b) The ratio of boys to girls in a school is 12:25. If there are 120 boys.
(i) how many girls are in the school?
(ii) what is the total number of boys and girls in the school?

The gradient of a line which perpendicular to C is -3/2

The gradient of a line shows how steep it is. Gradient is also called the slope of a line.

Let's use the fact that the product of the gradients of two perpendicular lines is -1 to determine the gradient of a line perpendicular to line C.

We can determine the gradient of the line perpendicular to C if the gradient of line C is 2/3.

Take the negative reciprocal of the gradient, we have;

-3/2

Since the negative reciprocal of 2/3 is -3/2.

Therefore, the gradient of the line perpendicular to C is -3/2.

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Answer:

h≤18

Step-by-step explanation:

Step  1  :

Solve Basic Inequality : 1.1      

Add  18  to both sides h ≤ 18

Inequality Plot

Inequality plot for

        h  - 18.000  ≤  0

Answer: h≤18

Hope this helps.

Answer:

41

Step-by-step explanation:

Matrix Multiplication follows a row-column format. In order to compute this, you must be familiar with vector dot products.

With that in mind, lets get straight into it.

The order that matrix multiplication follows means that the terms in the result are filled in left to right, then top to bottom.

Therefore, a21 will be the 3 value that is computed. This is important becuase this allows to directly compute a21, instead of using up a lot of time computing all the values before.

As a21 is located in the bottom row 1st column, we take the dot product of the 2nd row in matrix 1 and the 1 column in matrix two.

So we have:

(7 2) dot (5 3) = 7*5 + 2*3 = 41

Answer:

a = 20.79cm ( 2 decimal places)

Step-by-step explanation:

find the length of the identical sides (i name it "x") first using Pythagoras theorem

[tex]14.8^{2}[/tex] = [tex]x^{2} + x^{2}[/tex]

219.04 = [tex]2x^{2}[/tex]

[tex]x^{2}[/tex] = 219.04/2 = 109.52

x = [tex]\sqrt{109.52}[/tex]

now find a,

[tex]a^{2}[/tex] = [tex](\sqrt{109.52}) ^{2}[/tex] + [tex](7.5 + \sqrt{109.52}) ^{2}[/tex]

[tex]a^{2}[/tex] = 109.52 + 322.7477 = 432.2677

a = [tex]\sqrt{432.2677}[/tex] = 20.791048

Answer:

150

Step-by-step explanation:

A=bh

A=15×10

A=150

Answer:

150

Step-by-step explanation:

it is just like finding the area of a rectangle! 10*15=150

to do this all you have to do is make the denominator 1 and the numerator should be 1.566666667

Answer:

To find the y-intercept, graph the points, and draw a line that passes through them. the place that it passes the y-axis is the y-intercept. To find the slope, find two points on the line. Take the increase in the y-coordinate and divide it by the increase in the x-coordinate.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

She made [tex]18\frac{1}{15}[/tex] cups of lemonade in total.

Step-by-step explanation:

A fraction contains a numerator(upper value) and denominator(lower value). The total cup of lemonade that Beatrice made is 25 1/3.

A fraction contains a numerator(upper value) and denominator(lower value).

When the numerator is less than the denominator, the fraction is called a proper fraction, otherwise, it is called an improper fraction.

A mixed fraction can be converted as,

2 1/2

= (2×2 + 1)/2

= 5/2

= 2.5

Given that Beatrice made lemonade twice, first, she made 7 2/3 cups of lemonade and in the second turn, she made 10 3/5 more cups of lemonade. Therefore, the total cups of lemonade that Beatrice made is,

Total cups of lemonade = 7 2/3 + 10 3/5

= 23/3 + 53/5

= (23×5 + 53×3)/(3×5)

= (115 + 265)/15

= 380/15

= 25 5/15

= 25 1/3

Hence, the total cup of lemonade that Beatrice made is 25 1/3.

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Answer:

Step-by-step explanation:

(f+g)(x) = f(x) + g(x)

           = 4x + 1 + x² - 5

            = x² + 4x  - 4

Answer:

x^2 +4x -4

Step-by-step explanation:

f(x) = 4x+1

g(x) = x^2-5

(f+g)(x) =  4x+1 + x^2 -5

Combine like terms

            = x^2 +4x +1-5

              =x^2 +4x -4

Answer:

Shape

Step-by-step explanation:

Shape because if you make the boat the right shape, it has a better chance of floating.

Answer:

[tex] \frac{400 \times 5 \times 2}{100} [/tex]

Answer A is correct

Step-by-step explanation:

[tex]p = 400 \\ r = 5\% \\ t = 2 \: \: years[/tex]

Now let's find the simple interest.

[tex] \frac{prt}{100 } \\ = \frac{40 0 \times 5 \times 2}{100} \\ = 40[/tex]

hope this helps

brainliest appreciated

good luck! have a nice day!

Answer:

It's a).

Step-by-step explanation:

I = PRT/100

- where I = the interest , P = initial amount, R = annual rate and T is the time in years.

So the answer is (400*5*2) / 100.

Answer:

x^2 + 11x - 13

Step-by-step explanation:

A = 3x^2 + 5x - 6

B = 2x^2 - 6x + 7

=> A - B = (3x^2 + 5x - 6) - (2x^2 - 6x + 7)

             = (3x^2 - 2x^2) + (5x + 6x) - (6 + 7)

             = x^2 + 11x - 13

I hope this helps!

Answer:

=

−

1

2

×

3

2

=

1

×

9

=

9

Step-by-step explanation:

f

(

−

3

)

=

9

Explanation:

f

(

x

)

=

x

2

To find f(-3) replace

x

in the function by

−

3

Therefore:

f

(

−

3

)

=

(

−

3

)

2

=

−

1

2

×

3

2

=

1

×

9

=

9

Answer:

9

Step-by-step explanation:

f(x) = x²

f(-3) =(-3)² = (-3)*(-3) = 9

Answer:

2/3

Step-by-step explanation:

32/48= 16*2/16*3= 2/3

Answer:

You have the right answer.

Step-by-step explanation:

The image might be blurry but its the best I can post.

That's solving it without the x and y values. Its still the answer you picked.

Hope this helps, have a good day! :)

(Brainliest would be appreciated?)

Answer:

5√xy

Step-by-step explanation:

√25x²y²/√xy= √25x²y²/xy= √25xy= 5√xy

Answer:

Step-by-step explanation:

The next term of a Fibonacci sequence is generated by taking the sum of the 2 preceding value of the sequence. Given the the first and third term of a Fibonacci sequence to be x and y

x, _, y...

let the second term be a, fourth term be b and fifth term be c to have the sequence;

x, a, y, b, c...

According to the definition;

x+a = y... 1

a+y = b... 2 and;

y+b = c... 3

From equation 1, a = y-x

Substituting a = y-x into equation 2 to get b we have;

(y-x)+y = b

2y-x = b

b = 2y-x

Substituting b = 2y-x into equation 3 to get 'c'

y +  2y-x = c

3y-x = c

c = 3y-x

The second term of the sequence is y-x

The fourth term of the sequence is 2y-x

The fifth term of the sequence is 3y-x

Answer:

r=8

Step-by-step explanation:

Because 16 divided by 2 is 8

The radius of a circle has a circumference of 16 at r = 8.

Given: the formula for the circumference of a circle is C = 2r, where r is the radius and C is the circumference.

The circumference of a circle is equal to π.

π ≈ 3.14

multiplied by the diameter of the circle.

Therefore, the diameter has twice the length of the radius.

In equation form:

2r = d.

2r = 16.

r = 8.

Note, 2r = d,

Then, the equation C = 2πr holds and can be used in place of C = πd.

The radius of a circle has a circumference of 16 at r = 8.

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Answer:

Both brothers will have the same amount of money is their saving accounts after six months.

Step-by-step explanation:

I worked this out by finding out the first 8 months of savings for both brothers:

Patrick:               His brother:

200                     150

225                     185

250                     220

275                     253

300                     290

325                     325

375                     360

400                     395

I then looked across my results to see that at 6 months both brothers had $325.

Hope this helped.

Answer:

The answer would be 18

Step-by-step explanation:

the formula for area of a triangle is 1/2b*h

so would mulitply 3*3 and get 9/2 which would be 4.5 do that on the otherside and you would get 4.5 again add together and you would get 9

for the square you would calculate the area by multplying b*h to get 9 so 9+9=18

Answer:

The answer is D.

Step-by-step explanation:

Angle 1 and 2 are equivalent to the measure of angles 3+4. We know this because both sides on the middle line form a 90 degree angle

I hope this helps :)

Answer:

x^2+x+3

Step-by-step explanation:

y=x-7

x-7=x^2+2x-4

x^2+2x-4-x+7

x^2+x+3

Answer: x-7=x^2+2x-4

A P E X

Step-by-step explanation:

but also, if you are wondering how I got to that answer, you substitute y in for the y equation. Since y=x-7 you’ll take that why and put in in the y in (y)=x^2+2x-4.

Answer:

75

Step-by-step explanation:

It's D on edg

The number of minutes it take Arnob to catch up to Kathleen is 75 minutes.

Given:

Mile head start=5 mile

Distance along y-axis=2 lines

Hence:

y=1/15x+5

=y=2/15x

So,

1/15x+5=2/15x

1/15x=5

x=75 minutes

The correct option is D.

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Answer:

(2,-1)

Step-by-step explanation:

Multiply the original coordinates by 1/3

Answer:

[tex]n^{26}[/tex]

Step-by-step explanation:

[tex]n^{3 \times 2} \times n^{5 \times 4}[/tex]

[tex]n^{6} \times n^{20}[/tex]

[tex]n^{6+20}[/tex]

[tex]n^{26}[/tex]

Answer:

N^26

Step-by-step explanation:

N ^3^2 = n^6

N^5^4 = n^20

Multiply. Use laws of exponents

N^6 x n^20 = n^20+6 = n^26

Hope this helps

1) 180 square cm

Answer:

2) 41 cubic cm

Step-by-step explanation:

1)

Area of pool = 12 * 15 = 180 square cm

2) Volume of water = 1/3 * Volume of pool

= 1/3 *123

= 41 cubic cm

Answer:

The correct answer is D. 360°

Step-by-step explanation:

The sum of all the exterior angles of a regular n-gon or a polygon is always equal to 360°.

Let us consider the image attached.

First of all let us consider the triangle.

As per the property of exterior angles: The exterior angle is equal to the sum of 2 opposite interior angles.

[tex]\Rightarrow \angle 1=\angle B + \angle C\\\Rightarrow \angle 2=\angle A + \angle C\\\Rightarrow \angle 3=\angle A + \angle B[/tex]

Where [tex]\angle A, \angle B\ and\ \angle C[/tex] are the interior angles of the triangle.

Adding the above equations:

[tex]\angle 1 +\angle 2 +\angle 3 = 2 \times (\angle A +\angle B +\angle C )[/tex]

The sum of interior angles of a triangle is always equal to 180°

[tex]\angle A +\angle B +\angle C = 180^\circ[/tex]

[tex]\angle 1 +\angle 2 +\angle 3 = 2 \times 180^\circ\\\Rightarrow \angle 1 +\angle 2 +\angle 3 = 360^\circ[/tex]

Hence, proved that the sum of exterior angles is [tex]360^\circ[/tex].

So, the correct answer is D. [tex]360^\circ[/tex]