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4 years ago

Is -√50 natural, whole, integer, rational, or irrational number

Mathematics

2 answers:

vladimir2022 [97]4 years ago

3 0

Answer:

irrational

Step-by-step explanation:

faust18 [17]4 years ago

3 0

Answer:

-√50 is an irrational number

Step-by-step explanation:

The negative sign doesn't affect the question here, and √50 is not a perfect square, so we know that it is irrational.

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The following trapezoid JKLM is translated by the rule (x - 2, y + 8). What are the coordinates for J'K'L'M'?

Andrew [12]

The coordinates of trapezoid vertices are:

J(-7,-2);
K(-4,-2);
L(-2,-5);
M(-9,-5).

The translation rule is

(x,y)→(x-2,y+8).

Then the image trapezoid vertices are:

J'(-7-2,-2+8) that is J'(-9,6);
K'(-4-2,-2+8) that is K'(-6,6);
L'(-2-2,-5+8) that is L'(-4,3);
M'(-9-2,-5+8) that is M'(-11,3)

7 0

3 years ago

I need to simplify<br><br>3 + 4 10 -8<br><br>and<br><br>(3+4)(10-8)

myrzilka [38]

Answer: 14

Step-by-step explanation: (3+8)*(10-8) = 14

5 0

2 years ago

Read 2 more answers

Can you please help me on my review?

dimaraw [331]

Answer:

g(x) = -∛(x-7)

Step-by-step explanation:

Reflection in the y-axis changes the sign of x, so after this transformation, the function is ...

g(x) = f(-x)

Then, translation 7 units to the right replaces x by (x-7), so after both transformations, the function is ...

g(x) = f(-(x -7)) = f(-(x -7))

Using the given definition for f(x), we have ...

$g(x)=\sqrt[3]{-(x-7)}\\\\g(x)=-\sqrt[3]{x-7}$

7 0

3 years ago

A 50-gal tank initially contains 10 gal of fresh water. At t = 0, a brine solution

scZoUnD [109]

$\huge \mathbb{SOLUTION:}$

$\begin{array}{l} \textsf{Let }A(t)\textsf{ be the function which gives the amount} \\ \textsf{of the salt dissolved in the liquid in the tank at} \\ \textsf{any time }t. \textsf{ We want to develop a differential} \\ \textsf{equation that, when solved, will give us an} \\ \textsf{expression for }A(t). \\ \\ \textsf{The basic principle determining the differential} \\ \textsf{equation is} \\ \\ \end{array}$

$\boxed{ \footnotesize \begin{array}{l} \qquad\quad \quad\Large{\dfrac{dA}{dt} = R_{in} - R_{out}} \\ \\ \textsf{where:} \\ \\ \begin{aligned} \bullet\: R_{in} &= \textsf{rate of the salt entering} \\ &= \left({\footnotesize \begin{array}{c}\textsf{Concentration of} \\\textsf{salt inflow}\end{array}}\right) \times \small(\textsf{Input of brine}) \\ \\ \bullet\: R_{out} &= \textsf{rate of the salt leaving} \\ &= \left({\footnotesize \begin{array}{c}\textsf{Concentration of} \\\textsf{salt outflow}\end{array}}\right) \times \small(\textsf{Output of brine}) \end{aligned} \end{array}} \\ \\$

$\begin{array}{l} \textsf{On the problem, the amount of salt in the tank,} \\ A(t), \textsf{changes overtime is given by the differential} \\ \textsf{equation} \\ \\ \footnotesize A'(t) = \left(\dfrac{4\ \textsf{gal}}{1\ \textsf{min}}\right)\!\!\left(\dfrac{1\ \textsf{lb}}{1\ \textsf{gal}}\right) - \left(\dfrac{2\ \textsf{gal}}{1\ \textsf{min}}\right)\!\!\left(\dfrac{A(t)\ \textsf{lb}}{10 + (4 - 2)t\ \textsf{gal}}\right) \\ \\ \textsf{There's no salt in the tank (fresh water) at the} \\ \textsf{start, so }A(0) = 0. \textsf{ The amount of solution in the} \\ \textsf{tank is given by }10 + (4 -2)t, \textsf{so the tank will} \\ \textsf{overflow once this expression is equal to the total} \\ \textsf{volume or capacity of the tank.} \\ \\ 10 + (4 - 2)t = 50 \\ \\ \textsf{Solving for }t,\textsf{ we get} \\ \\ \implies \boxed{t = 20\textsf{ mins}} \\ \\ A'(t) = 4 - \dfrac{2A(t)}{10 + 2t} \\ \\ A'(t) = 4 - \dfrac{1}{5 + t} A(t) \\ \\ A'(t) + \dfrac{1}{5 + t} A(t) = 4 \\ \\ \textsf{This is a linear ODE with integrating factor} \\ \mu (t) = e^{\int \frac{1}{5 + t}\ dt} = e^{\ln |5 + t|} = 5 + t \\ \\ \textsf{Multiplying this to the ODE, we get} \\ \\ (5 + t)A'(t) + A(t) = 4(5 + t) \\ \\ [(5 + t)A(t)]' = 20 + 4t \\ \\ (5 + t)A(t) = 20t + 2t^2 + C \\ \\ \textsf{Since }A(0) = 0, \textsf{ we get } C = 0. \\ \\ A(t) = \dfrac{2t^2 + 20t}{t + 5} \\ \\ A(t) = 2t + 10 - \dfrac{50}{t + 5} \\ \\ \textsf{So the function that gives the amount of salt at} \\ \textsf{any given time }t,\textsf{ is given by} \\ \\ \implies A(t) = 2t + 10 - \dfrac{50}{t + 5} \\ \\ \textsf{The amount of salt in the tank at the moment} \\ \textsf{of overflow or at }t = 20\textsf{ mins is equal to} \\ \\ A(20) = 2(20) + 10 - \dfrac{50}{20 + 5} \\ \\ \implies \boxed{A = 48\ \textsf{gallons}} \end{array}$

$\Large \mathbb{ANSWER:}$

$\qquad\red{\boxed{\begin{array}{l} \textsf{a. }20\textsf{ mins} \\ \\ \textsf{b. }48\textsf{ gallons}\end{array}}}$

#CarryOnLearning

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#5-MinutesAnswer

5 0

3 years ago

NEED NOW!!! WILL GIVE BRAINLIEST!!! 17-19!!!

Sholpan [36]

For the given systems of equations, we have that:

17. The solution is: x = 3, y = 4.

18. The company can afford to promote 2 engineers to level II.

19. The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For item 17, the system is:

3x + 2y = 17.

4x - 2y = 4.

Adding the equations, we can eliminate y and solve for x, hence:

7x = 21

x = 3.

Then the solution for y is given as follows:

3x + 2y = 17

3(3) + 2y = 17

2y = 8

y = 4.

For item 18, the variables are given as follows:

Variable x: number of level I engineers.

Variable y: number of level II engineers.

The company has 8 engineers, hence:

x + y = 8 -> x = 8 - y.

The company can afford to pay a total of $472,000 to the engineers, hence, considering the salaries(in thousands of dollars) of each:

56x + 68y = 472.

We want to solve for y, hence, since x = 8 - y:

56x + 68y = 472.

56(8 - y) + 68y = 472.

12y = 24.

y = 2.

The company can afford to promote 2 engineers to level II.

The substitution method was used, as writing x as a function of y in the given equation was quite straight forward, as was replacing into the second equation to find y.

More can be learned about a system of equations at brainly.com/question/24342899

#SPJ1

5 0

1 year ago

Read 2 more answers