1. ABCD is a square with side length 12 cm.
a) Find the exact area of the shaded
[2 MARKS]
b) Find the area, correct to 2 decimal places. Use =3.142. [1 MARK]
region. [Leave your answer in terms of #]
NOT
A
6
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The LCM of the given numbers have been determined.

LCM stands for Least Common Multiple .

For two numbers , LCM is the number that is the smallest number of which they both are a factor.

It is asked to determine

LCM of 6 and 9

6 = { 6 , 12 , 18 , 24 , 30 , 36 , 42 .....}

9 = { 9 , 18 ,27 .....}

The LCM of 6 , 9 is 18

LCM of 8 and 12

8 = { 8,16,24,32....}

12 = {12 , 24 ,36....}

The LCM of 8 and 12 is 24

LCM of 4 , 6 and 8

4 = {4 , 8 , 12 , 16 , 20,24,28 ....}

6 = { 6 ,12 ,18,24......}

8 = {8 , 16,24 .....}

The LCM of 4,6 and 8  is 24

The LCM of 6 and 15 is 30  

The LCM of 20 and 30 is  60

The LCM of 25,30 and 75 is 150

The image of the solution is attached .

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Answer:

The answer is C (0,4)

Step-by-step explanation:

Looking at the graph we have to find a point (x,y) of D.

Find point D. It is on the y-axis, but which one? Positive/Negative y-axis.

It appears to be on the positive y-axis.

Now we have to choose either option C or D.

Option C seems like the best choice since the point is (x,y) is (0,4) on the positive y-axis.

Option D is quite the opposite of point D since the point (0, -4) is on the negative y-axis.

The answer is C. (0,4)

Answer:

In triangle TEI and ERI

TI = RE ( given)

angle TDI = angle ROE ( given).

TE = RI ( given).

by side angle side criteria

both the triangles are congruent

by cpct ( corresponding parts of congruent triangles)

TD is congruent to RO

Answer:

  (a)  18%

Step-by-step explanation:

The debt to credit ratio is found by dividing his debt by his credit limit.

__

  ratio = debt/credit limit = $1551.42/$8619.00 ≈ 0.18 = 18%

Quentin's debt to credit ratio is 18%.

Answer:

38.4 miles per hour

Step-by-step explanation:

30 miles in 45 minutes

18 miles in 30 minutes

Average speed =   total distance / total time

                          =    (30+18) / ( 45 min + 30 min)

                          = 48 miles / ( 1.25 hr ) = 38.4 miles per hour

Answer: B. 3.25 inches

Step-by-step explanation:

two months right next to each other

65.5 = final

62.25 = start

65.5 - 62.25 = 3.25 inches

Answer:

3.25

Step-by-step explanation:

65.5 - 62.25

Answer:

since the triangle has a line on 2 sides, it means that it is equal. Also, every triangle has 180 degrees so the missing degree is 70

Step-by-step explanation:

Figured it out

Answer:

x = 70°

Step-by-step explanation:

Since 2 sides are marked as congruent then the triangle is isosceles with 2 base angles being congruent , both 55°

the sum of the 3 angles in the triangle = 180° , so

x + 55° + 55° = 180°

x + 110° = 180° ( subtract 110° from both sides )

x = 70°

Answer:

18

Step-by-step explanation:

 (6 * 3 )  - (8 * 0)  = 18

The correct statements are options C and option D.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

The inequality is -3(2x - 5) < 5(2 - x)

At first, simplify each side

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

Remember (-)(-) = (+)

-3(2x - 5) = - 6x + 15

5(2 - x) = 5(2) + 5(-x)

Remember (+)(-) = (-)

5(2 - x) = 10 - 5x

- 6x + 15 < 10 - 5x

Subtract 15 from both sides

- 6x < -5 - 5x

Add 5x to both sides

- x < - 5

Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality

The coefficient of x is -1

Divide both sides by -1

x > 5

Therefore the correct statements are options C and option D.

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Answer:

11.3057558

Step-by-step explanation:

Answer:

 (x-1)^4    +  (y-4)^2  = 25

Step-by-step explanation:

Center at 1,4 means the circle is of the form:

   (x-1)^4    +  (y-4)^2  = r^2

Find r^2 using distance formula from center to the given point

 r ^2 = ( 8-4)^2 + (4-1)^2

 r^2 = 16 +9 = 25

so you answer is      (x-4)^4    +  (y-8)^2  = 25

Answer

100 multiples of 5 greater than 100 are:

Step-by-step explanation:

105, 110, 115, 120, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 220, 225, 230, 235, 240, 245, 250, 255, 260, 265, 270, 275, 280, 285, 290, 295, 300, 305, 310, 315, 320, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 380, 385, 390, 395, 400, 405, 410, 415, 420, 425, 430, 435, 440, 445, 450, 455, 460, 465, 470, 475, 480, 485, 490, 495, 500, 505, 510, 515, 520, 525, 530, 535, 540, 545, 550, 555, 560, 565, 570, 575, 580,

Answer: y = (x-1)(x-1)

Step-by-step explanation:

There is pretty much no vertical shift so that immediately rules out B and C.

We can solve y = (x-1)(x-1) and get x = 1

The graph shows x = 1 as a zero, so we know this graph is correct.

What must have motivated the behavior of the Investor to commit to such a large stock is; Option C: High Total Earnings

A) Low real returns; This cannot be his motivation to buy large shares because real return is what is earned on an investment after accounting for taxes and inflation. Thus, the lower, the less encouraging to investors.

B) Higher shares costs; This only means that the share cost is currently high which indicates strength of the company but it does not guarantee that it will scale up at a very fast rate again.

C) High total earnings; Thus would be an encouragement to the investor because the higher the total earning potential of an investment, the more the profitability and the more attractive to others.

