what are the ex and Y coordinates of point E, which partition the directed line segment from A to B into a ratio of 1:2?
Answers
Answer:
Step-by-step explanation:
The formula for this is the one we use when we are given the ratio the directed line segment is separated into as opposed to the point being, say, one-third of the way from one point to another. The 2 equations we use to find the x and y coordinates of this separating point are:
[tex]x=\frac{bx_1+ax_2}{a+b}[/tex] and [tex]y=\frac{by_1+ay_2}{a+b}[/tex] where x1, x2, y1, y2 come from the coordinates of A and B, and a = 1 (from the ratio) and b = 2 (from the ratio). Filling in for x first:
[tex]x=\frac{2(2)+1(-4)}{1+2}=\frac{4-4}{3}=0[/tex] and then y:
[tex]y=\frac{2(-3)+1(9)}{1+2}=\frac{-6+9}{3}=\frac{3}{3}=1[/tex]
The coordinates of point E, then, are (0, 1).
Answer:
(-1,3)
Step-by-step explanation:
Mathematically, what we have to do here is to get the coordinates of the midpoint of the line AB
we have this as;
(x,y) = (x1 + y1)/2, (y1 + y2)/2
(x,y) = (-4+2)/2, (9-3)/2 = (-1, 3)
Related Questions
Can someone please help me really struggling
Answers
And I don’t know about point slope form, it wasn’t in my standards, I’m sorry.
Answer:
your y-intercept is 5 and your slope is 1 hope this helps with translating into the form you want
Step-by-step explanation:
write an expression for 15 divided by a number
show your work
Answers
Answer:
15/X
Step-by-step explanation:
a number divided by 15
15/X
A square pyramid is inscribed in a rectangular prism. A cone is inscribed in a cylinder. The pyramid and the cone have the same volume. Part of the volume of the rectangular prism, 1 V 1 , is not taken up by the square pyramid. Part of the volume of the cylinder, 2 V 2 , is not taken up by the cone. What is the relationship of these two volumes, 1 V 1 and 2 V 2 ?
Answers
Answer:
V₂ = V₁
Step-by-step explanation:
Let the height of the rectangular prism = h
Let s represent the side length of the base of the square prism, we have;
The volume of the prism, [tex]V_{prism}[/tex] = s²·h
The volume of the square pyramid, [tex]V_{pyramid}[/tex] = (1/3)·s²·h
∴ V₁ = The area not taken up by the square pyramid = [tex]V_{prism}[/tex] - [tex]V_{pyramid}[/tex]
∴ V₁ = s²·h - (1/3)·s²·h = (2/3)·s²·h
Similarly, for the cylinder, we have;
Let h represent the height of the cylinder
Let r represent the radius of the base of the cone, we have;
Therefore;
The volume of the cylinder, [tex]V_{cylinder}[/tex] = π·r²·h
The volume of the cone, [tex]V_{cone}[/tex] = (1/3)·π·r²·h
∴ V₂ = π·r²·h - (1/3)·π·r²·h = (2/3)·π·r²·h
V₂ = (2/3)·π·r²·h
[tex]V_{cone}[/tex] = [tex]V_{pyramid}[/tex]
Therefore;
(1/3)·π·r²·h = (1/3)·s²·h
∴ π·r² = s²
Therefore, V₂ = (2/3)·π·r²·h = V₂ = (2/3)·s²·h = V₁
V₂ = V₁.
