Answers
Answer:
Therefore, Point M( 1 , -2 ) is the Mid point of segment ST.
Step-by-step explanation:
Given:
Let,
point S( x₁ , y₁) ≡ ( -1 , 1)
point T( x₂ , y₂) ≡ (3 , -5)
Point M( x , y ) is the Mid point of segment ST.
To Find:
Point M( x , y )= ?
Solution:
As Point M( x , y ) is the Mid point of segment ST.
So we have Mid Point Formula as
[tex]Mid\ pointM(x,y)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})[/tex]
On substituting the given values in above equation we get
[tex]M(x,y)=(\frac {-1+3}{2},\frac{-5+1}{2})\\\\M(x,y)=(\frac{2}{2},\frac{-4}{2}) \\\\M(x,y)=(1,-2)\ \textrm{which the required midpoint}[/tex]
Therefore, Point M( 1 , -2 ) is the Mid point of segment ST.
Related Questions
Consider the expressions:
Expression 1: −9x + 8y
Expression 2: −8x − 2y
Subtract expression 1 from expression 2?
A)
x + 6y
B)
6y − x
C)
10y − x
D)
x − 10y
Answers
Answer:
D
Step-by-step explanation:
= −8x − 2y - (−9x + 8y)
Open bracket
= -8x -2y + 9x - 8y
= x - 10y
Final answer:
Subtracting Expression 1 from Expression 2 term by term results in x - 10y, which corresponds to option D).
Explanation:
To subtract Expression 1 from Expression 2, we perform the subtraction operation term by term.
For the x-terms: (-8x) - (-9x) simplifies to x.
For the y-terms: (-2y) - (8y) simplifies to -10y.
Subtracting expression 1 from expression 2:
Expression 2 - Expression 1 = (-8x - 2y) - (-9x + 8y)
Simplify to get: (-8x - 2y) + (9x - 8y)
Combining like terms, the result is x - 10y.
Therefore, subtracting Expression 1 from Expression 2 gives us x - 10y, which matches option D).
30 points Asap Recall that Seth's house is 17 miles from school. Which
location should Seth start off at to get to school faster
and how long will it take?
from the bus stop is faster, taking 17 minutes
from the bus stop is faster, taking 24 minutes
from his friend's house is faster, taking 15 minutes
from his friend's house is faster, taking 22.5 minutes
Answers
Answer: D
Step-by-step explanation: I just did the quiz
Answer: D
Step-by-step explanation:
Yeah the quiz was like, dud the answers D, so I was like okay it's D
Determine the y intercept of the graph y-7 =3(x+5) rearrange in slope intercept form
Answers
Answer:
y = 3x + 22
Step-by-step explanation:
y - 7 = 3(x+5)
Distribute,
y - 7 = 3x + 15.
Add 7 to both sides.
Final answer, y = 3x + 22.
Hope this helps!
Answer:
22
Step-by-step explanation:
Remove the brackets on the right.
y - 7 = 3x + 15
Add 7 to both sides.
y - 7 + 7 = 3x + 15 + 7
y = 3x + 22
The y intercept occurs when x = 0
y = 3*(0) + 22
y = 22
On Monday, Luis picked up seven scones and four large coffees for the office staff. he paid $25.76. On Tuesday Rachel picked up two scones and five large coffees for the office staff. She paid $14.92. What is the cost of one scone? What is the cost of one large coffee?
Answers
Answer:
let the scone be x and the large coffees be y.
7x+4y=$25.76-----equ(I)
2x+5y=$14.92-----equ(2)
make x the subject of the formulae in equation(ii).
x=$14.92/2-5y
x=7.46-5y
Let x = the price of one scone. Let y = the price of one large coffee.
For Luis, the equation is 5x + 4y = 25.76
For Rachel, the equation is 2x + 5y = 14.92
Here is what I did for this problem:
What is an equation of a line that passes through the points (8 , -3) (8 , 4)
Answers
Answer:
[tex]\displaystyle x = 8[/tex]
Step-by-step explanation:
Anything set to equal x is considered an undefined rate of change [slope], which is a vertical line. This is not a function, since it flunks the vertical line test.
I am joyous to assist you anytime.
ed bought a box of candies for $10.54. There were 16 candies in the box . How much did each candy cost
Answers
The cost of one candy is 66 cents.
Step-by-step explanation:
Given,
Purchase price of box of candies = $10.54
Number of candies in the box = 16
To find the cost of each candy, we will divide the purchase price of candies with total number of candies.
Cost of each candy = [tex]\frac{10.54}{16}[/tex]
Cost of each candy = $0.658
Rounding off to nearest hundredth;
Cost of each candy = $0.66 = 0.66 * 100 = 66 cents
The cost of one candy is 66 cents.
Keywords: division, multiplication
Learn more about division at:
brainly.com/question/10772249brainly.com/question/10781917#LearnwithBrainly
Alexis runs a small business and creates recordings of her friend’s skateboard stunts. She puts the recordings onto Instagram. She currently has 100 Instagram followers. If the number of followers grows at a rate of 1% every 12 hours. The following function represents this situation.
f(x) = f(1. + r)^t where f is the number of initial followers and r is the grown rate and t is time.
1) Alexis wants to figure out how many followers she will have after 5 days, use the equation to solve.
2) Alexis hopes to eventually have 1,000,000 followers, how long will it take her to reach this level of followers.
3) Fill in the chart below.
#Days since upload 0 10 20 50 100 300 500
Number of Instagram followers
4) In words, explain why the rate increases so fast.
5) Create an equation for the number of followers if the rate increased 3% every 24 hours.
Answers
Answer:
(1). 110 followers
(2). 463 days
(3). Days since upload 0 10 20 50 100 300 500
Number of Instagram followers 100 122 149 270 732 39158 2,000,000
(5) [tex]f(x)=100(1.03)^d[/tex]
Step-by-step explanation:
Part 1:
The function that represents the situation is:
[tex]f(x) = 100(1 .01)^{2d}[/tex]
Where [tex]d[/tex] is number of days.
Using this equation we find the number of followers after 5 days:
[tex]f(d) = 100(1 .01)^{2*5}=110[/tex] followers.
Part 2:
We solve the equation
[tex]1,000,000 = 100(1 .01)^{2d}[/tex]
for [tex]d[/tex] and get:
[tex]d=463\: days.[/tex]
It takes Alexis 463 days to reach 1,000,000 followers.
Part 3:
Days since upload 0 10 20 50 100 300 500
Number of Instagram followers 100 122 149 270 732 39158 2,000,000
This is obtained from the graph of the function f(x).
Part 4:
The number of Instagram followers increases fast because the rate of increase is 1% of the previous number of followers, and as the followers increase, this 1% takes increasingly big values, leading to increasingly fast growth rate of followers. Put simply, we would say that f(x) is an exponential function.
Par 5:
If the rate is increased to 3% every 24 hours, then the function f(x) becomes:
[tex]f(x)=100(1.03)^d[/tex]
where [tex]d[/tex] is days. and if we represent this in terms of every 12 hours then
[tex]f(x)=100(1.03)^{t/2}[/tex]
where [tex]t[/tex] is every 12 hours.
Can you please help me solve and if you show work I would really appreciate it
Answers
You got the equations correct, great job on that!
Let "s" be the variable that represents how many shirts were bought. Let "p" represent the total price/cost.
Equation for the store at Town Center mall:
p = 80 + 3.5s (80 is base cost, and cost increases 3.5 per shirt)
Equation for the store in Arlington:
p = 120 + 2.5s (120 is base cost, and cost increases 2.5 per shirt)
We want to find a point where the systems are equal; thus, we are solving for a system of linear equations, and we already have the equations we need.
p = 80 + 3.5s
p = 120 + 2.5s
We know that variable "p" is equal for both equations; thus, we can combine both equations into:
80 + 3.5s = 120 + 2.5s
Subtract both sides by 2.5s
80 + 3.5s - 2.5s = 120 + 2.5s - 2.5s
80 + s = 120
Subtract both sides by 80
s = 40
Thus, both equations are equal when 40 shirts are bought.
To find the cost, use any of the two equations (or both) to find the total cost, which should be equal.
p = 80 + 3.5(40) = 220
p = 120 + 2.5(40) = 220
Thus, the total price/cost at both stores is $220.
