Answer:
9 possible values of length and breadth.
Step-by-step explanation:
Given that the area of the rectangle is 18cm² . And the lengths of the sides are whole numbers. We need to tell the possible dimensions of the rectangle .
Let :-
[tex]\rm\implies Length = x [/tex]
[tex]\rm\implies Breadth = y [/tex]
We know that :-
[tex]\rm\implies Area = length \times breadth [/tex]
Put in the assumed variables[tex]\rm\implies Area = x y \\\\\rm\implies xy = 18cm^2 [/tex]
Now look out for the possible factors of 18 . That is , ( 1 × 18 ) , ( 2 × 9) , ( 3 × 6 ) , ( 6 × 3 ) , ( 9 × 2 ) , (18 × 1 ) . That is total 9 possible values .
Solve the equation: 12 - x (x - 3) = (6 - x)(x + 2)
Answer: the answer is 0
Why 0?:
Step 1: Simplify both sides of the equation
-x * x= -x²
-x * -3= 3x all together it is ( -x²+3x+12)
for the other side:
-x * x= -x²
6 * x= 6x and x * 2= 2x and 6 * 2= 12
then subtract 6x-4x= 2x so final would be = −x²+4x+12
Step 2: Add x² to both sides.
−x²+3x+12+x²=−x²+4x+12+x² then we are left with 3x+12=4x+12
Step 3: Subtract 4x from both sides.
3x+12−4x=4x+12−4x --> −x+12=12
Step 4: Subtract 12 from both sides.
−x+12−12=12−12
−x=0
Step 5: Divide both sides by -1 or -x
x=0
WILL MARK BRAINLIEST!!
I. Write 2-7i in polar coordinates on the complex plane.
II. Find (1+i)^8 using DeMoivre's theorem.
(r,θ) = (7.28,254.05°) are 2-7i in polar coordinates on the complex plane.
What are polar coordinates?The polar coordinates system is a two-dimensional coordinate system in which each point is determined by distance from the point and an angle from the reference direction.
I. Polar form = (r,θ) = (7.28,254.05°)
z = 2 - i7
r= [tex]\sqrt{ 2^2+-7^2}[/tex]
= √53
= 7.28
θ = tan^-1 (-7/-2)
=3.5
= 74.05
Point lies in the third quadrant
Hence θ = 180+74.05
= 254.05°
Polar form = (r,θ) = (7.28,254.05°)
II. Z=16
De Moivre's theorem states if
z= r(cos(θ) + i sin (θ)) , then
[tex]z^2=r^2(cos(n\theta)+ i sin (n\theta))[/tex]
[tex]r= \sqrt{1^2+1^2}[/tex]
= √2
θ= arc tan (1/1)
= π / 4
z= √2 (cos (π / 4)+i sin (π / 4))
z^8 = (√2 (cos (π / 4)+i sin (π / 4)))^8
= (√2 (cos (8π / 4)+i sin (8π / 4)))^8
=16 (cos(2π) + i sin (2π)
=16
Learn more about polar form;
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please help me i need this asap
Answer:
-2, -1
Step-by-step explanation:
B is the answer for you. Have a good day!
f(b) = 7b^3 +8b and g(b) = b ^2+ b - 10. What is f(b)-g(b)?
Answer:
[tex]{ \bf{f(b) - g(b) : }} \\ { \tt{ = ( {7b}^{3} + 8b) - ( {b}^{2} + b - 10)}} \\ = ( {7b}^{3} - {b}^{2} + 7b + 10)[/tex]
Answer:
[tex]f(b) - g(b) = 7b^3 -b^2 + 7b +10[/tex]
Step-by-step explanation:
[tex]f(b) = 7b^3 + 8b \\\\g(b) = b^2 + b - 10\\\\f(b) - g(b) = (7b^3 + 8b ) - ( b^2 + b -10)[/tex]
[tex]= 7b^3 + 8b - b^2 - b + 10\\\\=7b^3 - b^2 +7b + 10[/tex]
If you know the answer to any of these please Ill mark brainliest.
Answer:
Step-by-step explanation:
1) 2/9 = 185/x
2x = 1665
x = 832.5 or 8.325 meters
2) unit rate is the cost of one unit
i.e a dozen eggs cost $1.20 that
would be 10 cents each
3) 300 tissues for $3.75 vs. 250 for $2.99
one is 1.24 cents per tissue
the other 1.19 ... the 250 package is a better buy
On a coordinate plane, triangle F D E has points (negative 3, 3), (negative 1, negative 1), (negative 3, negative 1). Triangle C B A has points (3, 3), (3, negative 1), (1, negative 1).
What happens to a point when it is reflected over the y-axis?
The coordinates stay the same.
The x-coordinate changes.
The y-coordinate changes.
Both coordinates change.
Answer:
When a point is reflected across the y axis the values of x change. They become negative values of x.
Answer:
(B) The x-coordinate changes.
Step-by-step explanation:
What is the surface area of this right circular cone?
radius=12
height=40
Answer:
2026.75 (units) squared
Step-by-step explanation:
SA of a cone = πr(r+h2+r2)
SA = π(12)(12+√(40^2)+(12^2))
SA = 12π(12+√1744)
Put in calculator and get 2026.75
Verda used a sensor to measure the speed of a moving car at different times. At each time, the sensor measured the speed of the car in both miles per hour and kilometers per hour. The table below shows her results
Answer:
Option A
Step-by-step explanation:
If the speed of a car in miles per hour (m) is proportional to the speed in kilometers per hour (k),
m ∝ k
m = ck
Here, c = Proportionality constant
Therefore, c = [tex]\frac{m}{k}[/tex] should be constant for each value given in the table.
For m = 11 and k = 17.699,
c = [tex]\frac{11}{17.699}[/tex]
c = 0.6215
For m = 26 and k = 41.834,
c = [tex]\frac{26}{41.834}[/tex]
c = 0.6215
For m = 34 and k = 54.706,
c = [tex]\frac{34}{54.706}[/tex]
c = 0.6215
Therefore, c is constant for each value of m and k.
Option A will be the correct option.
Which inverse trig function could I use to solve this problem?
Answer:
Inverse sine
Step-by-step explanation:
Recall the three common trig ratios
Remember SohCahToa
Sine = Opposite over Hypotenuse (SOH)
Cosine = Adjacent over Hypotenuse (CAH)
Tangent = Opposite over Adjacent (TOA)
Now let's look back at the question
It asks us which inverse function would we use to solve for angle Z
Looking at angle Z, we are given it's opposite side length and the hypotenuse ( longest side ).
When dealing with the opposite side length and hypotenuse we use trig function sine.
When trying to find the angle we use inverse so we would use inverse sine to find the measure of angle A
Selecting a few households from New York City and observing whether or not they own stocks when it is known that 28% of all households in New York City own stocks. Is this experiment a binomial experiment? Explain why.
Answer:
Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.
Step-by-step explanation:
We have to take into consideration three things:
For each household, there are only two possible outcomes, either they own stocks, or they do not.
The probability of a household owning stock is independent of any other household, that is, for any household, the probability of someone owning stocks is 28%.
There is a fixed number of trials.
Is this experiment a binomial experiment?
Since for each household there are only two possible outcomes, the a household owning stock is independent of any other household and there is a fixed number of trials, this experiment is a binomial experiment.
how do i answer this?
Step-by-step explanation:
here is the answer. Hope that helps.
Solve the equation and enter the value of x below. 7(x + 9) + 5 = 96
Hello!
[tex]\large\boxed{x = 4}[/tex]
7(x + 9) + 5 = 96
Distribute:
7x + 63 + 5 = 96
Combine like terms:
7x + 68 = 96
Subtract 68 from both sides:
7x = 28
Divide both sides by 7:
x = 4
Answer:
[tex]\fbox{x = 7}[/tex]
Step-by-step explanation:
7(x + 9) + 5 = 96
Solve for x.
7(x + 9 ) + 5 = 96Step 1 :- Distribute 7.
7 × x + 7 × 9 + 5 = 967x + 63 + 5 = 96Step 2:- Add 63 and 5.
7x + 68 = 96Step 3 :- Move constant to the right-hand side and change their sign.
7x = 96 - 68Step 4 :- Subtract 68 from 96.
7x = 28Step 5 :- Divide both side by 7.
[tex]\frac{7x}{7} \\ [/tex] = [tex]\frac{ 28} {7}\\[/tex] x = 4Come get your point with me :)
Answer:
IK≅WY
Step-by-step explanation:
helppp!! I NEED HELP PLEASE
Given:
The table of values for the function f(x).
To find:
The values [tex]f^{-1}(f(3.14))[/tex] and [tex]f(f(-7))[/tex].
Solution:
From the given table, it is clear that the function f(x) is defined as:
[tex]f(x)=\{(-14,11),(-7,-12),(-12,-5),(9,1),(10,-2),(-2,13)\}[/tex]
We know that if (a,b) is in the function f(x), then (b,a) must be in the function [tex]f^{-1}(x)[/tex]. So, the inverse function is defined as:
[tex]f^{-1}(x)=\{(11,-14),(-12,-7),(-5,-12),(1,9),(-2,10),(13,-2)\}[/tex]
And,
[tex]f^{-1}(f(a))=f^{1}(b)[/tex]
[tex]f^{-1}(f(a))=a[/tex] ...(i)
Using (i), we get
[tex]f^{-1}(f(3.14))=3.14[/tex]
Now,
[tex]f(f(-7))=f(-12)[/tex]
[tex]f(f(-7))=5[/tex]
Therefore, the required values are [tex]f^{-1}(f(3.14))=3.14[/tex] and [tex]f(f(-7))=5[/tex].
Find the coordinates of the
midpoint M. *
A(-4,-8) and B(-1,4)
Please provide an explanation
Answer:
M(-5/2, -2)
Step-by-step explanation:
Add the x-coordinates & divide by 2.
Add the y-coordinates and divide by 2.
x-coordinates: -4, -1
(-4 + (-1))/2 = -5/2
y-coordinates: -8, 4
(-8 + 4)/2 = -4/2 = -2
M(-5/2, -2)
A new school has x day students and y boarding students.
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720 000 a term.
Show that this information can be written as x + 2y ≥ 1200.
Given:
The fees for a day student are $600 a term.
The fees for a boarding student are $1200 a term.
The school needs at least $720000 a term.
To show:
That the given information can be written as [tex]x + 2y\geq 1200[/tex].
Solution:
Let x be the number of day students and y be the number of boarding students.
The fees for a day student are [tex]\$600[/tex] a term.
So, the fees for [tex]x[/tex] day students are [tex]\$600x[/tex] a term.
The fees for a boarding student are [tex]\$1200[/tex] a term.
The fees for [tex]y[/tex] boarding student are [tex]\$1200y[/tex] a term.
Total fees for [tex]x[/tex] day students and [tex]y[/tex] boarding student is:
[tex]\text{Total fees}=600x+1200y[/tex]
The school needs at least $720000 a term. It means, total fees must be greater than or equal to $720000.
[tex]600x+1200y\geq 720000[/tex]
[tex]600(x+2y)\geq 720000[/tex]
Divide both sides by 600.
[tex]\dfrac{600(x+2y)}{600}\geq \dfrac{720000}{600}[/tex]
[tex]x+2y\geq 1200[/tex]
Hence proved.
Find the missing angle in the image below. Do not include spaces in your answers ** Can somebody help me fr everybody keep giving me the wrong answer
Answer:
measure of angle V + measure angle W = VUF
Answer:
∠ VUF = 94°
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles
∠ VUF is an exterior angle of the triangle, then
∠ VUF = 71° + 23° = 94°
Simplificar 2/3+1/5+2/4
Answer:
41/30
Step-by-step explanation:
2/3 + 1/5 + 2/4
= 41/30
Solve an equation to find the missing angle
11.
[tex]6x = 30 \\ x = \frac{30}{6} \\ x = 5[/tex]
Missing angle:
[tex]6x \\ = 6 \times 5 \\ = 30[/tex]
_________________________________________
12.
[tex](4 + 5x) + (x + 2) = 180 \\ 6x + 6 = 180 \\ 6x = 180 - 6 \\ 6x = 174 \\ x = \frac{174}{6} \\ x = 29[/tex]
Missing angle 1:
[tex](4 + 5x) \\ = 4 + (5 \times 29) \\ = 4 + 145 \\ = 149[/tex]
Missing angle 2:
[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]
_________________________________________
13.
[tex]5x + (3x + 12) = 180 \\ 8x + 12 = 180 \\ 8x = 180 - 12 \\ 8x = 168 \\ x = \frac{168}{8} \\ x = 21[/tex]
Missing angle 1:
[tex]5x \\ = 5 \times 21 \\ = 105[/tex]
Missing angle 2:
[tex](3x + 12) \\ = (3 \times 21) + 12 \\ = 63 + 12 \\ = 75[/tex]
_________________________________________
14.
[tex]32 + (6x + 4) = 90 \\ 36 + 6x = 90 \\ 6x = 90 - 36 \\ 6x = 54 \\ x = \frac{54}{6} \\ x = 9[/tex]
Missing angle:
[tex](6x + 4) \\ = (6 \times 9) + 4 \\ = 54 + 4 \\ = 58[/tex]
_________________________________________
15.
[tex](2x + 1) + (x + 2) = 90 \\ 3x + 3 = 90 \\ 3x = 90 - 3 \\ 3x = 87 \\ x = \frac{87}{3} \\ x = 29[/tex]
Missing angle 1:
[tex](2x + 1 ) \\ = ( 2 \times 29) + 1 \\ = 58 + 1 \\ = 59[/tex]
Missing angle 2:
[tex]x + 2 \\ = 29 + 2 \\ = 31[/tex]
_________________________________________
16.
[tex](3x + 1) + (4 + 2x) = 90 \\ 5x + 5 = 90 \\ 5x = 90 - 5 \\ 5x = 85 \\ x = \frac{85}{5} \\ x = 17[/tex]
Missing angle 1:
[tex](3x + 1) \\ = (3 \times 17) + 1 \\ = 51 + 1 \\ = 52[/tex]
Missing angle 2:
[tex](4 + 2x) \\ = 4 + (2 \times 17) \\ = 4 + 34 \\ = 38[/tex]
Six liters of paint will cover 50 square meters. How many square meters will nine liters cover?
Answer:
75 m²Step-by-step explanation:
Six liters of paint will cover 50 square meters.
6L ⇒ 50m²
then,
1L ⇒ 50/6 m²
9L ⇒ 50 × [tex]\frac{9}{6}[/tex] m²
⇒ 75 m²
A 4-column table with 4 rows. Column 1 is labeled number of friends with entries 3, 5, 7, 9. Column 2 is labeled Carnival Cost with entries 51.5, 75.5, 99.5, 123.5. Column 3 is labeled Aquarium Cost with entries 43.5, 72.5, 101.5, 130.5. Column 4 is labeled Wave Pool Cost with entries 50.25, 61.25, 85.75, 110.25.
Gale wants to compare the cost of the events.
Aquarium: $14.50 each ticket
Carnival: c = 15.5 + 12f
Wave pool: $16.75 each, but $12.25 each for groups larger than 4
Which of the claims Gale makes is true?
The table represents all possibilities.
The carnival always costs the least.
The Aquarium always costs the most.
(7, 101.5) is an ordered pair used to represent the aquarium cost.
Answer:
D.(7, 101.5) is an ordered pair used to represent the aquarium cost.
