ABC is a straight line.




The length AB is five times the length BC .

AC =90 cm.


Work out the length AB .


(3 marks)

Use the Pythagorean Theorem  [tex]a^2 + b^2 = c^2[/tex].

Since we have 2 sides we can easily solve for the third.

[tex]c^2 = 10^2 + 14 ^2[/tex]

[tex]c = \sqrt{100 + 196}[/tex][tex]= \sqrt{296}[/tex] ≈[tex]17.205[/tex]

Revenue, profit and expenses are all integral parts of a company's balance sheet

The expense function is given as:

[tex]\mathbf{E = 8q + 12000}[/tex]

The demand function is given as:

[tex]\mathbf{p = -10p + 20000}[/tex]

(a) The expense in terms of q

This is already given as: [tex]\mathbf{E = 8q + 12000}[/tex]

(b) The expense in terms of p

Substitute -10p + 20000 for p in [tex]\mathbf{E = 8q + 12000}[/tex]

[tex]\mathbf{E = 8(-10p + 20000) + 12000}[/tex]

Expand

[tex]\mathbf{E = -80p + 160000 + 12000}[/tex]

[tex]\mathbf{E = -80p + 172000}[/tex]

(c) The revenue in terms of P

This is calculated as:

[tex]\mathbf{R = p \times q}[/tex]

So, we have:

[tex]\mathbf{R = p \times (-10p + 20000)}[/tex]

Expand

[tex]\mathbf{R = -10p^2 + 20000p}[/tex]

(d) The profit in terms of p

We have:

[tex]\mathbf{R = -10p^2 + 20000p}[/tex] and [tex]\mathbf{E = -80p + 172000}[/tex]

So, the profit P is calculated as:

[tex]\mathbf{P =R - E}[/tex]

This gives

[tex]\mathbf{P =-10p^2 + 20000p +80p - 172000}[/tex]

[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

(e) The price that yields maximum profit

In (d), we have:

[tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

The maximum price is calculated using:

[tex]\mathbf{p = -\frac{b}{2a}}[/tex]

Where:

[tex]\mathbf{b =20080}[/tex]

[tex]\mathbf{a = -10}[/tex]

So, the equation becomes

[tex]\mathbf{p = -\frac{20080}{2 \times -10}}[/tex]

[tex]\mathbf{p = 1004}[/tex]

Hence, the price that yields the maximum profit is $1004

(f) The maximum profit

In (e), we have: [tex]\mathbf{p = 1004}[/tex]

Substitute 1004 for p in [tex]\mathbf{P =-10p^2 + 20080p - 172000}[/tex]

[tex]\mathbf{P =-10(1004)^2 + 20080(1004) - 172000}[/tex]

[tex]\mathbf{P =9908160}[/tex]

Hence, the maximum profit is $9908160

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Answer:

y = 2x +2

Step-by-step explanation:

The general slope-intercept equation of a line is y=mx+b , where m is the slope and b is the y-intercept ( where the line intersects the y-axis)

From the graph we see that

m= difference in y/difference in x = (6 - -6)/ (2- -4) = 12/6 = 2

m=2 is the slope

b is where the line cuts the y-axis and is at 2

b=2 is the y-intercept

Substitute m and b in the general equation to find the equation of the graphed line.

y = 2x +2

the answer is 524.47500

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Answer:

Parallel

Step-by-step explanation:

Using these points, we can determine that the equation is as follows:

Line B: y = -2/3x + 7/3

And since Line A has the same slope, it would make Line A's equations like this:

Line A: y = -2/3x - 11/3

This makes these equations Parallel to each other because they have the same slope with different y-intercepts.

Answer:

not enough info .

Step-by-step explanation:

sorry it needs more info

Answer: Permutation is 30

Step-by-step explanation:

Answer:

81/256

Step-by-step explanation:

The exponent 4 is meaning how many times you have to multiply a number it is on top of.

So you need to multiply 3/4, 4 times by itself

So

3/4* 3/4* 3/4* 3/4

3 times 3 times 3 times 3 is 81

4 times 4 times 4 times 4 is 256

So the answer is 81/256

Hope this helps!

Answer: Obtuse

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Answer: z = 18

Step-by-step explanation:

180 = 90 + (3z+4) + (2z-4)

z = 18

Answer:

C

Step-by-step explanation:

Slope of a line that goes trough the points (x1=9, y1=1) and (x2=17, y2=2)

m= (y2-y1)/(x2-x1) = (2-1) / (17-9) = 1/8

Answer:

9 1/3

Step-by-step explanation:

7 - 75%

x - 100%

[tex]\frac{7 * 100}{75} = 9\frac{1}{3}[/tex]

Answer:

7 is 75% of What Number? - 7 is 75% of 9.33. 100% of 9.33 is 9.33, therefore 75 percent of 9.33 equals 7.

Step-by-step explanation:

7 is 75% of What Number? - 7 is 75% of 9.33. 100% of 9.33 is 9.33, therefore 75 percent of 9.33 equals 7.

c because the center of dilation is the multiplicatory value of the original point

Answer:

4x  + 2y  ≤  25   ,      x + y ≥  8     is the required system of inequalities to represent the given situation.

