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3 years ago

Please help?! Which of the following represents the zeros of f(x)=5x^3-6x^2-59x+12?

Mathematics

2 answers:

Kaylis [27]3 years ago

8 0

Given function : $f(x)=5x^3-6x^2-59x+12.$

$\mathrm{Factor\:}5x^3-6x^2-59x+12$

Splitting terms to factor it out.

$5x^3-x^2-5x^2+x-60x+12$

Making it into groups

(5x^3-x^2) + (-5x^2+x) + (-60x+12)

Factoring out GCF of each group.

$x^2(5x-1)-x(5x-1)-12(5x-1)$

$=(5x-1)(x^2-x-12)$

Factoring x^2-x-12 into (x+3)(x-4)

$(5x-1)(x^2-x-12) = (5x-1)(x+3)(x-4)$

Applying zero product rule.

5x-1 =0

x+3=0 and

x-4= 0

On solving

x = 1/5 , x=-3 and x=4.

Therefore, zeros of the given function are $x=-3,\:x=4,\:x=\frac{1}{5}$ .

lara31 [8.8K]3 years ago

5 0

Hello,

5x^3-6x²-59x+12=5x^3-x²-5x²+x-60x+12
=x²(5x-1)-x(5x-1)-12(5x-1)
=(5x-1)(x²-x-12)
=(5x-1)(x²+3x-4x-12)
=(5x-1)(x(x+3)-4(x+3))
=(5x-1)(x+3)(x-4)

zeros are -3,4,1/5

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Assuming [x] means the closest integer to x

Answer:

$(-\infty, \infty)$

Step-by-step explanation:

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$[x]$ can be any integer from $-\infty$ to $\infty$ , and as $\infty+1=\infty$ (at least in terms of a function's range and domain), the range of $[x]+1$ is equal to the range of $[x]$ , which is $(-\infty, \infty)$ .

So, the answer is $\boxed{(-\infty, \infty)}$ and we're done!

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3 years ago

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Suppose the ages of multiple birth mothers (4 or more births) are normally distributed with a mean age of 35.5 years and a stand

Ann [662]

Answer:

40.65% of these mothers are between the ages of 32 to 40

23.27% of these mothers are less than 30 years old

37.07% of these mothers are more than 38 years old

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 35.5, \sigma = 7.5$

What percent of these mothers are between the ages of 32 to 40?

This is the pvalue of Z when X = 40 subtracted by the pvalue of Z when X = 32.

X = 40

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{40 - 35.5}{7.5}$

$Z = 0.6$

$Z = 0.6$ has a pvalue of 0.7257

X = 32

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{32 - 35.5}{7.5}$

$Z = -0.47$

$Z = -0.47$ has a pvalue of 0.3192

0.7257 - 0.3192 = 0.4065

40.65% of these mothers are between the ages of 32 to 40

What percent of these mothers are less than 30 years old?

This is the pvalue of Z when X = 30.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{30 - 35.5}{7.5}$

$Z = -0.73$

$Z = -0.73$ has a pvalue of 0.2327

23.27% of these mothers are less than 30 years old

What percent of these mothers are more than 38 years old?

This is 1 subtracted by the pvalue of Z when X = 38.

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{38 - 35.5}{7.5}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293

1 - 0.6293 = 0.3707

37.07% of these mothers are more than 38 years old

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3 years ago

Eric's father Works two part-time jobs one in the morning and one in the afternoon and works a total of 40 hours each five day w

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Answer:

Step-by-step explanation:

because 40 devided by 5 equals 8 so thats how many hours in the afternoon

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3 years ago

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I’ll give you brainliest for the first person with an answer

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Answer:

1296mm^2

Step-by-step explanation:

Surface Area of the Rectangular Prism to the left on top of the box:

Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving 162mm^2

Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving 162mm^2

So, the total surface area of the rectangular prism to the left on top, is 324mm^2

Surface Area of the Triangular Prism:

Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get 108mm^2.

Area of the rectangle: lw, so 15mm * 9mm = 135mm^2

So, the total surface area of the triangular prism is 243mm^2

Surface Area of the Rectangular Prism at the bottom:

Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, 378mm^2

Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, 162mm^2

Area of the rectangle at the very bottom = lw, 21mm * 9mm = 189mm^2

So, the total surface area of the rectangular prism at the bottom is 729mm^2

Add all the total surface areas of each shape to get the total surface area of the figure:

324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2

The surface area of the figure above is 1296mm^2

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2 years ago

Which expression is equivalent to 4+2(1+3x)?

Likurg_2 [28]

Answer:

6+18x

Step-by-step explanation:

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