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Sergeu [11.5K]
4 years ago
12

A system of equations is shown below:

Mathematics
1 answer:
gtnhenbr [62]4 years ago
8 0
Y = 8x - 2
y = 9x - 7

  8x - 2 = 9x - 7
- 8x       - 8x
        -2 = x - 7
      + 7      + 7
         5 = x

y = 8x -2
y = 8(5) - 2
y = 40 - 2
y = 38
(x, y) = (5, 38)

The answer is C.
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Answer:

<h3>The slope is -1.</h3>

Step-by-step explanation:

To find an equation of the line that passes through the points, you have to use the slope formula.

Slope:

\Rightarrow \sf{\dfrac{y_2-y_1}{x_2-x_1} }

y2=3

y1=(-2)

x2=(-1)

x1=4

Solve.

3--2/-1-4=5/-5=-1

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Identify the vertex, focus, and directrix. y=1/8y^2
Brut [27]
If all the equations for the directrix are "x = " lines then this is a y^2 parabola.  The actual equation is x= \frac{1}{8}y^2.  The standard form for a positive sideways-opening parabola is  (y-k)^2=4p(x-h).  We know from the equation that the vertex of the parabola is at the origin, or else the translation would be reflected within the parenthesis in the equation.  Our equation has no parenthesis to indicate movement from the origin.  The vertex is (0, 0).  Got that out of the way.  That simplifies our standard form down to  y^2=4p(x).  Let's take a look at our equation now.  It is  x= \frac{1}{8}y^2.  We could rewrite it and make it a closer match to the standard form if we multiply both sides by 8 to get rid of the fraction.  That gives us an equation that looks like this:  y^2=8x.  That means that 4p = 8, and p = 2.  p is the distance that the focus and the directrix are from the vertex.  Since this is a positive parabola, it opens up to the right.  Which means, then, that the focus is to the right of the vertex, 2 units to be exact, and the directrix is 2 units to the left of the vertex.  The formula for the focus is (h + p, k).  Our h is 0, our k is 0 and our p is 2, so the coordinates of the focus are (2, 0).  Going 2 units to the left of the origin then puts our directrix at the line x = -2.  Your choice then as your answer is b. 
6 0
3 years ago
Dots sells t-shirts ($2) and shorts ($4). In April total sales were $456. People bought 4 times as many t-shirts as shorts. How
Doss [256]

Answer:

Dots sold 152 t-shirts and 38 shorts sold.

Step-by-step explanation:

Let t = t-shirts and s = shorts.

We know that people bought 4 times as many t-shorts as shorts, which can be set to the equation t = 4s

Since t-shirts cost $2, shorts cost $4, and the total sales was $456, we can set the equation 2t +4s = 456

So our two equations are:

t = 4s

2t + 4s = 456

Substitute t from the 1st equation into the 2nd:

2(4s) + 4s = 456

8s + 4s = 456

12s = 456

s = 38

There were 38 shorts sold.

Since we have the number of shorts, we can plug that back into the 1st equation to find the number of t-shirts sold:

t = 4s

t = 4(38)

t = 152

There were 152 t-shirts sold.

4 0
4 years ago
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