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3 years ago

The length of a rectangle is three times its width. The perimeter is 64 feet. What are the dimensions of the rectangle?

Mathematics

1 answer:

sergejj [24]3 years ago

7 0

Answer:

8 and 24

Step-by-step explanation:

let width be X

then length will be 3x

2(3x+X)=64

3x+X=32

4x=32

X=8

then 3x=24

You might be interested in

how long will it take an investment of $300 to triple, if the interest rate is 3.5% per year, compounded continuously?

Rashid [163]

Answer:

31 years to triple the investment

Step-by-step explanation:

Initial investment = 300

Triple amount that is final amount = 300*3= 900

rate of interest = 3.5 % = 0.035

we need to find out number of years (t)

for compounded continuously we use formula

$A= Pe^{rt}$

A is the final amount

P is the initial amount

r is the rate of interest

t is the number of years

$900 = 300e^{0.035*t}$

Divide both sides by 300

$3 =e^{0.035*t}$

take 'ln' on both sides

$ln(3) =ln(e^{0.035*t})$

ln(3) = 0.035t ln(e)

ln(e)= 1

$\frac{ln(3)}{0.035} = t$

t= 31.3889

Round to nearest whole number

t= 31 years

4 0

3 years ago

Find three consecutive odd integers such that three times the square of the first integer is twelve more than the product of the

7nadin3 [17]

Consecutive odd integers are 2 apart
they are
n,n+2,n+4

3(n²)=12+(n+2)(n+4)
expand
3n²=12+n²+6n+8
3n²=n²+6n+20
minus n² both sides
2n²=6n+20
divide bot sides by 2
n²=3n+10
minus 3n+10 both sides
n²-3n-10=0
factor
(n-5)(n+2)=0
n-5=0
n=5

n+2=0
n=-2
has to be odd, so no

n=5
n+2=7
n+4=9

the integers are 5,7,9

4 0

3 years ago

Plz help ASAP please please

jeyben [28]

It should be figure B

Hope it helps :)

5 0

4 years ago

Help solving this math problem

ladessa [460]

Formula for Mid Point between two points= (x1 + x2)/2, (y1 + y2)/2,

Mid points: SU= (-3,2), TU= (1,0), and ST= (1,2).

Step-by-step explanation:

U = (-3,0)

S= (-3,4)

T= (5,0)

Mid Point Formula= (x1 + x2)/2, (y1 + y2)/2.

With points S(-3,4) and U(-3,0),

Mid point of SU = (-3+(-3))/2, (0+4)/2.

⇒Mid point of SU = (-6/2,4/2).

∴Mid point of SU= (-3,2).

With points T(5,0) and U(-3,0),

Mid point of TU = (5+(-3))/2, (0+0)/2.

⇒Mid point of TU = (2/2,0).

∴Mid point of TU= (1,0)

With points S(-3,4) and T(5,0),

Mid point of ST = (-3+5)/2, (4+0)/2.

⇒Mid point of ST =(2/2, 4/2).

∴Mid point of ST= (1,2)

8 0

4 years ago

Plz I can’t do this

zheka24 [161]

Answer: f(g(x))=x and g(f(x)) = x

f⁻¹(x) = g(x) YES ARE INVERSES

f⁻¹(x) ≠ g(x) NOT INVERSES

Step-by-step explanation:

Inverse is when you swap the x's and y's and then solve for y.

If f⁻¹(x) = g(x), then they are inverses of each other.

Similarly, if g⁻¹(x) = f(x), they are inverses of each other.

NOTE: You can also use composition to determine if they are inverses --> If (fog)(x) = x, then they are inverses of each other.

$f(x) = \dfrac{1}{x+4}-9\\\\\\\text{Swap the x's and y's. NOTE: f(x) is y}\\x=\dfrac{1}{y+4}-9\\\\\\\text{Add 9 to both sides}\\x+9=\dfrac{1}{y+4}\\\\\\\text{Flip the fractions}\\\dfrac{1}{x+9}=y+4\\\\\\\text{Subtract 4 from both sides}\\\dfrac{1}{x+9}-4=y\\\\\\\boxed{f^{-1}(x)=g(x)\text{ so f(x) and g(x) are inverses of each other}}$

$f(x) = 3x+27\\\\\\\text{Swap the x's and y's NOTE f(x) is y}\\x=3y+27\\\\\\\text{Subtract 27 from both sides}\\x-27=3y\\\\\\\text{Divide everything by 3}\\\dfrac{1}{3}x-\dfrac{27}{3}=y\\\\\\\text{Simplify}\\\dfrac{1}{3}x-9=y\\\\\\\boxed{f^{-1}(x)\neq g(x)\text{ so f(x) and g(x) are NOT inverses of each other}}$

7 0

3 years ago