Answer:
Length of the rectangle = 18 mWidth of the rectangle = 7 mStep-by-step explanation:
Given:
Area of the Rectangle = 126 m²Length of the rectangle is 4 more than 2 times its width.To Find:
Length and widthSolution:
Let's assume :
Width of the rectangle = xLength of the recangle = 2x + 4We know that,
[tex]\: \: \dashrightarrow\sf \: \: \: Length \times Width = Area_{(Rectangle)} \\ \\ [/tex]
On Substituting the required values, we get:
[tex] \\ \: \: \dashrightarrow\sf \: \: \:(2x+ 4)(x) = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x - 126 =0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2( {x}^{2} + 2x - 63) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} + 2x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} - 7x + 9x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:x(x - 7) + 9(x - 7) \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:(x - 7)(x + 9) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: \purple {x = 7 \: or \: - 9} \\ \\ [/tex]
Length of the side of the rectangle can't be negative. So, x = 7
Hence,
Width of the rectangle = x = 7 mLength of the rectangle = 2x + 4 = 2(7) + 4 = 18 mAnswer:
length = 18 m
width = 7 m
Step-by-step explanation:
Finding the length and width of rectangleLet the width of the rectangle = w m
Length = ( 2w + 4) m
Area of rectangle = 126 square meters
length * width = 126
(2w + 4) * w = 126
2w² + 4w = 126
2w² + 4w - 126 = 0
Divide the entire equation by 2
w² + 2w - 63 = 0
Sum = 2
Product = -63
Factors = 9 , (-7) { 9 +(-7) = 2 & 9*(-7) = -63}
w² + 9w - 7w - 63 = 0 {rewrite the middle term using the factors}
w( w + 9) - 7(w + 9) =0
(w +9)(w - 7) = 0
{Ignore w +9 = 0, as measurement will not come in negative}
w - 7 = 0
w = 7
length = 2w + 4
= 2*7 + 4
= 14 + 4
= 18
length = 18 m width = 7 m9x^8 y^2 - 6x^3 y^4 / 3xy
simplified
Answer:
None of the choices are correct
Stefofp-by-step explanation:
Simplify the following:
(-6 x^3 y^4 + 9 x^8 y^2)/(3 x y)
Factor 3 x^3 y^2 out of -6 x^3 y^4 + 9 x^8 y^2:
(3 x^3 y^2 (-2 y^2 + 3 x^5))/(3 x y)
(3 x^3 y^2 (-2 y^2 + 3 x^5))/(3 x y) = 3/3×(x^3 y^2 (-2 y^2 + 3 x^5))/(x y) = (x^3 y^2 (-2 y^2 + 3 x^5))/(x y):
(x^3 y^2 (-2 y^2 + 3 x^5))/(x y)
Combine powers. (x^3 y^2 (-2 y^2 + 3 x^5))/(x y) = x^(3 - 1) y^(2 - 1) (-2 y^2 + 3 x^5):
x^(3 - 1) y^(2 - 1) (-2 y^2 + 3 x^5)
3 - 1 = 2:
x^2 y^(2 - 1) (-2 y^2 + 3 x^5)
2 - 1 = 1:
Answer: x^2 y (-2 y^2 + 3 x^5)
a circle has a diameter of 8 m. what is the circumference? use 3.14 for pie
A shoreline is eroding at a rate of 1/3 foot per 2 months how many feet are eroding this year
Answer:
2 feet
Step-by-step explanation:
The shoreline is eroding at 1/3 foot per 2 months. There are 12 months in a year so you multiply 1/3 x 6 and you get 2.
Really tired and need help 100 points
Answer:
purple
Step-by-step explanation:
Write a recursive formula for the sequence 7, 4, 1, -2, -5, .... Then find the next term.
A. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = -8[/tex]; 7
B. [tex]a_{n} = a_{n - 1} - 3[/tex], where [tex]a_{1} = 7[/tex]; -8
C. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = -3[/tex]; 22
D. [tex]a_{n} = a_{n - 1} + 3[/tex], where [tex]a_{1} = 7[/tex]; -8
Answer:
option B
Explanation:
Recursive Formula: aₙ = aₙ₋₁ + d
Given Sequence: 7, 4, 1, -2, -5,....
