Mr. Watkins earns $35 an hour at his new job. During a typical month, he works a total of 160 hours. Mrs. Watkins is a homemaker. After meeting the estimated monthly expenses, how much money will the family have left to spend on other items?
A) $1150
B) $1322
C) $1445
D) $1500

Final answer:

To find the slope-intercept form of a line with a given slope of -5/2 that passes through the point (8, -1), we use the point-slope form and then rearrange to get the final equation: y = (-5/2)x + 19.

Explanation:

To write the equation of a line in slope-intercept form (which is y = mx + b), we need to know the slope (m) of the line and the y-intercept (b). In this case, we are given the slope of the line as -5/2 and a point through which the line passes, which is (8, -1). Using the point-slope form, which is y - y1 = m(x - x1) where (x1, y1) is the given point and m is the slope, we can substitute the given slope and the coordinates of the given point to derive the slope-intercept form.

The equation starts with y - (-1) = (-5/2)(x - 8). Simplifying the equation, we get:

y + 1 = (-5/2)x + (5/2)*8

y = (-5/2)x + 20 - 1

y = (-5/2)x + 19

So, the equation of the line in slope-intercept form is y = (-5/2)x + 19.

To write an equation in slope-intercept form, substitute the given values of the slope and a point on the line into the equation. The equation of the line passing through the point (8, -1) with a slope of -5/2 is y = -5/2x + 19.

To write an equation in slope-intercept form, we need to use the given slope and the coordinates of the point through which the line passes. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept. We're given that the slope of the line is -5/2, so we can substitute this value for m. We're also given that the line passes through the point (8, -1), so we can substitute these coordinates to find the value of b.

Using the point-slope form of a line, we have y - y1 = m(x - x1). Substituting the given values, we get y - (-1) = -5/2(x - 8). Simplifying, we have y + 1 = -5/2x + 20. Moving the 1 to the other side, we have y = -5/2x + 19. This is the equation of the line in slope-intercept form.

Answer:

366.16

Step-by-step explanation:

i promise

Answer:

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.

My answer:

a. Carpeting a floor

To carpet a floor, you need to find the area of it so that we can have an appropriate plan to buy material. Hence, it represented by are

b. Fencing a garden

If you want to fence a garden, we need to know the the total length around it or we can say that is the perimeter of the garden. So this situation is represented by perimeter.

Hope it will find you well.

Answer:

Step-by-step explanation:

Answer:

1=1

Step-by-step explanation:

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Answer:

D.

Step-by-step explanation:

Intuitively it's a volleyball game reaching its maximum height, then we must discard the 1st option because of its parameter a >0, and whenever a>0 the parabola makes a curve, rather different than in a volleyball game.

Also, considering Vertex of this parabola by (-b/2a, -Δ/4a) given the fact that the question says the maximum height.

Taking

y= height in feet

x= time in second

Function Vertex (-b/2a, -Δ/4a)=(-3, -13)

A: f(x)=2x²+12x+5 False

B: f(x)=-2x²+12x-5 Function Vertex (-b/2a, -Δ/4a) = (3,23) False

C: f(x)=-2x²-12x+5  Function Vertex (-b/2a, -Δ/4a) = (-3,23) False

D: f(x)=-2(x-3)²+13 Function Vertex (-b/2a, -Δ/4a) = (3,13) True

E: f(x)=-2(x+3)²+13 Function Vertex (-b/2a, -Δ/4a) =(-3,13) False

Answer:

  √2

Step-by-step explanation:

You want the distance between the lines y = -x +2 and y = -x +4.

The distance from point (x, y) to line ax +by +c = 0 is given by the formula ...

  [tex]d=\dfrac{|ax+by+c|}{\sqrt{a^2+b^2}}[/tex]

Rewriting the equation of the second line to general form, we have ...

  y = -x +4

  x +y -4 = 0 . . . . . . . a=1, b=1, c=-4

The equation of the first line is written in slope intercept form, so we can identify the y-intercept as (0, 2). Using this point in the formula for the distance to the second line, we have ...

  [tex]d=\dfrac{|1(0)+1(2)-4|}{\sqrt{1^2+1^2}}=\dfrac{|-2|}{\sqrt{2}}=\sqrt{2}[/tex]

The distance between the lines is √2 units.

__

Additional comment

As you can see from the graph, the distance between the lines is the length of the diagonal of a unit square, √2.

Answer:

Yup...it's 36.

