8 - (-d) = 43
8 + d = 43 <==
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.
You have a 300 feet side length square and you need to calculate the length of the diagonal. When you split the square along one diagonal you get triangles, so you can apply Pythagoras' Theorem, with the hypotenuse as the needed diagonal.
a²+b²=c²
300²+300²=c²
2*300²=c²
√(2*300²)=c
√(2) * √(300²)=c
√(2) * 300=c
c~424.26 ft which is the solution/option c
We can see that there are 5 CDs, each of radius 9 cm
<u>Area occupied by 1 disc:</u>
Area of a circle = πr²
Area of disc = π(9)²
Area of disc = 3.14 * 81 = 254 cm²
<u>Area occupied by 5 discs:</u>
Area occupied by 5 discs = Area occupied by 1 disc * 5
Area occupied by 5 discs = 254 * 5
Area occupied by 5 discs = 1270 cm²
Answer:
m∠QTR = 98°
Step-by-step explanation:
From the picture attached,
Radii of the circle are TQ and TR measuring equal lengths.
Therefore, ΔTQR is a isosceles triangle.
Opposite angles of the equal sides will be equal in measure.
m∠RQT = m∠TRQ = 41°
By angle sum theorem,
m∠RQT + m∠TRQ + m∠QTR = 180°
41° + 41° + m∠QTR = 180°
m∠QTR = 180° - 82°
= 98°
Therefore, m∠QTR = 98°
