What is true and what is false
True or False x = −3 is a solution to the equation −3x^2 = −27
true or false (-4, 10) is a solution to the equation 10 − 5x = y
True -3 is indeed a solution to the equation −3x^2 = −27.
False (-4, 10) is not a solution to the equation 10 − 5x = y.
b−4=−3
b=
y/3=−12
y=
−2(r+4)=36
r=
a/2−4+a/4=14
a=
2+1/3t=1+1/4t
t=
8(h−1)=6h+4+2h h=
b = -1
y = -36
r = -21
a = 12
t = -24
h = -4
The formula for the area of a triangle is A = bh/2 .
Solve the formula for height. h =
A triangle has a base of 7cm and an area of 28 sq cm. What is its height?
To solve the formula for height, we can rearrange it as follows:
A = bh/2
Multiply both sides of the equation by 2:
2A = bh
Divide both sides of the equation by b:
h = 2A/b
Given that the base (b) is 7 cm and the area (A) is 28 sq cm, we can substitute these values into the equation to find the height (h):
h = 2(28)/7
h = 56/7
h = 8 cm
Therefore, the height of the triangle is 8 cm.
For the equation −3x^2 = −27, we can check if x = -3 is a solution by substituting -3 into the equation and simplifying it:
Replace x with -3:
-3(-3)^2 = -3(9) = -27
Since -27 is equal to -27, the equation holds true when x = -3. Therefore, the statement "x = −3 is a solution to the equation −3x^2 = −27" is true.
For the equation 10 − 5x = y, we need to check if the point (-4, 10) satisfies the equation.
Replace x with -4 and y with 10:
10 - 5(-4) = 10 + 20 = 30
Since 30 is not equal to 10, the equation does not hold true for the point (-4, 10). Therefore, the statement "(-4, 10) is a solution to the equation 10 − 5x = y" is false.
To determine whether a given statement is true or false, we need to substitute the values given and check if they satisfy the equation.
1. True or False x = −3 is a solution to the equation −3x^2 = −27:
To solve this, we substitute x = -3 into the equation and check if both sides are equal.
When x = -3:
-3(-3)^2 = -3(9) = -27
Since both sides are equal to -27, the statement is true.
2. True or False (-4, 10) is a solution to the equation 10 − 5x = y:
To check this statement, we substitute x = -4 and y = 10 into the equation and verify if both sides are equal.
When x = -4 and y = 10:
10 - 5(-4) = 10 + 20 = 30
Since the left side of the equation is 30 and the right side is y = 10, the statement is false.
In summary:
1. x = −3 is a solution to the equation −3x^2 = −27 (True).
2. (-4, 10) is a solution to the equation 10 − 5x = y (False).