The equation for that graph is f(x) = 3 sin 8x. Nothing else is correct. THere is no horizontal shift (phase shift), nor is there vertical shift. Just a period adjustment.
3 sin 8x
49x^2-84x+k
Step-by-step explanation:
step 1. the perfect square will look like this: (7x + a)(7x + a) = (7x + a)^2.
step 2. by performing FOIL you will get 49x^2 + 14xa + a^2.
step 3. 14a = 84. a = 6
step 4. a^2 = 36.
step 5. k = 36.
2) x²+10x+21=0
3) x²+8x+15=0
4) x²+9x+14=0
5) x²-2x35=0
Answer:
Step-by-step explanation:
To solve these quadratic equations by factoring, you need to find two numbers that multiply to the constant term (the number without x^2) and add up to the coefficient of the linear term (the number with x). Here are the solutions for each of the equations:
1. x² + 5x + 6 = 0
We need two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.
So, we can factor the equation as (x + 2)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 2 = 0 => x = -2
x + 3 = 0 => x = -3
So, the solutions are x = -2 and x = -3.
2. x² + 10x + 21 = 0
We need two numbers that multiply to 21 and add up to 10. The numbers are 7 and 3.
So, we can factor the equation as (x + 7)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 7 = 0 => x = -7
x + 3 = 0 => x = -3
So, the solutions are x = -7 and x = -3.
3. x² + 8x + 15 = 0
We need two numbers that multiply to 15 and add up to 8. The numbers are 5 and 3.
So, we can factor the equation as (x + 5)(x + 3) = 0.
Now, set each factor equal to zero and solve for x:
x + 5 = 0 => x = -5
x + 3 = 0 => x = -3
So, the solutions are x = -5 and x = -3.
4. x² + 9x + 14 = 0
We need two numbers that multiply to 14 and add up to 9. The numbers are 7 and 2.
So, we can factor the equation as (x + 7)(x + 2) = 0.
Now, set each factor equal to zero and solve for x:
x + 7 = 0 => x = -7
x + 2 = 0 => x = -2
So, the solutions are x = -7 and x = -2.
5. x² - 2x - 35 = 0
To factor this equation, we need two numbers that multiply to -35 and add up to -2. The numbers are -7 and 5.
So, we can factor the equation as (x - 7)(x + 5) = 0.
Now, set each factor equal to zero and solve for x:
x - 7 = 0 => x = 7
x + 5 = 0 => x = -5
So, the solutions are x = 7 and x = -5.
For this case, we have that by definition, the proportions can be expressed in different ways. Example, if we have a dog and three cats:
75%: It's percentage
0.75: In decimal (75% are cats)
: In fraction. (There are of cats)
: Using ":" to separate sample values. (For every three cats there is a dog)
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.
Example:
Answer:
Care should be taken with the proportions, always multiplying the numbers in the proportion by the same value.