Your family took a road trip on Saturday. You were in the car for 4.5 hours and averaged 70 miles per hour. How many miles did you travel?
equation:
( pls explain how i got the answer)

The plot of the given line is required.

The graph is shown below with two points [tex](0,-6)[/tex] and [tex](-3,0)[/tex].

The line is

[tex]y-2=-2(x+4)\\\Rightarrow y=-2x-8+2\\\Rightarrow y=-2x-6[/tex]

Let us find two points on the line

[tex]x=0[/tex]

[tex]y=-2\times0-6=-6[/tex]

[tex](0,-6)[/tex]

[tex]y=0[/tex]

[tex]0=-2x-6\\\Rightarrow x=\dfrac{6}{-2}=-3[/tex]

[tex](-3,0)[/tex]

Join the two points on the graph and the line will be constructed.

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To find the dimensions of an open rectangular tank that holds 4.5 m3 of liquid with minimal material, set the length as twice the breadth and use calculus optimization to derive the breadth, length, and height.

The student is asking for the dimensions of an open rectangular tank that can hold 4.5 m3 of liquid, where the length is twice the breadth, and the amount of material used should be minimal. To solve this, we will use optimization techniques often found in calculus.

Let the breadth be b, the length be l = 2b, and the height be h. The volume V of the tank is given by V = l \b \h = 4.5 m3. Therefore, 2b2h = 4.5.

The surface area A of the tank, which we need to minimize, is A = 2lh + 2bh + lb (since the top is open). Substituting l = 2b, we get A = 2(2b)h + 2bh + (2b)b.

From the volume equation, we can express h in terms of b, which is h = 4.5 / (2b2). Substituting this into the area equation and differentiating it with respect to b will give us a minimum. Finally, solving the equations will determine the breadth, from which we can find the length and height. By this process, we can find the dimensions with the least surface area.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question reads....}[/tex]

[tex]\large\textbf{What is }\rm{\bf \dfrac{3}{8}}\large\textbf{ equivalent to?}[/tex]

[tex]\huge\textbf{Now, let's solve for the given question:}[/tex]

[tex]\mathbf{\dfrac{3}{8}}[/tex]

[tex]\mathbf{= \dfrac{3\times2}{8\times2}}[/tex]

[tex]\mathbf{\approx \dfrac{3 + 3}{8 + 8}}[/tex]

[tex]\mathbf{= \dfrac{6}{16}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{6}{16}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: False

Step-by-step explanation:

You can see 7*3*2*f*g is not the same as 7fg3, so the statement is false.

The graph of g(x)=⌈x⌉+7 differ from the graph of f(x)=⌈x⌉ as the graph of g(x)=⌈x⌉+7 is the graph of f(x)=⌈x⌉ shifted up 7 units.

A modulus function is a function that determines a number or variable's absolute value. No matter what input was provided to this function, the outcome is always positive.

Consider different values for x.

Say,

x = -1; f(-1) = [-1] = 1

x = 1; f(1) = [1] = 1

For any value of the x, the value of the function will be positive only.

The graph is attached in the image.

Consider different values for x.

Say,

x = 0; f(0) = [0] + 7 = 0 + 7; f(0) = 7

x = -1; f(-1) = [-1] + 7 = 1 + 7; f(-1) = 8

x = 1; f(1) = [1] = 1 + 7; f(1) = 8

For any value of the x, the value of the function will be positive only, but it would be 7 units shifted up on the y axis.

The graph is attached in the image.

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Answer:

Graph 2

Step-by-step explanation:

Given system of inequalities,

−2x + y ≤ 4,

y > x + 2

∵ Related equation of −2x + y ≤ 4 is,

-2x + y = 4 ⇒ y = 4 + 2x ----(1)

While, the related equation of y > x + 2 is,

y = x + 2

From equation (1),

4 + 2x = x + 2 ⇒ 4 + 2x - x = 2 ⇒ 4 + x = 2 ⇒ x = 2 - 4 ⇒ x = -2

Again by equation (1),

y = 4 + 2(-2) = 4 - 4 = 0

Hence, the intersection point of the related equation is (-2,0),

∴ Graph 1 and graph 3 can not be the graph of the given system.

Now, −2(0) + (0)  ≤ 4 ( true )

That is, −2x+y ≤ 4 would contain the origin,

Also, 0 > 0 + 2 ( False )

That is, y > x + 2 does not contain the origin.

Therefore, by the above explanation it is clear that,

Grap 2 represents the solution set of the system of inequalities.

Answer:

T = HN + r

Step-by-step explanation:

A handyman charges $H for each hour worked.

If the handyman works for N hours then the expression for the charges will be = $HN

Handyman charges a fixed amount = $r

Then the total amount charged T will be represented by

T = HN + r

Therefore, formula to calculate the total charges by handyman will be

T = HN + r

Final answer:

The electrician would take approximately 3 months to wire 55 houses at a rate of 4.5 houses per week.

Explanation:

An electrician can wire 4.5 houses per week.

To wire 55 houses at a rate of 4.5 houses per week, the electrician would take 55 / 4.5 = 12.22 weeks. As there are 4.5 weeks per month, dividing the total weeks by the weeks per month gives 12.22 / 4.5 = 2.72 months, which rounds up to 3 months.

For this case, what you should do is observe in the graph the value of the function when x = -4.

The value of the function is observed when looking at the vertical axis.

Remember that in a function of the form y = f (x) we have:

x: independent variable

y: dependent variable.

Therefore, for x = -4 we have:

f (-4) = 4

Answer:

The value of the function evaluated at x = -4 is given by:

f (-4) = 4