What is the ratio in which the point P(3/4,5/12) decides the line segment joining points A(1/2,3/2) and B(2,-5)
Given:
The point [tex]P\left(\dfrac{3}{4},\dfrac{5}{12}\right)[/tex] divides the line segment joining points [tex]A\left(\dfrac{1}{2},\dfrac{3}{2}\right)[/tex] and [tex]B(2,-5)[/tex].
To find:
The ratio in which he point P divides the segment AB.
Solution:
Section formula: If a point divides a segment in m:n, then the coordinates of that point are,
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Let point P divides the segment AB in m:n. Then by using the section formula, we get
[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{m(2)+n(\dfrac{1}{2})}{m+n},\dfrac{m(-5)+n(\dfrac{3}{2})}{m+n}\right)[/tex]
[tex]\left(\dfrac{3}{4},\dfrac{5}{12}\right)=\left(\dfrac{2m+\dfrac{n}{2}}{m+n},\dfrac{-5m+\dfrac{3n}{2}}{m+n}\right)[/tex]
On comparing both sides, we get
[tex]\dfrac{3}{4}=\dfrac{2m+\dfrac{n}{2}}{m+n}[/tex]
[tex]\dfrac{3}{4}(m+n)=\dfrac{4m+n}{2}[/tex]
Multiply both sides by 4.
[tex]3(m+n)=2(4m+n)[/tex]
[tex]3m+3n=8m+2n[/tex]
[tex]3n-2n=8m-3m[/tex]
[tex]n=5m[/tex]
It can be written as
[tex]\dfrac{1}{5}=\dfrac{m}{n}[/tex]
[tex]1:5=m:n[/tex]
Therefore, the point P divides the line segment AB in 1:5.
can any one figure this out plz
Answer:
(a)(b)=0.45
a/b=0.8
Step-by-step explanation:
a=0.6
b=0.75
(a)(b)=(0.6)(0.75)=0.45
a/b=0.6/0.75=0.8
Answer:
a*b = 0.5
a/b = 0.888...
Step-by-step explanation:
0.6666... = 2/3
a*b = 2/3 * 3/4 = 1/2 = 0.5
a/b = (2/3) / (3/4) = 8/9 = 0.888...
Lines a and b are parallel.
What is the measure of angle s?
Enter your answer in the box
S=
Answer:
22 degrees
Step-by-step explanation:
The angle that measures 158 degrees and angle u are supplementary angles, meaning they add up to 180 degrees.
Angle s and angle u are corresponding angles, meaning that they are congruent.
This means that the angle that measures 158 degrees and angle s are supplementary as well. Knowing this, we can construct the following equation:
[tex]180=158+s[/tex]
Subtract both sides by 158
[tex]180-158=158+s-158\\22=s[/tex]
Therefore, angle s has a measure of 22 degrees.
I hope this helps!
Find the measure of the indicated angel.
A) 30 degrees
B) 35 degrees
C) 25 degrees
D) 40 degrees
Answer:
D
Step-by-step explanation:
44+32=76
180-76=104
104+36=140
180-140=40
D)40
Evaluate 42 – a² + ab for a = 6 and b = 5.
Answer:
42-a²+ab
42-6²+6×5
42-36+30
6+30
36.
Please solve for y in this equation!
0.5y -2 2/5 = 1/2y +2.4
Answer:
No solution
Step-by-step explanation:
Move all the variables to one side and all the numbers to the other side.
0.5y-2*2/5=1/2y+2.4
-2*2/5=1/2y+2.4-0.5y
-2*2/5-2.4=0
thus there is no solution
HELP PLSSSSSS
Mallory bought pizza and soda for her End of Summer party. If she spent $12.57 on the
sodas and $10.95 for each pizza, how many pizzas did she buy if she spent $89.22?
Which equation models this scenario?
12.57 + 10.95 = 89.22
10.95x + 12.57 =
89.22
12.57x + 10.95 =
89.22
89.22x - 10.95 = 12.57
Answer:
10.95x + 12.57 = 89.22
Step-by-step explanation:
Find the area:
HELP PLEASE
Answer:
Area = 30.3 ft²
Step-by-step explanation:
Area = area of a semicircle + area of a rectangle
= (½*πr²) + L*W
Where,
radius (r) = ½ of 4 = 2 ft
Length (L) = 6 ft
Width (W) = 4 ft
Plug in the values
Area = (½*π*2²) + (6*4)
Area = 30.3 ft² (nearest tenth)
Is this non linear or linear sorry i couldn't fit the whole thing
I am not understanding this topic in math and I have a huge test tomorrow, I forgot about this assignment and I would really appreciate it if someone could help me out with this!!! ❤️
(6, -12), (15,-3)
slopeee
Solve 136 = 17b.
The solution is b=
Answer:
18
Step-by-step explanation:
5d/9=10
5d=10*9
5d=90
d=90/5
d=18
Michaela buys 2 cartons of eggs at $1.58 a carton, 4 pounds of ground turkey at $6.99 a pound, and a jar of
strawberry jam for $4.38. She gives the cashier four $10 bills.
Answer:
your answer is 4.50. the total of cartons eggs is 3.16+ the total of turkey 27.96+ the jar 4.38= 35.50 now we can do the math 40-35.50= 4.50. I hope it helps!
Step-by-step explanation:
it is
4.50
why os ot because 9 did the math
A line passes through the points (0, 2) and (1, 8). What is its equation in slope-intercept form?
Answer:
y=6x+2
Step-by-step explanation:
y=mx+b
-the y and x are variables and your going to want to leave them that way.
