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3 years ago

Justin sane's flag has a perimeter of 28ft. find the dimension of the flag if one length is 2 feet more than twice it's width

1 answer:

4 0

Let
x-------> the length of the flag
y-------> the width of the flag

we know that
the flag has a rectangular shape
perimeter of rectangle=2*[x+y]
perimeter=28 ft
so
28=2*[x+y]----> divide by 2 both sides----> 14=x+y
x=14-y----> equation 1
if one length is 2 feet more than twice it's width
x=2+2y-----> equation 2

equate equation 1 and equation 2
14-y=2+2y
2y+y=14-2
3y=12
y=12/3
y=4 ft
x=14-y----> x=14-4----> x=10 ft

the answer is
the dimension of the flag is
10 ft x 4 ft

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Given tan 0= -15/8 where 270º < 0 < 360° Given tan 0 = Find cos 0

horsena [70]

Answer:=8/17

Step-by-step explanation:

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2 years ago

If a bacteria population starts with 80 bacteria and doubles every three hours, then the number of bacteria after t hours is n =

Thepotemich [5.8K]

Answer:

$f^{-1}(x)=3\frac{ln(\frac{t}{80})}{ln(2)}$

It will take 20.9 hours to reach 10000

Step-by-step explanation:

$f(t)=80(2)^{\frac{t}{3}}$

To find inverse of the function , replace f(x) with y

$y=80(2)^{\frac{t}{3}}$

swap the variables

$t=80(2)^{\frac{y}{3}}$

solve the equation for y

$t=80(2)^{\frac{y}{3}}\\\\\frac{t}{80} =(2)^{\frac{y}{3}}$

take ln on both sides

$ln(\frac{t}{80} )= \frac{y}{3} ln(2)\\\\\frac{ln(\frac{t}{80} }{ln(2)} =\frac{y}{3}\\3\frac{ln(\frac{t}{80} }{ln(2)} =y$

the inverse function is

$f^{-1}(x)=3\frac{ln(\frac{t}{80})}{ln(2)}$

for part b plug in 10000 for t in f^-1(x)

$f^{-1}(10000)=3\frac{ln(\frac{t}{80} }{ln(2)} \\f^{-1}(10000)=3\frac{ln(\frac{10000}{80} }{ln(2)} \\=20.89$

It will take 20.9 hours to reach 10000

7 0

3 years ago

Write a polynomial that represents the area of the square.

Anika [276]

Answer: $x^2+8x+16$

Step-by-step explanation:

It is important to remember that the formula for calculate the area of a square is:

$A=s^2$

Where "s" is the side lenght of the square.

From the figure you can identify that the side lenght of the square can be represented with this expression:

$x+4$

Therefore, the following expression represents the area of the square:

$(x+4)^2$

In order to simplify it, you need to remember that:

$(a\±b)^2=a^2\±2ab+b^2$

Then, you get that the polynomial that represents the area of the given square, is:

$=x^2+2(x)(4)+4^2=x^2+8x+16$

4 0

3 years ago

Can anyone help me????

Mila [183]

Answer:

16, 8, 28, 84, 10, 16, and 96

Step-by-step explanation:

Bc its a parallelogram, the opposite sides are equal. so HI is equal to KJ which is 16. For GH its parallel to GJ so its 8. For the measure of KIH, we know that the measure of IKJ is 28, so the opposite side, it would be 28 for KIH. For the measure angle of KJI, the same applies, the opposite is KHI which is 84. KH is the opposite of JI which is 10. For HJ, you have half the line which we know from GJ is 8, so the other half would also be 8 making HJ 16 in total. For the measure angle of JIH, the opposite is JKH, we know that 28 makes up a small part of that. The angle KHI also distributes into this, 28+84=112. Each triangles angles should equal up to 180 so 180-112= 68 so the other side of 28 is 68. Now the 84 angle isn't completely distributed into the angle but we needed that to figure out the 68 part. So now that we have 28 and 68 we add that together and get 96.

Hope this helped :) sorry if it got a little confusing

4 0

3 years ago

Polygon Q(16, 4), R(8, 16), S(4, 4) was mapped to polygon T(–2, 5), U(–4, 8), V(–5, 5). First by the dilation: (x, y) → (0.25x,

mash [69]

Answer:

D M: (x, y) → (x – 6, y + 4)

Step-by-step explanation:

Polygon Q(16, 4), R(8, 16), S(4, 4) was mapped to polygon T(–2, 5), U(–4, 8), V(–5, 5). First by the dilation: (x, y) → (0.25x, 0.25y).

This means that:

$Q(16,4)\to (0.25\times 16,0.25\times4)=(4,1)$

$R(8,16)\to (0.25\times 8,0.25\times16)=(2,4)$

$S(4,4)\to (0.25\times 4,0.25\times4)=(1,1)$

Now we want to find the translation rule that takes

(4,1) to (-2,5)

(2,4) to (-4,8)

(1,1) to (-5,5)

In each case, 6 is subtracted from the first coordinates and 4 added to the second coordinates.

Therefore, the translation rule is:

(x-6,y+4)

Option D is correct.

3 0

3 years ago