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3 years ago

I need help with math

Mathematics

1 answer:

GrogVix [38]3 years ago

8 0

Answer:

x < 3

Step-by-step explanation:

The standard linear equation of a vertical line with an undefined slope is x = a, where "a" represents the x-intercept of the graph. Vertical lines have an undefined slope because it doesn't have any horizontal change.

The given graph represents the graph of a vertical line, whose x-intercept occurs at point (3, 0). Since the graph has a dashed boundary line, then it means that the linear inequality symbol used to represent the graph is "<," which implies that the endpoint, x = 3, is not included as part of the solution. Additionally, since the shaded half-plane region is towards the left-hand side of the boundary line, it means that the solution must less than 3.

Therefore, the linear equation that represents the given graph is x < 3.

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Aleah enjoys swimming and skating with her friends. She has a budget where she spends no more than $80 a month for her activitie

kari74 [83]

a) define the variables
The variables are x and y ; x can represent the number of times Aleah goes swimming ; while y can represents the number of times Aleah goes skating.

b) are there any restrictions on the variables?
The total sum of both activities must be equal or less than $80 a month

c) write a linear inequality to represent this situation
Swimming costs $5 each time and skating costs $4 each time. No more than $80 a month.

5x + 4y < 80

You can graph linear inequality using these coordinates.
x y
16 0
12 5
8 10
4 15
0 20

5 0

3 years ago

(3x2 + 9x + 6) - (8x2 + 3x - 10) + (2x + 4)(3x - 7)

nika2105 [10]

Answer:

Let's simplify step-by-step.

3x2+9x+6−(8x2+3x−10)+(2x+4)(3x−7)

Distribute:

=3x2+9x+6+−8x2+−3x+10+(2x)(3x)+(2x)(−7)+(4)(3x)+(4)(−7)

=3x2+9x+6+−8x2+−3x+10+6x2+−14x+12x+−28

Combine Like Terms:

=3x2+9x+6+−8x2+−3x+10+6x2+−14x+12x+−28

=(3x2+−8x2+6x2)+(9x+−3x+−14x+12x)+(6+10+−28)

=x2+4x+−12

Answer:

=x2+4x−12

3 0

3 years ago

I need helps someone

UNO [17]

A is the correct answer

7 0

3 years ago

8. An artist creates 8 identical ceramic bowls. The bowls contains some glass and 59.2 pounds of clay. The artist uses a

Aleksandr [31]

Answer:

021110321....1.12...1.1.631.6301

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Solve the following exact ordinary differential equation:

Sonja [21]

Answer:

The level curves F(t,z) = C for any constant C in the real numbers

where

$F(t,z)=z^3t^2+e^{tz}-4t+2z$

Step-by-step explanation:

Let's call

$M(t,z)=2tz^3+ze^{tz}-4$

$N(t,z)=3t^2z^2+te^{tz}+2$

Then our differential equation can be written in the form

1) M(t,z)dt+N(t,z)dz = 0

To see that is an exact differential equation, we have to show that

2) $\frac{\partial M}{\partial z}=\frac{\partial N}{\partial t}$

But

$\frac{\partial M}{\partial z}=\frac{\partial (2tz^3+ze^{tz}-4)}{\partial z}=6tz^2+e^{tz}+zte^{tz}$

In this case we are considering t as a constant.

Similarly, now considering z as a constant, we obtain

$\frac{\partial N}{\partial t}=\frac{\partial (3t^2z^2+te^{tz}+2)}{\partial t}=6tz^2+e^{tz}+zte^{tz}$

So, equation 2) holds and then, the differential equation 1) is exact.

Now, we know that there exists a function F(t,z) such that

3) $\frac{\partial F}{\partial t}=M(t,z)$

AND

4) $\frac{\partial F}{\partial z}=N(t,z)$

We have then,

$\frac{\partial F}{\partial t}=2tz^3+ze^{tz}-4$

Integrating on both sides

$F(t,z)=\int (2tz^3+ze^{tz}-4)dt=2z^3\int tdt+z\int e^{tz}dt-4\int dt+g(z)$

where g(z) is a function that does not depend on t

so,

$F(t,z)=\frac{2z^3t^2}{2}+z\frac{e^{tz}}{z}-4t+g(z)=z^3t^2+e^{tz}-4t+g(z)$

Taking the derivative of F with respect to z, we get

$\frac{\partial F}{\partial z}=3z^2t^2+te^{tz}+g'(z)$

Using equation 4)

$3z^2t^2+te^{tz}+g'(z)=3z^2t^2+te^{tz}+2$

Hence

$g'(z)=2\Rightarrow g(z)=2z$

The function F(t,z) we were looking for is then

$F(t,z)=z^3t^2+e^{tz}-4t+2z$

The level curves of this function F and not the function F itself (which is a surface in the space) represent the solutions of the equation 1) given in an implicit form.

That is to say,

The solutions of equation 1) are the curves F(t,z) = C for any constant C in the real numbers.

Attached, there are represented several solutions (for c = 1, 5 and 10)

3 0

3 years ago