Given:
A line passes through the points (-1, -1) and (5,8).
To find:
Which points lie on the same line?
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:
[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]
[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]
[tex]y+1=\dfrac{9}{6}(x+1)[/tex]
[tex]y+1=\dfrac{3}{2}(x+1)[/tex]
Multiply both sides by 2.
[tex]2(y+1)=3(x+1)[/tex]
[tex]2y+2=3x+3[/tex]
[tex]2y=3x+3-2[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].
Now, check each point for this equation.
Putting [tex]x=-3[/tex], we get
[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]
[tex]y=\dfrac{-9+1}{2}[/tex]
[tex]y=\dfrac{-8}{2}[/tex]
[tex]y=-4[/tex]
Similarly,
For [tex]x=9,y=15[/tex].
For [tex]x=1,y=2[/tex].
For [tex]x=4,y=6.5[/tex].
For [tex]x=3,y=5[/tex].
For [tex]x=-2,y=-2.5[/tex].
Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.
2√4^3
find the rationalizing factor
Hello!
2√4³ =
2 × √4 ³ =
2 × 2³ =
2 × 8 = 16
Good luck! :)
What is the product?
(7x^2y^3)(3x^5y^8)
10x^7+y^11
10X^10y^24
21x^7y^11
21x^10y^24
Answer:
21x^7y^11.
Step-by-step explanation:
:D
I Am offline or Raindowsalt please answer this !
❀ [tex]\huge\underline{ \underline{Solution :-}}[/tex]
[tex]( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} )[/tex]
To solve, use the algebraic identity ➺
(x + a)( x + b) = x² + (a + b)x + ab[tex]( {y}^{2} + \frac{5}{7} )( {y}^{2} - \frac{14}{5} ) \\ = ({y}^{2}) ^{2} + ( \frac{5}{7} + - \frac{14}{5} ) {y}^{2} + \frac{5}{7} \times - \frac{14}{5} \\ = {y}^{4} - \frac{73}{35} {y}^{2} - 2[/tex]
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Find two positive numbers so that twice their sum equals their product and one number is 10 times the other number. Enter the smaller number first.
Answer:
Step-by-step explanation:
We'll call the 2 numbers x and y. Starting with the last part of that first sentence "one number is 10 times the other number" can be written, in algebraic form:
y = 10x
Now on to the first statement about the numbers: "twice their sum" is 2(x + y) and "equals their product" is = xy. Putting that all together:
2(x + y) = xy and we know that y = 10x so
2(x + 10x) = x(10x) and
[tex]2(11x)=10x^2[/tex] and
[tex]10x^2-22x=0[/tex] and
x(10x - 22) = 0 so
x = 0 or 10x - 22 = 0 which makes
x equal to [tex]\frac{22}{10}=2.2[/tex]
So x = 2.2 and y = 22.
Find the value of x and y from the equation
Answer:
x = 5 and y = 3
Step-by-step explanation:
5x - 3y = 16
3x - y = 12 multiply second equation by (-3)
(-3)*(3x-y) = 12*(-3) (remember we need to multiply both sides of the equation)
-9x + 3y = -36 now subtract this from the first equation
5x - 3y -9x + 3y = 16 - 36 (-3y will eliminate +3y)
-4x = -20 and 4x = 20 divide both sides by 4
x = 5 if 3x - y = 12 then 3*5 - y = 12
15 - y = 12
-y = -3 and y = 3
- (For 10 points!)
Alfred draws candles randomly from a pack containing 4 colored candles of the same shape and size. There are 2 red candles, 1 green candle, and 1 blue candle. He draws 1 candle and then draws another candle without replacing the first one. Find the probability of picking 1 red candle followed by another red candle, and show the equation used.
(don't joke around please?? /gen)
Answer:
The probability of picking 1 red candle followed by another red candle is 16.66%.
Step-by-step explanation:
Since Alfred draws candles randomly from a pack containing 4 colored candles of the same shape and size, and there are 2 red candles, 1 green candle, and 1 blue candle, and he draws 1 candle and then draws another candle without replacing the first one, to find the probability of picking 1 red candle followed by another red candle, the following calculation must be performed:
2/4 x 1/3 = X
0.5 x 0.333 = X
0.16666 = X
Therefore, the probability of picking 1 red candle followed by another red candle is 16.66%.
Answer:
1/6
Step-by-step explanation:
2/4 x 1/3 = 1/6
What are the coordinates of points E, F, and GS
A. E (2, 3), F (8,5), G (5,8)
B. E (3, 2), F (8,3), G (5,6)
C. E (3, 2), F (8,4), G (5,7)
D. E (3, 3), F (9, 4), G (6,7)
Answer:
its a i think
Step-by-step explanation:
Please help me with this
Answer:
120 in^2
Hope it helps
Devaughn is 7 years older than Sydney. The sum of their ages is 95. What is Sydney's age?
Answer:
44
Step-by-step explanation:
Let's say that Devaughn's age is D, and Sydney's age is S.
We know that D is 7 greater than S, so D = 7 + S.
We know that the sum of their ages, or D + S, is equal to 95, so D+S = 95
We have
D = 7 + S
D + S = 95
What we can do is plug D= 7 + S into the second equation to get
D + S = 95
= (7+ S) + S
= 7 + 2 * S
7+2 * S - 95
subtract 7 from both sides to isolate the coefficient and the variable
2 * S = 88
divide both sides by 2 to isolate the variable
S = 44
Sydney is therefore 44 years old
H Solve the following questions.
| Mrs Liya cut a cake into 10 parts and give it out to her 3 children. Liza got the largest parts while Lina got the smallest parts. The difference between the number of parts Liza had and the number of
parts Lina had is equal to the number of parts Lini had. How many
parts did each of them have?
Answer:
Liza: 5 parts
Lina: 2 parts
Lini: 3 parts
Step-by-step explanation:
Basically, the parts whould equal ten. By following the criteria, Lina must have the least parts, while LIza has the most parts. If the difference between Liza and Lina should be equal to the number of parts Lina had
5-2=3 parts for Lini
Thank you. Tell me if any incorrections.
The volume of air inside a rubber ball with radius r can be found using the function V(r)= 4/3pier^3 what does V(5/7) represent?
Answer:
Step-by-step explanation:
I can tell you what it represents, but not what it means. Or maybe the units.
V(5/7) means that wherever you see an r on the right hand side, you put in 5/7 where the R is.
V = 4/3 * pi * r^3
V(5/7) = 4/3 * 3.14 * (5/7)^3
V(5/7) = 4/3 * 3.14 * 125 / 343
V(5/7) = 4/3 * 3.14 * 0.3644
V(5/7) = 1.526 cubic units (of whatever the units of 5/7 were to begin with)
which graph best represents the line y= -1/5x+2
Answer:
B
Step-by-step explanation:
Line crosses y-axis at 2.
Slope = [tex]\frac{-1}{5}[/tex]
For each 1 square the line rises/falls it moves to the right/left 5 squares.
Negative slope lines are downhill left to right.
The correct graph to represent the line y = -1/5 x + 2 will be;
⇒ Graph 2
What is Equation of line?
The equation of line with slope m and y intercept at point b is given as;
y = mx + b
Given that;
The equation of line is;
⇒ y = - 1/5 x + 2
Now,
The standard form of the equation of line with slope m and y intercept at point b is given as;
y = mx + b
By comparing we get;
Slope (m) = - 1/5
In the second figure;
Let two points on the graph (0, 2) and (5 , 1).
So, Slope is defined as;
m = (1 - 2) / (5 - 0)
m = - 1 / 5
And, Clearly the y - intercept is at point 2.
Therefore,
Graph 2 shows the correct graph to represent the line y = -1/5 x + 2.
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Please help :(((((((((((((((((((((((((
jeez that looks really hard
Step-by-step explanation:
please help....Which fraction has the greatest value?
Answer:
5/6
Step-by-step explanation:
Answer:
5/6
Step-by-step explanation:
Any negative number couldn't count as more than a positive. 5 is more than 1, so the correct answer has to be 5/6.
PLEASE SHOW ALL WORK
The function s(t) = t2+2t+5shows the height s(t), in feet, of a water balloon after t seconds. A second water balloon moves in the air along a path represented by p(t)=11+3t where p(t) is the height, in feet, of the balloon from the ground at time t seconds.
Part A: Create a table using integers 1 through 4 for the two functions. What is the solution for s(t) = p(t)? How do you know? Include the table in your answer.
Part B: Explain what the solution from Part A means in context of the problem.
Answer:
t = 2,3
Step-by-step explanation:
s (t) = t^2 + 2 t + 5
p (t) = 11 + 3 t
A:
s (1) = 8
s (2) = 13
s (3) = 20
s (4) = 29
Now
[tex]t^2 + 2 t + 5 = 11 t + 3t \\\\t^2 - t - 6 = 0\\\\t^2 - 3 t - 2 t - 6 = 0 \\\\(t-2)(t-3)=0\\\\t = 2, 3[/tex]
(b) The values are same at t =2 an t =3.
PLEASE HELP URGENT!!!!
The following table shows the estimated populations and annual growth rates for four countries in the year 2000. Find the expected population of each country in 2025, assuming their annual growth rates remain steady.
Answer:
Australia will have about 27 million
China will have about 1.41 billion
Mexico will have 133.35 million
Zaire will have about 100.9 million
Australia 2000 19,169,200 multiply your growth rate by 2 then divide it by your population your growth rate
China 1.2 billion in 2000 multiply your growth rate by 2 then divide it by your population your growth rate
Same for Mexico
and Zaire
Peter's father told Peter to buy four-tenths of a pound of chili powder. Each
package is marked with its weight. What package should Peter buy?
Answer:
The one with 6.4 ounces or multiple that are equivalent to that
Step-by-step explanation:
4/10 of a pound is equivalent to 2/5 of a pound. 2/5 of a pound is 6.4 ounces.
find the length of the line segment whose endpoints are (-5,6) and (6,6)
Answer: 11 units
Step-by-step explanation:
Use the distance formula: [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
[tex](x_{1}, y_{1})=(-5, 6)\\(x_{2}, y_{2})=(6, 6)\\\\\sqrt{(6-(-5)^{2}+(6-6)^{2}} =\sqrt{(11)^{2}+(0)^{2}} =\sqrt{121+0}=\sqrt{121}=11[/tex]
The length of the line is 11 units.
What is distance?The distance between two points is the length of the line joining the two points.
Formula: distance= √(x_2-x_1)²+(y_2-y_1)²
Given that, endpoints are (-5,6) and (6,6) of the line segment.
The length= √(6+5)²-(6-6)²
=11 units
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Consider the probability distribution shown below. x 0 1 2 P(x) 0.15 0.80 0.05 Compute the expected value of the distribution. (Enter a number.) Compute the standard deviation of the distribution. (Enter a number. Round your answer to four decimal places.)
Answer:
Expected value =0.9
Standard deviation = 0.4359
Step-by-step explanation:
Let's use the formula to find expected value or mean.
Expected value =Σ x *P(x)
x 0 1 2
P(x) ) .15 .8 .05
So, expected value = (0)(0.15) +1(0.8)+2(0.05)
= 0 +0.8 +0.1
=0.9
Expected value =0.9
Now, let's find standard deviation
x [tex](x- E(x))^{2}[/tex] [tex](x-E(x))^{2} *p(x)[/tex]
0 [tex](0-0.9)^{2}[/tex] [tex](0-0.9)^{2} *0.15[/tex] =0.1215
1 [tex](1-0.9)^{2}[/tex] [tex](1-0.9)^{2} *0.8[/tex] =0.008
2 [tex](2-0.9)^{2}[/tex] [tex](2-0.9)^{2} *0.05[/tex] =0.0605
Now, add the last column together and then take square root to find standard deviation.
Standard deviation of the distribution =[tex]\sqrt{0.1215+0.008+0.0605)}[/tex]
Simplify it, so standard deviation =0.4358898...
Round the answer to nearest four decimal places
Standard deviation = 0.4359
find the slope between the points (-10,8) and (-7,5)
Answer:
-1
Step-by-step explanation:
Slope = (y2 - y1) / (x2 - x1)
Slope = (8 - 5) / (-10 - -7)
Slope = 3 / (-3)
Slope = -1
What is the area of this figure
Help please!!!!
Answer:
the area is 279 mm squared
Step-by-step explanation:
Using the figure below, find the value of x. Enter your answer as a simplified radical or improper fraction (if necessary) into the equation box below.
Hello,
M=middle[AB]
The triangle ABC is equilateral :
x= 15/2
what do you understand by socialization
Solve the inequality.
–13.4 ≥ 6.7 + 4.3 + w
–24.4 ≥ w
24.4 ≥ w
23.4 ≥ w
–23.4 ≥ w
Answer:
-24.4 ≥ w
Step-by-step explanation:
-13.4 ≥ 6.7 + 4.3 + w
-13.4 - 6.7 - 4.3 ≥ w
-24.4 ≥ w
The farmer wants the ratio of horses to cows to equal 5 to 3. He keeps his 45 horses and buys more cows. Workout the number of cows he must buy
An airplane 30,000 feet above the ground begins descending at the rate of 2000 feet per minute. Assume the plane continues at the same rate of descent. How long will it take the plane to reach 12,000 feet above the ground
Answer:
Step-by-step explanation:
Let the time taken to reach 12,000 feet = x
Distance traveled in 1 minute = 2000 ft
Distance traveled in 'x' minute = 2000 * x = 2000x
30,000 - 2000x = 12000
Add 2000x to both sides
30,000 = 12000 + 2000x
Now subtract 12,000 from both sides
30000 - 12 000 = 2000x
2000x = 18 000
Divide both sides by 2000
x = 18000/2000
x = 9 minutes
The polygons are similar, but not necessarily drawn to scale. Find the value of x. PLEASE HELPPPP
Answer:
x = 27.5.
Step-by-step explanation:
There are given numbers on each side. If the figures are similar, then they have a set ratio for each value.
So, 55:8 and x:4. If you want to, you can flip it, so that it is 8:55 and 4:x.
With that in mind, it is easy to see what the ratio is. Because 4 is half of 8, x is half of 55. 55 divided by 2 is 27.5.
Therefore, x = 27.5.
PLEASE HELP
1. what’s 7n +9+8(2n+5)-4=
2. 7n+9+8n+5-4n=
3. 7(a+3)-3a+2=
PLEASE HELP
Answer:
1)duno
2)duno
3)duno
Step-by-step explanation:
glad i can help hahahaahhaa
75% of bis 12. What is b?
Answer:
9
Step-by-step explanation:
Answer: 16
Step-by-step explanation:
75=75/100=3/4
3/4*b=12
b=12/1*4/3
Someone please help me on this and please tell me the answer directly please !!
Answer:
I find this question
and I suppose your first question is should be 12 ( I'm not sure)
Answer:
The first one is: 12
The second one is: Subtract 1.1j from both sides.
The third one is: i'm not sure about that one
The fourth one is: 1/2
Step-by-step explanation:
