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8_murik_8 [283]
3 years ago
15

Distribute and simplify: 7 (2x - 4) + 2 (3x + 1)

Mathematics
1 answer:
Alenkinab [10]3 years ago
3 0
7(2x-4)+2(3x+1)\\\\[(7*2x)+(7*-4)]+[(2*3x)+(2*1)]\\\\(14x-28)+(6x+2)\\\\14x+6x-28+2\\\\\\20x-25
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Casey can buy 3 sandwiches and 5 cups of coffee for $26. Eric can buy 4
ioda

Answer:

Step-by-step explanation:

Let's identify what we are looking for in terms of variables.  Sandwiches are s and coffee is c.  Casey buys 3 sandwiches, which is represented then by 3s, and 5 cups of coffee, which is represented by 5c.   Those all put together on one bill comes to 26.  So Casey's equation for his purchases is 3s + 5c = 26.  Eric buys 4 sandwiches, 4s, and 2 cups of coffee, 2c, and his total purchase was 23.  Eric's equation for his purchases then is 4s + 2c = 23.  In order to solve for c, the cost of a cup of coffee, we need to multiply both of those bolded equations by some factor to eliminate the s's.  The coefficients on the s terms are 4 and 3.  4 and 3 both go into 12 evenly, so we will multiply the first bolded equation by 4 and the second one by -3 so the s terms cancel out.  4[3s + 5c = 26] means that 12s + 20c = 104.  Multiplying the second  bolded equation   by -3:  -3[4s + 2c = 23] means that -12s - 6c = -69.  The s terms cancel because 12s - 12s = 0s.  We are left with a system of equations that just contain one unknown now, which is c, what we are looking to solve for.  20c = 104 and -6c = -69.  Adding those together by the method of elimination (which is what we've been doing all this time), 14c = 35.  That means that c = 2.5 and a cup of coffee is $2.50.  There you go!

3 0
3 years ago
On a number line, point A has a coordinate of -6, and point B has a coordinate of 2. Which is the coordinate of point M, the mid
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5 0
3 years ago
Help Please!!!!!!!!!!!
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Find the equation of a line that is parallel to the line x equals negative 1x=−1 and contains the point left parenthesis negativ
sineoko [7]
The equation of the line is given as y-x=-1

A straight line equation is given in the form y=mx+c where m is the gradient and c is the y-interest.

We need to rearrange y-x=-1 to make y the subject. 
y= x-1 ⇒ from here we can read the gradient and the y-intercept. The gradient, m=1 and c=-1.

<span>A line that is parallel to y=x-1 will have the same gradient, m=1 but different y-intercept. One example of equation of a line that is parallel to y=x-1 is y=x+3


</span>
8 0
3 years ago
A rock is thrown upward from a bridge that is 22 feet above a road. The rock reaches its maximum height above the road 0.69 seco
Flura [38]

Answer:

  • <u>f(t) = -7.561(t + 1.15)(t - 2.53)</u>

Explanation:

The<em> hint </em>is that the function f can be written in the form:

  • f(t) = c (t - t₁) (t - t₂)

It is a quadratic function, i.e. a parabola.

The maximum point, maximum height, of a parabola is its vertex.

And the x-coordinate of the vertex is at the midpoint between the two x-intercepts.

The time when the rock reaches the road is one x-intercept: t = 2.53 seconds: (2.53, 0).

The other x-intercept is sucht that (x + 2.53) / 2 = 0.69

  • (x + 2.53) / 2 = 0.69
  • x + 2.53 = 1.38
  • x = 1.38 - 2.53
  • x = -1.15

Thus, the equation is:

  • f(t) = c(t + 1.15) (t - 2.53).

You can find c by doing t = 0, because at t = 0 the height, f(t), is 22 feet:

  • f(0) = 22 = c (0 +1.15)(0 - 2.53)
  • 22 = c(1.15)(-2.53)
  • 22 = c (-2.9095)
  • c = - 22/(2.9095)
  • c = - 7.561

Then, the function can be written as:

  • f(t) = -7.561(t + 1.15) (t - 2.53) ← answer
6 0
3 years ago
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