All categories

3 years ago

Write an expression for the perimeter of this pentagon. If the perimeter is 157 units, find x.

Mathematics

1 answer:

Nat2105 [25]3 years ago

4 0

This the only option to find x since doing the other way like 3x + 2 = 3x + 2 gives it an infinite solution.

4x - 1 = 3x + 2

-3x -3x

1x - 1 = 2

+1 +1

1x = 3

--- ----

1 1

x = 3

Check:

4(3) - 1 = 3(3) + 2

12 - 1 = 9 + 2

11 = 11

You might be interested in

Match the steps to find the equation of the parabola with focus (-1, 2) and directrix x = 5.

Archy [21]

Answer:

The matched options to the given problem is below:

Step1: Choose a point on the parabola

Step2: Find the distance from the focus to the point on the parabola.

Step3: Use (x, y).

Find the distance from the point on the parabola to the directrix.

Step4: Set the distance from focus to the point equal to the distance from directrix to the point.

Step5: Square both sides and simplify.

Step6: Write the equation of the parabola.

Step by step Explanation:

Given that the focus (-1,2) and directrix x=5

To find the equation of the parabola:

By using focus directrix property of parabola

Let S be a point and d be line

focus (-1,2) and directrix x=5 respectively

If P is any point on the parabola then p is equidistants from S and d

Focus S=(-1,2), d:x-5=0

Step1: Let P(x,y) be any point on parabola

Step2: Therefore the $d=\sqrt{(x+1)^2+(y-2)^2}\hfill (1)$

Step3: The perpendicular distance from p to d is

$\frac{|x-5|}{\sqrt{(-1)^2+2^2}}$

$=\frac{|x-5|}{\sqrt{5}}\hfill (2)$

Step4: equating (1) and (2)

$\sqrt{(x+1)^2+(y-2)^2}=\frac{|x-5|}{\sqrt{5}}$

Step5: squaring on both sides

$(x+1)^2+(y-2)^2=\frac{|x-5|^2}{5}$

$5[(x+1)^2+(y-2)^2]=(x-5)^2$

$5[x^2+2x+1+y^2-2y+4-x^2+10x-25]=0$

$12x+y^2-2y-24=0$

Step6: Equation of the parabola is

$y^2-2y+12x-24=0$

8 0

3 years ago

What is the most efficient way to solve this equation?

oee [108]

Answer:

Divide both sides by 18

Step-by-step explanation:

This is the most efficient way to solve this equation because you can find the variable (c) in one step.

4 0

3 years ago

Read 2 more answers

Solve 2(x-1)+2(3x-1)=0

sertanlavr [38]

Answer:

(x-1)+2(3x-1)=0

2x-2+6x-2=0

8x-4=0

8x=4

x=4/8

×=1/2

8 0

3 years ago

2392 ÷ 64 what is the answear

Diano4ka-milaya [45]

Answer:

37.375

Step-by-step explanation:

5 0

3 years ago

A dose of medicine is made by diluting one part of concentrate to 5 parts of water. How much of the concentrate should there be

Anastasy [175]

Answer:

15 ml

Step-by-step explanation:

If we mix 1 part concentrate and 5 parts water, we have 6 parts in total.

To create 90ml medicine, <em>how many "6 parts" are there?</em>

There would be 90/6 = 15 total "6 parts".

Each of the "6 parts's" 1 part is concentrate, so concentrate would be 1 * 15 = 15 ml.

<u>In ratio:</u>

$\frac{Concentrate}{Total(Water+Concentrate)}=\frac{1}{5+1}=\frac{1}{6}\\\frac{1}{6}*90=15$

6 0

3 years ago