
Answer: 35
Step-by-step explanation:
How is sin 10° = cos 80°??
Answers
Check the picture below.
Answer:
See below.
Step-by-step explanation:
Location is Q1
Angle is less than 90
cos Ф = sin(90° - Ф)
cos 80° = sin (90° - 80°)
cos 80° = sin 10° set your calculator in degree mode
Check
cos 80° = 0.1736481777
sin 10° = 0.1736481777
Here's Robert's spending diary for one week. It may not look like he's spending much. Use a calculator to add up Robert's total spending for the week. Monday Tuesday Wednesday Thursday Friday Saturday Sunday Lunch $7.00 Shampoo $6.00 Lunch $7.00 Jacket $40.00 Lunch $7.00 Breakfast $4.50 Coffee $2.00 Bus $3.00 CD $14.00 Lunch $7.00 Lunch $7.00 Movie $12.00 Haircut $40.00 Total: $21.00 $13.00 $10.00 $47.00 $19.00 $44.50 $2.00 How much does Robert spend on lunch in a week, in a year? If Robert continues to buy his lunch every weekday, he will be spending /week. S weeks in a year = $ spent during the year.
Answers
how many prime numbers are multiples of 8
Answers
Step-by-step explanation:
four prime numbers..,..,,
What is the least common denominator of
1/3 and 7/9
Answers
Answer:
9
Step-by-step explanation:
9 is the LCD. So you have to multiply 3 by 3 to get 9, so multiply the numerator (1) by 3. 3/9 is the answer to that.
Molly needs to rent a car while on vacation. The rental company charges $19.95, plus 17 cents for each mile driven. If Molly only has $40 to spend on the car rental, what is the maximum number of miles she can drive?
Answers
Usually a company may charge a startup fee, is a charge for some things they need to do to start the service, in this case may just be paperwork, and it's $19.95, a fixed cost, and they're charging 17 cents or $0.17 for every mile driven, let's say that Molly is going to drive "m" miles, so the cost equation in "m" terms will be C(m) = 19.95 + 0.17m.
Now, we know she only has 40 bucks to spend, so, if she can keep her Cost to 40 bucks, how many miles can she go for?
[tex]C(m) = 19.95+0.17m\qquad \qquad \stackrel{\stackrel{cost}{\downarrow }}{40}=19.95+0.17m\implies 20.05=0.17m \\\\\\ \cfrac{20.05}{0.17}=m\implies 117.94\approx m[/tex]
now, if we were to round that up to whole miles, it'd be only 117.
The mileage on Ori's car is 73,033 miles. What is the fewest number of miles that Ori needs to drive before the mileage shows three identical digits again?
Answers
Step-by-step explanation:
The fewest number of miles that Ori needs to drive before the mileage shows three identical digits again is 40.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that the mileage on Ori's car is 73,033 miles.
We need to find the fewest number of miles that Ori needs to drive before the mileage shows three identical digits again.
Therefore, the mileage on Ori's car = 73,033 miles.
identical digits = 40
The fewest number of miles that Ori needs to drive before the mileage shows three identical digits again is 40.
To learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ3
I need help with my math
Answers
Answer:
x^7
Step-by-step explanation:
Answer:
(x)(x)(x) . (x)(x)(x)(x)
Step-by-step explanation:
That's the answer. Hope it helps:)
Use this data set to answer the following question: 5, 10, 12, 4, 6, 11, 13, 5. Remember to show your work.
Calculate the median.
Question 8 options:
Answers
8
Step-by-step explanation:
Put them in order from smallest to largest,
4, 5, 5, 6, 10, 11, 12, 13
The median is the middle value, but because there are 8 numbers, you need to do between 6 and 10 which is:
8
An electrician charges a flat fee plus an hourly rate for a service call. She charges a total of $94 for a 3-hour service call on Monday and $130 for a 5-hour service call on Tuesday. How much should she charge for a 2-hour service call?
$36
$52
$76
$98
Answers
Answer:
$76.
Step-by-step explanation:
help pls ill give brainly
Answers
Answer:
Find the Diameter!
To find the diameter, get the cirumference, divide it by 2, and multiply it by Pi (3.14)
For this certain equation, it appears the circumference is 13. 13/2 is 6.5. 6.5 times 3.14 is 20.41.
Answer:
I think the other guy is correct I'm just putting this here so you can give him/her brainliest
Step-by-step explanation:
Solve for the value of q.
Answers
Answer:
q=13
Step-by-step explanation:
(8q-5)°+81°=180° (angles on a str line)
8q-5+81=180
8q=180+5-81
=104
q=104÷8
=13
Using supplementary angle theorem
[tex]\\ \sf\longmapsto 8q-5+81=180[/tex]
[tex]\\ \sf\longmapsto 8q+76=180[/tex]
[tex]\\ \sf\longmapsto 8q=104[/tex]
[tex]\\ \sf\longmapsto q=13[/tex]
708 Х 34
I have to Estimate I need help please I don't like math
Answers
Answer:
708 times 34 = 24,072
estimated = 710 times 30 = 21,300
Step-by-step explanation:
hope this helped!
mark me brainliest :D
Answer:
Estimate: 21,000 or 21,300 (the answer depends on what your teacher is looking for. you didnt give a lot of information so i apologise if its wrong)
Exact: 24,072
Step-by-step explanation:
Estimate -
700 x 30 = 21,000
or
710 x 30 = 21,300
Exact -
708 x 34 = 24,072
Hope this helps!! :)
1. A ride descends from 100 meters straight down to 0 meters. The distance from the ground at any time is represented by the graph. The slope of the line is -4/5 between 0 and 125 seconds. How far did the ride descend in the time indicated by the marked vertical distance on the graph? (Orange line)
2. A car travels at a rate of 65 mph on a flat highway. How long did it take the car to get from a distance of 123 miles to 318 miles on its journey? (purple line)
Answers
9514 1404 393
Answer:
12 m3 hoursStep-by-step explanation:
1.The slope of the line is "rise"/"run". Here, the "run" is given as (27 s -12 s) = 15 s. So, we have ...
(change in distance)/(15 s) = -4/5 m/s
change in distance = (-4/5 m/s)(15 s) = -12 m
The ride descended 12 meters in the time indicated on the graph.
__
2.Again, the slope is "rise"/"run".
65 mi/h = (318 mi -123 mi)/(travel time)
travel time = (195 mi)/(65 mi/h) = 3 h
The car took 3 hours to get from 123 miles to 318 miles.
What is the numerical answer?
length = inches
Answers
Answer:
31.5 inches
Step-by-step explanation:
If 2 centimeters is 9 inches, then 1 centimeter is 4.5 inches. Then, just multiply by 7.
Lin’s father is paying for a $35 meal. He has a 15%-off coupon for the meal. After the discount, a 4% sales tax is applied.
What is the discount amount? $
What is the subtotal? $
What is the amount of tax added? $
What does Lin’s father pay for the meal? $
also there are suppose to be 4 answers so if you do know it please tell me 4 answers
Answers
Answer:
discount: $5.25
subtotal: $29.75
added tax: $1.19
total: $30.94
Step-by-step explanation:
15% of 35 = $5.25
$35 - $5.25 = $29.75
$29.75 + 4% = $30.94 Sales tax = $1.19
Answer:
Step-by-step explanation:
100% - 15% = 85% = 0.85
$35 × 0.85 = $29.75 (Subtotal)
100% + 4% = 104% = 1.04
$29.75 × 1.04 = $30.94
~~~~~~~~~~~~~~~
What is the discount amount?
$35 × 0.15 = $5.25
What is the subtotal? $29.75
What is the amount of tax added?
$29.75 × 0.04 = $1.19
What does Lin’s father pay for the meal? $30.94
Fill in the blank with a number to make the expression a perfect square.
y^2 + 6y + ?
Answers
Answer:
(y+3)^2 - 9
Step-by-step explanation: