Mathematics High School

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?

Answers

Answer 1

Answer:

look above

Step-by-step explanation:

hopeit hepls

1. The Area Of A Rectangular Carpet Is X + X - 2. HINT: Area = Length X Breadth A). If X Is A Whole Number,

Related Questions

Zane works for a catering company and is bringing a total of 160 servings of food to a conference. If 40 people come to the conference, there would be enough for each person to have 4 servings of food. If 80 people come to the conference, there would be enough for each person to have 2 servings of food.

Does this situation represent an indirect variation? If so, what are the independent and dependent variables?

A.
No, this is not an indirect variation. The product of the variables is not constant.
B.
Yes, this is an indirect variation. The number of servings per person is the independent variable, and the number of people is the dependent variable.
C.
Yes, this is an indirect variation. The number of people is the independent variable, and the number of servings per person is the dependent variable.
D.
Yes, this is an indirect variation. However, because the number of people is undetermined, the variables cannot be determined.

Answers

Answer:

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

Find the midpoint of A and B where A has coordinates (8, 2)
and B has coordinates (3,8).

Answers

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 )

10 The length of a piece of wood is 294 cm when truncated to the nearest centimetre. Complete the error interval for the length of the piece of wood.

Answers

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

What is Error Interval ?

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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You are packing for a road trip and you buy snack packages (same size, same weight) for the trip. you buy 6 potato chips, 5 doritos, and 3 corn curls. you put them in a bag and mix them up. during the trip, you reach into the bag and pull out two packages at random, one at a time. draw a tree and calculate the probability of each outcome. use p for potato chips, d for doritos, and c for corn curls. what is the probability of picking two snacks of the same type?

Answers

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

How to calculate the probability?

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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Where did he even get the 5 and the -1?

Answers

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:)

In the given figure, if y = 30, find (i) x (ii) z and (iii) u

Answers

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^

What is the common ratio for this geometric sequence?
16, 8, 4, 2, ...

Answers

the answer is 1/2 !!

The answer is 1/2. The answer is 1/2 because for every number following the first, the value is multiplied by 1/2 (or divided by 2) to get half of the first number.

What is the recursive rule for the sequence?

Answers

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

John is buying a new car. The value of one car he is considering is $20,000. The value of the car as it ages can be modeled by the
function v= 20, 000 (0. 84), where t is the number of years from the time of purchase. One of the factors John is using to make his decision is
the value of the car over time until it reaches half its original value. What values of domain are reasonable for the given function in this
context?
O
A. all real numbers greater than or equal to 0 and less than 4
O B. all real numbers greater than or equal to 0
O
C. all real numbers greater than or equal to 10,000 and less than or equal to 20,000
O
D. all real numbers greater than or equal to 0 and less than 2.8

Answers

Answer:

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

Step-by-step explanation:

Prove (1+tanx)/(1+cotx)=tanx by algebra

Answers

[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]

A box contains 50 batteries, of which 10 are dead and 5 are weak. Suppose you select batteries at random from the box and set them aside for recycling if they are dead or weak. If the first battery you select is dead and the second one is weak, what is the probability that the next battery you select will be weak?

Answers

This is the answer to your question hope it helps

Determine the value of "a" for which g(h(a)) = 13

Answers

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

What is the value of n?
38°

Answers

Answer: 247 the Answer

10. rhombus abcd has vertices at a(-2, 7), b(8, 7), c(2, -1), and d (-8, -1).
determine the area of abcd.

Answers

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]

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. Find, using vectors, the tension in the cables.

Answers

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

What is newton's first law?

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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What is the area of the rhombus in simplest radical form? The figure is not drawn to scale.

0162 √3
0162
081 √6
018 √3

Answers

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

What is a Rhombus ?

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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c) What is the equation of line a? (2 points)

Answers

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

How to determine the equation of the data?

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

Answers

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

How to determine the area of the entire rectangle?

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

Answers

Answer:

Happy birthday <3

Step-by-step explanation:

Is b=2a+10 equal to 4a+2b=10

Answers

Answer:

Yes

Step-by-step explanation:

please help if u know :D

Answers

Answer:

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.

Your mortgage is a 30-year fixed at 8% on $150,000. you are considering refinancing at 3.5% fixed for 30 years. the bank charges you 1.5% of your debt in closing fees. approximately how long will it take you to recoup the closing fees from the reduced loan payment amount?

Answers

It would take approximately around 4 months to recoup the closing fees from the reduced loan payment amount.

5. Find the value of x so that lines s and t are parallel.
(7x - 20)°
(4x + 16)

Answers

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

How to find angles involving parallel lines?

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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What is the answer to 2/5 - 1/3?

Answers

Answer: 1/15

Work Shown:

2/5 - 1/3

6/15 - 5/15

(6-5)/15

1/15

Here are two ways to check the answer:

Type 2/5 - 1/3 into your calculator to get roughly 0.06667. The 6's actually repeat forever, but of course the calculator rounds at some point. You should notice that 1/15 has the same decimal value. Therefore 2/5 - 1/3 = 1/15Type (2/5-1/3) - (1/15) into your calculator. You should get zero or very close to it. I'm using the fact that if A = B, then A-B = 0.

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

[tex]\frac{2}{5}-\frac{1}{3}[/tex][tex]\frac{2*3}{5*3}-\frac{1*5}{3*5}[/tex][tex]\frac{2*3}{15}-\frac{1*5}{15}[/tex][tex]\frac{6}{15}-\frac{5}{15}[/tex]

Subtract

[tex]\frac{6}{15}-\frac{5}{15}[/tex][tex]\frac{6-5}{15}[/tex][tex]\frac{1}{15}[/tex]

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

A data set is represented by the box-and-whisker plot below.

Answers

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

How does a boxplot show the data points?

A box plot has 5 data descriptions.

The leftmost whisker shows the minimum value in the data.The rightmost whisker shows the maximum value in the data.The leftmost line in the box shows the first quartile.The middle line shows the median, also called the second quartile.The last line of the box shows the third quartile.

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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One angle of a right-angled triangle is 60 grades . Find the other angle in degree.

Answers

Answer:

30°

Step-by-step explanation:

This right triangle has :

right angle (90°)One angle of 60°

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

Solving :

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

⇒ x + 90° + 60° = 180°

⇒ x + 150° = 180°

⇒ x = 30°

Step-by-step explanation:

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

x + 90° +60°

= 180°

x + 150°

= 180°

⇒x = 30°

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solve the equation for a? z=mab. a)a=z+mb b)a=z-mb c)a= mb/z d)a=z/mb

Answers

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!

TIME SENSITIVE!!! What will the first row of this multiplication be? (first image is the problem, second is the options)

Answers

Answer:

the first option

Step-by-step explanation:

hope the answer helps...

A tractor costs $20000 and depreciates in value by 15% per year. how much will the tractor be worth after 5 years?

Answers

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

Which equation can be solved by using this system of equations?

StartLayout Enlarged left-brace 1st Row y = 3 x Superscript 5 Baseline minus 5 x cubed + 2 x squared minus 10 x + 4 2nd Row y = 4 x Superscript 4 Baseline + 6 x cubed minus 11 EndLayout

Answers

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

How to determine the equation?

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