Identify the common difference:
second term - first term
4 - 7 = -3 or 1 - 4 = -3 or -2 - 1 = -3
So formula:
[tex]\sf a_n = a_{n-1}-3[/tex], where [tex]\sf a_1 = 7[/tex]
Find next term:
[tex]\sf a_6 = a_{6-1}-3 = -5-3 = -8[/tex]
find x
K (7x + 217
47
M
Answer:
x=16
Step-by-step explanation:
The opposite angles will always be supplementary
<K + < M = 180
47+ 7x+21 = 180
Combine like terms
7x+68 = 180
Subtract 68
7x = 180-68
7x = 112
Divide by 7
7x/7 = 116/7
x =16
A storage tank is in the shape of a cylinder with a hemisphere on the top. The highest point on the inside of the storage tank is 13 meters above the floor of the storage tank, and the diameter inside the cylinder is 8 meters. Determine and state, to the nearest cubic meter, the total volume inside the storage tank.
The volume of the tank of water is 653.12 cubic meters.
How to get the volume?
For a cylinder of height H and diameter D, the total volume is given by:
[tex]V = 3.14*(D/2)^2*H[/tex]
In this case, we know that:
D = 8m
H = 13m
Replacing that in the above equation:
[tex]V = 3.14*(8m/2)^2*13m = 653.12 m^3[/tex]
So the volume of the tank of water is 653.12 cubic meters.
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X+8
What is the solution of 5x=T > 0?
XS-8 Or X2 }
L
X <-8 or X › 5
-8≤x<5
-8
PLEASE HELP
Answer:
but good luck with that man
30% of 210 is what number?
multiply 30% by 210
210 x 0.30 = 63
answer: 63
Given →n = (1, 2) and →m = (6, 12) , Find the magnitude of 1/2 →m - 2→n
A.√3
B.√5
C.3
D.5
Answer:
b
Step-by-step explanation:
................................
what is the complete factorization of the polynomial below?
x^3 - 4x^2 + x - 4
Answer:
[tex](x-4)(x^2+1)[/tex]
Step-by-step explanation:
[tex]x^3-4x^2+x-4[/tex][tex]=x^2(x-4)+1(x-4)[/tex][tex]=(x-4)(x^2+1)[/tex]please help due soon
Answer:
$4742.10
Step-by-step explanation:
Exponential depreciation formula :-
, where y is the value of good after t years , r is rate of depreciation and A is the initial value.
Given : A= $20800 ; r=10.75%=0.1075
The equation models this situation:
Then, the value of car after t=13 years :-
Hence, the value of car after 13 years = $4742.10
The velocity of v in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop h in feet and the velocity v° in feet per second of the coaster at the top of the hill by the formula v°=[tex]\sqrt{v^{2}-64h[/tex] . What velocity must a coaster have at the top of a 50-foot hill to achieve a velocity of 57 feet per second.
The velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.
What is Velocity?Velocity is the rate of change of its position with respect to time.
[tex]V = \dfrac{dy}{dt}[/tex]
Given the velocity(v) in feet per second of a roller coaster at the bottom of a hill is related to the vertical drop(h) in feet and the velocity(v°) in feet per second of the coaster at the top of the hill by the formula v°=√(v²-64h).
Therefore, the velocity of the coaster at the top should be,
[tex]v^o=\sqrt{(v^2-64h)}\\\\v^o=\sqrt{[57^2-(64\times 50)]}\\\\v^o=\sqrt{49}\\\\v^o = 7\rm\ feet/second[/tex]
Hence, the velocity that the coaster must have at the top of a 50-foot hill to achieve a velocity of 57 feet per second is 7 feet/second.
Learn more about Velocity:
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A job cost the customer $28,244 66. If 41% of this job was labor, what was the actual labor cost to the customer?
Answer:
$11,580.31
Step-by-step explanation:
turn 41% into a decimal:
0.41
$28,244.66 * 0.41
11,580.31
mark brainliest pls
Jarrett Webster leased a sports car for $299.50 per month for
60 months. He paid a deposit of $250.00, a title fee of $95.00,
and a license fee of $220.00. What is the total least cost?
Answer: 15.095$
Step-by-step explanation:
solve this system using the Elimination method
-4x - 2y =-18 x + 3y = 8
Answer:
Elimination:
-4x - 2y = -18 -4x - 2y = -18
x + 3y = 8 | ×4 ------> 4x + 12y = 32 +
10y = 14
y = 1,4
x + 3y = 8
x + 3(1,4) = 8
x + 4,2 = 8
x = 3,8
PLEASE HELP, URGENT!!!!
Find M
Answer:
Step-by-step explanation:
cos^-1(√(111))/2√(37) = 30°
m<C = 30°
Find the value of x. Geometry Magic 20 set 3
Answer:
The value of x is 64.
Step-by-step explanation:
The base angles of an isoceles triangle are congruent.
[tex]x + 58 + 58 = 180[/tex]
[tex]x + 116 = 180[/tex]
[tex]x = 64[/tex]
50 points
Use the table to identify values of p and q that can be used to facto
x2 + x - 12 as (x + p)(x + 4).