Step-by-step explanation:

we are given

radius=r=12m

height=h=9m

now, we can use formula of volume of cylinder

[tex] V=\pi r^2 h [/tex]

now, we can plug values

and we get

[tex] V=\pi (12)^2 *9 [/tex]

we get

[tex] V=1296 \pi m^3 [/tex]

so, the exact volume of the cylinder is [tex] 1296 \pi m^3 [/tex]..........Answer

Answer:

(D)

Step-by-step explanation:

It is given that a cylinder has a radius of 12 m and a height of 9 m.  Then,

Volume of the cylinder is given as:

[tex]V={\pi}r^{2}h[/tex]

⇒[tex]V={\pi}(12)^2(9)[/tex]

⇒[tex]V={\pi}(144)(9)[/tex]

⇒[tex]V=1296{\pi}m^3[/tex]

Therefore, the volume of the cylinder is [tex]1296{\pi}m^3[/tex].

Thus, Option D is correct.

Answer:

The scale factor is equal to [tex]\frac{1}{2}[/tex] or [tex]0.5[/tex]

Step-by-step explanation:  

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

[tex]z^{3}=\frac{45}{360}= \frac{1}{8}\\ \\z=\sqrt[3]{\frac{1}{8}}\\ \\z=\frac{1}{2}[/tex]

  -8x + 35y - 23  =   -1 • (8x - 35y + 23) 

The solution for (w) is  W= 4k-2b / -5, corresponding to option A.

To solve the equation [tex]\(k = \frac{2b - 5w}{3k}\)[/tex] for (w), we follow these steps:

1. Isolate the term containing (w):

  Multiply both sides of the equation by (3k) to eliminate the denominator:

[tex]\[3k^2 = 2b - 5w\][/tex]

2. Isolate (w):

  Subtract \(2b\) from both sides of the equation:

[tex]\[3k^2 - 2b = -5w\][/tex]

3. Divide both sides by (-5):

  Divide both sides of the equation by (-5) to isolate (w):

[tex]\[w = \frac{3k^2 - 2b}{-5}\][/tex]

Now, let's summarize the answer:

The solution for (w) is given by option:

[tex]\[\boxed{\text{(A) } w = \frac{4k - 2b}{-5}}\][/tex]

Answer:

1 The pressure approaches infinity.

2 The function is undefined for V = 0.

3 There is an asymptote at V = 0.

The pressure tends to infinity.

Given information,

The equation [tex]p=\frac{8.31}{v}[/tex]

Where p= pressure,

v= volume

If the volume approaches [tex]0[/tex] then the pressure [tex]p=\frac{8.31}{v}[/tex] will reach to infinity.

Therefore, the pressure tends to infinity.

For further details refer to the link:

https://brainly.com/question/356585

Answer: The correct answer is true

Step-by-step explanation:

Answer:

A. Solve w+2 = 7w-16 to find the value of w.

Step-by-step explanation:

Here p represents the age of Peter and w represents the age of Winnie,

Given,

Peter is 2 years older than Winnie.

⇒ p = w + 2 -----(1)

Also, Peter's age is 16 years less than seven times Winnie's age.

⇒ p = 7w - 16 -----(2),

By equating right sides of equation (1) and (2),

We get,

w + 2 = 7w - 16,

Since, this equation is only in the variable w,

Thus, we can find the value of w with help of the above equation,

After putting this value in either of equation (1) or (2),

We can find the value of p.

Hence, option A is correct.

Note : From equation (1) and (2),

w = p - 2 and [tex]w=\frac{p+16}{7}[/tex]

[tex]\implies p-2=\frac{p+16}{7}[/tex]

⇒ Option B is incorrect.

Now, let x represents w and y represents p in the graph,

Then, the solution will be the intersection point of lines y=x+2 and y=7x-16,

Which is shown below,

⇒ Options C and D are incorrect.

Answer:

The given expression is irrational because one factor is irrational

Step-by-step explanation:

Given the expression

[tex](\sqrt{576})(\sqrt{684})[/tex]

we have to find that the product is rational or irrational.

[tex]\sqrt{576}=\sqrt{26\times 26}=26[/tex]

[tex]\sqrt{684}=\sqrt{2 \times 2 \times 3 \times 3 \times 19}=2\times 3\sqrt{19}=6\sqrt{19}[/tex]

[tex]\text{The square root of 19 is irrational }[/tex]

[tex]\text{The square root of 684 is irrational }[/tex]

Hence, the first factor of the expression is rational and the second factor is irrational therefore the product is irrational.

∴ option 3 is correct

The given expression is irrational because one factor is irrational

Answer:

The given expression is irrational because one factor is irrational

Step-by-step explanation: