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Kisachek [45]
3 years ago
14

The length of a rectangle is represented by (2x2−5x+5)cm and the width is represented by (x2+4x−3)cm. What is the representation

of the perimeter
Mathematics
1 answer:
Katarina [22]3 years ago
7 0

Answer: 6x^2-2x+4

Step-by-step explanation:

Given

The length of a rectangle is given by

l=2x^2-5x+5

and the breadth is given by

w=x^2+4x-3

Perimeter is the sum of the sides of rectangle

\therefore \text{Perimeter P= }2(2x^2-5x+5+x^2+4x-3)\\\Rightarrow P=2(3x^2-5x+4x+5-3)\\\Rightarrow P=2(3x^2-x+2)\\\Rightarrow P=6x^2-2x+4

Thus, the perimeter is given by 6x^2-2x+4.

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1. In a pet store, there are 6 dogs and 10 cats. What is the ratio of cats to dogs as
Alinara [238K]

Answer:

1.66

Step-by-step explanation:

For every cat there are 1.66 cats.

It sound weird, lol. That’s why we’re not suppose to use in-dividable things in math.

XD

7 0
3 years ago
You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along
sukhopar [10]

Answer:

The lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

Step-by-step explanation:

This is a problem of optimization.

We have to minimize the time it takes for the lifeguard to reach the child.

The time can be calculated by dividing the distance by the speed for each section.

The distance in the shore and in the water depends on when the lifeguard gets in the water. We use the variable x to model this, as seen in the picture attached.

Then, the distance in the shore is d_b=x and the distance swimming can be calculated using the Pithagorean theorem:

d_s^2=(60-x)^2+40^2=60^2-120x+x^2+40^2=x^2-120x+5200\\\\d_s=\sqrt{x^2-120x+5200}

Then, the time (speed divided by distance) is:

t=d_b/v_b+d_s/v_s\\\\t=x/4+\sqrt{x^2-120x+5200}/1.1

To optimize this function we have to derive and equal to zero:

\dfrac{dt}{dx}=\dfrac{1}{4}+\dfrac{1}{1.1}(\dfrac{1}{2})\dfrac{2x-120}{\sqrt{x^2-120x+5200}} \\\\\\\dfrac{dt}{dx}=\dfrac{1}{4} +\dfrac{1}{1.1} \dfrac{x-60}{\sqrt{x^2-120x+5200}} =0\\\\\\  \dfrac{x-60}{\sqrt{x^2-120x+5200}} =\dfrac{1.1}{4}=\dfrac{2}{7}\\\\\\ x-60=\dfrac{2}{7}\sqrt{x^2-120x+5200}\\\\\\(x-60)^2=\dfrac{2^2}{7^2}(x^2-120x+5200)\\\\\\(x-60)^2=\dfrac{4}{49}[(x-60)^2+40^2]\\\\\\(1-4/49)(x-60)^2=4*40^2/49=6400/49\\\\(45/49)(x-60)^2=6400/49\\\\45(x-60)^2=6400\\\\

x

As d_b=x, the lifeguard should run across the shore a distance of 48.074 m before jumpng into the water in order to minimize the time to reach the child.

7 0
3 years ago
Plz help!!! Will mark brainliest if answer is correct. <br> FIND M
lesya [120]
Both angles are complementary and add up to 90 degrees. If you do that in an equation it should be like this:

2x + 14 + x + 7 = 90

Simplify:

3x + 21 = 90
3x = 69
X = 23

Now just plug that into angle CBD and you get:

2(23) + 14 = y
46 + 14 = y
60 = y

Angle CBD is 60 degrees
3 0
3 years ago
Read 2 more answers
A jar at the fishing shop holds 72 worms. A cup holds 8 worms. How many times
Anettt [7]

Answer:

9 times. 72/8=t or 72=8t.

Explanation:

I'm afraid the answer choices are slightly mixed up, but acceptable answers would probably include 72/8=t or 72=8t. Simply put the two numbers into a fraction (72/8) to get how many times larger or smaller the thing is. In this case, it would be 9 times as many worms.

5 0
3 years ago
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Which ordered pairs make both inequalities true?
Arlecino [84]

Answer:

(0,-2) and (1, 1)

Step-by-step explanation:

7 0
3 years ago
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