Hope it helps :)
Step-by-step explanation:
Answer: it is d - (7, 101.5) is an ordered pair used to represent the aquarium cost
Step-by-step explanation: got it right on edge 2022
A rocket is launched vertically from the ground with an initial velocity of 64 ft/sec determine the rocket’s maximum height, the amount of time it took to reach its maximum height, and the amount of time it was in the air. graph if possible also
Answer:
Step-by-step explanation:
The easiest way to solve this is with calculus, believe it or not. The position function is
[tex]s(t)=-16t^2+64t[/tex]. The first derivative of this is the velocity function:
v(t) = -32t + 64. From physics, we know that at the max height of an object's path, the velocity is equal to 0, so setting this velocity equation equal to 0 and solving for time, will tell us the time it took to get to the max height (which we don't know yet, but we will in a bit):
0 = -32t + 64 and
-64 = -32t so
t = 2 seconds. It takes 2 seconds to reach a max height. Plugging that 2 in for t in the position function will tell you the max height that corresponds to this time:
[tex]s(2)=-16(2)^2+64(2)[/tex] and
s(2) = 64 feet.
So the max height is 64 feet and it is reached at 2 seconds after launching.
Also from physics we know that at halfway through a parabolic path, which is also the max height, we are halfway through time-wise as well. That means that if it takes 2 seconds to reach the max height from the ground, it will take another 2 seconds to fall to the ground.
So the total time the rocket is in the air is 4 seconds: 2 seconds to reach the max height and another 2 to fall back down.
Answer:
Step-by-step explanation:
SOMEONE PLEASE HELP ME WITH THIS PROBLEM!!!!
9514 1404 393
Answer:
20.0 square units
Step-by-step explanation:
There are many ways the area can be computed here. Perhaps the intended one is to find the length of the third side, then use the usual triangle area formula.
b = √(c² -a²) = √(9² -7²) = √32 ≈ 5.7
Then the area is ...
A = 1/2bh = 1/2(5.7)(7) ≈ 20.0
The area is approximately 20.0 square units.
_____
Additional comment
It is highly unusual to make use of rounded intermediate results. That is a guarantee that the final answer will have more error than necessary. Ordinarily, you would never do that.
An alternate solution might be ...
angle = arccos(7/9) ≈ 38.9°
area = 1/2(7)(9)sin(38.9°) ≈ 19.8 . . . . square units (assuming the sine value is not rounded to 0.6)
Plss Answer!!!!!!!!!
Answer:
Ecosystem: Trees
Ways to protect are as follows:-
Control over Forest FireDon't waste paper. Plant a treeThe dimensions of the rectangular pool shown below are 60 yards by 30
yards. A fence will be built around the outside of the deck. The ratio of the
dimensions of the pool to the dimensions of the fence is .. How many yards
of fence should be purchased to enclose the deck?
Answer:
ok so we have to find the perimiter so
60+60=120
30+30=60
120+60=180
Hope This Helps!!!
Describe how you would simplify rootof300. Be thorough and clear in your explanation.
Marcella incarica Dora di aiutarla a suddividere 35 perle tra le sue tre figlie. Alla figlia maggiore vuole regalare la metà, alla mediana la terza parte e alla minore la nona parte. Inoltre Marcella vuole dare una perla a Dora come ricompensa. Quante perle riceverà ciascuna figlia?
Answer:
La hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.
Step-by-step explanation:
Dado que Marcella le pide a Dora que la ayude a dividir 35 perlas entre sus tres hijas, y quiere darle la mitad a la hija mayor, la tercera parte a la del medio y la novena a la menor y, además, Marcella quiere darle una perla a Dora como recompensa, para determinar cuántas perlas recibirá cada hija se debe realizar el siguiente cálculo:
35 / 2 = Mayor = 17.5 perlas
35 / 3 = Medio = 11.66 perlas
35 / 9 = Menor = 3.88 perlas
Así, la hija mayor recibirá 17.5 perlas, la hija del medio recibirá 11.66 perlas, y la hija menor recibirá 3.88 perlas.
The price of a pair of trainers was £85 The price was reduced to £47 Work out the percentage change in price.
Answer:
The trainers are 44.71% off the original price i think.
Step-by-step explanation:
Record the length of these
segments
PC =
PC' =
units
units
There's all the lengths so you don't have to search them all up
Can someone help me solving this problem? I'm confuse so I want help..
question :
a) The length and breadth of a rectangular room are 10m and 8m respectively. How many pieces of carpet 5m long and 2m wide are required to cover it's floor?
Please help me solving this problem !
Answer: 8
Step-by-step explanation: