Which sum or difference is equivalent to the following expression? 5-3x

Mathematics

1 answer:

nikklg [1K]3 years ago

6 0

Answer:

Step-by-step explanation:

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the height of a triangle is 9m less than its base. the area of the triangle is 56 m^2 find the length of the base (SHOW STEPS)

Veronika [31]

Hey there :)

We know the area formula of a triangle
$\frac{1}{2} (base)(height)$

We are given:
The area = 56 m²
The base = let p represent this
The height = 9 m less than the base = p - 9

Apply the formula
56 = $\frac{1}{2}$ × ( p ) × ( p - 9 )
56 = $\frac{1}{2}$ × ( p² - 9p )

Divide $\frac{1}{2}$ on both sides
56 ÷ $\frac{1}{2}$ = p² - 9p
112 = p² - 9p

Bring 112 to the other side and equate equation to 0
p² - 9p - 112

Factorise { Sum = -9 , Product = - 112 , therefore suitable factors = - 16 × 7 )
( p - 16 )( p + 7 ) = 0
↓ ↓
p = 16 p = - 7 ← Reject p = - 7 since length cannot be negative

So, the length of the base is 16 m

Check:
56 m² = $\frac{1}{2}$ × 16 × ( 16 - 9 )
56 m² = 8 × 7
56 m² = 56 m²

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3 years ago

If ED is tangent to circle H, find the value of x

AnnyKZ [126]

Answer:

x = 8

Step-by-step explanation:

Here, we want to find the value of x

According to the theorem;

45 = 1/2(147 - (7x-5))

90 = 147 -7x + 5

90 = -7x + 147