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?​​​

Answer:

Step-by-step explanation:

Equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it define​s.

The quadratic expressions can be simplified as follows;

Equation C is simplified as follows;

y = 3(x - 1)² + 18

y = 3(x² - 2x + 1) + 18

y = 3x² - 6x + 3 + 18

y = 3x² - 6x + 21

Thus, equation A and equation C are equivalent , and of those, equation C is in the form most useful for identifying the extreme value of the function it define​s.

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Answer:

(-7, -10)

Step-by-step explanation:

Solve for x and y in double variable equation

y = 2x + 4

y = x - 3

y = x - 3, plug in to first equation

x - 3 = 2x + 4

x = -7

y = -7 - 3

y = -10

(-7, -10)

Answer: [tex]y\leq -3x-3[/tex] [tex]< --Graph[/tex]

In order to graph the equation "y ≤-3x - 3", we need to graph the inequality by finding the boundary line, then shading the appropriate area.

Answer:

27 units

Step-by-step explanation:

6 (base) × 9 (height) = 54

54 × 1/2 = 27

Answer:

(0, -5)

Step-by-step explanation:

the y-intercept of the parabola is when x = 0 (crossing the y axis)

The reasonable domain of the function is [0,4)

The function of the car value is given as:

V(x) = 20000 * (0.84)^x

When the car reaches half its value, we have:

V(x) = 10000

Substitute V(x) = 10000 in V(x) = 20000 * (0.84)^x

10000 = 20000 * (0.84)^x

Divide both sides by 20000

0.84^x = 0.5

Take the logarithm of both sides

x log(0.84) = log(0.5)

Divide both sides by log(0.84)

x = 4

This means that the maximum value of x is 4

Hence, the reasonable domain of the function is [0,4)

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For this exercise, the graph of a logarithmic function is shown in the image attached below.

A logarithmic function is a type of function that graphically represents the inverse of an exponential function. Mathematically, a standard logarithmic function is written as [tex]y = log_nx[/tex].

In Mathematics, the domain of any logarithmic function is from (x > 0) to infinity (+∞). Thus, its graph moves to the right on the vertical axis and it increases to infinity (+∞) as the value of x increases.

In this scenario, an image of all the graphs wasn't provided, so, I would proceed to add an attachment to illustrate the graph of a logarithmic function.

Note: The graph (u-shaped) shown in the image attached above is that of a parabolic function.

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The probability that he will receive the job will be 1 / 6

The complete question is given below:-

A job applicant estimates that his chance of passing a qualifying examination is 2/3, and his chance of being appointed if he does pass is 1/4. What is the probability that he will receive the job?

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

It is given that:

The chance of passing a qualifying examination is 2/3=P

and chance of being appointed, if he does pass, is 1/4=P'

Now, we are asked to find the probability that he will receive the job.

We are asked to find the probability that he will receive the job.

The probability is calculated as The probability that he qualify the exam×Probability that he is being appointed.

=P×P'

=(2/3)×(1/4)

=1/6

Therefore the probability that he will receive the job will be 1 / 6

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Answer: The value of x is 3.5

Explanation:

Equation:

y = 2x - 7

When the equation's Line intersects the x-axis, the value of y shall be always 0

Insert y = 0, to find x intercept

⇒ 0 = 2x - 7

⇒ 2x - 7 = 0

⇒ 2x = 7

⇒ x = 3.5

So coordinates: (x, y) → (3.5, 0)

By solving a linear equation, we will see that after 3 hours, both companies will charge the same amount.

We know that company A charges $200 plus $50 per hour. So if they work for x hours, they charge:

A(x) = $200 + $50*x

And company B charges $125 plus $75 per hour, so if they work for x hours, they charge:

B(x) = $125 + $75*x

We want to find the value of x such that A(x) = B(x), then we want to solve the linear equation:

$200 + $50*x = $125 + $75*x

$200 - $125 = $75*x - $50*x

$75 = $25*x

$75/$25 = x = 3

This means that after 3 hours, both companies will charge the same amount.

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Answer:

Blue Rectangle: 135 mm²

Blue Triangle: 45 mm²

Not sure if you need this but the Total Square: 225 mm²

Step-by-step explanation:

Area of a rectangle: length x width

Area of a triangle: [tex]\frac{1}{2}[/tex] x base x height

First find the area of the blue rectangle.

