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2 years ago

Which shows one way to determine the factors of 4x3 + x2 – 8x – 2 by grouping?

Mathematics

2 answers:

lawyer [7]2 years ago

8 0

Answer:

Step-by-step explanation:

lara31 [8.8K]2 years ago

6 0

Group first 2 and group last 2 and find factors and undistribute

(4x^3+x^2)+(-8x-2)
(x^2)(4x+1)+(-2)(4x+1)
x^2(4x+1)-2(4x+1)
answer is first one

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Which of the following functions gives the radius, r(v), of a conical artifact that is 20 inches tall as a function of its volum

irinina [24]

<h3>Radius as function of volume is:</h3>

$r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches$

Solution:

The volume of cone is given as:

$v = \frac{1}{3}\pi r^{2} h$

Where,

r is the radius

h is the height

From given,

height = 20 inches

From formula,

$v = \frac{1}{3}\pi r^{2} h$

Rearrange , so that r is alone in left side of equation

$3v = \pi r^2 h\\\\\pi r^2 h = 3v\\\\r^2 = \frac{3v}{\pi h}\\\\Take\ square\ root\ on\ both\ sides\\\\r = \sqrt{\frac{3v}{\pi h}}$

Substitute h = 20

$r = \sqrt{\frac{3v}{20 \pi }}$

Thus, radius as function of volume is:

$r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches$

4 0

2 years ago

The vertex of this parabola is at (-2,-3). When the x-value is -1, the y-value is -5. What is the coefficient of the squared exp

elena55 [62]

Answer:

Option C is correct

Step-by-step explanation:

Given: vertex of this parabola is at (-2,-3)

To find: coefficient of the squared expression in the parabola’s equation if the x-value is -1, the y-value is -5

Solution:

The equation of parabola is of the form $y=a(x-h)^2+k$

Here, a is the coefficient of the squared expression in the parabola’s equation.

Put $(h,k)=(-2,-3)\,,\,(x,y)=(-1,-5)$

$-5=a(-1+2)^2-3\\-5+3=a(1)^2\\-2=a\\a=-2$

So, the coefficient of the squared expression in the parabola’s equation is $-2$

6 0

2 years ago

In Texas, the coldest temperature ever recorded is -23 F. That's a lot chillier than in Florida, where the coldest recorded temp

beks73 [17]

Answer:

Step-by-step explanation:

21+-23=-2

3 0

2 years ago

Read 2 more answers

A nutritionist attempts to determine an association between where food is prepared and the number of calories the food contains.

Oksi-84 [34.3K]

Given the conditional relative frequency table below which was generated by column using frequency table data comparing the number of calories in a meal to whether the meal was prepared at home or at a restaurant.

Number of Calories and Location of Meal Preparation.
Home Restaurant Total
≥ 500 calories 0.15 0.55 0.28

< 500 calories 0.85 0.45 0.72

Total 1.0 1.0 1.0

To determine whether there is an association between where food is prepared and the number of carories the food contain, we recall that an "association" exists between two categorical variables if the column conditional relative frequencies are different for the columns of the table. The bigger the differences in the conditional relative frequencies, the stronger the association between the variables. If the conditional relative frequencies are nearly equal for all categories, there may be no association between the variables. Such variables are said to be independent.

For the given conditional relative freduency, we can see that there is a significant difference between the columns of the table.
i.e. 0.15 is significantly different from 0.55 and 0.85 is significantly different from 0.45

Therefore, we can conclude from the given answer options that there is an association because the value 0.15 is not similar to the value 0.55

8 0

2 years ago

A contaminant is leaking into a lake at a rate of R(t) = 1400e0.06t gallons/h. Enzymes have been added to the lake that neutrali

ruslelena [56]

Answer:

Step-by-step explanation:

Rate of leakage, R(t) = 1400 e^0.06t gallons/h

fraction remains , S(t) = e^(-0.32t)

initial contaminant = 1000 gallon

gallons contaminant present after t hour is S(t) R(t)

G(t) = S(t) R(t)

$G(t) = 1400 e^{0.06t}\times e^{-0.32t}$

$G(t) = 1400 e^{- 0.26t}$

Put t = 18 hours

$G(t) = 1400 e^{- 0.26\times 18}$

Taking log on both the sides

ln G = ln 1400 - 0.26 x 18

ln G = 7.244 - 4.68

ln G = 2.564

G = 13 gallons

5 0

2 years ago