Find the values of x and y from the following equal ordered pairs. a) (x,-2) = (4,y) b) (3x, 4) = (6, 2y) c) (2x-1, y + 2) = (-1,2) d) (2x + 4, y + 5) = (3x + 3,6) e) (x + y,y + 3) = (6, 2y) f) (x + y, x - y) - (8,0)
Answers
Answer:
a)
x=4, y=-2
b)
x=2, y=2
c)
x=0, y=0
d)
x=1, y=1
e)
x=3, y=3
f)
x=4, y=4
Step-by-step explanation:
a) (x,-2) = (4,y)
x=4
y=-2
b) (3x, 4) = (6, 2y)
3x=6 => x=2
2y=4 => y=2
c) (2x-1, y + 2) = (-1,2)
2x-1 =-1 => x=0
y+2 = 2 => y=0
d) (2x + 4, y + 5) = (3x + 3,6)
2x+4 = 3x+3 => x=1
y+5 = 6 => y=1
e) (x + y,y + 3) = (6, 2y)
x+y = 6 => x+3 = 6 => x=3
y+3 = 2y => y=3
f) (x + y, x - y) - (8,0)
x+y = 8 => 2x=8 => x=4
x-y = 0 => x=y => y=4
John finds that the sum of two numbers is 24 and their difference is one sixth of the sum. Find the smallest number between the two numbers
Answers
Answer:
The smallest number is 10
Step-by-step explanation:
x+y=24---equation 1
x-y=¹/6×24=>x-y=4---equation 2
Add both equations
2x=28
x=14
put x=14 into equation 1
14+y=24
y=24-14=10
is AC greater than, less than, or equal to BC? explain your reasoning
Answers
Answer:
AC is greater than BC
Step-by-step explanation:
First, we know that the angle of a straight line is 180°, so angle B as a whole is equal to 180 degrees. Therefore, angle YBC + angle ABC = 180 degrees. As angle YBC is a right angle, signified by the small square on the angle, it is 90 degrees. Therefore,
90 degrees + angle ABC = 180 degrees
subtract 90 degrees from both sides to isolate angle ABC
angle ABC = 90 degrees
Therefore, as angle ABC is equal to 90 degrees, and a right angle is 90 degrees, triangle ABC has a right angle, making it a right triangle.
In a right triangle, using the Pythagorean Theorem, the square of the side opposite the right angle is equal to the sum of the squares of the other side. Since side AC is opposite the right angle, we can say that
AC² = AB² + BC²
As the length of a side has to be greater than 0, we can say that
AC² = AB² + BC²
AB² > 0
AC² > BC²
square root both sides
AC > BC
Therefore, AC is greater than BC
A radar station located at ground level picks up a plane flying at a direct distance of 47,440 feet
away. If the angle of elevation from the station to the plane is 29°, what is the altitude of the plane?
Answers
Answer:
22,999 feets
Step-by-step explanation:
Given the solution diagram attached,
The altitude, h of the plane can be solved using trigonometry :
Using :
Sin θ = opposite / hypotenus
Opposite = h
Hypotenus = 47440
Sin 29 = h / 47440
h = 47440 * sin29
h = 22999.368
h = 22,999 feets
If f(x) = 3x + 10 and g(x) = 2x - 4, find (f+g)(x).
O A. (f+g)(x) = -34 - 2x - 14
B. (f+ g)(x) = 3x - 2x + 14
O C. (f+ g)(x) = 5x + 6
D. (f+ g)(x) = 3x + 2x + 6
Help! I’m getting really confused which one it is
Answers
Answer:
O D
Step-by-step explanation:
f+g(x)
3x+10+2x-4
3x +2x+6
Find the value of x that will make A||B.
Please help!
Answers
Answer:
x=30
Step-by-step explanation:
Hi there!
For A to be parallel to B, 5x would be equal to 3x+60. (If they were parallel, these two angles would be alternate exterior angles, which are equal.)
[tex]5x=3x+60[/tex]
Subtract 3x from both sides
[tex]5x-3x=3x+60-3x\\2x=60[/tex]
Divide both sides by 2
[tex]x=30[/tex]
I hope this helps!
What is the vertex form of the quadratic function that has a vertex at (5, 4)
and goes through the point (6, 1)?
O A. y= (x - 5)2 + 4
B. y=-3(x - 5)2 + 4
C. y = 3(x - 5)2 + 4
O D. y = 5(x - 5)2 - 3
Answers
I think it’s D-y=5(x - 5)2 - 3
I’m sorry if this is wrong
Tommy's birthday party costs $2.94 for every guest the invites. If there are 4 guests, how much will Tommy's birthday party cost?
