(a) y = [tex]\frac{-1}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
(b) y = 2x + 3
Step-by-step explanation:
(a) The equation of a line given by points M(x₁, y₁) and N(x₂, y₂) is given by:
y - y₁ = m(x - x₁) -------------------(i)
Where;
m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = slope or gradient of the line ---------------(ii)
Given points on the triangle are:
A(2,5)
B(1,-2)
C(-5,1)
To find the equation of line BC, we use the formulas in equations (i) and (ii) where the points of the line are B(1,-2) and C(-5,1) and;
x₁ = 1
y₁ = -2
x₂ = -5
y₂ = 1
==> First get the gradient using equation (ii) as follows;
m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = [tex]\frac{1 - (-2)}{-5 -1}[/tex]
m = [tex]\frac{3}{-6}[/tex]
m = [tex]\frac{-1}{2}[/tex]
==> Now, use equation (i) to find the equation of the line as follows;
y - (-2) = [tex]\frac{-1}{2}[/tex](x - 1)
y + 2 = [tex]\frac{-1}{2}[/tex](x - 1)
Multiply both sides by 2
2(y+2) = -1 ( x - 1 )
2y + 4 = -x + 1
2y = -x + 1 - 4
2y = - x - 3
y = [tex]\frac{-1}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
Therefore, the equation of the line is y = [tex]\frac{-1}{2}[/tex]x - [tex]\frac{3}{2}[/tex]
(b) To find the perpendicular line from A to BC, note that
i. two lines are perpendicular if they meet at 90°
ii. the general equation of a line could also be written as y = mx + c where m is the slope and c is the intercept.
iii. when one line has a slope of m, then a perpendicular line to that line will have a slope of [tex]\frac{-1}{m}[/tex]
The equation of line BC is y = [tex]\frac{-1}{2}[/tex]x - [tex]\frac{3}{2}[/tex].
This means that BC has a slope of [tex]\frac{-1}{2}[/tex]
A perpendicular line from A to BC will have a slope of 2.
Now to get the equation of this perpendicular line from A(2, 5) to BC, we use the general equation of a line given in equation (i)
where;
m = 2
x₁ = 2
y₁ = 5
Substitute these values into equation (i)
y - 5 = 2(x - 2)
Solving by simplification gives;
y - 5 = 2x - 2
y = 2x + 3
Therefore, the equation of the perpendicular line is y = 2x + 3
ANSWER ASAP NO LINKS WILL GIVE BRAINLIEST
a place from this table is chosen at random let event 4= the place is a city what is p(a^c)
a 3/7
b 4/7
c 2/7
d 5/7
Answer:
A
Step-by-step explanation:
What is the area of this triangle? I need help!! pleaseee
Answer:72
Step-by-step explanation: 9x8 =72
What is the sum of all interior angles of a regular hexagon? A. 120° B. 360° C. 540° D. 720°
Condense the expression to a single logarithm. 3 log subscript 5 10 - 12 log subscript 5 7
Answer:
A is correct
Step-by-step explanation:
Mathematically from logarithmic laws, we have it that;
x log a = log a^x
and also;
log a - log b = log (a/b)
So we have;
log 5 10^3 - log 5 7^12
and finally log 5 (10^3/7^12)
Which number could be included in Group B
Answer:
C
Step-by-step explanation:
Just did the test
GIVING BRAINLIEST -23 points-
URGENT HELP ME PLEASE!!!
Answer:
See a sides are equal so your answer is 8.2 in.
Need answer for only number 15! please help!
What is the diameter of a cone with height 8 m and volume 150 pi m3 ?
A. 7.5 m
B. 5V3 m
o C. 7.573 m
D. 15 m
Answer:
V = pi*r^2*h
V = 150 m^3
h = 8 m
150 = pi*r^2*8
Solve for r (the radius) then multiply by 2 to obtain the diameter.Only, this is a cone, not a cylinder.
V = 1/3 pi r^2 h
Diameter of the cone is 15 m. So, option D is correct.
