The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.
What is the equation of a line passing through two given points in 2 dimensional plane?Suppose the given points are (x_1, y_1) and (x_2, y_2),
then the equation of the straight line joining both two points is given by
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).
So, the equation would be
[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]
[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]
Hence, the equation of line is option B. y = -5/2 x + 8.
Learn more about straight line equation here:
https://brainly.com/question/380976
#SPJ1
Answer:B
Step-by-step explanation:
5. Gaur Grandeur is a society which has a garden of length 45 5/7 m and breadth 16 3/4m. Find area of garden
Step-by-step explanation:
Here,
given length= 45 5/7 m( mixed fraction)
= 320/7 m( simple fraction)
similar breadth= 16 3/4 m
= 67/4 m
Now,
Area= length* breadth
= 320/7 * 67/4
=5360/7 m²
Step-by-step explanation:
I guess this means the garden is a rectangle.
the area is
length × breadth (or width or ...)
so,
45 5/7 × 16 3/4 =
= (45×7 + 5)/7 × (16×4 + 3)/4 =
= 320/7 × 67/4 = 320×67 / 7×4 = 80×67 / 7 =
= 5360/7 = 765 5/7 m²
A highway patrol officer is seated on a motorcycle on a curvy section of Highway 1. The posted speed limit is 45 miles per hour on this stretch of highway. The officer is monitoring traffic using radar. The next exit is 3.6 miles up the road. The radar picks up a speeding car averaging 68 mph. When the officer tries to start his motorcycle to follow the car, it won’t start. He tries again and again, and soon he fears that he won’t be able to catch the speeding car before it turns off the highway. Finally, his motorcycle starts and he begins the pursuit 30 seconds after the speeding car has passed him on the roadside.
How fast does the officer need to go to catch up to the speeding car? What is his average speed in pursuit?
Answer:
80.7 mph
Step-by-step explanation:
In order to catch the car at the exit, the officer must cover the distance in 30 seconds less time than the car does. The time, speed, distance relation can be used.
Time for car to reach the exitThe relation between time, speed, and distance is ...
time = distance/speed
Here, speed is in miles per hour, and distance is in miles. That means time will be given in hours by the straightforward application of this formula.
time = (3.6 mi)/(68 mi/h) = (3.6/68) h = 9/170 h
Time for the motorcycle to reach the exitThere are 3600 seconds in 1 hour, so 30 seconds represents this fraction of 1 hour:
30/3600 = 1/120
The motorcycle will have this amount of time less than the time the car takes to reach the exit, so ...
(9/170 -1/120) h = (9(120)-170)/(170×120) h = 910/20400 h = 91/2040 h
Motorcycle speedThe speed required to cover 3.6 miles in 91/2040 hours is ...
speed = distance/time
(3.6 mi)/(91/2040 h) = 3.6×2040/91 mph = 7344/91 mph ≈ 80.7 mph
The officer's average speed in pursuit must be 80.7 miles per hour (or faster).
__
Additional comment
There are other ways the problem can be worked. One of them is to consider the remaining distance the car must travel when the officer begins pursuit. That will be 3.6 mi less (1/120 h)(68 mi/h) = 17/30 miles. The ratio of the officer's speed to the car's speed will be the same as the ratio of the officer's miles to the car's miles: 3.6/(3.6 -17/30) × 68 mph ≈ 80.7 mph.
Intermediate values used in the calculations should be kept at full calculator precision. Rounding should only be done at the end. Here, the actual speed required is 80.7032967... mph, rounded down for the above result.
How would you graph y-intercept is 8 and x-intercept is 9
Answer:
all shown below
Step-by-step explanation:
y-intercept means a dot's y coordinate is 8 and on the y axis, x-i intercept means a dot's x coordinate is 9 and on the x axis
Answer:
see the attached graph
Step-by-step explanation:
The intercepts are the points where a graph crosses the coordinate axes.
Y-interceptThe y-intercept is the the point where the graph crosses the y-axis. The value of x is zero there. The coordinates of the y-intercept are (0, 8).
X-interceptThe x-intercept is the point where the graph crosses the x-axis. The value of y is zero there. The coordinates of the x-intercept are (9, 0).
You graph these intercepts by plotting the points at these coordinates.
__
In the attached graph, the intercepts are blue dots, and we have drawn a line through them. The line is not part of the graph of the intercepts. It is merely an instance of a function that has these intercepts.