Answers
Answer:
$11.76
Step-by-step explanation:
2.94×4=$11.76
plz help me with this math and also explain
Answers
Step-by-step explanation:
[1]SI = $250Rate (R) = 12[tex] \sf \dfrac{1}{2}[/tex] %Time (t) = 4 years[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]
Therefore principal is $500.
__________________[2]2/7 of the balls are red.3/5 of the balls are blue.Rest are yellow.Number of yellow balls = 36Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]
What is the value of x |-16|
Answers
16
Step-by-step explanation:
|-16| = the distance between -16 and 0
Hence, the answer is 16
Find the product: 3/4 x 2/3. What's the product? 5/7, 6/12, 5/12, 6/7. What is it please help me!!!!
Answers
Answer:
1/2
Step-by-step explanation:
3/4 x 2/3
= 1/2
Jeff and Cameron are arguing about which one of them is faster. Jeff says "I can run 777 kilometers per hour!" and Cameron says "I can run 100100100 meters per minute!
Answers
Answer:
Jeff is moving faster.
Step-by-step explanation:
To compare two speeds, first we make them in one unit.
We know that,
1 km/h = 0.2777 m/s
7 km/h = 1.94 m/s
Jeff can run at a speed of 7 km/h i.e. 1.94 m/s while Cameron can run with a speed of 10 m/min or 0.167 m/s.
On comparing 1.94 m/s and 0.167 m/s, we found that Jeff is moving with more speed.
So, Jeff is faster.
A solid box with height 20cm, width 50cm and length 60cm needs to be painted.
The paint costs £0.06 per cm2.
How much will it cost to paint the box?
Answers
Answer:
£624
Step-by-step explanation:
Surface area of a box = 2(length*width + length*height + width*height)
Length = 60 cm
Width = 50 cm
Height = 20 cm
Surface area of a box = 2(length*width + length*height + width*height)
= 2(60*50 + 60*20 + 50*20)
= 2(3000 + 1200 + 1000)
= 2(5,200)
= 10,400 cm²
Surface area of a box = 10,400 cm²
The paint costs = £0.06 per cm²
Total cost of painting the box = 10,400 cm² × £0.06
= £624
Find the number of degrees in the measure of angle x
Answers
Answer: x = 82°
Step-by-step explanation:
The angle on the other side of 108° can be calculated as 180° - 108° = 72°
All angles within a triangle add up to 180°, so the x-value can be found as:
x = 180° - 72° - 26° = 82°
Which one of these would be geometry or is it none of the above.
Answers
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Write using exponents.
5.5.5. b. b. b.b
1 2 3 4 5 6 89
F9 CDI
a|b|x
NEXT QUESTION
O ASK FOR HELP
TURN IT IN
Answers
The answer will just be 125b^4
Step-by-step explanation:
Basically multiply 5 by 5 by 5 and then count all of the b’s (4 b’s) and add it to the product as an exponent
Final answer: 125b^4
Work out the area of the shaded shape.
Answers
Answer:
65 m²
Step-by-step explanation:
Area 1 :-
A = 3m * 9m A = 27 m²Area 2 :-
A = (12-3-2) m * (9 - 5) m A = 7m * 4 mA = 28 m²Area 3 :-
Area = 2m * 5 m A = 10 m²Total Area :-
A = ( 27 + 28 + 10 ) m²A = 65 m²how do I solve this question (step by step)?
Answers
Answer:
see explanation
Step-by-step explanation:
Angles on the circumference subtended on the same arc are equal
Angle at the centre is twice the angle at the circumference subtended on the same arc.
Then
∠ BAC = ∠ BDC = 29°
∠ BOC = 2 × ∠ BDC = 2 × 29° = 58°
Given a line segment that contains the points A,B, & C in order, if AB = 2x - 2, and BC = 2x + 10, and AC = 32, find x.
