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3 years ago

If the difference of two numbers is 43 and the sum of the numbers is 13, what are the numbers?

Mathematics

1 answer:

meriva3 years ago

4 0

Answer:

Numbers are 28 and -15

Step-by-step explanation:

Mark first number X, and second number Y, then:

x-y=43

and

x+y=13

We get system of two equations. Solve it by add both them together:

x-y+x+y=43+13

2x=56

x=28 we get first number

x+y=13

28+y=13

y=13-28

y=-15

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

brilliants [131]

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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Step-by-step explanation:

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tensa zangetsu [6.8K]

Answer:

(a) AH < HC is No

(b) AH < AC is Yes

Step-by-step explanation:

Given

See attachment for triangle

Solving (a): AH < HC

Line AH divides the triangle into two equal right-angled triangles which are: ABH and ACH (both right-angled at H).

To get the lengths of AH and HC, we need to first determine the measure of angles HAC and ACH. The largest of those angles will determine the longest of AH and HC. Since the measure of the angles are unknown, then we can not say for sure that AH < HC because the possible relationship between both lines are: AH < HC, AH = HC and AH > HC

Hence: AH < HC is No

Solving (b): AH < AC

Length AC represents the hypotenuse of triangle ACH, hence it is the longest length of ACH.

This means that:

AH < AC is Yes

Solving (c): △AHC ≅ △AHB

This has been addresed in (a);

Hence:

△AHC ≅ △AHB is Yes

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