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3 years ago

If f(x) = x2 and g(x)= 3x + 1, which expression represents g(f(x))?

Mathematics

1 answer:

Romashka [77]3 years ago

6 0

Answer:

g(f(x)) =3(x2)+1

Step-by-step explanation:

g(f(x)) means substitute f(x) in the eqn g(x)

That is anywhere you see x2, use it to replace x in the eqn g(x)

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Describe the transformations of f(x) when compared to the parent function. f(x)=(x+7) a) horizontal shift left 7 units b) horizo

Nikolay [14]

We have the function:

$f(x)=x+7$

The parent function is the linear parent function p(x)=x.

We can see that f(x) is 7 units above p(x) for any value of p(x), so we can transform p(x) to f(x) by a translation of 7 units in the y-axis.

We can see this in the graph:

Then, the transformation is a vertical shift up 7 units.

3 0

1 year ago

Bruce has a bottle that contains 60% lemon juice and the rest water. The bottle has 1 liter of water. Part A: Write an equation

ser-zykov [4K]

Answer:

Part A: (40/100)*x = 1 where x is the total contents of the bottle.

Part B: 1.5 Liters = the Lemon Juice

Step-by-step explanation:

Part A

Let the full contents of the bottle = x

Equation

Since 60% of it is lemon juice, then 100% - 60% = 40% must be water.

(60/100) * x = ?? Equation for Lemon Juice. You have to solve the water first.

(40/100) * x = 1 Equation for water

Part B

(40/100) * x = 1 change the 40% to a decimal

0.4x = 1 Divide by 0.4

x = 1/0.4 = 2.5 L

Now to find out the amount of lemon juice

0.6 * 2.5 = Lemon Juice

1.5 L = the amount of Lemon Juice.

4 0

3 years ago

Kylie buys a ceramic case priced at $75. Shipping and handling are an additional 9 2/5% of the price. How much shopping and hand

salantis [7]

$\bf \begin{array}{ccllll}
amount&\%\\
\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\
75&100\\
x&9\frac{2}{5}
\end{array}\implies \cfrac{75}{x}=\cfrac{100}{9\frac{2}{5}}\implies \cfrac{75}{x}=\cfrac{100}{\frac{9\cdot 5+2}{5}}$

$\bf \cfrac{75}{x}=\cfrac{\frac{100}{1}}{\frac{47}{5}}\implies \cfrac{75}{x}=\cfrac{100}{1}\cdot \cfrac{5}{47}\implies \cfrac{75}{x}=\cfrac{500}{47}\implies 75\cdot 47=500\cdot x
\\\\\\
\cfrac{3525}{500}=x\implies \cfrac{141}{20}=x\implies 7.05=x$

7 0

3 years ago

Write an equation for each line in slope-intercept form.

Lady bird [3.3K]

Answer:

y = x + 7

Step-by-step explanation:

The slope-intercept form of a line is:

y = mx + b

where m is the slope and b is the y-intercept.

Looking at the graph, we can see that the line intersects the y-axis at y = 7. So 7 would be our y-intercept.

To find the slope, we would divide the rise of the line by the run. Or m = rise/run. From looking at the graph, we can see that for every 1 unit the line moves in the x-direction, the line moves in the y-direction by 1 unit. Therefore, the rise would be 1 and the run would be 1. 1/1 = 1 so the slope of the line would be 1.

Plugging in 7 for b and 1 for m into the equation for the slope-intercept form, we get:

y = x + 7

So that would be the equation for the line in slope-intercept form.

I hope you find my answer and explanation to be helpful. Happy studying.

3 0

3 years ago

PLEASE SOLVE DUE RIGHT NOW!!!!!!!!!!!!

erma4kov [3.2K]

Solution:

We know that:

$Area \ of \ triangle = \dfrac{1}{2} \times Base \times Height$