Select one: a. 6
b. 24
c. 8
d. - 4
Answers
Answer:
a. 6
Step-by-step explanation:
AB +BC =AC
2x-2+2x+10=32
4x+8=32
4x=32-8
4x=24
x=24/4
x=6
product of (n+bv^2) (5n+3bv2)
Answers
Answer:
5n² + 8bnv² + 3b²v^4
Step-by-step explanation:
(n+bv²) (5n+3bv²)
5n² + 3bnv² + 5bnv² + 3b²v^4
5n² + 8bnv² + 3b²v^4
Can someone help with 13 and 14
Answers
Step-by-step explanation:
Question 13 :-
-4c³ . 7d² . 2c -²( -4c ³ - ² ) . 7d² -4c . 7d²-28cd²Question 14 :-
n-⁴ w⁰n-⁴ . 1 n -⁴Answer:
13.) -56cd²
14.) n-⁴
Step-by-step explanation:
Question 13 :- -4c³• 7d² • 2c-²
-4c³• 7d² • 2c-²Calculate the products.
-4•7•2 c³ d²c-²-56c³ d²c-²Multiplying the terms with the same base by adding their exponents.
-56c³-²d²Calculate the exponents.
-56cd²Question 14 :- n-⁴w⁰
n-⁴w⁰Any non - zero expression raised to the power 0 equals 1.
n-⁴ 1Any expression multiplied by 1 remains the same.
n-⁴Which shape has the greatest number of lines of symmetry?
A. rhombus
B. square
C. rectangle
D. parallelogram
Answers
which point is a solution to y>2x-1?
Answers
Answer:
B) (0,2)
Step-by-step explanation:
We substitute the values of x and y into this inequality:
2 ≥ 2(0)-1
2 ≥ 0-1
2 ≥ -1
This is true, so this is the correct point
hope this helps have a good day
Answer:
there it is
Step-by-step explanation:
Which of the following is the constant ratio of the relation shown in the table?
Answers
Answer:
hello!
where are you from ?
Step-by-step explanation:
option 4 is correct ...there is no constant ratio.
Help fast
Luke and Owen have \$100$100dollar sign, 100 each. Their friend offered to invest their money, promising to return a sum rrr times as great as what they invested. Luke was suspicious, so he invested \$10$10dollar sign, 10 only, but Owen invested his entire \$100$100dollar sign, 100. Fortunately, the friend did indeed return a sum rrr times as great to each.
They decided to make another investment. This time, Owen invested all of the money returned to him, and Luke invested the money returned to him and the remaining \$90$90dollar sign, 90. Again, they got a sum rrr times as great as what they invested. In the end, Owen had \$337.50$337.50dollar sign, 337, point, 50 more than Luke.
Write an equation in terms of rrr that models the situation.
Answers
An equation in terms of r which models the situation described is : 100r² = 10r² + 90r - 337.50
First investment :
Luke:
Total amount had = $100
Amount invested = $10
Amount left = $100 - $10 = $90
Return = r times the amount invested = (10 × r) = 10r
Owen:
Total amount had = $100
Amount invested = $100
Return = r times the amount invested = (100 × r) = 100r
Second investment :
Luke :
Amount invested = Return on first + amount left = 10r + 90
Return is r times the amount invested :
Return on second investment = (10r + 90) × r = (10r² + 90r)
Total amount earned after both investment = 10r² + 90r
Owen :
Amount invested = Return on first = 100r
Return is r times the amount invested :
Return on second investment = (100r × r) = 100r²
Total amount earned after both investment = 100r²
Owen made 337.50 more than Luke ; This means that :
Total earned by Owen = Total earned by Luke + 337.50
100r² = 10r² + 90r + 337.50
Hence, the equation in terms of r is : 100r² = 10r² + 90r - 337.50
Learn more : https://brainly.com/question/18796573
Question 1 (5 points)
Determine the value of x.
3
3V2
6
3V3
Answers
Answer:
Step-by-step explanation:
what is the value of x? (3x-14)°=180° [4(x-9)]°=180°
Answers
Answer:
3x-14=180
3x=194
x= 64 2/3
4(x-9)=180
4x-36=180
4x=216
x=54
Hope This Helps!!!
Step-by-step explanation:
(3x-14)°=180°
3x-14=180
3x=180+14
3x=194
x=64.6
[4(x-9)]°=180°
4x-36=180
4x=180+36
4x=216
x=54