Length = 15 mm

Width = 9 mm

Area = 135 mm²

Now find the area of the blue triangle:

Base = 6 mm (because the bottom is 15 total and you subtract the 9)

Height = 15 mm

Area = 45 mm²

Hope it helps!

Answer:

Step-by-step explanation:

5.9 1014 kg (1300 trillion pounds)

5.9 108 kg (1.3 billion pounds)

5.9 1017 kg (1.3 quadrillion pounds)

5.9 1011 kg (1.3 trillion pounds)

those are the options

Answer:

122.5 degrees

Step-by-step explanation:

A six sided polygon's interior angles sum to

  (n-2)(180) =  (6-2) (180) = 720 degrees

then   x + x + x +     x+10    + 130   + 90 = 720

                          4x = 490        so x = 122.5 degrees

When the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be C. 540 centimeters cubed.

From the information given, the metronome ticks at adjustable intervals to help keep time when playing music.

In rhis case, when the metronome was created out of a piece of solid wood, the minimum amount of solid wood that was used from the pyramid will be:

= 20 × 9 × ✓9

= 20 × 9 × 3

= 540

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Answer:

540

Step-by-step explanation:

C

Answer:d.33

Step-by-step explanation: To begin we convert his living room floor length and width to inches. 8 1 slash 3 feet = 100 inches
10feet= 120 inches

hence the area in square inches of the living room floor is 100 inches times120 inches = 12000 inches squared.

Each carpet tile has an area of 20 by 20 which = 400inches squared. dividing the area of the living room by 400inches of each carpet tile, would yield 30 carpet tiles needed to cover this area.

As per linear equation, the minimum number of carpet tiles that Aurelio must purchase to cover the area of his living room floor is 29.

A linear equation is an equation that has one or multiple variables with the highest power of the variable is 1.

Given, the room has a length of 10 feet = 12 × 10 inches = 120 inches

The width of the room is = 8 feet = 12 × 8 inches = 96 inches

Therefore, the area of the room is

= 120 × 96 square inches

= 11520 square inches

Length of each carpet tile is 20 inches

Width of each carpet tile is 20 inches

Therefore, the area of each tile is

= (20)² square inches

= 400 square inches

The number of tiles require

= (11520/400)

= 28.8

≈ 29

Therefore, 29 tiles will be required.

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x = 53/80 = 0.6625

​

if isn't right I have another equation

Answer:

13.25

Step-by-step explanation:

[tex]x - 7 \div 20 = 5 \div 16[/tex]

by cross multiplying

16(x-7)=5(20)

16x-112=100

16x=100+112

16x=212

x=212 /16

×=13.25

if the question is this

Ann and Bob's age is 21 years  and 28 years respectively and after 14 years the ratio will be 5:6.

What is Ratio ?

The comparison of one quantity to other is called a ratio and when two ratios are equal they are said to be in proportion.

It is given in the question that

The ratio of Ann's age to bob's age is 3:4

in 7 years time this ratio will be 4:5

their ages now = ?

Let the age of Ann and Bob is x and y

x:y = 3:4

x =(3/4)y

After seven years

(x+7):(y+7) = 4 :5

(x+7)/(y+7) = 4/5

((3/4)y +7)/(y+7) = 4/5

(3y +28)/(y+7) = 16/5

5*(3y+28)= 16(y+7)

15y +140 = 16y+112

y = 140-112

y =28 years

x = 21 years.

After x years suppose the ratio is 5 :6

(21+x)/(28+x) = 5:6

126 +6x = 140 + 5x

x = 14 years.

Therefore after 14 years the ratio will be 5:6.

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Answer:

8

Step-by-step explanation:

2 pattern block trapezoids makes one hexagon

There are 4 hexagons so you have to multiply 2 by 4

you get 8

8 is your answer

If the degree of the polynomial is 3. Then the value of m will be 2. Then the correct option is B.

The complete question is attached below.

Let the polynomial is given below.

axⁿ + bxⁿ⁻¹ + .... + kx¹ + lx⁰

Then the highest power of the polynomial is known as the degree of the polynomial.

