A. Vertical stretch of 1/4 hortionzal stretch to a period of 2pi , phase shift of pi/6 units to the left
Point slope form: y - y1 = m (x - x1)
-------------------------------------------------
first you need to find the slope(m) by using the slope formula (seen below)
y2 - y1
m= ---------
x2 - x1
9 - 15
m= ---------
1 - (-2)
-6
m= --------- = -2
3
then choose either one of the coordinates you'd like and plug it in.
Im gonna use (-2, 15)
(y - 15) = -2 (x - (-2))
or
(y - 15) = -2 (x + 2)
slope intercept form: y = mx + b
-----------------------------------------------
you can use the slope formula to find that the slope(m) is -2
y = -2x + b
you can then plug in a coordinate to find b (the y-intercept)
I'll use (-2,15)
15 = -2(-2) +b
15 = 4 + b
-4 -4
---------
11 = b
in conclusion:
the slope(m) = -2
when (-2,15) is used
x = -2
y = 15
b = 11
standard form: ax + by = c
----------------------------------------
using the same coordinate (-2,15)
-2a + 15b = c
Answer:
The answer is 7 cups
Step-by-step explanation:
1 cake-2 2/6 cups
Which can also be written as
1 cake-14/6 cups
3 cakes-x cup
Cross multiply
x=14/2
x=7
Therefore Karen needs 7 cups of flour to make 3 cakes
The solution of the system of equations is (6 , -7)
Step-by-step explanation:
There are two method to solve the system of equations
- Elimination method: we make the coefficients of one variable in the two equations have same values and different signs, then we add the two equations to eliminate this variable and have an equation of other variable, we solve it to find the other variable, then substitute the value of this variable in one of the two equations to find the first variable
- Substitution method: We use one of the two equations to find one variable in terms of the other, then substitute it in the second equation to have an equation of the other variable, we solve it to find the other variable, then substitute the value of this variable in the equation of the first variable
Let us use the elimination method with your problem
∵ 3x + 2y = 4 ⇒ (1)
∵ 3x + 6y = -24 ⇒ (2)
- Multiply equation (1) by -1 to eliminate x ⇒ to make the coefficients of x in the two equations have same values and different signs
∵ -3x - 2y = -4 ⇒ (3)
- Add equations (2) and (3)
∴ 4y = -28
- Divide both sides by 4
∴ y = -7
Substitute value of y in equations (1) OR (2) to find x
∵ 3x + 2(-7) = 4
∴ 3x - 14 = 4
- Add 14 for both sides
∴ 3x = 18
- Divide both sides by 3
∴ x = 6
The solution of the system of equations is (6 , -7)
<em>I hope this explanation help you</em>
Learn more:
You can learn more about the system of linear equations in brainly.com/question/6075514
#LearnwithBrainly
Answer:
x = 10
Step-by-step explanation:
Using the Pythagorean theorem:
8² + 6² = x²
64 + 36 = x²
x² = 100
x = 10