2.1 If 5 + 3 = 0 and < 0, evaluate (without using a calculator):
2.1.1 22 − 1 (4)
2.1.2 2 + 2 (3)
2.1.3 1 − 2
1. 18
2.8
3.-1
What is expression?An expression is a set of terms combined using the operations +, – , x or ,/.
Given:
1. 22 − 1 (4)
=22- 1*4
= 22-4
= 18
2. 2 + 2 (3)
=2+2*3
=2+6
=8
3. 1 − 2
= -1
Learn more about expression here:
https://brainly.com/question/14083225
#SPJ1
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is twice the measure of the first angle. The third angle is fourteen more than the second. Find the measures (in degrees) of the three angles.
Jimmy’s original account balance when he opened up his savings account was $3,450.00. In the last two years, he has made no other deposits and it has a current balance of $3,485.95. How much interest did he earn?
The interest that Jimmy's account has earned is $35.95.
What is the interest that Jimmy's account has earned?Interest is the total increase in excess of the amount deposited in the account. Interest earned can be determined by subtracting the amount deposited from the current balance.
Interest = current balance - amount deposited
$3,485.95 - $3,450.00 = $35.95
To learn more about interest, please check: https://brainly.com/question/14935026
#SPJ1
Which represents the inverse of the function f(x) = 4x?
• h(x) = X + 4
• h(x) =x-4
O h(x) = -x
• h(x) = x
Find M∠BFE.
A. 116
B. 58
C. 148
D. 164
Answer:
C
Step-by-step explanation:
57+57+34=148
Given f(x) = 4x + 2, find f-1(3).
Answer:
1/4
Step-by-step explanation:
The inverse function tells you the input value that corresponds to the given output value of the function.
ApplicationYou want f^-1(3), which is the value of x such that f(x) = 3.
f(x) = 3 = 4x +2
1 = 4x . . . . . . subtract 2
1/4 = x . . . . . divide by 4
The inverse function of 3 is 1/4:
[tex]\boxed{f^{-1}(3)=\dfrac{1}{4}}[/tex]
Betty wants to put new cabinets in her kitchen. She measures one side of her kitchen and finds it measures 181818 meters.
Which measurement did Betty find?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Area
(Choice B)
B
Perimeter
(Choice C)
C
Length
Answer:
lenght
Step-by-step explanation:
I think it is that because it says ONE SIDE and for area and perimeter of a square/ rectangle you need more than one side
hope it helps
A person invested $7700 for 1 year, part at 8%, part at 9%, and the remainder at 12%. The total annual income from these investments was $811. The amount of money invested at 12% was $1100 more than the amounts invested at 8% and 9% combined. Find the amount invested at each rate.
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 8%, y represent the amount of money invested at 9% and z represent the amount of money invested at 12%
x + y + z = 7700 (1)
Total interest is:
(x * 1 * 0.08) + (y * 1 * 0.09) + (z * 1 * 0.12) = total interest
0.08x + 0.09y + 0.12z = 811 (
Also:
z = 1100 + x + y (3)
From equation 1, 2 and 3:
x = 1400, y = 1900 and z = 4400
T
The amount invested at 8% was $1400, $1900 was invested at 9% and $4400 was invested at 12% making a total annual income of $811.
Find out more on equation at: https://brainly.com/question/2972832
#SPJ1
f(x) = -3x³ + x² - 3, find f(1).
Answer:
Step-by-step explanation:
hello :
f(x) = -3x³ + x² - 3, find f(1).
f(1) = -3(1)³ +(1)² - 3=-3+1+3 = -5
An artist sells her sculptures for $250. Each piece costs her $150 to make, and she spends $11000 per year for her studio and other fixed costs. How many sculptures must she sell if she wants to make $10000 in profit
l don't know if you know it tell please
32 randomly picked people were asked if they rented or owned their own home, 8 said they rented. Obtain a point estimate of the proportion of home owners.
Group of answer choices
0.250
0.600
0.750
0.200
0.500
Answer:
.750
Step-by-step explanation:
Can anyone help me solve this question?
Answer:
corresponding angles
Step-by-step explanation:
i dont cap
For a certain company, the cost for producing x items is 50x+300 and the revenue for selling x items is 90x−0.5x^2 .
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300 .
