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natulia [17]
3 years ago
15

Hello I don’t understand question 9 a and b. Please show working out. Thanks

Mathematics
1 answer:
brilliants [131]3 years ago
3 0
A) I would make the positive integer x and then form an equation.

x + 30 = x^2 - 12
x + 42 = x^2
0 = x^2 - x - 42 this can be factorised
(x - 7) ( x + 6) Therefore x = 7 or x = -6

Since the question asks for a positive integer the answer is 7.

B) two positive numbers x and y.

X - y = 3
x^2 + y^2 = 117

Use these simultaneous equations to figure out each number.

Rearrange the first equation

x = y + 3

Then substitute it into the second equation.

(y+3)^2 + y^2 = 117
y^2 + 6y + 9 + y^2 = 117
2y^2 + 6y - 108 = 0
then factorise this.
(2y - 12) (y + 9)

This means that y = 6 or y = -9 but it’s 6 because that’s the only positive number.

Use y to find x

x = y + 3
x = 6 + 3
x = 9

So the answers are x = 9 and y = 6.
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3 years ago
Find the measure of the missing angles.<br> 62°<br> b\co
tiny-mole [99]

The measures of angles B and C are 118° and 62°, respectively.

<h3>What are the measures of two missing angles generated by the intersection of two lines?</h3>

A system of three angles is generated by two lines intersecting each other. In accordance with Euclidean geometry, angle C is opposite to the angle with measure 62° and angle B is supplementary to the same angle.

When two angles are opposite, then both have the same measure, and when two angles are supplementary, then the sum of their measures equals 180°. Therefore, the measures of angles B and C are 118° and 62°, respectively.

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Leto [7]

Answer: B, angle 1 and angle 7.

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2 years ago
At what point is the function y=(x+3)/(x^(2)-7x+12) continuous
nika2105 [10]

If a function is defined as

h(x)=\dfrac{f(x)}{g(x)}

where both f(x),g(x) are continuous functions, then h(x) is also continuous where defined, i.e. where g(x)\neq0

So, in your case, this function is continous everywhere, except where

x^2-7x+12=0

To solve this equation, we can use the formula x^2-sx+p=0

It means that, if the leading terms is 1, then the x coefficient is the opposite of the sum of the roots, and the constant term is the product of the roots.

So, we're looking for two terms whose sum is 7, and whose product is 12. These numbers are easily found to be 3 and 4.

So, this function is continuous for every real number different than 3 or 4.

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A Number decreased by the square of 9
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3 years ago
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