What is meant by solid shape ?Solid shapes are defined as the three-dimensional objects that are described by the three dimensions length, breadth and height.
Here,
Volume of the cone is given by,
V = 150[tex]\pi[/tex] m³
Height of the cone, h = 8 m
We know, the equation for the volume of a cone is,
V = 1/3[tex]\pi[/tex]r²h
where r is the radius and h is the height of the cone.
So,
(1/3) [tex]\pi[/tex]r²h = 150[tex]\pi[/tex]
r²x 8 = 3 x 150 = 450
r² = 450/8
r² = 56.25
r = 7.5 m
Therefore, diameter of the cone,
d = 2r
d = 2 x 7.5
d = 15 m
Hence,
Diameter of the cone is 15 m.
To learn more about solid shapes, click:
https://brainly.com/question/22731242
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28/10 simplify fraction
What is the area of the square?
What’s the area of the circle
Answer:
Square: 144 m²
Circle: 113.04 m²
Step-by-step explanation:
The formula for area of a square: side × side.
The formula for area of a circle: r²π (radius × radius × pi)
**SQUARES HAVE EQUAL SIDES**
As shown in the photo, the side lengths of the square are 12.
side × side
12 × 12 = 144
Therefore, 144 m² is the area of the square.
-------------------------------------------------------------------------------------------------------------
The diameter of the circle is 12 as well.
But, to find the area of the circle, we need the radius.
To find the radius of a circle, divide the diameter by 2.
12 ÷ 2 = 6.
6 is the radius.
Now we plug the numbers into the equation.
**3.14 IS A SUBSTITUTE FOR PI**
r²π (radius × radius × pi)
6²π (6 × 6 × 3.14) = 113.04
Therefore, 113.04 m² is the area of the circle.
Answer:
the person above me is correct
Step-by-step explanation:
Find the perimeter of the figure to the nearest hundredth.
Answer: 90.75 mm
Step-by-step explanation:
Given
The radius of the hemisphere is 16 mm
length of the inclined sides are 20 mm
The perimeter of the figure is the sum of the length of two inclined sides and a semi-circle circumference
[tex]\Rightarrow \text{Perimeter P=}\dfrac{2\pi r}{2}+2\times 20\\\\\Rightarrow P=\pi \times 16+40\\\Rightarrow P=50.75+40\\\Rightarrow P=90.75\ mm[/tex]
|Calculate the midpoint (-5,5), K(-3,-2)
Answer:
(-4,1.5)
Step-by-step explanation:
Given :-
Two points (-5,5) and (-3,-2)And we need to find out the midpoint of the two points. The midpoint of two points is given by the ,
[tex]:\implies[/tex] Midpoint =( x1+x2/2 , y1+y2/2)
[tex]:\implies[/tex] Midpoint =( -5-3/2 , 5-2/2)
[tex]:\implies[/tex] Midpoint =(-8/2,3/2)
[tex]:\implies[/tex] Midpoint = (-4 , 1.5)
Hence the midpoint of the two points is (-4,1.5) .Here we would be using the midpoint formula to find the co-ordinates of the line segment joining the two given points.
Given points,
(-5,5) and (-3,-2)
★ Midpoint of two points:-
[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]
★ We have :
x1 = -5 y1 = 5 x2= -3 y2 = -2★ Putting the values :
Refer the attachment.Additional Information :★ Centroid of a triangle :-
[tex]\boxed{ \sf{Centroid \: = \: \dfrac{x_1 \: + \: x_2 \: + \: x_3}{3} }} \: \pink\bigstar[/tex]★ Distance Formula :-
[tex]\huge \large \boxed{\sf{{d \: = \: \sqrt{(x _{2} - x _{1}) {}^{2} \: + \: (y _{2} - y _{1}) {}^{2} }}}} \: \red\bigstar[/tex]who is correct
please answer ASAP!!! pls (:
Answer:Dwight is correct
Step-by-step explanation:
El valor numérico de la expresión 〖P(y)=y〗^2-7y+10 para y=2 es: a. P(2)=9 b. P(2)=0 c. P(2)=-2 d. P(2)=-5
Answer:
Opción b, P(2) = 0
Step-by-step explanation:
Tenemos la expresión:
P(y) = y^2 - 7*y + 10
Para encontrar el valor P(2), simplemente debemos remplazar todas las "y" en la expresión de arriba por el valor 2, asi obtenemos:
P(2) = 2^2 - 7*2 + 10 = 4 - 14 + 10 = (4 - 14) + 10 = -10 + 10 = 0
P(2) = 0
La opción correcta es b.