Part c: Is it possible for the company to make a profit of $15,000 ?
a. The expression for profit is p(x) = -0.5x² + 40x - 300
b. The two values of x that will create a profit of $300 is 20 and 60
c. it is not possible for the company to make a profit of $15,000
What is profit?The profit is the selling price minus the cost price.
Therefore,
Profit = revenue - cost
a.
The expression for profit is as follows;
p(x) = 90x − 0.5x² - (50x + 300)
p(x) = 90x − 0.5x² - 50x - 300
p(x) = -0.5x² + 40x - 300
b.
The two values of x that will create a profit of $300 is as follows;
-0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
0.5x² - 40x + 600 = 0
x² - 80x + 1200 = 0
(x - 20)(x - 60) = 0
x = 20 and 60
Therefore, the two value of x are 20 and 60
c.
-0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 300 - 15000 = 0
-0.5x² + 40x - 15300 = 0
x² - 80x + 30600 = 0
There is no real solution. Therefore, it is not possible for the company to make a profit of $15,000
learn more on profit here: https://brainly.com/question/24238456
#SPJ1
triangle ABC is isosceles, angle B is vertex angle , AB = 20x -2, AC =25x, and BC =12 x +20. Find x and the length of each side of the triangle?
Length of AB = 18. 92
Length of AC = 26. 15
Length of BC = 32. 552
How to determine the sides of the triangleUsing the Pythagorean theorem, we have that
[tex](20 x-2)^2 = (12x + 20)^2 + (25x)^2[/tex]
Expand the bracket
[tex]400x^2- 4 = 144x^2 + 400 + 625x^2[/tex]
Collect like terms
[tex]400x^2 - 144x^2 - 625x^2 = 400 + 4[/tex]
[tex]-369x^2 = 404[/tex]
Make x^2 subject
[tex]x^2 = \frac{404}{369}[/tex]
[tex]x = \sqrt{1.0948}[/tex]
[tex]x = 1. 046[/tex]
Thus,
Length of AB = 20x -2 = 20(1. 046) - 2 = 18. 92
Length of AC = 25x = 25* 1.046 = 26. 15
Length of BC = 12x + 20 = 12(1. 046) + 20 = 32. 552
Learn more about isosceles triangles here:
https://brainly.com/question/1475130
#SPJ1
A cabbage is worth 55 points, an apple is worth 40 points, a potato is worth 45 points and a pumpkin is worth 60 points. How many points is a cauliflower worth?
A parallelogram has sides measuring 200mm by 150mm. what would be the length of side of a square having the same perimeter?
Answer:
175mmStep-by-step explanation:
To find the total perimeter of the parallelogram we must add 200+200+150+150
This equals 700. Then, since squares have side lengths that are all equal, we have to divide by 4.
700 / 4 = 175
So, the length of a side of a square having this perimeter would be 175mm
Hope this helps!
Find the interval in which the function is positive. f(x) = x2 - 7x + 10 I. (-, 2) II. (2, 5) III. (5,)
Step-by-step explanation:
f(x) = x2-7x+10
f(x) = -5x+10 = -5(x-2)
= 10-5x
Let, f(x) = 0
0 = 10-5x
5x = 10
x = 2
f(2) = 10 - 10 = 0
f(5) = 10-5(5) = 10-25 = -15
Let, f(y) = f(x)
= 10-5x
y = -0
So, the correct answer is I. (- , 2) ✔✔
What will be the firm's quick ratio after Nelson has raised the maximum amount of short-term funds? Do not round intermediate calculations. Round your answer to two decimal places.
Based on the short-term debt that Nelson raises, the firm's quick ratio will be 1.204.
What is the firm's quick ratio?First, find the maximum amount of short-term funds that Nelson can raise?
Assuming this amount is x, we can find it with the current ratio formula:
Current ratio = Current assets / Current liabilities
2 = (1,260,000 + x) / ( 450,000 + x)
x = $360,000
The quick ratio would therefore be:
= ( New Current assets - New inventory) / New current liabilities
= ( (1,260,000 + 360,000) - (285,000 + 360,000) ) / (450,000 + 360,000)
= 1.204
Find out more on quick ratio at https://brainly.com/question/13917900.
#SPJ1
Expand. Your answer should be a polynomial in standard form. -p^2(p^2-p-1) =
Answer:
[tex]\huge\boxed{\sf -p^4+p^3+1}[/tex]
Step-by-step explanation:
Given expression:[tex]=-p^2(p^2-p-1)\\\\Distribute \\\\= -p^4+p^3+1\\\\\rule[225]{225}{2}[/tex]
If we run the following program:
a = 2 + 6
b = 7 % 3
c = a - b
c = c * 5
print(c)
what gets printed?
If you run the program and print(c), your result will be: c = 35
Meaning of ProgramA program can be defined in terms of arithmetical functions as a set of instructions that are used to arrive at a solution.
A program guides the computer system on what the user wants.
Analysis
a = 2 + 6 = 8
b = 7 % 3 = 1
c = a - b = 7
c = c * 5 = 35
In conclusion, If you run the program and print(c), your result will be: c = 35
Learn more about program: https://brainly.com/question/22654163
#SPJ1
Interpret, in a written description, what the graph is saying about the relationship between the variables. A graph has time (hours) on the x-axis, and distance (miles) on the y-axis. A line increases to 2 hours, is constant through 3 hours, and then increases through 6 hours. a. You leave home and drive for 6 hours with no stops. b. You leave home, drive for 1 hours at a constant speed, stop for 30 minutes, continue at the same speed, stop for 1 hour and then continue at the same speed as before. c. You leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally you continue at a slower (but constant) speed than before. d. You leave home, drive for 3 hours at a constant speed, and then stop for 2 hours. Finally you continue at the same speed as before. Please select the best answer from the choices provided
An interpretation of the relationship between the variables in this graph is that: C. you leave home, drive for 2 hours at a constant speed, and then stop for 1 hour. Finally, you continue at a slower (but constant) speed than before.
What is a graph?A graph can be defined as a type of chart which is used to graphically represent the relationship between the variables in a data set, on both the horizontal and vertical lines of a cartesian coordinate i.e x-axis and y-axis.
By critically observing the graph attached in the image below, we can infer and logically deduce that an interpretation of the relationship between the variables in this graph is that you drove at a constant speed for 2 hours, and then stopped for 1 hour. Finally, you continued at a slower, but constant speed than before.
Read more on graphs here: brainly.com/question/25875680
#SPJ1
Which expression is
equivalent to the following complex fraction?
Answer:
(y - x)/(y + x)
Step-by-step explanation:
(1/x - 1/y)/(1/x + 1/y) =
= (1/x - 1/y)/(1/x + 1/y) × (xy)/(xy)
= (y - x)/(y + x)
PLS ANSWER THESE TWO QUESTIONS
EXPLANATION IS NOT NEEDED
MAKE SURE IT IS CORRECT
The answers to the following word problems are given below:
(C). [tex]1\frac{1}{2}[/tex](C). 0Meaning of word problemA Word problem can be defined as a mathematical problem that is given in a sentence format.
A word problem needs the student to decipher it and then translate it to a normal arithmetic problem.
In conclusion, The answers to the word problems are given
Learn more about word problems: https://brainly.com/question/13818690
#SPJ1
28 students; 14 students what is the percentage of it?
Answer:
The percentage of 28 students who are 14 students is 50%.
Step-by-step explanation:
Simplify: (−12az2−2z3)+(−2a3+7a2z)−(−4a2z+8az2)
Answer:
[tex] \large{ \boxed{ \tt{ - 20a {z}^{2} - 2 {z}^{3} - 2 {a}^{3} + 11 {a}^{2} z }}}[/tex]
- Please see the attached picture for full solution!:)
----------------- HappY LearninG <3 --------------
Below are the weekly salaries, in dollars, of nine recent college graduates. Utilize the data to calculate the midrange.
833 692 1057 955 749 1113 857 946 907
The midrange of the weekly salaries is $902.50.
What is the midrange?Midrange is a measure of variation of a data set. Midrange is the mean of the lowest and highest salary.
Midrange + (lowest salary + highest salary) / 2
(692 + 1113) / 2 = $902.50
To learn more about range, please check: https://brainly.com/question/12372689
#SPJ1
Complete the following, using ordinary interest. (Use Days in a year table.) (Do not round intermediate calculations. Round the "Interest" and "Maturity value" to the nearest cent.)
Principal: 1,000
Interest rate: 8%
Date borrowed: March 8
Date repaid: June 9
Exact time:
Interest:
Maturity value:
Answer:
75
Step-by-step explanation: