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2 years ago

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number

Mathematics

1 answer:

Wittaler [7]2 years ago

5 0

Answer:

Step-by-step explanation:

Let the number = x

2x + 8 ≥ 4x Subtract 2x from both sides.

8 ≥ 4x - 2x Combine

8 ≥ 2x Divide by 2

8/2 ≥ 2x/2 Combine

4 ≥ x

What this means is that the largest value the x can have is 4. Any number greater that 4 will make the use of ≥ incorrect.

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SH What is the greatest common factor (GCF) of 35 and 28?

Brilliant_brown [7]

Answer: 7

Step-by-step explanation:

We found the factors and prime factorization of 28 and 35. The biggest common factor number is the GCF number. So the greatest common factor 28 and 35 is 7.

Hope this helps :)

6 0

3 years ago

Read 2 more answers

In this problem we consider an equation in differential form Mdx+Ndy=0. (4x+2y)dx+(2x+8y)dy=0 Find My= 2 Nx= 2 If the problem is

zheka24 [161]

Answer:

$f(x,y)=2x^2+4y^2+2xy=C_1\\\\Where\\\\y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

Step-by-step explanation:

Let:

$M(x,y)=4x+2y\\\\and\\\\N(x,y)=2x+8y$

This is and exact equation, because:

$\frac{\partial M(x,y)}{\partial y} =2=\frac{\partial N}{\partial x}$

So, define f(x,y) such that:

$\frac{\partial f(x,y)}{\partial x} =M(x,y)\\\\and\\\\\frac{\partial f(x,y)}{\partial y} =N(x,y)$

The solution will be given by:

$f(x,y)=C_1$

Where C1 is an arbitrary constant

Integrate $\frac{\partial f(x,y)}{\partial x}$ with respect to x in order to find f(x,y):

$f(x,y)=\int\ {4x+2y} \, dx =2x^2+2xy+g(y)$

Where g(y) is an arbitrary function of y.

Differentiate f(x,y) with respect to y in order to find g(y):

$\frac{\partial f(x,y)}{\partial y} =2x+\frac{d g(y)}{dy}$

Substitute into $\frac{\partial f(x,y)}{\partial y} =N(x,y)$

$2x+\frac{dg(y)}{dy} =2x+8y\\\\Solve\hspace{3}for\hspace{3}\frac{dg(y)}{dy}\\\\\frac{dg(y)}{dy}=8y$

Integrate $\frac{dg(y)}{dy}$ with respect to y:

$g(y)=\int\ {8y} \, dy =4y^2$

Substitute g(y) into f(x,y):

$f(x,y)=2x^2+4y^2+2xy$

The solution is f(x,y)=C1

$f(x,y)=2x^2+4y^2+2xy=C_1$

Solving y using quadratic formula:

$y(x)=\frac{1}{4} (-x\pm \sqrt{-7x^2+C_1} )$

4 0

3 years ago

What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2 (2 points) (3, 11) and (−3, −7) (11, 3)

Minchanka [31]

ANSWER

(3, 11) and (−3, −7)

EXPLANATION

The given system of equations are:

$y = {x}^{2} + 3x - 7$

and

$3x - y = - 2$

or

$y = 3x + 2$

We equate the two equations to obtain,

${x}^{2} + 3x - 7 = 3x + 2$

We rewrite in standard quadratic form to obtain,

${x}^{2} + 3x - 3x - 7 - 2 = 0$

This simplifies to

${x}^{2}- 9= 0$

We solve for x to obtain,

${x}^{2} = 9$

$x = \pm \sqrt{9}$

$x = \pm 3$

$x = 3 \: or \: x = - 3$

When
$x = 3$

$y = 3(3) + 2 = 11$

When x=-3,

$y = 3( - 3) + 2 = - 7$

Therefore the solution for the system is (3, 11) and (−3, −7).

7 0

2 years ago

Read 2 more answers

Which undefined term can contain parallel lines? O line O plane o point O ray

lapo4ka [179]

Answer:

should be a plane.

a plane is two dimensional and has intimate length and width. so it contains infinite lines.

4 0

2 years ago

A pair of shoes costs $30.99 and the state sales tax is 5%. Use the formula C = p + rp to find the total cost of the shoes, wher

liberstina [14]

First, write the rate as a decimal by moving the decimal point two places to the left from the percent.

r = 5% = 0.05

C = p + rp

C = 30.99 + 0.05 * 30.99

C = 30.99 + 1.55

C = 32.54

Answer: The total cost is $32.54

5 0

3 years ago

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number​

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number