Let me know if you need any clarifications, thanks!
The image below shows two dilated figures with lines WX and W'X' drawn. If the larger figure was dilated using a scale factor of 4, what relationship do lines WX and W'X'have?
Answers
The relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.
In a dilation, lines that pass through the center of dilation (the point about which the dilation occurs) remain unchanged.
This means that the line WX and its corresponding line W'X' would be collinear and have the same length if they pass through the center of dilation.
If the larger figure was dilated using a scale factor of 4, it means that every point in the larger figure is four times farther from the center of dilation than its corresponding point in the smaller figure. In this case, line WX would be four times longer than line W'X', and they would be parallel since they maintain the same direction.
So, the relationship between lines WX and W'X' would be that line WX is four times the length of line W'X', and they are parallel.
for such more question on length
https://brainly.com/question/28322552
#SPJ2
Choose the graph which represents -6x - 5y = -10
Answers
Answer:
y = 2 + ((-)6/5)x
Step-by-step explanation:
-6x-5y=-10
add 6x to both sides.
-5y = -10 +6x
divide both sides by -5
y = 2 - (6/5)x
Plug in 0 for x to get the y intercept:
f(0) = 2 - (6/5) (0)
y = 2
(0, 2) is the y intercept.
Do the same for values such as -1, -2, 1, and 2, etc.
Then graph it.
To find the correct graph for -6x - 5y = -10, transform it to the slope-intercept form y = 6/5x - 2, which reveals a slope of 6/5 and a y-intercept at -2. Seek a graph with a line that increases 6 units vertically for every 5 units horizontally and intersects the y-axis at -2.
Explanation:To find the graph that represents the equation -6x - 5y = -10,
we first need to manipulate the equation into slope-intercept form,
which is y = mx + b where m is the slope and b is the y-intercept. Starting with the given equation:
-6x - 5y = -10
Let's isolate y by adding 6x to both sides:
-5y = 6x - 10
Now, divide each term by -5 to solve for y:
y = -6x / -5 + 10 / -5
y = 6/5x - 2
The slope-intercept form of the equation is now y = 6/5x - 2. This tells us that the slope (m) of the line is 6/5 and the y-intercept (b) is -2. You will look for the graph with a line that rises 6 units for every 5 units it moves to the right (since the slope is positive) and crosses the y-axis at -2.
West high schools population is 250 students fewer then twice the population of East High school the two schools have a total of 2858 students how many students attend the East high school
Answers
Answer:
1036 students
Step-by-step explanation:
Let the number of students at West High be "w" and the number of students at East High be "e"
West High population is 250 FEWER than TWICE of East High, we can write:
w = 2e - 250
Total students in both schools is 2858, so we can write 2nd equation as:
e + w = 2858
We can replace 1st equation in 2nd to get an equation in e, and find "e":
e + w = 2858
e + (2e - 250) = 2858
3e - 250 = 2858
3e = 2858 + 250
3e = 3108
e = 3108/3
e = 1036
Hence,
number of students attending East High School = 1036 students
Gary drove to the park at a rate of 50 miles per hour if it took him 2.5 hours to get from his house to the park how far away is the park from his house
Answers
Answer:
The distance of the park from the Gary's house is 125 miles.
Step-by-step explanation:
Speed of Gary = 50 miles/hour
Time taken by Gary to reach the park from his house = 2.5 hours
Now, we know that,
Distance travelled = speed × time
So, distance between park and Gary's house = speed × time
= 50 × 2.5
= 125 miles
So, the park is 125 miles away from the Gary's house.
Car A travels 120 miles in the same time that car B travels 150 miles. If car B averages 10 mph faster than car A, what is the speed of each car?
Answers
Answer:
Speed of car A = 40 mph
Speed of car B = 50 mph
Step-by-step explanation:
Given:
Distance travelled by car A = 120 miles
Distance travelled by car B = 120 miles
To Find:
speed of each car = ?
Solution:
Let the speed of car A be x
then speed of car B is (x +10)
The Time taken for each car is same
Time taken for car A = Time taken for car B
We know that time = [tex]\frac{distance}{speed}[/tex]
Time taken for car A
=> [tex]\frac{120}{x}[/tex]---------------------------(1)
Similarly
Time taken for car B
=> [tex]\frac{150}{x+10}[/tex]-----------------------(2)
Equating (1) and (2), we get
[tex]\frac{120}{x}[/tex] = [tex]\frac{150}{x+10}[/tex]
[tex]120 \times (x+10) = 150 \times x[/tex]
120x + 1200 = 150x
1200 = 150x-120 x
1200 = 30x
[tex]x= \frac{1200}{30}[/tex]
x= 40
Speed of car A = 40mph
Speed of car B = (x+10) = (x+40) = 50mph
Equation of the line that passes through (8,-7) (-6,-7)
Answers
Answer:
y = - 7
Step-by-step explanation:
line pass (8, - 7) (- 6, -7)
y = mx + b m: slope b: y intercept
m = difference of y / difference of x
m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0 ... line parallel to x axis
b = y - mx = - 7 - 0*8 = -7
equation : y = -7
Answer:
y = - 7
Step-by-step explanation:
line pass (8, - 7) (- 6, -7)
y = mx + b m: slope b: y intercept
m = difference of y / difference of x
m = (- 7 - (- 7)) / (- 6 - 8) = 0 / (-14) = 0 ... line parallel to x axis
b = y - mx = - 7 - 0*8 = -7
equation : y = -7
Nicole’s job pays her salary plus commission. She earns a daily salary of $60 plus 15% commission of her total sales. On Monday, she earned a total of $63.75. What were her total sales?
Answers
Answer:
25
Step-by-step explanation:
60 per day 25 in sales 63.75-60=3.75
3.75÷.15=25
If Nicole's earns 15% commission of her total sales, then Nicole's total sale of Monday is 25.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Total salary of Nicole's = $60.
Also,
Nicole gets 15% commission of her total sales,
Total earning on Monday = $63.75
The commission earned on Monday = 63.75 - 60 = 3.75
According to given condition,
15 % = 3.75
1 % = 3.75 / 15
100 % = 3.75 / 15 x 100
100 % = 25
Total sale of Nicole's on Monday is 25.
To know more about Percentage on:
https://brainly.com/question/24120406
#SPJ2
simplify the expression- 3w+8+1–8
Answers
Answer:
Step-by-step explanation:
-3w+9-8
=-3w+1
10 POINTS!! Brainliest.!!!!
For the pair of similar solids, find the scale factor of the solid on the left to the solid on the right. Then find the ratios of the surface areas and the volumes.
Answers
Answer:
C
Step-by-step explanation:
Given 2 similar figures with linear ratio = a : b, then
ratio of areas = a² : b² and
ratio of volumes = a³ : b³
Here linear ratio = 42 : 56 ← divide both parts by 14
linear ratio = 3 : 4 ← in simplest form, thus
ratio of areas = 3² : 4² = 9 : 16
ratio of volumes = 3³ : 4³ = 27 : 64
Are u smarter than an 8th grader!?!
Answers
Answer:
The function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2.
The vertex of the function is (-2,-1)
Domain of the function is (-∞, +∞)
Range of the function is [-1, +∞).
Step-by-step explanation:
The function has a graph in two parts.
The right side part passes through the points (-2,-1) and (0,3).
So, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - 0}{0 - (- 2)}[/tex]
⇒ y - 3 = 2x
⇒ y = 2x + 3
Again, the left side part of the graph passes through the points (-2,-1) and (-4,3).
Therefore, the equation of this part will be
[tex]\frac{y - 3}{3 - (- 1)} = \frac{x - (- 4)}{- 4 - (- 2)}[/tex]
⇒ y - 3 = - 2(x + 4)
⇒ y - 3 = - 2x - 8
⇒ y = - 2x - 5
Therefore, the function is f(x) = 2x + 3 for x ≥ - 2 and f(x) = - 2x - 5 for, x < - 2. (Answer)
The vertex of the function is (-2,-1) (Answer)
Domain of the function is (-∞, +∞) (Answer)
Range of the function is [-1, +∞). (Answer)
1) Members at a yoga school pay $10 per class plus a one-time $100 membership fee. Non-members pay$15 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
2) Translate the statement into an equation. Then solve the equation. The sum of 8 and 3 times a number is 23.
6) Members at a yoga school pay $7 per class plus a one-time $120 membership fee. Non-members pay $11 per class. How many classes would a member have to take to save money compared to taking classes as a non-member?
Answer all questions please, and if u can show u work, please...
3)A rental car costs $36 for one day plus an additional $0.42 per mile. What is the cost of renting a car for one day and driving it 78 miles?
4) Alice earns 1.5 times her normal hourly rate for each hour she works after 40 hours in a week. She worked 50 hours this week and earned $660. What is her normal hourly rate?
5) Cynthia orders 27 prints of a photograph she took. It costs her a total of $242.73. Which equation can be used to find how much each print cost?
Answers
Answer:
Part 1) The number of classes must be greater than 20
Part 2) see the explanation
Part 3) [tex]\$68.76[/tex]
Part 4) [tex]\$12\ per\ hour[/tex]
Part 5) The equation that can be used is [tex]27x=242.73[/tex] and the cost of one print is [tex]\$8.99[/tex]
Part 6) The number of classes must be greater than 30
Step-by-step explanation:
Part 1) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost
x ----> the number of classes
we have
Members
The slope is [tex]m=\$10\ per\ class[/tex]
The y-intercept is [tex]b=\$100[/tex]
so
[tex]y=10x+100[/tex] ----> equation A
Non-Members
The slope is [tex]m=\$15\ per\ class[/tex]
so
[tex]y=15x[/tex] ----> equation B
To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality
[tex]10x+100 < 15x[/tex]
Solve for x
subtract 10 x both sides
[tex]100 < 15x-10x[/tex]
[tex]100 < 5x[/tex]
Divide by 5 both sides
[tex]20 < x[/tex]
Rewrite
[tex]x > 20[/tex]
therefore
The number of classes must be greater than 20
Part 2) we have
The sum of 8 and 3 times a number is 23.
Let
x ----> the number
Remember that
3 times a number is the same that multiply 3 by the number ----> 3x
so
The sum of 8 and 3 times a number is 23 is the same that
[tex]8+3x=23[/tex]
solve for x
subtract 8 both sides
[tex]3x=23-8[/tex]
[tex]3x=15[/tex]
Divide by 3 both sides
[tex]x=5[/tex]
Part 3) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost of renting a car for one day
x ----> the number of miles
we have
The slope is [tex]m=\$0.42\ per\ mile[/tex]
The y-intercept is [tex]b=\$36[/tex]
so
[tex]y=0.42x+36[/tex]
For x=78 miles
substitute in the linear equation and solve for y
[tex]y=0.42(78)+36[/tex]
[tex]y=\$68.76[/tex]
Part 4) Let
x ----> Alice's normal hourly rate
we know that
40 hours multiplied by her normal hourly rate plus 10 hours (50 h-40 h) multiplied by 1.5 times her normal hourly rate must be equal to $660
so
The linear equation that represent this situation is
[tex]40x+10(1.5x)=660[/tex]
solve for x
[tex]40x+15x=660[/tex]
[tex]55x=660[/tex]
Divide by 55 both sides
[tex]x=\$12\ per\ hour[/tex]
Part 5) Let
x ----> the cost of one print
we know that
The cost of one print multiplied by 27 prints must be equal to $242.73
so
The linear equation is equal to
[tex]27x=242.73[/tex]
solve for x
Divide by 27 both sides
[tex]x=\$8.99[/tex]
Part 6) we know that
The linear equation in slope intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope or unit rate
b is the y-intercept or initial value
Let
y ----> the total cost
x ----> the number of classes
we have
Members
The slope is [tex]m=\$7\ per\ class[/tex]
The y-intercept is [tex]b=\$120[/tex]
so
[tex]y=7x+120[/tex] ----> equation A
Non-Members
The slope is [tex]m=\$11\ per\ class[/tex]
so
[tex]y=11x[/tex] ----> equation B
To find out how many classes would a member have to take to save money compared to taking classes as a non-member, solve the following inequality
[tex]7x+120 < 11x[/tex]
Solve for x
subtract 7x both sides
[tex]120 < 11x-7x[/tex]
[tex]120 < 4x[/tex]
Divide by 4 both sides
[tex]30 < x[/tex]
Rewrite
[tex]x > 30[/tex]
therefore
The number of classes must be greater than 30
30 points and brainliest for the correct answers.
Answers
Question # 1
Use the points in the diagram to name the figure?
Answer:
Option B is correct. The figure is named as a line 'CD'. The symbol '⟷' is placed UPPER on a line 'CD'.
Explanation:
As we know that a line is a set of points which tend to extend infinitely in two directions. So, in question 1, two points C and D are shown on a line. As a line carries these two points - the infinite line that includes C and D. Double arrow indicates that line is extended infinitely in both directions. While the order of the points does not matter for a line, it is conventional to name the two points in alphabetical order. So, the figure is named as a line 'CD'. So, option B is correct.Note: The symbol '⟷' is placed UPPER on a line 'CD'. Also remember, that the a line is named in alphabetical order.
Question # 2
Which of the following correctly names a line shown in the figure?
Answer:
The option A is correct as the line AP carries the points A and P and extends infinitely in two directions, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.
Explanation:
Let us look at some definitions.
Point - has no length, no width, and no height, but it carries a location. Line - a set of points which tend to extend infinitely in two directions. For example line AB.Line Segment - is a piece of line having two end points. For example, segment [tex]{\overline {AB}}[/tex].Ray - a part of line with one end point. For example, Ray [tex]{\overrightarrow {AB}}[/tex]As we have to determine the correct name of a line shown in figure in question 2. So, we need to recall that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions.
In question 2, the figure shows that:
[tex]{\overrightarrow {EC}}[/tex] is a ray as it is a part of line with one end point, heading towards infinity in only one direction. Hence, option B is also not a line. [tex]{\overline {NH}}[/tex] is a line segment because it has two end points. Hence, option C is not a line.Option D can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on AP. This symbol represents the segment. As we know that a line is a set of points which tend to extend infinitely in two directions. Double arrow indicates that line is extended infinitely in both directions. The symbol '⟷' is placed UPPER on a line 'AP'. Hence, the option A is correct as the line AP carries the points A and P, and the symbol '⟷' is placed UPPER on a line 'AP' which represents the line.So, option A is correct.
Question 3.
Which of the following correctly names a ray shown in the figure?
Answer:
option B is correct. i.e. [tex]{\overrightarrow {EG}}[/tex] correctly names a ray.Explanation:
The option A can not be correct as the symbol ' [tex]{\overline {~~}}[/tex] 'is placed upper on EP. This symbol represents the segment as EP is a line segment. The option C cannot be true as the '⟷' is placed UPPER on 'LG' which represents the line.The option D cannot be true also as it is showing the wrong end point of a ray. As the actual ray would have had E as the end point, and directed towards C, and would have mentioned as [tex]{\overrightarrow {CE}}[/tex]. But, the option D is wrongly mentioning as [tex]{\overrightarrow {EC}}[/tex].As we know that a ray is a part of line with one end point. If we carefully observe the figure, only option B i.e. [tex]{\overrightarrow {EG}}[/tex] is correct. As E is the end point, and directed towards G. So, it becomes [tex]{\overrightarrow {EG}}[/tex]. We cannot call it [tex]{\overrightarrow {GE}}[/tex] as G is not the end point. An array has only one arrow. So, option B is correct.Keywords: ray, segment, line
Learn more about rays, lines, and segments from brainly.com/question/909890
#learnwithBrainly
A line passes through the points (–5, 2) and (10, –1). Which is the equation of the line? 025-1. c025-2 y = –5x – 23 y = 5x + 27
Answers
Answer:
y=-1/5x+1
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-2)/(10-(-5))
m=-3/(10+5)
m=-3/15
m=-1/5
y-y1=m(x-x1)
y-2=-1/5(x-(-5))
y-2=-1/5(x+5)
y=-1/5x-5/5+2
y=-1/5x-1+2
y=-1/5x+1
What is -10x divided by -11 yall? im tired i have no clue what im doing plz answer quick its for my algebra hw and my teacher is So mean
Answers
Answer:
wouldn't it just be [tex]\frac{10}{11} x[/tex]
Step-by-step explanation:
this is also: [tex]\frac{-10*x}{-11}[/tex]
which is why it simplifies to the answer
find an equation of the line satisfying the given condition in standard form . Through {0, -35/3} ; slope 7/3
Answers
For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis.
According to the statement data we have:
[tex]m = \frac {7} {3}[/tex]
Thus, the equation is of the form:
[tex]y = \frac {7} {3} x + b[/tex]
We substitute the given point and find the cut-off point:
[tex]- \frac {35} {3} = \frac {7} {3} (0) + b\\- \frac {35} {3} = b[/tex]
Finally, the equation is:
[tex]y = \frac {7} {3} x- \frac {35} {3}[/tex]
We manipulate algebraically to obtain the standard form:
We multiply by 3 on both sides of the equation:
[tex]3y = 7x-35\\3y-7x = -35[/tex]
We multiply by -1 on both sides:
[tex]7x-3y = 35[/tex]
Answer:
[tex]7x-3y = 35[/tex]
Rita is hiking along a trail that is 14.3 miles long. So far she has hiked along one-tenth of the trail
How far has Rita hiked?
Rita has hiked miles
Answers
Just multiply the total length by the fraction:
14.3 * 1/10 = 1.43 miles
Answer:
1.43
Step-by-step explanation:
NOTE: This is the way I do it , other people may have a other/faster way to do it.
For this question you simpily have to divide 14.3 by 10:
1. Convert 14.3 into a mixed number - 14 3/10
2. Divide 14 by 10 - 1.4
3. Divide 3/10 by 10 - 3/100
4. Convert 3/100 into a decimal- 0.03
5. Add the two decimals - 0.03 + 1.4 = 1.43
Write an equation that is perpendicular to
3x - 5y = 5 and passes through the point
(9, -14).
Answers
Answer:
[tex]y=-\frac{5}{3}x+1[/tex]
Step-by-step explanation:
Given:
Equation of the line.
[tex]3x-5y=5[/tex]
And passes through the point (9, -14)
Solution:
Now, we have to write an equation that is perpendicular to 3x -5y = 5 and passes through the point (9, -14).
Now, we write the given equation in [tex]y=mx+b[/tex] form.
[tex]3x-5y=5[/tex]
[tex]5y=3x-5[/tex]
[tex]y=\frac{3}{5}x-\frac{5}{5}[/tex]
[tex]y=\frac{3}{5}x-1[/tex]
So, the slope of the line is [tex]m=\frac{3}{5}[/tex].
The slope of the perpendicular line is [tex]-\frac{1}{m}[/tex]
now, we substitute m value in above relation.
[tex]=-\frac{1}{\frac{3}{5}}[/tex]
[tex]=-\frac{5}{3}[/tex]
So the equation of the perpendicular line is:
[tex]y=-\frac{5}{3}x+b[/tex]--------(1)
Lets us find b from the given points (9, -14).
[tex]-14=-\frac{5}{3}\times 9+b[/tex]
[tex]-14=-5\times 3+b[/tex]
[tex]-14=-15+b[/tex]
[tex]b=15-14[/tex]
[tex]b=1[/tex]
Now, we substitute b value in equation 1.
[tex]y=-\frac{5}{3}x+1[/tex]
Therefore, the equation of the perpendicular line is
[tex]y=-\frac{5}{3}x+1[/tex]
The equation of the line that is perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.
Explanation:To find the equation of a line that is perpendicular to a given line, we first need to find the slope of the given line. The equation in the question is given in standard form (Ax + By = C), so we need to convert it into slope-intercept form (y = mx + b), where m is the slope. In slope-intercept form, the given equation becomes y = 3x/5 + 1.
The slope of this line is 3/5. The slope of a line perpendicular to this one is the negative reciprocal, or -5/3. This is because the product of the slopes of two perpendicular lines is -1.
We now know that the equation of the line perpendicular to the given one has the form y = -5x/3 + b. To find b (the y-intercept), we can use the point that the line has to pass through (9, -14). We substitute these values into the equation, and solve for b. This gives: -14 = -5(9)/3 + b. Solving for b gives, b = -14 + 15 = 1.