Step-by-step explanation:

Here, let  the number of color copies =  x

Now, the time taken to print each color copy = 4 minutes

⇒Time taken to print x color copies = x times ( Time taken by each copy)

= 4 (x)   = 4x

and let  the number gray scale copies =  y

The time taken to print each gray scale copy = 2 minutes

⇒Time taken to print y gray scale copy = y times (Time taken by each copy)

= 2 (y)   = 2y

Total copies printed = x + y

Maximum time taken to print x  color copies and y grayscale copies

= 4x  + 2y

So, according to the question:

4x  + 2y  ≤  25 ( as maximum allotted time is 25 minutes)

and x + y ≥  8      (as minimum number of copies is 8)

hence, the above system is the required system of inequalities to represent the given situation.

I hope this helps.

Answer:

61 miles

does this help??

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

Answer:

[tex]\boxed{\sf Slope:3/8}[/tex]

Step-by-step explanation:

To determine the slope of a line given the coordinates of two points on the line, use the slope formula.

[tex]\boxed{\sf \sf{Slope\;(m)}=\frac{y_2-y_1}{x_2-x_1}}[/tex]

x1 and y1 are the coordinates of the first point. The second point's coordinates are x2, y2.

Points: [tex]\sf (-6, 4) \:and \:(2, 7)[/tex]

[tex]\longmapsto\sf \left(x_1,\:y_1\right):\left(-6,\:4\right)[/tex]

[tex]\longmapsto\sf \left(x_2,\:y_2\right)=\left(2,\:7\right)[/tex]

_______________

[tex]\leadsto\sf m=\cfrac{7-4}{2-\left(-6\right)}[/tex]

[tex]\leadsto\sf m=\cfrac{3}{8}[/tex]

_________________________________________

Answer: where is the question??

what do you need help with?

Answer:

Step-by-step explanation:

Remove The decimal,

= > 0.012 = 12/100

= > 3/25...ans

Answer:

Zara ate 50 almonds last week

Step-by-step explanation:

part to whole ratio is 50 : 100

150 divided by 2 is 75

100 divided by 50 is equal to 2

Zara ate 50 almonds last week

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Answer:

The value of this expression is 48

Step-by-step explanation:

15 + c2 * d - c3

c = 3

d = 7

Substitute the values of c and d

15 + (3)2 * 7 - (3)3

Multiply the parenthesis first

15 + 6 * 7 - 9

Now multiply 6 and 7

15 + 42 - 9

Now add 15 and 42

57 - 9

Now subtract

= 48

Answer:

48

Step-by-step explanation:

When you write out the problem it should look like this

15+c⋅2⋅d-c⋅3

or in other form

15+3⋅2⋅7-3⋅3

You can solve using PEMDAS

Paratheses

Exponents

Multiplication

Division

Addition

Subtraction

Just use those in order and you should find to answer.

-Rocketgamer360

Answer:

Y=-4x+99

Step-by-step explanation:

Your y intercept is always the last number in the equation

The equation in slope-intercept form to represent the temperature y after x hour is Y=-4x+99

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

Given that At 1:40 PM, the temperature is 99˚F. For the rest of the evening, the temperature drops an average of 4˚F per hour.

Therefore, the slope of the line is;

m = Δy/Δx

m = 4

The equation in slope-intercept form is;

Y=-4x+99

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Option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Radius of a circle is the distance from the center of the circle to any point on it's circumference.

The distance across a circle through the centre is called the diameter.

Diameter = 2 × radius

In the given figures, option B has a diameter of 20

so radius = diameter /2

=20/2

=10 units

Hence, option B is correct, the circle with center F and diameter 20 units is the circle which has a radius of 10 units.

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Answer:The first option is correct

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

3rd option because m is bigger than or equal -2 which means that it is going to be from [-2,infinity[

Answer:

8 months

Step-by-step explanation:

12/3 = 4, 1/3 is 4 so 1/3 + 1/3 = 2/3 or 8

Answer:

Step-by-step explanation:

12-b

13-c

14-a

15-d

16-b

17-c

18-d]

Step-by-step explanation:

Answer:

The car will drive 60 miles in 60 minutes (an hour)

Step-by-step explanation:

For every hour driven (60 minutes) the person will drive 60 miles, therefore it will travel a distance of 60 miles in 60 minutes

Answer:

7 and 1 / 2

Step-by-step explanation:

xy = 9

( 1 / x ) = 4 ( 1 / y )

y = 4x

x ( 4x ) = 9

4x^2 = 9

x = 3 / 2

( 3 / 2 ) y = 9

y = 6

6 + ( 3 / 2 ) = 7 and 1 / 2

The two numbers are 3/2 and 6.

The reciprocal of a number is this fraction flipped upside down.

Given that, The product of two positive numbers is 9. The reciprocal of one of these numbers is 4 times the reciprocal of the other number.

Let the numbers be a and b.

ab = 9.......(i)

1/a = 4/b

a = 4b..........(ii)

Using (i) in (ii)

4b×b = 9

b² = 9/4

b = 3/2

a×3/2 = 9

a = 6

Hence, The two numbers are 3/2 and 6.

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