NEED HELP ASAP
Answer:
-3, 4
Explanation:
x² + x - 12
factorize
x² + 4x -3x - 12
take out common terms
x(x + 4) -3(x + 4)
collect into groups
(x-3)(x+4)
p = -3, q = 4
Answer:
C. -3 and 4
Step-by-step explanation:
In order to factor a quadratic equation in the form [tex]ax^2+bx+c[/tex]
we need to find a pair of numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
Therefore, in order to factor [tex]x^2+x-12[/tex] we need to find a pair of numbers that multiply to -12 and sum to 1.
The only pair of numbers in the table that sum to 1 are:
p = -3 and q = 4
Therefore, the solution is option C.
Four athletes from the Republic of Korea competed in a team wheelchair race at
the Paralympic Games. The team finished the race in a total of 190.729 seconds.
First team member: 46.685 seconds
Second team member: 48.869 seconds
Third team member: 49.33 seconds
How it many seconds did it take the fourth team member to complete his part of
the race?
The number of seconds taken by the fourth team to complete his part of the race is 45.116 seconds.
What is subtraction?It simply means to deduct something from the object or number of group, place, etc. Subtraction means to take away from the group or a number of objects.
Four athletes from the Republic of Korea competed in a team wheelchair race at the Paralympic Games.
The team finished the race in a total of 190.729 seconds.
First team member: 46.685 seconds
Second team member: 48.869 seconds
Third team member: 49.33 seconds
Then the number of the seconds is taken by the fourth team will be
Let x be the number of the second taken by the fourth team.
Then we have
x + 46.685 + 48.869 + 49.33 = 190.729
x + 144.884 = 190.729
x = 45.116
More about the subtraction link is given below.
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Answer:
x= 45.845
Step-by-step explanation:
190.729-144.884
in the triangle below CFED is a rectangle. If the measure of CFD= 4x and the measure of DFE is 5x, find the value of x
1. Let u (1.-3,2), v= (-1.4.2). Then find b) a unit vector in the same direction of 4v.
4v points in the same direction as v, so all you need to do is normalize v.
Simply multiply it by the reciprocal of its magnitude:
[tex]v = (-1, 4, 2) \implies \|v\| = \sqrt{(-1)^2 + 4^2 + 2^2} = \sqrt{21}[/tex]
[tex]\implies \dfrac{v}{\|v\|} = \dfrac{(-1,4,2)}{\sqrt{21}} = \left(-\dfrac1{\sqrt{21}}, \dfrac4{\sqrt{21}}, \dfrac2{\sqrt{21}}\right)[/tex]
If you invest $1600 at 5% for 3 years, how much simple interest is earned? ***Look at your formula chart for the interest formula!!***
FOR 25 POINTS
Answer:
$240
Step-by-step explanation:
[tex]1600 \times .05 \times 3 = 240[/tex]
Find the total amount
$1580 is compounded daily at a rate of 10% for 7 years. Let 1 year = 365 days.
Answer:
$3181.42
Step-by-step explanation:
The balance of an account earning compound interest is given by the formula ...
A = P(1 +r/n)^(nt)
where P is the principal invested at annual rate r for t years, compounded n times per year.
__
You have P=1580, r=0.10, n=365, t=7, so the balance is ...
A = $1580(1 +0.10/365)^(365×7) ≈ $3181.42
_____
Additional comment
Your graphing calculator may have a financial function that will calculate this for you.
Let h = number of hours to bike 165 mi. Let m = number of miles biked in 7 hr. Which proportion can be used to determine the value of h?
Answer:
[tex] \frac{m}{h} = \frac{165}{7} [/tex]
<~~• ¥ Pls HELP me!! ¥ • ~~>
Answer:
A = 16
Step-by-step explanation:
Formula b*h/2
b =8
h =4
so
A= 8*4/2
A = 16
If A is a prime factor of 36, and B is a prime factor of 15, what is the greatest possible difference between A and B?
Answer:
3
Step-by-step explanation:
Prime factorization
36 = 3 * 3 *2 * 2
15 = 3 * 5 The biggest difference is 5 -2 = 3
PLEASE ANSWER ALOT OF POINTS
The graph shows two lines, A and B.
Part A: How many solutions does the pair of equations or lines A and B have? Explain your answer.
Part B: What is the solution to the equations of lines A and B? Explain your answer.
Answer:
Part A 1 solution
Part B 1,4
Answer:
Part A : It has one solution because the lines intersect at one point
Part B : The solution is the points where the lines intersect
Which is (3,4)
Two events can have a strong, weak, or no correlation.
True or false
can you please help me I pay you £50