15 men can do a piece of work in 80 days. How long will it take to complete the work of 5 men are reduced?​

We can actually see that the statements that are true are:

A. x = 1 is a solution.

C. x = –1 is a solution.

Rational equation is actually known as an equation that contains at least one fraction. The denominator and numerator are known to be polynomials.

We can see then that:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{x + 10}{ {x}^{3} + 6 {x}^{2} } [/tex]

It's clear that: x ≠ 0 and x ≠ -6.

Looking for the LCM of the left hand side, we will have:

[tex] \frac{4}{x + 6} + \frac{1}{ {x}^{2} } = \frac{4 {x}^{2 } + (x + 6)}{(x + 6) {x}^{2} } [/tex]

So, we will see that left hand side and right hand side are equal.

[tex]4 {x}^{2} + x + 6 = x + 10[/tex]

[tex]4 {x}^{2} = 10 - 6[/tex]

[tex]4 {x}^{2} = 4[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] x = 1[/tex]

or

[tex]x = - 1[/tex]

So, we can see that options A and C are correct.

Learn more about rational equation on https://brainly.com/question/11611235

Answer:

-1 and 1  or A and C

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

That is the number of permutations of 2 from 3

= 3P2

= 3!/(3-2(!

= 3*2

= 6.

Answer:

-33.6

Step-by-step explanation:

1. Solve inside the brackets = 4.2

2. Multiply that by -8 = -33.6

Answer:

-33.6

Step-by-step explanation:

Answer:

1,200

Step-by-step explanation:

Divide 800 by 40

Then take that answer which is 20 and multiply it by 60

Then you get 1,200

Answer:

The answer is C.

Step-by-step explanation:

C. 50-59 since it has the same number of employees as 10-19.

Answer:

$ 1.65 per gallon

Step-by-step explanation:

4 quarts in 1 gallon so 8 quarts in 2 gallons.

Cost for 2 gallons $13.20 so $13.20 ÷ 8 =  $1.65

Answer:

There would be 5.5 or 5 1/2 classes

Step-by-step explanation:

Turn fractions into decimals

Multiply each by 60

Then Divide

Answer:

42°

Step-by-step explanation:

Angles on one side of a straight line always add up to 180.

Therefore: 180° - 123° = 57°

So, 57° + 81° =138°

x=180° -138° = 42°

The inequalities that Heather could have written to compare the temperatures will be:

B. 2 < -10

C. 4 >-20

E. -8 < -15

It should be noted that inequality us the relation between two expressions that aren't equal.

Therefore, the inequalities that Heather could have written to compare the temperatures will be: 2 < -10, 4 >-20,and -8 < -15.

Learn more about inequalities on:

https://brainly.com/question/24372553

Answer:

Less than

Step-by-step explanation:

1/3 * 7/15 is less than 1/3 because 1/3 * 7/15 is being multiplied by a number that is less than 1.

Answer:

x=13

Step-by-step explanation:

<FGA is a vertical angle to <EGB, so both = to 77. Then since < CGB=90, we do 90-77=13

Answer:

maria: $2,500
henry:$750

Step-by-step explanation:

all you have to do is multiply them each by 6

Answer:

Maria will have $1500

Henry will have $750

Step-by-step explanation:

Maria - Multiply 250 x 6

Henry- Multiply 125 x 6

Answer:

Step-by-step explanation:

so the dvd player is 984 dollars so now we multiply it by three and our total would be 2,952

Answer:

See below ~

Step-by-step explanation:

First 3 blanks

Final blank

Answer:

3.62

Step-by-step explanation:

118 square rooted is 10.86

10.86/3 = 3.62

Answer:

[tex]x=\pm6.27\: \textsf{(nearest hundredth)}[/tex]

Step-by-step explanation:

Given equation:

[tex]3x^2=118[/tex]

Divide both sides by 3:

[tex]\implies \dfrac{3x^2}{3}=\dfrac{118}{3}[/tex]

[tex]\implies x^2=\dfrac{118}{3}[/tex]

Square root both sides:

[tex]\implies \sqrt{x^2}=\sqrt{\dfrac{118}{3}}[/tex]

[tex]\implies x=\pm\sqrt{\dfrac{118}{3}}[/tex]

[tex]\implies x=\pm6.27\: \textsf{(nearest hundredth)}[/tex]

Answer:

4

Step-by-step explanation:

1/3 = x/12

12 * 1/3 =x      x = 4  

Answer:

PO

Step-by-step explanation:

Answer:

9c4

factoring the monomial

(3c2)(-3c2)

Divide 50 by 20%

50/20% = 50/0.20 = 250

Answer: 250

Answer:

Step-by-step explanation:

so he got for £95 and sold it for £133, so  hmmmm the difference is simply £38.

if we take 95 to be the 100%, what is 38 off of it in percentage?