The polynomial is given as

[tex]\rm 10x^2 + 2x^my-4y[/tex]

The degree of the polynomial is 3. Then the value of m will be

m + 1 = 3

    m = 2

Then the correct option is B.

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k(2)=

Option C is true

k(3)

D is true

k(4)

k(5)

k(6)

E is not true

k(1)

So

B is false

Similarly

-1 is not in domain even though

A is false

Answer:

[tex]k(2) = 2[/tex]

[tex]k(3) = 0[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}k(1)=4\\k(n)=k(n-1)-2\end{cases}[/tex]

The function [tex]k(n)[/tex] tells us that each term is 2 less than the preceding term.

Therefore:

[tex]\implies k(1)=4[/tex]

[tex]\implies k(2)=k(1)-2=4-2=2[/tex]

[tex]\implies k(3)=k(2)-2=2-2=0[/tex]

[tex]\implies k(4)=k(3)-2=0-2=-2[/tex]

[tex]\implies k(5)=k(4)-2=-2-2=-4[/tex]

[tex]\implies k(6)=k(5)-2=-4-2=-6[/tex]

Rearranging the formula to make the preceding term the subject:

[tex]\begin{aligned} k(n) & = k(n-1) - 2\\\implies k(n)+2 & = k(n-1)\\k(n-1) & =k(n)+2\end{aligned}[/tex]

Therefore:

[tex]\implies k(1)=4[/tex]

[tex]\implies k(0)=k(1)+2=4+2=6[/tex]

[tex]\implies k(-1)=k(0)+2=6+2=8[/tex]

Conclusion

Therefore, the correct answers from the answer options are:

[tex]k(2) = 2[/tex]   and   [tex]k(3) = 0[/tex]

The simplification of the indices can be seen in the explanation below.

[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]

The simplification of indices entails simplifying the indices to the simplest form possible by using the laws of indices.

From the information given, we have:

1.

[tex]\mathbf{= \dfrac{1^3}{32r^5y^3}}[/tex]

2.

[tex]\mathbf{= \dfrac{214}{2ry^3}}\\[/tex]

[tex]\mathbf{=\dfrac{ 107}{ry^3}}[/tex]

3.

= 2×4 √4xy³

= 8 √4xy³

= 8 × 2√xy³

= 16√xy³

4.

= 2rty 4ry³

= 2tr²y⁴

5

= 413/21²y³

= 413/441 y³

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Answer:

1.

2.

3.

= 2×4 √4xy³

= 8 √4xy³

= 8 × 2√xy³

= 16√xy³

4.

= 2rty 4ry³

= 2tr²y⁴

5

= 413/21²y³

= 413/441 y³

Step-by-step explanation:

Answer:

  54 chickens

Step-by-step explanation:

This problem requires you find the area of Thomas's field, then use that area to find the number of chickens he can keep. The irregularly-shaped field can be considered as composed of shapes that you know how to find the area of.

__

There are many ways the area can be divided. One of them is shown in the attachment. That shows the area to be the sum of the areas of a triangle and a trapezoid.

The triangle has a base of 20 m and a height of 7 m, so an area of ...

  A = 1/2bh

  A = 1/2(20 m)(7 m) = 70 m²

The trapezoid has bases of 11 m and 18 m, and a height of 14 m. Its area is ...

  A = 1/2(b1 +b2)h

  A = 1/2(11 m +18 m)(14 m) = 1/2(29 m)(14 m) = 203 m²

The area of the field is the sum of these areas:

  field area = triangle area + trapezoid area

  field area = 70 m² +203 m² = 273 m²

__

Each chicken requires an area of 5 m², so the total area for n chickens is ...

  area for n chickens = 5n . . . . square meters

This area cannot exceed the area of the field, so an inequality can be written:

  area for n chickens ≤ field area

  5n ≤ 273

  n ≤ 54.6 . . . . . . divide by 5

Thomas can keep a maximum of 54 chickens in the field.

The probability of winning when betting on two lines that touch each other on the table is 6/38

The sample size is given as:

n = 38

The numbers on the range 1-2-3-4-5-6 is:

Range = 6

So, the probability is calculated as:

P = Range/n

This gives

P = 6/38

Hence, the probability of winning is 6/38

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Answer: 40°

40 * 9 =360° Each part has 40° angle