Let's start by assuming Armando's house is between Joey's and the park.
Let

be the distance Joey walked to Armando's house.
<span>The park is 9/10 mile from Joey's home. Joey leaves home and walks to Armando's home. Then Joey and Armando walk 3/5 mile to the park.
</span>


That's probably the answer they're looking for. But what if the park is between Joey and Armando's houses or Joey is between the park and Armando? (The latter isn't really possible with the given distances.)
Let

be the distances between three collinear points like we have here. Our equation is really a few equations in one, something like

Let's get rid of the plus/minuses. Squaring,



For us, that's a quadratic equation for


I'll skip right to the solutions,


We could have gotten the 3/2 just by adding 9/10+3/5 but this was more fun.
Answer:
D. 13.79
Step-by-step explanation:
74.6-50.25-10.56=13.79
Answer:
<u><em></em></u>
- <u><em>Event A: 1/35</em></u>
- <u><em>Event B: 1/840</em></u>
<u><em></em></u>
Explanation:
<u>Event A</u>
For the event A, the order of the first 4 acts does not matter.
The number of different four acts taken from a set of seven acts, when the order does not matter, is calculated using the concept of combinations.
Thus, the number of ways that the first <em>four acts</em> can be scheduled is:


And<em> the number of ways that four acts is the singer, the juggler, the guitarist, and the violinist, in any order</em>, is 1: C(4,4).
Therefore the<em> probability of Event A</em> is:

Event B
Now the order matters. The difference between combinations and permutations is ordering. When the order matters you need to use permutations.
The number of ways in which <em>four acts </em>can be scheculed when the order matters is:


The number of ways <em>the comedian is first, the guitarist is second, the dancer is third, and the juggler is fourth</em> is 1: P(4,4)
Therefore, <em>the probability of Event B</em> is:

Answer:
Cross section is a rectangle.
Area of cross section = 16 sqrt(2) = 22.63 sq. units (to 2 decimals)
Step-by-step explanation:
Given a cube.
top face ABCD is parallel and congruent to bottom face EFGH ........(1)
justified by the properties of cubes
Sides AE and CH are perpendicular to faces ABCD and EFGH ..........(2)
justified by the properties of cubes
Diagonals AC and EH are congruent ......................(3)
justified by (1), congruent top and bottom faces
Consider cross-section ACHE
AC is congruent and parallel to EH (1) & (3)
EA & HC are perpendicular to AC (2)
Therefore the quadrilateral ACHE is a rectangle.
Length of diagonal AC = sqrt(4^2+4^2) = 4 sqrt(2) ..........pythagoras theorem
AE = CH = DG = 4 properties of cube, all sides equal
Area of ACHE = 4* 4sqrt(2) = 16 sqrt(2) = 22.63 sq. units
Answer:
a ) y = 1 and x = -1
d) y = 5 and x = -1/2
Step-by-step explanation:
<h2><u>
Substitution method</u></h2><h2><u>Question a</u></h2>
y = x+ 2
y = 2x + 3
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = x + 2
x = y - 2
now put y - 2 where x is in the second equation
y = 2x + 3
y = 2(y - 2) + 3
y = 2y - 4 +3
now solve
4 - 3 = 2y -y
y = 1
since y = 1 we can find what x is by putting into the first formula
y = x +2
x = y - 2
x = (1) -2
x = -1
<h3><u>hence y = 1 and x = -1 </u></h3><h3><u /></h3><h2><u>Question d</u></h2>
y = 2x + 6
y = 4 - 2x
<em>we can make the first formula in terms of x , so we can place in into the second formula</em>
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
now place (y-6)/2 where x is in the second formula
y = 4 -2x
y = 4 - 2 (
)
now solve
the multiplication by 2 and division by 2 are cancelled out
hence making the simplified equation as:
y = 4 - y + 6
2y = 4 + 6
2y = 10
y = 5
now place this into the first equation
y = 2x + 6
y - 6 = 2x
x = (y-6)/ 2
x = (5-6)/2
x = -1/2
<h3><u>
hence y = 5 and x = -1/2</u></h3>