Plz help.........................

A rectangle has a length of 34 inches less than 5 times it’s width. If the area of the rectangle is 867 square inches, find the

pshichka [43]

Length of the rectangle is 51 inches

Solution:

Given that

Length of the rectangle in 34 miles less than 5 times its width

Area of rectangle = 867 square inches

Need to determine length of the rectangle.

Let assume width of the rectangle be represented by variable x.

So 5 times width of the rectangle =5x

34 inches less than 5 times width of the rectangle = 5x – 34

As Length of the rectangle in 34 miles less than 5 times its width

=> Length of the rectangle = 5x – 34

The formula for rectangle is given as:

$\text { area of rectangle }=length \times width$

As given that Area of rectangle = 867 square inches

$\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}$

On solving quadratic equation by using quadratic formula

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

In our case a = 5, b = -34 and c = -867

On substituting value of a, b and c in quadratic formula we get

$\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}$

Since x represents width, it cannot be negative, so x = 17

Length of the rectangle = 5x – 34 = 5(17) – 34 = 51

Hence length of the rectangle is 51 inches

5 0

3 years ago

0.9 of Karen's Science score is equal to 0.75 of her Math score and 0.8 of her Chemistry score. Given that Karen scored 96 marks

DochEvi [55]

You have to formulate equations for this problem.

Let S = Science score

M = Math score

C = Chemistry score

To illustrate the given:

0.9S = 0.75M

0.9S = 0.8C

You are given that Karen’s Math score is 96 marks. You have to substitute the Math score to the first equation.

0.9S = 0.75(96)

0.9S = 72

S = 80

Therefore, Karen’s Science score is 80. Now, you have to substitute the Science score to the second equation.

0.9(80) = 0.8C

0.8C = 72

C = 90

So, Karen’s Chemistry score is 90.

Therefore, the total score of the 3 subjects is 266 (96 + 80 + 90).

5 0

3 years ago

Item 17 The amount of chlorine in a swimming pool varies directly with the volume of water. The pool has 2.5 milligrams of chlor

zvonat [6]

$8000 gal *\frac{ 1 L}{0.264 gal}*\frac{2.5 mg}{1 L} = 75,757 mg$

Rounding to nearest thousand gives 76,000 mg of chlorine

7 0

2 years ago

I need help with number 19

inysia [295]

Let's start by understanding that the graph is a linear line. We have a common difference if 4.5 for every 10x we have more.

We can start by finding the gradient, using rise over run. Let's take (10, 4.5) and (20, 9)

Our rise is 9 - 4.5 = 4.5 and our run is 10. Then, our gradient becomes 4.5/10 = 0.45

Now, we can substitute points using the point-slope form.

y - 4.5 = 0.45(x - 10)
y - 4.5 = 0.45x - 4.5
Hence, our line becomes y = 0.45x and you can verify by substituting in points from the table.

4 0

3 years ago

Multiply and simplify

aleksandr82 [10.1K]

Answer and explanation:

1. 2 × 3/10 = 6/10 = 3/5

2. 8 × 4/8 = 32/8 = 4

3. 9 × 3/9 = 27/9 = 3

4. 12 × 2/11 = 24/11 = 2 2/11

5. 3 × 5/7 = 15/7 = 2 1/7

6. 2 × 3/5 = 6/5 = 1 1/5

7. 11 × 4/8 = 44/8 = 5 4/8 = 5 1/2

8. 10 × 1/4 = 10/4 = 2 2/4 = 2 1/2

9. 5 × 1/4 = 5/4 = 1 1/4

10. 11 × 2/7 = 22/7 = 3 1/7

Hope this helps!

4 0

3 years ago