The length of a rectangle is 20cm longer than its width.
The area of the rectangle is 1000cm?
Find the width and length of the rectangle.
Give your answers in surd form.

Answers

Answer 1

[tex]\text{Width} ~= w ~ cm \\\\ \text{Length}~,l = (20+ w) ~ cm \\\\\text{Area of rectangle} = 1000 cm^2\\\\\\\text{Now,}\\\\l \cdot w = 1000\\\\\implies (20 + w) w= 1000\\\\\implies w^2 +20w -1000=0\\\\\\\implies w = \dfrac{-20 \pm \sqrt{20^2 - 4 \cdot 1 \cdot (-1000)}}{2 \cdot 1}\\\\\\\implies w = \dfrac{-20 \pm \sqrt{4400}}{2}= \dfrac{-20\pm 20\sqrt{11}}2 = -10 \pm 10\sqrt{11}\\\\\text{Width cannot be negative so,} \\\\w= -10+10\sqrt{11}=10\left(\sqrt{11} - 1 \right) ~ cm\\\\[/tex]

[tex]\text{And length,}[/tex]

[tex]l= 20+ 10\left(\sqrt{11} - 1} \right) = 20 + 10\sqrt{11} - 10 = 10 + 10\sqrt{11} = 10 \left(1+ \sqrt{11} \right)~ cm[/tex]


Related Questions

A scientist tracks wolf populations in two parks. One population consists of 20 wolves and is increasing by an average of 2 per year. The other consists of 15 wolves and is increasing by an average of 3 per year. Write an equation that can be used to determine how many years, y, it will take for the two populations to be equal.

Answers

Answer:

it will take 5 years for them to be equal

Step-by-step explanation:

1st year they will be 22-18

2nd year they will be 24-21

3rd year they will be 26-24

4th year they will be 28-27

Finally the 5th year they will be 30-30

PLS help im stuck i dont understand how to do the problem

Answers

5/3x+8
5/3 is the slope

I WILL MARK BRAINEST!!!
#6 D and E please!

Answers

6d: lower q is 15
6e upper q is 18

Answer:

Q1 = 13.5

Q3 = 17.5

Step-by-step explanation:

6d) ===============

12, 12, 13, 14, 14, 17, 17, 17, 17, 18, 19, 20

I counted 12 numbers in this set. The median is the middle number of a sorted set. It's also the 2nd quartile as it is 2 quarters in, or 50% in.

First, find the median. In an even-numbered set, that's the average of the 2 middle numbers. In this case, it's between 17 and 17:

12, 12, 13, 14, 14, 17 === 17, 17, 17, 18, 19, 20

Now the set is split into 2 sets with 6 numbers each. Now, find the median of each of those sets. Again, the median of an even-numbered set is the average of the 2 middle numbers.

To find the first quartile (Q1), find the median of the lower set.

12, 12, 13 === 14, 14, 17

The median here is the average of 13 and 14, so 13.5.

6e) ==============

Exactly the same process as above.

7, 12, 12, 13, 14, 14, 17, 17, 17, 18, 19, 20

12 numbers again.

7, 12, 12, 13, 14, 14 === 17, 17, 17, 18, 19, 20

Now, to find the third quartile, find the median of the upper set.

17, 17, 17 === 18, 19, 20

The median is the average of 17 and 18, or 17.5.

Fatima writes down three square numbers.
The total of the square numbers is 30.
Which square numbers did Fatima write down?

Answers

Answer:

10

Step-by-step explanation:

Fatima wrote down 3 square numbers

since we don't know the three square we will represent it by any variable (X)

3x=30

so you divide both sides by 3

so we have 3x/3=30/3=10

therefore the answer is 10

The total of the square numbers is 30.

The squares can be from the following.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

1 + 4 + 25 = 30

The three square numbers are 1, 4, and 25.

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The total of the square numbers is 30.

The squares can be from the following.

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

We can take three squares.

1 + 4 + 25 = 30

This is a perfect case.

