Keith is racing his little sister Pattie and has given her a 15 foot head start. She runs 5ft/sec and he is chasing at 8ft/sec. For how long can Pattie stay ahead of Keith? Write and solve an inequality and show your work. Plz Help!

Answers

Answer 1

Answer: Pattie runs at 5 ft/sec
She has got a head start of 15 feet.
So after 1 second, Pattie runs = (5+15) ft
      = 20 ft
After 2 second Pattie runs = (20+5)ft
   = 25 ft
After 3 second Pattie runs = (25+5) ft
   = 30 ft
After 4 seconds Pattie runs = (30+5) ft
   = 35 ft
After 5 seconds Pattie runs = (35+5) ft
   = 40 ft
After 6 seconds Pattie runs = (40+5) ft
   = 45 ft
Now Keith runs at 8 ft/sec
After 1 second Keith runs = 8 ft
After 2 second Keith runs = (8+8) ft
   = 16 ft
After 3 second Keith runs = (16+8) ft
   = 24 ft
After 4 second Keith runs = (24+8) ft
      = 32 ft
After 5 second Keith runs = (32+8) ft
   = 40 ft
After 6 second Keith runs = (40+8) ft
   = 48 ft
So Pattie will stay ahead of Keith upto 4 seconds. In the 5th second Pattie and Keith will be level and in the 6th second Pattie will be overtaken by Keith.

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A dartboard consists of two concentric circles. The probability of hitting the inner circle is64%. If the outer circle has a diameter of 20 inches, what is the radius of the inner circle?

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8 inches
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Answers

Given:
Diameter of outer circle = 20 inches.

We need to find the Area of the outer circle to get the radius of the inner circle.

Area = πr²

Outer circle Area = 3.14 * (10in)² = 314 in²

314 in² * 64% probability = 200.96 in² Area of the inner circle.

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What can be concluded if angle 1 =angle7

Answers

From the information given in the question,
the only possible conclusion is:

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When a pair of blue jeans is made the leftover denim scraps can be recycled to make stationerypencils and more denim One pound of denim is left after making every five pairs of jeans. How
many pounds of denim would be left from 250 pairs of jeans

Answers

Answer:

50 pounds

Step-by-step explanation:

One positive integer is 1 greater than 3 times another positive integer. If the product of the two integers is 154, then what is the sum of the two integers?

Answers

Answer:

Step-by-step explanation:

Let the smaller integer be x.

The other integer is 1 greater than 3 times x, or 3x + 1.

The product is 154.

x(3x + 1) = 154

3x^2 + x - 154 = 0

157 = 2 * 7 * 11

14 * 11 = 154

22 * 7 = 154

(3x + 22)(x - 7) = 0

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3x = -22 or x = 7

x = -22/3 or x = 7

-22/3 is not a positive integer, so we discard that solution.

The smaller integer is 7.

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Step-by-step explanation:

Solve each equation
x^2+6x+9=1

Answers

x= -4 and x=-2

x^2+6x+9=1
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x+3=-1 / x-3=1
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x=-2

Answer:x=-2,-4

Step-by-step explanation:

Rewrite without rational exponents, and simplify, if possible.. (x^4y^4) ^1/3

Answers

$\left(x^4y^4\right)^(1)/(3)=x^{4\cdot(1)/(3)}y^{4\cdot(1)/(3)}=x^(4)/(3)y^(4)/(3)=x^{1(1)/(3)}y^{1(1)/(3)}=x^{1+(1)/(3)}y^{1+(1)/(3)}=x^1x^(1)/(3)y^1y^(1)/(3)\n\n=x\sqrt[3]{x}\cdot y\sqrt[3]y=xy\sqrt[3]{xy}$

That would become (XY)^4/3 . The exponent is still rational. Sorry.

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