B=5
You need to get b by itself on the left side. 4b is multiplying 4 to b. You need to the opposite when you want the variable by itself. You would divide 4 to each side. 4 cancels out on the b so it turns into b. Then 4 divided by 20 is 5. B=5
Answer:
a) b = 8, c = 13
b) The equation of graph B is y = -x² + 3
Step-by-step explanation:
* Let us talk about the transformation
- If the function f(x) reflected across the x-axis, then the new function g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then the new function g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then the new function g(x) = f(x + h)
In the given question
∵ y = x² - 3
∵ The graph is translated 4 units to the left
→ That means substitute x by x + 4 as 4th rule above
∴ y = (x + 4)² - 3
→ Solve the bracket to put it in the form of y = ax² + bx + c
∵ (x + 4)² = (x + 4)(x + 4) = (x)(x) + (x)(4) + (4)(x) + (4)(4)
∴ (x + 4)² = x² + 4x + 4x + 16
→ Add the like terms
∴ (x + 4)² = x² + 8x + 16
→ Substitute it in the y above
∴ y = x² + 8x + 16 - 3
→ Add the like terms
∴ y = x² + 8x + 13
∴ b = 8 and c = 13
a) b = 8, c = 13
∵ The graph A is reflected in the x-axis
→ That means y will change to -y as 1st rule above
∴ -y = (x² - 3)
→ Multiply both sides by -1 to make y positive
∴ y = -(x² - 3)
→ Multiply the bracket by the negative sign
∴ y = -x² + 3
b) The equation of graph B is y = -x² + 3
Answer:
Angle 1 is 112°, 2 is 68°, 3 is 90°, 4 is also 90°, 5 is 22° and angle 6 is 158°
Step-by-step explanation:
To find angles 3 &4 and 2 &1, you subtract the measurement given in each intersection from 180 (all straight lines are 180) to find the other angle measurements. To find 5 I used the 4th angle and the 2nd angle to find the missing number out of 180 since all of the angles in a triangle have a sum of 180°. The missing angle was 22. You can use the angle measurement of #5 to find 6 like how I mentioned before about all straight lines equaling 180°. If this all sounds like mumbo-jumbo I can elaborate a little more in the comment section!
Answer:
first side=40
second side=20
third side=22
Step-by-step explanation:
LET THE SIDES OF THE TRIANGLES BE y
Perimeter=82
first side=2 x y = 2y
second side=y
third side=2 +y
2y + y + 2 + y=82
4y+2=82
4y= 82-2
4y=80
y=80/4
y=20
first side=2y=2(20)=40
second side=y=20
third side= 2 + y= 2 + 20 = 22