Thus,

The three square numbers are 1, 4, and 25.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ2

Solve for x:
-15 = x/-0.5
x =

/ = fraction symbol

Answers

Answer:

7.5

Step-by-step explanation:

You first have to switch the sides of the numbers. After you do that you multiply both sides by -0.5. Finally, you simplify and get 7.5

Brainliest pls?

Answer:

7.5

Step-by-step explanation:

You can multiply both sides by -0.5.

-15×-0.5=7.5

x=7.5

Hope that helps! :)

Find the equation of the line perpendicular to the given line and passing through the given point.

y = -4x + 2;(-1,4)

Answers

Step-by-step explanation:

hope it helps you.......

Here is your answer refer to the attachment .

jonshelle is developing a new bread recipe. the relationship between cups of water,w, and cups of flour,f, is w= 3/5f. what is the scale to water to flour

Answers

Answer:

3:5

Step-by-step explanation:

ratio!

Last year the French club raised $300 at their fall fundraiser. This year they raised $450. What is the percent increase in the amount raised?

(IN YOUR OWN WORD'S)

Answers

Answer:

50%

Step-by-step explanation:

Actual increase = $150

% increase = (actual change ÷ start value) × 100

                   = (150 ÷ 300) × 100

                    = 0.5 × 100

                    = 50%

(2x+5) (3x-15)

solve for x

•x=27
•x=20
•x=38

Answers

Answer:4799,2475,4941,

Step-by-step

I'm not sure,

but I solved replace the given numbes

For first, (2×27+5)(3×27-15)=4799, for second (2×20+5)(3×20-15)=2475

For third(2×38+5)(3×38-15)=4941

what is 22 over 7 - 2 over 3 divided by 2

Answers

22/7-2/3 divided by 2. first, you would do 2/3 divided by 2, which can be rewritten as 2/3 times 1/2, which is 2/6. 2/6 can be simplified as 1/3. next, you do 22/7-1/3, which is 59/21, or 2 17/21.

20
18. Find the values of x and y in the parallelogram PQRS.
vat
PT = 2x, TR = y +3, QT = 3x, TS = 2y
T
27
2x
Р
S
0

Answers

Answer:

Step-by-step explanation:

What property is illustrated in the following equation?

8 + 5 = 5 + ?

Answers

The answer is communitive property.

Answer: 3

Step-by-step explanation: Did it recently.

Please help mee please plese

Answers

Answer:

C=66, C=25 1/7

Step-by-step explanation:

i

C=pi(d)

C=22/7*21

C=66

ii

C=pi(d)

C=22/7*16

C=25 1/7

7 Mathexcellup logo

I answered the question and got it right.

seven million five hundred and forty-two eight hundred in number form pls

Answers

Answer:

7,542,800

Step-by-step explanation:

please ehlp delta math with explanation please

Answers

Answer:

134.3

Step-by-step explanation:

In [tex]\triangle{WXZ},[/tex] a right triangle, look at sides XW and XZ.

[tex]\frac{XW}{XZ}=\frac{\text{adjacent}}{\text{hypotenuse}}=\cos{82^\circ}\\\\XW=(XZ)\cos{82^\circ}[/tex]

You now need to find XW.

In [tex]\triangle{XYZ},[/tex] the measure of angle XZY (the one at the top) is 180 - (82 + 67) = 31 degrees.

Using the Law of Sines in triangle XYZ,

[tex]\frac{XZ}{\sin{67^\circ}}=\frac{540}{\sin{31^\circ}}\\\\XZ=\frac{540 \sin{67^\circ}}{\sin{31^\circ}}[/tex]

Put that into the equation for XW above...

[tex]XW=\frac{540\sin{67^\circ}\cos{82^\circ}}{\sin{31^\circ}}[/tex]

A calculator shows that this is approximately 134.3

someone plz help me!!!!!!!!!!!!!!

Answers

Step-by-step explanation:

In the given set of questions regarding the concept of division, it is important to understand the parts of a division problem.

Definitions:

In a division problem such as 15 ÷ 3 = 5:

15 represents the dividend, which is the number being divided into groups. 3 represents the divisor, which is the number of groups that divides the dividend.  5 represents the quotient, which is the result of dividing the dividend and the divisor. Solution:

Now that we have defined the parts of a division problem, we can proceed to matching the division problems to its corresponding representation of equal groups.

