Answer:
(-5, -3)
Step-by-step explanation:
Scale factor 1/2 means divide points by 2
The perimeter is just adding all the sides together.
a.) 180 = 40 + 40 + x + x
180 = 80 + 2x Subtract 80 on both sides
100 = 2x Take 1/2 of 100 to get x
x= 50cm
b.) 1000 = 150 + 150 + x + x
1000 = 300 + 2x Subtract 300 on both sides
700 = 2x Take 1/2 of 700 to get x
x = 350
Answer:
x³ + 3x² - 46
Step-by-step explanation:
note that (f + g)(x) = f(x) + g(x)
f(x) + g(x)
= x² - 36 + x³ + 2x² - 10 ← collect like terms
= x³ + 3x² - 46
Answer:
y = x^2 +6x +8
Step-by-step explanation:
The vertex is (-3, -1), and the vertical scale factor is 1. (You can tell this because the graph goes up 1 unit for 1 unit either side of the vertex.) So, the vertex form of the equation is ...
y = (x +3)^2 -1 . . . . . . . . . vertex form; sometimes called standard form
Expanding this, we get ...
y = x^2 +6x +8 . . . . . . . . also called the standard form equation
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<em>Comment on standard form</em>
There are different versions of "standard form" depending on what you're concerned with and where you are. Please consult your text or other reference material for the version of standard form you need. (The attachments show the conflict with respect to quadratic equations.)
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<em>Comment on the graph</em>
The purpose of the graph attached is to show that the equation we propose produces the same curve as the one given.
Answer:
y = 48
Step-by-step explanation:
given y is directly proportional to x then the equation connecting them is
y = kx ← k is the constant of proportionality
To find k use the condition y = 36 when x = 30
k = = =
y = x ← equation of proportionality
When x = 40 then
y = × 40 = 48