Given that OA = 2x + 9y , OB = 4x + 8y and CD = 4x - 2y , explain the geometrical relationships between the straight line AB and CD.
It’s a 3 mark question sooo if someone could help then thanks.

Answer:

x = 8

Step-by-step explanation:

Every angle in an EQUILATERAL triangle = 60°

so   9x -12 = 60

       9x = 72

         x = 8  

Step-by-step explanation:

[tex]9x - 12 = \frac{180}{3} = 60 \\ [/tex]

[tex]9x = 60 + 12[/tex]

[tex]9x = 72[/tex]

[tex]x = \frac{72}{9} \\ [/tex]

[tex]x = 8[/tex]

hence the value of x is 8...

Answer:

[tex]y = 3x + 40[/tex]

Step-by-step explanation:

The slope-intercept equation takes the form

[tex]y = mx + c[/tex]

Where m is the gradient, and c is the y-intercept.

If we assume we are plotting a graph where the X axis is time, and the y axis is distance, and we know our time value starts at 40, then we can say that our y intercept value is 40.

Next, let's figure out how far she has travelled. 130-40 = 90, and she has travelled this distance in 30 seconds, so dividing 90 by 30, we know that she is travelling 3 feet a second. This leaves us with a gradient of 3.

Putting these two values together, we can find the final form of the equation to be:

[tex]y = 3x + 40[/tex]

Answer:

d = 3t + 40

Step-by-step explanation:

So, since you have a constant speed you're going to have a linear equation, which was also stated in the question. So it's asking for slope-intercept form which is expressed as: y=mx+b, where m=slope, and b=y-intercept. So it's important to know what these two things mean in certain contexts. In every single case, the slope is how much the y-value is changing as x increases by 1, and in this specific case, the distance is what is changing as time goes by. So this means that the distance would be the y-value, and x would be the t variable (time). And remember how it mentioned "constant speed", this means as one second passes, the distance increases by a constant distance. We can solve for this by using the given information.

She's already 40 feet from her starting position, and after 30 seconds she's 130 feet from her starting position. This means she traveled (130 - 40) feet, because she was already 40 feet away from her starting position. This means she traveled 90 feet. Now to find how much she travels in a second, divide it by the time which is 30 seconds, and you get: 90 feet / 30 seconds = 3 ft/s, this is her constant speed. This is the slope of the equation. So now we have the equation: d = 3t + b. Now all we need to find is the y-intercept

The y-intercept in this context, is how far away she is from her starting position initially. This is given in the problem, it's 40 feet. She's already 40 feet away when 0 seconds have passed. So this gives us the equation: d = 3t + 40

Answer:

33:21

Step-by-step explanation:

The way I look at it is that 11:7 is 18 parts of 54. So I divide 54 by 18 and get 3 per. Then multiply, 11 * 3 is 33 and 7 * 3 is 21.

The expression is 12 x 2 / 7 will be 24/7. And the number 54 into the ratio 11:7 will be 33 and 21.

The utilization of two or more additional numbers that compares is known as the ratio.

The expression is given below.

⇒ 12 x 2 / 7

⇒ 24 / 7

Divide 54 into the ratio 11:7.

⇒ 54 x 11 / (11 + 7)

⇒ 594 / 18

⇒ 33

⇒ 54 x 7 / (11 + 7)

⇒ 378 / 18

⇒ 21

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Step-by-step explanation:

So a three digit number can be expressed as: [tex]100a + 10b + c[/tex] where a is the third digit, b is the second digit, and c is the first digit. Or in other words a is the hundreds place, b is the tens place, and c is the ones place. When something "increases" by 30%, it is 130% it's original value, and to calculate how much that is, you simply convert 130% to a decimal by dividing by 100, which gives you 1.30. And since all the digits are increased by 1, you have the equation:

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.30(100a+10b+c)[/tex]

Distribute the multiplication on the left side:

[tex]100a+100+10b+10+c+1=1.30(100a+10b+c)[/tex]

Distribute the multiplication on the right side:

[tex]100a+100+10b+10+c+1=130a+13b+1.3c[/tex]

Add like terms on the left side:

[tex]100a+10b+c+111=130a+13b+1.3c[/tex]

Subtract 100a, 10b, and c from both sides

[tex]111=30a+3b+0.3c[/tex]

So "technically" you can just plug in any two values, and then solve for the last value, but since you have a 3 digit number, you have the restriction of a < 10, b < 10, and c < 10, and also a, b, and c, should only be integers and all have the same sign or it wouldn't be a 3 digit number.

So let's start with a, since it has the highest coefficient, well you can fit 30 into 111, 3 times without going over so that's the first value

111 = 30(3) + 3b + 0.3c

111 = 90 + 3b + 0.3c

Now subtract the 90 from both sides

21=3b+0.3c

Well 3 can fit into 21, 7 times!

21 = 3(7) + 0.3c

21 = 21 + 0.3c

subtract 21 from both sides

0 = 0.3c

and now obviously c is 0, if you want you can divide both sides by 0.3 but it's a bit redundant

c = 0

This gives you the three values, a=3, b=7, c=0. which is the number 370. Now let's double check. Adding 1 to each digit would give you 481 and 481/370 = 1.3, so it is correct!

part b:

So to prove there is no three digit number, is to realize there is no solution, given the restriction or integers, greater than or equal to 0, and less than 10, and all of them must have the same sign.

So let's start with the same equation except this time instead of 1.3 it's 1.4

[tex]100(a+1) + 10(b+1) + 1(c+1) = 1.40(100a+10b+c)[/tex]

Distribute on the left side;

[tex]100a+100+10b+10+c+1=1.40(100a+10b+c)[/tex]

Distribute on the right side:

[tex]100a+100+10b+10+c+1=140a + 14b + 1.4c[/tex]

Add like terms on left side:

[tex]100a + 10b + c + 111 = 140a + 14b + 1.4c[/tex]

Subtract 100a, 10b, and c from both sides:

[tex]111 = 40a + 4b + 0.4c[/tex]

Now to do the same process, let's start by finding how many times we can fit 40 into 111, and if you're wondering why we start with 40, it's because let's say for example I just say, I can fit another 40 into it, but I decide not to, and let b do that, well even if it's just 40, b will have be at least 10, which does not fit our restrictions, so you have to fit as many 40's into the number first then go the other numbers.

So only 2 40's can fit in 111 without going over the value

111 = 40(2) + 4b + 0.4c

Subtract 80 from both sides

[tex]31=4b+0.4c[/tex]

4 can fit into 31, 7 times

31 = 4(7) + 0.4c

31 = 28 + 0.4c

subtract 28 from both sides

3 = 0.4c

divide both sides by 0.4

7.5 = c.

Since c is not an integer there is no 3 digit number that exists that increases by 40% whenever you increase it by 1.

1. y= 2x

2.  (0, 5)

3. y  = 3x + 12

Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions.

1. let us take (0,0) and (1, 2)

m= 2-0/1-0

m= 2

So equation of line

y- 0 = 2(x-0)

b

2. y= 3x+5

passes through (0, 5)

3. y= 3x+5

  m = 3

We need the equation of a line with slope 3 that passes through point (0, 12).

y - y1 = m(x - x1)

y - 12 = 3(x - 0)

y - 12 = 3x

y  = 3x + 12

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Answer:

337.5Ft

Step-by-step explanation:

The weight of James cake in ounces is 52 ounces and the Pint of water dispensed in 20 seconds is 24 pints

1 pound = 16 ounces

Number of ounces the cake weigh = 3 1/4 pounds × 16 ounces

= 13/4 × 16

= (208) / 4

= 52 ounces

1 gallon = 4 quarts

0.15 gallon = 0.6 quarts

1 quart = 2 pints

0.6 quart = 1.2 pints

Pint of water dispensed in 20 seconds = 1.2 × 20

= 24 pints of water

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Hello,

Answer:

C. (b - c)(a + b)

Step-by-step explanation:

A = (b - c)(a - c)

A = ba - bc - ac - c² ≠ ab + b² - ac - bc

B = (b + a)(b + c)

B = b² + bc + ab + ac ≠ ab + b² - ac - bc

C = (b - c)(a + b)

C = ba + b² - ca - cb

= ab + b² - ac - bc

→ That is answer C

Answer:

The answers are:
(i) 108.33%
(ii) 93.75%

Step-by-step explanation:

The original area and perimeter are as follow:

Perimeter = 2l + 2w
                = 2(2p) + 2(p)
                = 4p + 2p
                = 6p cm

Area = l * w
        = 2p * p
        = 2p^2 cm^2

A 25% increase of the length is = 2p * (1 + 25%) = 2p * 1.25 = 2.5p cm

A 25% decrease of the breadth is = p * (1 - 25%) = p * 0.75 = 0.75p cm

Perimeter = 2l + 2w
                 = 2(2.5p) + 2(0.75p)
                 = 5p + 1.5p
                 = 6.5p cm

Area = l * w
        = 2.5p * 0.75p
        = 1.875p^2 cm^2

Now that we have found the changes, let's calculate the percentage changes

Percentage change of perimeter:

x% * 6p = 6.5p
x/100 * 6p = 6.5p
x * 6p = 6.5p * 100
x = 650p/6p
x = 108.33

Percentage change of area:

x% * 2p^2 cm^2 = 1.875p^2 cm^2
x/100 * 2p^2 cm^2 = 1.875p^2 cm^2
x * 2p^2 cm^2 = 1.875p^2 cm^2 * 100
x = 187.5p^2 cm^2 / 2p^2 cm^2
x = 93.75

Answer:

i = 8 1/3%

ii = -6 1/4%

Step-by-step explanation:

The previous answer is wrong this is the correct one:

Because they are using the same variable P let's assume P = 10
Length increase 25% = 10 + (10 x 25%) = 10 + 2,5 = 12,5 cm
Breath decreased 25% = 10 - (10 x 25%) = 10 - 2,5 = 7,5 cm

i. Original Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x10) + 2(10) = 2(20) + 2(10) = 60cm
Modified Perimeter : 2(L) + 2(B) = 2(2p) + 2(p) = 2(2x12,5) + 2(7,5) = 2(25) + 2(7,5) = 65cm

The percentage change is

65-60/60 x 100

= 5/60 x 100

= 500/60

= 8 2/6% simplified 8 1/3%

ii. Original Area: L x B = 2p x p = 2(10) x 10 = 20 x 10 = 200 cm^2
Modified Area: L x B = 2p x p = 2(12,5) x 7,5 = 25 x 7,5 = 187,5 cm^2

The percentage change is

187,5-200/200x 100

= - 12,5/200 x 100

= - 1250/200 = - 6 1/4 %

That is the Correct answer. Hope that help

Using translation concepts, a stretch of a decay exponential function is given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

An exponential decay function is given by:

[tex]y = ab^x[/tex]

In which |b| < 1.

A stretch means that the function is multiplied by a factor with absolute value greater than 1, hence the function would be given by:

[tex]f(x) = 5\left(\frac{1}{5}\right)^x[/tex]

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The age that has the maximum number of arrest is 25 years

The equation of the function is given as:

[tex]f\left(x\right)\ =\ \frac{27725\left(x\ -\ 14\right)}{x^{2\ }+\ 9}-5x[/tex]

See attachment for the graph of the function.

The end behavior of the graph is

[tex]\mathrm{as}\:x\to \:+\infty \:,\:f\left(x\right)\to \:-\infty \:,\:\:\mathrm{and\:as}\:x\to \:-\infty \:,\:f\left(x\right)\to \:+\infty \:[/tex]

This means that:

As the age of the driver increases, arrested drivers decreases and as the age of the driver decreases, arrested drivers increases

From the graph, the maximum is:

Maximum = (25.388, 356.166)

Remove the y values

Maximum = 25.388

Approximate

Maximum = 25

Hence, the age that has the maximum arrest is 25

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The correct answer is option D which is the side length will be (64n)¹⁸.

The square is defined as a quadrilateral having all four sides equal to each other and the area of the square is the product of its sides.

Given that:-

The sides of the square will be calculated as follows:-

A = (64n)³⁶

a² = (64n)³⁶    Here a = Side of the square.

a = √ (64n)³⁶

a = 64n¹⁸

Therefore the correct answer is option D which is the side length will be (64n)¹⁸.

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Answer: 1 bottle, 6 bottle, 8 bottle

Answer: 1 bottle for $1.07, 8 bottles for $8.56 and 6 bottles for $6.42

The equation [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex] has x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞). Thus Option A,B and C are correct.

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is independent variable while Y is dependent variable.

Given function,
= [tex]y\ =-2\log_{2}\left(x+2\right)+8[/tex]
Domain of the above function is grater than -2 because at -2 system goes to infinity. Domain can be given as(-2, ∞).

Given function has x intercept at (14, 0) and y intercept at (0, 6).

Thus, the given function of log has following characteristic i.e.
x Intercept at (14, 0) and Y intercept (0,6) and domain is (-2, ∞).

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The transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

Transformation is the technique used to change the position of a figure on an xy-plane.

Given the parent function f(x) = x², the transformation needed to form g(x) = 3(x + 2)^2-1 is a vertical translation of the function down by 1 unit, horizontal shift to the right by 2 units and a vertical stretch by 3 units

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The 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).

Given sample size=1002 and confidence level of 99%.

In a sample with a number n of people surveyed with a probability of a success of π and a confidence level of 1-α, we have the following confidence interval of proportions.

π±z[tex]\sqrt{}[/tex]π(1-π)/n

in which z is the z score that has a p value of 1-α/2

n=1002,π=701/1002

So α=0.01, z is the value of Z that has a p value of 1-0.01/2=0.995, so Z=2.575.

Lower limit=π-[tex]z\sqrt{}[/tex]π(1-π)/n

=0.6996-2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]

=0.6623

Upper limit=π+[tex]z\sqrt{}[/tex]π(1-π)/n

= 0.6996+2.575[tex]\sqrt{0.6996*0.3004/1002}[/tex]

=0.7369

Hence the 99% confidence interval estimate of the proportion of people who say that they voted is (0.6623,0.7369).

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Steve is 1.2 times faster than Paul.

The quantitative relationship between two values indicating how frequently one value is contained within the other.

For example: Speed = Distance / Time

Total distance covered by both Steve and Paul = 100m

Total time taken by Steve = 10s

Steve's speed = 100 / 10 = 10m/s

Total time taken by Paul = 12s

Paul's speed = 100 / 12 = 8.33m/s

Ratio of Steve's speed to Paul's speed = 10 / 8.33 = 1.2

Hence we can say that Steve is 1.2 times faster than Paul.

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A radius and diameter are parts of a circle. Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

A circle is a figure that is bounded by a curved line which is called its circumference. Some of its parts are radius, diameter, chord, sector, etc.

Thus the reasons required in the question are given as;

i. A tangent is always perpendicular to the radius of a circle because they are always at a right angle.

ii. A line that is drawn from the end of a diameter of a circle to its circumference form a right angle because they are always perpendicular.

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The statement of expressions is two terms and three factors.

According to the question, the statement that teaches us about expression is made up of two terms, each of which has three factors.

The ABC and DEF expressions define the expression of two terms, each of which comprises two elements.

As a result, the answer is two terms and three factors.

Therefore, the answer is two terms and three factors.

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Answer:

Step-by-step explanation:

A ferris wheel has 32 passenger cabins. if you are sitting in cabin 14 which is currently at the top of the wheel, what is the number of the cabin at the bottom of the wheel?

32 : 2 + 14 = 30

Answer:

Step-by-step explanation:

Since there are 32 passenger cabins, each half of the wheel has:

It means the opposite cabins on the Ferris wheel have number difference of 16.

If one of the cabins has a number 14, the opposite cabin has number of:

The polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

Given the polynomial function below

F(x)=x³-x² + 4x-4

Group

F(x)=(x³-x²) + (4x-4)

f(x) = x²(x-1)+4(x-1)

f(x) = (x²+4)(x-1)

If f(x) = 0

x²+4 = 0 and x -1. = 0

x² = -4 and x = 1

x = ±2i and -1

Hence polynomial with a root 2i and exactly 2 real roots is F(x)=x³-x² + 4x-4

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Answer:

x=1

Step-by-step explanation:

Answer:

1960

Step-by-step explanation:

1960

times 56 times 7 time 5 = 1960

Answer:

66.4 in^2

Step-by-step explanation:

Surface area is defined as the area around the surface of a 3-dimensional solid. The shape we are given here is a triangular prism with a square base. This means it contains one square and 4 triangles on the surface. To find the surface area, we just need to find the areas of all 5 surface shapes and add them up. We have been given that the square has a side length of 4 inches, meaning the area is 4^2 or 16. The area of a triangle is (1/2)base*height. The base length is 4 inches and the height is 6.3, and (1/2)*4*6.3 is 12.6. Note that, since there are four triangles, we have to multiply this value by 4 (12.6*4 = 50.4). Now we have the area of the square and the area of all the triangles put together, so we can just add them up:

16 + 50.4 = 66.4

500 people

200 people wearing red shirts

200x15%= 30 people

30 =6% of 500

n^3 + 6

I'll make n stand for the number

Six more means adding extra 6 onto our number cubed.

So, n x n x n = n^3

(n^3 means n cubed)

Thus, answer is n^3 + 6

Hope this helps!

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

According to the triangle inequality theorem, the sum of any two sides of a given triangle must be greater than the length of the measure of the third side of the triangle.

Thus, given an acute triangle has sides, 8 cm and 10 cm, applying the triangle inequality theorem, the range of sides would be calculated as shown below:

10 - 8 < s > 8 + 10

2 < s > 18

The range of values for the third side is: A. 2 < s < 18.

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Answer: A. 2 < s < 18.

Step-by-step explanation:

Applying the triangle inequality theorem, the best representation for the third side is: A. 2 < s < 18.

Answer:

I don't know how to answer this, sorry!

Step-by-step explanation:

By combining the equations we can found that the number of impulse clothing and Opal essence stores by equations be C (3x+5)/2 where x is the number of years after the brand's founding.

Given The equation showing number of impulse clothing stores is C=2x. The equation showing number of clothing stores be C=x+5.

We have to first plot both the equations on the graph.

For plotting we need points which can be calculated as

C=2x

when x=1 ,C or y=2

when x=3 , C or y=6

C=x+5

when x=0 ,C or y=5

when x=1 ,C or y=6

By combining both equations we get

C=(3x+5)/2

Plot this also and finding points

when x=0  , C=5/2

when x=1 , C=4

Hence the combination of both statements which shows the total stores owned is C=(3x+5)/2

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Answer:

So, after

3

years, Impulse Clothing and Opal Essence will own the same number of clothing stores.

The total number of stores during that year will be 8.

Answer: 65

Step-by-step explanation:

By the geometric mean theorem, the length of the altitude to the hypotenuse has length [tex]\sqrt{25 \cdot 144}=60[/tex]

So, by the Pythagorean theorem,

[tex]x=\sqrt{60^2 + 25^2}=65[/tex]