Answer:
Step-by-step explanation:
let the height of the room(h) = x
Length(l) = 3*x = 3x
length = 2 * breadth
breadth(b) = length /2 = 3x/2
Cost of whitewashing the 4 walls = ₹ 7200
Area of 4 walls = 7200 ÷ 50 = 144 m² ------(I)
Area of walls = 2lh + 2bh
= 2*3x*x + 2 *[tex]\frac{3x}{2}[/tex] * x
= 6x² + 3x²
= 9x²
9x² = 144 {From (I)}
x² = 144/9
x² = 16
x = [tex]\sqrt{16}=\sqrt{4*4}[/tex]
x = 4 m
height = 4 m
length = 3*4 = 12m
Breadth = [tex]\frac{3}{2}*4=3*2=6 \ m[/tex]
Area of floor = l*b
= 12 * 6
= 72 m²
Cost of carpeting the floor = 72 * 325 = ₹ 23400
URGENT! The range of y=Arccosx is (-pi/2,pi/2). True or False?
false. range of [tex] \cos^{-1}(x)[/tex] is $[0,\pi]$
6 points are place on the line a, 4 points are placed on the line b. How many triangles is it possible to form such that their verticies will be the given points, if a ∥b?
Answer: 96
Step-by-step explanation:
Ok, lines a and b are parallel.
We can separate this problem in two cases:
Case 1: 2 vertex in line a, and one vertex in line b.
Here we use the relation:
"In a group of N elements, the total combinations of sets of K elements is given by"
[tex]C = \frac{N!}{(N - K)!*K!}[/tex]
Here, the total number of points in the line is N, and K is the ones that we select to make the vertices of the triangle.
Then if we have two vertices in line a, we have:
N = 6, K = 2
[tex]C = \frac{6!}{4!*2!} = \frac{6*5}{2} = 3*5 = 15[/tex]
And the other vertex can be on any of the four points on the line b, so the total number of triangles is:
C = 15*4 = 60.
But we still have the case 2, where we have 2 vertices on line b, and one on line a.
First, the combination for the two vertices in line b is:
We use N = 4 and K = 2.
[tex]C = \frac{4!}{2!*2!} = \frac{4*3}{2} = 6[/tex]
And the other vertice of the triangle can be on any of the 6 points in line a, so the total number of triangles that we can make in this case is:
C = 6*6 = 36
Then, putting together the two cases, we have a total of:
60 + 36 = 96 different triangles
If two angles are complements of each other then each angle is
Answer:
each angle is less than 90 degrees. angle 1+angle2=90 degrees
Step-by-step explanation:
This figure shows how to create a six-pointed star from twelve equilateral triangle tiles: (SEE FIGURE ATTACHED) If each of the original tiles has a perimeter of 10 cm, what is the perimeter of the final star in cm?
Answer:
Perimeter of the final star = 40 cm²
Step-by-step Explanation:
The perimeter of the six-pointed star is the sum of the sides of the 6 equilateral triangles that form a boundary around the star.
1 triangular tiles gas a perimeter of 10cm.
Only 2 out of the 3 equal sides of each of the 6 equilateral triangles form the boundary of the final star.
Therefore, perimeter of the final star = ⅔ of the total perimeter of 6 triangular tiles
= ⅔ of (10*6)
= ⅔*60
= 2*20
Perimeter of the final star = 40 cm²
Help please on question 61!!
Answer:
r = 1
Step-by-step explanation:
2πr = x
πr² = y
x = 2y
2πr = 2πr²
r = 1
what is y ? x=1 y=? y=3x-7
Answer:
-4.
Step-by-step explanation:
y = 3x - 7; x = 1.
y = 3(1) - 7
= 3 - 7
= -4
Hope this helps!
Answer:
y = - 4
Step-by-step explanation:
y=3x-7
Let x =1
y = 3*1 -7
y = 3-7
y = - 4
Help please Algebra 1
Simplify 4y-6yx+y
help..? why are there so many parentheses..?can you plz give a step by step on how to slove the equation?
Answer:
= -11
Step-by-step explanation:
-(-(11-22))
= -(-11+22)
= 11 - 22
= -11
El Pirata Barba Plata ha llegado a la isla del Coral para buscar un tesoro. En el mapa pone que, desde la orilla, debe recorrer 37 hm a la pata coja hacia el centro de la isla, y después otros 85 dam dando volteretas en la misma dirección. ¿Cuántos metros recorrerá en total desde la orilla hasta el tesoro? Expresa el resultado también en kilómetros.
Answer:
4550m ; 4
Step-by-step explanation:
Recall
1 hectometre = 100m
1 decameter = 10m
Distance from shore to center of island = 37hm
Another 85 decameter toward stge se direction
Therefore total metres it will travel in other to get to the treasure :
37 hectometre + 85 decameter
(37 * 100)m + (85 * 10)m
3700m + 850m = 4550m
In kilometers :
1000 meters = 1 kilometers
4550 meters =
(4550 / 1000)meters
= 4.55km
The linear scale factor of two shapes is 3:4. If the area of the smallest shape is 72^2 what is the area of the big shape?
Answer:
[tex]\boxed{6912 units^2}[/tex]
Step-by-step explanation:
Hey there!
Well using the given ratio,
3:4
And the area of the small shape we need to do,
72*72 = 5184
Now we can make the following fractions,
[tex]\frac{3}{4}[/tex] = [tex]\frac{5184}{x}[/tex]
Now we can solve,
3*x = 3x
4 * 5184 = 20736
3x = 20736
20736 / 3
x = 6912
So the area of the bigger shape is 6912 units^2
Hope this helps :)
Simplify 25/81 ……………
Answer:
25/81 is already in the simplest form. It can be written as 0.308642 in decimal form (rounded to 6 decimal places).
Please answer question
Answer:
87.6yd²
Step-by-step explanation:
Base: =1/2bh
=1/2(6)(5.2)=15.6
Sides: =1/2bh
=1/2(6)(8)=24 (3 of them)
15.6+24+24+24=87.6yd²
The length of a rectangle is 3 inches more than its width. The perimeter of the rectangle is 34 inches. The length of the rectangle is inches, and its width is inches.
Answer: Width= 7 in.
Length= 10 in.
Step-by-step explanation:
[tex]l=w+3[/tex]
The perimeter of the rectangle is 34 inches.
[tex]2(w+l)=34[/tex]
substitute
[tex]2(w+w+3)=34[/tex]
[tex]2(2w+3)=34[/tex]
distributive property [tex]a(b+c)=ab+ac[/tex]
[tex]2\cdot 2w+2\cdot 3=34[/tex]
[tex]4w+6=34[/tex]
[tex]4w+6-6=34-6[/tex]
[tex]4w=28[/tex]
divide 4 on both sides
[tex]w=7[/tex]
Width is 7 inches
substitute w=7 in equation [tex]l=w+3[/tex]
[tex]l=7+3[/tex]
[tex]l=10[/tex]
Length is 10 inches
Find the area of quadrilateral ABCD. [Hint: the diagonal divides the quadrilateral into two triangles.]
A. 28.93 units²
B. 29.98 units²
C. 29.79 units²
D. 30.73 units²
Answer:
Area of quadrilateral ABCD = 29.79 units² (Approx)
Step-by-step explanation:
Area of triangle ABD
s = (3.48+8.66+8.6) / 2
s = 10.37
Area of triangle ABD = √10.37(10.37-8.66)(10.37-8.6)(10.37-3.48)
Area of triangle ABD = √212.4616
Area of triangle ABD = 14.5760625 unit²
Area of triangle ACD
s = (3.54+8.84+8.6) / 2
s = 10.49
Area of triangle ACD = √10.49(10.49-8.6)(10.49-8.84)(10.49-3.54)
Area of triangle ACD = √227.3558
Area of triangle ACD = 15.0783222 unit²
Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle ACD
Area of quadrilateral ABCD = 14.5760625 unit² + 15.0783222 unit²
Area of quadrilateral ABCD = 29.6542units²
Area of quadrilateral ABCD = 29.79 units² (Approx)
2.
three vertius of sect. A B C D are A (2, 2), B (-3,2), ((
Plot those point and find the quad of D and find the area
of dood. ABCD.
If x/y = 2/3 what is the value of 6x/y
If x/y = 2/3, then all we have to do is multiply x/y by 6. Another way to look at this (the same thing) would be to see 6 as 6/1, so 6 is multiplied by x, and y is multiplied by 1.
But, all the same, you multiply 6 by x/y and you get (2·6)/3 = 12/3 = 4
Diagram shows helicopter H flying towards an island P
When the helicopter is 100 m above sea level, the pilot sees a man fishing from boat Q. Given the angles of depression of the island P and boat Q from H are 22° and 61.5° respectively.
Calculate the distance, in M, of PQ
Please help me to explain :(
Answer:
193.21 m
Step-by-step explanation:
make a vertical line down from the helicopter that is 100m
tan 61.5 = 100/x x = 54.3 (distance from the point directly below helicopter to boat)
tan 22 = 100/x x = 247.51 (distance from the point directly below helicopter to the island
247.51 - 54.3 = 193.21 (distance from boat to island)
1. Find the slope of a line passing through points (0,0) and (4,5)
o 4/5
5/4
4/9
5/9
Option 5
Answer:
slope = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (4, 5)
m = [tex]\frac{5-0}{4-0}[/tex] = [tex]\frac{5}{4}[/tex]
Answer:
The answer is 5/4Step-by-step explanation:
Slope of a line is given by
[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]where
m is the slope and
( x1 , y1) and (x2 , y2) are the points of the line
Slope of the line between the points
(0,0) and (4,5) is
[tex]m = \frac{5 - 0}{4 - 0} = \frac{5}{4} [/tex]Hope this helps you
4 is a square number and also an even number. How many other whole numbers less than 50 are an even, square number?
(2p-1)^2 Multiplying polynomials
Answer:
1
Step-by-step explanation:
X+y=2 và x-y=4 tim x và y
Step-by-step explanation:
X
[tex]xx - xxyy - yy = 8[/tex]
If A = {2,4,6,8,}, write the set A by description method
Step-by-step explanation:
Set-builder notation is a notation for describing a set by indicating the properties that its members must satisfy.
C={2,4,6,8}
C={2×1,2×2,2×3,2×4}
thus set builder form is:
{x:x=2n,n∈N} and this set is also call even number set in description mathod
Find the value of v in the equation below(in picture)
Answer:
v =3Step-by-step explanation:
[tex]v=\log _7\left(343\right)\\\\\mathrm{Rewrite\:}343\mathrm{\:in\:power-base\:form:}\quad 343=7^3\\\\\log _7\left(7^3\right)=3\log _7\left(7\right)\\\\v=3\log _7\left(7\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(a\right)=1\\\\\log _7\left(7\right)=1\\\\v=3\times \:1\\\\=3[/tex]
Could you pretty please answer these? I really need this done now
Thank you!
21in. = _____ft. terminating or repeating
Answer:
Terminating
Step-by-step explanation:
We know that 12 inches is 1 foot. We can divide to find how many feet we have.
21 / 12 = 1.75
Since the decimal ends at 0.05, the decimal is terminating.
Best of Luck!
HELP ME IM GONNA CRY PLEASE
A car was purchased for $20,000. The car depreciates by 22% of each year.
a) What is the value of the car when it is 12 years
old?
b) How long will it take for the car to be worth less than $100?
Hello, a car was purchased for $20,000.
This is the initial value.
The car depreciates by 22% of each year.
After 1 year, the value is the initial value 20,000 minus 22% of 20,000.
[tex]20000-20\%*20000=20000\cdot (1-20\%)=20000\cdot (1-0.20)=20000\cdot 0.8=16000[/tex]
After 2 years, the value is.
[tex]20000\cdot 0.8\cdot 0.8=20000\cdot0.8^2=12800[/tex]
Let's take n a positive integer, after n years, the value is.
[tex]\large \boxed{\sf \bf \ 20000\cdot0.8^n \ }[/tex]
a) After 12 years, the value is.
[tex]20000\cdot0.8^{12}=1374.389...[/tex]
This is rounded to $1,374
b) We need to find n such that
[tex]20000\cdot0.8^n=100\\\\ln(20000)+nln(0.8)=ln(100)\\\\n=\dfrac{ln(100)-ln(20000)}{ln(0.8)}=23.74...[/tex]
This is around 23.75 meaning 23 years and 75% of 1 year (meaning 9 months).
So to be worth less than $100, 23 years and 9 months are required.
Thank you
asking this out of spite <3
Which statement is true about the climbers’ heights?
A) Brynn was resting at a constant climbing height when Abby’s climbing height was decreasing.
B) Abby’s climbing height was decreasing when Brynn’s climbing height was increasing.
C) The heights of both climbers increased, then decreased, with no rest at a constant height.
D) Both climbers rested on the wall at a constant height for 2 minutes.
The distance between two schools A and B is 2km.A market is situated 3/4 of the distance from A to B.How far is the market from B?
Answer:
0.5 km
Step-by-step explanation:
the schools are 2km apart, so we are trying to find 3/4 of 2km, which is 1.5. So, the market is 1.5km from school A, which means that it is .5km from school b since they are 2km apart
which is the solution to this system of equations?
x + y = 3
x - y = -3
A. (3,0)
B. (0,3)
C. (0,6)
D. (0,-3)
x+y,=3
x_y=-3
A.,(0,3)
B. (0,3)
C. (0,6)
D. (0 _3)
make u the subject of the formula
u-x/v-x=u/v²
Answer:
See below.
Step-by-step explanation:
[tex]\frac{u-x}{v-x}=\frac{u}{v^2} \\[/tex]
Cross multiply and distribute.
[tex]u(v-x)=v^2(u-x)\\uv-ux=uv^2-xv^2[/tex]
Move all the u to the left side:
[tex]uv-ux-uv^2=-xv^2[/tex]
Factor out a u:
[tex]u(v-x-v^2)=-xv^2[/tex]
Divide:
[tex]u=\frac{-xv^2}{v-x-v^2}=\frac{xv^2}{x+v^2-v}[/tex]
(I factored out a negative in the second term.)