Which system of equations can you use to find the roots of the equation?<br> x3 – 10x = x2

The construction of copying ∠"QPR" is started below. The next step is to set the width of the compass to the length of ("AB" ).

zzz [12365]

Answer:

The length AB equals length TU.

Step-by-step explanation:

Procedure: Replicate angle <QPR so that;

<QPR matches <TSU

Set the compass so that each leg touches points A and B to replicate the distance AB.

Next, position the compass at T to draw an arc that marks point U. Draw a straight line from S to U.

Consequently,

<QPR is congruent to <TSU

This method guarantees that angles are congruent by maintaining the same radius, thus AB = TU.

4 0

3 months ago

What is the following product? RootIndex 3 StartRoot 16 x Superscript 7 Baseline EndRoot times RootIndex 3 StartRoot 12 x Supers

PIT_PIT [12445]

Response:

I'm uncertain about the problem, but I believe it relates to: $4x^5\sqrt[3]{3x}$

$\sqrt[3]{16x^7} \times \sqrt[3]{12x^9} =$

$= \sqrt[3]{16 \times 12 \times x^{16}}$

$= \sqrt[3]{192 \times x^{15} \times x}$

$= \sqrt[3]{64 \times 3 \times (x^5)^3 \times x}$

$= \sqrt[3]{4^3 \times 3 \times (x^5)^3 \times x}$

$= 4x^5\sqrt[3]{3x}$

8 0

2 months ago

Gabi wants to drive to and from the airport. She finds two companies near her that offer short-term car rental service at differ

Inessa [12570]

Answer:

The cost difference per mile between the two companies is $0.12.

Step-by-step explanation:

Gabi formulates the equation $0.22m+7.20=0.1m+8.40$ to determine after how many miles, denoted as m, the charges of both companies will be equal.

The first company levies $c_1=0.22m+7.20$ for m miles traveled.

The second company's charge for the same m miles is $c_2=0.1m+8.40$ .

In these equations, the figures 7.20 and 8.40 signify the initial fees the companies impose.

The values 0.22 and 0.1 represent the respective costs per mile.

As such, the disparity in per-mile charges amounts to $0.22-0.1=0.12$ .

An alternative method to tackle this problem is by calculating the per-mile rate for each company:

1. Cost per mile for the first company

$c_1(0)=0.22\cdot 0+7.20=7.20\\ \\c_1(1)=0.22\cdot 1+7.20=7.42\\ \\c_1(1)-c_1(0)-7.42-7.20=0.22$

2. Cost per mile for the second company

$c_2(0)=0.1\cdot 0+8.40=8.40\\ \\c_2(1)=0.1\cdot 1+8.40=8.50\\ \\c_2(1)-c_2(0)=8.50-8.40=0.1$

3. The difference:

$0.22-0.1=0.12$

6 0

3 months ago

11 Points Estimate the average by first rounding to the nearest 1,000: 1,000 2,300 2,600

Zina [12379]

Response:

Average = 2000

Step-by-step breakdown:

The numbers provided are:

1,000 2,300 2,600

To calculate the average:

Initially, round each number to the nearest 1000, then determine the average.

Solution:

1000 is already rounded, so it stays the same.

To round to the nearest thousand, check the hundred's digit.

If the hundred’s digit exceeds 5, the thousand’s digit increases by 1, and the hundred’s digit is set to 0.

If it’s less than 5, the thousand’s digit remains the same, changing the hundred’s digit to 0.

Thus, 2300 rounds to 2000.

and 2600 rounds to 3000.

Consequently, the numbers for averaging are 1000, 2000, 3000.

The formula for average is as follows:

$Average = \dfrac{\text{Sum of all numbers}}{\text{Count of numbers}}$

upon applying the formula:

$Average = \dfrac{1000+2000+3000}{3}\\\Rightarrow Average = \dfrac{6000}{3}\\\Rightarrow \bold{Average = 2000}$

So, the average after rounding to the nearest 1000 is 2000.

7 0

1 month ago

∠UVW and ∠XYZ are complementary angles, m∠UVW=(x−10)º , and m∠XYZ=(4x−10)º .

lawyer [12517]

We recognize that two angles, ∠UVW and ∠XYZ, are complementary, which means their sum is 90°.

Their measures are given as:

∠UVW = x - 10

∠XYZ = 4x - 10

Adding these, we have:

(x - 10) + (4x - 10) = 90

Simplifying:

5x - 20 = 90

Adding 20 to both sides:

5x = 110

Dividing by 5:

x = 22

Substituting back:

∠UVW = 22 - 10 = 12°

∠XYZ = 4(22) - 10 = 78°

Therefore, the values are:

x = 22°

∠UVW = 12°

∠XYZ = 78°

6 0

3 months ago

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Which system of equations can you use to find the roots of the equation? x3 – 10x = x2 – 6