Find any rational root of P(x). p(x) = x^3 + 5x^2 + x + 5

A farmer collected 12 dozen eggs from her chickens. She sold 5/6 of the eggs to the farmers market and gave the rest to friends

Aleks [24]

Multiply 12 x 12 which is 144. And then you divide that by 6 and you get 24

7 0

3 years ago

Read 2 more answers

A person on tour has dollar 360 for his daily expenses. If he extends his tour for 4 days, he has to cut down his daily expenses

mash [69]

Answer:

The original duration of the tour = 20 days

Step-by-step explanation:

Solution:

Total expenses for the tour = $360

Let the original tour duration be for $x$ days.

So, for $x$ days the total expense = $360

Thus the daily expense in dollars can be given by = $\frac{360}{x}$

Tour extension and effect on daily expenses.

The tour is extended by 4 days.

Tour duration now = $(x+4)$ days

On extension, his daily expense is cut by $3

New daily expense in dollars = $(\frac{360}{x}-3)$

Total expense in dollars can now be given as: $(x+4)(\frac{360}{x}-3)$

Simplifying by using distribution (FOIL).

$(x.\frac{360}{x})+(x(-3)+(4.\frac{360}{x})+(4(-3))$

$360-3x+\frac{1440}{x}-12$

$348-3x+\frac{1440}{x}$

We know total expense remains the same which is = $360.

So, we have the equation as:

$348-3x+\frac{1440}{x}=360$

Multiplying each term with $x$ to remove fractions.

$348x-3x^2+1440=360x$

Subtracting $348x$ both sides

$348x-348x-3x^2+1440=360x-348x$

$-3x^2+1440=12x$

Dividing each term with -3.

$\frac{-3x^2}{-3}+\frac{1440}{-3}=\frac{12x}{-3}$

$x^2-480=-4x$

Adding $4x$ both sides.

$x^2+4x-480=-4x+4x$

$x^2+4x-480=0$

Solving using quadratic formula.

For a quadratic equation: $ax^2+bx+c=0$

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Plugging in values from the equation we got.

$x=\frac{-4\pm\sqrt{(4)^2-4(1)(-480)}}{2(1)}$

$x=\frac{-4\pm\sqrt{16+1920}}{2}$

$x=\frac{-4\pm\sqrt{1936}}{2}$

$x=\frac{-4\pm44}{2}$

So, we have

$x=\frac{-4+44}{2}$ and $x=\frac{-4-44}{2}$

$x=\frac{40}{2}$ and $x=\frac{-48}{2}$

∴ $x=20$ and $x=-24$

Since number of days cannot be negative, so we take $x=20$ as the solution for the equation.

Thus, the original duration of the tour = 20 days

6 0

3 years ago

What is 2/5 v + 3/4 = 2/3x² as a sentence

Bond [772]

The representation of the equation given in the task content; 2/5 v + 3/4 = 2/3x² as a s sentence is; The sum of Two-fifths of a number, v and quarters is equal to two-thirds of the square of the number x.

<h3>What is the representation of the equation as given in the task content?</h3>

It follows from the convention that the following fractions can be named as follows;

2/5 means two-fifths.
3/4 means three-quarters.
2/3 means two-thirds.

Hence, it follows from the iterations above and how they relate to the equation given in the task content that the representation is; The sum of Two-fifths of a number, v and quarters is equal to two-thirds of the square of the number x.

Read more on equations as words;

brainly.com/question/21405634

#SPJ1

8 0

2 years ago

HELP!!!!!!!!!!!

Svetradugi [14.3K]

Using the mean concept, it is found that:

Relative to Sabrina's goal, her average swim time over the last five weeks is 0.1 hours.

-----------------------

The mean of a data-set is given by the sum of all observations divided by the number of observations.

In this problem:

The data-set is her swim time relative to her goal, which is: {1.25, -1, 2.25, 0, -2.}

5 observations.

Thus, the mean is:

$M = \frac{1.25 - 1 + 2.25 + 0 - 2}{5} = 0.1$

Relative to Sabrina's goal, her average swim time over the last five weeks is 0.1 hours.

A similar problem is given at brainly.com/question/24787716

7 0

3 years ago

What is the equation of the following graph in vertex form? parabolic function going down from the left through the point negati

Anestetic [448]

A parabolic function's key characteristic is either having 2 x-intercepts or 2 y-intercepts. That is the reason why the standard form of parabolic functions are:

(x-h)^2 = +/- 4a(y-k) or (y-k)^2 = +/- 4a(x-h), where

(h,k) is the coordinates of the vertex
4a is the lactus rectum
a is the distance from the focus to the vertex

This is also called vertex form because the vertex (h,k) is grouped according to their variable.

Since we don't know any of those parameters, we'll just have to graph the data points given as shown in the picture. From this data alone, we can see that the parabola has two x-intercepts, x=-4 and x=-2. Since it has 2 roots, the parabola is a quadratic equation. Its equation should be

y = (x+4)(x+2)
Expanding the right side
y = x²+4x+2x+8
y = x²+6x+8
Rearrange the equation such that all x terms are on one side of the equation
x²+6x+___=y-8+___
The blank is designated for the missing terms to complete the square. Through completing the squares method, you can express the left side of the equation into (x-h)² form. This is done by taking the middle term, dividing it by two, and squaring it. So, (6/2)²=9. Therefore, you put 9 to the 2 blanks. The equation is unchanged because you add 9 to both sides of the equation.

The final equation is
x²+6x+9=y-8+9
(x+3)²=y+1

6 0

3 years ago