Write an equation and solve:

Mathematics

1 answer:

MA_775_DIABLO [31]2 years ago

3 0

Answer:

55p

Step-by-step explanation:

iced cake = 10p more than a plain cake

iced cake = 10p + plain cake

iced cake and a plain cake together = £1

iced cake + plain cake = £1

if iced cake = 10p + plain cake, we can plug this into our second formula to get

(10p + plain cake) + plain cake = £1

10p + 2 * plain cake = £1 = 100p

subtract 10p from both sides to isolate the variable and its coefficient

2 * plain cake = 90p

divide both sides by 2 to isolate the variable

plain cake = 45p

iced cake = 10p + plain cake = 55p

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Match each transformation of function f to a feature of the transformed function.

andrezito [222]

By analyzing the parent function graph, we will see that:

1) m(x) = -f(x) ⇒ "function decreases as x increases"
2) h(x) = f(x) + 2 ⇒ "asymptote of y = 2"
3) j(x) = f(x + 2) ⇒ "y-intercept at (0, 4)"
4) g(x) = 2*f(x) ⇒ "y-intercept at (0, 2)"

<h3>What thing does each transformation?</h3>

Let's list each transformation and let's see which is the correct option for each one.

1) m(x) = -f(x).

This is a reflection over the x-axis, so, now the curve will open downwards. This means that now we have a decreasing function, so the correct option here is: <em>"function decreases as x increases"</em>

2) h(x) = f(x) + 2

This is a vertical translation of 2 units upwards. So it moves the whole graph 2 units upwards. Originally, you can see that in the left side we have an asymptote at y = 0, now that asymptote will be at y = 2.

So the correct option is: <em>"asymptote of y = 2.</em>

3) j(x) = f(x + 2)

This is a shift of 2 units to the left, notice that when we evaluate this in x = 0 we et:

j(0) = f(2) = 2^2 = 4

So the y-intercept os (0, 4).

4) g(x) = 2*f(x)

This is a vertical stretch of scale factor 2.

When we evaluate this in x = 0, we get:

g(0) = 2*f(1) = 2

So the y-intercept is at (0, 2).

If you want to learn more about transformations, you can read:

brainly.com/question/4289712