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3 years ago

Four times the difference of a number and 7 is 32

1 answer:

6 0

I'm not exactly sure but I think it might be but if you were to do 4(x-7) that would be 15 because fifteen minutes seven equals eight and eight time four is thirty two Hope this helps!

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A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plate

yulyashka [42]

Answer:

Step-by-step explanation:

From the given information;

Numbers of posters that can be printed in an hour = no of impression/hour × no of plate utilized in each impression.

= 1000x

Thus, the required number of hours it will take can be computed as:

$\implies \dfrac{100000}{1000x} \\ \\ =\dfrac{100}{x}$

cost per hour = 125

If each plate costs $20 to make, then the total number of plate will equal to 40x

∴

The total cost can be computed as:

$C(x) = (\dfrac{100}{x}) \times 125 + 20 x --- (1)$

$C'(x) = (-\dfrac{12500}{x^2}) + 20 --- (2)$

At C'(x) = 0

$\dfrac{12500}{x^2} = 20$

$\dfrac{12500}{20} = x^2$

$x^2= 625$

$x = \sqrt{625}$

x = 25

$C'' (x) = -12500 \times \dfrac{-2}{x^3} +0$

$C'' (x) = \dfrac{25000}{x^3}$

where; x = 25

$C'' (x) = \dfrac{25000}{25^3}$

C''(x) = 1.6

Thus, at x = 25, C'' > 0

As such, to minimize the cost, the printer needs to make 25 metal plates.

4 0

3 years ago

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.

34kurt

Answer:

Infinitely many solutions

Step-by-step explanation:

First, let's organize the equations of the lines into slope-intercept form.

x + 4y = 1
=> 4y = -x + 1
=> y = -x/4 + 1/4

And,

2x + 8y = 2
=> 8y = -2x + 2
=> y = -2x/8 + 2/8
=> y = -x/4 + 1/4

Since both the graphs are the same, the two equations have infinitely many solutions.

5 0

2 years ago

Find the constant of variation (k) for the inverse variation. Then write an equation for the inverse situation.

notka56 [123]

y = k/x

5 =k/7.5

k = 7.5/*5= 37.5

answer is D

7 0

3 years ago

Read 2 more answers

Find the measures of 21 and 2

KatRina [158]

Measure 1 would be 59 degrees (180-121)
Measure 2 would be 121 degrees (vertical angle theorem)

6 0

3 years ago

A satellite dish is shaped like a paraboloid of revolution. The signals that emanate from a satellite strike the surface of the

allochka39001 [22]

Answer:

The receiver must be placed at a distance of 6.125 ft from the center.

Step-by-step explanation:

The dish is of parabola shape with the length of 14 feet and 2 feet deep from the center.

A parabola is a curve which is a set of all points in the plane which are at equal distance away from a given point called focus and given line called directrix.

We have to find out the point at which all the waves comes to one point where the receiver must be placed is the focus of the parabola.

The above scenario is shown in the image which can be converted in mathematical graphical representation of the parabolic curve.

The extreme two end points becomes, (-7,2) and (7,2)

The general equation for such parabola is:

x² = 4ay

where, a is the distance from the center and the focus.

Since, (7,2) satisfy the equation so,

7² = 4a×2

a = 49 /8

Thus,

<u>The receiver must be placed at a distance of 6.125 ft from the center.</u>

5 0

3 years ago