The length of a rectangle is 5 greater than 3 times the width. The area of the rectangle is 22cm. Find the length and the width. (SHOW STEPS)

Answers

Answer 1

Answer: $x-width\n3x+5-length\n22cm^2-area\ of\ the\ rectangle\n\nx\cdot(3x+5)=22\n3x^2+5x-22=0\n\na=3;\ b=5;\ c=-22\n\n\Delta=b^2-4ac\n\n\Delta=5^2-4\cdot3\cdot(-22)=25+264=289\n\nx_1=(-b-\sqrt\Delta)/(2a);\ x_2=(-b+\sqrt\Delta)/(2a)\n\n\sqrt\Delta=√(289)=17$

$x_1=(-5-17)/(2\cdot3)=(-22)/(6) < 0\n\nx_2=(-5+17)/(2\cdot3)=(12)/(6)=2\n\n3x+5=3\cdot2+5=6+5=11\n\nAnswer:the\ width\ is\ 2cm\ and\ the\ lenght\ is\ 11cm.$

Answer 2

Answer: $a-the\ length\ of\ a\ rectangle,\ \ \ a>0\nb-the\ width\ of\ a\ rectangle,\ \ \ b>0\n\na=3b+5\ \ \ \wedge\ \ \ A=22\ cm^2\n \nA=a\cdot b\ \ \ \Leftrightarrow\ \ \ (3b+5)\cdot b=22\ \ \Leftrightarrow \ \ 3b^2+5b-22=0\n \n\Delta=5^2-4\cdot3\cdot(-22)=25+264=289\ \ \Rightarrow\ \ √(\Delta) =17\n \nb_1= (-5-17)/(2\cdot3) = (-22)/(6)=-3 (2)/(3) <0,\ \ \ \ \ \ \ \ \ b_2= (-5+17)/(2\cdot3) = (12)/(6)=2\n \nb=2\ \ \ \Rightarrow\ \ \ \ a=3 b+5=3\cdot2+5=6+5=11$

$Ans.\ the\ length\ is\ 11\ cm,\ \ the\ width\ is\ 2\ cm.$

Related Questions

Last year, the school library had a total of x books. Over the summer, the library acquired another 42 books and now has a total of 2,402 books. Which equation could be used to find x, the number of books the library had last year?A.2,402 + x = 42 B.x + 42 = 2,402 C.42x = 2,402 D.x - 42 = 2,402
What is bigger?? 2.5 feet or 32 inches?
Please help with this
Yasmine bought 4 bracelets each bracelet cost 3 Numerical Expressions
For questions 1-3, find the function that represents the relationship1.) x - 0| 1| 2| 3 | 4|------------------------- y - 3 | 6| 9| 12| 15|2.) x - 0 | 1 | 2 | 3 | 4 | -----------------------y - 4 | 9| 14| 19| 24|3.)x - 0 | 1 | 2 | 3 | 4 | -----------------------------y - -2| 7 | 16| 25| 34 |

- Trevon invested $1.500 in an account with an interest rate of 4.25%. If he plans to retire in 18 1/2 years, how much total will be in theaccount?

Answers

Answer:

I=PRT is the formula

Step-by-step explanation:

Principal is $1,500. The interest rate is 4.25% and the time is 18.5 years.

That's all i know good luck

If a round pizza is cut into twelve equal pieces through the center, what is the central angle of each piece?

Answers

Answer:

360/12 = ...

Step-by-step explanation:

The central angle is the angle of each slice at the center, and since they are equal pieces they will have the same angles and side lengths and everything.

Now, to solve this you just have to know two things, what is the angle for a full circle, and what happens if you strt cutting it.

So easy, there are 360 degrees in a circle. Now, what if you cut a circle in half, now there are two semicircles, and since you cut it in half the 360 gets cut in half to 180. Same if you cut it into 4 slices then 360/4.

So you want to find 360/12 to find the central angle of each piece.

Final answer:

A round pizza cut into twelve equal pieces will have a central angle of 30 degrees for each slice as the total 360 degrees of the circle are divided by the 12 slices.

Explanation:

The subject of this question is mathematics, specifically geometry as it involves finding the central angle of a sliced pizza. To find the central angle for each slice of pizza, you need to know that a circle has 360 degrees. When the pizza is cut into twelve equal slices, the total degrees (360) will be divided by the number of slices (12).

Here is the step-by-step way to solve it:

Start by writing out the total number of degrees in a circle, which is 360.
Next, divide the total degrees by the number of slices, which in this case is 12.

So the central angle for each slice of the pizza will be: 360 degrees / 12 slices = 30 degrees per slice.