-m is the slope
-b is the y-intercept
after plotting your points and drwaing a line through them you get your final equation
CAN SOMEONE PLEAASSSEE HELP ME WITH THIS TRIGONOMETRIC FUNCTION PROBLEM? I AM REALLY STRUGGLING AND IT WOULD MEAN A LOT
Answer:
the sine Is 5/13
Step-by-step explanation:
use the trigonometric identity : sin^2+ cos^2 = 1
so the sine Is sqrt(1-(12/13)^2) = 5/13
sqrt means Square root btw
Which expression is equivalent to 2(5 – 3x)? 10 - 5x B B) 10 - 6x 0 7 - 5x D) 7 - 6x
Answer:
B) 10-6x is the answer ...
A carpet salesman sold 5,000 yards of carpet in one month at an average of $3 per yard. His commission was 16%. How much money did he make that month?
Answer:
5000x3.00= total sales 15000 x 16% or.16
= 2400
Step-by-step explanation:
1.Find Gross Sales
2. Get retail sales 3.00 x 5000
3. Total Sales times commission 15000 x .16
What does the caste system stand for?
Leeza’s aquarium holds 55 gallons of water. She is filling the tank and has already put in 22 gallons. Which inequality can determine out how many more gallons she might put in the tank?
Answer:
The inequality that will be used would be
x + 22 <= 55
The polynomial 4x2 - 16 is a difference of squares.
True
False
Write a word description of the set.
{10, 11, 12, 13, ...}
absolute value for |27 1/4|
Answer:
27 1/4
Step-by-step explanation:
what is the value of 3-6(z-2) if z=-2
Answer:
27
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
3 - 6(z - 2)
z = -2
Step 2: Evaluate
Substitute in z: 3 - 6(-2 - 2)(Parenthesis) Subtract: 3 - 6(-4)Multiply: 3 + 24Add: 27By substituting value of z = - 2 in 3 - 6(z - 2), we get :
[tex] \tt : \implies 3 - 6(z - 2) = 3 - 6((-2) - 2)[/tex]
[tex] \tt : \implies 3 - 6(z - 2) = 3 - 6(-2 - 2)[/tex]
[tex] \tt : \implies 3 - 6(z - 2) = 3 - 6(- 4)[/tex]
[tex] \tt : \implies 3 - 6(z - 2) = 3 + 24[/tex]
[tex] \tt : \implies 3 - 6(z - 2) = 27[/tex]
[tex] \large \underline{\boxed{\bf{ 3 - 6(z - 2) = 27}}}[/tex]
Hence, value of 3 - 6(z - 2) = 27.
In 1989 the population of Arizona was 3,622,184. In 1999 the population was 4,778,332. What is the percent of change from 1989 to 1999?
Find the coordinates of the point that is located 8 units below the x-axis and 3 units to the left of the y-axis
HELP ME PLEASEEEEE THIS IS SO HARD
Answer:
4. Given
6. Definition of verticle angles
7. Algebra/part-whole-postulate/sum of interior angles in a triangle/CPTCTC (Corresponding parts of congruent triangles are congruent)
Step-by-step explanation:
number 4 is just...given because it shows that they're both right angles
6, it's literally the definition of verticle angles
7, since we know that angle TQU and angle RSU are congruent and angle QUT and SUR are congruent, if we subtract those from 180, that means those two angles also have to be congruent
Also, the two triangles are congruent by LA or ASA, so CPCTC would also work
Part-whole-postulate, same reasoning as algebra.
Sum of interior angles in a triangle, same as algebra.
Hope this helped, let me know if you have any questions.
if paul rode at a constant speed, how fast did he travel in miles per hour(please help me i will give brainliest i promise)
Answer:
Raul traveled 31.25 miles an from 1:50 to 4:20. So, subtract those, you get 2:30. Turn 2:30 into a decimal (2.30) and now divide 31.25 by 2.30. the answer is 13.59 rounded That number turned into a Fraction is about 13 miles an hour.
Step-by-step explanation:
Answer: A
Step-by-step explanation:
the difference between the start time and end time is 2hrs and 30mins
So this means we have to multiply the number and add half of it.
12[tex]\frac{1}{2}[/tex] + 12[tex]\frac{1}{2}[/tex]+ 6[tex]\frac{1}{4}[/tex]= 31[tex]\frac{1}{4}[/tex]
(now can get a brainliest lol)
Find the length of line AC. Use that length to find the length of line CD. What is the length of line CD? Round to the nearest tenth.
a. 2.3 cm
b. 4.0 cm
c. 10.7 cm
d. 18.6 cm
Answer:
C on edge 2021
Step-by-step explanation:
What is the distance from X to Y?
A. 15 units
B. 3 units
C. 225 units
D. 21 units
Answer:
15, A
Step-by-step explanation:
(0,6) (9,-6)
distance formula =
[tex]d= \sqrt{(x_2-x_1)²+(y_2-y_1)² }[/tex]
lets put our numbers
[tex]d= \sqrt{(0 - 9)²+(6+ 6)² }[/tex]
so answer will be = 15, A
Kiran and Clare like to race each other home from school. They run at the same speed, but Kiran's house is slightly closer to school than Clare's house. On a graph, their distance from their homes in meters is a function of the time from when they begin the race in seconds.
As you read the graphs left to right, would the lines go up or down?
What is different about the lines representing Kiran's run and Clare's run?
What is the same about the lines representing Kiran's run and Clare's run?
Answer:
1. Down.
2. Clare's line would be higher because she begun further away from her house.
3. The lines would have the same slope since they are going the same speed.
Step-by-step explanation: