How many solutions does the
equation have?
3(7/3 + 4/3) - 2x + 8 = 5x + 12

It only has one solution.

Step-by-step explanation:

Let's solve your equation step-by-step.

3( 7 /3 + 4 /3 )−2x+8=5x+12

Step 1: Simplify both sides of the equation.

3( 7 /3 + 4 /3 )−2x+8=5x+12

11+−2x+8=5x+12

(−2x)+(11+8)=5x+12(Combine Like Terms)

−2x+19=5x+12

−2x+19=5x+12

Step 2: Subtract 5x from both sides.

−2x+19−5x=5x+12−5x

−7x+19=12

Step 3: Subtract 19 from both sides.

−7x+19−19=12−19

−7x=−7

Step 4: Divide both sides by -7.

−7x /−7 = −7 /−7

x=1

x=1

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°