[tex]\begin{array}{ccll} \pounds&\%\\ \cline{1-2} 95 & 100\\ 38& x \end{array} \implies \cfrac{95}{38}=\cfrac{100}{x}\implies \cfrac{5}{2}=\cfrac{100}{x} \\\\\\ 5x=200\implies x=\cfrac{200}{5}\implies x=40[/tex]

1) (-5, 5), 2) (7, -5), 3) (- 3, 28), 4) (- 12, 0), 5) 10, 6) 14, 7) (- 9, 9), 8) [tex]\sqrt{26}[/tex], 9) - 2, 10) 10, 11) [tex]\left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex], 12) [tex]\left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex], 13) (0, 7), 14) [tex](- 3\sqrt{3}, - 3)[/tex], 15) The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal, 16) [tex]7\sqrt{2}[/tex], [tex]135^{\circ}[/tex], 17) [tex]17[/tex], [tex]137^{\circ}[/tex], 18) [tex]12[/tex], [tex]240^{\circ}[/tex], 19) [tex](19.700, 15.392)[/tex]

Vectors are elements that are charaterized for having a magnitude and a direction, whereas scalar are only characterized by magnitude. In this question we must apply different vector properties to obtain the corresponding results.

The first two exercises consist in calculating each vector based on its initial and terminal points, whose results are obtained below by sum of vectors with initial points at origin:

1) (-1, 3) - (4, -2) = (-5, 5)

2) (2, -6) - (- 5, -1) = (7, -5)

The following eight exercises are resolved by applying the operations of addition of vectors and multiplication of a vector by a scalar, and the definition of norm and dot product as well:

3) 3 · (3, 4) + 2 · (- 6, 8) = (9, 12) + (- 12, 16) = (- 3, 28)

4) (- 6, 8) - 2 · (3, 4) = (- 12, 0)

5) [tex]\| \vec v\| = \sqrt{(-6)^{2}+8^{2}}[/tex] = 10

6) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · (- 6) + 4 · 8 = 14

7) 3 · [(0, 2) - (3, -1)] = 3 · (- 3, 3) = (- 9, 9)

8) [tex]\|\vec v\| = \sqrt{1^{2}+5^{2}} = \sqrt{26}[/tex]

9) [tex]\vec u \,\bullet \,\vec v =[/tex] 3 · 1 + (- 1) · 5 = - 2

10) [tex]\vec w \,\bullet \, \vec v =[/tex] 0 · 1 + 5 · 2 = 10

11) The unit vector is obtained by dividing the vector by its magnitude:

[tex]\vec u_{v} = \frac{1}{\sqrt{26}}\cdot \left(1, 5\right) = \left(\frac{1}{\sqrt{26}}, \frac{5}{\sqrt{26}} \right) = \left(\frac{\sqrt{26}}{26}, \frac{5\sqrt{26}}{26}\right)[/tex]

12) The vector is equal to the product of the magnitude and its unit vector:

[tex]\vec r = 7 \cdot \frac{\vec u}{\|\vec u\|}[/tex]

[tex]\vec r = \frac{7}{\sqrt{10}}\cdot (3, -1) = \left(\frac{21}{\sqrt{10}}, -\frac{7}{\sqrt{10}} \right) = \left(\frac{21\sqrt{10}}{10}, -\frac{7\sqrt{10}}{10} \right)[/tex]

13) and 14) The vector is the product of the magnitude and the directional vector:

13) [tex]\vec r = 7 \cdot (\cos 90^{\circ}, \sin 90^{\circ}) = (0, 7)[/tex]

14) [tex]\vec r = 6\cdot (\cos 210^{\circ}, \sin 210^{\circ}) = (- 3\sqrt{3}, - 3)[/tex]

15) Two vectors are orthogonal if and only if their dot product is zero:

[tex](3.2, 4.8) \,\bullet\,(-3, 2) =[/tex] 3.2 · (- 3) + 4.8 · 2 = 0

The vectors [tex]\vec a[/tex] and [tex]\vec b[/tex] are orthogonal.

The next three exercises are resolved by definitions of norm and direction:

16) [tex]\|\vec v\| = \sqrt{(-7)^{2}+7^{2}} = 7\sqrt{2}[/tex], [tex]\theta = 135^{\circ}[/tex]

17) [tex]\|\vec v\| = 17[/tex], [tex]\theta = 137^{\circ}[/tex]

18) [tex]\|\vec q\| = 12[/tex], [tex]\theta = 240^{\circ}[/tex]

The last exercise consist in defining the vector as a product of magnitude and direction vector:

19) [tex]\vec v = 25\cdot (\cos 38^{\circ}, \sin 38^{\circ}) = (19.700, 15.392)[/tex]

To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477

Answer:

  3/7

Step-by-step explanation:

Write the division of the pizzas as a ratio, and you will have it.

  (3 pizzas)/(7 persons) = (3/7) pizza/person

__

Each person gets 3/7 of a pizza.

Answer:

C

Step-by-step explanation:

Multiplying the sequence by 2 gives us the next term. Therefore it has to be the formula a1 x r^n-1. If we substitute the values it would end up as the answer C

Answer:

The correct answer would be option C; 12 x 2ⁿ⁻¹

Step-by-step explanation:

You can check this using any number

since n is the term number we can check it;

let's say we have to find out the answer to the third term number, so we will substitute the n by 3 in the equation from option C and solve

term = 12 x 2ⁿ⁻¹

term = 12 x 2 ³ ⁻¹

term = 12 x 2 ²

term = 12 x 4

term = 48

The term does match the third number in the series given above and hence the equation works!

Hope this helps!

Answer:

[tex]4)\ = \frac{5}{\pi}[/tex]

Step-by-step explanation:

Formula:________________

circumference = Diameter × π

_______________________

Then

5 = Diameter × π

Then

[tex]Diameter \ = \frac{5}{\pi}[/tex]

Answer:

help

Step-by-step explanation:

with what what is the question

Answer: The second histogram a.k.a choice B is correct.