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3 years ago

Find all x and y intercepts of the graph of the function f(x)= 2x^3+6x^2-2x-6

Mathematics

1 answer:

topjm [15]3 years ago

4 0

9514 1404 393

Answer:

y-intercept: (0, -6)
x-intercepts: (-3, 0), (-1, 0), (1, 0)

Step-by-step explanation:

We notice the first pair of coefficients is the same as the last pair (with the sign changed). This means we can factor by grouping.

f(x) = (2x^3 +6x^2) -(2x +6)

f(x) = 2x^2(x +3) -2(x +3)

f(x) = 2(x^2 -1)(x +3) = 2(x -1)(x +1)(x +3)

The factors are made to be zero when x is 1, -1, or -3.

The x-intercepts are (1, 0), (-1, 0), (-3, 0).

The y-intercept is the constant, -6.

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A family spends 1/10 of its annual income for housing, 1/4 for food and clothes, 1/5 for general expenses, and 2/15 for entertai

AlexFokin [52]

Add all the fractions together:
to do this find the lcd:
which is 60
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6 0

3 years ago

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The scatter plot shows a scuba diver's depth in the ocean. The equation of the trend link shown is y = -3.29x - 10. Predict what

TiliK225 [7]

It's not given a scatter plot not the characteristics of the variables, but it can be safely assumed as shown below

Answer:

The diver's depth will be -42.9 after 30 minutes

Step-by-step explanation:

The equation of the trend (or best fit line) for the scuba diver's depth in the ocean is:

y = -3.29x - 10

Where y is the diver's depth and x is the time in minutes.

To predict the diver's depth at x=30 minutes, substitute in the equation:

y = -3.29(10) - 10

y = -32.9 - 10

y = -42.9

Since no units are provided for y, the answer is:

The diver's depth will be -42.9 after 30 minutes

6 0

3 years ago

Emma has 18 yellow flowers and 30 white flowers. She wants to split them into vases in equal groups. What is the largest number

likoan [24]

Answer:

Flowers, yellow flowers, white flowers, group, GCF

For this case we have 18 yellow flowers and 30 white flowers, we must find a number that represents the largest number of groups of flowers that can be formed, bearing in mind that each group must contain the same number of yellow and white flowers. To do this, we must find the GCF (Greatest Common Factor) of yellow flowers and white flowers.

We look for the factors of 18, that is, the numbers for which 18 is divisible, these are:

18, 9, 6, 3, 2 and 1

We look for the factors of 30, that is, the numbers for which 30 is divisible, these are:

30, 15, 10, 6, 5, 3, 2, 1

Thus, we can see that GCF of both numbers is 6.

Then we can form 6 groups of flowers. To know the amount of flowers of each color in each group, we divide:

Thus, 6 groups of flowers can be formed with 3 yellow flowers and 5 white flowers each.

Answer:

The largest number of groups that can be done is 6.

Read more on Brainly.com - brainly.com/question/950582#readmore

Step-by-step explanation:

4 0

3 years ago

Help and explain please!

Igoryamba

84, first you multiply and divide then you add

6 0

2 years ago

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Which statement is true about the domain of y = 3(2^-x)? Explain.

SVEN [57.7K]

We want to determine the domain of ${y=3 \cdot 2^{-x}=3 \cdot ({2^{-1}})^x=3 \cdot ({ \frac{1}{2}})^x$

any function of the form $y=f(x)=a \cdot b^x$ is called an "exponential function",
the only condition is that b is positive and different from 1, and a is a nonzero real number.

The domain of such functions is all real numbers.

That is for any x, the expression 3(2^-x) "makes sense".

Answer: The domain is all real numbers

8 0

3 years ago