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The figure is the combination of trapezoid and square. Then the area of the figure will be 39 square meters.

The complete question is attached below.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

The figure is the combination of trapezoid and square.

Then the area of the geometry will be

Area = Area of trapezoid + Area of square

Area = 1/2 x (3 + 9) x 5 + 3 x 3

Area = 30 + 9

Area = 39 square meters

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Answer: C. 7.5%

Solve as decimal

0.5*0.15=0.075

Move two decimal points over

0.075 -> 7.5

Change back to percent

7.5%

Answer:

x-intercept: (-5, 0)

y-intercept: (0, -4)

Step-by-step explanation:

The x-intercept is as the name implies when the line intersects the x-axis (the horizontal axis) or when y is equal to 0. If you look at the graph it intersects the x-axis at (-5, 0). The y-intercept follows the same concept except it's when it intersects the y-intercept (vertical axis) or when x is equal to 0. If you look at the graph it, it intersects the y-axis at (-4, 0).

The common ratio of the given Geometric progression is one-half.

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is the form a,ar,ar^2, ...

Given that the sequence begins with 12, i.e a = 12

and also given that the sequence are in Geometric Progression.

By dividing the preceeding number by 2, we get the successive number

Then the Geometric sequence is 12, 12×1/2, 12×1/4, 12×1/8, 12×1/16 ...

= 12, 6, 3, 3/2, 3/4, ...

Common ratio = Second term / First term

= 6/12

=1/2

Therefore, the common ratio of the given geometric progression is one-half.

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Answer:

its a

Step-by-step explanation:

The only option that meets the root theorem is option b.

The polynomial function is:

[tex]f(x) = 2x^2 - 4x + 9[/tex]

The rational root theorem says that if a root is a rational number, then the leading coefficient must be divisible by the denominator of the rational number and the constant term must be divisible by the numerator.

In this case, the constant is 9, and the only option such that the constant is divisible by the numerator is option b: 3

Where 3 is a rational number:

3 = 3/1

The numerator is 3 (which divides 9) and the denominator is 1 (which divides the leading coefficient 9. (notice that it meets the theorem, but it is not an actual root).

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Answer:

Show the process

Answer:

An expression for the temperature on February 10  =  -15F +42F = 27F

Step-by-step explanation:

the problem given is based on the algebra of simple addition : -

Addition of Algebraic Expressions : -

In addition of algebraic expressions while adding algebraic expressions we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.

Two ways to solve addition of algebraic expressions.

Horizontal Method: In this method, all expressions are written in a horizontal line and then the terms are arranged to collect all the groups of like terms and then added.

Column Method: In this method each expression is written in a separate row such that there like terms are arranged one below the other in a column. Then the addition of terms is done column wise.

so the question can be solved using Horizontal method :-

temperature on 9 Feb = -15F

temperature rose on 10th Feb = 42F

so the temperature on 10th Feb is :

-15F +42F = 27F

therefore, an expression for the temperature on February 10 is

-15F +42F = 27F (answer)

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Answer:

1. 1

2. 6/5

5. 0

6. -1/2

9. -1

10. 0

Step-by-step explanation:

Well you should just the slope formula (y2-y1)/(x2-x1)

1. (8-5)/(0-(-3)) = 3/3 = 1

2. (-3-(-9))/(4-(-1)) = 6/5

5. (3 - 3) / (0-2.5)  = 0/(-2.5) = 0

6. (0-(-4))/(0-8) = 4/(-8) = -1/2

9. (4-1)/(9-12) = 3/(-3) = -1

10. (7-7) / (1-(-5)) = 0/6 = 0

Answer:

Eric´s mom had:

31 years 11 months

Step-by-step explanation:

1 year = 12 months

40 years = 39 years + 12 months

40 years 3 months = 39 years + 12 monts + 3 monts = 39 years 15 months

Then:

 40 years 3 months

-   8 years 4 months

it´s equivalent to:

 39 years 15 months

-   8 years  4 months

= 31 years  11 monts

Answer:

14.16

Step-by-step explanation:

we first calculate the total amount of money paid, which is 35.40 plus 20%, we use this calculation:

35.40×1.20 = 42.48

now, this amount is split to 3 people, so:

42.48/3 = 14.16

and that is our answer

Answer:

I will assume the equation is supposed to be f(x) = x^2 – 5x + 12 since it is said to be a quadratic equation.

Step-by-step explanation:

See attached graph.

The value of f(–10) = 82     False

      f(-10) = (-10)^2 - 5*(-10) + 12

       f(-10) = (100) +50 + 12

      f(-10) = 162

The graph of the function is a parabola.  True

The graph of the function opens down.   False

The graph contains the point (20, –8).      False

The graph contains the point (0, 0).          False

Answer:

x= 4

y= -2

Step-by-step explanation:

[tex]-3y+5x=26\\-2y-5x=-16[/tex]

Solve by using the Elimination Method.

[tex]-5y=10\\\\\frac{-5y}{-5} =\frac{10}{-5} \\\\y=-2[/tex]

Now plug y into one of the original equation.

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

[tex]-2y-5x=-16[/tex]

[tex](-2*-2)-5x=-16[/tex]

[tex]4-5x=-16[/tex]

[tex]4-5x+5x=-16+5x[/tex]

[tex]4+16=-16+5x+16[/tex]

[tex]20=5x\\\\\frac{20}{5} =\frac{5x}{5} \\\\x=4[/tex]

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

[tex]\left \{ {{x=4} \atop {y=-2}} \right.[/tex]

Answer:

2(0.4)^-2 = 12.5

Step-by-step explanation:

do math noob

Answer:

the first one

Step-by-step explanation:

0.0206×0.188<0.0769/0.000023