A holiday park is digging a swimming pool.
The volume of earth to be removed is 120m^3.
A mechanical digger can remove 0.15m^3 of earth with each scoop.
a) How many scoops will be needed to remove all the earth?
Please it’s urgent!
The volume of a rectangular prism is 48 cubic centimeters. The volume of a similar rectangular prism is 6 cubic centimeters.
What is the scale factor for the rectangle?
a. 8
c. 4
b. 6
d. 2
what is f(-1) for the function given?
f(x)=x^2-3x+8
Answer: 12
Work is provided in the image I attached
Please help quickly!!!! I will give brainiest
Answer:
A
Step-by-step explanation:
10% raise in $20 is $2, so its only $2 more, so each hour she would earn $2 more.
Option D is the answer. $200
Help I need the answer dont send NO FILE only answer if you know it step by step explanation
Step-by-step explanation:
B (-8,-6)
C (-10, -6)
D (-10,2)
E (-8,2)
Item 7
Michael arrives at the basketball court at 5:52 p.m. He plays basketball for 1 hour 12 minutes.
What time does Michael stop playing basketball?
6:04 p.m.
7:02 p.m.
7:04 p.m.
7:12 p.m.
Answer:
he stops playing at 7:04
Step-by-step explanation:
Please help! I don’t really understand
Drag a company name into each box to show the total cost from least to greatest.
Answer:
Company A:
150 x 3 = $450
6/100 x 150 = $9
450 + 9 = $459
Company B:
3.10 x 150 = 465
4/100 x 150 = 6
465 + 6 = $471
Company C:
3.20 x 150 = $480
Now the order (Answer):
A(459), B(471), C(480)
imagine paying attention in class
What is the measure, in degrees, of angle x?
Answer:
121°
Step-by-step explanation:
they're basically the same
Answer:
121°
Step-by-step explanation:
Theorem of vertical angles state that the opposite angles formed by two intersecting lines are congruent.
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
find a fraction or mixed number equivalent to each decimal.
13. 0.3333...
14. 0.050505...
15. 0.454545...
16. 0.045045...
17. 10.121212...
18. 3.9999...
Please help me asap
Answer:
13. 1/3
14. 1/20
15. 9/20
16. 9/200
17. 253/25
18. 39/10
Ram is 20 years older than Sam. In 5 years, Ram will be twice old as Sam .Find their present ages.
Answer:
Sam is 15 years old and Ram is 35.
in five years Sam will be 20 and Ram will be 40, which is twice as old in age.
Preform the indecated operation 1/3x6/7
Answer:
0.257
Step-by-step explanation:
Which equation describes the relationship shown in the table?
Items Sold
A- p=2i
B- i=2p
C- p=i+5
D- i=p+5
Answer:
A
Step-by-step explanation:
i = items sold
p = profit
Based on the table, the profit is twice the number of items sold. Therefore the answer is A. Correct me if I'm wrong. I hope it helps.
A bin of winter hats on clearance contains 6 green caps, 7 blue caps, and 9 red caps If you pick one without looking, what is the total number of outcomes? Answer: 1 Part B What is the probability that the cap will be green?
Answer:
Since it is the case of independent the answer will be 6/22
Helpppppppppppppppppp
Pppppo
Answer:
(2 * L)+(2 * W)
Step-by-step explanation: