1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth

a). if X is a whole number, use factorization to find the length and the breadth of the carpet in terms of X.

b). if X = 2 m, find the actual dimensions of the carpet.


c). it costs R50 per square metre to make such this carpet. how much will it cost to manufacture 5 carpets?​ ​​

[tex]\text{L.H.S}\\\\=\dfrac{1+\tan x}{ 1+ \cot x}\\\\\\=\dfrac{1+ \tan x}{ 1+ \tfrac 1{\tan x}}\\\\\\=\dfrac{1+\tan x}{\tfrac{\tan x+1}{\tan x}}\\\\\\=(1+\tan x) \times \dfrac{\tan x}{1+ \tan x}\\\\=\tan x\\\\=\text{R.H.S}\\\\\text{Proved.}[/tex]

The tension in the cable is given by the newton's first law will be 163.622 N.

The summation of the force is equal to zero.

The formula is given as

ΣF = 0

Where m is the mass of the body and a is the acceleration.

A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29 degrees and 53 degrees with the beam.

Then the tension in the cable will be

Let T be the tension in the cable.

T sin 29° + T sin 53° – 210 = 0

On simplifying, we have

T (sin 29° + sin 53°) = 210

                             T = 163.622 N

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Answer:

a = 6

Step-by-step explanation:

g(x) = 5x - 2

h(x) = √(x + 3)

g(h(x)) = 5[tex]\sqrt{x+3}[/tex] - 2

g(h(a)) = 5[tex]\sqrt{a+3}[/tex] - 2

5[tex]\sqrt{a+3}[/tex] - 2 = 13

5[tex]\sqrt{a+3}[/tex] = 15

[tex]\sqrt{a+3}[/tex] = 3

( [tex]\sqrt{a+3}[/tex] )² = 3²

a + 3 = 9

a = 6

Answer:

Yes

Step-by-step explanation:

The area of the entire rectangle is 4x² + 12x + 8

The given parameters are:

height = 4

Width = x² + 3x + 2

The area of the rectangle is:

Area = Width * Height

So, we have:

Area = (x² + 3x + 2) * 4

Expand

Area = 4x² + 12x + 8

Hence, the area of the entire rectangle is 4x² + 12x + 8

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The error interval for the length of the piece of wood is 293.5 ≤ length < 294.5

Error Interval can be defined as the limit of Accuracy when a number has been truncated.

It is given that the length of the piece of wood is 294 cm truncated to the nearest centimeter.

To determine the error interval for the length of the piece of wood

length ≥ 293.5

length < 294.5

293.5 ≤ length < 294.5

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The area of the Rhombus is 162√3 sq.unit , Option A is the correct answer.

A rhombus is a polygon , which has four equal sides , its diagonal bisect each other at 90 degree.

Let x be the half of the other diagonal.

tan 60 = x / 9

x = 9 tan 60

x = 9√3

Area of the Rhombus = (d1 * d2 /2 )

d1 and d2 are the length of the diagonal.

Area of the Rhombus = (9*2)(2 *9√3)/2

Area of the Rhombus =162√3 sq.unit

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Answer:

D

Step-by-step explanation:

Since we don't know how many people we don't know how many servings would be consumed. therefore this is an indirect variation

Answer:

a = z/mb

Step-by-step explanation:

Given:

[tex]\displaystyle \large{z=mab}[/tex]

To solve for a, divide both sides by the variables mb to isolate a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=\dfrac{mab}{mb}}[/tex]

Simplify the expression and we finally have solved for a-term.

[tex]\displaystyle \large{\dfrac{z}{mb}=a}\\\\\displaystyle \large{a=\dfrac{z}{mb}}[/tex]

Therefore, the answer to this question is a = z/mb.

Please let me know if you have any questions regarding my answer or explanation!

Answer:

the first option

Step-by-step explanation:

hope the answer helps...

The equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

The correct formats of the equations are:

y = 3x^5 - 5x^3 + 2x^2 - 10x + 4

y = 4x^4 + 6x^3 - 11

To determine the equation, we substitute 4x^4 + 6x^3 - 11 for y in the first equation.

So, we have:

4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

Hence, the equation that can be solved using the system of equations is 4x^4 + 6x^3 - 11 = 3x^5 - 5x^3 + 2x^2 - 10x + 4

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The line a is an illustration of a proportional linear equation, and the equation of line a is y = 1.4x

The line a passes through the following points:

(x,y) = (0,0) and (1.3, 1.82(

The above means that line a is a proportional linear equation

The constant of proportionality (k) is calculated using:

k = y/x

Using the values on the table, we have:

k = 1.82/1.3

Divide

k = 1.4

Substitute k = 1.4 in k = y/x

y/x = 1.4

Multiply both sides by 1.4

y = 1.4x

Hence, the equation of the line a is y = 1.4x

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Answer:

the arrows and dots show where

Hey there!

Look at your graph… then look at your points (the green dots) and it should be there.

Your x-values are across (just think of its saying “East” and ”West”) & your y-values are up and down (just think of it as “North” and “South”)

So, based on that that information:

ANSWER:

Your x-value would be: -1 because the point landed on it whereas the y-value would be: 5 because the point landed on it.

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer: 80

Step-by-step explanation:

We can use the formula [tex]A=\frac{d_{1}d_{2}}{2}[/tex], where [tex]d_{1}, d_{2}[/tex] are the lengths of the diagonals.

By the distance formula,

[tex]AC=\sqrt{(-2-2)^{2}+(-1-7)^{2}}=\sqrt{16+64}=4\sqrt{5}\\BD=\sqrt{(-8-8)^{2}+(-1-7)^{2}}=\sqrt{256+64}=8\sqrt{5}[/tex]

So, the area is [tex]\frac{(4\sqrt{5})(8\sqrt{5})}{2}=\boxed{80}[/tex]

Answer: 247 the Answer

The probability of picking two snacks of the same type is 0.308.

The probability of picking 2 potato will be:

= 6/14 × 5/13

= 0.429 × 0.385

= 0.165

The probability of picking 2 doritos will be:

= 5/14 × 4/13

= 0.357 × 0.308

= 0.110

The probability of picking 2 corn curls will be:

= 3/14 × 2/13

= 0.214 × 0.154

= 0.033

Therefore, the probability of picking two snacks of the same type will be:

= 0.165 + 0.110 + 0.033

= 0.308

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Answer:

30°

Step-by-step explanation:

This right triangle has :

=========================================================

Solving :

We know the angle sum of a triangle is 180°.

⇒ x + 90° + 60° = 180°

⇒ x + 150° = 180°

⇒ x = 30°

We know the angle sum of a triangle is 180° so

= 180°

= 180°

⇒x = 30°

[tex]\boxed{\blue{ » \: Lear \: math \: with \: Kareninajovanka \: « コ:彡}}[/tex]

The value of x so that lines s and t are parallel is 12

The angle are alternate exterior angles.

Therefore, alternate exterior angle theorem states that when two parallel lines are intersected by a transversal, then the exterior angles formed on either side of the transversal are equal.

Hence,

7x - 20 = 4x + 16

7x - 4x= 16 + 20

3x = 36

x = 36 / 3

x = 12

Therefore, the value of x is 12.  

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Work Shown:

2/5 - 1/3

6/15 - 5/15

(6-5)/15

1/15

Here are two ways to check the answer:

Hi Student!

Looking at the problem statement and them just asking for us to determine the difference between two numbers seems like an easy task.  The first thing that we must do is to find a common denominator so we subtract them otherwise we can not since the denominators are different.

The denominators of the fractions are 5 and 3 and we know that they both multiply up to 15 so that can be our common denominator.

Convert to common denominator

Subtract

Therefore, the final answer to the question asking the difference between 2/5 and 1/3 would be 1/15.

Answer:

2nd option

Step-by-step explanation:

the recursive rule is

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] + d ( d is the common difference )

use the explicit rule to find a₁ and d

a₁ = 48 - 11(1) = 48 - 11 = 37

a₂ = 48 - 11(2) = 48 - 22 = 26

then

d = a₂ - a₁ = 26 - 37 = - 11

recursive rule is then

[tex]a_{n}[/tex] = [tex]a_{n-1}[/tex] - 11

a₁ = 37

Answer:

$ 8874.11 after 5 years

Step-by-step explanation:

 Each year it is worth 85 % of its value

20 000 ( .85)^5 = 8874.11

Answer:

B.

Step-by-step explanation:

We can start by dividing 3.5 and 0.75.

3.5/0.75 is 4.67.

Now, we multiply 4.67 by 1 since we are finding how much she walks in 1 hour.

1*4.67 is 4.67.

Answer:

Happy birthday <3

Step-by-step explanation:

:)

Answer:

(5.5, 5 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = A (8, 2 ) and (x₂, y₂ ) = B (3, 8 ) , then

midpoint = ( [tex]\frac{8+3}{2}[/tex] , [tex]\frac{2+8}{2}[/tex] ) = ( [tex]\frac{11}{2}[/tex] , [tex]\frac{10}{2}[/tex] ) = (5.5, 5 )

Answer:

u=30

x=150

z=150

y=30

Step-by-step explanation:

u=y [ being vertically opposite angle]

x+u=180[ being linear pair]

x+30=180

x=180-30

x=150

z=x[being vertically opposite angle]

z=150

y=u[ being voa]

Answer:

=40°

Step-by-step explanation:

Sorry that's all I know

^keep safe^

Answer:

all real numbers greater than or equal to 10,000 and less than or equal to 20,000

Step-by-step explanation:

ye

A box plot has 5 data descriptions. The correct option is 87 and 132.

A box plot has 5 data descriptions.

Since each quartile of the box-and-whisker plot represents 25% of the data. Therefore, values between which there are 3 quartiles present will represent 75% of the data.

Hence, the correct option is 87 and 132.

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