Answer: the number of roses sold is 69 while number of tulips is 37
Step-by-step explanation:
Let x represent the number of roses that the flower shop sold.
Let y represent the number of tulips that the flower shop sold.
The number of roses sold was 5 less than twice the number of tulips sold. This means that
x = 2y - 5 - - -- -- - - - - - ;1
If the shop sold 106 flowers in total, it means that
x + y = 106
Substituting x = 106 - y into equation 1, it becomes
106 - y = 2y - 5
3y = 106 + 5 = 111
y = 111/3 = 37
x = 106 - y = 106 - 37
x = 69
Here are some things you should know when solving algebraic equations.
If you add an expression to both sides of an equation, the resulting equation will have the same solution set as the original equation. In other words, they will be equivalent. This is true for all operations. As long both sides are treated the same, the equation will stay balanced.
You will also need to know how to combine like terms. But what are like terms to begin with? Like terms are defined as two terms having the same variable(s) (or lack thereof) and are raised to the same power. In mathematics, something raised to the first power stays the same. So, 5x and 10x are like terms because they both have the same variable and are raised to the first power. You don’t see the exponents because it doesn’t change the value of the terms.
To combine like terms, simplify add the coefficients and keep the common variable(s) and exponent.
The distributive property is another important rule you will need to understand.
The distributive property is used mostly for simplifying parentheses in expressions/equations.
For example, how would you get rid of the parentheses here?
6(x + 1)
If there wasn’t an unknown in between the parentheses, you could just add then multiply. That is what the distributive property solves. The distributive property states that a(b + c) = ab + ac
So, now we can simplify our expression.
6(x + 1) = 6x + 6
Now let's solve your equation.
9v = 8 + v
8v = 8 <-- Subtract v from each side
v = 1 <-- Divide both sides by 8
So, v is equal to 1.
Y-Intercept= -9
Your equation is Y=mx+b, and b is the Y-Intercept
Answer:
3x - y = 0; 2x - y = -5
Step-by-step explanation:
Let x be the present age of Hans and y be the present age of Grace,
Since, in present Grace is three times as old as Hans,
⇒ y = 3x
⇒ 3x - y = 0
Now, after 5 years,
The age of Hans = x + 5,
And, the age of Grace = y + 5
Also, in 5 years Grace will be twice as old as Hans is then,
⇒ y + 5 = 2 ( x + 5 )
⇒ y + 5 = 2x + 10
⇒ 2x - y = -5
Hence, the required system of linear equations is,
3x - y = 0; 2x - y = -5
Answer:
If it is ax^2 + bx + c = 0 then it is a quadratic equation
Step-by-step explanation:
