) b−4=−3 b= y3=−12 y= −2(r+4)=36 r= a2−4+a4=14 a= 2+13t=1+14t t= 8(h−1)=6h+4+2h h=

Answer 1

To solve the equations given:

1) b - 4 = -3

Adding 4 to both sides gives:

b = 1

2) y/3 = -12

Multiplying both sides by 3 gives:

y = -36

3) -2(r + 4) = 36

Expanding and simplifying gives:

-2r - 8 = 36

Adding 8 to both sides gives:

-2r = 44

Dividing both sides by -2 gives:

r = -22

4) a^2 - 4 + a^4 = 14

Rearranging the terms gives:

a^4 + a^2 - 18 = 0

This can be factored as:

(a^2 - 3)(a^2 + 6) = 0

Setting each factor equal to zero gives:

a^2 - 3 = 0 or a^2 + 6 = 0

Solving the first equation gives:

a^2 = 3

Taking the square root of both sides gives:

a = ±√3

Solving the second equation gives:

a^2 = -6

But since square roots of negative numbers are not real, there are no solutions for this equation.

So the possible solutions for a are:

a = √3 or a = -√3

5) 2 + 13t = 1 + 14t

Subtracting 1 and 13t from both sides gives:

1 = 14t - 13t

Simplifying gives:

1 = t

6) 8(h - 1) = 6h + 4 + 2h

Expanding and simplifying gives:

8h - 8 = 8h + 4

Subtracting 8h from both sides gives:

-8 = 4

This is not a true statement, so there is no solution for this equation.

Answer 2

The formula for the area of a triangle is A = bh/2 .(2 points) Solve the formula for height. h = A triangle has a base of 7cm and an area of 28 sq cm. What is its height? cm

Answer 3

To solve the formula for height, we need to isolate the variable h.

A = (bh) / 2

Multiply both sides of the equation by 2:

2A = bh

Divide both sides of the equation by b:

(2A) / b = h

So the formula for height is:

h = (2A) / b

Now, let's find the height of a triangle with a base of 7cm and an area of 28 sq cm.

Given:
b = 7 cm
A = 28 sq cm

Plugging these values into the formula for height, we have:

h = (2 * 28) / 7

Simplifying further:

h = 56 / 7

h = 8 cm

Therefore, the height of the triangle is 8 cm.