Therefore, the equation of the line perpendicular to 3x - 5y = 5 passing through the point (9, -14) is y = -5x/3 + 1.
Learn more about Perpendicular Line Equation here:https://brainly.com/question/25790244
#SPJ3
The area of a rectangular wall of a barn is 32 square feet. It’s length is 4 feet longer than the width. Find the length and width of the wall of the barn
Answers
Answer:
Step-by-step explanation:
Givens
Area = L * w
w = x
l = x + 4
Area = 32
Solution
32 = x(x + 4)
32 = x^2 + 4x
x^2 + 4x - 32
(x + 8)(x - 4)
Only x - 4 is going to make any sense
x - 4 = 0
x = 4
The width is 4
The length is 4 + 4 = 8
4*8 = 32 which is the area.
Final answer:
To find the length and width of the barn wall, set the width as w and form a quadratic equation w(w + 4) = 32. Solve the equation to find that the width is 4 feet and the length is 8 feet.
Explanation:
The student is asking how to find the length and width of a rectangular barn wall when the area is given (32 square feet) and the length is 4 feet longer than the width. To solve this, let's represent the width of the wall as w feet. Thus, the length will be w + 4 feet. The area of a rectangle is found by multiplying the length by the width, which gives us the equation w(w + 4) = 32.
Let's solve this quadratic equation:
Rewrite the equation: w² + 4w = 32.
Subtract 32 from both sides to set the equation to zero: w² + 4w - 32 = 0.
Factor the quadratic equation: (w + 8)(w - 4) = 0.
Solve for w: w = -8 (reject because width can't be negative) or w = 4 (accept).
Thus, the width of the wall is 4 feet and the length is 4 + 4 = 8 feet.
Helppp can someone solve this please
Answers
Answer:
[tex]\displaystyle x=-15[/tex]
Step-by-step explanation:
Solution Of A System Of Equations
A system of linear equations is given as
[tex]\displaystyle \left\{\begin{matrix}ax+by=c\\ dx+ey=f\end{matrix}\right.[/tex]
There are many methods to solve them. We will use the method of reduction
The given system is
[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ x+y=10\end{matrix}\right.[/tex]
Multiplying the second equation by -3
[tex]\displaystyle \left\{\begin{matrix}2x+3y=45\\ -3x-3y=-30\end{matrix}\right.[/tex]
Adding the resulting equations
[tex]\displaystyle -x=15[/tex]
[tex]\displaystyle x=-15[/tex]
A sofa was sold at a price of $270 with a 25% profit. What is the cost of the sofa?
Answers
Answer:
The cost of the sofa is $216
Step-by-step explanation:
The sofa was sold at cost plus 25% profit
let the cost of the sofa be = x
therefore x + 25% of x = 270
x + .25x = 270
1.25x = 270
1.25x/1.25 = 270/1.25
x = $216
Three more than twice k is thirteen write the equation
Answers
2*k + 3 = 13
2*k = 13 - 3
2*k = 10
k = 10/2
k = 5
The verbal statement 'Three more than twice k is thirteen' translates into the mathematical equation 2k + 3 = 13. Solving this equation, we find that k equals 5. This is an example of forming and solving an algebraic equation from a word problem.
Explanation:The question asks to translate a verbal statement involving a variable into a mathematical equation. The statement is 'Three more than twice k is thirteen.' To form an equation, we first identify the mathematical operations described in the statement. 'Twice k' means we need to multiply k by 2, so we have 2k. 'Three more than' suggests an addition of 3 to the previous result, so we add 3 to 2k to get 2k + 3. Finally, 'is thirteen' tells us that this expression is equal to 13. The equation becomes 2k + 3 = 13.
To solve for k, we subtract 3 from both sides to obtain 2k = 10, and then divide by 2, resulting in k = 5. This completes the exercise of writing and solving the equation.
Example of a similar equation:
Let's say we have 'Four less than half of x is twenty.' The equation would be (1/2)x - 4 = 20. We would solve by adding 4 to get (1/2)x = 24, and then multiply by 2 to find x = 48.
1/4÷5 equal what? Djdjjdjdjdjdjdjdjdd
Answers
Answer:
1/20
Step-by-step explanation: