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neonofarm [45]
3 years ago
15

the cost of printing 200 business cards is $23. The cost of printing 500 business cards at the same business is $35. Write and s

olve a linear equation to find the cost for printing 700 business cards.
Mathematics
1 answer:
lana66690 [7]3 years ago
4 0
 It should be $80.50. 
Divide 23 by 200,
Times that number by 700, 
Wella! there's your answer.
~Glad to help.
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Factor the polynomial by its greatest common monomial factor<br><br> 9b^8+24b^3
velikii [3]

9b^8 + 24b^3

= 3b^3 ( 3b^5 + 8 )

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3 years ago
1. Find equation (both the normal equation and the parametric equation) for the plane (in R3) so that (a) the plane contains the
kherson [118]

Answer:

For a part:

(x-1,  y,  z-3) * (-6, -3, -2) = 0   (Normal equation)

P = (1,0,3) + (1,-2,0)*s + (0,-2,3)*t   (Parametric equation)

For b part:

(x-1,  y,  z-3) * (1, 1, 1) = 0   (Normal equation)

P = (4, 0, 0) + (-1, 1, 0)*s + (-1, 0, 1)*t   (Parametric equation)

Step-by-step explanation:

a)

The parametric equation of a plane is defined by three things: a point, and two non-colinear vectors in the plane. We already have three points, so we only need to find two vectors contained in the plane (we will call them V1 and V2):

V1 = P-Q = (1,0,3)-(0,2,3) = (1,-2,0)

V2 = P-R = (1,0,3)-(1,2,0) = (0,-2,3)

Therefore, the parametric equation of our plane is given by:

P = P + V1*s + V2*t = (1,0,3) + (1,-2,0)*s + (0,-2,3)*t

The normal equation of any plane is given by [x-P]*n = 0, where x is the vector(x,y,z), P is a point contained in the plane, n is a vector normal to the plane and * stands for the dot product. Therefore, for finding the normal form of the equation, we need an orthogonal vector to the plane (n), which we find by doing the cross product of our previous vectors V1 and V2:

n = V1xV2 = (-6,-3,-2)

Substituting the required values in the formula mentioned above, we can write the normal equation of our plane as:

[(x,y,z) - (1,0,3)]*(-6,-3,-2) = 0 or (x-1,  y,  z-3) * (-6, -3, -2) = 0

b)

In this second exercise, it is straightforward to give the normal equation:

[(x,y,z) - (1,0,3)]*(1,1,1) = 0  or  (x-1,  y,  z-3) * (1, 1, 1) = 0

For transforming this equation to its parametric form, first we transform it to its cartesian form:

x-1 +y +z-3 = 0,  then :  x+y+z = 4

Now that we have the cartesian form, we solve for variable x and get:

x = 4 -y -z

Then, we know that every point in the plane can be expressed as:

P = (4 -y -z, y, z).

Finally, rewriting the expression and converting y and z to the parameters s and t respectively we get:

P = (4, 0, 0) + (-y, y, 0) + (-z, 0, z) = (4, 0, 0) + (-1, 1, 0)*s + (-1, 0, 1)*t

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3 years ago
What is -5/8 + -8/9=
mariarad [96]

Answer:

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Step-by-step explanation:

-5/8 = -0.625

-8/9 = -0.8888888888

-0.625 + -0.8888888888 = -1.513888889

If you round this to the nearest tenth you get

<u>-1.51</u>

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Which of the following shows the correct simplification of the quadratic formula used to solve 8x2 - 2x = 1?
spayn [35]

Step-by-step explanation:

can you properly format this question its so hadd to understand

8 0
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the temperature was 15 .it dropped so that the temperature was 0 . what integer represents the change in temperature?
Nataliya [291]

Answer:

if the temperature was at 15 and dropped to zero the amount it changed would be is -15. The integer is -15 because an integer is a whole number and it can also be a negative or positive number it just can not be a fraction

3 0
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