What is the slope of the line that goes through the points (-4,-1) and (-2, 9)?

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

Choose all the expressions that are equal to 5/9 multiply 8

Lesechka [4]

Answer:

4.44

Step-by-step explanation:

the real answer is 4.44444444444

5 0

2 years ago

Winston's team participated in a total of 22 chess matches. Winston

Zepler [3.9K]

Answer:

Peter Jonathan Winston (March 18, 1958 – disappeared January 26, 1978) was an American chess player from New York City

Step-by-step explanation:

In late 1977, Winston attended a FIDE-rated tournament at Hunter College High School in New York City. Despite being one of the highest-rated players in the tournament, Winston lost all nine of his games. A few months later, on January 26, 1978, following further surprising game losses, Peter Winston vanished and was never heard from again. According to some sources, Winston's disappearance occurred when he left his home without money, identification, or luggage during a severe winter storm. Many chess players who were close to or acquainted with Winston claim that the champion chess player's mental health had deteriorated, along with his game performance, in the last few years of his life, and that the decline in his mental health may have led to his disappearance.

3 0

2 years ago

Read 2 more answers

A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, t

Ivanshal [37]

S(t) = 3.82 - 0.2t

Step-by-step explanation:

After 7 weeks, the ice is 2.42 meters thick. The ice loses 0.2 meters of thickness per week; this means on the 7th week, it has lost 7(0.2) = 1.4 meters of thickness.

This means the ice started at 2.42+1.4 = 3.82 meters thick.

Our function will start at the original thickness of the ice, 3.82 meters.

Since the ice is losing thickness, we will subtract; it loses at a rate of 0.2 meters per week (t), which gives us 0.2t. This is subtracted from the original, 3.82 meters, giving us

S(t) = 3.82 - 0.2t

7 0

3 years ago

Read 2 more answers

Pls help need it for tommorow

ANEK [815]

Step-by-step explanation:

$\frac{3}{10 } = .3$

7 0

3 years ago

Read 2 more answers

What is the slope of the line that goes through the points (-4,-1) and (-2, 9)?​

What is the slope of the line that goes through the points (-4,-1) and (-2, 9)?