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3 years ago

The length of a rectangle is 3 feet more than twice the width. The perimeter is 128 feet. Find the length and width.

1 answer:

7 0

We are going to consider a rectangle with length called "a" and width "b" Then we know that perimeter is the sum of both sides 2*a + 2*b = 128 And also the following equation given by the question: a = 2*b + 3 So solving the first equation: 2*(2*b+3) + 2*b = 128 4*b+6+2*b=128 6*b = 122 b = 122/6 = 61/3 Then a=2*122/6+3 = 244/6+3 = 262/6 = 131/3 Solution: Length = 131/3 Width = 61/3

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A reflecting pool is shaped like a right triangle with one leg along the wall of a building. the hypotenuse is 9 feet longer tha

morpeh [17]

Answer:

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

Step-by-step explanation:

In the question, the shape of the pool is right triangle.

Let the leg side along the wall to be the x ft

Let the other leg side to be 7+x ft

Let the longest side/hypotenuse to be x+9 ft

Apply the Pythagorean relationship where the sum of squares of the legs equals the square of the hypotenuse

This means;

$x^2 +(x+7)^2=(x+9)^2\\\\$

Expand the terms in brackets

$x^2+(x+7)^2=(x+9)^2\\\\\\x^2+x^2+14x+49=x^2+18x+81$

collect like terms

$x^2+x^2-x^2=18x-14x+81-49\\\\\\x^2=4x+32\\\\\\x^2-4x-32=0$

solve for x in the quadratic equation by factorization

$x^2-4x-32=0\\\\\\x^2-8x+4x-32=0\\\\\\x(x-8)+4(x-8)=0\\\\\\(x+4)(x-8)=0\\\\\\x+4=0,x=-4\\\\x-8=0,x=8$

Taking the positive value of x;

x=8ft

Finding the lengths

Leg side along the wall = x ft = 8 ft

The other leg side = 7+x ft = 7+8=15 ft

The Hypotenuse =9+x ft = 9+8 = 17 ft

6 0

3 years ago

Discrete Math

andrezito [222]

Answer:

Part c: Contained within the explanation

Part b: gcd(1200,560)=80

Part a: q=-6 r=1

Step-by-step explanation:

I will start with c and work my way up:

Part c:

Proof:

We want to shoe that bL=a+c for some integer L given:

bM=a for some integer M and bK=c for some integer K.

If a=bM and c=bK,

then a+c=bM+bK.

a+c=bM+bK

a+c=b(M+K) by factoring using distributive property

Now we have what we wanted to prove since integers are closed under addition. M+K is an integer since M and K are integers.

So L=M+K in bL=a+c.

We have shown b|(a+c) given b|a and b|c.

Part b:

We are going to use Euclidean's Algorithm.

Start with bigger number and see how much smaller number goes into it:

1200=2(560)+80

560=80(7)

This implies the remainder before the remainder is 0 is the greatest common factor of 1200 and 560. So the greatest common factor of 1200 and 560 is 80.

Part a:

Find q and r such that:

-65=q(11)+r

We want to find q and r such that they satisfy the division algorithm.

r is suppose to be a positive integer less than 11.

So q=-6 gives:

-65=(-6)(11)+r

-65=-66+r

So r=1 since r=-65+66.

So q=-6 while r=1.

3 0

3 years ago

1) Lynda runs the 400 meter for her school's track team. She beat her best time by 3.6

Dmitriy789 [7]

Answer:

52.9

Step-by-step explanation:

49.3+3.6=52.9 seconds

5 0

3 years ago

What number is 15% of 325?

Rudiy27

Answer:

48.75

Step-by-step explanation:

$325 \times .15$

$= 48.75$

48 3/4

6 0

3 years ago

PLEASE HELP!!! ILL GIVE BRAINLIEST!

inn [45]

Answer: Last Option (Red In Colour)

Reason: Since Point Slope Form is y -y1 = m(x-x1), We just plug in the numbers. Four will go into the x1 spot, and Zero will go into the y1 spot, and 1/2 in the m spot since it's the slope. So, after plugging everything in, the equation is y - 0 = 1/2 ( x- 4)

<em>I hope this helps, and Happy Holidays! :)</em>

5 0

3 years ago