the ratio of boys to girls in the class is 5:7. there are 36 children in the class. how many more girls then boys are there in the class?

Answer:

q=35

Step-by-step explanation:

x2 - 12x + q = 0

Let the two roots be r and r+2.

Factor the quadratic expression:

(x - r)[x - (r + 2)] = 0

Expand, simplify, group like terms, and get

x2 - 2(r + 1)x + r(r + 2) = 0

Compare to

x2 - 12x + q = 0

and set equal the coefficients of like terms:

Coefficient of x:

-2(r + 1) = -12 ⇒ r + 1 = 6 ⇒ r = 5

(Then the other root is r + 2 = 5 + 2 = 7)

Constant term:

r(r + 2) = q ⇒ 5(5 + 2) = q

q = 35

Test the solution:

(x - 5)(x - 7) = x2 - 12x + 35

With two roots differing by 2, you get an equation of the form

x2 - 12x + q = 0

with q = 35.

When a subtraction problem is performed, the answer is the difference between the two numbers being subtracted.

What is subtraction

Subtraction is the mathematical operation of finding the result when one quantity is taken away from another.

For example, if you have the subtraction problem 7 - 3, the answer would be 4, as you are subtracting 3 from 7, resulting in a difference of 4.

Similarly, in the subtraction problem 15 - 8, the answer would be 7, as you are subtracting 8 from 15, resulting in a difference of 7.

In general, when performing a subtraction problem, you are finding the numerical difference between two values.

Learn more about subtraction at

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Answer:

v= whl

1200= h X 80

1200/ 80 = h

so the height is 15 unit

Step-by-step explanation:

Answer: (a) y = -3x + 10

Step-by-step explanation:

The slope of line CD is perpendicular to line OB, which means they have opposite and reciprocal slopes.

Step 1: Find the slope of OB using the formula:

(x₁, y₁) = (0, 0) and (x₂, y₂) = (3, 1)

Step 2: Find the slope of CD (opposite and reciprocal of OB)

Step 3: Input the perpendicular slope and the slope into the Point-Slope formula: y - y₁ = m(x - x₁)

(x₁, y₁) = (3, 1) because it is the point the line will pass through

y - 1 = -3(x - 3)

y - 1 = -3x + 9      distributed -3 into (x - 3)

y      = -3x + 10    added 1 to both sides

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The x-intercept of DQ is the same x-intercept as CD.  The x-intercept is when y = 0

y = -3x + 10

0 = -3x + 10

-10 = -3x       subtracted 10 from both sides

   divided both sides by -3