1.) 15 ÷ 3 = 5 "There are 5 equal groups of 3."  

If you multiply the quotient, 5, by the divisor, 3, it results in the dividend: 5 × 3 = 15. This occurs because multiplication is the opposite mathematical operation of division.  

2.) 45 ÷ 5 = 9 "There are 9 equal groups of 5."  

      9 equal groups of 5 = 9 × 5 = 45.

3.)   8 ÷ 4 = 2 "There are 4 equal groups of 2."  

      4 equal groups of 2 = 4 × 2 = 8.

4.) 18 ÷ 6 = 3 "There are 3 equal groups of 6."  

      3 equal groups of 6 = 3 × 6 = 18.

Complete the description of the piecewise function graphed below.

Answers

Step-by-step explanation:

not everything is visible, and the points' coordinates have to optically estimated (particularly for the leftmost point).

I assume, we have the following points :

(-6, 1.5) (-3, 3)

(-3, 2) (1, 2)

(1, 1) (6, -9)

all 3 segments are lines with the basic function definition

y = ax + b

a is the slope of the line function and is always the factor of x.

it is the ratio y/x indicating how many units y changes, when x changes a certain amount of units when going from one point on the line to another.

b is the y-intercept (the y value when x = 0).

the first segment goes from (-6, 1.5) to (-3, 3).

x changes by +3 units (from -6 to -3).

y changes by +1.5 or 3/2 units (from 1.5 to 3).

the slope of the line is 3/2 / 3 = 3/(2×3) = 1/2

giving us the first part

y = (1/2)x + b

b we get by using the coordinates of one point (e.g. -3, 3) as x and y values and solve for b :

3 = (1/2)×-3 + b

3 = -3/2 + b

6/2 + 3/2 = b

9/2 = b

the full equation is

y = (1/2)x + 9/2 = (x + 9)/2

the second segment is a flat, horizontal line and is simply

y = 2

the third segment goes from (1, 1) to (6, -9) :

x changes by +5 units (from 1 to 6).

y changes by -10 units (from 1 to -9).

the slope of the line is -10/5 = -2

giving us the first part

y = -2x + b

b we get by using the coordinates of one point (e.g. 1, 1) as x and y values and solve for b :

1 = -2×1 + b

1 = -2 + b

3 = b

the full equation is

y = -2x + 3

The answer is in the pic below!

what’s y = x +-2 -76

Answers

Answer:

y = x - 78

Step-by-step explanation:

y = x +-2 -76

y = x -78

Helppp!! I cant get this wrong lol

Answers

Answer:

x = 2

y = -7

Step-by-step explanation:

First, we see that all the terms in the first equation can be divided by 7:

-x + y = - 9

Then we solve for x by adding adding x and 9 to both sides:

-x + x + y + 9 = -9 + 9 + x

it cancels out to:

y + 9 = x

Now, replace x in the second equation with (y + 9):

28(y + 9) - y = 63

Now simplify:

28(y) + 28(9) - y = 63

27y + 252 = 63

27y = 63 - 252

27y = -189

y = -7

Plug in the value for y in the equation for x:

y + 9 = x

-7 + 9 = x

x = 2

Answer:

-7x +7y = -63(i)

28x -y = 63 (ii)

Divide eq(i) by 7

-x + y = -9 (iii)

28x -y= 63 (ii)

Add (iii) and ii

-x + y = -9

28x - y = 63

------------------------

-x +28x +0 = -9 +63

27x = 54

●x = 2

Put x=2 in any eq..

Lets put in eq[i]

-7 (2) + 7y =-63

-14 + 7y = -63

7y = -63 +14

7y=49

●y=7

BRAINLIST PLS

3. Given: DE is a midsegment of AABC. Show all work.
a. Find the value of x and y.
b. What is the length of AC?

Answers

Answer:

x = 10

y = 1

DE = 7

AC = 14

Step-by-step explanation:

x + 2 = 24/2

x = 12 - 2

x = 10

y + 6 = x - 3

y = 10 - 3 - 6

y = 1

0.36 in simpliest form with the line over the 6

Answers

Answer:

11/30

Step-by-step explanation:

Let x = 0.366666666.....

