To set up your system of equations is to have 2 equations. They both would have 1 similar variable. For example, Jenny is 5 more her brother's age. She is also 2 more than twice her brother's age. You would set this up as Y, which is Jenny, and X, her brother. Y = 5 + x and Y = 2x + 2. Make sure you put Y in the same spot in both equations. Then take the other half of the equations and simplify them. 5 + x = 2x + 2. Subtract x from both sides to get 5 = x + 2. Subtract 2 from both sides to get 3 = x. Now replace the X from both equations to get Y = 5+3, and Y = 2(3) + 2. You will see both add up to 8, which is how old Jenny is in this example. Hope this helped!
See the attached figure.
<span>ad is a diameter of the circle with center p
</span>
∵ pd = radius = 7 ⇒⇒⇒ ∴ ad = 2 * radius = 2 * 7 = 14
∵ ae = 4 ⇒⇒⇒ ∴ ed = ad - ae = 14 - 4 = 10
∵ ad is a diameter
Δ acd is a triangle drawn in a half circle
∴ Δ acd is a right triangle at c
∵ bc ⊥ ad at point e
By applying euclid's theorem inside Δ acd
∴ ce² = ae * ed
∴ ce² = 4 * 10 = 40
∴ ce = √40 = 2√10 ≈ 6.325
Answer:
The statements describe transformations performed in f(x) to create g(x) are:
a translation of 5 units up ⇒ c
a vertical stretch with a scale factor of 2 ⇒ d
Step-by-step explanation:
- If f(x) stretched vertically by a scale factor m, then its image g(x) = m·f(x)
- If f(x) translated vertically k units, then its image h(x) = f(x) + k
Let us use these rule to solve the question
∵ f(x) = x²
∵ g(x) is created from f(x) by some transformation
∵ g(x) = 2x² + 5
→ Substitute x² by f(x) in g(x)
∴ g(x) = 2f(x) + 5
→ Compare it with the rules above
∴ m = 2 and k = 5
→ That means f(x) is stretched vertically and translated up
∴ f(x) is stretched vertically by scal factor 2
∴ f(x) is translated 5 uints up
The statements describe transformations performed in f(x) to create g(x) are:
- a translation of 5 units up
- a vertical stretch with a scale factor of 2
The expressions that can represent the dimensions of the prim is (x), (3x+1) and (4x-1).
