x+y+3z=-16 ... (1)
x+y+7z=-32 ...(2)
x-8y-6z=11 ... (3)
Let's subtract equation (1) and (2) so that we can eliminate x and y. So,
x+y+3z=-16
x+y+7z=-32
____________________
(x-x)+(y-y)+(3z-7z)=(-16)-(-32)
0+0-4z=-16+32
-4z= +16
Dividing each sides by -4.
z=-4
Now plug in z=-4 in equation (2) and (3). So, by plug in -4 for z in equation (2) we will get
x+y+7(-4)=-32
x+y-28=-32
x+y=-32+28
x+y=-4 ....(equation (4)
Now let's plug into equation (3). So,
x-8y-6(-4)=11
x-8y+24=11
x-8y=11-24
x-8y=-13 ......... equation(5)
Now we have two equations (4) and (5) with two variables x and y which we can solve now.
We can eliminate y from equation (4) and (5) by making equal and opposite coefficient of y's. So, multiply equation (4) by 8.
(x+y=-4)x8
8x+8y=-32....... (6)
Now after adding equation (5) and (6) wewill get,
9x=-45
9x/9=-45/9
x=-5
Now we can plug in x=-5 and z=-4 in any equation to get the value of y. So, let's plug in to equation (1).
-5+y+3(-4)=-16
-5+y-12=-16
y-17=-16
y=17-16
y=1
So, x=-5, y=1 and z=-4
Answer:
48
Step-by-step explanation:
Answer:
7/16 of a yard
Step-by-step explanation:
Let's put the boards to the same denominator so it's easier.
Let's go with a denominator of 16
1/4= 4/16
7/8= 14/16
3/16 stays the same.
So, 4/16+3/16+x=14/16
7/16+x=14/16
x=7/16 of a yard, the length of the 3rd board.
Answer:
<h2>The slope of AB = 2</h2>
Step-by-step explanation:
We have a circle described on the triangle. If one side of the triangle is the diameter of the circle, then the triangle is the right triangle.
Therefore m∠B = 90°.
AB is perpendicular to BC.
Let
k: y = m₁x + b₁ and l: y = m₂x + b₂
l ⊥ k ⇔ m₁m₂ = -1 ⇒ m₂ = - 1/m₁
We have the slope of BC m₁ = - 1/2.
Therefore the slope of AB m₂ = - 1/(- 1/2) = 2
Answer:
P(2.50 < Xbar < 2.66) = 0.046
Step-by-step explanation:
We are given that Population Mean, 
= 2.58 and Standard deviation, 
= 0.75
Also, a random sample (n) of 110 households is taken.
Let Xbar = sample mean household size
The z score probability distribution for sample mean is give by;
Z = 
~ N(0,1)
So, probability that the sample mean household size is between 2.50 and 2.66 people = P(2.50 < Xbar < 2.66)
P(2.50 < Xbar < 2.66) = P(Xbar < 2.66) - P(Xbar 
2.50)
P(Xbar < 2.66) = P( < 
) = P(Z < -1.68) = 1 - P(Z 1.68)
= 1 - 0.95352 = 0.04648
P(Xbar 2.50) = P( 
) = P(Z -3.92) = 1 - P(Z < 3.92)
= 1 - 0.99996 = 0.00004
Therefore, P(2.50 < Xbar < 2.66) = 0.04648 - 0.00004 = 0.046