Then

100x = 36.6666666....

10x =     3.6666666...

subtracting 100x - 10x eliminates the trailing 6s

90x = 33

divide both sides by 90

x = 33/90

reduce

x = 11/30

A bird flying 45 feet above a river dives
down 58 feet to catch a fish. Find the
location of the fish relative to the surface of
the water.

Answers

The bird touches the water at 45 feet below, the fish is at 13 ft below the water surface :)

Use the simple interest formula 1=prt find the amount that needs to be invested at 7%per year for 12 years in order to earn 2500$in interest

Answers

the answer is 1358.70

Find the value for x
15 points for you plus brainliest, 5 star and thanks on answer and profile

Answers

Answer:

117 units

Step-by-step explanation:

Stop and answer this question

The first truck carries 35 tons less rice than the second truck. The number of paddy in the first truck is 2/3 of the amount in the second truck. How many tons of paddy does each cart hold?

Answers

First truck = x

Second truck = y

x + 35 = y

x = 2/3y

So

2/3y +35=y

1/3y = 35

y = 35*3

y = 105

And ,

x = 2/3y = 70

What list shows these in order from least to greatest?

Square W: A= √325 in.2

Square X: A= 3π/.5 in.2

Square Y: A= 5.5π in.2

Square Z: A= 17.92 in.2


1. Z, Y, W, X
2. X, W, Z, Y
3. Y, Z, W, X
4. W, X, Y, Z

Answers

Answer:

4 i am not sure for this answer guess

Help algebra 2 please

Answers

Answer:

it should be C I guess.

Im sorry if it is wrong

Write a proportion relating the side lengths of the triangle to any other triangle that has the line as a hypotenuse, a horizontal length of x units, and a vertical length of y units.

Answers

Answer:

y/x = 2 or y = 2x

Step-by-step explanation:

The given triangle has:

Vertical segment = 2 unitsHorizontal segment = 1 unit

The ratio (slope) is:

2/1 = 2

For any triangle using same line the proportion is:

y/x = 2 ory = 2x

Write a conditional statement that represents the Euler Diagram.
If a plant is a _________ , then the plant is a _________.

Answers

Answer:

if a plant is a carrot , then the plant is a vegetable

Step-by-step explanation:

it just a grammar you should think

Give coordinates for three possible pairs of points for the other two verticies...

Answers

Answer:

A) (-1,3) and (4,3)

B) (-1,-7) and (4,-7)

C) (1.5, .5) and (1.5, -4.5)

Step-by-step explanation:

For 1 and 2, because the y-values of the points are the same, the length of the square can be found by subtracting the x-coordinates.

4-(-1)=4+1=5

The length of the side of the square is 5.

1. For the first set of points, the square is above the two given points so just add 5 to the y-values

-2+5=3

This gives you the points:

(-1,3) and (4,3)

2. For the second set of points, the square is below the two given points so subtract 5 from the y-values.

-2-5=-7

This give you the points:

(-1,-7) and (4,-7)

3. The third answer is when the two given points are on opposite corners

of the square.

Here the diagonal is equal to 5 since they are on opposite corners of the square.

The diagonal of a square can be found with the pythagorean theorem

Since we have the diagonal we can find the side lengths we need.

[tex]2s^2=25[/tex]

s=[tex]\sqrt{\frac{25}{2} }[/tex]

s=3.5355

We want the new vertices to be in the middle of the other vertices x-coordinates

[tex]\frac{4-(-1)}{2} =\frac{5}{2} =2.5[/tex]

The new vertices will be 2.5 units away from the other vertices

-1+2.5=1.5

The new vertices will be at x=1.5

Now we need the pythagorean theorem again to find the y-values

[tex](2.5)^2+h^2=(3.5355)^2[/tex]

[tex]6.25+h^2=\frac{25}{2}[/tex]

[tex]h=\sqrt{\frac{25}{2} -6.25}[/tex]

h=2.5

The new vertices will be:

(1.5, -2+2.5)=(1., .5)

(1.5, -2-2.5)=(1.5, -4.5)

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